Finite Group Databasebeta

← C17×#36849 #16894593

Subgroups — C17×#36849 #16894593

Order 4352.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2854C211yesmaximal, characteristic, complemented
2C17×#2852C211yesmaximal, characteristic, complemented
3C17×#2802C211yesmaximal, characteristic, complemented
4C17×#2797C211yesmaximal, characteristic, complemented
5C17×#2780C211yesmaximal, characteristic, complemented
6C17×#2780C211yesmaximal, characteristic, complemented
7C17×#2770C211yesmaximal, characteristic, complemented
8C17×#2764C211yesmaximal, characteristic, complemented
9C17×#2749C211yesmaximal, characteristic, complemented
10C17×#2748C211yesmaximal, characteristic, complemented
11C17×#2740C211yesmaximal, characteristic, complemented
12C17×#2739C211yesmaximal, characteristic, complemented
13C17×#2727C211yesmaximal, characteristic, complemented
14C17×#2715C211yesmaximal, characteristic, complemented
15C17×#2711C211yesmaximal, characteristic, complemented
16C17×#2704C211yesmaximal, characteristic, complemented
17C17×#2691C211yesmaximal, characteristic, complemented
18C17×#2676C211yesmaximal, characteristic
19C17×#2664C211yesmaximal, characteristic, complemented
20C17×#2651C211yesmaximal, characteristic, complemented
21C17×#2558C211yesmaximal, characteristic, complemented
22C17×#2554C211yesmaximal, characteristic, complemented
23C17×#2475C211yesmaximal, characteristic, complemented
24C17×#2470C211yesmaximal, characteristic, complemented
25C17×#2469C211yesmaximal, characteristic, complemented
26C17×#2468C211yesmaximal, characteristic, complemented
27C17×#2457C211yesmaximal, characteristic, complemented
28C17×#2448C211yesmaximal, characteristic, complemented
29C17×#2336C211yesmaximal, characteristic, complemented
30C17×#2324C211yesmaximal, characteristic, complemented
31C4×C17×C22⋊Q8C211yesmaximal, characteristic, complemented
32C2×C17×#126C2211yescharacteristic
33C2×C17×#126C2211yescharacteristic
34C2×C17×#126C2211yescharacteristic
35C2×C17×#125C2211yescharacteristic
36C2×C17×#125C2211yescharacteristic
37C2×C17×#124C2211yescharacteristic
38C2×C17×#123C2211yescharacteristic
39C2×C17×#123C2211yescharacteristic
40C2×C17×C22⋊Q8C2211yescharacteristic
41C2×C17×#121C2211yescharacteristic
42C2×C17×#121C2211yescharacteristic
43C2×C4×Q8×C17C2211yescharacteristic
44C2×C4×D4×C17C2211yescharacteristic
45C2×C17×#117C2211yescharacteristic
46C22×C42×C17C2211yescharacteristic
47C17×#400C2211yescharacteristic
48C17×#400C2211yescharacteristic
49C17×#400C2211yescharacteristic
50C17×#400C2211yescharacteristic
51C17×#400C2211yescharacteristic
52C17×#400C2211yescharacteristic
53C17×#399C2211yescharacteristic
54C17×#399C2211yescharacteristic
55C17×#399C2211yescharacteristic
56C17×#399C2211yescharacteristic
57C17×#398C2211yescharacteristic
58C17×#398C2211yescharacteristic
59C17×#398C2211yescharacteristic
60C17×#398C2211yescharacteristic
61C17×#398C2211yescharacteristic
62C17×#398C2211yescharacteristic
63C17×#398C2211yescharacteristic
64C17×#398C2211yescharacteristic
65C17×#398C2211yescharacteristic
66C17×#397C2211yescharacteristic
67C17×#397C2211yescharacteristic
68C17×#397C2211yescharacteristic
69C17×#397C2211yescharacteristic
70C17×#397C2211yescharacteristic
71C17×#397C2211yescharacteristic
72C17×#397C2211yescharacteristic
73C17×#396C2211yescharacteristic
74C17×#396C2211yescharacteristic
75C17×#396C2211yescharacteristic
76C17×#396C2211yescharacteristic
77C17×#396C2211yescharacteristic
78C17×#396C2211yescharacteristic
79C17×#396C2211yescharacteristic
80C17×#396C2211yescharacteristic
81C17×#396C2211yescharacteristic
82C17×#396C2211yescharacteristic
83C17×#395C2211yescharacteristic
84C17×#394C2211yescharacteristic
85C17×#394C2211yescharacteristic
86C17×#394C2211yescharacteristic
87C17×#394C2211yescharacteristic
88C17×#394C2211yescharacteristic
89C17×#394C2211yescharacteristic
90C17×#394C2211yescharacteristic
91C17×#394C2211yescharacteristic
92C17×#393C2211yescharacteristic
93C17×#392C2211yescharacteristic
94C17×#392C2211yescharacteristic
95C17×#391C2211yescharacteristic
96C17×#391C2211yescharacteristic
97C17×#390C2211yescharacteristic
98C17×#390C2211yescharacteristic
99C17×#390C2211yescharacteristic
100C17×#390C2211yescharacteristic
101C17×#390C2211yescharacteristic
102C17×#390C2211yescharacteristic
103C17×#390C2211yescharacteristic
104C17×#390C2211yescharacteristic
105C17×#389C2211yescharacteristic
106C17×#389C2211yescharacteristic
107C17×#389C2211yescharacteristic
108C17×#389C2211yescharacteristic
109C17×#389C2211yescharacteristic
110C17×#389C2211yescharacteristic
111C17×#389C2211yescharacteristic
112C17×#389C2211yescharacteristic
113C17×#389C2211yescharacteristic
114C17×#389C2211yescharacteristic
115C17×#388C2211yescharacteristic
116C17×#388C2211yescharacteristic
117C17×#388C2211yescharacteristic
118C17×#388C2211yescharacteristic
119C17×#388C2211yescharacteristic
120C17×#388C2211yescharacteristic
121C17×#388C2211yescharacteristic
122C17×#388C2211yescharacteristic
123C17×#388C2211yescharacteristic
124C17×#388C2211yescharacteristic
125C17×#388C2211yescharacteristic
126C17×#388C2211yescharacteristic
127C17×#388C2211yescharacteristic
128C17×#388C2211yescharacteristic
129C17×#388C2211yescharacteristic
130C17×#388C2211yescharacteristic
131C17×#388C2211yescharacteristic
132C17×#388C2211yescharacteristic
133C17×#388C2211yescharacteristic
134C17×#387C2211yescharacteristic
135C17×#387C2211yescharacteristic
136C17×#387C2211yescharacteristic
137C17×#387C2211yescharacteristic
138C17×#387C2211yescharacteristic
139C17×#387C2211yescharacteristic
140C17×#387C2211yescharacteristic
141C17×#387C2211yescharacteristic
142C17×#387C2211yescharacteristic
143C17×#387C2211yescharacteristic
144C17×#387C2211yescharacteristic
145C17×#387C2211yescharacteristic
146C17×#387C2211yescharacteristic
147C17×#387C2211yescharacteristic
148C17×#387C2211yescharacteristic
149C17×#386C2211yescharacteristic
150C17×#386C2211yescharacteristic
151C17×#386C2211yescharacteristic
152C17×#386C2211yescharacteristic
153C17×#386C2211yescharacteristic
154C17×#386C2211yescharacteristic
155C17×#386C2211yescharacteristic
156C17×#386C2211yescharacteristic
157C17×#386C2211yescharacteristic
158C17×#386C2211yescharacteristic
159C17×#385C2211yescharacteristic
160C17×#385C2211yescharacteristic
161C17×#385C2211yescharacteristic
162C17×#385C2211yescharacteristic
163C17×#385C2211yescharacteristic
164C17×#385C2211yescharacteristic
165C17×#385C2211yescharacteristic
166C17×#385C2211yescharacteristic
167C17×#385C2211yescharacteristic
168C17×#385C2211yescharacteristic
169C17×#385C2211yescharacteristic
170C17×#385C2211yescharacteristic
171C17×#383C2211yescharacteristic
172C17×#383C2211yescharacteristic
173C17×#381C2211yescharacteristic
174C17×#381C2211yescharacteristic
175C17×#380C2211yescharacteristic
176C17×#380C2211yescharacteristic
177C17×#380C2211yescharacteristic
178C17×#380C2211yescharacteristic
179C17×#380C2211yescharacteristic
180C4×C4⋊C4×C17C2211yescharacteristic
181C4×C4⋊C4×C17C2211yescharacteristic
182C4×C4⋊C4×C17C2211yescharacteristic
183C4×C4⋊C4×C17C2211yescharacteristic
184C4×C4⋊C4×C17C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic
187C22×Q8×C17C2311yescharacteristic
188C22×D4×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C23×C4×C17C2311yescharacteristic
200C17×#126—42no—
201C17×#126—42no—
202C17×#126—42no—
203C17×#125—24no—
204C17×#125—42no—
205C17×#124—42no—
206C17×#123—42no—
207C17×#123—42no—
208C17×C22⋊Q8—24no—
209C17×#121—24no—
210C17×#121—42no—
211C4×Q8×C17—42no—
212C4×D4×C17—42no—
213C17×#117—42no—
214C2×C4⋊C4×C17C2311yescharacteristic
215C2×C4⋊C4×C17C2311yescharacteristic
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
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×C4⋊C4×C17C2311yescharacteristic
251C2×C4⋊C4×C17C2311yescharacteristic
252C2×C4⋊C4×C17C2311yescharacteristic
253C2×C4⋊C4×C17C2311yescharacteristic
254C2×C4⋊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×C22⋊C4×C17C2311yescharacteristic
297C2×C42×C17—42no—
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
307C2×C42×C17C2311yescharacteristic
308C2×C42×C17C2311yescharacteristic
309C2×C42×C17C2311yescharacteristic
310C2×C42×C17C2311yescharacteristic
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
361C2×Q8×C17—22no—
362C2×Q8×C17—22no—
363C2×Q8×C17—41no—
364C2×D4×C17—22no—
365C2×D4×C17—22no—
366C2×D4×C17—22no—
367C2×D4×C17—22no—
368C2×D4×C17—22no—
369C2×D4×C17—22no—
370C2×D4×C17—41no—
371C2×D4×C17—41no—
372C2×D4×C17—41no—
373C2×D4×C17—41no—
374C2×D4×C17—41no—
375C2×D4×C17—41no—
376C2×D4×C17—41no—
377C2×D4×C17—41no—
378C2×D4×C17—41no—
379C2×D4×C17—41no—
380C2×D4×C17—41no—
381C2×D4×C17—41no—
382C22×C4×C17—22no—
383C22×C4×C17—22no—
384C22×C4×C17—22no—
385C22×C4×C17—22no—
386C22×C4×C17—22no—
387C22×C4×C17—41no—
388C22×C4×C17—41no—
389C22×C4×C17—41no—
390C22×C4×C17—41no—
391C22×C4×C17—41no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17—41no—
395C22×C4×C17—41no—
396C22×C4×C17—41no—
397C22×C4×C17—41no—
398C22×C4×C17—41no—
399C22×C4×C17—41no—
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C4⋊C4×C17—22no—
428C4⋊C4×C17—22no—
429C4⋊C4×C17—22no—
430C4⋊C4×C17—22no—
431C4⋊C4×C17—22no—
432C4⋊C4×C17—22no—
433C4⋊C4×C17—22no—
434C4⋊C4×C17—22no—
435C4⋊C4×C17—22no—
436C4⋊C4×C17—22no—
437C4⋊C4×C17—22no—
438C4⋊C4×C17—22no—
439C4⋊C4×C17—41no—
440C4⋊C4×C17—41no—
441C4⋊C4×C17—41no—
442C4⋊C4×C17—41no—
443C4⋊C4×C17—41no—
444C4⋊C4×C17—41no—
445C4⋊C4×C17—41no—
446C4⋊C4×C17—41no—
447C4⋊C4×C17—41no—
448C4⋊C4×C17—41no—
449C4⋊C4×C17—41no—
450C4⋊C4×C17—41no—
451C4⋊C4×C17—41no—
452C4⋊C4×C17—41no—
453C4⋊C4×C17—41no—
454C4⋊C4×C17—41no—
455C4⋊C4×C17—41no—
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#4114yes—
468C22⋊C4×C17—22no—
469C22⋊C4×C17—22no—
470C22⋊C4×C17—22no—
471C22⋊C4×C17—22no—
472C22⋊C4×C17—22no—
473C22⋊C4×C17—22no—
474C22⋊C4×C17—22no—
475C22⋊C4×C17—22no—
476C22⋊C4×C17—22no—
477C22⋊C4×C17—22no—
478C22⋊C4×C17—22no—
479C22⋊C4×C17—41no—
480C22⋊C4×C17—41no—
481C22⋊C4×C17—41no—
482C22⋊C4×C17—41no—
483C22⋊C4×C17—41no—
484C22⋊C4×C17—41no—
485C22⋊C4×C17—41no—
486C22⋊C4×C17—41no—
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—
510C42×C17—22no—
511C42×C17—22no—
512C42×C17—22no—
513C42×C17—22no—
514C42×C17—22no—
515C42×C17—41no—
516C42×C17—41no—
517C42×C17—41no—
518C42×C17—41no—
519C42×C17—41no—
520C42×C17—41no—
521C42×C17—41no—
522C42×C17—41no—
523#36849C1711yesmaximal, characteristic, direct product factor, Sylow
524C23×C17—21no—
525C23×C17—21no—
526C23×C17—21no—
527C23×C17—21no—
528C23×C17—21no—
529C23×C17—21no—
530C23×C17—21no—
531C23×C17—21no—
532C23×C17—21no—
533C23×C17—21no—
534C23×C17—21no—
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×C172−1+412yes—
552C23×C17C2511yescharacteristic
553Q8×C17—44no—
554D4×C17—44no—
555D4×C17—82no—
556D4×C17—82no—
557D4×C17—82no—
558D4×C17—82no—
559D4×C17—82no—
560C2×C4×C17—21no—
561C2×C4×C17—21no—
562C2×C4×C17—21no—
563C2×C4×C17—21no—
564C2×C4×C17—21no—
565C2×C4×C17—21no—
566C2×C4×C17—21no—
567C2×C4×C17—21no—
568C2×C4×C17—21no—
569C2×C4×C17—21no—
570C2×C4×C17—21no—
571C2×C4×C17—21no—
572C2×C4×C17—21no—
573C2×C4×C17—21no—
574C2×C4×C17—21no—
575C2×C4×C17—21no—
576C2×C4×C17—21no—
577C2×C4×C17—21no—
578C2×C4×C17—21no—
579C2×C4×C17—21no—
580C2×C4×C17—21no—
581C2×C4×C17—21no—
582C2×C4×C17—21no—
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—44no—
637C2×C4×C17—44no—
638C2×C4×C17—44no—
639C2×C4×C17—44no—
640C2×C4×C17—82no—
641C2×C4×C17—82no—
642C2×C4×C17C2×#4112yes—
643C2×C4×C17C2×#4112yes—
644C2×C4×C17C2×#4112yes—
645C2×C4×C17H(5,𝔽2)12yes—
646C2×C4×C17H(5,𝔽2)12yes—
647#2854C2×C1711yescharacteristic, complemented
648#2852C2×C1711yescharacteristic, complemented
649#2802C2×C1711yescharacteristic, complemented
650#2797C2×C1711yescharacteristic, complemented
651#2780C2×C1711yescharacteristic, complemented
652#2780C2×C1711yescharacteristic, complemented
653#2770C2×C1711yescharacteristic, complemented
654#2764C2×C1711yescharacteristic, complemented
655#2749C2×C1711yescharacteristic, complemented
656#2748C2×C1711yescharacteristic, complemented
657#2740C2×C1711yescharacteristic, complemented
658#2739C2×C1711yescharacteristic, complemented
659#2727C2×C1711yescharacteristic, complemented
660#2715C2×C1711yescharacteristic, complemented
661#2711C2×C1711yescharacteristic, complemented
662#2704C2×C1711yescharacteristic, complemented
663#2691C2×C1711yescharacteristic, complemented
664#2676C2×C1711yescharacteristic
665#2664C2×C1711yescharacteristic, complemented
666#2651C2×C1711yescharacteristic, complemented
667#2558C2×C1711yescharacteristic, complemented
668#2554C2×C1711yescharacteristic, complemented
669#2475C2×C1711yescharacteristic, complemented
670#2470C2×C1711yescharacteristic, complemented
671#2469C2×C1711yescharacteristic, complemented
672#2468C2×C1711yescharacteristic, complemented
673#2457C2×C1711yescharacteristic, complemented
674#2448C2×C1711yescharacteristic, complemented
675#2336C2×C1711yescharacteristic, complemented
676#2324C2×C1711yescharacteristic, complemented
677C4×C22⋊Q8C2×C1711yescharacteristic, complemented
678C22×C17—22no—
679C22×C17—22no—
680C22×C17—22no—
681C22×C17—41no—
682C22×C17—41no—
683C22×C17—41no—
684C22×C17—41no—
685C22×C17—41no—
686C22×C17—41no—
687C22×C17—41no—
688C22×C17—41no—
689C22×C17—41no—
690C22×C17—41no—
691C22×C17—41no—
692C22×C17—41no—
693C22×C17—41no—
694C22×C17—41no—
695C22×C17—41no—
696C22×C17—41no—
697C22×C17—41no—
698C22×C17—41no—
699C22×C17—41no—
700C22×C17—41no—
701C22×C17—41no—
702C22×C17—41no—
703C22×C17—41no—
704C22×C17—41no—
705C22×C17—41no—
706C22×C17C22×#4111yescharacteristic
707C22×C17C2×H(5,𝔽2)11yescharacteristic
708C22×C17C2×H(5,𝔽2)11yescharacteristic
709C22×C17C2×2−1+411yescharacteristic
710C22×C17#58511yescharacteristic
711C22×C17#58511yescharacteristic
712C22×C17#58511yescharacteristic
713C4×C17—22no—
714C4×C17—22no—
715C4×C17—22no—
716C4×C17—22no—
717C4×C17—22no—
718C4×C17—41no—
719C4×C17—41no—
720C4×C17—41no—
721C4×C17—41no—
722C4×C17—41no—
723C4×C17—41no—
724C4×C17—41no—
725C4×C17—41no—
726C4×C17—41no—
727C4×C17—41no—
728C4×C17—41no—
729C4×C17—41no—
730C4×C17—41no—
731C4×C17—41no—
732C4×C17—41no—
733C4×C17—41no—
734C4×C17—41no—
735C4×C17—41no—
736C4×C17—41no—
737C4×C17—41no—
738C4×C17—41no—
739C4×C17—41no—
740C2×#126C22×C1711yescharacteristic
741C2×#126C22×C1711yescharacteristic
742C2×#126C22×C1711yescharacteristic
743C2×#125C22×C1711yescharacteristic
744C2×#125C22×C1711yescharacteristic
745C2×#124C22×C1711yescharacteristic
746C2×#123C22×C1711yescharacteristic
747C2×#123C22×C1711yescharacteristic
748C2×C22⋊Q8C22×C1711yescharacteristic
749C2×#121C22×C1711yescharacteristic
750C2×#121C22×C1711yescharacteristic
751C2×C4×Q8C22×C1711yescharacteristic
752C2×C4×D4C22×C1711yescharacteristic
753C2×#117C22×C1711yescharacteristic
754C22×C42C22×C1711yescharacteristic
755#400C22×C1711yescharacteristic
756#400C22×C1711yescharacteristic
757#400C22×C1711yescharacteristic
758#400C22×C1711yescharacteristic
759#400C22×C1711yescharacteristic
760#400C22×C1711yescharacteristic
761#399C22×C1711yescharacteristic
762#399C22×C1711yescharacteristic
763#399C22×C1711yescharacteristic
764#399C22×C1711yescharacteristic
765#398C22×C1711yescharacteristic
766#398C22×C1711yescharacteristic
767#398C22×C1711yescharacteristic
768#398C22×C1711yescharacteristic
769#398C22×C1711yescharacteristic
770#398C22×C1711yescharacteristic
771#398C22×C1711yescharacteristic
772#398C22×C1711yescharacteristic
773#398C22×C1711yescharacteristic
774#397C22×C1711yescharacteristic
775#397C22×C1711yescharacteristic
776#397C22×C1711yescharacteristic
777#397C22×C1711yescharacteristic
778#397C22×C1711yescharacteristic
779#397C22×C1711yescharacteristic
780#397C22×C1711yescharacteristic
781#396C22×C1711yescharacteristic
782#396C22×C1711yescharacteristic
783#396C22×C1711yescharacteristic
784#396C22×C1711yescharacteristic
785#396C22×C1711yescharacteristic
786#396C22×C1711yescharacteristic
787#396C22×C1711yescharacteristic
788#396C22×C1711yescharacteristic
789#396C22×C1711yescharacteristic
790#396C22×C1711yescharacteristic
791#395C22×C1711yescharacteristic
792#394C22×C1711yescharacteristic
793#394C22×C1711yescharacteristic
794#394C22×C1711yescharacteristic
795#394C22×C1711yescharacteristic
796#394C22×C1711yescharacteristic
797#394C22×C1711yescharacteristic
798#394C22×C1711yescharacteristic
799#394C22×C1711yescharacteristic
800#393C22×C1711yescharacteristic
801#392C22×C1711yescharacteristic
802#392C22×C1711yescharacteristic
803#391C22×C1711yescharacteristic
804#391C22×C1711yescharacteristic
805#390C22×C1711yescharacteristic
806#390C22×C1711yescharacteristic
807#390C22×C1711yescharacteristic
808#390C22×C1711yescharacteristic
809#390C22×C1711yescharacteristic
810#390C22×C1711yescharacteristic
811#390C22×C1711yescharacteristic
812#390C22×C1711yescharacteristic
813#389C22×C1711yescharacteristic
814#389C22×C1711yescharacteristic
815#389C22×C1711yescharacteristic
816#389C22×C1711yescharacteristic
817#389C22×C1711yescharacteristic
818#389C22×C1711yescharacteristic
819#389C22×C1711yescharacteristic
820#389C22×C1711yescharacteristic
821#389C22×C1711yescharacteristic
822#389C22×C1711yescharacteristic
823#388C22×C1711yescharacteristic
824#388C22×C1711yescharacteristic
825#388C22×C1711yescharacteristic
826#388C22×C1711yescharacteristic
827#388C22×C1711yescharacteristic
828#388C22×C1711yescharacteristic
829#388C22×C1711yescharacteristic
830#388C22×C1711yescharacteristic
831#388C22×C1711yescharacteristic
832#388C22×C1711yescharacteristic
833#388C22×C1711yescharacteristic
834#388C22×C1711yescharacteristic
835#388C22×C1711yescharacteristic
836#388C22×C1711yescharacteristic
837#388C22×C1711yescharacteristic
838#388C22×C1711yescharacteristic
839#388C22×C1711yescharacteristic
840#388C22×C1711yescharacteristic
841#388C22×C1711yescharacteristic
842#387C22×C1711yescharacteristic
843#387C22×C1711yescharacteristic
844#387C22×C1711yescharacteristic
845#387C22×C1711yescharacteristic
846#387C22×C1711yescharacteristic
847#387C22×C1711yescharacteristic
848#387C22×C1711yescharacteristic
849#387C22×C1711yescharacteristic
850#387C22×C1711yescharacteristic
851#387C22×C1711yescharacteristic
852#387C22×C1711yescharacteristic
853#387C22×C1711yescharacteristic
854#387C22×C1711yescharacteristic
855#387C22×C1711yescharacteristic
856#387C22×C1711yescharacteristic
857#386C22×C1711yescharacteristic
858#386C22×C1711yescharacteristic
859#386C22×C1711yescharacteristic
860#386C22×C1711yescharacteristic
861#386C22×C1711yescharacteristic
862#386C22×C1711yescharacteristic
863#386C22×C1711yescharacteristic
864#386C22×C1711yescharacteristic
865#386C22×C1711yescharacteristic
866#386C22×C1711yescharacteristic
867#385C22×C1711yescharacteristic
868#385C22×C1711yescharacteristic
869#385C22×C1711yescharacteristic
870#385C22×C1711yescharacteristic
871#385C22×C1711yescharacteristic
872#385C22×C1711yescharacteristic
873#385C22×C1711yescharacteristic
874#385C22×C1711yescharacteristic
875#385C22×C1711yescharacteristic
876#385C22×C1711yescharacteristic
877#385C22×C1711yescharacteristic
878#385C22×C1711yescharacteristic
879#383C22×C1711yescharacteristic
880#383C22×C1711yescharacteristic
881#381C22×C1711yescharacteristic
882#381C22×C1711yescharacteristic
883#380C22×C1711yescharacteristic
884#380C22×C1711yescharacteristic
885#380C22×C1711yescharacteristic
886#380C22×C1711yescharacteristic
887#380C22×C1711yescharacteristic
888C4×C4⋊C4C22×C1711yescharacteristic
889C4×C4⋊C4C22×C1711yescharacteristic
890C4×C4⋊C4C22×C1711yescharacteristic
891C4×C4⋊C4C22×C1711yescharacteristic
892C4×C4⋊C4C22×C1711yescharacteristic
893C4×C22⋊C4C22×C1711yescharacteristic
894C4×C22⋊C4C22×C1711yescharacteristic
895C2×C17—42no—
896C2×C17—81no—
897C2×C17—81no—
898C2×C17—81no—
899C2×C17#346011yescharacteristic
900C2×C17#351311yescharacteristic
901C2×C17#351611yescharacteristic
902C2×C17#353611yescharacteristic
903C2×C17#353911yescharacteristic
904C2×C17#356211yescharacteristic
905C2×C17#356411yescharacteristic
906C22×Q8C23×C1711yescharacteristic
907C22×D4C23×C1711yescharacteristic
908C22×D4C23×C1711yescharacteristic
909C22×D4C23×C1711yescharacteristic
910C22×D4C23×C1711yescharacteristic
911C22×D4C23×C1711yescharacteristic
912C22×D4C23×C1711yescharacteristic
913C23×C4C23×C1711yescharacteristic
914C23×C4C23×C1711yescharacteristic
915C23×C4C23×C1711yescharacteristic
916C23×C4C23×C1711yescharacteristic
917C23×C4C23×C1711yescharacteristic
918C23×C4C23×C1711yescharacteristic
919#126—42no—
920#126—42no—
921#126—42no—
922#125—24no—
923#125—42no—
924#124—42no—
925#123—42no—
926#123—42no—
927C22⋊Q8—24no—
928#121—24no—
929#121—42no—
930C4×Q8—42no—
931C4×D4—42no—
932#117—42no—
933C2×C4⋊C4C23×C1711yescharacteristic
934C2×C4⋊C4C23×C1711yescharacteristic
935C2×C4⋊C4C23×C1711yescharacteristic
936C2×C4⋊C4C23×C1711yescharacteristic
937C2×C4⋊C4C23×C1711yescharacteristic
938C2×C4⋊C4C23×C1711yescharacteristic
939C2×C4⋊C4C23×C1711yescharacteristic
940C2×C4⋊C4C23×C1711yescharacteristic
941C2×C4⋊C4C23×C1711yescharacteristic
942C2×C4⋊C4C23×C1711yescharacteristic
943C2×C4⋊C4C23×C1711yescharacteristic
944C2×C4⋊C4C23×C1711yescharacteristic
945C2×C4⋊C4C23×C1711yescharacteristic
946C2×C4⋊C4C23×C1711yescharacteristic
947C2×C4⋊C4C23×C1711yescharacteristic
948C2×C4⋊C4C23×C1711yescharacteristic
949C2×C4⋊C4C23×C1711yescharacteristic
950C2×C4⋊C4C23×C1711yescharacteristic
951C2×C4⋊C4C23×C1711yescharacteristic
952C2×C4⋊C4C23×C1711yescharacteristic
953C2×C4⋊C4C23×C1711yescharacteristic
954C2×C4⋊C4C23×C1711yescharacteristic
955C2×C4⋊C4C23×C1711yescharacteristic
956C2×C4⋊C4C23×C1711yescharacteristic
957C2×C4⋊C4C23×C1711yescharacteristic
958C2×C4⋊C4C23×C1711yescharacteristic
959C2×C4⋊C4C23×C1711yescharacteristic
960C2×C4⋊C4C23×C1711yescharacteristic
961C2×C4⋊C4C23×C1711yescharacteristic
962C2×C4⋊C4C23×C1711yescharacteristic
963C2×C4⋊C4C23×C1711yescharacteristic
964C2×C4⋊C4C23×C1711yescharacteristic
965C2×C4⋊C4C23×C1711yescharacteristic
966C2×C4⋊C4C23×C1711yescharacteristic
967C2×C4⋊C4C23×C1711yescharacteristic
968C2×C4⋊C4C23×C1711yescharacteristic
969C2×C4⋊C4C23×C1711yescharacteristic
970C2×C4⋊C4C23×C1711yescharacteristic
971C2×C4⋊C4C23×C1711yescharacteristic
972C2×C4⋊C4C23×C1711yescharacteristic
973C2×C4⋊C4C23×C1711yescharacteristic
974C2×C22⋊C4C23×C1711yescharacteristic
975C2×C22⋊C4C23×C1711yescharacteristic
976C2×C22⋊C4C23×C1711yescharacteristic
977C2×C22⋊C4C23×C1711yescharacteristic
978C2×C22⋊C4C23×C1711yescharacteristic
979C2×C22⋊C4C23×C1711yescharacteristic
980C2×C22⋊C4C23×C1711yescharacteristic
981C2×C22⋊C4C23×C1711yescharacteristic
982C2×C22⋊C4C23×C1711yescharacteristic
983C2×C22⋊C4C23×C1711yescharacteristic
984C2×C22⋊C4C23×C1711yescharacteristic
985C2×C22⋊C4C23×C1711yescharacteristic
986C2×C22⋊C4C23×C1711yescharacteristic
987C2×C22⋊C4C23×C1711yescharacteristic
988C2×C22⋊C4C23×C1711yescharacteristic
989C2×C22⋊C4C23×C1711yescharacteristic
990C2×C22⋊C4C23×C1711yescharacteristic
991C2×C22⋊C4C23×C1711yescharacteristic
992C2×C22⋊C4C23×C1711yescharacteristic
993C2×C22⋊C4C23×C1711yescharacteristic
994C2×C22⋊C4C23×C1711yescharacteristic
995C2×C22⋊C4C23×C1711yescharacteristic
996C2×C22⋊C4C23×C1711yescharacteristic
997C2×C22⋊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×C42—42no—
1017C2×C42C23×C1711yescharacteristic
1018C2×C42C23×C1711yescharacteristic
1019C2×C42C23×C1711yescharacteristic
1020C2×C42C23×C1711yescharacteristic
1021C2×C42C23×C1711yescharacteristic
1022C2×C42C23×C1711yescharacteristic
1023C2×C42C23×C1711yescharacteristic
1024C2×C42C23×C1711yescharacteristic
1025C2×C42C23×C1711yescharacteristic
1026C2×C42C23×C1711yescharacteristic
1027C2×C42C23×C1711yescharacteristic
1028C2×C42C23×C1711yescharacteristic
1029C2×C42C23×C1711yescharacteristic
1030#95C23×C1711yescharacteristic
1031#95C23×C1711yescharacteristic
1032#95C23×C1711yescharacteristic
1033#95C23×C1711yescharacteristic
1034#95C23×C1711yescharacteristic
1035#95C23×C1711yescharacteristic
1036#95C23×C1711yescharacteristic
1037#95C23×C1711yescharacteristic
1038#95C23×C1711yescharacteristic
1039#95C23×C1711yescharacteristic
1040#95C23×C1711yescharacteristic
1041#95C23×C1711yescharacteristic
1042#95C23×C1711yescharacteristic
1043#95C23×C1711yescharacteristic
1044#95C23×C1711yescharacteristic
1045#95C23×C1711yescharacteristic
1046#95C23×C1711yescharacteristic
1047#95C23×C1711yescharacteristic
1048#95C23×C1711yescharacteristic
1049#95C23×C1711yescharacteristic
1050#95C23×C1711yescharacteristic
1051#95C23×C1711yescharacteristic
1052#95C23×C1711yescharacteristic
1053#95C23×C1711yescharacteristic
1054#95C23×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
1076C17#3684911yescharacteristic, direct product factor, Sylow
1077C24C24×C1711yescharacteristic
1078C24C24×C1711yescharacteristic
1079C24C24×C1711yescharacteristic
1080C24C24×C1711yescharacteristic
1081C2×Q8—22no—
1082C2×Q8—22no—
1083C2×Q8—41no—
1084C2×D4—22no—
1085C2×D4—22no—
1086C2×D4—22no—
1087C2×D4—22no—
1088C2×D4—22no—
1089C2×D4—22no—
1090C2×D4—41no—
1091C2×D4—41no—
1092C2×D4—41no—
1093C2×D4—41no—
1094C2×D4—41no—
1095C2×D4—41no—
1096C2×D4—41no—
1097C2×D4—41no—
1098C2×D4—41no—
1099C2×D4—41no—
1100C2×D4—41no—
1101C2×D4—41no—
1102C22×C4—22no—
1103C22×C4—22no—
1104C22×C4—22no—
1105C22×C4—22no—
1106C22×C4—22no—
1107C22×C4—41no—
1108C22×C4—41no—
1109C22×C4—41no—
1110C22×C4—41no—
1111C22×C4—41no—
1112C22×C4—41no—
1113C22×C4—41no—
1114C22×C4—41no—
1115C22×C4—41no—
1116C22×C4—41no—
1117C22×C4—41no—
1118C22×C4—41no—
1119C22×C4—41no—
1120C22×C4C24×C1711yescharacteristic
1121C22×C4C24×C1711yescharacteristic
1122C22×C4C24×C1711yescharacteristic
1123C22×C4C24×C1711yescharacteristic
1124C22×C4C24×C1711yescharacteristic
1125C22×C4C24×C1711yescharacteristic
1126C22×C4C24×C1711yescharacteristic
1127C22×C4C24×C1711yescharacteristic
1128C22×C4C24×C1711yescharacteristic
1129C22×C4C24×C1711yescharacteristic
1130C22×C4C24×C1711yescharacteristic
1131C22×C4C24×C1711yescharacteristic
1132C22×C4C24×C1711yescharacteristic
1133C22×C4C24×C1711yescharacteristic
1134C22×C4C24×C1711yescharacteristic
1135C22×C4C24×C1711yescharacteristic
1136C22×C4C24×C1711yescharacteristic
1137C22×C4C24×C1711yescharacteristic
1138C22×C4C24×C1711yescharacteristic
1139C22×C4C24×C1711yescharacteristic
1140C22×C4C24×C1711yescharacteristic
1141C22×C4C24×C1711yescharacteristic
1142C22×C4C24×C1711yescharacteristic
1143C22×C4C24×C1711yescharacteristic
1144C22×C4C24×C1711yescharacteristic
1145C22×C4C24×C1711yescharacteristic
1146C22×C4C24×C1711yescharacteristic
1147C4⋊C4—22no—
1148C4⋊C4—22no—
1149C4⋊C4—22no—
1150C4⋊C4—22no—
1151C4⋊C4—22no—
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—22no—
1155C4⋊C4—22no—
1156C4⋊C4—22no—
1157C4⋊C4—22no—
1158C4⋊C4—22no—
1159C4⋊C4—41no—
1160C4⋊C4—41no—
1161C4⋊C4—41no—
1162C4⋊C4—41no—
1163C4⋊C4—41no—
1164C4⋊C4—41no—
1165C4⋊C4—41no—
1166C4⋊C4—41no—
1167C4⋊C4—41no—
1168C4⋊C4—41no—
1169C4⋊C4—41no—
1170C4⋊C4—41no—
1171C4⋊C4—41no—
1172C4⋊C4—41no—
1173C4⋊C4—41no—
1174C4⋊C4—41no—
1175C4⋊C4—41no—
1176C4⋊C4—41no—
1177C4⋊C4—41no—
1178C4⋊C4—41no—
1179C4⋊C4—41no—
1180C4⋊C4—41no—
1181C4⋊C4—41no—
1182C4⋊C4—41no—
1183C4⋊C4—41no—
1184C4⋊C4—41no—
1185C4⋊C4—41no—
1186C4⋊C4—41no—
1187C4⋊C4#41×C1714yes—
1188C22⋊C4—22no—
1189C22⋊C4—22no—
1190C22⋊C4—22no—
1191C22⋊C4—22no—
1192C22⋊C4—22no—
1193C22⋊C4—22no—
1194C22⋊C4—22no—
1195C22⋊C4—22no—
1196C22⋊C4—22no—
1197C22⋊C4—22no—
1198C22⋊C4—22no—
1199C22⋊C4—41no—
1200C22⋊C4—41no—
1201C22⋊C4—41no—
1202C22⋊C4—41no—
1203C22⋊C4—41no—
1204C22⋊C4—41no—
1205C22⋊C4—41no—
1206C22⋊C4—41no—
1207C22⋊C4—41no—
1208C22⋊C4—41no—
1209C22⋊C4—41no—
1210C22⋊C4—41no—
1211C22⋊C4—41no—
1212C22⋊C4—41no—
1213C22⋊C4—41no—
1214C22⋊C4—41no—
1215C22⋊C4—41no—
1216C22⋊C4—41no—
1217C22⋊C4—41no—
1218C22⋊C4—41no—
1219C22⋊C4—41no—
1220C22⋊C4—41no—
1221C22⋊C4—41no—
1222C22⋊C4—41no—
1223C22⋊C4—41no—
1224C22⋊C4—41no—
1225C22⋊C4—41no—
1226C22⋊C4—41no—
1227C22⋊C4—41no—
1228C22⋊C4—41no—
1229C22⋊C4—41no—
1230C42—22no—
1231C42—22no—
1232C42—22no—
1233C42—22no—
1234C42—22no—
1235C42—41no—
1236C42—41no—
1237C42—41no—
1238C42—41no—
1239C42—41no—
1240C42—41no—
1241C42—41no—
1242C42—41no—
1243C23—21no—
1244C23—21no—
1245C23—21no—
1246C23—21no—
1247C23—21no—
1248C23—21no—
1249C23—21no—
1250C23—21no—
1251C23—21no—
1252C23—21no—
1253C23—21no—
1254C23—21no—
1255C23—21no—
1256C23—21no—
1257C23—21no—
1258C23—21no—
1259C23—21no—
1260C23—21no—
1261C23—21no—
1262C23—21no—
1263C23—21no—
1264C23—21no—
1265C23—21no—
1266C23—21no—
1267C23—21no—
1268C23—21no—
1269C23—21no—
1270C23C17×2−1+412yes—
1271C23C25×C1711yescharacteristic
1272Q8—44no—
1273D4—44no—
1274D4—82no—
1275D4—82no—
1276D4—82no—
1277D4—82no—
1278D4—82no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
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—44no—
1356C2×C4—44no—
1357C2×C4—44no—
1358C2×C4—44no—
1359C2×C4—82no—
1360C2×C4—82no—
1361C2×C4C2×#41×C1712yes—
1362C2×C4C2×#41×C1712yes—
1363C2×C4C2×#41×C1712yes—
1364C2×C4C17×H(5,𝔽2)12yes—
1365C2×C4C17×H(5,𝔽2)12yes—
1366C22—22no—
1367C22—22no—
1368C22—22no—
1369C22—41no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—41no—
1374C22—41no—
1375C22—41no—
1376C22—41no—
1377C22—41no—
1378C22—41no—
1379C22—41no—
1380C22—41no—
1381C22—41no—
1382C22—41no—
1383C22—41no—
1384C22—41no—
1385C22—41no—
1386C22—41no—
1387C22—41no—
1388C22—41no—
1389C22—41no—
1390C22—41no—
1391C22—41no—
1392C22—41no—
1393C22—41no—
1394C22C22×#41×C1711yescharacteristic
1395C22C2×C17×H(5,𝔽2)11yescharacteristic
1396C22C2×C17×H(5,𝔽2)11yescharacteristic
1397C22C2×C17×2−1+411yescharacteristic
1398C22C17×#58511yescharacteristic
1399C22C17×#58511yescharacteristic
1400C22C17×#58511yescharacteristic
1401C4—22no—
1402C4—22no—
1403C4—22no—
1404C4—22no—
1405C4—22no—
1406C4—41no—
1407C4—41no—
1408C4—41no—
1409C4—41no—
1410C4—41no—
1411C4—41no—
1412C4—41no—
1413C4—41no—
1414C4—41no—
1415C4—41no—
1416C4—41no—
1417C4—41no—
1418C4—41no—
1419C4—41no—
1420C4—41no—
1421C4—41no—
1422C4—41no—
1423C4—41no—
1424C4—41no—
1425C4—41no—
1426C4—41no—
1427C4—41no—
1428C2—42no—
1429C2—81no—
1430C2—81no—
1431C2—81no—
1432C2C17×#346011yescharacteristic
1433C2C17×#351311yescharacteristic
1434C2C17×#351611yescharacteristic
1435C2C17×#353611yescharacteristic
1436C2C17×#353911yescharacteristic
1437C2C17×#356211yescharacteristic
1438C2C17×#356411yescharacteristic
subgroupG/H
center, socleC23×C17C25
commutator, Frattini, cosocleC23C25×C17
prime radicalC17×#2676C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#2854C2semidirect
2. C17×#2852C2semidirect
3. C17×#2802C2semidirect
4. C17×#2797C2semidirect
5. C17×#2780C2semidirect
6. C17×#2780C2semidirect
7. C17×#2770C2semidirect
8. C17×#2764C2semidirect
9. C17×#2749C2semidirect
10. C17×#2748C2semidirect
11. C17×#2740C2semidirect
12. C17×#2739C2semidirect
13. C17×#2727C2semidirect
14. C17×#2715C2semidirect
15. C17×#2711C2semidirect
16. C17×#2704C2semidirect
17. C17×#2691C2semidirect
19. C17×#2664C2semidirect
20. C17×#2651C2semidirect
21. C17×#2558C2semidirect
22. C17×#2554C2semidirect
23. C17×#2475C2semidirect
24. C17×#2470C2semidirect
25. C17×#2469C2semidirect
26. C17×#2468C2semidirect
27. C17×#2457C2semidirect
28. C17×#2448C2semidirect
29. C17×#2336C2semidirect
30. C17×#2324C2semidirect
31. C4×C17×C22⋊Q8C2semidirect
523. #36849C17direct (N × H)
647. #2854C2×C17semidirect
648. #2852C2×C17semidirect
649. #2802C2×C17semidirect
650. #2797C2×C17semidirect
651. #2780C2×C17semidirect
652. #2780C2×C17semidirect
653. #2770C2×C17semidirect
654. #2764C2×C17semidirect
655. #2749C2×C17semidirect
656. #2748C2×C17semidirect
657. #2740C2×C17semidirect
658. #2739C2×C17semidirect
659. #2727C2×C17semidirect
660. #2715C2×C17semidirect
661. #2711C2×C17semidirect
662. #2704C2×C17semidirect
663. #2691C2×C17semidirect
665. #2664C2×C17semidirect
666. #2651C2×C17semidirect
667. #2558C2×C17semidirect
668. #2554C2×C17semidirect
669. #2475C2×C17semidirect
670. #2470C2×C17semidirect
671. #2469C2×C17semidirect
672. #2468C2×C17semidirect
673. #2457C2×C17semidirect
674. #2448C2×C17semidirect
675. #2336C2×C17semidirect
676. #2324C2×C17semidirect
677. C4×C22⋊Q8C2×C17semidirect
1076. C17#36849direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#28542
C17×#28522
C17×#28022
C17×#27972
C17×#27802
C17×#27702
C17×#27642
C17×#27492
C17×#27482
C17×#27402
C17×#27392
C17×#27272
C17×#27152
C17×#27112
C17×#27042
C17×#26912
C17×#26762
C17×#26642
C17×#26512
C17×#25582
C17×#25542
C17×#24752
C17×#24702
C17×#24692
C17×#24682
C17×#24572
C17×#24482
C17×#23362
C17×#23242
C4×C17×C22⋊Q82
#3684917