Finite Group Databasebeta

← #15830459

Subgroups — #15830459

Order 3328.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123871C211yesmaximal, characteristic, complemented
2#13117469C211yesmaximal, characteristic, complemented
3#13113413C211yesmaximal, characteristic, complemented
4#13113408C211yesmaximal, characteristic, complemented
5#13113400C211yesmaximal, characteristic, complemented
6#13113392C211yesmaximal, characteristic, complemented
7#13113387C211yesmaximal, characteristic, complemented
8#13113379C211yesmaximal, characteristic, complemented
9#13113374C211yesmaximal, characteristic, complemented
10#13113369C211yesmaximal, characteristic, complemented
11#13113356C211yesmaximal, characteristic, complemented
12#13113340C211yesmaximal, characteristic, complemented
13#13113327C211yesmaximal, characteristic, complemented
14C2×#11718130C211yesmaximal, characteristic, complemented
15C13×#3520C211yesmaximal, characteristic
16C13×#556C411yescharacteristic, complemented
17C13×#554—21no—
18C13×#552C411yescharacteristic, complemented
19C13×#552C411yescharacteristic, complemented
20C13×#551—21no—
21C13×#551—21no—
22D4×Q8×C13C411yescharacteristic, complemented
23C13×#548C411yescharacteristic, complemented
24C13×#548C411yescharacteristic, complemented
25C13×#547C411yescharacteristic, complemented
26C13×#547C411yescharacteristic, complemented
27C13×#546—21no—
28C13×#542—21no—
29C13×#539—21no—
30C13×#539—21no—
31C13×#533C2211yescharacteristic
32C13×#529C2211yescharacteristic
33C13×#525C2211yescharacteristic
34C13×#525C2211yescharacteristic
35C2×C13×C22⋊Q8C2211yescharacteristic
36C2×C13×C22⋊Q8C2211yescharacteristic
37C13×#520—21no—
38C2×C4×D4×C13C2211yescharacteristic
39#11718881—21no—
40#11718873C2211yescharacteristic
41#11718872C2211yescharacteristic
42C4×C22⋊Dic13C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44#11718868C2211yescharacteristic
45#11718868C2211yescharacteristic
46C2×C22⋊#1055C2211yescharacteristic
47C2×C22⋊#1055C2211yescharacteristic
48#11718673—21no—
49#11718672—21no—
50#11718672—21no—
51D4×#1055—21no—
52#11718642—21no—
53#11718612—21no—
54#11718611—21no—
55#11718598C2211yescharacteristic
56#11718597C2211yescharacteristic
57#11718587C2211yescharacteristic
58#11718586C2211yescharacteristic
59#11718130C2211yescharacteristic
60#11718130C2211yescharacteristic
61#11718130C2211yescharacteristic
62#11718130C2211yescharacteristic
63#11718130C2211yescharacteristic
64#11718130C2211yescharacteristic
65#11718130C2211yescharacteristic
66#11718130C2211yescharacteristic
67#11718130C2211yescharacteristic
68#11718130C2211yescharacteristic
69#11718130C2211yescharacteristic
70#11718130C2211yescharacteristic
71#11718129C2211yescharacteristic
72#11718129C2211yescharacteristic
73#11718129C2211yescharacteristic
74#11718129C2211yescharacteristic
75C2×C13×#41—21no—
76C2×C13×#41C2×C411yescharacteristic
77C2×C13×#41C2×C411yescharacteristic, complemented
78C22×Q8×C13C2×C411yescharacteristic
79C22×Q8×C13C2×C411yescharacteristic, complemented
80C22×D4×C13D411yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×Dic13—21no—
84C13×C4⋊Q8—21no—
85C13×C4⋊Q8C2×C411yescharacteristic, complemented
86C13×C4⋊Q8C2×C411yescharacteristic, complemented
87C13×#126—21no—
88C13×#126—21no—
89C13×#126—21no—
90C13×#126—21no—
91C13×#126—21no—
92C13×#125—21no—
93C13×#125—21no—
94C13×#125—21no—
95C13×#125C2×C411yescharacteristic, complemented
96C13×#124—21no—
97C13×#124—21no—
98C13×#124—21no—
99C13×#124C2×C411yescharacteristic, complemented
100C13×#123—21no—
101C13×#123—21no—
102C13×#123—21no—
103C13×#123—21no—
104C13×#123—21no—
105C13×#123—21no—
106C13×#123—21no—
107C13×#123—21no—
108C13×#123—21no—
109C13×C22⋊Q8—21no—
110C13×C22⋊Q8—21no—
111C13×C22⋊Q8—21no—
112C13×C22⋊Q8—21no—
113C13×C22⋊Q8—21no—
114C13×C22⋊Q8—21no—
115C13×C22⋊Q8—21no—
116C13×C22⋊Q8—21no—
117C13×C22⋊Q8—21no—
118C13×C22⋊Q8—21no—
119C13×C22⋊Q8C2×C411yescharacteristic
120C13×C22⋊Q8C2×C411yescharacteristic
121C13×C22⋊Q8C2×C411yescharacteristic
122C13×C22⋊Q8C2×C411yescharacteristic, complemented
123C13×C22⋊Q8C2×C411yescharacteristic, complemented
124C13×C22⋊Q8C2×C411yescharacteristic, complemented
125C13×C22⋊Q8C2311yescharacteristic
126C13×C22⋊Q8C2311yescharacteristic
127C13×C22⋊Q8C2311yescharacteristic
128C13×#121—21no—
129C13×#121—21no—
130C13×#121—21no—
131C13×#121C2×C411yescharacteristic
132C13×#121C2×C411yescharacteristic, complemented
133C13×#121C2311yescharacteristic
134C13×#120—21no—
135C13×#120—21no—
136C4×Q8×C13—21no—
137C4×Q8×C13—21no—
138C4×Q8×C13C2×C411yescharacteristic, complemented
139C4×Q8×C13C2×C411yescharacteristic, complemented
140C4×Q8×C13C2×C411yescharacteristic, complemented
141C4×D4×C13—21no—
142C4×D4×C13—21no—
143C4×D4×C13—21no—
144C4×D4×C13—21no—
145C4×D4×C13—21no—
146C4×D4×C13—21no—
147C4×D4×C13—21no—
148C4×D4×C13—21no—
149C4×D4×C13C2×C411yescharacteristic
150C4×D4×C13C2×C411yescharacteristic
151C4×D4×C13C2×C411yescharacteristic
152C4×D4×C13C2×C411yescharacteristic
153C4×D4×C13C2×C411yescharacteristic, complemented
154C4×D4×C13D411yescharacteristic
155C4×D4×C13D411yescharacteristic
156C4×D4×C13D411yescharacteristic
157C4×D4×C13D411yescharacteristic
158C13×#117—21no—
159C13×#117—21no—
160C13×#117—21no—
161C13×#117—21no—
162C13×#117C2×C411yescharacteristic
163C13×#117C2×C411yescharacteristic, complemented
164C2×C13×C4⋊C4—21no—
165C2×C13×C4⋊C4—21no—
166C2×C13×C4⋊C4—21no—
167C2×C13×C4⋊C4C2×C411yescharacteristic
168C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
169C2×C13×C4⋊C4D411yescharacteristic
170C2×C13×C22⋊C4—21no—
171C2×C13×C22⋊C4—21no—
172C2×C13×C22⋊C4D411yescharacteristic
173C2×C13×C22⋊C4D411yescharacteristic
174C2×C42×C13C2311yescharacteristic
175C2×C22⋊Dic13—21no—
176C2×C22⋊Dic13—21no—
177C2×C22⋊Dic13—21no—
178C2×C4⋊Dic13—21no—
179C2×C4⋊Dic13—21no—
180C2×C4×Dic13—21no—
181C2×#6099—21no—
182C2×#6099—21no—
183C22×#1055—21no—
184C22×#1055—21no—
185#88071—21no—
186#88071—21no—
187#88071—21no—
188#88071—21no—
189#88071—21no—
190#88071C2311yescharacteristic
191#88071C2311yescharacteristic
192#88071C2311yescharacteristic
193#88071C2311yescharacteristic
194C22⋊#1055—21no—
195C22⋊#1055—21no—
196C22⋊#1055—21no—
197C22⋊#1055—21no—
198C22⋊#1055C2311yescharacteristic
199C22⋊#1055C2311yescharacteristic
200C22⋊#1055C2311yescharacteristic
201C22⋊#1055C2311yescharacteristic
202C4⋊#1055—21no—
203C4⋊#1055—21no—
204#88043—21no—
205C4×#1055—21no—
206#17598—131nomaximal, Sylow
207C24×C13C2×D411yescharacteristic
208C24×C13C2×D411yescharacteristic
209C13×#41—44no—
210C13×#41—81no—
211C13×#41—81no—
212C2×Q8×C13—21no—
213C2×Q8×C13—21no—
214C2×Q8×C13—21no—
215C2×Q8×C13—81no—
216C2×Q8×C13—81no—
217C2×Q8×C13C22×C411yescharacteristic
218C2×Q8×C13C22×C411yescharacteristic
219C2×Q8×C13C22×C411yescharacteristic
220C2×D4×C13—21no—
221C2×D4×C13—21no—
222C2×D4×C13—21no—
223C2×D4×C13—21no—
224C2×D4×C13—21no—
225C2×D4×C13—42no—
226C2×D4×C13C22⋊C411yescharacteristic
227C2×D4×C13C22⋊C411yescharacteristic
228C2×D4×C13C22⋊C411yescharacteristic
229C2×D4×C13C22⋊C411yescharacteristic
230C2×D4×C13C22×C411yescharacteristic
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—81no—
239C22×C4×C13—81no—
240C22×C4×C13C22×C411yescharacteristic
241C22×C4×C13C22×C411yescharacteristic
242C22×C4×C13C22×C411yescharacteristic
243C22×C4×C13C22×C411yescharacteristic
244C22×C4×C13C2×D411yescharacteristic
245C22×C4×C13C2×D411yescharacteristic
246C22×C4×C13C2×D411yescharacteristic
247C22×C4×C13C2×D411yescharacteristic
248C22×C4×C13C2×D411yescharacteristic
249C22×C4×C13C2×D411yescharacteristic
250C22×C4×C13C2×D411yescharacteristic
251C22×C4×C13C2×D411yescharacteristic
252C22×C4×C13C2411yescharacteristic
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—42no—
258C22×Dic13—81no—
259C22×Dic13—81no—
260C13×C4⋊C4—21no—
261C13×C4⋊C4—21no—
262C13×C4⋊C4—21no—
263C13×C4⋊C4—21no—
264C13×C4⋊C4—21no—
265C13×C4⋊C4—21no—
266C13×C4⋊C4—21no—
267C13×C4⋊C4—21no—
268C13×C4⋊C4—21no—
269C13×C4⋊C4—21no—
270C13×C4⋊C4—21no—
271C13×C4⋊C4—21no—
272C13×C4⋊C4—21no—
273C13×C4⋊C4—21no—
274C13×C4⋊C4—21no—
275C13×C4⋊C4—21no—
276C13×C4⋊C4—21no—
277C13×C4⋊C4—21no—
278C13×C4⋊C4—21no—
279C13×C4⋊C4C22⋊C411yescharacteristic
280C13×C4⋊C4C22⋊C411yescharacteristic
281C13×C4⋊C4C22⋊C411yescharacteristic
282C13×C4⋊C4C22⋊C411yescharacteristic
283C13×C4⋊C4C22×C411yescharacteristic
284C13×C4⋊C4C22×C411yescharacteristic
285C13×C4⋊C4C22×C411yescharacteristic
286C13×C4⋊C4C22×C411yescharacteristic
287C13×C22⋊C4—21no—
288C13×C22⋊C4—21no—
289C13×C22⋊C4—21no—
290C13×C22⋊C4—21no—
291C13×C22⋊C4—21no—
292C13×C22⋊C4—21no—
293C13×C22⋊C4—21no—
294C13×C22⋊C4—21no—
295C13×C22⋊C4—21no—
296C13×C22⋊C4—21no—
297C13×C22⋊C4—21no—
298C13×C22⋊C4—21no—
299C13×C22⋊C4—21no—
300C13×C22⋊C4—21no—
301C13×C22⋊C4—21no—
302C13×C22⋊C4—21no—
303C13×C22⋊C4—21no—
304C13×C22⋊C4C22⋊C411yescharacteristic
305C13×C22⋊C4C22⋊C411yescharacteristic
306C13×C22⋊C4C22⋊C411yescharacteristic
307C13×C22⋊C4C22⋊C411yescharacteristic
308C13×C22⋊C4C22⋊C411yescharacteristic
309C13×C22⋊C4C22⋊C411yescharacteristic
310C13×C22⋊C4C22⋊C411yescharacteristic
311C13×C22⋊C4C22⋊C411yescharacteristic
312C42×C13—21no—
313C42×C13—21no—
314C42×C13—21no—
315C42×C13—21no—
316C42×C13—21no—
317C42×C13C22×C411yescharacteristic
318C42×C13C22×C411yescharacteristic
319C42×C13C2×D411yescharacteristic
320C42×C13C2×D411yescharacteristic
321C22⋊Dic13—42no—
322C22⋊Dic13—81no—
323C22⋊Dic13—81no—
324C4⋊Dic13—81no—
325C4⋊Dic13—81no—
326C4×Dic13—81no—
327#6099—81no—
328#6099—81no—
329C2×#1055—21no—
330C2×#1055—21no—
331C2×#1055—21no—
332C2×#1055—21no—
333C2×#1055—81no—
334C2×#1055—81no—
335#3520D1311yescharacteristic
336#2974—131no—
337#2318—131no—
338#1521—131no—
339#1520—131no—
340#1518—131no—
341#1516—131no—
342#1515—131no—
343#1513—131no—
344#1512—131no—
345#1511—131no—
346#1508—131no—
347#1504—131no—
348#1501—131no—
349C2×#328—131no—
350C23×C13—21no—
351C23×C13—21no—
352C23×C13—22no—
353C23×C13—21no—
354C23×C13—21no—
355C23×C13—21no—
356C23×C13—41no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13C2×C22⋊C411yescharacteristic
360C23×C13C2×C22⋊C411yescharacteristic
361C23×C13C2×C22⋊C411yescharacteristic
362C23×C13C2×C22⋊C411yescharacteristic
363C23×C13C22×D411yescharacteristic
364Q8×C13—42no—
365Q8×C13—41no—
366Q8×C13—41no—
367Q8×C13—41no—
368Q8×C13—81no—
369Q8×C13—81no—
370D4×C13—22no—
371D4×C13—22no—
372D4×C13—41no—
373D4×C13—41no—
374D4×C13—41no—
375D4×C13—42no—
376D4×C13—41no—
377D4×C13—41no—
378D4×C13—42no—
379D4×C13—81no—
380D4×C13—81no—
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×C13—21no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—42no—
403C2×C4×C13—42no—
404C2×C4×C13—42no—
405C2×C4×C13—81no—
406C2×C4×C13—81no—
407C2×C4×C13—81no—
408C2×C4×C13—81no—
409C2×C4×C13C2×C22⋊C411yescharacteristic
410C2×C4×C13C2×C22⋊C411yescharacteristic
411C2×C4×C13C2×C22⋊C411yescharacteristic
412C2×C4×C13C2×C22⋊C411yescharacteristic
413C2×C4×C13C2×C22⋊C411yescharacteristic
414C2×C4×C13C2×C22⋊C411yescharacteristic
415C2×C4×C13C2×C22⋊C411yescharacteristic
416C2×C4×C13C2×C22⋊C411yescharacteristic
417C2×C4×C13C23×C411yescharacteristic
418C2×C4×C13C22×D411yescharacteristic
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—84no—
432#1055—41no—
433#1055—41no—
434#1055—41no—
435#1055—41no—
436#556Dic1311yescharacteristic, complemented
437#554—21no—
438#552Dic1311yescharacteristic, complemented
439#552Dic1311yescharacteristic, complemented
440#551—21no—
441#551—21no—
442D4×Q8Dic1311yescharacteristic, complemented
443#548Dic1311yescharacteristic, complemented
444#548Dic1311yescharacteristic, complemented
445#547Dic1311yescharacteristic, complemented
446#547Dic1311yescharacteristic, complemented
447#546—21no—
448#542—21no—
449#539—21no—
450#539—21no—
451#533C2×D1311yescharacteristic
452#529C2×D1311yescharacteristic
453#525C2×D1311yescharacteristic
454#525C2×D1311yescharacteristic
455C2×C22⋊Q8C2×D1311yescharacteristic
456C2×C22⋊Q8C2×D1311yescharacteristic
457#520—21no—
458C2×C4×D4C2×D1311yescharacteristic
459#436—261no—
460#435—261no—
461#435—261no—
462C8×D4—261no—
463#432—131no—
464#431—131no—
465#407—131no—
466#407—131no—
467C2×C22⋊C8—131no—
468C2×C22⋊C8—131no—
469#388—261no—
470#387—261no—
471#386—261no—
472#385—261no—
473#383—131no—
474#382—131no—
475#381—131no—
476#380—131no—
477C4×C22⋊C4—131no—
478C2×#95—131no—
479#328—131no—
480#328—131no—
481#328—131no—
482#328—131no—
483#328—131no—
484#328—131no—
485#328—131no—
486#328—131no—
487#328—131no—
488#328—131no—
489#328—131no—
490#328—131no—
491#327—131no—
492#327—131no—
493#327—131no—
494#327—131no—
495C22×C13—21no—
496C22×C13—21no—
497C22×C13—21no—
498C22×C13—21no—
499C22×C13—21no—
500C22×C13—21no—
501C22×C13—21no—
502C22×C13—21no—
503C22×C13—21no—
504C22×C13—21no—
505C22×C13—21no—
506C22×C13—21no—
507C22×C13—21no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—41no—
511C22×C13—41no—
512C22×C13—41no—
513C22×C13—81no—
514C22×C13—81no—
515C22×C13#42112yes—
516C22×C13C22×C22⋊C411yescharacteristic
517C22×C13#57711yescharacteristic
518C22×C13#57811yescharacteristic
519C4×C13—21no—
520C4×C13—21no—
521C4×C13—21no—
522C4×C13—21no—
523C4×C13—21no—
524C4×C13—21no—
525C4×C13—21no—
526C4×C13—21no—
527C4×C13—21no—
528C4×C13—21no—
529C4×C13—41no—
530C4×C13—41no—
531C4×C13—41no—
532C4×C13—41no—
533C4×C13—41no—
534C4×C13—41no—
535C4×C13—41no—
536Dic13—81no—
537Dic13—81no—
538Dic13—81no—
539Dic13—81no—
540C2×#41—21no—
541C2×#41C2×Dic1311yescharacteristic
542C2×#41C2×Dic1311yescharacteristic, complemented
543C22×Q8C2×Dic1311yescharacteristic
544C22×Q8C2×Dic1311yescharacteristic, complemented
545C22×D4C22⋊D1311yescharacteristic
546C23×C4—261no—
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1311yescharacteristic
549C2×M16—261no—
550C2×M16—261no—
551C22×C8—261no—
552C22×C8—261no—
553C4⋊Q8—21no—
554C4⋊Q8C2×Dic1311yescharacteristic, complemented
555C4⋊Q8C2×Dic1311yescharacteristic, complemented
556#126—21no—
557#126—21no—
558#126—21no—
559#126—21no—
560#126—21no—
561#125—21no—
562#125—21no—
563#125—21no—
564#125C2×Dic1311yescharacteristic, complemented
565#124—21no—
566#124—21no—
567#124—21no—
568#124C2×Dic1311yescharacteristic, complemented
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8—21no—
585C22⋊Q8—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8C2×Dic1311yescharacteristic
589C22⋊Q8C2×Dic1311yescharacteristic
590C22⋊Q8C2×Dic1311yescharacteristic
591C22⋊Q8C2×Dic1311yescharacteristic, complemented
592C22⋊Q8C2×Dic1311yescharacteristic, complemented
593C22⋊Q8C2×Dic1311yescharacteristic, complemented
594C22⋊Q8C22×D1311yescharacteristic
595C22⋊Q8C22×D1311yescharacteristic
596C22⋊Q8C22×D1311yescharacteristic
597#121—21no—
598#121—21no—
599#121—21no—
600#121C2×Dic1311yescharacteristic
601#121C2×Dic1311yescharacteristic, complemented
602#121C22×D1311yescharacteristic
603#120—21no—
604#120—21no—
605C4×Q8—21no—
606C4×Q8—21no—
607C4×Q8C2×Dic1311yescharacteristic, complemented
608C4×Q8C2×Dic1311yescharacteristic, complemented
609C4×Q8C2×Dic1311yescharacteristic, complemented
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4C2×Dic1311yescharacteristic
619C4×D4C2×Dic1311yescharacteristic
620C4×D4C2×Dic1311yescharacteristic
621C4×D4C2×Dic1311yescharacteristic
622C4×D4C2×Dic1311yescharacteristic, complemented
623C4×D4C22⋊D1311yescharacteristic
624C4×D4C22⋊D1311yescharacteristic
625C4×D4C22⋊D1311yescharacteristic
626C4×D4C22⋊D1311yescharacteristic
627#117—21no—
628#117—21no—
629#117—21no—
630#117—21no—
631#117C2×Dic1311yescharacteristic
632#117C2×Dic1311yescharacteristic, complemented
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—261no—
637C2×C4⋊C4—261no—
638C2×C4⋊C4C2×Dic1311yescharacteristic
639C2×C4⋊C4C2×Dic1311yescharacteristic, complemented
640C2×C4⋊C4C22⋊D1311yescharacteristic
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—261no—
644C2×C22⋊C4—261no—
645C2×C22⋊C4—261no—
646C2×C22⋊C4C22⋊D1311yescharacteristic
647C2×C22⋊C4C22⋊D1311yescharacteristic
648C2×C42—261no—
649C2×C42C22×D1311yescharacteristic
650C4⋊C8—261no—
651C4⋊C8—261no—
652C22⋊C8—131no—
653C22⋊C8—131no—
654C22⋊C8—131no—
655C22⋊C8—131no—
656C22⋊C8—261no—
657C22⋊C8—261no—
658C22⋊C8—261no—
659C22⋊C8—261no—
660#97—261no—
661C4×C8—261no—
662#95—131no—
663#95—131no—
664#95—131no—
665#95—131no—
666#95—261no—
667#95—261no—
668#95—261no—
669#95—261no—
670#95—261no—
671C2×C13—21no—
672C2×C13—21no—
673C2×C13—22no—
674C2×C13—41no—
675C2×C13—41no—
676C2×C13—41no—
677C2×C13—81no—
678C2×C13#288311yescharacteristic
679C2×C13#289811yescharacteristic
680C2×C13C2×#42111yescharacteristic
681C24C2×C22⋊D1311yescharacteristic
682C24C2×C22⋊D1311yescharacteristic
683#41—44no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8—81no—
691C2×Q8C22×Dic1311yescharacteristic
692C2×Q8C22×Dic1311yescharacteristic
693C2×Q8C22×Dic1311yescharacteristic
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—42no—
700C2×D4C22⋊Dic1311yescharacteristic
701C2×D4C22⋊Dic1311yescharacteristic
702C2×D4C22⋊Dic1311yescharacteristic
703C2×D4C22⋊Dic1311yescharacteristic
704C2×D4C22×Dic1311yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—81no—
713C22×C4—81no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—522no—
719C22×C4—1041no—
720C22×C4—1041no—
721C22×C4C22×Dic1311yescharacteristic
722C22×C4C22×Dic1311yescharacteristic
723C22×C4C22×Dic1311yescharacteristic
724C22×C4C22×Dic1311yescharacteristic
725C22×C4C2×C22⋊D1311yescharacteristic
726C22×C4C2×C22⋊D1311yescharacteristic
727C22×C4C2×C22⋊D1311yescharacteristic
728C22×C4C2×C22⋊D1311yescharacteristic
729C22×C4C2×C22⋊D1311yescharacteristic
730C22×C4C2×C22⋊D1311yescharacteristic
731C22×C4C2×C22⋊D1311yescharacteristic
732C22×C4C2×C22⋊D1311yescharacteristic
733C22×C4C23×D1311yescharacteristic
734M16—1041no—
735M16—1041no—
736C2×C8—261no—
737C2×C8—261no—
738C2×C8—261no—
739C2×C8—261no—
740C2×C8—1041no—
741C2×C8—1041no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—1041no—
762C4⋊C4—1041no—
763C4⋊C4C22⋊Dic1311yescharacteristic
764C4⋊C4C22⋊Dic1311yescharacteristic
765C4⋊C4C22⋊Dic1311yescharacteristic
766C4⋊C4C22⋊Dic1311yescharacteristic
767C4⋊C4C22×Dic1311yescharacteristic
768C4⋊C4C22×Dic1311yescharacteristic
769C4⋊C4C22×Dic1311yescharacteristic
770C4⋊C4C22×Dic1311yescharacteristic
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—522no—
789C22⋊C4—1041no—
790C22⋊C4—1041no—
791C22⋊C4C22⋊Dic1311yescharacteristic
792C22⋊C4C22⋊Dic1311yescharacteristic
793C22⋊C4C22⋊Dic1311yescharacteristic
794C22⋊C4C22⋊Dic1311yescharacteristic
795C22⋊C4C22⋊Dic1311yescharacteristic
796C22⋊C4C22⋊Dic1311yescharacteristic
797C22⋊C4C22⋊Dic1311yescharacteristic
798C22⋊C4C22⋊Dic1311yescharacteristic
799C42—21no—
800C42—21no—
801C42—21no—
802C42—21no—
803C42—21no—
804C42—1041no—
805C42C22×Dic1311yescharacteristic
806C42C22×Dic1311yescharacteristic
807C42C2×C22⋊D1311yescharacteristic
808C42C2×C22⋊D1311yescharacteristic
809C13#1759811yescharacteristic, complemented, Sylow
810C23—21no—
811C23—21no—
812C23—22no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23C2×C22⋊Dic1311yescharacteristic
820C23C2×C22⋊Dic1311yescharacteristic
821C23C2×C22⋊Dic1311yescharacteristic
822C23C2×C22⋊Dic1311yescharacteristic
823C23C22×C22⋊D1311yescharacteristic
824Q8—41no—
825Q8—41no—
826Q8—41no—
827Q8—42no—
828Q8—81no—
829Q8—81no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—42no—
836D4—41no—
837D4—41no—
838D4—42no—
839D4—81no—
840D4—81no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
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—1044no—
882C2×C4C2×C22⋊Dic1311yescharacteristic
883C2×C4C2×C22⋊Dic1311yescharacteristic
884C2×C4C2×C22⋊Dic1311yescharacteristic
885C2×C4C2×C22⋊Dic1311yescharacteristic
886C2×C4C2×C22⋊Dic1311yescharacteristic
887C2×C4C2×C22⋊Dic1311yescharacteristic
888C2×C4C2×C22⋊Dic1311yescharacteristic
889C2×C4C2×C22⋊Dic1311yescharacteristic
890C2×C4C23×Dic1311yescharacteristic
891C2×C4C22×C22⋊D1311yescharacteristic
892C8—521no—
893C8—521no—
894C8—521no—
895C8—521no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—81no—
915C22—81no—
916C22#1171889712yes—
917C22#1171954211yescharacteristic
918C22#1171954311yescharacteristic
919C22C22×C22⋊Dic1311yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—1041no—
938C4—1041no—
939C4—1041no—
940C4—1041no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—81no—
948C2#1312329711yescharacteristic
949C2#1312336911yescharacteristic
950C2C2×#1171889711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC13×#3520C2
socleC22×C13C22×C22⋊C4
cosocleC22×C4×C13C24
hypercenter#3520D13
hypocenterC13#17598
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #13123871C2semidirect
2. #13117469C2semidirect
3. #13113413C2semidirect
4. #13113408C2semidirect
5. #13113400C2semidirect
6. #13113392C2semidirect
7. #13113387C2semidirect
8. #13113379C2semidirect
9. #13113374C2semidirect
10. #13113369C2semidirect
11. #13113356C2semidirect
12. #13113340C2semidirect
13. #13113327C2semidirect
14. C2×#11718130C2semidirect
16. C13×#556C4semidirect
18. C13×#552C4semidirect
19. C13×#552C4semidirect
22. D4×Q8×C13C4semidirect
23. C13×#548C4semidirect
24. C13×#548C4semidirect
25. C13×#547C4semidirect
26. C13×#547C4semidirect
77. C2×C13×#41C2×C4semidirect
79. C22×Q8×C13C2×C4semidirect
85. C13×C4⋊Q8C2×C4semidirect
86. C13×C4⋊Q8C2×C4semidirect
95. C13×#125C2×C4semidirect
99. C13×#124C2×C4semidirect
122. C13×C22⋊Q8C2×C4semidirect
123. C13×C22⋊Q8C2×C4semidirect
124. C13×C22⋊Q8C2×C4semidirect
132. C13×#121C2×C4semidirect
138. C4×Q8×C13C2×C4semidirect
139. C4×Q8×C13C2×C4semidirect
140. C4×Q8×C13C2×C4semidirect
153. C4×D4×C13C2×C4semidirect
163. C13×#117C2×C4semidirect
168. C2×C13×C4⋊C4C2×C4semidirect
436. #556Dic13semidirect
438. #552Dic13semidirect
439. #552Dic13semidirect
442. D4×Q8Dic13semidirect
443. #548Dic13semidirect
444. #548Dic13semidirect
445. #547Dic13semidirect
446. #547Dic13semidirect
542. C2×#41C2×Dic13semidirect
544. C22×Q8C2×Dic13semidirect
554. C4⋊Q8C2×Dic13semidirect
555. C4⋊Q8C2×Dic13semidirect
564. #125C2×Dic13semidirect
568. #124C2×Dic13semidirect
591. C22⋊Q8C2×Dic13semidirect
592. C22⋊Q8C2×Dic13semidirect
593. C22⋊Q8C2×Dic13semidirect
601. #121C2×Dic13semidirect
607. C4×Q8C2×Dic13semidirect
608. C4×Q8C2×Dic13semidirect
609. C4×Q8C2×Dic13semidirect
622. C4×D4C2×Dic13semidirect
632. #117C2×Dic13semidirect
639. C2×C4⋊C4C2×Dic13semidirect
809. C13#17598semidirect

Maximal subgroups

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

subgroupindex
#131238712
#131174692
#131134132
#131134082
#131134002
#131133922
#131133872
#131133792
#131133742
#131133692
#131133562
#131133402
#131133272
C2×#117181302
C13×#35202
#1759813