Finite Group Databasebeta

← C17×#36820 #16894564

Subgroups — C17×#36820 #16894564

Order 4352.

1768 conjugacy classes of subgroups.

The subgroup lattice has 1498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2853C211yesmaximal, characteristic, complemented
2C17×#2853C211yesmaximal, characteristic, complemented
3C17×#2797C211yesmaximal, characteristic, complemented
4C17×#2786C211yesmaximal, characteristic, complemented
5C17×#2761C211yesmaximal, characteristic, complemented
6C17×#2758C211yesmaximal, characteristic, complemented
7C17×#2754C211yesmaximal, characteristic, complemented
8C17×#2750C211yesmaximal, characteristic, complemented
9C17×#2749C211yesmaximal, characteristic, complemented
10C17×#2749C211yesmaximal, characteristic, complemented
11C17×#2711C211yesmaximal, characteristic, complemented
12C17×#2708C211yesmaximal, characteristic, complemented
13C17×#2703C211yesmaximal, characteristic, complemented
14C17×#2703C211yesmaximal, characteristic, complemented
15C17×#2703C211yesmaximal, characteristic, complemented
16C17×#2701C211yesmaximal, characteristic, complemented
17C17×#2690C211yesmaximal, characteristic, complemented
18C17×#2687C211yesmaximal, characteristic, complemented
19C17×#2652C211yesmaximal, characteristic, complemented
20C17×#2648C211yesmaximal, characteristic, complemented
21C17×#2602C211yesmaximal, characteristic, complemented
22C17×#2597C211yesmaximal, characteristic, complemented
23C17×#2578C211yesmaximal, characteristic, complemented
24C17×#2569C211yesmaximal, characteristic, complemented
25C17×#2475C211yesmaximal, characteristic, complemented
26C17×#2471C211yesmaximal, characteristic, complemented
27C17×#2430C211yesmaximal, characteristic, complemented
28C17×#2407C211yesmaximal, characteristic, complemented
29C17×#2335C211yesmaximal, characteristic, complemented
30C17×#2318C211yesmaximal, characteristic, complemented
31C17×#2297C211yesmaximal, characteristic, complemented
32C22×#41×C17C2211yescharacteristic
33C2×C17×#125C2211yescharacteristic
34C2×C17×#123C2211yescharacteristic
35C2×C17×#123C2211yescharacteristic
36C2×C17×#123C2211yescharacteristic
37C2×C17×#123C2211yescharacteristic
38C2×C17×C22⋊Q8C2211yescharacteristic
39C2×C17×#121C2211yescharacteristic
40C2×C17×#121C2211yescharacteristic
41C2×C17×#121C2211yescharacteristic
42C2×C4×D4×C17C2211yescharacteristic
43C2×C17×#117C2211yescharacteristic
44C22×C42×C17C2211yescharacteristic
45C17×#400C2211yescharacteristic
46C17×#400C2211yescharacteristic
47C17×#400C2211yescharacteristic
48C17×#400C2211yescharacteristic
49C17×#400C2211yescharacteristic
50C17×#400C2211yescharacteristic
51C17×#400C2211yescharacteristic
52C17×#400C2211yescharacteristic
53C17×#400C2211yescharacteristic
54C17×#399C2211yescharacteristic
55C17×#398C2211yescharacteristic
56C17×#398C2211yescharacteristic
57C17×#398C2211yescharacteristic
58C17×#398C2211yescharacteristic
59C17×#397C2211yescharacteristic
60C17×#397C2211yescharacteristic
61C17×#397C2211yescharacteristic
62C17×#397C2211yescharacteristic
63C17×#397C2211yescharacteristic
64C17×#397C2211yescharacteristic
65C17×#397C2211yescharacteristic
66C17×#397C2211yescharacteristic
67C17×#397C2211yescharacteristic
68C17×#397C2211yescharacteristic
69C17×#397C2211yescharacteristic
70C17×#397C2211yescharacteristic
71C17×#396C2211yescharacteristic
72C17×#396C2211yescharacteristic
73C17×#396C2211yescharacteristic
74C17×#396C2211yescharacteristic
75C17×#395C2211yescharacteristic
76C17×#394C2211yescharacteristic
77C17×#394C2211yescharacteristic
78C17×#394C2211yescharacteristic
79C17×#394C2211yescharacteristic
80C17×#394C2211yescharacteristic
81C17×#394C2211yescharacteristic
82C17×#394C2211yescharacteristic
83C17×#394C2211yescharacteristic
84C17×#394C2211yescharacteristic
85C17×#394C2211yescharacteristic
86C17×#393C2211yescharacteristic
87C17×#392C2211yescharacteristic
88C17×#392C2211yescharacteristic
89C17×#392C2211yescharacteristic
90C17×#392C2211yescharacteristic
91C17×#392C2211yescharacteristic
92C17×#392C2211yescharacteristic
93C17×#391C2211yescharacteristic
94C17×#391C2211yescharacteristic
95C17×#391C2211yescharacteristic
96C17×#390C2211yescharacteristic
97C17×#390C2211yescharacteristic
98C17×#390C2211yescharacteristic
99C17×#390C2211yescharacteristic
100C17×#390C2211yescharacteristic
101C17×#390C2211yescharacteristic
102C17×#390C2211yescharacteristic
103C17×#389C2211yescharacteristic
104C17×#389C2211yescharacteristic
105C17×#388C2211yescharacteristic
106C17×#388C2211yescharacteristic
107C17×#388C2211yescharacteristic
108C17×#388C2211yescharacteristic
109C17×#388C2211yescharacteristic
110C17×#388C2211yescharacteristic
111C17×#388C2211yescharacteristic
112C17×#388C2211yescharacteristic
113C17×#388C2211yescharacteristic
114C17×#388C2211yescharacteristic
115C17×#388C2211yescharacteristic
116C17×#388C2211yescharacteristic
117C17×#388C2211yescharacteristic
118C17×#388C2211yescharacteristic
119C17×#388C2211yescharacteristic
120C17×#388C2211yescharacteristic
121C17×#388C2211yescharacteristic
122C17×#388C2211yescharacteristic
123C17×#387C2211yescharacteristic
124C17×#387C2211yescharacteristic
125C17×#387C2211yescharacteristic
126C17×#387C2211yescharacteristic
127C17×#387C2211yescharacteristic
128C17×#387C2211yescharacteristic
129C17×#387C2211yescharacteristic
130C17×#387C2211yescharacteristic
131C17×#387C2211yescharacteristic
132C17×#387C2211yescharacteristic
133C17×#387C2211yescharacteristic
134C17×#387C2211yescharacteristic
135C17×#387C2211yescharacteristic
136C17×#387C2211yescharacteristic
137C17×#387C2211yescharacteristic
138C17×#387C2211yescharacteristic
139C17×#386C2211yescharacteristic
140C17×#386C2211yescharacteristic
141C17×#386C2211yescharacteristic
142C17×#386C2211yescharacteristic
143C17×#386C2211yescharacteristic
144C17×#386C2211yescharacteristic
145C17×#386C2211yescharacteristic
146C17×#386C2211yescharacteristic
147C17×#386C2211yescharacteristic
148C17×#386C2211yescharacteristic
149C17×#386C2211yescharacteristic
150C17×#386C2211yescharacteristic
151C17×#386C2211yescharacteristic
152C17×#386C2211yescharacteristic
153C17×#386C2211yescharacteristic
154C17×#386C2211yescharacteristic
155C17×#386C2211yescharacteristic
156C17×#386C2211yescharacteristic
157C17×#385C2211yescharacteristic
158C17×#385C2211yescharacteristic
159C17×#385C2211yescharacteristic
160C17×#385C2211yescharacteristic
161C17×#385C2211yescharacteristic
162C17×#385C2211yescharacteristic
163C17×#385C2211yescharacteristic
164C17×#385C2211yescharacteristic
165C17×#385C2211yescharacteristic
166C17×#385C2211yescharacteristic
167C17×#385C2211yescharacteristic
168C17×#385C2211yescharacteristic
169C17×#383C2211yescharacteristic
170C17×#383C2211yescharacteristic
171C17×#382C2211yescharacteristic
172C17×#381C2211yescharacteristic
173C17×#381C2211yescharacteristic
174C17×#381C2211yescharacteristic
175C17×#380C2211yescharacteristic
176C17×#380C2211yescharacteristic
177C17×#380C2211yescharacteristic
178C17×#380C2211yescharacteristic
179C17×#380C2211yescharacteristic
180C4×C4⋊C4×C17C2211yescharacteristic
181C4×C22⋊C4×C17C2211yescharacteristic
182C4×C22⋊C4×C17C2211yescharacteristic
183C4×C22⋊C4×C17C2211yescharacteristic
184C4×C22⋊C4×C17C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic
186C2×C17×#95C2211yescharacteristic
187C2×#41×C17—24no—
188C2×#41×C17—42no—
189C2×#41×C17—42no—
190C22×Q8×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C22×D4×C17C2311yescharacteristic
198C22×D4×C17C2311yescharacteristic
199C22×D4×C17C2311yescharacteristic
200C22×D4×C17C2311yescharacteristic
201C23×C4×C17C2311yescharacteristic
202C23×C4×C17C2311yescharacteristic
203C23×C4×C17C2311yescharacteristic
204C23×C4×C17C2311yescharacteristic
205C23×C4×C17C2311yescharacteristic
206C23×C4×C17C2311yescharacteristic
207C23×C4×C17C2311yescharacteristic
208C23×C4×C17C2311yescharacteristic
209C23×C4×C17C2311yescharacteristic
210C17×#125—42no—
211C17×#123—24no—
212C17×#123—42no—
213C17×#123—42no—
214C17×#123—42no—
215C17×C22⋊Q8—42no—
216C17×#121—42no—
217C17×#121—42no—
218C17×#121—42no—
219C4×D4×C17—24no—
220C17×#117—42no—
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C4⋊C4×C17C2311yescharacteristic
238C2×C4⋊C4×C17C2311yescharacteristic
239C2×C4⋊C4×C17C2311yescharacteristic
240C2×C4⋊C4×C17C2311yescharacteristic
241C2×C4⋊C4×C17C2311yescharacteristic
242C2×C4⋊C4×C17C2311yescharacteristic
243C2×C4⋊C4×C17C2311yescharacteristic
244C2×C4⋊C4×C17C2311yescharacteristic
245C2×C4⋊C4×C17C2311yescharacteristic
246C2×C4⋊C4×C17C2311yescharacteristic
247C2×C4⋊C4×C17C2311yescharacteristic
248C2×C4⋊C4×C17C2311yescharacteristic
249C2×C4⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C22⋊C4×C17C2311yescharacteristic
252C2×C22⋊C4×C17C2311yescharacteristic
253C2×C22⋊C4×C17C2311yescharacteristic
254C2×C22⋊C4×C17C2311yescharacteristic
255C2×C22⋊C4×C17C2311yescharacteristic
256C2×C22⋊C4×C17C2311yescharacteristic
257C2×C22⋊C4×C17C2311yescharacteristic
258C2×C22⋊C4×C17C2311yescharacteristic
259C2×C22⋊C4×C17C2311yescharacteristic
260C2×C22⋊C4×C17C2311yescharacteristic
261C2×C22⋊C4×C17C2311yescharacteristic
262C2×C22⋊C4×C17C2311yescharacteristic
263C2×C22⋊C4×C17C2311yescharacteristic
264C2×C22⋊C4×C17C2311yescharacteristic
265C2×C22⋊C4×C17C2311yescharacteristic
266C2×C22⋊C4×C17C2311yescharacteristic
267C2×C22⋊C4×C17C2311yescharacteristic
268C2×C22⋊C4×C17C2311yescharacteristic
269C2×C22⋊C4×C17C2311yescharacteristic
270C2×C22⋊C4×C17C2311yescharacteristic
271C2×C22⋊C4×C17C2311yescharacteristic
272C2×C22⋊C4×C17C2311yescharacteristic
273C2×C22⋊C4×C17C2311yescharacteristic
274C2×C22⋊C4×C17C2311yescharacteristic
275C2×C22⋊C4×C17C2311yescharacteristic
276C2×C22⋊C4×C17C2311yescharacteristic
277C2×C22⋊C4×C17C2311yescharacteristic
278C2×C22⋊C4×C17C2311yescharacteristic
279C2×C22⋊C4×C17C2311yescharacteristic
280C2×C22⋊C4×C17C2311yescharacteristic
281C2×C22⋊C4×C17C2311yescharacteristic
282C2×C22⋊C4×C17C2311yescharacteristic
283C2×C22⋊C4×C17C2311yescharacteristic
284C2×C22⋊C4×C17C2311yescharacteristic
285C2×C22⋊C4×C17C2311yescharacteristic
286C2×C22⋊C4×C17C2311yescharacteristic
287C2×C22⋊C4×C17C2311yescharacteristic
288C2×C22⋊C4×C17C2311yescharacteristic
289C2×C22⋊C4×C17C2311yescharacteristic
290C2×C22⋊C4×C17C2311yescharacteristic
291C2×C22⋊C4×C17C2311yescharacteristic
292C2×C22⋊C4×C17C2311yescharacteristic
293C2×C22⋊C4×C17C2311yescharacteristic
294C2×C22⋊C4×C17C2311yescharacteristic
295C2×C22⋊C4×C17C2311yescharacteristic
296C2×C42×C17—42no—
297C2×C42×C17C2311yescharacteristic
298C2×C42×C17C2311yescharacteristic
299C2×C42×C17C2311yescharacteristic
300C2×C42×C17C2311yescharacteristic
301C2×C42×C17C2311yescharacteristic
302C2×C42×C17C2311yescharacteristic
303C2×C42×C17C2311yescharacteristic
304C2×C42×C17C2311yescharacteristic
305C2×C42×C17C2311yescharacteristic
306C2×C42×C17C2311yescharacteristic
307C17×#95C2311yescharacteristic
308C17×#95C2311yescharacteristic
309C17×#95C2311yescharacteristic
310C17×#95C2311yescharacteristic
311C17×#95C2311yescharacteristic
312C17×#95C2311yescharacteristic
313C17×#95C2311yescharacteristic
314C17×#95C2311yescharacteristic
315C17×#95C2311yescharacteristic
316C17×#95C2311yescharacteristic
317C17×#95C2311yescharacteristic
318C17×#95C2311yescharacteristic
319C17×#95C2311yescharacteristic
320C17×#95C2311yescharacteristic
321C17×#95C2311yescharacteristic
322C17×#95C2311yescharacteristic
323C17×#95C2311yescharacteristic
324C17×#95C2311yescharacteristic
325C17×#95C2311yescharacteristic
326C17×#95C2311yescharacteristic
327C17×#95C2311yescharacteristic
328C17×#95C2311yescharacteristic
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349C17×#95C2311yescharacteristic
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
353C17×#95C2311yescharacteristic
354C17×#95C2311yescharacteristic
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357C24×C17C2411yescharacteristic
358C24×C17C2411yescharacteristic
359C24×C17C2411yescharacteristic
360C24×C17C2411yescharacteristic
361C24×C17C2411yescharacteristic
362#41×C17—416no—
363C2×Q8×C17—22no—
364C2×Q8×C17—22no—
365C2×Q8×C17—41no—
366C2×D4×C17—22no—
367C2×D4×C17—22no—
368C2×D4×C17—22no—
369C2×D4×C17—22no—
370C2×D4×C17—22no—
371C2×D4×C17—22no—
372C2×D4×C17—22no—
373C2×D4×C17—22no—
374C2×D4×C17—22no—
375C2×D4×C17—22no—
376C2×D4×C17—41no—
377C2×D4×C17—41no—
378C2×D4×C17—41no—
379C2×D4×C17—41no—
380C2×D4×C17—41no—
381C2×D4×C17—41no—
382C2×D4×C17—41no—
383C2×D4×C17—41no—
384C2×D4×C17—41no—
385C2×D4×C17—41no—
386C2×D4×C17—41no—
387C2×D4×C17—41no—
388C2×D4×C17—41no—
389C2×D4×C17—41no—
390C2×D4×C17—41no—
391C2×D4×C17—41no—
392C2×D4×C17—41no—
393C2×D4×C17—41no—
394C2×D4×C17—41no—
395C2×D4×C17—41no—
396C22×C4×C17—22no—
397C22×C4×C17—22no—
398C22×C4×C17—22no—
399C22×C4×C17—22no—
400C22×C4×C17—22no—
401C22×C4×C17—22no—
402C22×C4×C17—22no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17—41no—
409C22×C4×C17—41no—
410C22×C4×C17—41no—
411C22×C4×C17—41no—
412C22×C4×C17—41no—
413C22×C4×C17—41no—
414C22×C4×C17—41no—
415C22×C4×C17—41no—
416C22×C4×C17—41no—
417C22×C4×C17—41no—
418C22×C4×C17—41no—
419C22×C4×C17—41no—
420C22×C4×C17—41no—
421C22×C4×C17—41no—
422C22×C4×C17#4114yes—
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C22×C4×C17C2411yescharacteristic
438C22×C4×C17C2411yescharacteristic
439C22×C4×C17C2411yescharacteristic
440C22×C4×C17C2411yescharacteristic
441C22×C4×C17C2411yescharacteristic
442C22×C4×C17C2411yescharacteristic
443C22×C4×C17C2411yescharacteristic
444C22×C4×C17C2411yescharacteristic
445C22×C4×C17C2411yescharacteristic
446C22×C4×C17C2411yescharacteristic
447C22×C4×C17C2411yescharacteristic
448C22×C4×C17C2411yescharacteristic
449C4⋊C4×C17—22no—
450C4⋊C4×C17—22no—
451C4⋊C4×C17—22no—
452C4⋊C4×C17—22no—
453C4⋊C4×C17—22no—
454C4⋊C4×C17—22no—
455C4⋊C4×C17—22no—
456C4⋊C4×C17—41no—
457C4⋊C4×C17—41no—
458C4⋊C4×C17—41no—
459C4⋊C4×C17—41no—
460C4⋊C4×C17—41no—
461C4⋊C4×C17—41no—
462C4⋊C4×C17—41no—
463C4⋊C4×C17—41no—
464C4⋊C4×C17—41no—
465C4⋊C4×C17—41no—
466C4⋊C4×C17—41no—
467C4⋊C4×C17—41no—
468C4⋊C4×C17—41no—
469C4⋊C4×C17—41no—
470C4⋊C4×C17—41no—
471C4⋊C4×C17—41no—
472C4⋊C4×C17—41no—
473C4⋊C4×C17—41no—
474C4⋊C4×C17—41no—
475C4⋊C4×C17—41no—
476C4⋊C4×C17—41no—
477C4⋊C4×C17—41no—
478C22⋊C4×C17—22no—
479C22⋊C4×C17—22no—
480C22⋊C4×C17—22no—
481C22⋊C4×C17—22no—
482C22⋊C4×C17—22no—
483C22⋊C4×C17—22no—
484C22⋊C4×C17—22no—
485C22⋊C4×C17—22no—
486C22⋊C4×C17—22no—
487C22⋊C4×C17—41no—
488C22⋊C4×C17—41no—
489C22⋊C4×C17—41no—
490C22⋊C4×C17—41no—
491C22⋊C4×C17—41no—
492C22⋊C4×C17—41no—
493C22⋊C4×C17—41no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17—41no—
501C22⋊C4×C17—41no—
502C22⋊C4×C17—41no—
503C22⋊C4×C17—41no—
504C22⋊C4×C17—41no—
505C22⋊C4×C17—41no—
506C22⋊C4×C17—41no—
507C22⋊C4×C17—41no—
508C22⋊C4×C17—41no—
509C22⋊C4×C17—41no—
510C22⋊C4×C17—41no—
511C22⋊C4×C17—41no—
512C22⋊C4×C17—41no—
513C22⋊C4×C17—41no—
514C22⋊C4×C17—41no—
515C22⋊C4×C17—41no—
516C22⋊C4×C17—41no—
517C22⋊C4×C17—41no—
518C22⋊C4×C17—41no—
519C22⋊C4×C17—41no—
520C22⋊C4×C17—41no—
521C22⋊C4×C17—41no—
522C22⋊C4×C17—41no—
523C22⋊C4×C17—41no—
524C42×C17—22no—
525C42×C17—41no—
526C42×C17—41no—
527C42×C17—41no—
528C42×C17—41no—
529C42×C17—41no—
530C42×C17—41no—
531C42×C17—41no—
532C42×C17—41no—
533C42×C17—41no—
534#36820C1711yesmaximal, characteristic, direct product factor, Sylow
535C23×C17—21no—
536C23×C17—21no—
537C23×C17—21no—
538C23×C17—21no—
539C23×C17—21no—
540C23×C17—21no—
541C23×C17—21no—
542C23×C17—21no—
543C23×C17—21no—
544C23×C17—21no—
545C23×C17—21no—
546C23×C17—21no—
547C23×C17—21no—
548C23×C17—21no—
549C23×C17—21no—
550C23×C17—21no—
551C23×C17—21no—
552C23×C17—21no—
553C23×C17—21no—
554C23×C17—21no—
555C23×C17—21no—
556C23×C17—21no—
557C23×C17—21no—
558C23×C17—21no—
559C23×C17—21no—
560C23×C17—21no—
561C23×C17—21no—
562C23×C17—21no—
563C23×C17—21no—
564C23×C17—21no—
565C23×C17—21no—
566C23×C17—21no—
567C23×C17—21no—
568C23×C17C2×#4112yes—
569C23×C17H(5,𝔽2)12yes—
570C23×C17C2511yescharacteristic
571Q8×C17—44no—
572D4×C17—44no—
573D4×C17—44no—
574D4×C17—44no—
575D4×C17—44no—
576D4×C17—82no—
577D4×C17—82no—
578D4×C17—82no—
579D4×C17—82no—
580D4×C17—82no—
581D4×C17—82no—
582C2×C4×C17—28no—
583C2×C4×C17—21no—
584C2×C4×C17—21no—
585C2×C4×C17—21no—
586C2×C4×C17—21no—
587C2×C4×C17—21no—
588C2×C4×C17—21no—
589C2×C4×C17—21no—
590C2×C4×C17—21no—
591C2×C4×C17—21no—
592C2×C4×C17—21no—
593C2×C4×C17—21no—
594C2×C4×C17—21no—
595C2×C4×C17—21no—
596C2×C4×C17—21no—
597C2×C4×C17—21no—
598C2×C4×C17—21no—
599C2×C4×C17—21no—
600C2×C4×C17—21no—
601C2×C4×C17—21no—
602C2×C4×C17—21no—
603C2×C4×C17—21no—
604C2×C4×C17—21no—
605C2×C4×C17—21no—
606C2×C4×C17—21no—
607C2×C4×C17—21no—
608C2×C4×C17—21no—
609C2×C4×C17—21no—
610C2×C4×C17—21no—
611C2×C4×C17—21no—
612C2×C4×C17—21no—
613C2×C4×C17—21no—
614C2×C4×C17—21no—
615C2×C4×C17—21no—
616C2×C4×C17—21no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—44no—
659C2×C4×C17—44no—
660C2×C4×C17—44no—
661C2×C4×C17—44no—
662C2×C4×C17—82no—
663C2×C4×C17—82no—
664C2×C4×C17—82no—
665C2×C4×C17—82no—
666C2×C4×C17C2×#4112yes—
667C2×C4×C17C2×#4112yes—
668C2×C4×C17H(5,𝔽2)12yes—
669#2853C2×C1711yescharacteristic, complemented
670#2853C2×C1711yescharacteristic, complemented
671#2797C2×C1711yescharacteristic, complemented
672#2786C2×C1711yescharacteristic, complemented
673#2761C2×C1711yescharacteristic, complemented
674#2758C2×C1711yescharacteristic, complemented
675#2754C2×C1711yescharacteristic, complemented
676#2750C2×C1711yescharacteristic, complemented
677#2749C2×C1711yescharacteristic, complemented
678#2749C2×C1711yescharacteristic, complemented
679#2711C2×C1711yescharacteristic, complemented
680#2708C2×C1711yescharacteristic, complemented
681#2703C2×C1711yescharacteristic, complemented
682#2703C2×C1711yescharacteristic, complemented
683#2703C2×C1711yescharacteristic, complemented
684#2701C2×C1711yescharacteristic, complemented
685#2690C2×C1711yescharacteristic, complemented
686#2687C2×C1711yescharacteristic, complemented
687#2652C2×C1711yescharacteristic, complemented
688#2648C2×C1711yescharacteristic, complemented
689#2602C2×C1711yescharacteristic, complemented
690#2597C2×C1711yescharacteristic, complemented
691#2578C2×C1711yescharacteristic, complemented
692#2569C2×C1711yescharacteristic, complemented
693#2475C2×C1711yescharacteristic, complemented
694#2471C2×C1711yescharacteristic, complemented
695#2430C2×C1711yescharacteristic, complemented
696#2407C2×C1711yescharacteristic, complemented
697#2335C2×C1711yescharacteristic, complemented
698#2318C2×C1711yescharacteristic, complemented
699#2297C2×C1711yescharacteristic, complemented
700C22×C17—22no—
701C22×C17—22no—
702C22×C17—22no—
703C22×C17—22no—
704C22×C17—22no—
705C22×C17—22no—
706C22×C17—41no—
707C22×C17—41no—
708C22×C17—41no—
709C22×C17—41no—
710C22×C17—41no—
711C22×C17—41no—
712C22×C17—41no—
713C22×C17—41no—
714C22×C17—41no—
715C22×C17—41no—
716C22×C17—41no—
717C22×C17—41no—
718C22×C17—41no—
719C22×C17—41no—
720C22×C17—41no—
721C22×C17—41no—
722C22×C17—41no—
723C22×C17—41no—
724C22×C17—41no—
725C22×C17—41no—
726C22×C17—41no—
727C22×C17—41no—
728C22×C17—41no—
729C22×C17—41no—
730C22×C17—41no—
731C22×C17—41no—
732C22×C17—41no—
733C22×C17—41no—
734C22×C17—41no—
735C22×C17C22×#4111yescharacteristic
736C22×C17C2×H(5,𝔽2)11yescharacteristic
737C22×C17C2×H(5,𝔽2)11yescharacteristic
738C22×C17#58511yescharacteristic
739C22×C17#58511yescharacteristic
740C22×C17#58511yescharacteristic
741C22×C17#58511yescharacteristic
742C4×C17—22no—
743C4×C17—22no—
744C4×C17—22no—
745C4×C17—41no—
746C4×C17—41no—
747C4×C17—41no—
748C4×C17—41no—
749C4×C17—41no—
750C4×C17—41no—
751C4×C17—41no—
752C4×C17—41no—
753C4×C17—41no—
754C4×C17—41no—
755C4×C17—41no—
756C4×C17—41no—
757C4×C17—41no—
758C4×C17—41no—
759C4×C17—41no—
760C4×C17—41no—
761C4×C17—41no—
762C4×C17—41no—
763C4×C17—41no—
764C4×C17—41no—
765C4×C17—41no—
766C4×C17—41no—
767C4×C17—41no—
768C22×#41C22×C1711yescharacteristic
769C2×#125C22×C1711yescharacteristic
770C2×#123C22×C1711yescharacteristic
771C2×#123C22×C1711yescharacteristic
772C2×#123C22×C1711yescharacteristic
773C2×#123C22×C1711yescharacteristic
774C2×C22⋊Q8C22×C1711yescharacteristic
775C2×#121C22×C1711yescharacteristic
776C2×#121C22×C1711yescharacteristic
777C2×#121C22×C1711yescharacteristic
778C2×C4×D4C22×C1711yescharacteristic
779C2×#117C22×C1711yescharacteristic
780C22×C42C22×C1711yescharacteristic
781#400C22×C1711yescharacteristic
782#400C22×C1711yescharacteristic
783#400C22×C1711yescharacteristic
784#400C22×C1711yescharacteristic
785#400C22×C1711yescharacteristic
786#400C22×C1711yescharacteristic
787#400C22×C1711yescharacteristic
788#400C22×C1711yescharacteristic
789#400C22×C1711yescharacteristic
790#399C22×C1711yescharacteristic
791#398C22×C1711yescharacteristic
792#398C22×C1711yescharacteristic
793#398C22×C1711yescharacteristic
794#398C22×C1711yescharacteristic
795#397C22×C1711yescharacteristic
796#397C22×C1711yescharacteristic
797#397C22×C1711yescharacteristic
798#397C22×C1711yescharacteristic
799#397C22×C1711yescharacteristic
800#397C22×C1711yescharacteristic
801#397C22×C1711yescharacteristic
802#397C22×C1711yescharacteristic
803#397C22×C1711yescharacteristic
804#397C22×C1711yescharacteristic
805#397C22×C1711yescharacteristic
806#397C22×C1711yescharacteristic
807#396C22×C1711yescharacteristic
808#396C22×C1711yescharacteristic
809#396C22×C1711yescharacteristic
810#396C22×C1711yescharacteristic
811#395C22×C1711yescharacteristic
812#394C22×C1711yescharacteristic
813#394C22×C1711yescharacteristic
814#394C22×C1711yescharacteristic
815#394C22×C1711yescharacteristic
816#394C22×C1711yescharacteristic
817#394C22×C1711yescharacteristic
818#394C22×C1711yescharacteristic
819#394C22×C1711yescharacteristic
820#394C22×C1711yescharacteristic
821#394C22×C1711yescharacteristic
822#393C22×C1711yescharacteristic
823#392C22×C1711yescharacteristic
824#392C22×C1711yescharacteristic
825#392C22×C1711yescharacteristic
826#392C22×C1711yescharacteristic
827#392C22×C1711yescharacteristic
828#392C22×C1711yescharacteristic
829#391C22×C1711yescharacteristic
830#391C22×C1711yescharacteristic
831#391C22×C1711yescharacteristic
832#390C22×C1711yescharacteristic
833#390C22×C1711yescharacteristic
834#390C22×C1711yescharacteristic
835#390C22×C1711yescharacteristic
836#390C22×C1711yescharacteristic
837#390C22×C1711yescharacteristic
838#390C22×C1711yescharacteristic
839#389C22×C1711yescharacteristic
840#389C22×C1711yescharacteristic
841#388C22×C1711yescharacteristic
842#388C22×C1711yescharacteristic
843#388C22×C1711yescharacteristic
844#388C22×C1711yescharacteristic
845#388C22×C1711yescharacteristic
846#388C22×C1711yescharacteristic
847#388C22×C1711yescharacteristic
848#388C22×C1711yescharacteristic
849#388C22×C1711yescharacteristic
850#388C22×C1711yescharacteristic
851#388C22×C1711yescharacteristic
852#388C22×C1711yescharacteristic
853#388C22×C1711yescharacteristic
854#388C22×C1711yescharacteristic
855#388C22×C1711yescharacteristic
856#388C22×C1711yescharacteristic
857#388C22×C1711yescharacteristic
858#388C22×C1711yescharacteristic
859#387C22×C1711yescharacteristic
860#387C22×C1711yescharacteristic
861#387C22×C1711yescharacteristic
862#387C22×C1711yescharacteristic
863#387C22×C1711yescharacteristic
864#387C22×C1711yescharacteristic
865#387C22×C1711yescharacteristic
866#387C22×C1711yescharacteristic
867#387C22×C1711yescharacteristic
868#387C22×C1711yescharacteristic
869#387C22×C1711yescharacteristic
870#387C22×C1711yescharacteristic
871#387C22×C1711yescharacteristic
872#387C22×C1711yescharacteristic
873#387C22×C1711yescharacteristic
874#387C22×C1711yescharacteristic
875#386C22×C1711yescharacteristic
876#386C22×C1711yescharacteristic
877#386C22×C1711yescharacteristic
878#386C22×C1711yescharacteristic
879#386C22×C1711yescharacteristic
880#386C22×C1711yescharacteristic
881#386C22×C1711yescharacteristic
882#386C22×C1711yescharacteristic
883#386C22×C1711yescharacteristic
884#386C22×C1711yescharacteristic
885#386C22×C1711yescharacteristic
886#386C22×C1711yescharacteristic
887#386C22×C1711yescharacteristic
888#386C22×C1711yescharacteristic
889#386C22×C1711yescharacteristic
890#386C22×C1711yescharacteristic
891#386C22×C1711yescharacteristic
892#386C22×C1711yescharacteristic
893#385C22×C1711yescharacteristic
894#385C22×C1711yescharacteristic
895#385C22×C1711yescharacteristic
896#385C22×C1711yescharacteristic
897#385C22×C1711yescharacteristic
898#385C22×C1711yescharacteristic
899#385C22×C1711yescharacteristic
900#385C22×C1711yescharacteristic
901#385C22×C1711yescharacteristic
902#385C22×C1711yescharacteristic
903#385C22×C1711yescharacteristic
904#385C22×C1711yescharacteristic
905#383C22×C1711yescharacteristic
906#383C22×C1711yescharacteristic
907#382C22×C1711yescharacteristic
908#381C22×C1711yescharacteristic
909#381C22×C1711yescharacteristic
910#381C22×C1711yescharacteristic
911#380C22×C1711yescharacteristic
912#380C22×C1711yescharacteristic
913#380C22×C1711yescharacteristic
914#380C22×C1711yescharacteristic
915#380C22×C1711yescharacteristic
916C4×C4⋊C4C22×C1711yescharacteristic
917C4×C22⋊C4C22×C1711yescharacteristic
918C4×C22⋊C4C22×C1711yescharacteristic
919C4×C22⋊C4C22×C1711yescharacteristic
920C4×C22⋊C4C22×C1711yescharacteristic
921C4×C22⋊C4C22×C1711yescharacteristic
922C2×#95C22×C1711yescharacteristic
923C2×C17—42no—
924C2×C17—42no—
925C2×C17—81no—
926C2×C17—81no—
927C2×C17—81no—
928C2×C17#345511yescharacteristic
929C2×C17#349011yescharacteristic
930C2×C17#351211yescharacteristic
931C2×C17#353311yescharacteristic
932C2×C17#353311yescharacteristic
933C2×C17#356211yescharacteristic
934C2×C17#356211yescharacteristic
935C2×#41—24no—
936C2×#41—42no—
937C2×#41—42no—
938C22×Q8C23×C1711yescharacteristic
939C22×D4C23×C1711yescharacteristic
940C22×D4C23×C1711yescharacteristic
941C22×D4C23×C1711yescharacteristic
942C22×D4C23×C1711yescharacteristic
943C22×D4C23×C1711yescharacteristic
944C22×D4C23×C1711yescharacteristic
945C22×D4C23×C1711yescharacteristic
946C22×D4C23×C1711yescharacteristic
947C22×D4C23×C1711yescharacteristic
948C22×D4C23×C1711yescharacteristic
949C23×C4C23×C1711yescharacteristic
950C23×C4C23×C1711yescharacteristic
951C23×C4C23×C1711yescharacteristic
952C23×C4C23×C1711yescharacteristic
953C23×C4C23×C1711yescharacteristic
954C23×C4C23×C1711yescharacteristic
955C23×C4C23×C1711yescharacteristic
956C23×C4C23×C1711yescharacteristic
957C23×C4C23×C1711yescharacteristic
958#125—42no—
959#123—24no—
960#123—42no—
961#123—42no—
962#123—42no—
963C22⋊Q8—42no—
964#121—42no—
965#121—42no—
966#121—42no—
967C4×D4—24no—
968#117—42no—
969C2×C4⋊C4C23×C1711yescharacteristic
970C2×C4⋊C4C23×C1711yescharacteristic
971C2×C4⋊C4C23×C1711yescharacteristic
972C2×C4⋊C4C23×C1711yescharacteristic
973C2×C4⋊C4C23×C1711yescharacteristic
974C2×C4⋊C4C23×C1711yescharacteristic
975C2×C4⋊C4C23×C1711yescharacteristic
976C2×C4⋊C4C23×C1711yescharacteristic
977C2×C4⋊C4C23×C1711yescharacteristic
978C2×C4⋊C4C23×C1711yescharacteristic
979C2×C4⋊C4C23×C1711yescharacteristic
980C2×C4⋊C4C23×C1711yescharacteristic
981C2×C4⋊C4C23×C1711yescharacteristic
982C2×C4⋊C4C23×C1711yescharacteristic
983C2×C4⋊C4C23×C1711yescharacteristic
984C2×C4⋊C4C23×C1711yescharacteristic
985C2×C4⋊C4C23×C1711yescharacteristic
986C2×C4⋊C4C23×C1711yescharacteristic
987C2×C4⋊C4C23×C1711yescharacteristic
988C2×C4⋊C4C23×C1711yescharacteristic
989C2×C4⋊C4C23×C1711yescharacteristic
990C2×C4⋊C4C23×C1711yescharacteristic
991C2×C4⋊C4C23×C1711yescharacteristic
992C2×C4⋊C4C23×C1711yescharacteristic
993C2×C4⋊C4C23×C1711yescharacteristic
994C2×C4⋊C4C23×C1711yescharacteristic
995C2×C4⋊C4C23×C1711yescharacteristic
996C2×C4⋊C4C23×C1711yescharacteristic
997C2×C4⋊C4C23×C1711yescharacteristic
998C2×C22⋊C4C23×C1711yescharacteristic
999C2×C22⋊C4C23×C1711yescharacteristic
1000C2×C22⋊C4C23×C1711yescharacteristic
1001C2×C22⋊C4C23×C1711yescharacteristic
1002C2×C22⋊C4C23×C1711yescharacteristic
1003C2×C22⋊C4C23×C1711yescharacteristic
1004C2×C22⋊C4C23×C1711yescharacteristic
1005C2×C22⋊C4C23×C1711yescharacteristic
1006C2×C22⋊C4C23×C1711yescharacteristic
1007C2×C22⋊C4C23×C1711yescharacteristic
1008C2×C22⋊C4C23×C1711yescharacteristic
1009C2×C22⋊C4C23×C1711yescharacteristic
1010C2×C22⋊C4C23×C1711yescharacteristic
1011C2×C22⋊C4C23×C1711yescharacteristic
1012C2×C22⋊C4C23×C1711yescharacteristic
1013C2×C22⋊C4C23×C1711yescharacteristic
1014C2×C22⋊C4C23×C1711yescharacteristic
1015C2×C22⋊C4C23×C1711yescharacteristic
1016C2×C22⋊C4C23×C1711yescharacteristic
1017C2×C22⋊C4C23×C1711yescharacteristic
1018C2×C22⋊C4C23×C1711yescharacteristic
1019C2×C22⋊C4C23×C1711yescharacteristic
1020C2×C22⋊C4C23×C1711yescharacteristic
1021C2×C22⋊C4C23×C1711yescharacteristic
1022C2×C22⋊C4C23×C1711yescharacteristic
1023C2×C22⋊C4C23×C1711yescharacteristic
1024C2×C22⋊C4C23×C1711yescharacteristic
1025C2×C22⋊C4C23×C1711yescharacteristic
1026C2×C22⋊C4C23×C1711yescharacteristic
1027C2×C22⋊C4C23×C1711yescharacteristic
1028C2×C22⋊C4C23×C1711yescharacteristic
1029C2×C22⋊C4C23×C1711yescharacteristic
1030C2×C22⋊C4C23×C1711yescharacteristic
1031C2×C22⋊C4C23×C1711yescharacteristic
1032C2×C22⋊C4C23×C1711yescharacteristic
1033C2×C22⋊C4C23×C1711yescharacteristic
1034C2×C22⋊C4C23×C1711yescharacteristic
1035C2×C22⋊C4C23×C1711yescharacteristic
1036C2×C22⋊C4C23×C1711yescharacteristic
1037C2×C22⋊C4C23×C1711yescharacteristic
1038C2×C22⋊C4C23×C1711yescharacteristic
1039C2×C22⋊C4C23×C1711yescharacteristic
1040C2×C22⋊C4C23×C1711yescharacteristic
1041C2×C22⋊C4C23×C1711yescharacteristic
1042C2×C22⋊C4C23×C1711yescharacteristic
1043C2×C22⋊C4C23×C1711yescharacteristic
1044C2×C42—42no—
1045C2×C42C23×C1711yescharacteristic
1046C2×C42C23×C1711yescharacteristic
1047C2×C42C23×C1711yescharacteristic
1048C2×C42C23×C1711yescharacteristic
1049C2×C42C23×C1711yescharacteristic
1050C2×C42C23×C1711yescharacteristic
1051C2×C42C23×C1711yescharacteristic
1052C2×C42C23×C1711yescharacteristic
1053C2×C42C23×C1711yescharacteristic
1054C2×C42C23×C1711yescharacteristic
1055#95C23×C1711yescharacteristic
1056#95C23×C1711yescharacteristic
1057#95C23×C1711yescharacteristic
1058#95C23×C1711yescharacteristic
1059#95C23×C1711yescharacteristic
1060#95C23×C1711yescharacteristic
1061#95C23×C1711yescharacteristic
1062#95C23×C1711yescharacteristic
1063#95C23×C1711yescharacteristic
1064#95C23×C1711yescharacteristic
1065#95C23×C1711yescharacteristic
1066#95C23×C1711yescharacteristic
1067#95C23×C1711yescharacteristic
1068#95C23×C1711yescharacteristic
1069#95C23×C1711yescharacteristic
1070#95C23×C1711yescharacteristic
1071#95C23×C1711yescharacteristic
1072#95C23×C1711yescharacteristic
1073#95C23×C1711yescharacteristic
1074#95C23×C1711yescharacteristic
1075#95C23×C1711yescharacteristic
1076#95C23×C1711yescharacteristic
1077#95C23×C1711yescharacteristic
1078#95C23×C1711yescharacteristic
1079#95C23×C1711yescharacteristic
1080#95C23×C1711yescharacteristic
1081#95C23×C1711yescharacteristic
1082#95C23×C1711yescharacteristic
1083#95C23×C1711yescharacteristic
1084#95C23×C1711yescharacteristic
1085#95C23×C1711yescharacteristic
1086#95C23×C1711yescharacteristic
1087#95C23×C1711yescharacteristic
1088#95C23×C1711yescharacteristic
1089#95C23×C1711yescharacteristic
1090#95C23×C1711yescharacteristic
1091#95C23×C1711yescharacteristic
1092#95C23×C1711yescharacteristic
1093#95C23×C1711yescharacteristic
1094#95C23×C1711yescharacteristic
1095#95C23×C1711yescharacteristic
1096#95C23×C1711yescharacteristic
1097#95C23×C1711yescharacteristic
1098#95C23×C1711yescharacteristic
1099#95C23×C1711yescharacteristic
1100#95C23×C1711yescharacteristic
1101#95C23×C1711yescharacteristic
1102#95C23×C1711yescharacteristic
1103#95C23×C1711yescharacteristic
1104#95C23×C1711yescharacteristic
1105C17#3682011yescharacteristic, direct product factor, Sylow
1106C24C24×C1711yescharacteristic
1107C24C24×C1711yescharacteristic
1108C24C24×C1711yescharacteristic
1109C24C24×C1711yescharacteristic
1110C24C24×C1711yescharacteristic
1111#41—416no—
1112C2×Q8—22no—
1113C2×Q8—22no—
1114C2×Q8—41no—
1115C2×D4—22no—
1116C2×D4—22no—
1117C2×D4—22no—
1118C2×D4—22no—
1119C2×D4—22no—
1120C2×D4—22no—
1121C2×D4—22no—
1122C2×D4—22no—
1123C2×D4—22no—
1124C2×D4—22no—
1125C2×D4—41no—
1126C2×D4—41no—
1127C2×D4—41no—
1128C2×D4—41no—
1129C2×D4—41no—
1130C2×D4—41no—
1131C2×D4—41no—
1132C2×D4—41no—
1133C2×D4—41no—
1134C2×D4—41no—
1135C2×D4—41no—
1136C2×D4—41no—
1137C2×D4—41no—
1138C2×D4—41no—
1139C2×D4—41no—
1140C2×D4—41no—
1141C2×D4—41no—
1142C2×D4—41no—
1143C2×D4—41no—
1144C2×D4—41no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—22no—
1149C22×C4—22no—
1150C22×C4—22no—
1151C22×C4—22no—
1152C22×C4—41no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—41no—
1163C22×C4—41no—
1164C22×C4—41no—
1165C22×C4—41no—
1166C22×C4—41no—
1167C22×C4—41no—
1168C22×C4—41no—
1169C22×C4—41no—
1170C22×C4—41no—
1171C22×C4#41×C1714yes—
1172C22×C4C24×C1711yescharacteristic
1173C22×C4C24×C1711yescharacteristic
1174C22×C4C24×C1711yescharacteristic
1175C22×C4C24×C1711yescharacteristic
1176C22×C4C24×C1711yescharacteristic
1177C22×C4C24×C1711yescharacteristic
1178C22×C4C24×C1711yescharacteristic
1179C22×C4C24×C1711yescharacteristic
1180C22×C4C24×C1711yescharacteristic
1181C22×C4C24×C1711yescharacteristic
1182C22×C4C24×C1711yescharacteristic
1183C22×C4C24×C1711yescharacteristic
1184C22×C4C24×C1711yescharacteristic
1185C22×C4C24×C1711yescharacteristic
1186C22×C4C24×C1711yescharacteristic
1187C22×C4C24×C1711yescharacteristic
1188C22×C4C24×C1711yescharacteristic
1189C22×C4C24×C1711yescharacteristic
1190C22×C4C24×C1711yescharacteristic
1191C22×C4C24×C1711yescharacteristic
1192C22×C4C24×C1711yescharacteristic
1193C22×C4C24×C1711yescharacteristic
1194C22×C4C24×C1711yescharacteristic
1195C22×C4C24×C1711yescharacteristic
1196C22×C4C24×C1711yescharacteristic
1197C22×C4C24×C1711yescharacteristic
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—22no—
1201C4⋊C4—22no—
1202C4⋊C4—22no—
1203C4⋊C4—22no—
1204C4⋊C4—22no—
1205C4⋊C4—41no—
1206C4⋊C4—41no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—41no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C22⋊C4—22no—
1228C22⋊C4—22no—
1229C22⋊C4—22no—
1230C22⋊C4—22no—
1231C22⋊C4—22no—
1232C22⋊C4—22no—
1233C22⋊C4—22no—
1234C22⋊C4—22no—
1235C22⋊C4—22no—
1236C22⋊C4—41no—
1237C22⋊C4—41no—
1238C22⋊C4—41no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C22⋊C4—41no—
1243C22⋊C4—41no—
1244C22⋊C4—41no—
1245C22⋊C4—41no—
1246C22⋊C4—41no—
1247C22⋊C4—41no—
1248C22⋊C4—41no—
1249C22⋊C4—41no—
1250C22⋊C4—41no—
1251C22⋊C4—41no—
1252C22⋊C4—41no—
1253C22⋊C4—41no—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—41no—
1257C22⋊C4—41no—
1258C22⋊C4—41no—
1259C22⋊C4—41no—
1260C22⋊C4—41no—
1261C22⋊C4—41no—
1262C22⋊C4—41no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4—41no—
1266C22⋊C4—41no—
1267C22⋊C4—41no—
1268C22⋊C4—41no—
1269C22⋊C4—41no—
1270C22⋊C4—41no—
1271C22⋊C4—41no—
1272C22⋊C4—41no—
1273C42—22no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42—41no—
1279C42—41no—
1280C42—41no—
1281C42—41no—
1282C42—41no—
1283C23—21no—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—21no—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—21no—
1306C23—21no—
1307C23—21no—
1308C23—21no—
1309C23—21no—
1310C23—21no—
1311C23—21no—
1312C23—21no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23C2×#41×C1712yes—
1317C23C17×H(5,𝔽2)12yes—
1318C23C25×C1711yescharacteristic
1319Q8—44no—
1320D4—44no—
1321D4—44no—
1322D4—44no—
1323D4—44no—
1324D4—82no—
1325D4—82no—
1326D4—82no—
1327D4—82no—
1328D4—82no—
1329D4—82no—
1330C2×C4—28no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—44no—
1407C2×C4—44no—
1408C2×C4—44no—
1409C2×C4—44no—
1410C2×C4—82no—
1411C2×C4—82no—
1412C2×C4—82no—
1413C2×C4—82no—
1414C2×C4C2×#41×C1712yes—
1415C2×C4C2×#41×C1712yes—
1416C2×C4C17×H(5,𝔽2)12yes—
1417C22—22no—
1418C22—22no—
1419C22—22no—
1420C22—22no—
1421C22—22no—
1422C22—22no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—41no—
1436C22—41no—
1437C22—41no—
1438C22—41no—
1439C22—41no—
1440C22—41no—
1441C22—41no—
1442C22—41no—
1443C22—41no—
1444C22—41no—
1445C22—41no—
1446C22—41no—
1447C22—41no—
1448C22—41no—
1449C22—41no—
1450C22—41no—
1451C22—41no—
1452C22C22×#41×C1711yescharacteristic
1453C22C2×C17×H(5,𝔽2)11yescharacteristic
1454C22C2×C17×H(5,𝔽2)11yescharacteristic
1455C22C17×#58511yescharacteristic
1456C22C17×#58511yescharacteristic
1457C22C17×#58511yescharacteristic
1458C22C17×#58511yescharacteristic
1459C4—22no—
1460C4—22no—
1461C4—22no—
1462C4—41no—
1463C4—41no—
1464C4—41no—
1465C4—41no—
1466C4—41no—
1467C4—41no—
1468C4—41no—
1469C4—41no—
1470C4—41no—
1471C4—41no—
1472C4—41no—
1473C4—41no—
1474C4—41no—
1475C4—41no—
1476C4—41no—
1477C4—41no—
1478C4—41no—
1479C4—41no—
1480C4—41no—
1481C4—41no—
1482C4—41no—
1483C4—41no—
1484C4—41no—
1485C2—42no—
1486C2—42no—
1487C2—81no—
1488C2—81no—
1489C2—81no—
1490C2C17×#345511yescharacteristic
1491C2C17×#349011yescharacteristic
1492C2C17×#351211yescharacteristic
1493C2C17×#353311yescharacteristic
1494C2C17×#353311yescharacteristic
1495C2C17×#356211yescharacteristic
1496C2C17×#356211yescharacteristic
subgroupG/H
center, socleC23×C17C25
commutator, Frattini, cosocleC23C25×C17
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C17 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C17×#2853C2semidirect
2. C17×#2853C2semidirect
3. C17×#2797C2semidirect
4. C17×#2786C2semidirect
5. C17×#2761C2semidirect
6. C17×#2758C2semidirect
7. C17×#2754C2semidirect
8. C17×#2750C2semidirect
9. C17×#2749C2semidirect
10. C17×#2749C2semidirect
11. C17×#2711C2semidirect
12. C17×#2708C2semidirect
13. C17×#2703C2semidirect
14. C17×#2703C2semidirect
15. C17×#2703C2semidirect
16. C17×#2701C2semidirect
17. C17×#2690C2semidirect
18. C17×#2687C2semidirect
19. C17×#2652C2semidirect
20. C17×#2648C2semidirect
21. C17×#2602C2semidirect
22. C17×#2597C2semidirect
23. C17×#2578C2semidirect
24. C17×#2569C2semidirect
25. C17×#2475C2semidirect
26. C17×#2471C2semidirect
27. C17×#2430C2semidirect
28. C17×#2407C2semidirect
29. C17×#2335C2semidirect
30. C17×#2318C2semidirect
31. C17×#2297C2semidirect
534. #36820C17direct (N × H)
669. #2853C2×C17semidirect
670. #2853C2×C17semidirect
671. #2797C2×C17semidirect
672. #2786C2×C17semidirect
673. #2761C2×C17semidirect
674. #2758C2×C17semidirect
675. #2754C2×C17semidirect
676. #2750C2×C17semidirect
677. #2749C2×C17semidirect
678. #2749C2×C17semidirect
679. #2711C2×C17semidirect
680. #2708C2×C17semidirect
681. #2703C2×C17semidirect
682. #2703C2×C17semidirect
683. #2703C2×C17semidirect
684. #2701C2×C17semidirect
685. #2690C2×C17semidirect
686. #2687C2×C17semidirect
687. #2652C2×C17semidirect
688. #2648C2×C17semidirect
689. #2602C2×C17semidirect
690. #2597C2×C17semidirect
691. #2578C2×C17semidirect
692. #2569C2×C17semidirect
693. #2475C2×C17semidirect
694. #2471C2×C17semidirect
695. #2430C2×C17semidirect
696. #2407C2×C17semidirect
697. #2335C2×C17semidirect
698. #2318C2×C17semidirect
699. #2297C2×C17semidirect
1105. C17#36820direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C17×#28532
C17×#27972
C17×#27862
C17×#27612
C17×#27582
C17×#27542
C17×#27502
C17×#27492
C17×#27112
C17×#27082
C17×#27032
C17×#27012
C17×#26902
C17×#26872
C17×#26522
C17×#26482
C17×#26022
C17×#25972
C17×#25782
C17×#25692
C17×#24752
C17×#24712
C17×#24302
C17×#24072
C17×#23352
C17×#23182
C17×#22972
#3682017