Finite Group Databasebeta

← #17049888

Subgroups — #17049888

Order 4352.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic34C211yesmaximal, characteristic
2C2×#11762881C211yesmaximal, characteristic
3C2×#11762817C211yesmaximal, characteristic, complemented
4C22×#10587481C211yesmaximal, characteristic, complemented
5#14529707C211yesmaximal, characteristic, complemented
6#14529603C211yesmaximal, characteristic, complemented
7#14529215C211yesmaximal, characteristic, complemented
8#14529205C211yesmaximal, characteristic, complemented
9#14529096C211yesmaximal, characteristic, complemented
10#14529091C211yesmaximal, characteristic, complemented
11#14528796C211yesmaximal, characteristic, complemented
12#14528718C211yesmaximal, characteristic, complemented
13#14528718C211yesmaximal, characteristic, complemented
14#14528617C211yesmaximal, characteristic, complemented
15C17×#2352C211yesmaximal, characteristic
16C23×Dic34C2211yescharacteristic
17C23×Dic34C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C23×#3622C2211yescharacteristic
20D4×Dic34—24no—
21D4×Dic34C418yescomplemented
22C2×#10587555C2211yescharacteristic
23C2×#10587574—21no—
24C2×#10587610C2211yescharacteristic
25C2×#10587610C2211yescharacteristic
26C2×#10587564—21no—
27C2×#10587564—21no—
28C2×C4×Dic34C2211yescharacteristic
29C2×D4×Dic17—21no—
30#11762881—24no—
31C2×C4⋊#3622C2211yescharacteristic
32#11762817—24no—
33C2×#10587481—24no—
34C2×#10587481C2211yescharacteristic
35C2×#10587481C2211yescharacteristic
36C2×#10587481C2211yescharacteristic
37C2×#10587481C2211yescharacteristic
38C2×#10587481C2211yescharacteristic
39C2×#10587481C2211yescharacteristic
40C2×#10587481C2211yescharacteristic
41C2×#10587481C2211yescharacteristic
42C2×#10587481C2211yescharacteristic
43C2×#10587481C2211yescharacteristic
44C2×#10587481C2211yescharacteristic
45C2×#10587481C2211yescharacteristic
46C2×C22⋊#3622C2211yescharacteristic
47C2×C22⋊#3622C2211yescharacteristic
48C2×#10587474C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53C2×C4×D4×C17C2211yescharacteristic
54C2×C17×#117C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C17×#388—21no—
57C17×#387—21no—
58C17×#386—21no—
59C17×#382C2211yescharacteristic
60C17×#380C2211yescharacteristic
61C17×#380C2211yescharacteristic
62C4×C4⋊C4×C17C2211yescharacteristic
63C4×C22⋊C4×C17—21no—
64C22×D4×C17D411yescharacteristic
65C23×C4×C17—21no—
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×Dic17—21no—
69C23×Dic17—21no—
70C22×Dic34—22no—
71C22×Dic34—22no—
72C22×Dic34—22no—
73C22×Dic34—22no—
74C22×Dic34—22no—
75C22×Dic34—22no—
76C22×Dic34—21no—
77C22×Dic34—21no—
78C22×Dic34—41no—
79C22×Dic34—41no—
80C22×Dic34—41no—
81C22×Dic34—41no—
82C22×Dic34C2×C414yes—
83C22×Dic34C2×C414yescomplemented
84C22×Dic34C2311yescharacteristic
85C22×Dic34C2311yescharacteristic
86C22×Dic34C2311yescharacteristic
87C4×D4×C17C2×C414yes—
88C4×D4×C17D414yes—
89C17×#117—22no—
90C17×#117—41no—
91C2×C4⋊C4×C17—22no—
92C2×C4⋊C4×C17—21no—
93C2×C4⋊C4×C17—41no—
94C2×C4⋊C4×C17D411yescharacteristic
95C2×C4⋊C4×C17C2311yescharacteristic
96C2×C4⋊C4×C17C2311yescharacteristic
97C2×C4⋊C4×C17C2311yescharacteristic
98C2×C4⋊C4×C17C2311yescharacteristic
99C2×C22⋊C4×C17—21no—
100C2×C22⋊C4×C17—21no—
101C2×C22⋊C4×C17—21no—
102C2×C22⋊C4×C17D411yescharacteristic
103C2×C22⋊C4×C17D411yescharacteristic
104C2×C42×C17—21no—
105C2×C42×C17—21no—
106C2×C42×C17C2311yescharacteristic
107C2×C22⋊Dic17—21no—
108C2×C22⋊Dic17—21no—
109D4×Dic17—28no—
110C2×C4⋊Dic17—21no—
111C2×C4⋊Dic17—21no—
112C2×C4⋊Dic17C2311yescharacteristic
113#10587610—22no—
114#10587610—22no—
115#10587610C2×C414yes—
116#10587610C2×C414yescomplemented
117C2×#63225—21no—
118C2×#63225—21no—
119C2×#63225—21no—
120C2×C4×Dic17—21no—
121C2×#63223—22no—
122C2×#63223—22no—
123C2×#63223—41no—
124C22×#3622—22no—
125C22×#3622—22no—
126C22×#3622—41no—
127C22×#3622C2311yescharacteristic
128C22×#3622C2311yescharacteristic
129C22×#3622C2311yescharacteristic
130C22×#3622C2311yescharacteristic
131#10587574—28no—
132#10587564—28no—
133#10587564—28no—
134#10587555—22no—
135#10587555C2×C414yescomplemented
136C4×Dic34—22no—
137C4×Dic34C2×C414yescomplemented
138C17×#95—21no—
139C17×#95—21no—
140C17×#95—21no—
141C17×#95—21no—
142C17×#95—21no—
143C22⋊#3622—22no—
144C22⋊#3622—22no—
145#10587481—22no—
146#10587481—22no—
147#10587481—22no—
148#10587481—22no—
149#10587481—22no—
150#10587481—22no—
151#10587481—22no—
152#10587481—41no—
153#10587481—41no—
154#10587481—41no—
155#10587481—41no—
156#10587481D414yescomplemented
157C4⋊#3622—22no—
158#10587474—22no—
159C24×C17C2×D411yescharacteristic
160C24×C17C2×D411yescharacteristic
161C2×D4×C17—22no—
162C2×D4×C17—22no—
163C2×D4×C17C22⋊C414yes—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—42no—
177C22×C4×C17—42no—
178C22×C4×C17—81no—
179C22×C4×C17C22×C412yes—
180C22×C4×C17C22×C412yes—
181C22×C4×C17C2×D412yes—
182C22×C4×C17C2×D412yes—
183C22×C4×C17C2×D411yescharacteristic
184C22×C4×C17C2×D411yescharacteristic
185C22×C4×C17C2×D411yescharacteristic
186C22×C4×C17C2×D411yescharacteristic
187C22×C4×C17C2411yescharacteristic
188C22×Dic17—21no—
189C22×Dic17—24no—
190C22×Dic17—24no—
191C22×Dic17—21no—
192C22×Dic17—21no—
193C22×Dic17—21no—
194C22×Dic17—42no—
195C22×Dic17—42no—
196C22×Dic17—42no—
197C22×Dic17—42no—
198C2×Dic34—21no—
199C2×Dic34—21no—
200C2×Dic34—21no—
201C2×Dic34—21no—
202C2×Dic34—21no—
203C2×Dic34—21no—
204C2×Dic34—21no—
205C2×Dic34—21no—
206C2×Dic34—21no—
207C2×Dic34—21no—
208C2×Dic34—21no—
209C2×Dic34—28no—
210C2×Dic34—28no—
211C2×Dic34—24no—
212C2×Dic34—24no—
213C2×Dic34—21no—
214C2×Dic34—21no—
215C2×Dic34—44no—
216C2×Dic34—44no—
217C2×Dic34—44no—
218C2×Dic34—44no—
219C2×Dic34—44no—
220C2×Dic34—44no—
221C2×Dic34—42no—
222C2×Dic34—42no—
223C2×Dic34—42no—
224C2×Dic34—42no—
225C2×Dic34C22×C412yes—
226C2×Dic34C22×C412yes—
227C2×Dic34C22×C412yes—
228C2×Dic34C2×D412yes—
229C2×Dic34#4112yes—
230C4⋊C4×C17—21no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17—21no—
233C4⋊C4×C17—21no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17—21no—
236C4⋊C4×C17—21no—
237C4⋊C4×C17—42no—
238C4⋊C4×C17C22⋊C414yes—
239C4⋊C4×C17C2×D412yes—
240C22⋊C4×C17—42no—
241C22⋊C4×C17—42no—
242C22⋊C4×C17—81no—
243C22⋊C4×C17C22⋊C414yes—
244C22⋊C4×C17C22⋊C414yes—
245C42×C17—42no—
246C42×C17—81no—
247C42×C17C22×C412yes—
248C42×C17C2×D412yes—
249C22⋊Dic17—24no—
250C22⋊Dic17—24no—
251C4⋊Dic17—24no—
252C4⋊Dic17—24no—
253C4⋊Dic17—21no—
254C4⋊Dic17C22×C412yes—
255#63225—24no—
256#63225—24no—
257#63225—24no—
258C4×Dic17—24no—
259#63223—44no—
260C2×#3622—21no—
261C2×#3622—21no—
262C2×#3622—21no—
263C2×#3622—21no—
264C2×#3622—21no—
265C2×#3622—21no—
266C2×#3622—21no—
267C2×#3622—21no—
268C2×#3622—21no—
269C2×#3622—21no—
270C2×#3622—21no—
271C2×#3622—44no—
272C2×#3622C2×D412yes—
273#22425—171nomaximal, Sylow
274C23×C17—21no—
275C23×C17—21no—
276C23×C17—21no—
277C23×C17—21no—
278C23×C17—21no—
279C23×C17—21no—
280C23×C17—21no—
281C23×C17—21no—
282C23×C17—21no—
283C23×C17—21no—
284C23×C17C2×C22⋊C412yes—
285C23×C17C2×C22⋊C412yes—
286C23×C17#13712yes—
287C23×C17#13712yes—
288C23×C17C22×D411yescharacteristic
289D4×C17—28no—
290C2×C4×C17—21no—
291C2×C4×C17—21no—
292C2×C4×C17—21no—
293C2×C4×C17—21no—
294C2×C4×C17—21no—
295C2×C4×C17—21no—
296C2×C4×C17—21no—
297C2×C4×C17—21no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—41no—
308C2×C4×C17—41no—
309C2×C4×C17—41no—
310C2×C4×C17—41no—
311C2×C4×C17—41no—
312C2×C4×C17—41no—
313C2×C4×C17—41no—
314C2×C4×C17—41no—
315C2×C4×C17—41no—
316C2×C4×C17—41no—
317C2×C4×C17—41no—
318C2×C4×C17—84no—
319C2×C4×C17C2×C22⋊C412yes—
320C2×C4×C17C2×C22⋊C412yes—
321C2×C4×C17C2×C22⋊C412yes—
322C2×C4×C17C2×C22⋊C412yes—
323C2×C4×C17C23×C411yescharacteristic
324C2×C4×C17C22×D411yescharacteristic
325C2×C4×C17C22×D411yescharacteristic
326C2×C4×C17C2×#4111yescharacteristic
327C2×C4×C17H(5,𝔽2)11yescharacteristic
328C2×C4×C17H(5,𝔽2)11yescharacteristic
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—48no—
336C2×Dic17—48no—
337C2×Dic17—41no—
338C2×Dic17—41no—
339C2×Dic17—41no—
340C2×Dic17—41no—
341C2×Dic17—41no—
342C2×Dic17—41no—
343Dic34—22no—
344Dic34—22no—
345Dic34—22no—
346Dic34—22no—
347Dic34—22no—
348Dic34—22no—
349Dic34—22no—
350Dic34—48no—
351Dic34—48no—
352Dic34—41no—
353Dic34—41no—
354Dic34—41no—
355Dic34—41no—
356Dic34C4×D414yes—
357#3622—22no—
358#3622—41no—
359#3622—41no—
360#3622—41no—
361C2×D4×Q8—171no—
362C2×#435—171no—
363C2×#419—171no—
364C22×#103—171no—
365#2352D1711yescharacteristic
366#1981—171no—
367#1960—171no—
368#1894—171no—
369#1892—171no—
370#1873—171no—
371#1872—171no—
372#1805—171no—
373#1787—171no—
374#1787—171no—
375#1763—171no—
376C22×C17—22no—
377C22×C17—22no—
378C22×C17—22no—
379C22×C17—22no—
380C22×C17—22no—
381C22×C17—22no—
382C22×C17—22no—
383C22×C17—22no—
384C22×C17—22no—
385C22×C17—41no—
386C22×C17—41no—
387C22×C17—41no—
388C22×C17—41no—
389C22×C17#41914yescomplemented
390C22×C17C22×C22⋊C411yescharacteristic
391C22×C17D4211yescharacteristic
392C22×C17#54611yescharacteristic
393C22×C17C2×#13711yescharacteristic
394C22×C17C2×#13711yescharacteristic
395C22×C17#57711yescharacteristic
396C22×C17#57811yescharacteristic
397C4×C17—22no—
398C4×C17—22no—
399C4×C17—22no—
400C4×C17—22no—
401C4×C17—42no—
402C4×C17—81no—
403C4×C17—81no—
404C4×C17—81no—
405C4×C17C2×C4×D411yescharacteristic
406C4×C17#51811yescharacteristic
407C4×C17D4211yescharacteristic
408C4×C17#54611yescharacteristic
409Dic17—24no—
410Dic17—42no—
411Dic17—42no—
412Dic17—42no—
413C23×Q8—171no—
414C23×Q8—171no—
415C22×M16—171no—
416C23×C8—171no—
417D4×Q8—178no—
418D4×Q8—344no—
419C2×C4⋊Q8—171no—
420C2×C4⋊Q8—341no—
421C2×C22⋊Q8—171no—
422C2×C22⋊Q8—171no—
423C2×C22⋊Q8—341no—
424C2×C22⋊Q8—341no—
425C2×C4×Q8—171no—
426C2×C4×D4—341no—
427C2×C4×D4C2×D1711yescharacteristic
428C2×#117C2×D1711yescharacteristic
429C22×C4⋊C4C2×D1711yescharacteristic
430#435—344no—
431C2×C4⋊C8—171no—
432#419—344no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#103—171no—
436C2×#103—171no—
437C2×#103—171no—
438C2×#103—171no—
439C2×#103—171no—
440C2×#103—171no—
441C2×#103—171no—
442C2×#103—171no—
443C2×#103—171no—
444C2×#103—171no—
445C2×#103—344no—
446C2×C22⋊C8—171no—
447C2×C22⋊C8—171no—
448C2×#97—171no—
449#388—21no—
450#387—21no—
451#386—21no—
452#382C2×D1711yescharacteristic
453#380C2×D1711yescharacteristic
454#380C2×D1711yescharacteristic
455C4×C4⋊C4C2×D1711yescharacteristic
456C4×C22⋊C4—21no—
457#340—171no—
458#340—171no—
459#340—171no—
460#340—171no—
461C2×C17—24no—
462C2×C17—42no—
463C2×C17D4×C22⋊C411yescharacteristic
464C2×C17C2×#41911yescharacteristic
465C2×C17#289811yescharacteristic
466C2×C17#326611yescharacteristic
467C2×C17#327011yescharacteristic
468C2×C17#331211yescharacteristic
469C2×C17#332011yescharacteristic
470C22×Q8—174no—
471C22×Q8—174no—
472C22×Q8—171no—
473C22×Q8—171no—
474C22×Q8—171no—
475C22×Q8—342no—
476C22×Q8—342no—
477C22×Q8—342no—
478C22×Q8—342no—
479C22×Q8—342no—
480C22×Q8—342no—
481C22×Q8—341no—
482C22×Q8—341no—
483C22×Q8—681no—
484C22×Q8—681no—
485C22×Q8—681no—
486C22×Q8—681no—
487C22×D4C22⋊D1711yescharacteristic
488C23×C4—21no—
489C23×C4—341no—
490C23×C4—341no—
491C23×C4C22×D1711yescharacteristic
492C23×C4C22×D1711yescharacteristic
493C2×M16—342no—
494C2×M16—342no—
495C2×M16—681no—
496C22×C8—171no—
497C22×C8—171no—
498C22×C8—171no—
499C22×C8—171no—
500C22×C8—342no—
501C22×C8—342no—
502C22×C8—681no—
503C4⋊Q8—174no—
504C4⋊Q8—348no—
505C4⋊Q8—342no—
506C22⋊Q8—174no—
507C22⋊Q8—174no—
508C22⋊Q8—342no—
509C22⋊Q8—342no—
510C22⋊Q8—348no—
511C22⋊Q8—348no—
512C4×Q8—174no—
513C4×Q8—342no—
514C4×D4—348no—
515C4×D4C4×D1714yes—
516C4×D4D6814yes—
517#117—22no—
518#117—41no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—171no—
523C2×C4⋊C4—341no—
524C2×C4⋊C4—341no—
525C2×C4⋊C4—341no—
526C2×C4⋊C4—341no—
527C2×C4⋊C4—341no—
528C2×C4⋊C4C22⋊D1711yescharacteristic
529C2×C4⋊C4C22×D1711yescharacteristic
530C2×C4⋊C4C22×D1711yescharacteristic
531C2×C4⋊C4C22×D1711yescharacteristic
532C2×C4⋊C4C22×D1711yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—341no—
537C2×C22⋊C4—341no—
538C2×C22⋊C4C22⋊D1711yescharacteristic
539C2×C22⋊C4C22⋊D1711yescharacteristic
540C2×C42—21no—
541C2×C42—21no—
542C2×C42—341no—
543C2×C42C22×D1711yescharacteristic
544C4⋊C8—342no—
545#103—174no—
546#103—342no—
547#103—342no—
548#103—342no—
549#103—342no—
550#103—342no—
551#103—342no—
552#103—342no—
553#103—681no—
554#103—681no—
555#103—681no—
556#103—681no—
557C22⋊C8—342no—
558C22⋊C8—342no—
559#97—342no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565C17#2242511yescharacteristic, complemented, Sylow
566C24C2×C22⋊D1711yescharacteristic
567C24C2×C22⋊D1711yescharacteristic
568C2×Q8—172no—
569C2×Q8—172no—
570C2×Q8—172no—
571C2×Q8—172no—
572C2×Q8—172no—
573C2×Q8—348no—
574C2×Q8—348no—
575C2×Q8—341no—
576C2×Q8—341no—
577C2×Q8—341no—
578C2×Q8—341no—
579C2×Q8—341no—
580C2×Q8—344no—
581C2×Q8—344no—
582C2×Q8—341no—
583C2×Q8—341no—
584C2×Q8—341no—
585C2×Q8—341no—
586C2×Q8—341no—
587C2×Q8—341no—
588C2×Q8—341no—
589C2×Q8—341no—
590C2×Q8—682no—
591C2×Q8—682no—
592C2×Q8—682no—
593C2×Q8—682no—
594C2×Q8—684no—
595C2×Q8—684no—
596C2×Q8—684no—
597C2×Q8—684no—
598C2×Q8—684no—
599C2×Q8—684no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4#6322714yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—341no—
619C22×C4—341no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—344no—
623C22×C4—344no—
624C22×C4—682no—
625C22×C4—682no—
626C22×C4—682no—
627C22×C4—682no—
628C22×C4C2×C4×D1712yes—
629C22×C4C2×C4×D1712yes—
630C22×C4C2×D6812yes—
631C22×C4C2×D6812yes—
632C22×C4C2×C22⋊D1711yescharacteristic
633C22×C4C2×C22⋊D1711yescharacteristic
634C22×C4C2×C22⋊D1711yescharacteristic
635C22×C4C2×C22⋊D1711yescharacteristic
636C22×C4C23×D1711yescharacteristic
637M16—684no—
638C2×C8—172no—
639C2×C8—341no—
640C2×C8—341no—
641C2×C8—341no—
642C2×C8—341no—
643C2×C8—341no—
644C2×C8—341no—
645C2×C8—341no—
646C2×C8—341no—
647C2×C8—341no—
648C2×C8—341no—
649C2×C8—341no—
650C2×C8—684no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—42no—
659C4⋊C4—172no—
660C4⋊C4—341no—
661C4⋊C4—344no—
662C4⋊C4—344no—
663C4⋊C4—344no—
664C4⋊C4—344no—
665C4⋊C4—344no—
666C4⋊C4#6322714yes—
667C4⋊C4D4×D1712yes—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—81no—
671C22⋊C4—344no—
672C22⋊C4—344no—
673C22⋊C4#6322714yes—
674C22⋊C4#6322714yes—
675C42—42no—
676C42—81no—
677C42—344no—
678C42C2×C4×D1712yes—
679C42C2×D6812yes—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23C2×#6322712yes—
691C23C2×#6322712yes—
692C23#1058763712yes—
693C23#1058763712yes—
694C23C22×C22⋊D1711yescharacteristic
695Q8—174no—
696Q8—342no—
697Q8—342no—
698Q8—342no—
699Q8—342no—
700Q8—342no—
701Q8—342no—
702Q8—342no—
703Q8—688no—
704Q8—688no—
705Q8—681no—
706Q8—681no—
707Q8—681no—
708Q8—681no—
709D4—28no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—342no—
744C2×C4—342no—
745C2×C4—688no—
746C2×C4—688no—
747C2×C4—681no—
748C2×C4—681no—
749C2×C4—681no—
750C2×C4—681no—
751C2×C4—681no—
752C2×C4—681no—
753C2×C4C2×#6322712yes—
754C2×C4C2×#6322712yes—
755C2×C4C2×#6322712yes—
756C2×C4C2×#6322712yes—
757C2×C4C22×C4×D1711yescharacteristic
758C2×C4C22×D6811yescharacteristic
759C2×C4C2×D4×D1711yescharacteristic
760C2×C4#1058769111yescharacteristic
761C2×C4#41×D1711yescharacteristic
762C2×C4#1058769611yescharacteristic
763C8—342no—
764C8—681no—
765C8—681no—
766C8—681no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#1176281714yescomplemented
781C22C22×#6322711yescharacteristic
782C22D4×C22⋊D1711yescharacteristic
783C22#1176344711yescharacteristic
784C22C2×#1058763711yescharacteristic
785C22C2×#1058763711yescharacteristic
786C22#1176362011yescharacteristic
787C22#1176362411yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—42no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—344no—
797C4—682no—
798C4—682no—
799C4—682no—
800C4C4×D4×D1711yescharacteristic
801C4#1176328111yescharacteristic
802C4D4×D6811yescharacteristic
803C4#1176345411yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×#6322711yescharacteristic
807C2C2×#1176281711yescharacteristic
808C2#1453731411yescharacteristic
809C2#1454029011yescharacteristic
810C2#1454035011yescharacteristic
811C2#1454082911yescharacteristic
812C2#1454094911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2352C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
cosocleC22×C4×C17C24
hypercenter#2352D17
hypocenterC17#22425
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. C2×#11762817C2semidirect
4. C22×#10587481C2semidirect
5. #14529707C2semidirect
6. #14529603C2semidirect
7. #14529215C2semidirect
8. #14529205C2semidirect
9. #14529096C2semidirect
10. #14529091C2semidirect
11. #14528796C2semidirect
12. #14528718C2semidirect
13. #14528718C2semidirect
14. #14528617C2semidirect
21. D4×Dic34C4semidirect
83. C22×Dic34C2×C4semidirect
116. #10587610C2×C4semidirect
135. #10587555C2×C4semidirect
137. C4×Dic34C2×C4semidirect
156. #10587481D4semidirect
389. C22×C17#419semidirect
565. C17#22425semidirect
780. C22#11762817semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic342
C2×#117628812
C2×#117628172
C22×#105874812
#145297072
#145296032
#145292152
#145292052
#145290962
#145290912
#145287962
#145287182
#145286172
C17×#23522
#2242517