Finite Group Databasebeta

← #16957183

Subgroups — #16957183

Order 4352.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2C2×#11762685C211yesmaximal, characteristic
3C2×#11762685C211yesmaximal, characteristic
4C2×#11762683C211yesmaximal, characteristic, complemented
5C2×#11762682C211yesmaximal, characteristic, complemented
6C2×#11762668C211yesmaximal, characteristic, complemented
7C2×#95×D17C211yesmaximal, characteristic, complemented
8#14527048C211yesmaximal, characteristic, complemented
9#14527042C211yesmaximal, characteristic, complemented
10#14527029C211yesmaximal, characteristic, complemented
11#14527027C211yesmaximal, characteristic, complemented
12#14527019C211yesmaximal, characteristic, complemented
13#14527015C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C2×C4×C22⋊D17—24no—
21C2×C4×C22⋊D17—24no—
22C2×C4×C22⋊D17—24no—
23C22×C4⋊Dic17C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762685—24no—
36#11762685C418yescomplemented
37#11762683—24no—
38#11762682—24no—
39#11762668—24no—
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52#95×D17—24no—
53C24×C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C24×D17C2311yescharacteristic
62C23×C4×C17—22no—
63C23×C4×C17—22no—
64C23×C4×C17—22no—
65C23×C4×C17—22no—
66C23×C4×C17—22no—
67C23×C4×C17—41no—
68C23×C4×C17—41no—
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C22×C22⋊D17—22no—
76C22×C22⋊D17—22no—
77C22×C22⋊D17—22no—
78C22×C22⋊D17—22no—
79C22×C22⋊D17C2×C414yes—
80C22×C22⋊D17D414yes—
81C22×C22⋊D17Q814yes—
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—22no—
94C22×C4×D17—22no—
95C22×C4×D17—22no—
96C22×C4×D17—22no—
97C22×C4×D17—22no—
98C22×C4×D17—22no—
99C22×C4×D17—22no—
100C22×C4×D17—22no—
101C22×C4×D17—22no—
102C22×C4×D17—41no—
103C22×C4×D17—41no—
104C22×C4×D17—41no—
105C22×C4×D17—41no—
106C22×C4×D17—41no—
107C22×C4×D17—41no—
108C22×C4×D17C2×C414yescomplemented
109C22×C4×D17D414yes—
110C2×C22⋊C4×C17—22no—
111C2×C22⋊C4×C17—22no—
112C2×C22⋊C4×C17—41no—
113C2×C22⋊C4×C17—41no—
114C2×C22⋊C4×C17—41no—
115C2×C22⋊C4×C17C2×C414yescomplemented
116C2×C22⋊Dic17—22no—
117C2×C22⋊Dic17—22no—
118C2×C22⋊Dic17—22no—
119C2×C22⋊Dic17—22no—
120C2×C22⋊Dic17—22no—
121C2×C22⋊Dic17—22no—
122C2×C22⋊Dic17—22no—
123C2×C22⋊Dic17—41no—
124C2×C22⋊Dic17C2×C414yescomplemented
125C4×C22⋊D17—232no—
126C2×#63227—22no—
127C2×#63227—22no—
128C2×#63227—22no—
129C2×#63227—22no—
130C2×#63227—22no—
131C2×#63227—22no—
132C2×#63227—22no—
133C2×#63227C2×C414yescomplemented
134C2×#63227D414yes—
135C2×C4⋊Dic17—22no—
136C2×C4⋊Dic17—41no—
137C2×C4⋊Dic17—41no—
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225—22no—
141C2×#63225—22no—
142C2×#63225—22no—
143C2×#63225—22no—
144C2×#63225—22no—
145C2×#63225—22no—
146C2×#63225—22no—
147C2×#63225—22no—
148C2×#63225—41no—
149C2×#63225—41no—
150C2×C4×Dic17—22no—
151C2×C4×Dic17—22no—
152C2×C4×Dic17—22no—
153C17×#95—22no—
154C17×#95—22no—
155C17×#95—22no—
156C17×#95—41no—
157#10587502—22no—
158#10587502—22no—
159#10587502—22no—
160#10587502—22no—
161#10587502—22no—
162#10587502—22no—
163#10587502—22no—
164#10587502—22no—
165#10587502—41no—
166#10587502C2×C414yescomplemented
167#10587502C2×C414yescomplemented
168#10587502D414yescomplemented
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17—21no—
173C24×C17—21no—
174C24×C17—21no—
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17C22×C412yes—
182C24×C17C2×D412yes—
183C24×C17C2×Q812yes—
184C24×C17C2411yescharacteristic
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C23×D17—21no—
190C23×D17—21no—
191C23×D17—21no—
192C23×D17—21no—
193C23×D17C22×C412yes—
194C23×D17C2×D412yes—
195C23×D17C2×D412yes—
196C23×D17C2×D412yes—
197C23×D17C2×Q812yes—
198C23×D17#4112yes—
199C23×D17#4112yes—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—28no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17—21no—
235C22×C4×C17—21no—
236C22×C4×C17—44no—
237C22×C4×C17—44no—
238C22×C4×C17—44no—
239C22×C4×C17—44no—
240C22×C4×C17—44no—
241C22×C4×C17—44no—
242C22×C4×C17C22×C412yes—
243C22×C4×C17C22×C412yes—
244C22×C4×C17C2×D412yes—
245C22×C4×C17C2×D412yes—
246C22×C4×C17C2×D412yes—
247C22×C4×C17#4112yes—
248C22×C4×C17#4112yes—
249C2×C22⋊D17—28no—
250C2×C22⋊D17—28no—
251C2×C22⋊D17—28no—
252C2×C22⋊D17—28no—
253C2×C22⋊D17—28no—
254C2×C22⋊D17—28no—
255C2×C22⋊D17C4⋊C4116yescomplemented
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17—21no—
285C22×Dic17—21no—
286C22×Dic17—21no—
287C22×Dic17—21no—
288C22×Dic17—21no—
289C22×Dic17—21no—
290C22×Dic17—21no—
291C22×Dic17—21no—
292C22×Dic17—21no—
293C22×Dic17—21no—
294C22×Dic17—21no—
295C22×Dic17C22×C412yes—
296C22×Dic17C22×C412yes—
297C22×Dic17C22×C412yes—
298C22×Dic17C2×D412yes—
299C22×Dic17C2×D412yes—
300C22×Dic17C2×D412yes—
301C22×Dic17C2×D412yes—
302C22×Dic17C2×D412yes—
303C22×Dic17C2×Q812yes—
304C22×Dic17#4112yes—
305C2×C4×D17—28no—
306C2×C4×D17—28no—
307C2×C4×D17—28no—
308C2×C4×D17—28no—
309C2×C4×D17—28no—
310C2×C4×D17—44no—
311C2×C4×D17—44no—
312C2×C4×D17—44no—
313C2×C4×D17—44no—
314C2×C4×D17—44no—
315C2×C4×D17—44no—
316C2×C4×D17—44no—
317C2×C4×D17—44no—
318C2×C4×D17—44no—
319C2×C4×D17—44no—
320C2×C4×D17—44no—
321C2×C4×D17—44no—
322C2×C4×D17—44no—
323C2×C4×D17—44no—
324C2×C4×D17—44no—
325C2×C4×D17—44no—
326C22⋊C4×C17—44no—
327C22⋊C4×C17—44no—
328C22⋊Dic17—28no—
329C22⋊Dic17—28no—
330C22⋊Dic17—44no—
331#63227—28no—
332#63227—28no—
333#63227—44no—
334C4⋊Dic17—44no—
335#63225—28no—
336#63225—44no—
337#63225—44no—
338#63225—44no—
339C4×Dic17—28no—
340#13975—171nomaximal, Sylow
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
344C23×C17—22no—
345C23×C17—22no—
346C23×C17—22no—
347C23×C17—22no—
348C23×C17—22no—
349C23×C17—22no—
350C23×C17—22no—
351C23×C17—22no—
352C23×C17—22no—
353C23×C17—22no—
354C23×C17—22no—
355C23×C17—22no—
356C23×C17—22no—
357C23×C17—22no—
358C23×C17—22no—
359C23×C17—41no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17—41no—
367C23×C17—41no—
368C23×C17—41no—
369C23×C17—41no—
370C23×C17—41no—
371C23×C17—41no—
372C23×C17—41no—
373C23×C17—41no—
374C23×C17—41no—
375C23×C17C2×C4⋊C414yes—
376C23×C17C23×C411yescharacteristic
377C23×C17C22×D411yescharacteristic
378C23×C17C22×D411yescharacteristic
379C23×C17C22×D411yescharacteristic
380C23×C17C22×D411yescharacteristic
381C23×C17C22×Q811yescharacteristic
382C23×C17C2×#4111yescharacteristic
383C23×C17C2×#4111yescharacteristic
384C23×C17C2×#4111yescharacteristic
385C23×C17C2×#4111yescharacteristic
386C23×C17C2×#4111yescharacteristic
387C23×C17H(5,𝔽2)11yescharacteristic
388C23×C17H(5,𝔽2)11yescharacteristic
389C23×C17H(5,𝔽2)11yescharacteristic
390C23×C172−1+411yescharacteristic
391C22×D17—22no—
392C22×D17—22no—
393C22×D17—22no—
394C22×D17—22no—
395C22×D17—22no—
396C22×D17—22no—
397C22×D17—22no—
398C22×D17—22no—
399C22×D17—22no—
400C22×D17—22no—
401C22×D17—22no—
402C22×D17—22no—
403C22×D17—22no—
404C22×D17—22no—
405C22×D17—22no—
406C22×D17—22no—
407C22×D17—22no—
408C22×D17—22no—
409C22×D17—22no—
410C22×D17—22no—
411C22×D17—22no—
412C22×D17—22no—
413C22×D17—22no—
414C22×D17—22no—
415C22×D17—22no—
416C22×D17—22no—
417C22×D17—22no—
418C22×D17—22no—
419C22×D17C2×C4⋊C414yes—
420C22×D17C4×D414yes—
421C22×D17C4×D414yes—
422C22×D17#12014yes—
423C22×D17C22⋊Q814yes—
424C22×D17C22⋊Q814yes—
425C22×D17#12314yes—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—22no—
434C2×C4×C17—22no—
435C2×C4×C17—22no—
436C2×C4×C17—22no—
437C2×C4×C17—22no—
438C2×C4×C17—22no—
439C2×C4×C17—22no—
440C2×C4×C17—22no—
441C2×C4×C17—22no—
442C2×C4×C17—22no—
443C2×C4×C17—22no—
444C2×C4×C17—416no—
445C2×C4×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17—41no—
448C2×C4×C17—41no—
449C2×C4×C17—41no—
450C2×C4×C17—41no—
451C2×C4×C17—41no—
452C2×C4×C17—41no—
453C2×C4×C17—41no—
454C2×C4×C17—41no—
455C2×C4×C17—41no—
456C2×C4×C17—41no—
457C2×C4×C17—41no—
458C2×C4×C17—41no—
459C2×C4×C17—41no—
460C2×C4×C17—41no—
461C2×C4×C17—41no—
462C2×C4×C17—41no—
463C2×C4×C17—41no—
464C2×C4×C17—41no—
465C2×C4×C17—41no—
466C2×C4×C17—41no—
467C2×C4×C17—41no—
468C2×C4×C17#12114yes—
469C22⋊D17—232no—
470C2×Dic17—22no—
471C2×Dic17—22no—
472C2×Dic17—22no—
473C2×Dic17—22no—
474C2×Dic17—22no—
475C2×Dic17—22no—
476C2×Dic17—22no—
477C2×Dic17—22no—
478C2×Dic17—22no—
479C2×Dic17—22no—
480C2×Dic17—22no—
481C2×Dic17—22no—
482C2×Dic17—22no—
483C2×Dic17—22no—
484C2×Dic17—22no—
485C2×Dic17—22no—
486C2×Dic17—22no—
487C2×Dic17—22no—
488C2×Dic17—22no—
489C2×Dic17—22no—
490C2×Dic17—22no—
491C2×Dic17—22no—
492C2×Dic17—22no—
493C2×Dic17—22no—
494C2×Dic17—41no—
495C2×Dic17—41no—
496C2×Dic17—41no—
497C2×Dic17—41no—
498C2×Dic17—41no—
499C2×Dic17—41no—
500C2×Dic17—41no—
501C2×Dic17—41no—
502C2×Dic17—41no—
503C2×Dic17—41no—
504C2×Dic17—41no—
505C2×Dic17—41no—
506C2×Dic17—41no—
507C2×Dic17—41no—
508C2×Dic17—41no—
509C2×Dic17—41no—
510C2×Dic17—41no—
511C2×Dic17—41no—
512C2×Dic17—41no—
513C2×Dic17—41no—
514C2×Dic17—41no—
515C2×Dic17—41no—
516C2×Dic17—41no—
517C2×Dic17C2×C4⋊C414yes—
518C2×Dic17C4×D414yescomplemented
519C4×D17—416no—
520C4×D17—416no—
521C4×D17—416no—
522C22×C4×D4—171no—
523C2×#386—171no—
524C2×#386—171no—
525C2×#385—171no—
526C2×#385—171no—
527C2×#380—171no—
528C22×#95—171no—
529#1444—171no—
530#1442—171no—
531#1439—171no—
532#1439—171no—
533#1436—171no—
534#1436—171no—
535C22⋊#95—171no—
536C22⋊#95D1711yescharacteristic, complemented
537C22×C17—24no—
538C22×C17—24no—
539C22×C17—24no—
540C22×C17—42no—
541C22×C17—42no—
542C22×C17—42no—
543C22×C17—42no—
544C22×C17—42no—
545C22×C17—42no—
546C22×C17—42no—
547C22×C17—42no—
548C22×C17—42no—
549C22×C17—42no—
550C22×C17—42no—
551C22×C17—42no—
552C22×C17C22×C4⋊C411yescharacteristic
553C22×C17C2×C4×D411yescharacteristic
554C22×C17C2×C4×D411yescharacteristic
555C22×C17C2×C4×D411yescharacteristic
556C22×C17C4×#4111yescharacteristic
557C22×C17#51811yescharacteristic
558C22×C17#52011yescharacteristic
559C22×C17C2×#12011yescharacteristic
560C22×C17C2×#12111yescharacteristic
561C22×C17C2×C22⋊Q811yescharacteristic
562C22×C17C2×C22⋊Q811yescharacteristic
563C22×C17C2×#12311yescharacteristic
564C22×C17#52511yescharacteristic
565C22×C17#52911yescharacteristic
566C22×C17#53211yescharacteristic
567C22×C17#53411yescharacteristic
568C22×C17#53711yescharacteristic
569C22×C17#53811yescharacteristic
570C22×C17#53911yescharacteristic
571C22×C17D4211yescharacteristic
572C22×C17D4211yescharacteristic
573C22×C17#54611yescharacteristic
574C22×C17#54611yescharacteristic
575C22×C17#54611yescharacteristic
576C22×C17#54611yescharacteristic
577C22×C17#54611yescharacteristic
578C22×C17#54711yescharacteristic
579C22×C17#54711yescharacteristic
580C22×C17D4×Q811yescharacteristic
581C22×C17#55111yescharacteristic
582C22×C17#55111yescharacteristic
583C22×C17#55211yescharacteristic
584C22×C17#55411yescharacteristic
585C22×C17#55411yescharacteristic
586C22×C17#55411yescharacteristic
587C2×D17—24no—
588C2×D17—24no—
589C2×D17—24no—
590C2×D17—24no—
591C2×D17—24no—
592C2×D17—24no—
593C2×D17—24no—
594C2×D17—24no—
595C2×D17—24no—
596C2×D17—24no—
597C2×D17—24no—
598C2×D17—24no—
599C2×D17—24no—
600C2×D17—24no—
601C2×D17#38518yescomplemented
602C4×C17—24no—
603C4×C17—42no—
604C4×C17—42no—
605C4×C17—42no—
606C4×C17—42no—
607C4×C17—81no—
608Dic17—24no—
609Dic17—24no—
610Dic17—42no—
611Dic17—42no—
612Dic17—42no—
613Dic17—42no—
614Dic17—81no—
615C23×D4—171no—
616C24×C4—171no—
617C24×C4—171no—
618C24×C4—171no—
619C24×C4C2×D1711yescharacteristic
620C2×C4×D4—344no—
621C2×C4×D4—344no—
622C2×C4×D4—344no—
623C22×C4⋊C4—171no—
624C22×C4⋊C4—171no—
625C22×C4⋊C4—171no—
626C22×C4⋊C4—171no—
627C22×C4⋊C4—171no—
628C22×C22⋊C4—171no—
629C22×C22⋊C4—171no—
630C22×C22⋊C4—171no—
631C22×C22⋊C4—171no—
632C22×C22⋊C4—171no—
633C22×C22⋊C4—171no—
634C22×C22⋊C4C2×D1711yescharacteristic
635C22×C22⋊C4C2×D1711yescharacteristic
636C22×C42—171no—
637#386—178no—
638#386—344no—
639#385—344no—
640#385—344no—
641#380—344no—
642C2×#95—171no—
643C2×#95—171no—
644C2×#95—171no—
645C2×#95—171no—
646C2×#95—171no—
647C2×#95—171no—
648C2×#95—171no—
649C2×#95—171no—
650C2×#95—171no—
651C2×#95—171no—
652C2×#95—171no—
653C2×#95—171no—
654C2×#95—344no—
655C2×#95C2×D1711yescharacteristic
656C2×#95C2×D1711yescharacteristic
657C2×#95C2×D1711yescharacteristic
658C2×#95C2×D1711yescharacteristic
659C2×C17—44no—
660C2×C17C2×#38511yescharacteristic
661C2×C17C4×#12111yescharacteristic
662C2×C17#232511yescharacteristic
663C2×C17D4×C4⋊C411yescharacteristic
664C2×C17#234911yescharacteristic
665C2×C17#235811yescharacteristic
666C2×C17#235911yescharacteristic
667C2×C17#241011yescharacteristic
668C2×C17#241711yescharacteristic
669C2×C17#241811yescharacteristic
670C2×C17#241911yescharacteristic
671C2×C17#243011yescharacteristic
672C2×C17#244911yescharacteristic
673C2×C17#245011yescharacteristic
674C2×C17#256411yescharacteristic
675D17—28no—
676C25—171no—
677C25C22×D1711yescharacteristic
678C22×D4—174no—
679C22×D4—174no—
680C22×D4—174no—
681C22×D4—342no—
682C22×D4—342no—
683C22×D4—342no—
684C22×D4—342no—
685C23×C4—22no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—171no—
693C23×C4—171no—
694C23×C4—171no—
695C23×C4—171no—
696C23×C4—171no—
697C23×C4—171no—
698C23×C4—174no—
699C23×C4—174no—
700C23×C4—171no—
701C23×C4—342no—
702C23×C4—342no—
703C23×C4—342no—
704C23×C4—342no—
705C23×C4—342no—
706C23×C4—342no—
707C23×C4—342no—
708C23×C4—342no—
709C23×C4—342no—
710C23×C4—342no—
711C23×C4—342no—
712C23×C4—342no—
713C23×C4—342no—
714C23×C4—681no—
715C23×C4—681no—
716C23×C4—681no—
717C23×C4—681no—
718C23×C4—681no—
719C23×C4—681no—
720C23×C4C22×D1711yescharacteristic
721C23×C4C22×D1711yescharacteristic
722C23×C4C22×D1711yescharacteristic
723C23×C4C22×D1711yescharacteristic
724C23×C4C22×D1711yescharacteristic
725C23×C4C22×D1711yescharacteristic
726C4×D4—3432no—
727C2×C4⋊C4—342no—
728C2×C4⋊C4—342no—
729C2×C4⋊C4—342no—
730C2×C4⋊C4—342no—
731C2×C4⋊C4—342no—
732C2×C4⋊C4—342no—
733C2×C4⋊C4—342no—
734C2×C4⋊C4—342no—
735C2×C4⋊C4—342no—
736C2×C4⋊C4—342no—
737C2×C4⋊C4—342no—
738C2×C4⋊C4—681no—
739C2×C4⋊C4—681no—
740C2×C4⋊C4—681no—
741C2×C4⋊C4—681no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4—41no—
746C2×C22⋊C4—41no—
747C2×C22⋊C4—174no—
748C2×C22⋊C4—174no—
749C2×C22⋊C4—174no—
750C2×C22⋊C4—342no—
751C2×C22⋊C4—342no—
752C2×C22⋊C4—342no—
753C2×C22⋊C4—342no—
754C2×C22⋊C4—342no—
755C2×C22⋊C4—342no—
756C2×C22⋊C4—342no—
757C2×C22⋊C4—342no—
758C2×C22⋊C4—342no—
759C2×C22⋊C4—342no—
760C2×C22⋊C4—342no—
761C2×C22⋊C4—342no—
762C2×C22⋊C4—342no—
763C2×C22⋊C4—342no—
764C2×C22⋊C4—681no—
765C2×C22⋊C4C4×D1714yescomplemented
766C2×C42—342no—
767C2×C42—342no—
768C2×C42—342no—
769#95—22no—
770#95—22no—
771#95—22no—
772#95—41no—
773#95—174no—
774#95—174no—
775#95—174no—
776#95—342no—
777#95—342no—
778#95—342no—
779#95—342no—
780#95—342no—
781#95—342no—
782#95—342no—
783#95—342no—
784#95—681no—
785C17#1397511yescharacteristic, complemented, Sylow
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—172no—
799C24—172no—
800C24—172no—
801C24—172no—
802C24—172no—
803C24—172no—
804C24—172no—
805C24—341no—
806C24—341no—
807C24—341no—
808C24—341no—
809C24—341no—
810C24—341no—
811C24—341no—
812C24—341no—
813C24C2×C4×D1712yes—
814C24D4×D1712yes—
815C24Q8×D1712yes—
816C24C23×D1711yescharacteristic
817C2×D4—1716no—
818C2×D4—348no—
819C2×D4—348no—
820C2×D4—348no—
821C2×D4—348no—
822C2×D4—348no—
823C2×D4—348no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—28no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—172no—
867C22×C4—172no—
868C22×C4—172no—
869C22×C4—172no—
870C22×C4—172no—
871C22×C4—172no—
872C22×C4—172no—
873C22×C4—172no—
874C22×C4—172no—
875C22×C4—172no—
876C22×C4—348no—
877C22×C4—348no—
878C22×C4—348no—
879C22×C4—348no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—341no—
883C22×C4—341no—
884C22×C4—341no—
885C22×C4—341no—
886C22×C4—341no—
887C22×C4—341no—
888C22×C4—341no—
889C22×C4—341no—
890C22×C4—341no—
891C22×C4—341no—
892C22×C4—341no—
893C22×C4—341no—
894C22×C4—341no—
895C22×C4—341no—
896C22×C4—341no—
897C22×C4—341no—
898C22×C4—341no—
899C22×C4—341no—
900C22×C4—341no—
901C22×C4—341no—
902C22×C4—341no—
903C22×C4—341no—
904C22×C4—341no—
905C22×C4—341no—
906C22×C4—341no—
907C22×C4—341no—
908C22×C4—341no—
909C22×C4—341no—
910C22×C4—341no—
911C22×C4—341no—
912C22×C4—348no—
913C22×C4—341no—
914C22×C4—341no—
915C22×C4—341no—
916C22×C4—341no—
917C22×C4—341no—
918C22×C4—341no—
919C22×C4—341no—
920C22×C4—684no—
921C22×C4—684no—
922C22×C4—684no—
923C22×C4—684no—
924C22×C4—684no—
925C22×C4—684no—
926C22×C4—684no—
927C22×C4—684no—
928C22×C4—684no—
929C22×C4—684no—
930C22×C4—684no—
931C22×C4—684no—
932C22×C4—684no—
933C22×C4—684no—
934C22×C4—684no—
935C22×C4—684no—
936C22×C4C2×C4×D1712yes—
937C22×C4C2×C4×D1712yes—
938C22×C4#6325212yes—
939C22×C4#6325212yes—
940C22×C4D4×D1712yes—
941C22×C4D4×D1712yes—
942C22×C4D4×D1712yes—
943C4⋊C4—348no—
944C4⋊C4—684no—
945C4⋊C4—684no—
946C4⋊C4—684no—
947C4⋊C4—684no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—348no—
951C22⋊C4—348no—
952C22⋊C4—348no—
953C22⋊C4—348no—
954C22⋊C4—684no—
955C22⋊C4—684no—
956C42—348no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—174no—
992C23—174no—
993C23—174no—
994C23—174no—
995C23—174no—
996C23—174no—
997C23—174no—
998C23—342no—
999C23—342no—
1000C23—342no—
1001C23—342no—
1002C23—342no—
1003C23—342no—
1004C23—342no—
1005C23—342no—
1006C23—342no—
1007C23—342no—
1008C23—342no—
1009C23—342no—
1010C23—342no—
1011C23—342no—
1012C23—342no—
1013C23—342no—
1014C23—342no—
1015C23—342no—
1016C23—342no—
1017C23—342no—
1018C23—342no—
1019C23—342no—
1020C23—342no—
1021C23—342no—
1022C23—342no—
1023C23—342no—
1024C23—342no—
1025C23—342no—
1026C23C4⋊C4×D1714yes—
1027C23C22×C4×D1711yescharacteristic
1028C23C2×#6325211yescharacteristic
1029C23C2×#6325211yescharacteristic
1030C23C2×D4×D1711yescharacteristic
1031C23C2×D4×D1711yescharacteristic
1032C23C2×D4×D1711yescharacteristic
1033C23C2×D4×D1711yescharacteristic
1034C23#1058769111yescharacteristic
1035C23#1058769111yescharacteristic
1036C23#1058769111yescharacteristic
1037C23C2×Q8×D1711yescharacteristic
1038C23#41×D1711yescharacteristic
1039C23#41×D1711yescharacteristic
1040C23#41×D1711yescharacteristic
1041C23#1058769711yescharacteristic
1042D4—3432no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—416no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—174no—
1086C2×C4—174no—
1087C2×C4—342no—
1088C2×C4—342no—
1089C2×C4—342no—
1090C2×C4—342no—
1091C2×C4—342no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—342no—
1095C2×C4—342no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—342no—
1099C2×C4—342no—
1100C2×C4—342no—
1101C2×C4—342no—
1102C2×C4—342no—
1103C2×C4—342no—
1104C2×C4—342no—
1105C2×C4—342no—
1106C2×C4—342no—
1107C2×C4—342no—
1108C2×C4—342no—
1109C2×C4—342no—
1110C2×C4—342no—
1111C2×C4—6816no—
1112C2×C4—6816no—
1113C2×C4—6816no—
1114C2×C4—681no—
1115C2×C4—681no—
1116C2×C4—681no—
1117C2×C4—681no—
1118C2×C4—681no—
1119C2×C4—681no—
1120C2×C4—681no—
1121C2×C4—681no—
1122C2×C4—681no—
1123C2×C4—681no—
1124C2×C4—681no—
1125C2×C4—681no—
1126C2×C4—681no—
1127C2×C4—681no—
1128C2×C4—681no—
1129C2×C4—681no—
1130C2×C4—681no—
1131C2×C4—681no—
1132C2×C4—681no—
1133C2×C4—681no—
1134C2×C4—681no—
1135C2×C4—681no—
1136C2×C4—681no—
1137C2×C4#1058757014yes—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—178no—
1154C22—344no—
1155C22—344no—
1156C22—344no—
1157C22—344no—
1158C22—344no—
1159C22—344no—
1160C22—344no—
1161C22—344no—
1162C22—344no—
1163C22—344no—
1164C22—344no—
1165C22—344no—
1166C22—344no—
1167C22—344no—
1168C22C2×C4⋊C4×D1711yescharacteristic
1169C22C4×D4×D1711yescharacteristic
1170C22C4×D4×D1711yescharacteristic
1171C22C4×D4×D1711yescharacteristic
1172C22C4×#6325211yescharacteristic
1173C22#1176328211yescharacteristic
1174C22#1176328811yescharacteristic
1175C22#120×D1711yescharacteristic
1176C22C2×#1058757011yescharacteristic
1177C22C22⋊Q8×D1711yescharacteristic
1178C22C22⋊Q8×D1711yescharacteristic
1179C22#123×D1711yescharacteristic
1180C22#1176331811yescharacteristic
1181C22#1176333711yescharacteristic
1182C22#1176335611yescharacteristic
1183C22#1176336911yescharacteristic
1184C22#1176338811yescharacteristic
1185C22#1176339111yescharacteristic
1186C22#1176340211yescharacteristic
1187C22#1176344111yescharacteristic
1188C22#1176344111yescharacteristic
1189C22#1176344911yescharacteristic
1190C22#1176344911yescharacteristic
1191C22#1176344911yescharacteristic
1192C22#1176345611yescharacteristic
1193C22#1176345611yescharacteristic
1194C22#1176345711yescharacteristic
1195C22#1176346411yescharacteristic
1196C22#1176347211yescharacteristic
1197C22#1176348711yescharacteristic
1198C22#1176348811yescharacteristic
1199C22#1176349811yescharacteristic
1200C22#1176351311yescharacteristic
1201C22#1176351411yescharacteristic
1202C22#1176351411yescharacteristic
1203C4—24no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—81no—
1209C4—344no—
1210C4—344no—
1211C4—682no—
1212C4—682no—
1213C4—682no—
1214C4—682no—
1215C4—1361no—
1216C2—44no—
1217C2—348no—
1218C2D17×#38511yescharacteristic
1219C2C4×#1058757011yescharacteristic
1220C2#1453148611yescharacteristic
1221C2#1453168211yescharacteristic
1222C2#1453169111yescharacteristic
1223C2#1453176711yescharacteristic
1224C2#1453177711yescharacteristic
1225C2#1453216011yescharacteristic
1226C2#1453223711yescharacteristic
1227C2#1453224511yescharacteristic
1228C2#1453225811yescharacteristic
1229C2#1453239111yescharacteristic
1230C2#1453259211yescharacteristic
1231C2#1453261511yescharacteristic
1232C2#1453396911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22⋊#95D17
hypocenterC17#13975
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11762683C2semidirect
5. C2×#11762682C2semidirect
6. C2×#11762668C2semidirect
7. C2×#95×D17C2semidirect
8. #14527048C2semidirect
9. #14527042C2semidirect
10. #14527029C2semidirect
11. #14527027C2semidirect
12. #14527019C2semidirect
13. #14527015C2semidirect
14. #14527005C2semidirect
15. C17×C22⋊#95C2semidirect
36. #11762685C4semidirect
108. C22×C4×D17C2×C4semidirect
115. C2×C22⋊C4×C17C2×C4semidirect
124. C2×C22⋊Dic17C2×C4semidirect
133. C2×#63227C2×C4semidirect
166. #10587502C2×C4semidirect
167. #10587502C2×C4semidirect
168. #10587502D4semidirect
255. C2×C22⋊D17C4⋊C4semidirect
518. C2×Dic17C4×D4semidirect
536. C22⋊#95D17semidirect
601. C2×D17#385semidirect
765. C2×C22⋊C4C4×D17semidirect
785. C17#13975semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D172
C2×#117626852
C2×#117626832
C2×#117626822
C2×#117626682
C2×#95×D172
#145270482
#145270422
#145270292
#145270272
#145270192
#145270152
#145270052
C17×C22⋊#952
#1397517