Finite Group Databasebeta

← C17×#36802 #16894546

Subgroups — C17×#36802 #16894546

Order 4352.

1534 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2853C211yesmaximal, characteristic, complemented
2C17×#2851C211yesmaximal, characteristic, complemented
3C17×#2808C211yesmaximal, characteristic, complemented
4C17×#2807C211yesmaximal, characteristic, complemented
5C17×#2804C211yesmaximal, characteristic, complemented
6C17×#2798C211yesmaximal, characteristic, complemented
7C17×#2775C211yesmaximal, characteristic, complemented
8C17×#2775C211yesmaximal, characteristic, complemented
9C17×#2770C211yesmaximal, characteristic, complemented
10C17×#2766C211yesmaximal, characteristic, complemented
11C17×#2757C211yesmaximal, characteristic, complemented
12C17×#2753C211yesmaximal, characteristic
13C17×#2745C211yesmaximal, characteristic, complemented
14C17×#2737C211yesmaximal, characteristic, complemented
15C17×#2719C211yesmaximal, characteristic, complemented
16C17×#2706C211yesmaximal, characteristic
17C17×#2694C211yesmaximal, characteristic, complemented
18C17×#2694C211yesmaximal, characteristic, complemented
19C17×#2653C211yesmaximal, characteristic, complemented
20C17×#2652C211yesmaximal, characteristic, complemented
21C17×#2612C211yesmaximal, characteristic, complemented
22C17×#2604C211yesmaximal, characteristic, complemented
23C17×#2603C211yesmaximal, characteristic
24C17×#2589C211yesmaximal, characteristic, complemented
25C17×#2580C211yesmaximal, characteristic, complemented
26C17×#2578C211yesmaximal, characteristic, complemented
27C17×#2475C211yesmaximal, characteristic, complemented
28C17×#2470C211yesmaximal, characteristic, complemented
29C17×#2334C211yesmaximal, characteristic, complemented
30C17×#2320C211yesmaximal, characteristic, complemented
31C17×#2290C211yesmaximal, characteristic, complemented
32C2×C17×#126C2211yescharacteristic
33C2×C17×#125C2211yescharacteristic
34C2×C17×#125C2211yescharacteristic
35C2×C17×#123C2211yescharacteristic
36C2×C17×#123C2211yescharacteristic
37C2×C4×Q8×C17C2211yescharacteristic
38C2×C4×D4×C17C2211yescharacteristic
39C2×C17×#117C2211yescharacteristic
40C22×C42×C17C2211yescharacteristic
41C17×#401C2211yescharacteristic
42C17×#400C2211yescharacteristic
43C17×#400C2211yescharacteristic
44C17×#400C2211yescharacteristic
45C17×#400C2211yescharacteristic
46C17×#400C2211yescharacteristic
47C17×#400C2211yescharacteristic
48C17×#400C2211yescharacteristic
49C17×#400C2211yescharacteristic
50C17×#400C2211yescharacteristic
51C17×#399C2211yescharacteristic
52C17×#399C2211yescharacteristic
53C17×#399C2211yescharacteristic
54C17×#399C2211yescharacteristic
55C17×#398C2211yescharacteristic
56C17×#398C2211yescharacteristic
57C17×#398C2211yescharacteristic
58C17×#398C2211yescharacteristic
59C17×#398C2211yescharacteristic
60C17×#398C2211yescharacteristic
61C17×#398C2211yescharacteristic
62C17×#397C2211yescharacteristic
63C17×#397C2211yescharacteristic
64C17×#397C2211yescharacteristic
65C17×#397C2211yescharacteristic
66C17×#397C2211yescharacteristic
67C17×#397C2211yescharacteristic
68C17×#397C2211yescharacteristic
69C17×#397C2211yescharacteristic
70C17×#397C2211yescharacteristic
71C17×#397C2211yescharacteristic
72C17×#396C2211yescharacteristic
73C17×#396C2211yescharacteristic
74C17×#396C2211yescharacteristic
75C17×#395C2211yescharacteristic
76C17×#395C2211yescharacteristic
77C17×#394C2211yescharacteristic
78C17×#394C2211yescharacteristic
79C17×#394C2211yescharacteristic
80C17×#394C2211yescharacteristic
81C17×#394C2211yescharacteristic
82C17×#393C2211yescharacteristic
83C17×#393C2211yescharacteristic
84C17×#393C2211yescharacteristic
85C17×#393C2211yescharacteristic
86C17×#393C2211yescharacteristic
87C17×#393C2211yescharacteristic
88C17×#392C2211yescharacteristic
89C17×#391C2211yescharacteristic
90C17×#391C2211yescharacteristic
91C17×#391C2211yescharacteristic
92C17×#391C2211yescharacteristic
93C17×#391C2211yescharacteristic
94C17×#390C2211yescharacteristic
95C17×#390C2211yescharacteristic
96C17×#390C2211yescharacteristic
97C17×#390C2211yescharacteristic
98C17×#389C2211yescharacteristic
99C17×#389C2211yescharacteristic
100C17×#389C2211yescharacteristic
101C17×#389C2211yescharacteristic
102C17×#389C2211yescharacteristic
103C17×#389C2211yescharacteristic
104C17×#389C2211yescharacteristic
105C17×#389C2211yescharacteristic
106C17×#389C2211yescharacteristic
107C17×#389C2211yescharacteristic
108C17×#389C2211yescharacteristic
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×#388C2211yescharacteristic
124C17×#388C2211yescharacteristic
125C17×#388C2211yescharacteristic
126C17×#388C2211yescharacteristic
127C17×#388C2211yescharacteristic
128C17×#387C2211yescharacteristic
129C17×#387C2211yescharacteristic
130C17×#387C2211yescharacteristic
131C17×#387C2211yescharacteristic
132C17×#387C2211yescharacteristic
133C17×#387C2211yescharacteristic
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×#385C2211yescharacteristic
156C17×#385C2211yescharacteristic
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×#383C2211yescharacteristic
172C17×#382C2211yescharacteristic
173C17×#382C2211yescharacteristic
174C17×#382C2211yescharacteristic
175C17×#382C2211yescharacteristic
176C17×#381C2211yescharacteristic
177C17×#380C2211yescharacteristic
178C17×#380C2211yescharacteristic
179C17×#380C2211yescharacteristic
180C4×C4⋊C4×C17C2211yescharacteristic
181C4×C4⋊C4×C17C2211yescharacteristic
182C4×C22⋊C4×C17C2211yescharacteristic
183C4×C22⋊C4×C17C2211yescharacteristic
184C4×C22⋊C4×C17C2211yescharacteristic
185C17×#376C2211yescharacteristic
186C17×#376C2211yescharacteristic
187C22×Q8×C17C2311yescharacteristic
188C22×Q8×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C17×#126—24no—
198C17×#125—42no—
199C17×#125—42no—
200C17×#123—42no—
201C17×#123—42no—
202C4×Q8×C17—24no—
203C4×D4×C17—24no—
204C17×#117—42no—
205C2×C4⋊C4×C17C2311yescharacteristic
206C2×C4⋊C4×C17C2311yescharacteristic
207C2×C4⋊C4×C17C2311yescharacteristic
208C2×C4⋊C4×C17C2311yescharacteristic
209C2×C4⋊C4×C17C2311yescharacteristic
210C2×C4⋊C4×C17C2311yescharacteristic
211C2×C4⋊C4×C17C2311yescharacteristic
212C2×C4⋊C4×C17C2311yescharacteristic
213C2×C4⋊C4×C17C2311yescharacteristic
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×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊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×C42×C17—42no—
279C2×C42×C17C2311yescharacteristic
280C2×C42×C17C2311yescharacteristic
281C2×C42×C17C2311yescharacteristic
282C2×C42×C17C2311yescharacteristic
283C2×C42×C17C2311yescharacteristic
284C2×C42×C17C2311yescharacteristic
285C2×C42×C17C2311yescharacteristic
286C2×C42×C17C2311yescharacteristic
287C2×C42×C17C2311yescharacteristic
288C2×C42×C17C2311yescharacteristic
289C2×C42×C17C2311yescharacteristic
290C2×C42×C17C2311yescharacteristic
291C2×C42×C17C2311yescharacteristic
292C2×C42×C17C2311yescharacteristic
293C17×#95C2311yescharacteristic
294C17×#95C2311yescharacteristic
295C17×#95C2311yescharacteristic
296C17×#95C2311yescharacteristic
297C17×#95C2311yescharacteristic
298C17×#95C2311yescharacteristic
299C17×#95C2311yescharacteristic
300C17×#95C2311yescharacteristic
301C17×#95C2311yescharacteristic
302C17×#95C2311yescharacteristic
303C17×#95C2311yescharacteristic
304C17×#95C2311yescharacteristic
305C17×#95C2311yescharacteristic
306C17×#95C2311yescharacteristic
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
351C24×C17C2411yescharacteristic
352C24×C17C2411yescharacteristic
353C24×C17C2411yescharacteristic
354C2×Q8×C17—22no—
355C2×Q8×C17—41no—
356C2×Q8×C17—41no—
357C2×Q8×C17—41no—
358C2×Q8×C17—41no—
359C2×Q8×C17—41no—
360C2×D4×C17—22no—
361C2×D4×C17—22no—
362C2×D4×C17—22no—
363C2×D4×C17—41no—
364C2×D4×C17—41no—
365C2×D4×C17—41no—
366C2×D4×C17—41no—
367C2×D4×C17—41no—
368C2×D4×C17—41no—
369C22×C4×C17—22no—
370C22×C4×C17—22no—
371C22×C4×C17—22no—
372C22×C4×C17—22no—
373C22×C4×C17—41no—
374C22×C4×C17—41no—
375C22×C4×C17—41no—
376C22×C4×C17—41no—
377C22×C4×C17—41no—
378C22×C4×C17—41no—
379C22×C4×C17—41no—
380C22×C4×C17—41no—
381C22×C4×C17—41no—
382C22×C4×C17—41no—
383C22×C4×C17—41no—
384C22×C4×C17C2411yescharacteristic
385C22×C4×C17C2411yescharacteristic
386C22×C4×C17C2411yescharacteristic
387C22×C4×C17C2411yescharacteristic
388C22×C4×C17C2411yescharacteristic
389C22×C4×C17C2411yescharacteristic
390C22×C4×C17C2411yescharacteristic
391C22×C4×C17C2411yescharacteristic
392C22×C4×C17C2411yescharacteristic
393C22×C4×C17C2411yescharacteristic
394C22×C4×C17C2411yescharacteristic
395C22×C4×C17C2411yescharacteristic
396C22×C4×C17C2411yescharacteristic
397C22×C4×C17C2411yescharacteristic
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
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
412C4⋊C4×C17—22no—
413C4⋊C4×C17—22no—
414C4⋊C4×C17—22no—
415C4⋊C4×C17—22no—
416C4⋊C4×C17—22no—
417C4⋊C4×C17—22no—
418C4⋊C4×C17—22no—
419C4⋊C4×C17—22no—
420C4⋊C4×C17—22no—
421C4⋊C4×C17—22no—
422C4⋊C4×C17—22no—
423C4⋊C4×C17—41no—
424C4⋊C4×C17—41no—
425C4⋊C4×C17—41no—
426C4⋊C4×C17—41no—
427C4⋊C4×C17—41no—
428C4⋊C4×C17—41no—
429C4⋊C4×C17—41no—
430C4⋊C4×C17—41no—
431C4⋊C4×C17—41no—
432C4⋊C4×C17—41no—
433C4⋊C4×C17—41no—
434C4⋊C4×C17—41no—
435C4⋊C4×C17—41no—
436C4⋊C4×C17—41no—
437C4⋊C4×C17—41no—
438C4⋊C4×C17—41no—
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—
451C22⋊C4×C17—22no—
452C22⋊C4×C17—22no—
453C22⋊C4×C17—22no—
454C22⋊C4×C17—22no—
455C22⋊C4×C17—22no—
456C22⋊C4×C17—22no—
457C22⋊C4×C17—22no—
458C22⋊C4×C17—22no—
459C22⋊C4×C17—22no—
460C22⋊C4×C17—41no—
461C22⋊C4×C17—41no—
462C22⋊C4×C17—41no—
463C22⋊C4×C17—41no—
464C22⋊C4×C17—41no—
465C22⋊C4×C17—41no—
466C22⋊C4×C17—41no—
467C22⋊C4×C17—41no—
468C22⋊C4×C17—41no—
469C22⋊C4×C17—41no—
470C22⋊C4×C17—41no—
471C22⋊C4×C17—41no—
472C22⋊C4×C17—41no—
473C22⋊C4×C17—41no—
474C22⋊C4×C17—41no—
475C22⋊C4×C17—41no—
476C22⋊C4×C17—41no—
477C22⋊C4×C17—41no—
478C22⋊C4×C17—41no—
479C22⋊C4×C17—41no—
480C22⋊C4×C17—41no—
481C22⋊C4×C17—41no—
482C22⋊C4×C17—41no—
483C22⋊C4×C17—41no—
484C22⋊C4×C17—41no—
485C42×C17—22no—
486C42×C17—22no—
487C42×C17—22no—
488C42×C17—22no—
489C42×C17—41no—
490C42×C17—41no—
491C42×C17—41no—
492C42×C17—41no—
493C42×C17—41no—
494C42×C17—41no—
495C42×C17—41no—
496C42×C17—41no—
497C42×C17—41no—
498C42×C17#4114yes—
499#36802C1711yesmaximal, characteristic, direct product factor, Sylow
500C23×C17—21no—
501C23×C17—21no—
502C23×C17—21no—
503C23×C17—21no—
504C23×C17—21no—
505C23×C17—21no—
506C23×C17—21no—
507C23×C17—21no—
508C23×C17—21no—
509C23×C17—21no—
510C23×C17—21no—
511C23×C17—21no—
512C23×C17—21no—
513C23×C17—21no—
514C23×C17—21no—
515C23×C17—21no—
516C23×C17—21no—
517C23×C17—21no—
518C23×C17—21no—
519C23×C17—21no—
520C23×C172−1+412yes—
521C23×C17C2511yescharacteristic
522Q8×C17—44no—
523Q8×C17—82no—
524D4×C17—44no—
525D4×C17—82no—
526D4×C17—82no—
527C2×C4×C17—21no—
528C2×C4×C17—21no—
529C2×C4×C17—21no—
530C2×C4×C17—21no—
531C2×C4×C17—21no—
532C2×C4×C17—21no—
533C2×C4×C17—21no—
534C2×C4×C17—21no—
535C2×C4×C17—21no—
536C2×C4×C17—21no—
537C2×C4×C17—21no—
538C2×C4×C17—21no—
539C2×C4×C17—21no—
540C2×C4×C17—21no—
541C2×C4×C17—21no—
542C2×C4×C17—21no—
543C2×C4×C17—21no—
544C2×C4×C17—21no—
545C2×C4×C17—21no—
546C2×C4×C17—21no—
547C2×C4×C17—21no—
548C2×C4×C17—21no—
549C2×C4×C17—21no—
550C2×C4×C17—21no—
551C2×C4×C17—21no—
552C2×C4×C17—21no—
553C2×C4×C17—21no—
554C2×C4×C17—21no—
555C2×C4×C17—21no—
556C2×C4×C17—21no—
557C2×C4×C17—21no—
558C2×C4×C17—21no—
559C2×C4×C17—21no—
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—44no—
608C2×C4×C17—44no—
609C2×C4×C17—44no—
610C2×C4×C17—44no—
611C2×C4×C17—82no—
612C2×C4×C17C2×#4112yes—
613C2×C4×C17C2×#4112yes—
614C2×C4×C17C2×#4112yes—
615C2×C4×C17H(5,𝔽2)12yes—
616#2853C2×C1711yescharacteristic, complemented
617#2851C2×C1711yescharacteristic, complemented
618#2808C2×C1711yescharacteristic, complemented
619#2807C2×C1711yescharacteristic, complemented
620#2804C2×C1711yescharacteristic, complemented
621#2798C2×C1711yescharacteristic, complemented
622#2775C2×C1711yescharacteristic, complemented
623#2775C2×C1711yescharacteristic, complemented
624#2770C2×C1711yescharacteristic, complemented
625#2766C2×C1711yescharacteristic, complemented
626#2757C2×C1711yescharacteristic, complemented
627#2753C2×C1711yescharacteristic
628#2745C2×C1711yescharacteristic, complemented
629#2737C2×C1711yescharacteristic, complemented
630#2719C2×C1711yescharacteristic, complemented
631#2706C2×C1711yescharacteristic
632#2694C2×C1711yescharacteristic, complemented
633#2694C2×C1711yescharacteristic, complemented
634#2653C2×C1711yescharacteristic, complemented
635#2652C2×C1711yescharacteristic, complemented
636#2612C2×C1711yescharacteristic, complemented
637#2604C2×C1711yescharacteristic, complemented
638#2603C2×C1711yescharacteristic
639#2589C2×C1711yescharacteristic, complemented
640#2580C2×C1711yescharacteristic, complemented
641#2578C2×C1711yescharacteristic, complemented
642#2475C2×C1711yescharacteristic, complemented
643#2470C2×C1711yescharacteristic, complemented
644#2334C2×C1711yescharacteristic, complemented
645#2320C2×C1711yescharacteristic, complemented
646#2290C2×C1711yescharacteristic, complemented
647C22×C17—22no—
648C22×C17—22no—
649C22×C17—22no—
650C22×C17—41no—
651C22×C17—41no—
652C22×C17—41no—
653C22×C17—41no—
654C22×C17—41no—
655C22×C17—41no—
656C22×C17—41no—
657C22×C17—41no—
658C22×C17—41no—
659C22×C17—41no—
660C22×C17—41no—
661C22×C17—41no—
662C22×C17—41no—
663C22×C17—41no—
664C22×C17—41no—
665C22×C17—41no—
666C22×C17—41no—
667C22×C17—41no—
668C22×C17C22×#4111yescharacteristic
669C22×C17C2×H(5,𝔽2)11yescharacteristic
670C22×C17C2×2−1+411yescharacteristic
671C22×C17#58511yescharacteristic
672C22×C17#58511yescharacteristic
673C22×C17#58511yescharacteristic
674C22×C17#58511yescharacteristic
675C4×C17—22no—
676C4×C17—22no—
677C4×C17—22no—
678C4×C17—22no—
679C4×C17—41no—
680C4×C17—41no—
681C4×C17—41no—
682C4×C17—41no—
683C4×C17—41no—
684C4×C17—41no—
685C4×C17—41no—
686C4×C17—41no—
687C4×C17—41no—
688C4×C17—41no—
689C4×C17—41no—
690C4×C17—41no—
691C4×C17—41no—
692C4×C17—41no—
693C4×C17—41no—
694C4×C17—41no—
695C4×C17—41no—
696C4×C17—41no—
697C4×C17—41no—
698C4×C17—41no—
699C4×C17—41no—
700C4×C17—41no—
701C4×C17—41no—
702C4×C17—41no—
703C2×#126C22×C1711yescharacteristic
704C2×#125C22×C1711yescharacteristic
705C2×#125C22×C1711yescharacteristic
706C2×#123C22×C1711yescharacteristic
707C2×#123C22×C1711yescharacteristic
708C2×C4×Q8C22×C1711yescharacteristic
709C2×C4×D4C22×C1711yescharacteristic
710C2×#117C22×C1711yescharacteristic
711C22×C42C22×C1711yescharacteristic
712#401C22×C1711yescharacteristic
713#400C22×C1711yescharacteristic
714#400C22×C1711yescharacteristic
715#400C22×C1711yescharacteristic
716#400C22×C1711yescharacteristic
717#400C22×C1711yescharacteristic
718#400C22×C1711yescharacteristic
719#400C22×C1711yescharacteristic
720#400C22×C1711yescharacteristic
721#400C22×C1711yescharacteristic
722#399C22×C1711yescharacteristic
723#399C22×C1711yescharacteristic
724#399C22×C1711yescharacteristic
725#399C22×C1711yescharacteristic
726#398C22×C1711yescharacteristic
727#398C22×C1711yescharacteristic
728#398C22×C1711yescharacteristic
729#398C22×C1711yescharacteristic
730#398C22×C1711yescharacteristic
731#398C22×C1711yescharacteristic
732#398C22×C1711yescharacteristic
733#397C22×C1711yescharacteristic
734#397C22×C1711yescharacteristic
735#397C22×C1711yescharacteristic
736#397C22×C1711yescharacteristic
737#397C22×C1711yescharacteristic
738#397C22×C1711yescharacteristic
739#397C22×C1711yescharacteristic
740#397C22×C1711yescharacteristic
741#397C22×C1711yescharacteristic
742#397C22×C1711yescharacteristic
743#396C22×C1711yescharacteristic
744#396C22×C1711yescharacteristic
745#396C22×C1711yescharacteristic
746#395C22×C1711yescharacteristic
747#395C22×C1711yescharacteristic
748#394C22×C1711yescharacteristic
749#394C22×C1711yescharacteristic
750#394C22×C1711yescharacteristic
751#394C22×C1711yescharacteristic
752#394C22×C1711yescharacteristic
753#393C22×C1711yescharacteristic
754#393C22×C1711yescharacteristic
755#393C22×C1711yescharacteristic
756#393C22×C1711yescharacteristic
757#393C22×C1711yescharacteristic
758#393C22×C1711yescharacteristic
759#392C22×C1711yescharacteristic
760#391C22×C1711yescharacteristic
761#391C22×C1711yescharacteristic
762#391C22×C1711yescharacteristic
763#391C22×C1711yescharacteristic
764#391C22×C1711yescharacteristic
765#390C22×C1711yescharacteristic
766#390C22×C1711yescharacteristic
767#390C22×C1711yescharacteristic
768#390C22×C1711yescharacteristic
769#389C22×C1711yescharacteristic
770#389C22×C1711yescharacteristic
771#389C22×C1711yescharacteristic
772#389C22×C1711yescharacteristic
773#389C22×C1711yescharacteristic
774#389C22×C1711yescharacteristic
775#389C22×C1711yescharacteristic
776#389C22×C1711yescharacteristic
777#389C22×C1711yescharacteristic
778#389C22×C1711yescharacteristic
779#389C22×C1711yescharacteristic
780#388C22×C1711yescharacteristic
781#388C22×C1711yescharacteristic
782#388C22×C1711yescharacteristic
783#388C22×C1711yescharacteristic
784#388C22×C1711yescharacteristic
785#388C22×C1711yescharacteristic
786#388C22×C1711yescharacteristic
787#388C22×C1711yescharacteristic
788#388C22×C1711yescharacteristic
789#388C22×C1711yescharacteristic
790#388C22×C1711yescharacteristic
791#388C22×C1711yescharacteristic
792#388C22×C1711yescharacteristic
793#388C22×C1711yescharacteristic
794#388C22×C1711yescharacteristic
795#388C22×C1711yescharacteristic
796#388C22×C1711yescharacteristic
797#388C22×C1711yescharacteristic
798#388C22×C1711yescharacteristic
799#387C22×C1711yescharacteristic
800#387C22×C1711yescharacteristic
801#387C22×C1711yescharacteristic
802#387C22×C1711yescharacteristic
803#387C22×C1711yescharacteristic
804#387C22×C1711yescharacteristic
805#387C22×C1711yescharacteristic
806#387C22×C1711yescharacteristic
807#387C22×C1711yescharacteristic
808#387C22×C1711yescharacteristic
809#387C22×C1711yescharacteristic
810#387C22×C1711yescharacteristic
811#387C22×C1711yescharacteristic
812#387C22×C1711yescharacteristic
813#387C22×C1711yescharacteristic
814#387C22×C1711yescharacteristic
815#387C22×C1711yescharacteristic
816#387C22×C1711yescharacteristic
817#387C22×C1711yescharacteristic
818#387C22×C1711yescharacteristic
819#387C22×C1711yescharacteristic
820#386C22×C1711yescharacteristic
821#386C22×C1711yescharacteristic
822#386C22×C1711yescharacteristic
823#386C22×C1711yescharacteristic
824#386C22×C1711yescharacteristic
825#386C22×C1711yescharacteristic
826#385C22×C1711yescharacteristic
827#385C22×C1711yescharacteristic
828#385C22×C1711yescharacteristic
829#385C22×C1711yescharacteristic
830#385C22×C1711yescharacteristic
831#385C22×C1711yescharacteristic
832#385C22×C1711yescharacteristic
833#385C22×C1711yescharacteristic
834#385C22×C1711yescharacteristic
835#385C22×C1711yescharacteristic
836#385C22×C1711yescharacteristic
837#385C22×C1711yescharacteristic
838#385C22×C1711yescharacteristic
839#385C22×C1711yescharacteristic
840#383C22×C1711yescharacteristic
841#383C22×C1711yescharacteristic
842#383C22×C1711yescharacteristic
843#382C22×C1711yescharacteristic
844#382C22×C1711yescharacteristic
845#382C22×C1711yescharacteristic
846#382C22×C1711yescharacteristic
847#381C22×C1711yescharacteristic
848#380C22×C1711yescharacteristic
849#380C22×C1711yescharacteristic
850#380C22×C1711yescharacteristic
851C4×C4⋊C4C22×C1711yescharacteristic
852C4×C4⋊C4C22×C1711yescharacteristic
853C4×C22⋊C4C22×C1711yescharacteristic
854C4×C22⋊C4C22×C1711yescharacteristic
855C4×C22⋊C4C22×C1711yescharacteristic
856#376C22×C1711yescharacteristic
857#376C22×C1711yescharacteristic
858C2×C17—42no—
859C2×C17—81no—
860C2×C17—81no—
861C2×C17#345511yescharacteristic
862C2×C17#349511yescharacteristic
863C2×C17#350611yescharacteristic
864C2×C17#353511yescharacteristic
865C2×C17#354011yescharacteristic
866C2×C17#355311yescharacteristic
867C2×C17#356611yescharacteristic
868C22×Q8C23×C1711yescharacteristic
869C22×Q8C23×C1711yescharacteristic
870C22×D4C23×C1711yescharacteristic
871C22×D4C23×C1711yescharacteristic
872C22×D4C23×C1711yescharacteristic
873C23×C4C23×C1711yescharacteristic
874C23×C4C23×C1711yescharacteristic
875C23×C4C23×C1711yescharacteristic
876C23×C4C23×C1711yescharacteristic
877C23×C4C23×C1711yescharacteristic
878#126—24no—
879#125—42no—
880#125—42no—
881#123—42no—
882#123—42no—
883C4×Q8—24no—
884C4×D4—24no—
885#117—42no—
886C2×C4⋊C4C23×C1711yescharacteristic
887C2×C4⋊C4C23×C1711yescharacteristic
888C2×C4⋊C4C23×C1711yescharacteristic
889C2×C4⋊C4C23×C1711yescharacteristic
890C2×C4⋊C4C23×C1711yescharacteristic
891C2×C4⋊C4C23×C1711yescharacteristic
892C2×C4⋊C4C23×C1711yescharacteristic
893C2×C4⋊C4C23×C1711yescharacteristic
894C2×C4⋊C4C23×C1711yescharacteristic
895C2×C4⋊C4C23×C1711yescharacteristic
896C2×C4⋊C4C23×C1711yescharacteristic
897C2×C4⋊C4C23×C1711yescharacteristic
898C2×C4⋊C4C23×C1711yescharacteristic
899C2×C4⋊C4C23×C1711yescharacteristic
900C2×C4⋊C4C23×C1711yescharacteristic
901C2×C4⋊C4C23×C1711yescharacteristic
902C2×C4⋊C4C23×C1711yescharacteristic
903C2×C4⋊C4C23×C1711yescharacteristic
904C2×C4⋊C4C23×C1711yescharacteristic
905C2×C4⋊C4C23×C1711yescharacteristic
906C2×C4⋊C4C23×C1711yescharacteristic
907C2×C4⋊C4C23×C1711yescharacteristic
908C2×C4⋊C4C23×C1711yescharacteristic
909C2×C4⋊C4C23×C1711yescharacteristic
910C2×C4⋊C4C23×C1711yescharacteristic
911C2×C4⋊C4C23×C1711yescharacteristic
912C2×C4⋊C4C23×C1711yescharacteristic
913C2×C4⋊C4C23×C1711yescharacteristic
914C2×C4⋊C4C23×C1711yescharacteristic
915C2×C4⋊C4C23×C1711yescharacteristic
916C2×C4⋊C4C23×C1711yescharacteristic
917C2×C4⋊C4C23×C1711yescharacteristic
918C2×C4⋊C4C23×C1711yescharacteristic
919C2×C4⋊C4C23×C1711yescharacteristic
920C2×C4⋊C4C23×C1711yescharacteristic
921C2×C4⋊C4C23×C1711yescharacteristic
922C2×C4⋊C4C23×C1711yescharacteristic
923C2×C4⋊C4C23×C1711yescharacteristic
924C2×C4⋊C4C23×C1711yescharacteristic
925C2×C22⋊C4C23×C1711yescharacteristic
926C2×C22⋊C4C23×C1711yescharacteristic
927C2×C22⋊C4C23×C1711yescharacteristic
928C2×C22⋊C4C23×C1711yescharacteristic
929C2×C22⋊C4C23×C1711yescharacteristic
930C2×C22⋊C4C23×C1711yescharacteristic
931C2×C22⋊C4C23×C1711yescharacteristic
932C2×C22⋊C4C23×C1711yescharacteristic
933C2×C22⋊C4C23×C1711yescharacteristic
934C2×C22⋊C4C23×C1711yescharacteristic
935C2×C22⋊C4C23×C1711yescharacteristic
936C2×C22⋊C4C23×C1711yescharacteristic
937C2×C22⋊C4C23×C1711yescharacteristic
938C2×C22⋊C4C23×C1711yescharacteristic
939C2×C22⋊C4C23×C1711yescharacteristic
940C2×C22⋊C4C23×C1711yescharacteristic
941C2×C22⋊C4C23×C1711yescharacteristic
942C2×C22⋊C4C23×C1711yescharacteristic
943C2×C22⋊C4C23×C1711yescharacteristic
944C2×C22⋊C4C23×C1711yescharacteristic
945C2×C22⋊C4C23×C1711yescharacteristic
946C2×C22⋊C4C23×C1711yescharacteristic
947C2×C22⋊C4C23×C1711yescharacteristic
948C2×C22⋊C4C23×C1711yescharacteristic
949C2×C22⋊C4C23×C1711yescharacteristic
950C2×C22⋊C4C23×C1711yescharacteristic
951C2×C22⋊C4C23×C1711yescharacteristic
952C2×C22⋊C4C23×C1711yescharacteristic
953C2×C22⋊C4C23×C1711yescharacteristic
954C2×C22⋊C4C23×C1711yescharacteristic
955C2×C22⋊C4C23×C1711yescharacteristic
956C2×C22⋊C4C23×C1711yescharacteristic
957C2×C22⋊C4C23×C1711yescharacteristic
958C2×C22⋊C4C23×C1711yescharacteristic
959C2×C42—42no—
960C2×C42C23×C1711yescharacteristic
961C2×C42C23×C1711yescharacteristic
962C2×C42C23×C1711yescharacteristic
963C2×C42C23×C1711yescharacteristic
964C2×C42C23×C1711yescharacteristic
965C2×C42C23×C1711yescharacteristic
966C2×C42C23×C1711yescharacteristic
967C2×C42C23×C1711yescharacteristic
968C2×C42C23×C1711yescharacteristic
969C2×C42C23×C1711yescharacteristic
970C2×C42C23×C1711yescharacteristic
971C2×C42C23×C1711yescharacteristic
972C2×C42C23×C1711yescharacteristic
973C2×C42C23×C1711yescharacteristic
974#95C23×C1711yescharacteristic
975#95C23×C1711yescharacteristic
976#95C23×C1711yescharacteristic
977#95C23×C1711yescharacteristic
978#95C23×C1711yescharacteristic
979#95C23×C1711yescharacteristic
980#95C23×C1711yescharacteristic
981#95C23×C1711yescharacteristic
982#95C23×C1711yescharacteristic
983#95C23×C1711yescharacteristic
984#95C23×C1711yescharacteristic
985#95C23×C1711yescharacteristic
986#95C23×C1711yescharacteristic
987#95C23×C1711yescharacteristic
988#95C23×C1711yescharacteristic
989#95C23×C1711yescharacteristic
990#95C23×C1711yescharacteristic
991#95C23×C1711yescharacteristic
992#95C23×C1711yescharacteristic
993#95C23×C1711yescharacteristic
994#95C23×C1711yescharacteristic
995#95C23×C1711yescharacteristic
996#95C23×C1711yescharacteristic
997#95C23×C1711yescharacteristic
998#95C23×C1711yescharacteristic
999#95C23×C1711yescharacteristic
1000#95C23×C1711yescharacteristic
1001#95C23×C1711yescharacteristic
1002#95C23×C1711yescharacteristic
1003#95C23×C1711yescharacteristic
1004#95C23×C1711yescharacteristic
1005#95C23×C1711yescharacteristic
1006#95C23×C1711yescharacteristic
1007#95C23×C1711yescharacteristic
1008#95C23×C1711yescharacteristic
1009#95C23×C1711yescharacteristic
1010#95C23×C1711yescharacteristic
1011#95C23×C1711yescharacteristic
1012#95C23×C1711yescharacteristic
1013#95C23×C1711yescharacteristic
1014#95C23×C1711yescharacteristic
1015#95C23×C1711yescharacteristic
1016#95C23×C1711yescharacteristic
1017#95C23×C1711yescharacteristic
1018#95C23×C1711yescharacteristic
1019#95C23×C1711yescharacteristic
1020#95C23×C1711yescharacteristic
1021#95C23×C1711yescharacteristic
1022#95C23×C1711yescharacteristic
1023#95C23×C1711yescharacteristic
1024#95C23×C1711yescharacteristic
1025#95C23×C1711yescharacteristic
1026#95C23×C1711yescharacteristic
1027#95C23×C1711yescharacteristic
1028#95C23×C1711yescharacteristic
1029#95C23×C1711yescharacteristic
1030#95C23×C1711yescharacteristic
1031#95C23×C1711yescharacteristic
1032C17#3680211yescharacteristic, direct product factor, Sylow
1033C24C24×C1711yescharacteristic
1034C24C24×C1711yescharacteristic
1035C24C24×C1711yescharacteristic
1036C2×Q8—22no—
1037C2×Q8—41no—
1038C2×Q8—41no—
1039C2×Q8—41no—
1040C2×Q8—41no—
1041C2×Q8—41no—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—22no—
1045C2×D4—41no—
1046C2×D4—41no—
1047C2×D4—41no—
1048C2×D4—41no—
1049C2×D4—41no—
1050C2×D4—41no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4C24×C1711yescharacteristic
1067C22×C4C24×C1711yescharacteristic
1068C22×C4C24×C1711yescharacteristic
1069C22×C4C24×C1711yescharacteristic
1070C22×C4C24×C1711yescharacteristic
1071C22×C4C24×C1711yescharacteristic
1072C22×C4C24×C1711yescharacteristic
1073C22×C4C24×C1711yescharacteristic
1074C22×C4C24×C1711yescharacteristic
1075C22×C4C24×C1711yescharacteristic
1076C22×C4C24×C1711yescharacteristic
1077C22×C4C24×C1711yescharacteristic
1078C22×C4C24×C1711yescharacteristic
1079C22×C4C24×C1711yescharacteristic
1080C22×C4C24×C1711yescharacteristic
1081C22×C4C24×C1711yescharacteristic
1082C22×C4C24×C1711yescharacteristic
1083C22×C4C24×C1711yescharacteristic
1084C22×C4C24×C1711yescharacteristic
1085C22×C4C24×C1711yescharacteristic
1086C22×C4C24×C1711yescharacteristic
1087C22×C4C24×C1711yescharacteristic
1088C22×C4C24×C1711yescharacteristic
1089C22×C4C24×C1711yescharacteristic
1090C22×C4C24×C1711yescharacteristic
1091C22×C4C24×C1711yescharacteristic
1092C22×C4C24×C1711yescharacteristic
1093C22×C4C24×C1711yescharacteristic
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—22no—
1098C4⋊C4—22no—
1099C4⋊C4—22no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—22no—
1103C4⋊C4—22no—
1104C4⋊C4—22no—
1105C4⋊C4—41no—
1106C4⋊C4—41no—
1107C4⋊C4—41no—
1108C4⋊C4—41no—
1109C4⋊C4—41no—
1110C4⋊C4—41no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—41no—
1114C4⋊C4—41no—
1115C4⋊C4—41no—
1116C4⋊C4—41no—
1117C4⋊C4—41no—
1118C4⋊C4—41no—
1119C4⋊C4—41no—
1120C4⋊C4—41no—
1121C4⋊C4—41no—
1122C4⋊C4—41no—
1123C4⋊C4—41no—
1124C4⋊C4—41no—
1125C4⋊C4—41no—
1126C4⋊C4—41no—
1127C4⋊C4—41no—
1128C4⋊C4—41no—
1129C4⋊C4—41no—
1130C4⋊C4—41no—
1131C4⋊C4—41no—
1132C4⋊C4—41no—
1133C22⋊C4—22no—
1134C22⋊C4—22no—
1135C22⋊C4—22no—
1136C22⋊C4—22no—
1137C22⋊C4—22no—
1138C22⋊C4—22no—
1139C22⋊C4—22no—
1140C22⋊C4—22no—
1141C22⋊C4—22no—
1142C22⋊C4—41no—
1143C22⋊C4—41no—
1144C22⋊C4—41no—
1145C22⋊C4—41no—
1146C22⋊C4—41no—
1147C22⋊C4—41no—
1148C22⋊C4—41no—
1149C22⋊C4—41no—
1150C22⋊C4—41no—
1151C22⋊C4—41no—
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—
1167C42—22no—
1168C42—22no—
1169C42—22no—
1170C42—22no—
1171C42—41no—
1172C42—41no—
1173C42—41no—
1174C42—41no—
1175C42—41no—
1176C42—41no—
1177C42—41no—
1178C42—41no—
1179C42—41no—
1180C42#41×C1714yes—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23C17×2−1+412yes—
1202C23C25×C1711yescharacteristic
1203Q8—44no—
1204Q8—82no—
1205D4—44no—
1206D4—82no—
1207D4—82no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
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—44no—
1289C2×C4—44no—
1290C2×C4—44no—
1291C2×C4—44no—
1292C2×C4—82no—
1293C2×C4C2×#41×C1712yes—
1294C2×C4C2×#41×C1712yes—
1295C2×C4C2×#41×C1712yes—
1296C2×C4C17×H(5,𝔽2)12yes—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22C22×#41×C1711yescharacteristic
1319C22C2×C17×H(5,𝔽2)11yescharacteristic
1320C22C2×C17×2−1+411yescharacteristic
1321C22C17×#58511yescharacteristic
1322C22C17×#58511yescharacteristic
1323C22C17×#58511yescharacteristic
1324C22C17×#58511yescharacteristic
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C2—42no—
1354C2—81no—
1355C2—81no—
1356C2C17×#345511yescharacteristic
1357C2C17×#349511yescharacteristic
1358C2C17×#350611yescharacteristic
1359C2C17×#353511yescharacteristic
1360C2C17×#354011yescharacteristic
1361C2C17×#355311yescharacteristic
1362C2C17×#356611yescharacteristic
subgroupG/H
center, socleC23×C17C25
commutator, Frattini, cosocleC23C25×C17
prime radicalC17×#392C22
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×#2851C2semidirect
3. C17×#2808C2semidirect
4. C17×#2807C2semidirect
5. C17×#2804C2semidirect
6. C17×#2798C2semidirect
7. C17×#2775C2semidirect
8. C17×#2775C2semidirect
9. C17×#2770C2semidirect
10. C17×#2766C2semidirect
11. C17×#2757C2semidirect
13. C17×#2745C2semidirect
14. C17×#2737C2semidirect
15. C17×#2719C2semidirect
17. C17×#2694C2semidirect
18. C17×#2694C2semidirect
19. C17×#2653C2semidirect
20. C17×#2652C2semidirect
21. C17×#2612C2semidirect
22. C17×#2604C2semidirect
24. C17×#2589C2semidirect
25. C17×#2580C2semidirect
26. C17×#2578C2semidirect
27. C17×#2475C2semidirect
28. C17×#2470C2semidirect
29. C17×#2334C2semidirect
30. C17×#2320C2semidirect
31. C17×#2290C2semidirect
499. #36802C17direct (N × H)
616. #2853C2×C17semidirect
617. #2851C2×C17semidirect
618. #2808C2×C17semidirect
619. #2807C2×C17semidirect
620. #2804C2×C17semidirect
621. #2798C2×C17semidirect
622. #2775C2×C17semidirect
623. #2775C2×C17semidirect
624. #2770C2×C17semidirect
625. #2766C2×C17semidirect
626. #2757C2×C17semidirect
628. #2745C2×C17semidirect
629. #2737C2×C17semidirect
630. #2719C2×C17semidirect
632. #2694C2×C17semidirect
633. #2694C2×C17semidirect
634. #2653C2×C17semidirect
635. #2652C2×C17semidirect
636. #2612C2×C17semidirect
637. #2604C2×C17semidirect
639. #2589C2×C17semidirect
640. #2580C2×C17semidirect
641. #2578C2×C17semidirect
642. #2475C2×C17semidirect
643. #2470C2×C17semidirect
644. #2334C2×C17semidirect
645. #2320C2×C17semidirect
646. #2290C2×C17semidirect
1032. C17#36802direct (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×#28512
C17×#28082
C17×#28072
C17×#28042
C17×#27982
C17×#27752
C17×#27702
C17×#27662
C17×#27572
C17×#27532
C17×#27452
C17×#27372
C17×#27192
C17×#27062
C17×#26942
C17×#26532
C17×#26522
C17×#26122
C17×#26042
C17×#26032
C17×#25892
C17×#25802
C17×#25782
C17×#24752
C17×#24702
C17×#23342
C17×#23202
C17×#22902
#3680217