Finite Group Databasebeta

← #17963585

Subgroups — #17963585

Order 4352.

1094 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14543973C211yesmaximal, characteristic
2#14543971C211yesmaximal, characteristic
3#14543971C211yesmaximal, characteristic
4#14543971C211yesmaximal, characteristic
5#14543971C211yesmaximal, characteristic
6#14543970C211yesmaximal, characteristic
7#14543969C211yesmaximal, characteristic
8#14543964C211yesmaximal, characteristic
9#14543964C211yesmaximal, characteristic
10#14543964C211yesmaximal, characteristic
11#14543964C211yesmaximal, characteristic
12#14543963C211yesmaximal, characteristic
13#14543963C211yesmaximal, characteristic
14#95×#595C211yesmaximal, characteristic
15D17×#400C211yesmaximal, characteristic
16C22×C4⋊#595C2211yescharacteristic
17C22×C4⋊#595C2211yescharacteristic
18C22×C4×#595C2211yescharacteristic
19C22×C4×#595C2211yescharacteristic
20C22×C4×#595C2211yescharacteristic
21C2×(C2×#595)⋊C4C2211yescharacteristic
22C2×(C2×#595)⋊C4C2211yescharacteristic
23C2×(C2×#595)⋊C4C2211yescharacteristic
24C2×(C2×#595)⋊C4C2211yescharacteristic
25C2×(C2×#595)⋊C4C2211yescharacteristic
26C2×(C2×#595)⋊C4C2211yescharacteristic
27C2×(C2×#595)⋊C4C2211yescharacteristic
28C2×(C2×#595)⋊C4C2211yescharacteristic
29C2×(C2×#595)⋊C4C2211yescharacteristic
30C2×(C2×#595)⋊C4C2211yescharacteristic
31C2×(C2×#595)⋊C4C2211yescharacteristic
32C2×(C2×#595)⋊C4C2211yescharacteristic
33C2×(C2×#595)⋊C4C2211yescharacteristic
34C2×(C2×#595)⋊C4C2211yescharacteristic
35C2×(C2×#595)⋊C4C2211yescharacteristic
36C2×(C2×#595)⋊C4C2211yescharacteristic
37C2×(C2×#595)⋊C4C2211yescharacteristic
38C2×(C2×#595)⋊C4C2211yescharacteristic
39C2×(C2×#595)⋊C4C2211yescharacteristic
40C2×(C2×#595)⋊C4C2211yescharacteristic
41C2×(C2×#595)⋊C4C2211yescharacteristic
42C2×(C2×#595)⋊C4C2211yescharacteristic
43C2×(C2×#595)⋊C4C2211yescharacteristic
44C2×C4⋊C4×D17C2211yescharacteristic
45C2×C4⋊C4×D17C2211yescharacteristic
46#11762751C411yescharacteristic, complemented
47#11762751C411yescharacteristic, complemented
48#11762750C411yescharacteristic, complemented
49#11762750C411yescharacteristic, complemented
50#11762749C411yescharacteristic, complemented
51#11762748C411yescharacteristic, complemented
52#11762747C411yescharacteristic, complemented
53#95×D17C2211yescharacteristic
54#95×D17C2211yescharacteristic
55#95×D17C2211yescharacteristic
56#95×D17C2211yescharacteristic
57#95×D17C2211yescharacteristic
58C17×#400C411yescharacteristic, complemented
59C23×#595C2311yescharacteristic
60C23×#595C2311yescharacteristic
61C23×#595C2311yescharacteristic
62C23×#595C2311yescharacteristic
63C23×#595C2311yescharacteristic
64C23×#595C2311yescharacteristic
65C23×#595C2311yescharacteristic
66C23×#595C2311yescharacteristic
67C22×C4×D17C2311yescharacteristic
68C22×C4×D17C2311yescharacteristic
69C22×C4×D17C2311yescharacteristic
70C22×C4×D17C2311yescharacteristic
71C22×C4×D17C2311yescharacteristic
72C22×C4×D17C2311yescharacteristic
73C22×C4×D17C2311yescharacteristic
74C2×C4⋊#595—22no—
75C2×C4⋊#595—22no—
76C2×C4⋊#595—22no—
77C2×C4⋊#595—22no—
78C2×C4⋊#595—41no—
79C2×C4⋊#595—41no—
80C2×C4×#595—22no—
81C2×C4×#595—22no—
82C2×C4×#595—22no—
83C2×C4×#595—41no—
84C2×C4×#595—41no—
85C2×C4×#595—41no—
86C2×C4×#595—41no—
87C2×C4×#595—41no—
88C2×C4×#595—41no—
89C2×C4⋊C4×C17C2×C411yescharacteristic
90C2×C4⋊C4×C17C2×C411yescharacteristic
91C2×C4⋊Dic17C2×C411yescharacteristic
92C2×C4⋊Dic17C2×C411yescharacteristic
93C2×#63225C2×C411yescharacteristic
94C2×#63225C2×C411yescharacteristic
95C2×#63225C2×C411yescharacteristic
96C2×#63225C2×C411yescharacteristic
97C4⋊C4×D17—41no—
98C4⋊C4×D17—41no—
99C4⋊C4×D17—41no—
100C4⋊C4×D17—41no—
101(C2×#595)⋊C4—22no—
102(C2×#595)⋊C4—22no—
103(C2×#595)⋊C4—22no—
104(C2×#595)⋊C4—22no—
105(C2×#595)⋊C4—22no—
106(C2×#595)⋊C4—22no—
107(C2×#595)⋊C4—22no—
108(C2×#595)⋊C4—22no—
109(C2×#595)⋊C4—22no—
110(C2×#595)⋊C4—22no—
111(C2×#595)⋊C4—22no—
112(C2×#595)⋊C4—41no—
113(C2×#595)⋊C4—41no—
114(C2×#595)⋊C4—41no—
115(C2×#595)⋊C4—41no—
116(C2×#595)⋊C4—41no—
117(C2×#595)⋊C4—41no—
118(C2×#595)⋊C4—41no—
119(C2×#595)⋊C4—41no—
120(C2×#595)⋊C4—41no—
121(C2×#595)⋊C4—41no—
122(C2×#595)⋊C4—41no—
123(C2×#595)⋊C4—41no—
124C17×#95C2×C411yescharacteristic
125C17×#95C2×C411yescharacteristic
126C17×#95C2×C411yescharacteristic
127C17×#95C2×C411yescharacteristic
128C17×#95C2×C411yescharacteristic
129#10587502C2×C411yescharacteristic
130#10587502C2×C411yescharacteristic
131#10587502C2×C411yescharacteristic
132#10587502C2×C411yescharacteristic
133#10587502C2×C411yescharacteristic
134#10587502C2×C411yescharacteristic
135#10587502C2×C411yescharacteristic
136#10587502C2×C411yescharacteristic
137#10587502C2×C411yescharacteristic
138#10587502C2×C411yescharacteristic
139#10587502C2×C411yescharacteristic
140#10587502C2×C411yescharacteristic
141#10587502C2×C411yescharacteristic
142#10587502C2×C411yescharacteristic
143#10587502C2×C411yescharacteristic
144C23×D17C2411yescharacteristic
145C22×#595—21no—
146C22×#595—21no—
147C22×#595—21no—
148C22×#595—21no—
149C22×#595—21no—
150C22×#595—21no—
151C22×#595—21no—
152C22×#595—21no—
153C22×#595—21no—
154C22×#595—21no—
155C22×#595—21no—
156C22×#595—21no—
157C22×#595—21no—
158C22×#595—21no—
159C22×#595—21no—
160C22×#595—21no—
161C22×#595—21no—
162C22×#595—21no—
163C22×#595—21no—
164C22×#595—21no—
165C22×#595—21no—
166C22×#595—21no—
167C22×#595—21no—
168C22×#595—21no—
169C22×#595—21no—
170C22×#595—21no—
171C22×#595—21no—
172C22×#595—21no—
173C22×#595—21no—
174C22×#595—21no—
175C22×#595—21no—
176C22×#595—21no—
177C22×#595—21no—
178C22×#595—21no—
179C22×#595—21no—
180C22×#595—21no—
181C22×#595—21no—
182C22×#595—21no—
183C22×#595—21no—
184C22×#595—21no—
185C22×#595—21no—
186C22×#595—21no—
187C22×#595—21no—
188C22×#595—21no—
189C22×#595—21no—
190C22×#595—21no—
191C22×#595—21no—
192C22×#595—21no—
193C22×#595—21no—
194C22×#595—21no—
195C22×#595#4112yes—
196C22×#595#4112yes—
197C22×#595#4112yes—
198C22×#595#4112yes—
199C22×#595#4112yes—
200C22×#595#4112yes—
201C22×C4×C17C22×C411yescharacteristic
202C22×C4×C17C22×C411yescharacteristic
203C22×C4×C17C22×C411yescharacteristic
204C22×C4×C17C22×C411yescharacteristic
205C22×C4×C17C22×C411yescharacteristic
206C22×C4×C17C22×C411yescharacteristic
207C22×C4×C17C22×C411yescharacteristic
208C22×Dic17C22×C411yescharacteristic
209C22×Dic17C22×C411yescharacteristic
210C22×Dic17C22×C411yescharacteristic
211C22×Dic17C22×C411yescharacteristic
212C22×Dic17C22×C411yescharacteristic
213C22×Dic17C22×C411yescharacteristic
214C22×Dic17C22×C411yescharacteristic
215C2×C4×D17—21no—
216C2×C4×D17—21no—
217C2×C4×D17—21no—
218C2×C4×D17—21no—
219C2×C4×D17—21no—
220C2×C4×D17—21no—
221C2×C4×D17—21no—
222C2×C4×D17—21no—
223C2×C4×D17—21no—
224C2×C4×D17—21no—
225C2×C4×D17—21no—
226C2×C4×D17—21no—
227C2×C4×D17—21no—
228C2×C4×D17—21no—
229C2×C4×D17—21no—
230C2×C4×D17—21no—
231C2×C4×D17—21no—
232C2×C4×D17—21no—
233C2×C4×D17—21no—
234C2×C4×D17—21no—
235C2×C4×D17—21no—
236C2×C4×D17—21no—
237C2×C4×D17—21no—
238C2×C4×D17—21no—
239C2×C4×D17—21no—
240C2×C4×D17—21no—
241C2×C4×D17—21no—
242C2×C4×D17—21no—
243C2×C4×D17—21no—
244C2×C4×D17—21no—
245C2×C4×D17—21no—
246C2×C4×D17—21no—
247C2×C4×D17—21no—
248C2×C4×D17—21no—
249C2×C4×D17—21no—
250C2×C4×D17—21no—
251C2×C4×D17—21no—
252C2×C4×D17—21no—
253C2×C4×D17—21no—
254C2×C4×D17—21no—
255C2×C4×D17—21no—
256C2×C4×D17—21no—
257C4⋊#595—44no—
258C4⋊#595—44no—
259C4×#595—44no—
260C4×#595—44no—
261C4×#595—44no—
262C4⋊C4×C17—41no—
263C4⋊C4×C17—41no—
264C4⋊Dic17—41no—
265C4⋊Dic17—41no—
266#63225—41no—
267#63225—41no—
268#63225—41no—
269#63225—41no—
270#14334—171nomaximal, Sylow
271C23×C17C23×C411yescharacteristic
272C22×D17C2×#4111yescharacteristic
273C22×D17C2×#4111yescharacteristic
274C22×D17C2×#4111yescharacteristic
275C22×D17C2×#4111yescharacteristic
276C22×D17C2×#4111yescharacteristic
277C22×D17C2×#4111yescharacteristic
278C22×D17H(5,𝔽2)11yescharacteristic
279C22×D17H(5,𝔽2)11yescharacteristic
280C22×D17H(5,𝔽2)11yescharacteristic
281C22×D17H(5,𝔽2)11yescharacteristic
282C22×D172−1+411yescharacteristic
283C22×D172−1+411yescharacteristic
284C22×D172−1+411yescharacteristic
285C22×D172−1+411yescharacteristic
286C2×#595—22no—
287C2×#595—22no—
288C2×#595—22no—
289C2×#595—22no—
290C2×#595—22no—
291C2×#595—22no—
292C2×#595—22no—
293C2×#595—22no—
294C2×#595—22no—
295C2×#595—22no—
296C2×#595—22no—
297C2×#595—22no—
298C2×#595—22no—
299C2×#595—22no—
300C2×#595—22no—
301C2×#595—41no—
302C2×#595—41no—
303C2×#595—41no—
304C2×#595—41no—
305C2×#595—41no—
306C2×#595—41no—
307C2×#595—41no—
308C2×#595—41no—
309C2×#595—41no—
310C2×#595—41no—
311C2×#595—41no—
312C2×#595—41no—
313C2×#595—41no—
314C2×#595—41no—
315C2×#595—41no—
316C2×#595—41no—
317C2×#595—41no—
318C2×#595—41no—
319C2×#595—41no—
320C2×#595—41no—
321C2×#595—41no—
322C2×#595—41no—
323C2×#595—41no—
324C2×#595—41no—
325C2×#595—41no—
326C2×#595—41no—
327C2×#595—41no—
328C2×#595—41no—
329C2×#595—41no—
330C2×#595—41no—
331C2×#595—41no—
332C2×#595—41no—
333C2×#595—41no—
334C2×#595—41no—
335C2×#595—41no—
336C2×#595—41no—
337C2×#595—41no—
338C2×#595—41no—
339C2×#595—41no—
340C2×#595—41no—
341C2×#595#12614yes—
342C2×C4×C17—21no—
343C2×C4×C17—21no—
344C2×C4×C17—21no—
345C2×C4×C17—21no—
346C2×C4×C17—21no—
347C2×C4×C17—21no—
348C2×C4×C17—21no—
349C2×C4×C17—21no—
350C2×C4×C17—21no—
351C2×C4×C17—21no—
352C2×C4×C17—21no—
353C2×C4×C17—21no—
354C2×C4×C17—21no—
355C2×C4×C17—21no—
356C2×C4×C17—21no—
357C2×C4×C17—21no—
358C2×C4×C17—21no—
359C2×C4×C17—21no—
360C2×C4×C17—21no—
361C2×C4×C17—21no—
362C2×C4×C17—21no—
363C2×Dic17—21no—
364C2×Dic17—21no—
365C2×Dic17—21no—
366C2×Dic17—21no—
367C2×Dic17—21no—
368C2×Dic17—21no—
369C2×Dic17—21no—
370C2×Dic17—21no—
371C2×Dic17—21no—
372C2×Dic17—21no—
373C2×Dic17—21no—
374C2×Dic17—21no—
375C2×Dic17—21no—
376C2×Dic17—21no—
377C2×Dic17—21no—
378C2×Dic17—21no—
379C2×Dic17—21no—
380C2×Dic17—21no—
381C2×Dic17—21no—
382C2×Dic17—21no—
383C2×Dic17—21no—
384C4×D17—41no—
385C4×D17—41no—
386C4×D17—41no—
387C4×D17—41no—
388C4×D17—41no—
389C4×D17—41no—
390C4×D17—41no—
391C4×D17—41no—
392C4×D17—41no—
393C4×D17—41no—
394C4×D17—41no—
395C4×D17—41no—
396C4×D17—41no—
397C4×D17—41no—
398C4×D17—41no—
399C4×D17—41no—
400C4×D17—41no—
401C4×D17—41no—
402C4×D17—41no—
403C4×D17—41no—
404C4×D17—41no—
405C4×D17—41no—
406C4×D17—41no—
407C4×D17—41no—
408C4×D17—41no—
409C4×D17—41no—
410C4×D17—41no—
411C4×D17—41no—
412C2×#400—171no—
413#1445—171no—
414#1443—171no—
415#1443—171no—
416#1443—171no—
417#1443—171no—
418#1442—171no—
419#1441—171no—
420#1436—171no—
421#1436—171no—
422#1436—171no—
423#1436—171no—
424#1436—171no—
425#1436—171no—
426C4×#95—171no—
427C22×C17C4×#4111yescharacteristic
428C22×C17C4×#4111yescharacteristic
429C22×C17C4×#4111yescharacteristic
430C22×C17#51811yescharacteristic
431C22×C17#51911yescharacteristic
432C22×C17#52011yescharacteristic
433C22×C17#52011yescharacteristic
434C2×D17C2×#12611yescharacteristic
435C2×D17#52911yescharacteristic
436C2×D17#52911yescharacteristic
437C2×D17#52911yescharacteristic
438C2×D17#53811yescharacteristic
439C2×D17#53811yescharacteristic
440C2×D17#53811yescharacteristic
441C2×D17#53811yescharacteristic
442C2×D17#53911yescharacteristic
443C2×D17#53911yescharacteristic
444C2×D17#53911yescharacteristic
445C2×D17#53911yescharacteristic
446C2×D17#53911yescharacteristic
447C2×D17#53911yescharacteristic
448C2×D17#53911yescharacteristic
449C2×D17#53911yescharacteristic
450C2×D17#54011yescharacteristic
451C2×D17#54111yescharacteristic
452C2×D17#54111yescharacteristic
453C2×D17#54111yescharacteristic
454C2×D17#54111yescharacteristic
455C2×D17#54111yescharacteristic
456C2×D17#54211yescharacteristic
457C2×D17#54211yescharacteristic
458C2×D17#54211yescharacteristic
459C2×D17#54211yescharacteristic
460C2×D17#54211yescharacteristic
461C2×D17#54211yescharacteristic
462#595—24no—
463#595—42no—
464#595—42no—
465#595—42no—
466#595—81no—
467#595—81no—
468#595—81no—
469#595—81no—
470C4×C17—41no—
471C4×C17—41no—
472C4×C17—41no—
473C4×C17—41no—
474C4×C17—41no—
475C4×C17—41no—
476C4×C17—41no—
477Dic17—41no—
478Dic17—41no—
479Dic17—41no—
480Dic17—41no—
481Dic17—41no—
482Dic17—41no—
483Dic17—41no—
484C22×C4⋊C4—171no—
485C22×C4⋊C4—171no—
486C22×C4⋊C4—171no—
487C22×C4⋊C4—171no—
488C22×C42—171no—
489C22×C42—171no—
490C22×C42—171no—
491#400—171no—
492#400—171no—
493#400—171no—
494#400—171no—
495#400—171no—
496#400—171no—
497#400—171no—
498#400#59511yescharacteristic, complemented
499C2×#95—171no—
500C2×#95—171no—
501C2×#95—171no—
502C2×#95—171no—
503C2×#95—171no—
504C2×#95—171no—
505C2×#95—171no—
506C2×#95—171no—
507C2×#95—171no—
508C2×#95—171no—
509C2×#95—171no—
510C2×#95—171no—
511C2×#95—171no—
512C2×#95—171no—
513C2×#95—171no—
514C2×#95—171no—
515C2×#95—171no—
516C2×#95—171no—
517C2×#95—171no—
518C2×#95—171no—
519C2×#95—171no—
520C2×#95—171no—
521C2×#95—171no—
522C2×#95—171no—
523C2×#95—171no—
524C2×#95—171no—
525C2×#95—171no—
526C2×#95—171no—
527C2×C17C4×#12611yescharacteristic
528C2×C17#233211yescharacteristic
529C2×C17#233411yescharacteristic
530C2×C17#233511yescharacteristic
531C2×C17#233611yescharacteristic
532C2×C17#233611yescharacteristic
533C2×C17#233711yescharacteristic
534D17#264311yescharacteristic
535D17#264511yescharacteristic
536D17#264911yescharacteristic
537D17#265011yescharacteristic
538D17#265211yescharacteristic
539D17#265211yescharacteristic
540D17#265411yescharacteristic
541D17#265511yescharacteristic
542C23×C4—171no—
543C23×C4—171no—
544C23×C4—171no—
545C23×C4—171no—
546C23×C4—171no—
547C23×C4—171no—
548C23×C4—171no—
549C23×C4—171no—
550C23×C4—171no—
551C23×C4—171no—
552C23×C4—171no—
553C23×C4—171no—
554C23×C4—171no—
555C23×C4—171no—
556C23×C4—171no—
557C2×C4⋊C4—171no—
558C2×C4⋊C4—171no—
559C2×C4⋊C4—171no—
560C2×C4⋊C4—171no—
561C2×C4⋊C4—171no—
562C2×C4⋊C4—171no—
563C2×C4⋊C4—342no—
564C2×C4⋊C4—342no—
565C2×C4⋊C4—342no—
566C2×C4⋊C4—342no—
567C2×C4⋊C4—681no—
568C2×C4⋊C4—681no—
569C2×C4⋊C4—681no—
570C2×C4⋊C4—681no—
571C2×C4⋊C4—681no—
572C2×C4⋊C4—681no—
573C2×C4⋊C4C2×#59511yescharacteristic
574C2×C4⋊C4C2×#59511yescharacteristic
575C2×C42—342no—
576C2×C42—342no—
577C2×C42—342no—
578C2×C42—681no—
579C2×C42—681no—
580C2×C42—681no—
581C2×C42—681no—
582C2×C42—681no—
583C2×C42—681no—
584#95—171no—
585#95—171no—
586#95—171no—
587#95—171no—
588#95—171no—
589#95—171no—
590#95—171no—
591#95—171no—
592#95—171no—
593#95—171no—
594#95—171no—
595#95—171no—
596#95—171no—
597#95—171no—
598#95—171no—
599#95—342no—
600#95—342no—
601#95—342no—
602#95—342no—
603#95—342no—
604#95—342no—
605#95—342no—
606#95—342no—
607#95—342no—
608#95—342no—
609#95—342no—
610#95—681no—
611#95—681no—
612#95—681no—
613#95—681no—
614#95—681no—
615#95—681no—
616#95—681no—
617#95—681no—
618#95—681no—
619#95—681no—
620#95—681no—
621#95—681no—
622#95C2×#59511yescharacteristic
623#95C2×#59511yescharacteristic
624#95C2×#59511yescharacteristic
625#95C2×#59511yescharacteristic
626#95C2×#59511yescharacteristic
627C17#1433411yescharacteristic, complemented, Sylow
628C24—171no—
629C22×C4—172no—
630C22×C4—172no—
631C22×C4—172no—
632C22×C4—172no—
633C22×C4—172no—
634C22×C4—172no—
635C22×C4—171no—
636C22×C4—171no—
637C22×C4—171no—
638C22×C4—171no—
639C22×C4—171no—
640C22×C4—171no—
641C22×C4—171no—
642C22×C4—341no—
643C22×C4—341no—
644C22×C4—341no—
645C22×C4—341no—
646C22×C4—341no—
647C22×C4—341no—
648C22×C4—341no—
649C22×C4—341no—
650C22×C4—341no—
651C22×C4—341no—
652C22×C4—341no—
653C22×C4—341no—
654C22×C4—341no—
655C22×C4—341no—
656C22×C4—341no—
657C22×C4—341no—
658C22×C4—341no—
659C22×C4—341no—
660C22×C4—341no—
661C22×C4—341no—
662C22×C4—341no—
663C22×C4—341no—
664C22×C4—341no—
665C22×C4—341no—
666C22×C4—341no—
667C22×C4—341no—
668C22×C4—341no—
669C22×C4—341no—
670C22×C4—341no—
671C22×C4—341no—
672C22×C4—341no—
673C22×C4—341no—
674C22×C4—341no—
675C22×C4—341no—
676C22×C4—341no—
677C22×C4—341no—
678C22×C4—341no—
679C22×C4—341no—
680C22×C4—341no—
681C22×C4—341no—
682C22×C4—341no—
683C22×C4—341no—
684C22×C4—341no—
685C22×C4—341no—
686C22×C4—341no—
687C22×C4—341no—
688C22×C4—341no—
689C22×C4—341no—
690C22×C4—341no—
691C22×C4—341no—
692C22×C4—341no—
693C22×C4—341no—
694C22×C4—341no—
695C22×C4—341no—
696C22×C4—341no—
697C22×C4—341no—
698C22×C4—341no—
699C22×C4—341no—
700C22×C4—341no—
701C22×C4—341no—
702C22×C4—341no—
703C22×C4—341no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4C22×#59511yescharacteristic
735C22×C4C22×#59511yescharacteristic
736C22×C4C22×#59511yescharacteristic
737C22×C4C22×#59511yescharacteristic
738C22×C4C22×#59511yescharacteristic
739C22×C4C22×#59511yescharacteristic
740C22×C4C22×#59511yescharacteristic
741C4⋊C4—41no—
742C4⋊C4—41no—
743C4⋊C4—681no—
744C4⋊C4—681no—
745C4⋊C4—681no—
746C4⋊C4—681no—
747C4⋊C4—681no—
748C4⋊C4—681no—
749C4⋊C4—684no—
750C4⋊C4—684no—
751C42—684no—
752C42—684no—
753C42—684no—
754C23—171no—
755C23—171no—
756C23—171no—
757C23—171no—
758C23—171no—
759C23—171no—
760C23—171no—
761C23—171no—
762C23—171no—
763C23—171no—
764C23—171no—
765C23—171no—
766C23—171no—
767C23—171no—
768C23C23×#59511yescharacteristic
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
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—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—174no—
791C2×C4—342no—
792C2×C4—342no—
793C2×C4—342no—
794C2×C4—342no—
795C2×C4—342no—
796C2×C4—342no—
797C2×C4—342no—
798C2×C4—342no—
799C2×C4—342no—
800C2×C4—342no—
801C2×C4—342no—
802C2×C4—342no—
803C2×C4—342no—
804C2×C4—342no—
805C2×C4—342no—
806C2×C4—341no—
807C2×C4—341no—
808C2×C4—341no—
809C2×C4—341no—
810C2×C4—341no—
811C2×C4—341no—
812C2×C4—341no—
813C2×C4—341no—
814C2×C4—341no—
815C2×C4—341no—
816C2×C4—341no—
817C2×C4—341no—
818C2×C4—341no—
819C2×C4—341no—
820C2×C4—341no—
821C2×C4—341no—
822C2×C4—341no—
823C2×C4—341no—
824C2×C4—341no—
825C2×C4—341no—
826C2×C4—341no—
827C2×C4—681no—
828C2×C4—681no—
829C2×C4—681no—
830C2×C4—681no—
831C2×C4—681no—
832C2×C4—681no—
833C2×C4—681no—
834C2×C4—681no—
835C2×C4—681no—
836C2×C4—681no—
837C2×C4—681no—
838C2×C4—681no—
839C2×C4—681no—
840C2×C4—681no—
841C2×C4—681no—
842C2×C4—681no—
843C2×C4—681no—
844C2×C4—681no—
845C2×C4—681no—
846C2×C4—681no—
847C2×C4—681no—
848C2×C4—681no—
849C2×C4—681no—
850C2×C4—681no—
851C2×C4—681no—
852C2×C4—681no—
853C2×C4—681no—
854C2×C4—681no—
855C2×C4—681no—
856C2×C4—681no—
857C2×C4—681no—
858C2×C4—681no—
859C2×C4—681no—
860C2×C4—681no—
861C2×C4—681no—
862C2×C4—681no—
863C2×C4—681no—
864C2×C4—681no—
865C2×C4—681no—
866C2×C4—681no—
867C2×C4—681no—
868C2×C4—681no—
869C2×C4—681no—
870C2×C4—681no—
871C2×C4—681no—
872C2×C4—681no—
873C2×C4—681no—
874C2×C4—681no—
875C2×C4—681no—
876C2×C4—681no—
877C2×C4—681no—
878C2×C4—681no—
879C2×C4—681no—
880C2×C4—681no—
881C2×C4—681no—
882C2×C4—681no—
883C2×C4—681no—
884C2×C4—681no—
885C2×C4—681no—
886C2×C4—681no—
887C2×C4—681no—
888C2×C4—681no—
889C2×C4—681no—
890C2×C4—681no—
891C2×C4—681no—
892C2×C4—681no—
893C2×C4—681no—
894C2×C4—681no—
895C22—171no—
896C22—171no—
897C22—171no—
898C22—171no—
899C22—171no—
900C22—171no—
901C22—171no—
902C22—171no—
903C22—171no—
904C22—171no—
905C22—171no—
906C22—171no—
907C22—171no—
908C22—171no—
909C22—171no—
910C22—171no—
911C22—171no—
912C22—171no—
913C22—171no—
914C22—171no—
915C22—171no—
916C22—171no—
917C22—171no—
918C22—171no—
919C22—171no—
920C22—171no—
921C22—171no—
922C22—171no—
923C22#41×#59511yescharacteristic
924C22#41×#59511yescharacteristic
925C22#41×#59511yescharacteristic
926C22#1176387611yescharacteristic
927C22#1176387711yescharacteristic
928C22#1176387811yescharacteristic
929C22#1176387811yescharacteristic
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—344no—
938C4—682no—
939C4—682no—
940C4—682no—
941C4—681no—
942C4—681no—
943C4—681no—
944C4—681no—
945C4—681no—
946C4—681no—
947C4—681no—
948C4—1361no—
949C4—1361no—
950C4—1361no—
951C4—1361no—
952C2—171no—
953C2—171no—
954C2—171no—
955C2—171no—
956C2—171no—
957C2—171no—
958C2—171no—
959C2—171no—
960C2#126×#59511yescharacteristic
961C2#1454528011yescharacteristic
962C2#1454528211yescharacteristic
963C2#1454528311yescharacteristic
964C2#1454528411yescharacteristic
965C2#1454528411yescharacteristic
966C2#1454528511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutator, socleC23×C17C23×C4
FittingC17×#400C4
prime radical, cosocleC23×D17C24
hypercenter#400#595
hypocenterC17#14334
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
46. #11762751C4semidirect
47. #11762751C4semidirect
48. #11762750C4semidirect
49. #11762750C4semidirect
50. #11762749C4semidirect
51. #11762748C4semidirect
52. #11762747C4semidirect
58. C17×#400C4semidirect
498. #400#595semidirect
627. C17#14334semidirect

Maximal subgroups

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

subgroupindex
#145439732
#145439712
#145439702
#145439692
#145439642
#145439632
#95×#5952
D17×#4002
#1433417