Finite Group Databasebeta

← #16792486

Subgroups — #16792486

Order 3328.

1074 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130025C211yesmaximal, characteristic
2#13130025C211yesmaximal, characteristic
3#13130024C211yesmaximal, characteristic
4#13130022C211yesmaximal, characteristic
5#13130022C211yesmaximal, characteristic
6#13130022C211yesmaximal, characteristic
7#13130021C211yesmaximal, characteristic
8#13130021C211yesmaximal, characteristic
9#13130021C211yesmaximal, characteristic
10#13130021C211yesmaximal, characteristic
11#13130021C211yesmaximal, characteristic
12#13130013C211yesmaximal, characteristic
13#13130011C211yesmaximal, characteristic
14#13130011C211yesmaximal, characteristic
15D13×#398C211yesmaximal, characteristic
16C22×C4⋊#261C2211yescharacteristic
17C22×C4⋊#261C2211yescharacteristic
18C22×C4⋊#261C2211yescharacteristic
19C22×C4⋊#261C2211yescharacteristic
20C22×C4×#261C2211yescharacteristic
21C2×C4⋊C4×D13C2211yescharacteristic
22C2×C4⋊C4×D13C2211yescharacteristic
23C2×C4⋊C4×D13C2211yescharacteristic
24C2×C4⋊C4×D13C2211yescharacteristic
25C2×(C2×#261)⋊C4C2211yescharacteristic
26C2×(C2×#261)⋊C4C2211yescharacteristic
27C2×(C2×#261)⋊C4C2211yescharacteristic
28C2×(C2×#261)⋊C4C2211yescharacteristic
29C2×(C2×#261)⋊C4C2211yescharacteristic
30C2×(C2×#261)⋊C4C2211yescharacteristic
31C2×(C2×#261)⋊C4C2211yescharacteristic
32C2×(C2×#261)⋊C4C2211yescharacteristic
33C2×(C2×#261)⋊C4C2211yescharacteristic
34C2×(C2×#261)⋊C4C2211yescharacteristic
35C2×(C2×#261)⋊C4C2211yescharacteristic
36C2×(C2×#261)⋊C4C2211yescharacteristic
37C2×(C2×#261)⋊C4C2211yescharacteristic
38C2×(C2×#261)⋊C4C2211yescharacteristic
39C2×(C2×#261)⋊C4C2211yescharacteristic
40C2×(C2×#261)⋊C4C2211yescharacteristic
41C2×(C2×#261)⋊C4C2211yescharacteristic
42C2×(C2×#261)⋊C4C2211yescharacteristic
43C2×(C2×#261)⋊C4C2211yescharacteristic
44C2×(C2×#261)⋊C4C2211yescharacteristic
45C2×(C2×#261)⋊C4C2211yescharacteristic
46C2×(C2×#261)⋊C4C2211yescharacteristic
47C2×(C2×#261)⋊C4C2211yescharacteristic
48C13×#398C411yescharacteristic, complemented
49#11718645C411yescharacteristic, complemented
50#11718645C411yescharacteristic, complemented
51#11718644C411yescharacteristic, complemented
52#11718641C411yescharacteristic, complemented
53D13×#95C2211yescharacteristic
54D13×#95C2211yescharacteristic
55D13×#95C2211yescharacteristic
56#11718322C411yescharacteristic, complemented
57#11718318C411yescharacteristic, complemented
58#11718318C411yescharacteristic, complemented
59C23×#261C2311yescharacteristic
60C23×#261C2311yescharacteristic
61C23×#261C2311yescharacteristic
62C23×#261C2311yescharacteristic
63C23×#261C2311yescharacteristic
64C23×#261C2311yescharacteristic
65C23×#261C2311yescharacteristic
66C23×#261C2311yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C22×C4×D13C2311yescharacteristic
69C22×C4×D13C2311yescharacteristic
70C22×C4×D13C2311yescharacteristic
71C22×C4×D13C2311yescharacteristic
72C22×C4×D13C2311yescharacteristic
73C22×C4×D13C2311yescharacteristic
74C2×C4⋊#261—22no—
75C2×C4⋊#261—41no—
76C2×C4⋊#261—41no—
77C2×C4⋊#261—41no—
78C2×C4⋊#261—41no—
79C2×C4⋊#261—41no—
80C2×C4⋊#261—41no—
81C2×C4⋊#261—41no—
82C2×C4⋊#261—41no—
83C2×C4⋊#261—41no—
84C2×C4⋊#261—41no—
85C2×C4⋊#261—41no—
86C2×C4×#261—41no—
87C2×C4×#261—41no—
88C2×C4×#261Q814yes—
89C2×C13×C4⋊C4C2×C411yescharacteristic
90C2×C13×C4⋊C4C2×C411yescharacteristic
91C2×C13×C4⋊C4C2×C411yescharacteristic
92C2×C13×C4⋊C4C2×C411yescharacteristic
93C2×C4⋊Dic13C2×C411yescharacteristic
94C2×C4⋊Dic13C2×C411yescharacteristic
95C2×C4⋊Dic13C2×C411yescharacteristic
96C2×C4⋊Dic13C2×C411yescharacteristic
97C2×#6101C2×C411yescharacteristic
98C2×#6101C2×C411yescharacteristic
99C2×#6101C2×C411yescharacteristic
100C2×#6101C2×C411yescharacteristic
101C2×#6101C2×C411yescharacteristic
102C2×#6101C2×C411yescharacteristic
103C2×#6101C2×C411yescharacteristic
104C2×#6101C2×C411yescharacteristic
105C4⋊C4×D13—41no—
106C4⋊C4×D13—41no—
107C4⋊C4×D13—41no—
108C4⋊C4×D13—41no—
109C4⋊C4×D13—41no—
110C4⋊C4×D13—41no—
111C4⋊C4×D13—41no—
112C4⋊C4×D13—41no—
113(C2×#261)⋊C4—22no—
114(C2×#261)⋊C4—22no—
115(C2×#261)⋊C4—41no—
116(C2×#261)⋊C4—41no—
117(C2×#261)⋊C4—41no—
118(C2×#261)⋊C4—41no—
119(C2×#261)⋊C4—41no—
120(C2×#261)⋊C4—41no—
121(C2×#261)⋊C4—41no—
122(C2×#261)⋊C4—41no—
123(C2×#261)⋊C4—41no—
124(C2×#261)⋊C4—41no—
125(C2×#261)⋊C4—41no—
126(C2×#261)⋊C4—41no—
127(C2×#261)⋊C4—41no—
128(C2×#261)⋊C4—41no—
129(C2×#261)⋊C4—41no—
130(C2×#261)⋊C4—41no—
131(C2×#261)⋊C4—41no—
132(C2×#261)⋊C4—41no—
133(C2×#261)⋊C4—41no—
134(C2×#261)⋊C4—41no—
135(C2×#261)⋊C4—41no—
136C13×#95C2×C411yescharacteristic
137C13×#95C2×C411yescharacteristic
138C13×#95C2×C411yescharacteristic
139#88071C2×C411yescharacteristic
140#88071C2×C411yescharacteristic
141#88071C2×C411yescharacteristic
142#88071C2×C411yescharacteristic
143#88071C2×C411yescharacteristic
144#88071C2×C411yescharacteristic
145#88071C2×C411yescharacteristic
146#88071C2×C411yescharacteristic
147#88071C2×C411yescharacteristic
148#14640—131nomaximal, Sylow
149C23×D13C2411yescharacteristic
150C22×#261—21no—
151C22×#261—21no—
152C22×#261—21no—
153C22×#261—21no—
154C22×#261—21no—
155C22×#261—21no—
156C22×#261—21no—
157C22×#261—21no—
158C22×#261—21no—
159C22×#261—21no—
160C22×#261—21no—
161C22×#261—21no—
162C22×#261—21no—
163C22×#261—21no—
164C22×#261—21no—
165C22×#261—21no—
166C22×#261—21no—
167C22×#261—21no—
168C22×#261—21no—
169C22×#261—21no—
170C22×#261—21no—
171C22×#261—21no—
172C22×#261—21no—
173C22×#261—21no—
174C22×#261—21no—
175C22×#261—21no—
176C22×#261—21no—
177C22×#261—21no—
178C22×#261—21no—
179C22×#261—21no—
180C22×#261—21no—
181C22×#261—21no—
182C22×#261—21no—
183C22×#261—21no—
184C22×#261—21no—
185C22×#261—21no—
186C22×#261—21no—
187C22×#261—21no—
188C22×#261—21no—
189C22×#261—21no—
190C22×#261—21no—
191C22×#261—21no—
192C22×#261—21no—
193C22×#261—21no—
194C22×#261—21no—
195C22×#261—21no—
196C22×#261—21no—
197C22×#261—21no—
198C22×#261—21no—
199C22×#261—21no—
200C22×#261—21no—
201C22×#261—21no—
202C22×#261—21no—
203C22×#261—21no—
204C22×#261C2×Q812yes—
205C22×#261C2×Q812yes—
206C22×C4×C13C22×C411yescharacteristic
207C22×C4×C13C22×C411yescharacteristic
208C22×C4×C13C22×C411yescharacteristic
209C22×C4×C13C22×C411yescharacteristic
210C22×C4×C13C22×C411yescharacteristic
211C22×C4×C13C22×C411yescharacteristic
212C22×C4×C13C22×C411yescharacteristic
213C22×Dic13C22×C411yescharacteristic
214C22×Dic13C22×C411yescharacteristic
215C22×Dic13C22×C411yescharacteristic
216C22×Dic13C22×C411yescharacteristic
217C22×Dic13C22×C411yescharacteristic
218C22×Dic13C22×C411yescharacteristic
219C22×Dic13C22×C411yescharacteristic
220C2×C4×D13—21no—
221C2×C4×D13—21no—
222C2×C4×D13—21no—
223C2×C4×D13—21no—
224C2×C4×D13—21no—
225C2×C4×D13—21no—
226C2×C4×D13—21no—
227C2×C4×D13—21no—
228C2×C4×D13—21no—
229C2×C4×D13—21no—
230C2×C4×D13—21no—
231C2×C4×D13—21no—
232C2×C4×D13—21no—
233C2×C4×D13—21no—
234C2×C4×D13—21no—
235C2×C4×D13—21no—
236C2×C4×D13—21no—
237C2×C4×D13—21no—
238C2×C4×D13—21no—
239C2×C4×D13—21no—
240C2×C4×D13—21no—
241C2×C4×D13—21no—
242C2×C4×D13—21no—
243C2×C4×D13—21no—
244C2×C4×D13—21no—
245C2×C4×D13—21no—
246C2×C4×D13—21no—
247C2×C4×D13—21no—
248C2×C4×D13—21no—
249C2×C4×D13—21no—
250C2×C4×D13—21no—
251C2×C4×D13—21no—
252C2×C4×D13—21no—
253C2×C4×D13—21no—
254C2×C4×D13—21no—
255C2×C4×D13—21no—
256C2×C4×D13—21no—
257C2×C4×D13—21no—
258C2×C4×D13—21no—
259C2×C4×D13—21no—
260C2×C4×D13C2×Q812yes—
261C2×C4×D13#4112yes—
262C4⋊#261—44no—
263C4⋊#261—44no—
264C4⋊#261—44no—
265C4⋊#261—44no—
266C4×#261—44no—
267C13×C4⋊C4—41no—
268C13×C4⋊C4—41no—
269C13×C4⋊C4—41no—
270C13×C4⋊C4—41no—
271C4⋊Dic13—41no—
272C4⋊Dic13—41no—
273C4⋊Dic13—41no—
274C4⋊Dic13—41no—
275#6101—41no—
276#6101—41no—
277#6101—41no—
278#6101—41no—
279#6101—41no—
280#6101—41no—
281#6101—41no—
282#6101—41no—
283C2×#398—131no—
284#1445—131no—
285#1445—131no—
286#1444—131no—
287#1442—131no—
288#1442—131no—
289#1442—131no—
290#1441—131no—
291#1441—131no—
292#1441—131no—
293#1441—131no—
294#1441—131no—
295C4⋊#95—131no—
296#1434—131no—
297#1434—131no—
298C23×C13C23×C411yescharacteristic
299C22×D13C22×Q811yescharacteristic
300C22×D13C2×#4111yescharacteristic
301C22×D13H(5,𝔽2)11yescharacteristic
302C22×D13H(5,𝔽2)11yescharacteristic
303C22×D13H(5,𝔽2)11yescharacteristic
304C22×D13H(5,𝔽2)11yescharacteristic
305C22×D13H(5,𝔽2)11yescharacteristic
306C22×D13H(5,𝔽2)11yescharacteristic
307C22×D13H(5,𝔽2)11yescharacteristic
308C22×D132−1+411yescharacteristic
309C22×D132−1+411yescharacteristic
310C22×D132−1+411yescharacteristic
311C22×D132−1+411yescharacteristic
312C22×D132−1+411yescharacteristic
313C2×#261—22no—
314C2×#261—22no—
315C2×#261—22no—
316C2×#261—22no—
317C2×#261—22no—
318C2×#261—22no—
319C2×#261—41no—
320C2×#261—41no—
321C2×#261—41no—
322C2×#261—41no—
323C2×#261—41no—
324C2×#261—41no—
325C2×#261—41no—
326C2×#261—41no—
327C2×#261—41no—
328C2×#261—41no—
329C2×#261—41no—
330C2×#261—41no—
331C2×#261—41no—
332C2×#261—41no—
333C2×#261—41no—
334C2×#261—41no—
335C2×#261—41no—
336C2×#261—41no—
337C2×#261—41no—
338C2×#261—41no—
339C2×#261—41no—
340C2×#261—41no—
341C2×#261—41no—
342C2×#261—41no—
343C2×#261—41no—
344C2×#261—41no—
345C2×#261—41no—
346C2×#261—41no—
347C2×#261—41no—
348C2×#261—41no—
349C2×#261—41no—
350C2×#261—41no—
351C2×#261—41no—
352C2×#261—41no—
353C2×#261—41no—
354C2×#261—41no—
355C2×#261—41no—
356C2×#261—41no—
357C2×#261—41no—
358C2×#261—41no—
359C2×#261—41no—
360C2×#261—41no—
361C2×#261—41no—
362C2×#261—41no—
363C2×#261—41no—
364C2×#261—41no—
365C2×#261—41no—
366C2×#261—41no—
367C2×#261—41no—
368C2×#261—41no—
369C2×C4×C13—21no—
370C2×C4×C13—21no—
371C2×C4×C13—21no—
372C2×C4×C13—21no—
373C2×C4×C13—21no—
374C2×C4×C13—21no—
375C2×C4×C13—21no—
376C2×C4×C13—21no—
377C2×C4×C13—21no—
378C2×C4×C13—21no—
379C2×C4×C13—21no—
380C2×C4×C13—21no—
381C2×C4×C13—21no—
382C2×C4×C13—21no—
383C2×C4×C13—21no—
384C2×C4×C13—21no—
385C2×C4×C13—21no—
386C2×C4×C13—21no—
387C2×C4×C13—21no—
388C2×C4×C13—21no—
389C2×C4×C13C4×Q812yes—
390C2×Dic13—21no—
391C2×Dic13—21no—
392C2×Dic13—21no—
393C2×Dic13—21no—
394C2×Dic13—21no—
395C2×Dic13—21no—
396C2×Dic13—21no—
397C2×Dic13—21no—
398C2×Dic13—21no—
399C2×Dic13—21no—
400C2×Dic13—21no—
401C2×Dic13—21no—
402C2×Dic13—21no—
403C2×Dic13—21no—
404C2×Dic13—21no—
405C2×Dic13—21no—
406C2×Dic13—21no—
407C2×Dic13—21no—
408C2×Dic13—21no—
409C2×Dic13—21no—
410C2×Dic13C4×Q812yes—
411C4×D13—22no—
412C4×D13—22no—
413C4×D13—22no—
414C4×D13—22no—
415C4×D13—41no—
416C4×D13—41no—
417C4×D13—41no—
418C4×D13—41no—
419C4×D13—41no—
420C4×D13—41no—
421C4×D13—41no—
422C4×D13—41no—
423C4×D13—41no—
424C4×D13—41no—
425C4×D13—41no—
426C4×D13—41no—
427C4×D13—41no—
428C4×D13—41no—
429C4×D13—41no—
430C4×D13—41no—
431C4×D13—41no—
432C4×D13—41no—
433C4×D13—41no—
434C4×D13—41no—
435C4×D13—41no—
436C4×D13—41no—
437C4×D13—41no—
438C4×D13—41no—
439C22×C4⋊C4—131no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—131no—
444C22×C4⋊C4—131no—
445C22×C4⋊C4—131no—
446C22×C4⋊C4—131no—
447C22×C42—131no—
448#398—131no—
449#398—131no—
450#398—131no—
451#398—131no—
452#398—131no—
453#398—131no—
454#398—131no—
455#398#26111yescharacteristic, complemented
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95—131no—
464C2×#95—131no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C22×C13C2×C4×Q811yescharacteristic
483C22×C13#51811yescharacteristic
484C22×C13#51811yescharacteristic
485C22×C13#51911yescharacteristic
486C22×C13#52011yescharacteristic
487C22×C13#52011yescharacteristic
488C22×C13#52011yescharacteristic
489C2×D13#53811yescharacteristic
490C2×D13#53911yescharacteristic
491C2×D13#54011yescharacteristic
492C2×D13#54111yescharacteristic
493C2×D13#54211yescharacteristic
494C2×D13#54211yescharacteristic
495C2×D13#54311yescharacteristic
496C2×D13#54411yescharacteristic
497C2×D13#54411yescharacteristic
498C2×D13#54411yescharacteristic
499C2×D13#54411yescharacteristic
500C2×D13#54411yescharacteristic
501C2×D13#56011yescharacteristic
502C2×D13#56011yescharacteristic
503C2×D13#56011yescharacteristic
504C2×D13#56211yescharacteristic
505C2×D13#56211yescharacteristic
506C2×D13#56211yescharacteristic
507C2×D13#56211yescharacteristic
508C2×D13#56211yescharacteristic
509C2×D13#56211yescharacteristic
510C2×D13#56211yescharacteristic
511C2×D13#56311yescharacteristic
512C2×D13#56311yescharacteristic
513C2×D13#56311yescharacteristic
514C2×D13#56311yescharacteristic
515C2×D13#56311yescharacteristic
516C2×D13#56411yescharacteristic
517#261—42no—
518#261—42no—
519#261—81no—
520#261—81no—
521#261—81no—
522#261—81no—
523#261—81no—
524#261—81no—
525C4×C13—22no—
526C4×C13—41no—
527C4×C13—41no—
528C4×C13—41no—
529C4×C13—41no—
530C4×C13—41no—
531C4×C13—41no—
532Dic13—22no—
533Dic13—41no—
534Dic13—41no—
535Dic13—41no—
536Dic13—41no—
537Dic13—41no—
538Dic13—41no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C2×C4⋊C4—131no—
555C2×C4⋊C4—131no—
556C2×C4⋊C4—131no—
557C2×C4⋊C4—131no—
558C2×C4⋊C4—131no—
559C2×C4⋊C4—131no—
560C2×C4⋊C4—131no—
561C2×C4⋊C4—131no—
562C2×C4⋊C4—131no—
563C2×C4⋊C4—131no—
564C2×C4⋊C4—131no—
565C2×C4⋊C4—131no—
566C2×C4⋊C4—262no—
567C2×C4⋊C4—521no—
568C2×C4⋊C4—521no—
569C2×C4⋊C4—521no—
570C2×C4⋊C4—521no—
571C2×C4⋊C4—521no—
572C2×C4⋊C4—521no—
573C2×C4⋊C4—521no—
574C2×C4⋊C4—521no—
575C2×C4⋊C4—521no—
576C2×C4⋊C4—521no—
577C2×C4⋊C4—521no—
578C2×C4⋊C4—521no—
579C2×C4⋊C4—521no—
580C2×C4⋊C4—521no—
581C2×C4⋊C4—521no—
582C2×C4⋊C4—521no—
583C2×C4⋊C4—521no—
584C2×C4⋊C4—521no—
585C2×C4⋊C4—521no—
586C2×C4⋊C4C2×#26111yescharacteristic
587C2×C4⋊C4C2×#26111yescharacteristic
588C2×C4⋊C4C2×#26111yescharacteristic
589C2×C4⋊C4C2×#26111yescharacteristic
590C2×C42—134no—
591C2×C42—521no—
592C2×C42—521no—
593#95—131no—
594#95—131no—
595#95—131no—
596#95—131no—
597#95—131no—
598#95—131no—
599#95—131no—
600#95—131no—
601#95—131no—
602#95—262no—
603#95—262no—
604#95—521no—
605#95—521no—
606#95—521no—
607#95—521no—
608#95—521no—
609#95—521no—
610#95—521no—
611#95—521no—
612#95—521no—
613#95—521no—
614#95—521no—
615#95—521no—
616#95—521no—
617#95—521no—
618#95—521no—
619#95—521no—
620#95—521no—
621#95—521no—
622#95—521no—
623#95—521no—
624#95—521no—
625#95C2×#26111yescharacteristic
626#95C2×#26111yescharacteristic
627#95C2×#26111yescharacteristic
628C2×C13#232911yescharacteristic
629C2×C13#233011yescharacteristic
630C2×C13#233111yescharacteristic
631C2×C13#237611yescharacteristic
632C2×C13#237711yescharacteristic
633C2×C13#237811yescharacteristic
634C2×C13#238211yescharacteristic
635D13#282911yescharacteristic
636D13#283111yescharacteristic
637D13#283711yescharacteristic
638D13#283911yescharacteristic
639D13#284111yescharacteristic
640D13#284111yescharacteristic
641D13#284311yescharacteristic
642D13#284511yescharacteristic
643C24—131no—
644C22×C4—131no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—132no—
648C22×C4—132no—
649C22×C4—131no—
650C22×C4—131no—
651C22×C4—131no—
652C22×C4—131no—
653C22×C4—131no—
654C22×C4—131no—
655C22×C4—261no—
656C22×C4—261no—
657C22×C4—261no—
658C22×C4—261no—
659C22×C4—261no—
660C22×C4—261no—
661C22×C4—261no—
662C22×C4—261no—
663C22×C4—261no—
664C22×C4—261no—
665C22×C4—261no—
666C22×C4—261no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4—261no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—261no—
673C22×C4—261no—
674C22×C4—261no—
675C22×C4—261no—
676C22×C4—261no—
677C22×C4—261no—
678C22×C4—261no—
679C22×C4—261no—
680C22×C4—261no—
681C22×C4—261no—
682C22×C4—261no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4C22×#26111yescharacteristic
750C22×C4C22×#26111yescharacteristic
751C22×C4C22×#26111yescharacteristic
752C22×C4C22×#26111yescharacteristic
753C22×C4C22×#26111yescharacteristic
754C22×C4C22×#26111yescharacteristic
755C22×C4C22×#26111yescharacteristic
756C4⋊C4—41no—
757C4⋊C4—41no—
758C4⋊C4—41no—
759C4⋊C4—41no—
760C4⋊C4—521no—
761C4⋊C4—521no—
762C4⋊C4—521no—
763C4⋊C4—521no—
764C4⋊C4—521no—
765C4⋊C4—521no—
766C4⋊C4—521no—
767C4⋊C4—521no—
768C4⋊C4—521no—
769C4⋊C4—521no—
770C4⋊C4—521no—
771C4⋊C4—521no—
772C4⋊C4—524no—
773C4⋊C4—524no—
774C4⋊C4—524no—
775C4⋊C4—524no—
776C42—524no—
777C13#1464011yescharacteristic, complemented, Sylow
778C23—131no—
779C23—131no—
780C23—131no—
781C23—131no—
782C23—131no—
783C23—131no—
784C23—131no—
785C23—131no—
786C23—131no—
787C23—131no—
788C23—131no—
789C23—131no—
790C23—131no—
791C23—131no—
792C23C23×#26111yescharacteristic
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—132no—
814C2×C4—262no—
815C2×C4—262no—
816C2×C4—262no—
817C2×C4—262no—
818C2×C4—261no—
819C2×C4—261no—
820C2×C4—262no—
821C2×C4—262no—
822C2×C4—262no—
823C2×C4—262no—
824C2×C4—262no—
825C2×C4—262no—
826C2×C4—261no—
827C2×C4—261no—
828C2×C4—261no—
829C2×C4—261no—
830C2×C4—261no—
831C2×C4—261no—
832C2×C4—261no—
833C2×C4—261no—
834C2×C4—261no—
835C2×C4—261no—
836C2×C4—261no—
837C2×C4—261no—
838C2×C4—261no—
839C2×C4—261no—
840C2×C4—261no—
841C2×C4—261no—
842C2×C4—261no—
843C2×C4—261no—
844C2×C4—521no—
845C2×C4—521no—
846C2×C4—521no—
847C2×C4—521no—
848C2×C4—521no—
849C2×C4—521no—
850C2×C4—521no—
851C2×C4—521no—
852C2×C4—521no—
853C2×C4—521no—
854C2×C4—521no—
855C2×C4—521no—
856C2×C4—521no—
857C2×C4—521no—
858C2×C4—521no—
859C2×C4—521no—
860C2×C4—521no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—521no—
865C2×C4—521no—
866C2×C4—521no—
867C2×C4—521no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4—521no—
875C2×C4—521no—
876C2×C4—521no—
877C2×C4—521no—
878C2×C4—521no—
879C2×C4—521no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
886C2×C4—521no—
887C2×C4—521no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
901C2×C4—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4Q8×#26112yes—
919C22—131no—
920C22—131no—
921C22—131no—
922C22—131no—
923C22—131no—
924C22—131no—
925C22—131no—
926C22—131no—
927C22—131no—
928C22—131no—
929C22—131no—
930C22—131no—
931C22—131no—
932C22—131no—
933C22—131no—
934C22—131no—
935C22—131no—
936C22—131no—
937C22—131no—
938C22—131no—
939C22—131no—
940C22—131no—
941C22—131no—
942C22—131no—
943C22—131no—
944C22—131no—
945C22—131no—
946C22—131no—
947C22#1171962311yescharacteristic
948C22#1171962311yescharacteristic
949C22C2×Q8×#26111yescharacteristic
950C22#1171962711yescharacteristic
951C22#1171963111yescharacteristic
952C22#1171963111yescharacteristic
953C22#1171963111yescharacteristic
954C4—22no—
955C4—41no—
956C4—41no—
957C4—41no—
958C4—41no—
959C4—41no—
960C4—41no—
961C4—262no—
962C4—522no—
963C4—522no—
964C4—521no—
965C4—521no—
966C4—521no—
967C4—521no—
968C4—521no—
969C4—521no—
970C4—1041no—
971C4—1041no—
972C4—1041no—
973C4—1041no—
974C4—1041no—
975C4—1041no—
976C2—131no—
977C2—131no—
978C2—131no—
979C2—131no—
980C2—131no—
981C2—131no—
982C2—131no—
983C2—131no—
984C2#1313132911yescharacteristic
985C2#1313133011yescharacteristic
986C2#1313133111yescharacteristic
987C2#1313137611yescharacteristic
988C2#1313137711yescharacteristic
989C2#1313137811yescharacteristic
990C2#1313138211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#398C4
prime radical, cosocleC23×D13C24
hypercenter#398#261
hypocenterC13#14640
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
48. C13×#398C4semidirect
49. #11718645C4semidirect
50. #11718645C4semidirect
51. #11718644C4semidirect
52. #11718641C4semidirect
56. #11718322C4semidirect
57. #11718318C4semidirect
58. #11718318C4semidirect
455. #398#261semidirect
777. C13#14640semidirect

Maximal subgroups

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

subgroupindex
#131300252
#131300242
#131300222
#131300212
#131300132
#131300112
D13×#3982
#1464013