Finite Group Databasebeta

← #17049657

Subgroups — #17049657

Order 4352.

1668 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762783C211yesmaximal, characteristic, complemented
2C22×#10587505C211yesmaximal, characteristic, complemented
3#14531633C212yesmaximal, complemented
4#14529621C212yesmaximal, complemented
5#14529243C212yesmaximal, complemented
6#14529238C212yesmaximal, complemented
7#14528772C211yesmaximal, characteristic, complemented
8#14528702C211yesmaximal, characteristic, complemented
9#14528699C211yesmaximal, characteristic, complemented
10C4×#10587505C211yesmaximal, characteristic, complemented
11C2×C17×#546C211yesmaximal, characteristic
12C2×#10587612C2212yescomplemented
13C22×C22⋊Dic17C2212yes—
14#11762783—24no—
15C2×#10587505—24no—
16C2×#10587505C2211yescharacteristic
17C2×#10587505C2211yescharacteristic
18C2×#10587505C2212yes—
19C2×#10587505C2211yescharacteristic
20C2×#10587505C2212yes—
21C2×#10587505C2211yescharacteristic
22C2×#10587505C2212yescomplemented
23C2×#10587505C2212yescomplemented
24#11762702—22no—
25#11762702—22no—
26#11762684—22no—
27#11762672C2212yescomplemented
28#11762669C2212yescomplemented
29#11762665C2212yes—
30C22⋊C4×Dic17—22no—
31C4×C22⋊Dic17C2212yescomplemented
32#11762576C2212yescomplemented
33#11762576C2212yescomplemented
34C22×#41×C17C2211yescharacteristic
35C23×D4×C17C2211yescharacteristic
36C17×#546—22no—
37C17×#546—22no—
38C17×#546—22no—
39C17×#546—22no—
40C2×C17×#124C411yescharacteristic, complemented
41C2×C17×#123C411yescharacteristic, complemented
42C2×C17×#123C2211yescharacteristic
43C2×C17×C22⋊Q8C411yescharacteristic, complemented
44C2×C17×#121C411yescharacteristic, complemented
45C2×C17×#121C411yescharacteristic, complemented
46C2×C17×#121C2211yescharacteristic
47C2×C17×#120C411yescharacteristic, complemented
48C2×C17×#120C2211yescharacteristic
49C2×C4×D4×C17C411yescharacteristic, complemented
50C2×C4×D4×C17C2211yescharacteristic
51C22×C22⋊C4×C17C411yescharacteristic, complemented
52C22×C22⋊C4×C17C2211yescharacteristic
53C25×C17C2×C411yescharacteristic
54C25×C17C2311yescharacteristic
55C2×#41×C17—22no—
56C2×#41×C17—22no—
57C2×#41×C17—22no—
58C2×#41×C17—22no—
59C2×#41×C17—42no—
60C22×Q8×C17C2×C411yescharacteristic, complemented
61C22×D4×C17—22no—
62C22×D4×C17—22no—
63C22×D4×C17—22no—
64C22×D4×C17—22no—
65C22×D4×C17—42no—
66C22×D4×C17C2×C411yescharacteristic
67C22×D4×C17C2×C411yescharacteristic
68C22×D4×C17C2×C411yescharacteristic
69C22×D4×C17C2×C411yescharacteristic
70C22×D4×C17C2×C411yescharacteristic, complemented
71C22×D4×C17C2×C411yescharacteristic, complemented
72C22×D4×C17C2311yescharacteristic
73C22×D4×C17C2311yescharacteristic
74C22×D4×C17C2311yescharacteristic
75C23×C4×C17C2×C411yescharacteristic
76C23×C4×C17C2×C411yescharacteristic, complemented
77C23×C4×C17C2×C411yescharacteristic, complemented
78C23×C4×C17C2×C411yescharacteristic, complemented
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×Dic17—22no—
82C17×#124—22no—
83C17×#124—22no—
84C17×#123—22no—
85C17×#123—22no—
86C17×#123—22no—
87C17×#123—22no—
88C17×C22⋊Q8—22no—
89C17×C22⋊Q8—22no—
90C17×#121—22no—
91C17×#121—22no—
92C17×#121—22no—
93C17×#121—22no—
94C17×#121—22no—
95C17×#121—22no—
96C17×#120—22no—
97C17×#120—22no—
98C17×#120—22no—
99C17×#120—22no—
100C4×D4×C17—22no—
101C4×D4×C17—22no—
102C4×D4×C17—21no—
103C4×D4×C17—21no—
104C4×D4×C17—21no—
105C4×D4×C17—21no—
106C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
107C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
108C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
109C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
110C2×C22⋊C4×C17—21no—
111C2×C22⋊C4×C17—21no—
112C2×C22⋊C4×C17—21no—
113C2×C22⋊C4×C17—21no—
114C2×C22⋊C4×C17C2×C411yescharacteristic
115C2×C22⋊C4×C17C2×C411yescharacteristic
116C2×C22⋊C4×C17C2×C411yescharacteristic
117C2×C22⋊C4×C17C2×C411yescharacteristic
118C2×C22⋊C4×C17C2×C411yescharacteristic
119C2×C22⋊C4×C17C2×C411yescharacteristic
120C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
121C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
122C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
123C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
124C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
125C2×C22⋊C4×C17D412yes—
126C2×C22⋊C4×C17D412yes—
127C2×C22⋊C4×C17D412yes—
128C2×C22⋊C4×C17D412yes—
129C2×C22⋊C4×C17C2311yescharacteristic
130C2×C42×C17C2×C411yescharacteristic, complemented
131C2×C22⋊Dic17—24no—
132C2×C22⋊Dic17—22no—
133C2×C22⋊Dic17—22no—
134C2×C22⋊Dic17—22no—
135C2×C22⋊Dic17—42no—
136C2×C22⋊Dic17C2312yes—
137C2×C22⋊Dic17C2312yes—
138C2×C22⋊Dic17C2312yes—
139C2×C22⋊Dic17C2312yes—
140#10587612—24no—
141#10587612—42no—
142C2×C4⋊Dic17—22no—
143C2×C4⋊Dic17—22no—
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146#10587505—22no—
147#10587505—22no—
148#10587505—22no—
149#10587505—24no—
150#10587505—24no—
151#10587505—42no—
152#10587505—42no—
153#10587505D414yescomplemented
154#10587502—22no—
155#10587502—22no—
156#10587502—22no—
157#10587502—22no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—22no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—22no—
164C24×C17—41no—
165C24×C17—42no—
166C24×C17—42no—
167C24×C17—81no—
168C24×C17—81no—
169C24×C17C22×C411yescharacteristic
170C24×C17C22×C411yescharacteristic
171C24×C17C22×C411yescharacteristic
172C24×C17C22×C411yescharacteristic
173C24×C17C22×C411yescharacteristic
174C24×C17C2×D412yes—
175C24×C17C2×D412yes—
176C24×C17C2411yescharacteristic
177#41×C17—44no—
178#41×C17—44no—
179#41×C17—44no—
180#41×C17—44no—
181C2×Q8×C17—22no—
182C2×Q8×C17—22no—
183C2×Q8×C17—41no—
184C2×D4×C17—22no—
185C2×D4×C17—22no—
186C2×D4×C17—22no—
187C2×D4×C17—22no—
188C2×D4×C17—21no—
189C2×D4×C17—21no—
190C2×D4×C17—22no—
191C2×D4×C17—22no—
192C2×D4×C17—22no—
193C2×D4×C17—21no—
194C2×D4×C17—21no—
195C2×D4×C17—22no—
196C2×D4×C17—21no—
197C2×D4×C17—21no—
198C2×D4×C17—22no—
199C2×D4×C17—22no—
200C2×D4×C17—22no—
201C2×D4×C17—22no—
202C2×D4×C17—22no—
203C2×D4×C17—22no—
204C2×D4×C17—41no—
205C2×D4×C17—41no—
206C2×D4×C17—41no—
207C2×D4×C17—44no—
208C2×D4×C17—44no—
209C2×D4×C17—44no—
210C2×D4×C17—44no—
211C2×D4×C17—42no—
212C2×D4×C17—81no—
213C2×D4×C17—81no—
214C2×D4×C17C2×D412yes—
215C2×D4×C17#4112yes—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—22no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—22no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—22no—
227C22×C4×C17—22no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—41no—
231C22×C4×C17—41no—
232C22×C4×C17—41no—
233C22×C4×C17—81no—
234C22×C4×C17—81no—
235C22×C4×C17C22×C411yescharacteristic
236C22×C4×C17C22×C411yescharacteristic
237C22×C4×C17C22×C411yescharacteristic
238C22×C4×C17C22×C411yescharacteristic
239C22×C4×C17C22×C411yescharacteristic
240C22×C4×C17C22×C411yescharacteristic
241C22×C4×C17C22×C411yescharacteristic
242C22×C4×C17C22×C411yescharacteristic
243C22×C4×C17C22×C411yescharacteristic
244C22×C4×C17C2×D412yes—
245C22×C4×C17C2×D412yes—
246C22×C4×C17C2×D412yes—
247C22×C4×C17C2×D412yes—
248C22×Dic17—22no—
249C22×Dic17—22no—
250C22×Dic17—22no—
251C22×Dic17—22no—
252C22×Dic17—44no—
253C22×Dic17—44no—
254C22×Dic17—82no—
255C4⋊C4×C17—22no—
256C4⋊C4×C17—22no—
257C4⋊C4×C17—22no—
258C4⋊C4×C17—21no—
259C4⋊C4×C17—21no—
260C22⋊C4×C17—21no—
261C22⋊C4×C17—21no—
262C22⋊C4×C17—22no—
263C22⋊C4×C17—22no—
264C22⋊C4×C17—22no—
265C22⋊C4×C17—21no—
266C22⋊C4×C17—21no—
267C22⋊C4×C17—22no—
268C22⋊C4×C17—21no—
269C22⋊C4×C17—21no—
270C22⋊C4×C17—21no—
271C22⋊C4×C17—21no—
272C22⋊C4×C17C22⋊C412yes—
273C22⋊C4×C17C22⋊C412yes—
274C22⋊C4×C17C22⋊C412yes—
275C22⋊C4×C17C22⋊C412yes—
276C22⋊C4×C17C22⋊C412yes—
277C22⋊C4×C17C22⋊C412yes—
278C22⋊C4×C17C22⋊C411yescharacteristic
279C22⋊C4×C17C22⋊C411yescharacteristic
280C22⋊C4×C17C22⋊C411yescharacteristic
281C22⋊C4×C17C22⋊C411yescharacteristic
282C42×C17—21no—
283C42×C17—21no—
284C22⋊Dic17—22no—
285C22⋊Dic17—22no—
286C22⋊Dic17—22no—
287C22⋊Dic17—22no—
288C22⋊Dic17—22no—
289C22⋊Dic17—22no—
290C22⋊Dic17—22no—
291C22⋊Dic17—44no—
292C22⋊Dic17—44no—
293C22⋊Dic17—82no—
294C22⋊Dic17C2×D414yes—
295C4⋊Dic17—44no—
296C4⋊Dic17—82no—
297C4×Dic17—44no—
298C4×Dic17—82no—
299#22405—171nomaximal, Sylow
300C23×C17—21no—
301C23×C17—21no—
302C23×C17—21no—
303C23×C17—21no—
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—24no—
307C23×C17—22no—
308C23×C17—21no—
309C23×C17—21no—
310C23×C17—22no—
311C23×C17—22no—
312C23×C17—21no—
313C23×C17—21no—
314C23×C17—21no—
315C23×C17—21no—
316C23×C17—21no—
317C23×C17—21no—
318C23×C17—42no—
319C23×C17—41no—
320C23×C17—41no—
321C23×C17—41no—
322C23×C17—42no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17—42no—
326C23×C17—42no—
327C23×C17—42no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—42no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—42no—
336C23×C17—81no—
337C23×C17—81no—
338C23×C17—82no—
339C23×C17—82no—
340C23×C17—84no—
341C23×C17—84no—
342C23×C17—84no—
343C23×C17C2×C22⋊C411yescharacteristic
344C23×C17C2×C22⋊C412yes—
345C23×C17C2×C22⋊C411yescharacteristic
346C23×C17C4×D412yes—
347C23×C17C23×C411yescharacteristic
348C23×C17C22×D411yescharacteristic
349C23×C17C22×D412yes—
350C23×C17C2×#4111yescharacteristic
351C23×C17H(5,𝔽2)12yes—
352Q8×C17—44no—
353D4×C17—24no—
354D4×C17—24no—
355D4×C17—44no—
356D4×C17—44no—
357D4×C17—44no—
358D4×C17—42no—
359D4×C17—42no—
360D4×C17—42no—
361D4×C17—42no—
362D4×C17—42no—
363D4×C17—42no—
364D4×C17—82no—
365D4×C17—82no—
366C2×C4×C17—21no—
367C2×C4×C17—21no—
368C2×C4×C17—21no—
369C2×C4×C17—21no—
370C2×C4×C17—21no—
371C2×C4×C17—21no—
372C2×C4×C17—22no—
373C2×C4×C17—22no—
374C2×C4×C17—22no—
375C2×C4×C17—22no—
376C2×C4×C17—21no—
377C2×C4×C17—21no—
378C2×C4×C17—21no—
379C2×C4×C17—21no—
380C2×C4×C17—21no—
381C2×C4×C17—21no—
382C2×C4×C17—21no—
383C2×C4×C17—21no—
384C2×C4×C17—41no—
385C2×C4×C17—41no—
386C2×C4×C17—42no—
387C2×C4×C17—42no—
388C2×C4×C17—42no—
389C2×C4×C17—42no—
390C2×C4×C17—42no—
391C2×C4×C17—42no—
392C2×C4×C17—42no—
393C2×C4×C17—42no—
394C2×C4×C17—41no—
395C2×C4×C17—41no—
396C2×C4×C17—81no—
397C2×C4×C17—81no—
398C2×C4×C17C2×C22⋊C411yescharacteristic
399C2×C4×C17C2×C22⋊C411yescharacteristic
400C2×C4×C17C2×C22⋊C412yes—
401C2×C4×C17C2×C22⋊C411yescharacteristic
402C2×C4×C17C2×C22⋊C411yescharacteristic
403C2×C4×C17C2×C22⋊C412yes—
404C2×C4×C17C4×D412yes—
405C2×Dic17—24no—
406C2×Dic17—42no—
407C2×Dic17—42no—
408C2×Dic17—42no—
409C2×Dic17—42no—
410C2×Dic17—42no—
411C2×Dic17—42no—
412C2×Dic17—42no—
413C2×Dic17—42no—
414C2×Dic17—42no—
415C2×Dic17—42no—
416C2×Dic17—42no—
417C2×Dic17—88no—
418C2×#546D1711yescharacteristic
419C2×#410—171no—
420C22×#99—171no—
421#2342—172no—
422#1964—172no—
423#1899—172no—
424#1898—172no—
425#1799—171no—
426#1782—171no—
427#1781—171no—
428C4×#99—171no—
429C22×C17—21no—
430C22×C17—22no—
431C22×C17—21no—
432C22×C17—22no—
433C22×C17—21no—
434C22×C17—21no—
435C22×C17—22no—
436C22×C17—21no—
437C22×C17—22no—
438C22×C17—21no—
439C22×C17—22no—
440C22×C17—22no—
441C22×C17—21no—
442C22×C17—41no—
443C22×C17—41no—
444C22×C17—42no—
445C22×C17—44no—
446C22×C17—44no—
447C22×C17—42no—
448C22×C17—42no—
449C22×C17—42no—
450C22×C17—42no—
451C22×C17—41no—
452C22×C17—41no—
453C22×C17—41no—
454C22×C17—41no—
455C22×C17—41no—
456C22×C17—41no—
457C22×C17—41no—
458C22×C17—41no—
459C22×C17—82no—
460C22×C17—82no—
461C22×C17—81no—
462C22×C17—81no—
463C22×C17—84no—
464C22×C17—81no—
465C22×C17—81no—
466C22×C17—81no—
467C22×C17—81no—
468C22×C17—84no—
469C22×C17#41012yescomplemented
470C22×C17C22×C22⋊C411yescharacteristic
471C22×C17C2×C4×D411yescharacteristic
472C22×C17#51811yescharacteristic
473C22×C17D4212yes—
474C22×C17#54612yes—
475C4×C17—21no—
476C4×C17—21no—
477C4×C17—22no—
478C4×C17—22no—
479C4×C17—21no—
480C4×C17—21no—
481C4×C17—22no—
482C4×C17—41no—
483C4×C17—41no—
484C4×C17—41no—
485C4×C17—41no—
486Dic17—44no—
487Dic17—82no—
488Dic17—82no—
489Dic17—82no—
490C22×#41C2×D1711yescharacteristic
491C23×D4C2×D1711yescharacteristic
492#546—22no—
493#546—22no—
494#546—22no—
495#546—22no—
496C2×#124Dic1711yescharacteristic, complemented
497C2×#123Dic1711yescharacteristic, complemented
498C2×#123C2×D1711yescharacteristic
499C2×C22⋊Q8Dic1711yescharacteristic, complemented
500C2×#121Dic1711yescharacteristic, complemented
501C2×#121Dic1711yescharacteristic, complemented
502C2×#121C2×D1711yescharacteristic
503C2×#120Dic1711yescharacteristic, complemented
504C2×#120C2×D1711yescharacteristic
505C2×C4×D4Dic1711yescharacteristic, complemented
506C2×C4×D4C2×D1711yescharacteristic
507C2×#117—172no—
508C22×C22⋊C4—172no—
509C22×C22⋊C4Dic1711yescharacteristic, complemented
510C22×C22⋊C4C2×D1711yescharacteristic
511#410—344no—
512C2×#99—171no—
513C2×#99—171no—
514C2×#99—171no—
515C2×#99—172no—
516C2×#99—172no—
517C2×#99—171no—
518C2×#99—172no—
519C2×#99—172no—
520C2×#99—344no—
521#388—342no—
522#388—342no—
523#385—342no—
524#381—172no—
525#380—172no—
526#379—172no—
527C4×C22⋊C4—172no—
528C4×C22⋊C4—342no—
529#342—172no—
530#342—172no—
531C2×C17—22no—
532C2×C17—22no—
533C2×C17—21no—
534C2×C17—21no—
535C2×C17—22no—
536C2×C17—42no—
537C2×C17—41no—
538C2×C17—42no—
539C2×C17—81no—
540C2×C17—81no—
541C2×C17D4×C22⋊C411yescharacteristic
542C2×C17C2×#41011yescharacteristic
543C2×C17#288311yescharacteristic
544C25C2×Dic1711yescharacteristic
545C25C22×D1711yescharacteristic
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—42no—
551C22×Q8C2×Dic1711yescharacteristic, complemented
552C22×D4—22no—
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—42no—
557C22×D4C2×Dic1711yescharacteristic
558C22×D4C2×Dic1711yescharacteristic
559C22×D4C2×Dic1711yescharacteristic
560C22×D4C2×Dic1711yescharacteristic
561C22×D4C2×Dic1711yescharacteristic, complemented
562C22×D4C2×Dic1711yescharacteristic, complemented
563C22×D4C22×D1711yescharacteristic
564C22×D4C22×D1711yescharacteristic
565C22×D4C22×D1711yescharacteristic
566C23×C4—342no—
567C23×C4C2×Dic1711yescharacteristic
568C23×C4C2×Dic1711yescharacteristic, complemented
569C23×C4C2×Dic1711yescharacteristic, complemented
570C23×C4C2×Dic1711yescharacteristic, complemented
571C23×C4C22×D1711yescharacteristic
572C23×C4C22×D1711yescharacteristic
573#124—22no—
574#124—22no—
575#123—22no—
576#123—22no—
577#123—22no—
578#123—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#120—22no—
588#120—22no—
589#120—22no—
590#120—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597#117—344no—
598#117—682no—
599C2×C4⋊C4—342no—
600C2×C4⋊C4—342no—
601C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
602C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
603C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
604C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—172no—
610C2×C22⋊C4—172no—
611C2×C22⋊C4—172no—
612C2×C22⋊C4—172no—
613C2×C22⋊C4—344no—
614C2×C22⋊C4—342no—
615C2×C22⋊C4—342no—
616C2×C22⋊C4—342no—
617C2×C22⋊C4—682no—
618C2×C22⋊C4C2×Dic1711yescharacteristic
619C2×C22⋊C4C2×Dic1711yescharacteristic
620C2×C22⋊C4C2×Dic1711yescharacteristic
621C2×C22⋊C4C2×Dic1711yescharacteristic
622C2×C22⋊C4C2×Dic1711yescharacteristic
623C2×C22⋊C4C2×Dic1711yescharacteristic
624C2×C22⋊C4C2×Dic1711yescharacteristic, complemented
625C2×C22⋊C4C2×Dic1711yescharacteristic, complemented
626C2×C22⋊C4C2×Dic1711yescharacteristic, complemented
627C2×C22⋊C4C2×Dic1711yescharacteristic, complemented
628C2×C22⋊C4C2×Dic1711yescharacteristic, complemented
629C2×C22⋊C4C22⋊D1712yes—
630C2×C22⋊C4C22⋊D1712yes—
631C2×C22⋊C4C22⋊D1712yes—
632C2×C22⋊C4C22⋊D1712yes—
633C2×C22⋊C4C22×D1711yescharacteristic
634C2×C42—342no—
635C2×C42—342no—
636C2×C42C2×Dic1711yescharacteristic, complemented
637#99—174no—
638#99—344no—
639#99—344no—
640#99—342no—
641#99—342no—
642#99—342no—
643#99—682no—
644#99—682no—
645#95—342no—
646#95—342no—
647#95—342no—
648#95—342no—
649C17#2240511yescharacteristic, complemented, Sylow
650C24—21no—
651C24—21no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—41no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C22×Dic1711yescharacteristic
662C24C22×Dic1711yescharacteristic
663C24C22×Dic1711yescharacteristic
664C24C22×Dic1711yescharacteristic
665C24C22×Dic1711yescharacteristic
666C24C2×C22⋊D1712yes—
667C24C2×C22⋊D1712yes—
668C24C23×D1711yescharacteristic
669#41—44no—
670#41—44no—
671#41—44no—
672#41—44no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—41no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4—41no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4D4×D1712yes—
707C2×D4#6325412yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4—41no—
725C22×C4—81no—
726C22×C4—81no—
727C22×C4—342no—
728C22×C4—342no—
729C22×C4—342no—
730C22×C4—342no—
731C22×C4—684no—
732C22×C4—684no—
733C22×C4—1362no—
734C22×C4C22×Dic1711yescharacteristic
735C22×C4C22×Dic1711yescharacteristic
736C22×C4C22×Dic1711yescharacteristic
737C22×C4C22×Dic1711yescharacteristic
738C22×C4C22×Dic1711yescharacteristic
739C22×C4C22×Dic1711yescharacteristic
740C22×C4C22×Dic1711yescharacteristic
741C22×C4C22×Dic1711yescharacteristic
742C22×C4C22×Dic1711yescharacteristic
743C22×C4C2×C22⋊D1712yes—
744C22×C4C2×C22⋊D1712yes—
745C22×C4C2×C22⋊D1712yes—
746C22×C4C2×C22⋊D1712yes—
747C4⋊C4—22no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—684no—
753C4⋊C4—1362no—
754C22⋊C4—22no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—22no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—22no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—22no—
766C22⋊C4—174no—
767C22⋊C4—342no—
768C22⋊C4—342no—
769C22⋊C4—342no—
770C22⋊C4—342no—
771C22⋊C4—342no—
772C22⋊C4—342no—
773C22⋊C4—342no—
774C22⋊C4—684no—
775C22⋊C4—684no—
776C22⋊C4—1362no—
777C22⋊C4C22⋊Dic1711yescharacteristic
778C22⋊C4C22⋊Dic1711yescharacteristic
779C22⋊C4C22⋊Dic1711yescharacteristic
780C22⋊C4C22⋊Dic1711yescharacteristic
781C22⋊C4C22⋊Dic1712yes—
782C22⋊C4C22⋊Dic1712yes—
783C22⋊C4C22⋊Dic1712yes—
784C22⋊C4C22⋊Dic1712yes—
785C22⋊C4C22⋊Dic1712yes—
786C22⋊C4C22⋊Dic1712yes—
787C42—21no—
788C42—21no—
789C42—684no—
790C42—1362no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—24no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—21no—
800C23—21no—
801C23—22no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—41no—
810C23—42no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—41no—
815C23—41no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—41no—
820C23—41no—
821C23—42no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—42no—
827C23—81no—
828C23—81no—
829C23—82no—
830C23—82no—
831C23—84no—
832C23—84no—
833C23—84no—
834C23D4×Dic1712yes—
835C23C2×C22⋊Dic1711yescharacteristic
836C23C2×C22⋊Dic1712yes—
837C23C2×C22⋊Dic1711yescharacteristic
838C23C2×D4×D1711yescharacteristic
839C23C2×#6325411yescharacteristic
840C23#1058769112yes—
841C23C23×Dic1711yescharacteristic
842C23C22×C22⋊D1712yes—
843Q8—44no—
844D4—24no—
845D4—24no—
846D4—44no—
847D4—44no—
848D4—44no—
849D4—42no—
850D4—42no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—82no—
856D4—82no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—344no—
890C2×C4—682no—
891C2×C4—682no—
892C2×C4—682no—
893C2×C4—682no—
894C2×C4—682no—
895C2×C4—682no—
896C2×C4—682no—
897C2×C4—682no—
898C2×C4—682no—
899C2×C4—682no—
900C2×C4—682no—
901C2×C4—1368no—
902C2×C4D4×Dic1712yes—
903C2×C4C2×C22⋊Dic1711yescharacteristic
904C2×C4C2×C22⋊Dic1711yescharacteristic
905C2×C4C2×C22⋊Dic1712yes—
906C2×C4C2×C22⋊Dic1711yescharacteristic
907C2×C4C2×C22⋊Dic1711yescharacteristic
908C2×C4C2×C22⋊Dic1712yes—
909C22—21no—
910C22—21no—
911C22—22no—
912C22—21no—
913C22—22no—
914C22—21no—
915C22—22no—
916C22—21no—
917C22—22no—
918C22—21no—
919C22—22no—
920C22—22no—
921C22—21no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—44no—
926C22—42no—
927C22—42no—
928C22—44no—
929C22—42no—
930C22—42no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—82no—
940C22—82no—
941C22—81no—
942C22—81no—
943C22—84no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22—84no—
949C22#1176278312yescomplemented
950C22C22×C22⋊Dic1711yescharacteristic
951C22C2×D4×Dic1711yescharacteristic
952C22#1176328411yescharacteristic
953C22D4×C22⋊D1712yes—
954C22#1176345312yes—
955C4—21no—
956C4—21no—
957C4—22no—
958C4—22no—
959C4—21no—
960C4—21no—
961C4—22no—
962C4—41no—
963C4—41no—
964C4—41no—
965C4—41no—
966C4—684no—
967C4—1362no—
968C4—1362no—
969C4—1362no—
970C2—22no—
971C2—22no—
972C2—21no—
973C2—21no—
974C2—22no—
975C2—41no—
976C2—42no—
977C2—42no—
978C2—81no—
979C2—81no—
980C2D4×C22⋊Dic1711yescharacteristic
981C2C2×#1176278311yescharacteristic
982C2#1453724511yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
Fitting, prime radicalC2×C17×#546C2
socleC22×C17C22×C22⋊C4
cosocleC24×C17C24
hypercenterC2×#546D17
hypocenterC17#22405
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#11762783C2semidirect
2. C22×#10587505C2semidirect
3. #14531633C2semidirect
4. #14529621C2semidirect
5. #14529243C2semidirect
6. #14529238C2semidirect
7. #14528772C2semidirect
8. #14528702C2semidirect
9. #14528699C2semidirect
10. C4×#10587505C2semidirect
12. C2×#10587612C22semidirect
22. C2×#10587505C22semidirect
23. C2×#10587505C22semidirect
27. #11762672C22semidirect
28. #11762669C22semidirect
31. C4×C22⋊Dic17C22semidirect
32. #11762576C22semidirect
33. #11762576C22semidirect
40. C2×C17×#124C4semidirect
41. C2×C17×#123C4semidirect
43. C2×C17×C22⋊Q8C4semidirect
44. C2×C17×#121C4semidirect
45. C2×C17×#121C4semidirect
47. C2×C17×#120C4semidirect
49. C2×C4×D4×C17C4semidirect
51. C22×C22⋊C4×C17C4semidirect
60. C22×Q8×C17C2×C4semidirect
70. C22×D4×C17C2×C4semidirect
71. C22×D4×C17C2×C4semidirect
76. C23×C4×C17C2×C4semidirect
77. C23×C4×C17C2×C4semidirect
78. C23×C4×C17C2×C4semidirect
106. C2×C4⋊C4×C17C2×C4semidirect
107. C2×C4⋊C4×C17C2×C4semidirect
108. C2×C4⋊C4×C17C2×C4semidirect
109. C2×C4⋊C4×C17C2×C4semidirect
120. C2×C22⋊C4×C17C2×C4semidirect
121. C2×C22⋊C4×C17C2×C4semidirect
122. C2×C22⋊C4×C17C2×C4semidirect
123. C2×C22⋊C4×C17C2×C4semidirect
124. C2×C22⋊C4×C17C2×C4semidirect
130. C2×C42×C17C2×C4semidirect
153. #10587505D4semidirect
469. C22×C17#410semidirect
496. C2×#124Dic17semidirect
497. C2×#123Dic17semidirect
499. C2×C22⋊Q8Dic17semidirect
500. C2×#121Dic17semidirect
501. C2×#121Dic17semidirect
503. C2×#120Dic17semidirect
505. C2×C4×D4Dic17semidirect
509. C22×C22⋊C4Dic17semidirect
551. C22×Q8C2×Dic17semidirect
561. C22×D4C2×Dic17semidirect
562. C22×D4C2×Dic17semidirect
568. C23×C4C2×Dic17semidirect
569. C23×C4C2×Dic17semidirect
570. C23×C4C2×Dic17semidirect
601. C2×C4⋊C4C2×Dic17semidirect
602. C2×C4⋊C4C2×Dic17semidirect
603. C2×C4⋊C4C2×Dic17semidirect
604. C2×C4⋊C4C2×Dic17semidirect
624. C2×C22⋊C4C2×Dic17semidirect
625. C2×C22⋊C4C2×Dic17semidirect
626. C2×C22⋊C4C2×Dic17semidirect
627. C2×C22⋊C4C2×Dic17semidirect
628. C2×C22⋊C4C2×Dic17semidirect
636. C2×C42C2×Dic17semidirect
649. C17#22405semidirect
949. C22#11762783semidirect

Maximal subgroups

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

subgroupindex
C2×#117627832
C22×#105875052
#145316332
#145296212
#145292432
#145292382
#145287722
#145287022
#145286992
C4×#105875052
C2×C17×#5462
#2240517