Finite Group Databasebeta

← #17049918

Subgroups — #17049918

Order 4352.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763455C211yesmaximal, characteristic
2C2×#11762887C211yesmaximal, characteristic, complemented
3C2×#11762808C211yesmaximal, characteristic, complemented
4C2×#11762813C211yesmaximal, characteristic, complemented
5#14529716C211yesmaximal, characteristic, complemented
6#14529593C211yesmaximal, characteristic, complemented
7#14529220C211yesmaximal, characteristic, complemented
8#14529215C211yesmaximal, characteristic, complemented
9#14529101C211yesmaximal, characteristic, complemented
10#14529096C211yesmaximal, characteristic, complemented
11#14528791C211yesmaximal, characteristic, complemented
12#14528722C211yesmaximal, characteristic, complemented
13#14528714C211yesmaximal, characteristic, complemented
14C4×#10587480C211yesmaximal, characteristic, complemented
15C17×#2352C211yesmaximal, characteristic, complemented
16C22×#63252C2211yescharacteristic
17C23×D68C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C22×#63223C2211yescharacteristic, complemented
20#11763455—24no—
21#11763455C418yescomplemented
22C2×#10587561C2211yescharacteristic
23C2×#10587580—21no—
24C2×#10587610C2211yescharacteristic
25C2×#10587616C2211yescharacteristic
26C2×#10587570—21no—
27C2×#10587623—21no—
28C2×C4×D68C2211yescharacteristic
29C2×C22⋊C4×D17—21no—
30#11762887—24no—
31C2×C4⋊#3622C2211yescharacteristic, complemented
32#11762813—24no—
33#11762808—24no—
34C2×#10587481C2211yescharacteristic, complemented
35C2×#10587481C2211yescharacteristic, complemented
36C2×#10587481C2211yescharacteristic, complemented
37C2×#10587481C2211yescharacteristic, complemented
38C2×#10587480C2211yescharacteristic
39C2×#10587480C2211yescharacteristic
40C2×#10587480C2211yescharacteristic
41C2×#10587480C2211yescharacteristic
42C2×#10587480C2211yescharacteristic
43C2×#10587480C2211yescharacteristic
44C2×#10587480C2211yescharacteristic
45C2×#10587480C2211yescharacteristic
46C2×C22⋊#3622C2211yescharacteristic
47C2×C22⋊#3622C2211yescharacteristic, complemented
48C2×C4×#3622C2211yescharacteristic, complemented
49#11762571C2211yescharacteristic, complemented
50#11762571C2211yescharacteristic, complemented
51#11762571C2211yescharacteristic, complemented
52#11762571C2211yescharacteristic, complemented
53C2×C4×D4×C17C2211yescharacteristic
54C2×C17×#117C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic, complemented
56C17×#388—21no—
57C17×#387—21no—
58C17×#386—21no—
59C17×#382C2211yescharacteristic, complemented
60C17×#380C2211yescharacteristic
61C17×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C17C2211yescharacteristic, complemented
63C4×C22⋊C4×C17—21no—
64C24×D17—21no—
65C22×D4×C17D411yescharacteristic
66C23×C4×C17—21no—
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C22×C22⋊D17—21no—
70C22×C22⋊D17—21no—
71C2×#63252—22no—
72C2×#63252—22no—
73C2×#63252—22no—
74C2×#63252—41no—
75C2×#63252—41no—
76C2×#63252C2×C414yes—
77C22×D68—22no—
78C22×D68—22no—
79C22×D68—21no—
80C22×D68—22no—
81C22×D68—41no—
82C22×D68—41no—
83C22×D68C2×C414yescomplemented
84C22×D68C2311yescharacteristic
85C22×D68C2311yescharacteristic
86C22×C4×D17—21no—
87C22×C4×D17—21no—
88C22×Dic34C2311yescharacteristic
89C4×D4×C17C2×C414yes—
90C4×D4×C17D414yes—
91C17×#117—22no—
92C17×#117—41no—
93C2×C4⋊C4×C17—22no—
94C2×C4⋊C4×C17—21no—
95C2×C4⋊C4×C17—41no—
96C2×C4⋊C4×C17D411yescharacteristic
97C2×C4⋊C4×C17C2311yescharacteristic
98C2×C4⋊C4×C17C2311yescharacteristic
99C2×C4⋊C4×C17C2311yescharacteristic
100C2×C4⋊C4×C17C2311yescharacteristic
101C2×C22⋊C4×C17—21no—
102C2×C22⋊C4×C17—21no—
103C2×C22⋊C4×C17—21no—
104C2×C22⋊C4×C17D411yescharacteristic
105C2×C22⋊C4×C17D411yescharacteristic
106C2×C42×C17—21no—
107C2×C42×C17—21no—
108C2×C42×C17C2311yescharacteristic
109C2×C22⋊Dic17—21no—
110#10587623—28no—
111#10587616—22no—
112#10587616C2×C414yes—
113C2×#63227—21no—
114C2×#63227—21no—
115C2×#63227—21no—
116C2×#63227—21no—
117C2×C4⋊Dic17C2311yescharacteristic
118#10587610—22no—
119#10587610C2×C414yescomplemented
120C2×#63225—21no—
121C2×#63223—22no—
122C2×#63223—22no—
123C2×#63223—22no—
124C2×#63223—22no—
125C2×#63223—41no—
126C2×#63223—41no—
127C22×#3622C2311yescharacteristic
128C22×#3622C2311yescharacteristic
129C22×#3622C2311yescharacteristic
130C22×#3622C2311yescharacteristic
131#10587580—28no—
132#10587570—28no—
133C22⋊C4×D17—28no—
134#10587561—22no—
135#10587561C2×C414yescomplemented
136C4×D68—22no—
137C4×D68C2×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—41no—
148#10587481—41no—
149#10587480—22no—
150#10587480—22no—
151#10587480—22no—
152#10587480—22no—
153#10587480—22no—
154#10587480—41no—
155#10587480—41no—
156#10587480D414yescomplemented
157C4⋊#3622—22no—
158C4×#3622—22no—
159C24×C17C2×D411yescharacteristic
160C24×C17C2×D411yescharacteristic
161C23×D17—21no—
162C23×D17—21no—
163C23×D17—24no—
164C23×D17—42no—
165C23×D17—42no—
166C23×D17—42no—
167C23×D17—42no—
168C23×D17—81no—
169C23×D17—81no—
170C2×D4×C17—41no—
171C2×D4×C17—41no—
172C2×D4×C17C22⋊C414yes—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—42no—
186C22×C4×C17—42no—
187C22×C4×C17—81no—
188C22×C4×C17C22×C412yes—
189C22×C4×C17C22×C412yes—
190C22×C4×C17C2×D412yes—
191C22×C4×C17C2×D412yes—
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17C2×D411yescharacteristic
194C22×C4×C17C2×D411yescharacteristic
195C22×C4×C17C2×D411yescharacteristic
196C22×C4×C17C2411yescharacteristic
197C2×C22⋊D17—24no—
198C2×C22⋊D17—24no—
199C2×C22⋊D17—42no—
200C2×C22⋊D17—42no—
201C2×C22⋊D17—81no—
202C2×C22⋊D17—81no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205#63252—28no—
206#63252—44no—
207#63252—44no—
208#63252—44no—
209C2×D68—21no—
210C2×D68—21no—
211C2×D68—21no—
212C2×D68—21no—
213C2×D68—21no—
214C2×D68—21no—
215C2×D68—21no—
216C2×D68—28no—
217C2×D68—24no—
218C2×D68—21no—
219C2×D68—44no—
220C2×D68—44no—
221C2×D68—44no—
222C2×D68—42no—
223C2×D68—42no—
224C2×D68C22×C412yes—
225C2×D68C22×C412yes—
226C2×D68C2×D412yes—
227C2×D68#4112yes—
228C2×C4×D17—24no—
229C2×C4×D17—24no—
230C2×C4×D17—42no—
231C2×C4×D17—42no—
232C2×C4×D17—81no—
233C2×C4×D17—81no—
234C2×Dic34—21no—
235C2×Dic34—21no—
236C2×Dic34—21no—
237C2×Dic34—21no—
238C2×Dic34—21no—
239C2×Dic34C22×C412yes—
240C4⋊C4×C17—21no—
241C4⋊C4×C17—21no—
242C4⋊C4×C17—21no—
243C4⋊C4×C17—21no—
244C4⋊C4×C17—21no—
245C4⋊C4×C17—21no—
246C4⋊C4×C17—21no—
247C4⋊C4×C17—42no—
248C4⋊C4×C17C22⋊C414yes—
249C4⋊C4×C17C2×D412yes—
250C22⋊C4×C17—42no—
251C22⋊C4×C17—42no—
252C22⋊C4×C17—81no—
253C22⋊C4×C17C22⋊C414yes—
254C22⋊C4×C17C22⋊C414yes—
255C42×C17—42no—
256C42×C17—81no—
257C42×C17C22×C412yes—
258C42×C17C2×D412yes—
259C22⋊Dic17—24no—
260#63227—24no—
261#63227—24no—
262#63227—24no—
263#63227—24no—
264C4⋊Dic17—21no—
265C4⋊Dic17C22×C412yes—
266#63225—24no—
267#63223—44no—
268#63223—44no—
269C2×#3622—21no—
270C2×#3622—21no—
271C2×#3622—21no—
272C2×#3622—21no—
273C2×#3622—21no—
274C2×#3622—21no—
275C2×#3622—21no—
276C2×#3622—21no—
277C2×#3622—21no—
278C2×#3622—21no—
279C2×#3622—21no—
280C2×#3622C2×D412yes—
281#22427—171nomaximal, Sylow
282C23×C17—21no—
283C23×C17—21no—
284C23×C17—21no—
285C23×C17—21no—
286C23×C17—21no—
287C23×C17—21no—
288C23×C17—21no—
289C23×C17—21no—
290C23×C17—21no—
291C23×C17—21no—
292C23×C17—21no—
293C23×C17—21no—
294C23×C17C2×C22⋊C412yes—
295C23×C17C2×C22⋊C412yes—
296C23×C17C22×D411yescharacteristic
297C22×D17—22no—
298C22×D17—22no—
299C22×D17—22no—
300C22×D17—22no—
301C22×D17—48no—
302C22×D17—41no—
303C22×D17—41no—
304C22×D17—41no—
305C22×D17—41no—
306C22×D17—48no—
307C22×D17—41no—
308C22×D17—41no—
309C22×D17—41no—
310C22×D17—41no—
311C22×D17—41no—
312C22×D17—41no—
313C22×D17—84no—
314C22×D17—84no—
315C22×D17—84no—
316C22×D17—84no—
317C22×D17—84no—
318D4×C17—44no—
319C2×C4×C17—21no—
320C2×C4×C17—21no—
321C2×C4×C17—21no—
322C2×C4×C17—21no—
323C2×C4×C17—21no—
324C2×C4×C17—21no—
325C2×C4×C17—21no—
326C2×C4×C17—21no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—41no—
337C2×C4×C17—41no—
338C2×C4×C17—41no—
339C2×C4×C17—41no—
340C2×C4×C17—41no—
341C2×C4×C17—41no—
342C2×C4×C17—41no—
343C2×C4×C17—41no—
344C2×C4×C17—41no—
345C2×C4×C17—41no—
346C2×C4×C17—41no—
347C2×C4×C17—84no—
348C2×C4×C17C2×C22⋊C412yes—
349C2×C4×C17C2×C22⋊C412yes—
350C2×C4×C17C2×C22⋊C412yes—
351C2×C4×C17C2×C22⋊C412yes—
352C2×C4×C17C23×C411yescharacteristic
353C2×C4×C17C22×D411yescharacteristic
354C2×C4×C17C22×D411yescharacteristic
355C2×C4×C17C2×#4111yescharacteristic
356C2×C4×C17H(5,𝔽2)11yescharacteristic
357C2×C4×C17H(5,𝔽2)11yescharacteristic
358C22⋊D17—48no—
359C22⋊D17—84no—
360C2×Dic17—22no—
361C2×Dic17—22no—
362C2×Dic17—41no—
363C2×Dic17—41no—
364C2×Dic17—41no—
365C2×Dic17—41no—
366D68—22no—
367D68—22no—
368D68—22no—
369D68—22no—
370D68—22no—
371D68—48no—
372D68—41no—
373D68—41no—
374D68C4×D414yes—
375C4×D17—48no—
376C4×D17—84no—
377Dic34—22no—
378Dic34—22no—
379Dic34—41no—
380Dic34—41no—
381#3622—22no—
382#3622—41no—
383#3622—41no—
384#3622—41no—
385C2×#546—171no—
386C2×#436—171no—
387C2×#417—171no—
388C2×#418—171no—
389#2352D1711yescharacteristic, complemented
390#1983—171no—
391#1958—171no—
392#1895—171no—
393#1894—171no—
394#1874—171no—
395#1873—171no—
396#1804—171no—
397#1788—171no—
398#1786—171no—
399C4×#102—171no—
400C22×C17—22no—
401C22×C17—22no—
402C22×C17—22no—
403C22×C17—22no—
404C22×C17—22no—
405C22×C17—22no—
406C22×C17—41no—
407C22×C17—41no—
408C22×C17—41no—
409C22×C17—41no—
410C22×C17—41no—
411C22×C17—41no—
412C22×C17—41no—
413C22×C17—41no—
414C22×C17C22×C22⋊C411yescharacteristic
415C22×C17D4211yescharacteristic
416C22×C17#54611yescharacteristic
417C22×C17#57511yescharacteristic
418C22×C17#57511yescharacteristic
419C22×C17#57611yescharacteristic
420C22×C17#57711yescharacteristic
421C2×D17—24no—
422C2×D17—42no—
423C2×D17—42no—
424C2×D17—42no—
425C2×D17—42no—
426C2×D17—42no—
427C2×D17—42no—
428C2×D17—42no—
429C2×D17—42no—
430C2×D17—42no—
431C2×D17—816no—
432C2×D17—81no—
433C2×D17—81no—
434C2×D17—81no—
435C2×D17—81no—
436C4×C17—22no—
437C4×C17—22no—
438C4×C17—22no—
439C4×C17—22no—
440C4×C17—42no—
441C4×C17—81no—
442C4×C17—81no—
443C4×C17—81no—
444C4×C17C2×C4×D411yescharacteristic
445C4×C17#51811yescharacteristic
446C4×C17D4211yescharacteristic
447C4×C17#54611yescharacteristic
448Dic17—42no—
449Dic17—42no—
450C22×#41—171no—
451C23×D4—171no—
452C22×M16—171no—
453C22×M16—171no—
454#546—178no—
455#546—344no—
456C2×#124—171no—
457C2×#123—341no—
458C2×C22⋊Q8—171no—
459C2×#121—171no—
460C2×#121—341no—
461C2×#120—341no—
462C2×C4×D4—171no—
463C2×C4×D4C2×D1711yescharacteristic
464C2×#117C2×D1711yescharacteristic
465C22×C4⋊C4C2×D1711yescharacteristic, complemented
466C22×C22⋊C4—341no—
467#436—344no—
468C2×C4⋊C8—171no—
469#418—344no—
470#417—344no—
471C2×#103—171no—
472C2×#103—171no—
473C2×#103—171no—
474C2×#103—171no—
475C2×#102—171no—
476C2×#102—171no—
477C2×#102—171no—
478C2×#102—171no—
479C2×#102—171no—
480C2×#102—171no—
481C2×#102—171no—
482C2×#102—171no—
483C2×C22⋊C8—171no—
484C2×C22⋊C8—171no—
485C2×C4×C8—171no—
486#388—21no—
487#387—21no—
488#386—21no—
489#382C2×D1711yescharacteristic, complemented
490#380C2×D1711yescharacteristic
491#380C2×D1711yescharacteristic, complemented
492C4×C4⋊C4C2×D1711yescharacteristic, complemented
493C4×C22⋊C4—21no—
494#340—171no—
495#340—171no—
496#340—171no—
497#340—171no—
498C2×C17—42no—
499C2×C17—42no—
500C2×C17D4×C22⋊C411yescharacteristic
501C2×C17#289611yescharacteristic
502C2×C17#289711yescharacteristic
503C2×C17#327311yescharacteristic
504C2×C17#327511yescharacteristic
505C2×C17#332211yescharacteristic
506C2×C17#332311yescharacteristic
507D17—44no—
508D17—82no—
509C25—341no—
510C2×#41—174no—
511C2×#41—342no—
512C2×#41—342no—
513C2×#41—342no—
514C2×#41—681no—
515C2×#41—681no—
516C22×Q8—171no—
517C22×D4—174no—
518C22×D4—171no—
519C22×D4—171no—
520C22×D4—342no—
521C22×D4—342no—
522C22×D4—341no—
523C22×D4—341no—
524C22×D4—342no—
525C22×D4—341no—
526C22×D4—681no—
527C22×D4—681no—
528C22×D4C22⋊D1711yescharacteristic
529C23×C4—21no—
530C23×C4—341no—
531C23×C4—341no—
532C23×C4C22×D1711yescharacteristic
533C23×C4C22×D1711yescharacteristic
534C2×M16—342no—
535C2×M16—342no—
536C2×M16—342no—
537C2×M16—342no—
538C2×M16—681no—
539C2×M16—681no—
540C22×C8—171no—
541C22×C8—171no—
542C22×C8—171no—
543C22×C8—171no—
544#124—174no—
545#124—342no—
546#123—348no—
547C22⋊Q8—174no—
548C22⋊Q8—342no—
549#121—174no—
550#121—342no—
551#121—348no—
552#120—348no—
553C4×D4—174no—
554C4×D4—342no—
555C4×D4C4×D1714yes—
556C4×D4D6814yes—
557#117—22no—
558#117—41no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—171no—
563C2×C4⋊C4—341no—
564C2×C4⋊C4C22⋊D1711yescharacteristic
565C2×C4⋊C4C22×D1711yescharacteristic
566C2×C4⋊C4C22×D1711yescharacteristic
567C2×C4⋊C4C22×D1711yescharacteristic
568C2×C4⋊C4C22×D1711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—341no—
573C2×C22⋊C4—341no—
574C2×C22⋊C4—341no—
575C2×C22⋊C4—341no—
576C2×C22⋊C4—341no—
577C2×C22⋊C4—348no—
578C2×C22⋊C4C22⋊D1711yescharacteristic
579C2×C22⋊C4C22⋊D1711yescharacteristic
580C2×C42—21no—
581C2×C42—21no—
582C2×C42C22×D1711yescharacteristic
583C4⋊C8—342no—
584#103—342no—
585#103—342no—
586#103—681no—
587#103—681no—
588#102—174no—
589#102—342no—
590#102—342no—
591#102—342no—
592#102—342no—
593#102—342no—
594#102—681no—
595#102—681no—
596C22⋊C8—342no—
597C22⋊C8—342no—
598C4×C8—342no—
599#95—21no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604C17#2242711yescharacteristic, complemented, Sylow
605C24—341no—
606C24—341no—
607C24—344no—
608C24—682no—
609C24—682no—
610C24—682no—
611C24—682no—
612C24—1361no—
613C24—1361no—
614C24C2×C22⋊D1711yescharacteristic
615C24C2×C22⋊D1711yescharacteristic
616#41—348no—
617#41—684no—
618#41—684no—
619#41—684no—
620C2×Q8—172no—
621C2×Q8—341no—
622C2×Q8—341no—
623C2×Q8—341no—
624C2×Q8—341no—
625C2×Q8—341no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—172no—
629C2×D4—172no—
630C2×D4—172no—
631C2×D4—172no—
632C2×D4—348no—
633C2×D4—344no—
634C2×D4—344no—
635C2×D4—341no—
636C2×D4—341no—
637C2×D4—341no—
638C2×D4—341no—
639C2×D4—341no—
640C2×D4—341no—
641C2×D4—341no—
642C2×D4—341no—
643C2×D4—344no—
644C2×D4—684no—
645C2×D4—684no—
646C2×D4—684no—
647C2×D4—682no—
648C2×D4—682no—
649C2×D4—682no—
650C2×D4—682no—
651C2×D4—1361no—
652C2×D4—1361no—
653C2×D4#6322714yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—341no—
670C22×C4—341no—
671C22×C4—344no—
672C22×C4—344no—
673C22×C4—682no—
674C22×C4—682no—
675C22×C4—1361no—
676C22×C4—1361no—
677C22×C4C2×C4×D1712yes—
678C22×C4C2×C4×D1712yes—
679C22×C4C2×D6812yes—
680C22×C4C2×D6812yes—
681C22×C4C2×C22⋊D1711yescharacteristic
682C22×C4C2×C22⋊D1711yescharacteristic
683C22×C4C2×C22⋊D1711yescharacteristic
684C22×C4C2×C22⋊D1711yescharacteristic
685C22×C4C23×D1711yescharacteristic
686M16—684no—
687M16—684no—
688C2×C8—172no—
689C2×C8—341no—
690C2×C8—341no—
691C2×C8—341no—
692C2×C8—341no—
693C2×C8—341no—
694C2×C8—341no—
695C2×C8—341no—
696C2×C8—341no—
697C2×C8—341no—
698C2×C8—341no—
699C2×C8—341no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4—172no—
709C4⋊C4—341no—
710C4⋊C4—344no—
711C4⋊C4#6322714yes—
712C4⋊C4D4×D1712yes—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—81no—
716C22⋊C4—344no—
717C22⋊C4—344no—
718C22⋊C4—344no—
719C22⋊C4—344no—
720C22⋊C4—344no—
721C22⋊C4#6322714yes—
722C22⋊C4#6322714yes—
723C42—42no—
724C42—81no—
725C42C2×C4×D1712yes—
726C42C2×D6812yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—342no—
740C23—342no—
741C23—342no—
742C23—342no—
743C23—688no—
744C23—688no—
745C23—681no—
746C23—681no—
747C23—681no—
748C23—681no—
749C23—681no—
750C23—681no—
751C23—681no—
752C23—681no—
753C23—681no—
754C23—681no—
755C23—1364no—
756C23—1364no—
757C23—1364no—
758C23—1364no—
759C23—1364no—
760C23C2×#6322712yes—
761C23C2×#6322712yes—
762C23C22×C22⋊D1711yescharacteristic
763Q8—342no—
764Q8—342no—
765Q8—681no—
766Q8—681no—
767D4—44no—
768D4—174no—
769D4—342no—
770D4—342no—
771D4—342no—
772D4—342no—
773D4—342no—
774D4—688no—
775D4—688no—
776D4—681no—
777D4—681no—
778D4—1364no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—84no—
808C2×C4—342no—
809C2×C4—342no—
810C2×C4—688no—
811C2×C4—681no—
812C2×C4—681no—
813C2×C4—681no—
814C2×C4—681no—
815C2×C4—1364no—
816C2×C4C2×#6322712yes—
817C2×C4C2×#6322712yes—
818C2×C4C2×#6322712yes—
819C2×C4C2×#6322712yes—
820C2×C4C22×C4×D1711yescharacteristic
821C2×C4C22×D6811yescharacteristic
822C2×C4C2×D4×D1711yescharacteristic
823C2×C4#1058769111yescharacteristic
824C2×C4#41×D1711yescharacteristic
825C2×C4#1058769611yescharacteristic
826C8—342no—
827C8—681no—
828C8—681no—
829C8—681no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—344no—
845C22—682no—
846C22—682no—
847C22—682no—
848C22—682no—
849C22—682no—
850C22—682no—
851C22—682no—
852C22—682no—
853C22—682no—
854C22—13616no—
855C22—1361no—
856C22—1361no—
857C22—1361no—
858C22—1361no—
859C22C22×#6322711yescharacteristic
860C22D4×C22⋊D1711yescharacteristic
861C22#1176344711yescharacteristic
862C22#1176360711yescharacteristic
863C22#1176360711yescharacteristic
864C22#1176361211yescharacteristic
865C22#1176361711yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—682no—
875C4—682no—
876C4C4×D4×D1711yescharacteristic
877C4#1176328111yescharacteristic
878C4D4×D6811yescharacteristic
879C4#1176345411yescharacteristic
880C2—42no—
881C2—42no—
882C2—684no—
883C2—1362no—
884C2D4×#6322711yescharacteristic
885C2#1453730111yescharacteristic
886C2#1453730711yescharacteristic
887C2#1454039111yescharacteristic
888C2#1454041611yescharacteristic
889C2#1454097911yescharacteristic
890C2#1454099411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2352C2
socleC23×C17C22×D4
prime radicalC2×#11763455C2
cosocleC22×C4×C17C24
hypercenter#2352D17
hypocenterC17#22427
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
2. C2×#11762887C2semidirect
3. C2×#11762808C2semidirect
4. C2×#11762813C2semidirect
5. #14529716C2semidirect
6. #14529593C2semidirect
7. #14529220C2semidirect
8. #14529215C2semidirect
9. #14529101C2semidirect
10. #14529096C2semidirect
11. #14528791C2semidirect
12. #14528722C2semidirect
13. #14528714C2semidirect
14. C4×#10587480C2semidirect
15. C17×#2352C2semidirect
19. C22×#63223C22semidirect
21. #11763455C4semidirect
31. C2×C4⋊#3622C22semidirect
34. C2×#10587481C22semidirect
35. C2×#10587481C22semidirect
36. C2×#10587481C22semidirect
37. C2×#10587481C22semidirect
47. C2×C22⋊#3622C22semidirect
48. C2×C4×#3622C22semidirect
49. #11762571C22semidirect
50. #11762571C22semidirect
51. #11762571C22semidirect
52. #11762571C22semidirect
55. C22×C4⋊C4×C17C22semidirect
59. C17×#382C22semidirect
61. C17×#380C22semidirect
62. C4×C4⋊C4×C17C22semidirect
83. C22×D68C2×C4semidirect
119. #10587610C2×C4semidirect
135. #10587561C2×C4semidirect
137. C4×D68C2×C4semidirect
156. #10587480D4semidirect
389. #2352D17semidirect
465. C22×C4⋊C4C2×D17semidirect
489. #382C2×D17semidirect
491. #380C2×D17semidirect
492. C4×C4⋊C4C2×D17semidirect
604. C17#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#117634552
C2×#117628872
C2×#117628082
C2×#117628132
#145297162
#145295932
#145292202
#145292152
#145291012
#145290962
#145287912
#145287222
#145287142
C4×#105874802
C17×#23522
#2242717