Finite Group Databasebeta

← #15830529

Subgroups — #15830529

Order 3328.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123494C211yesmaximal, characteristic, complemented
2#13117696C211yesmaximal, characteristic, complemented
3#13113413C211yesmaximal, characteristic, complemented
4#13113396C211yesmaximal, characteristic, complemented
5#13113392C211yesmaximal, characteristic, complemented
6#13113383C211yesmaximal, characteristic, complemented
7#13113374C211yesmaximal, characteristic, complemented
8#13113365C211yesmaximal, characteristic, complemented
9#13113361C211yesmaximal, characteristic, complemented
10#13113344C211yesmaximal, characteristic, complemented
11#13113340C211yesmaximal, characteristic, complemented
12#13113331C211yesmaximal, characteristic, complemented
13#13113322C211yesmaximal, characteristic, complemented
14C2×#11718129C211yesmaximal, characteristic, complemented
15C13×#3494C211yesmaximal, characteristic
16C13×#555—21no—
17C13×#553—21no—
18C13×#553—21no—
19C13×#551—21no—
20C13×#551—21no—
21C13×#547—21no—
22C13×#546—21no—
23C13×#546—21no—
24C13×#544C411yescharacteristic, complemented
25C13×#542C411yescharacteristic, complemented
26C13×#542C411yescharacteristic, complemented
27C13×#540C411yescharacteristic, complemented
28C13×#540C411yescharacteristic, complemented
29C13×#535C411yescharacteristic, complemented
30C13×#532C2211yescharacteristic
31C13×#532C2211yescharacteristic
32C13×#529C2211yescharacteristic
33C13×#529C2211yescharacteristic
34C13×#525C2211yescharacteristic
35C2×C13×#121C2211yescharacteristic
36C13×#520C411yescharacteristic, complemented
37C13×#518C411yescharacteristic, complemented
38C2×C13×#117C2211yescharacteristic
39#11718872C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41#11718868C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718661—21no—
44#11718661—21no—
45#11718660—21no—
46#11718658—21no—
47#11718642—21no—
48#11718642—21no—
49#11718611—21no—
50C22⋊C4×Dic13—21no—
51#11718598C2211yescharacteristic, complemented
52#11718597C2211yescharacteristic, complemented
53C4×C4⋊Dic13C2211yescharacteristic, complemented
54#11718593C2211yescharacteristic, complemented
55#11718587C2211yescharacteristic, complemented
56#11718587C2211yescharacteristic, complemented
57#11718586C2211yescharacteristic, complemented
58#11718586C2211yescharacteristic, complemented
59#11718130C2211yescharacteristic, complemented
60#11718130C2211yescharacteristic, complemented
61#11718130C2211yescharacteristic, complemented
62#11718130C2211yescharacteristic, complemented
63#11718129C2211yescharacteristic
64#11718129C2211yescharacteristic
65#11718129C2211yescharacteristic
66#11718129C2211yescharacteristic
67#11718129C2211yescharacteristic
68#11718129C2211yescharacteristic
69#11718129C2211yescharacteristic
70#11718129C2211yescharacteristic
71#11718129C2211yescharacteristic, complemented
72#11718129C2211yescharacteristic, complemented
73#11718129C2211yescharacteristic, complemented
74#11718129C2211yescharacteristic, complemented
75C2×C13×#41—21no—
76C2×C13×#41—21no—
77C2×C13×#41C2×C411yescharacteristic
78C22×D4×C13—21no—
79C22×D4×C13C2×C411yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×Dic13—21no—
82C13×C4⋊Q8—21no—
83C13×C4⋊Q8C2×C411yescharacteristic, complemented
84C13×C4⋊Q8C2×C411yescharacteristic, complemented
85C13×#127C2×C411yescharacteristic, complemented
86C13×#127C2×C411yescharacteristic, complemented
87C13×#126—21no—
88C13×#126—21no—
89C13×#126—21no—
90C13×#126—21no—
91C13×#125—21no—
92C13×#125C2×C411yescharacteristic, complemented
93C13×#125C2×C411yescharacteristic, complemented
94C13×#124—21no—
95C13×#124—21no—
96C13×#124—21no—
97C13×#124—21no—
98C13×#124C2×C411yescharacteristic, complemented
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⋊Q8C2×C411yescharacteristic
114C13×C22⋊Q8C2311yescharacteristic
115C13×#121—21no—
116C13×#121—21no—
117C13×#121—21no—
118C13×#121—21no—
119C13×#121—21no—
120C13×#121—21no—
121C13×#121—21no—
122C13×#121—21no—
123C13×#121—21no—
124C13×#121—21no—
125C13×#121C2×C411yescharacteristic
126C13×#121C2×C411yescharacteristic
127C13×#121C2×C411yescharacteristic
128C13×#121C2311yescharacteristic
129C13×#121C2311yescharacteristic
130C13×#121C2311yescharacteristic
131C13×#120—21no—
132C13×#120—21no—
133C13×#120—21no—
134C4×Q8×C13C2×C411yescharacteristic, complemented
135C4×Q8×C13C2×C411yescharacteristic, complemented
136C4×D4×C13—21no—
137C4×D4×C13—21no—
138C4×D4×C13—21no—
139C4×D4×C13—21no—
140C4×D4×C13—21no—
141C4×D4×C13—21no—
142C4×D4×C13—21no—
143C4×D4×C13—21no—
144C4×D4×C13—21no—
145C4×D4×C13—21no—
146C4×D4×C13C2×C411yescharacteristic, complemented
147C4×D4×C13C2×C411yescharacteristic, complemented
148C4×D4×C13C2×C411yescharacteristic, complemented
149C4×D4×C13C2×C411yescharacteristic, complemented
150C4×D4×C13C2×C411yescharacteristic, complemented
151C4×D4×C13C2×C411yescharacteristic, complemented
152C13×#117—21no—
153C13×#117—21no—
154C13×#117—21no—
155C13×#117C2×C411yescharacteristic
156C13×#117C2×C411yescharacteristic
157C13×#117C2×C411yescharacteristic
158C13×#117C2×C411yescharacteristic
159C13×#117C2×C411yescharacteristic
160C13×#117D411yescharacteristic
161C13×#117D411yescharacteristic
162C13×#117D411yescharacteristic
163C13×#117D411yescharacteristic
164C2×C13×C4⋊C4—21no—
165C2×C13×C4⋊C4C2×C411yescharacteristic
166C2×C13×C4⋊C4D411yescharacteristic
167C2×C13×C4⋊C4D411yescharacteristic
168C2×C13×C22⋊C4—21no—
169C2×C13×C22⋊C4—21no—
170C2×C13×C22⋊C4—21no—
171C2×C13×C22⋊C4D411yescharacteristic
172C2×C13×C22⋊C4D411yescharacteristic
173C2×C42×C13C2311yescharacteristic
174C2×C42×C13C2311yescharacteristic
175C2×C22⋊Dic13—21no—
176C2×C4⋊Dic13—21no—
177C2×C4⋊Dic13—21no—
178C2×C4×Dic13—21no—
179C2×C4×Dic13—21no—
180C2×#6099—21no—
181C22×#1055—21no—
182#88071—21no—
183#88071—21no—
184#88071—21no—
185#88071—21no—
186#88071—21no—
187#88071—21no—
188#88071C2311yescharacteristic
189#88071C2311yescharacteristic
190#88071C2311yescharacteristic
191#88071C2311yescharacteristic
192C22⋊#1055—21no—
193C22⋊#1055—21no—
194C22⋊#1055C2311yescharacteristic
195C22⋊#1055C2311yescharacteristic
196C22⋊#1055C2311yescharacteristic
197C22⋊#1055C2311yescharacteristic
198C4⋊#1055—21no—
199C4⋊#1055—21no—
200C4⋊#1055—21no—
201C4⋊#1055—21no—
202#88043—21no—
203#88043—21no—
204C4×#1055—21no—
205C4×#1055—21no—
206#17604—131nomaximal, Sylow
207C24×C13—21no—
208C24×C13C2×D411yescharacteristic
209C13×#41—42no—
210C13×#41—81no—
211C13×#41—81no—
212C13×#41—81no—
213C13×#41—81no—
214C2×Q8×C13—21no—
215C2×Q8×C13—21no—
216C2×Q8×C13C22×C411yescharacteristic
217C2×D4×C13—21no—
218C2×D4×C13—21no—
219C2×D4×C13—21no—
220C2×D4×C13—21no—
221C2×D4×C13—21no—
222C2×D4×C13—21no—
223C2×D4×C13—21no—
224C2×D4×C13—21no—
225C2×D4×C13—21no—
226C2×D4×C13—21no—
227C2×D4×C13—21no—
228C2×D4×C13—21no—
229C2×D4×C13—42no—
230C2×D4×C13—81no—
231C2×D4×C13—81no—
232C2×D4×C13C22×C411yescharacteristic
233C2×D4×C13C22×C411yescharacteristic
234C2×D4×C13C22×C411yescharacteristic
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—42no—
244C22×C4×C13C22×C411yescharacteristic
245C22×C4×C13C22×C411yescharacteristic
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×C13C2×D411yescharacteristic
253C22×C4×C13C2411yescharacteristic
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—42no—
259C22×Dic13—42no—
260C22×Dic13—81no—
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⋊C4C22⋊C411yescharacteristic
273C13×C4⋊C4C22⋊C411yescharacteristic
274C13×C4⋊C4C22⋊C411yescharacteristic
275C13×C4⋊C4C22⋊C411yescharacteristic
276C13×C4⋊C4C22⋊C411yescharacteristic
277C13×C4⋊C4C22⋊C411yescharacteristic
278C13×C4⋊C4C22⋊C411yescharacteristic
279C13×C4⋊C4C22⋊C411yescharacteristic
280C13×C4⋊C4C22×C411yescharacteristic
281C13×C4⋊C4C22×C411yescharacteristic
282C13×C4⋊C4C22×C411yescharacteristic
283C13×C4⋊C4C22×C411yescharacteristic
284C13×C22⋊C4—21no—
285C13×C22⋊C4—21no—
286C13×C22⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
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
311C42×C13—21no—
312C42×C13—21no—
313C42×C13—21no—
314C42×C13C22×C411yescharacteristic
315C42×C13C22×C411yescharacteristic
316C42×C13C22×C411yescharacteristic
317C42×C13C22×C411yescharacteristic
318C42×C13C2×D411yescharacteristic
319C42×C13C2×D411yescharacteristic
320C42×C13C2×D411yescharacteristic
321C42×C13C2×D411yescharacteristic
322C22⋊Dic13—42no—
323C4⋊Dic13—42no—
324C4⋊Dic13—81no—
325C4×Dic13—42no—
326C4×Dic13—81no—
327#6099—42no—
328C2×#1055—21no—
329C2×#1055—21no—
330C2×#1055—21no—
331C2×#1055—21no—
332C2×#1055—42no—
333#3494D1311yescharacteristic
334#2924—131no—
335#2343—131no—
336#1521—131no—
337#1517—131no—
338#1516—131no—
339#1514—131no—
340#1512—131no—
341#1510—131no—
342#1509—131no—
343#1505—131no—
344#1504—131no—
345#1502—131no—
346#1500—131no—
347C2×#327—131no—
348C23×C13—21no—
349C23×C13—21no—
350C23×C13—22no—
351C23×C13—21no—
352C23×C13—21no—
353C23×C13—21no—
354C23×C13—41no—
355C23×C13—42no—
356C23×C13—81no—
357C23×C13—81no—
358C23×C13C2×C22⋊C411yescharacteristic
359C23×C13C2×C22⋊C411yescharacteristic
360C23×C13C22×D411yescharacteristic
361Q8×C13—41no—
362Q8×C13—81no—
363Q8×C13—81no—
364D4×C13—42no—
365D4×C13—41no—
366D4×C13—41no—
367D4×C13—41no—
368D4×C13—41no—
369D4×C13—41no—
370D4×C13—41no—
371D4×C13—41no—
372D4×C13—41no—
373D4×C13—41no—
374D4×C13—42no—
375D4×C13—81no—
376D4×C13—81no—
377D4×C13—81no—
378D4×C13—81no—
379D4×C13—81no—
380D4×C13—81no—
381D4×C13—81no—
382C2×C4×C13—21no—
383C2×C4×C13—21no—
384C2×C4×C13—21no—
385C2×C4×C13—21no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—21no—
389C2×C4×C13—21no—
390C2×C4×C13—21no—
391C2×C4×C13—21no—
392C2×C4×C13—21no—
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—42no—
400C2×C4×C13—81no—
401C2×C4×C13—81no—
402C2×C4×C13—81no—
403C2×C4×C13—81no—
404C2×C4×C13—81no—
405C2×C4×C13—81no—
406C2×C4×C13—81no—
407C2×C4×C13C2×C22⋊C411yescharacteristic
408C2×C4×C13C2×C22⋊C411yescharacteristic
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—22no—
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#555—21no—
437#553—21no—
438#553—21no—
439#551—21no—
440#551—21no—
441#547—21no—
442#546—21no—
443#546—21no—
444#544Dic1311yescharacteristic, complemented
445#542Dic1311yescharacteristic, complemented
446#542Dic1311yescharacteristic, complemented
447#540Dic1311yescharacteristic, complemented
448#540Dic1311yescharacteristic, complemented
449#535Dic1311yescharacteristic, complemented
450#532C2×D1311yescharacteristic
451#532C2×D1311yescharacteristic
452#529C2×D1311yescharacteristic
453#529C2×D1311yescharacteristic
454#525C2×D1311yescharacteristic
455C2×#121C2×D1311yescharacteristic
456#520Dic1311yescharacteristic, complemented
457#518Dic1311yescharacteristic, complemented
458C2×#117C2×D1311yescharacteristic
459#433—261no—
460#433—261no—
461#432—131no—
462#432—131no—
463#431—131no—
464#431—131no—
465#424—261no—
466#407—131no—
467C2×C22⋊C8—131no—
468#405—261no—
469#387—261no—
470#387—261no—
471#385—261no—
472#383—131no—
473#382—131no—
474#381—131no—
475C4×C4⋊C4—131no—
476C4×C22⋊C4—261no—
477#376—131no—
478C2×#95—131no—
479#328—131no—
480#328—131no—
481#328—131no—
482#328—131no—
483#327—131no—
484#327—131no—
485#327—131no—
486#327—131no—
487#327—131no—
488#327—131no—
489#327—131no—
490#327—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—42no—
503C22×C13—42no—
504C22×C13—41no—
505C22×C13—41no—
506C22×C13—41no—
507C22×C13—41no—
508C22×C13—41no—
509C22×C13—41no—
510C22×C13—41no—
511C22×C13—41no—
512C22×C13—41no—
513C22×C13—162no—
514C22×C13#41012yes—
515C22×C13C22×C22⋊C411yescharacteristic
516C22×C13#57611yescharacteristic
517C22×C13#57711yescharacteristic
518C4×C13—21no—
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—21no—
530C4×C13—41no—
531C4×C13—41no—
532C4×C13—41no—
533C4×C13—41no—
534C4×C13—41no—
535Dic13—42no—
536Dic13—81no—
537Dic13—81no—
538Dic13—81no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41C2×Dic1311yescharacteristic
542C22×D4—21no—
543C22×D4C2×Dic1311yescharacteristic
544C23×C4—261no—
545C23×C4C22×D1311yescharacteristic
546C2×M16—261no—
547C22×C8—261no—
548C4⋊Q8—21no—
549C4⋊Q8C2×Dic1311yescharacteristic, complemented
550C4⋊Q8C2×Dic1311yescharacteristic, complemented
551#127C2×Dic1311yescharacteristic, complemented
552#127C2×Dic1311yescharacteristic, complemented
553#126—21no—
554#126—21no—
555#126—21no—
556#126—21no—
557#125—21no—
558#125C2×Dic1311yescharacteristic, complemented
559#125C2×Dic1311yescharacteristic, complemented
560#124—21no—
561#124—21no—
562#124—21no—
563#124—21no—
564#124C2×Dic1311yescharacteristic, complemented
565#124C2×Dic1311yescharacteristic, complemented
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8C2×Dic1311yescharacteristic
580C22⋊Q8C22×D1311yescharacteristic
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121C2×Dic1311yescharacteristic
592#121C2×Dic1311yescharacteristic
593#121C2×Dic1311yescharacteristic
594#121C22×D1311yescharacteristic
595#121C22×D1311yescharacteristic
596#121C22×D1311yescharacteristic
597#120—21no—
598#120—21no—
599#120—21no—
600C4×Q8C2×Dic1311yescharacteristic, complemented
601C4×Q8C2×Dic1311yescharacteristic, complemented
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4C2×Dic1311yescharacteristic, complemented
613C4×D4C2×Dic1311yescharacteristic, complemented
614C4×D4C2×Dic1311yescharacteristic, complemented
615C4×D4C2×Dic1311yescharacteristic, complemented
616C4×D4C2×Dic1311yescharacteristic, complemented
617C4×D4C2×Dic1311yescharacteristic, complemented
618#117—21no—
619#117—21no—
620#117—21no—
621#117C2×Dic1311yescharacteristic
622#117C2×Dic1311yescharacteristic
623#117C2×Dic1311yescharacteristic
624#117C2×Dic1311yescharacteristic
625#117C2×Dic1311yescharacteristic
626#117C22⋊D1311yescharacteristic
627#117C22⋊D1311yescharacteristic
628#117C22⋊D1311yescharacteristic
629#117C22⋊D1311yescharacteristic
630C2×C4⋊C4—21no—
631C2×C4⋊C4—261no—
632C2×C4⋊C4—261no—
633C2×C4⋊C4C2×Dic1311yescharacteristic
634C2×C4⋊C4C22⋊D1311yescharacteristic
635C2×C4⋊C4C22⋊D1311yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—261no—
640C2×C22⋊C4C22⋊D1311yescharacteristic
641C2×C22⋊C4C22⋊D1311yescharacteristic
642C2×C42—261no—
643C2×C42—261no—
644C2×C42C22×D1311yescharacteristic
645C2×C42C22×D1311yescharacteristic
646C4⋊C8—261no—
647C4⋊C8—261no—
648C4⋊C8—261no—
649C4⋊C8—261no—
650C22⋊C8—131no—
651C22⋊C8—131no—
652C22⋊C8—131no—
653C22⋊C8—131no—
654C22⋊C8—261no—
655C22⋊C8—261no—
656#97—261no—
657#97—261no—
658C4×C8—261no—
659C4×C8—261no—
660#95—131no—
661#95—131no—
662#95—131no—
663#95—131no—
664#95—261no—
665#95—261no—
666#95—261no—
667#95—261no—
668#95—261no—
669#95—261no—
670C2×C13—21no—
671C2×C13—21no—
672C2×C13—22no—
673C2×C13—41no—
674C2×C13—81no—
675C2×C13—81no—
676C2×C13—81no—
677C2×C13C2×#41011yescharacteristic
678C2×C13#289711yescharacteristic
679C2×C13#290111yescharacteristic
680C24—21no—
681C24C2×C22⋊D1311yescharacteristic
682#41—42no—
683#41—81no—
684#41—81no—
685#41—81no—
686#41—81no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C22×Dic1311yescharacteristic
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4C22×Dic1311yescharacteristic
706C2×D4C22×Dic1311yescharacteristic
707C2×D4C22×Dic1311yescharacteristic
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—42no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—522no—
722C22×C4—522no—
723C22×C4—1041no—
724C22×C4C22×Dic1311yescharacteristic
725C22×C4C22×Dic1311yescharacteristic
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—522no—
735C2×C8—261no—
736C2×C8—261no—
737C2×C8—261no—
738C2×C8—261no—
739C2×C8—522no—
740C4⋊C4—21no—
741C4⋊C4—21no—
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—522no—
752C4⋊C4—1041no—
753C4⋊C4C22⋊Dic1311yescharacteristic
754C4⋊C4C22⋊Dic1311yescharacteristic
755C4⋊C4C22⋊Dic1311yescharacteristic
756C4⋊C4C22⋊Dic1311yescharacteristic
757C4⋊C4C22⋊Dic1311yescharacteristic
758C4⋊C4C22⋊Dic1311yescharacteristic
759C4⋊C4C22⋊Dic1311yescharacteristic
760C4⋊C4C22⋊Dic1311yescharacteristic
761C4⋊C4C22×Dic1311yescharacteristic
762C4⋊C4C22×Dic1311yescharacteristic
763C4⋊C4C22×Dic1311yescharacteristic
764C4⋊C4C22×Dic1311yescharacteristic
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
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—522no—
785C22⋊C4C22⋊Dic1311yescharacteristic
786C22⋊C4C22⋊Dic1311yescharacteristic
787C22⋊C4C22⋊Dic1311yescharacteristic
788C22⋊C4C22⋊Dic1311yescharacteristic
789C22⋊C4C22⋊Dic1311yescharacteristic
790C22⋊C4C22⋊Dic1311yescharacteristic
791C22⋊C4C22⋊Dic1311yescharacteristic
792C22⋊C4C22⋊Dic1311yescharacteristic
793C42—21no—
794C42—21no—
795C42—21no—
796C42—522no—
797C42—1041no—
798C42C22×Dic1311yescharacteristic
799C42C22×Dic1311yescharacteristic
800C42C22×Dic1311yescharacteristic
801C42C22×Dic1311yescharacteristic
802C42C2×C22⋊D1311yescharacteristic
803C42C2×C22⋊D1311yescharacteristic
804C42C2×C22⋊D1311yescharacteristic
805C42C2×C22⋊D1311yescharacteristic
806C13#1760411yescharacteristic, complemented, Sylow
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—42no—
815C23—81no—
816C23—81no—
817C23C2×C22⋊Dic1311yescharacteristic
818C23C2×C22⋊Dic1311yescharacteristic
819C23C22×C22⋊D1311yescharacteristic
820Q8—41no—
821Q8—81no—
822Q8—81no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—42no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—81no—
835D4—81no—
836D4—81no—
837D4—81no—
838D4—81no—
839D4—81no—
840D4—81no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—262no—
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—1044no—
879C2×C4C2×C22⋊Dic1311yescharacteristic
880C2×C4C2×C22⋊Dic1311yescharacteristic
881C2×C4C2×C22⋊Dic1311yescharacteristic
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×C4C23×Dic1311yescharacteristic
890C2×C4C22×C22⋊D1311yescharacteristic
891C8—521no—
892C8—521no—
893C8—521no—
894C8—521no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—162no—
914C22#1171890112yes—
915C22#1171954011yescharacteristic
916C22#1171954111yescharacteristic
917C22C22×C22⋊Dic1311yescharacteristic
918C4—21no—
919C4—21no—
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—522no—
936C4—1041no—
937C4—1041no—
938C4—1041no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—81no—
946C2C2×#1171890111yescharacteristic
947C2#1312336211yescharacteristic
948C2#1312338311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC13×#3494C2
socleC22×C13C22×C22⋊C4
cosocleC22×C4×C13C24
hypercenter#3494D13
hypocenterC13#17604
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3494

Complements

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

NH ≅ G/Ntype
1. #13123494C2semidirect
2. #13117696C2semidirect
3. #13113413C2semidirect
4. #13113396C2semidirect
5. #13113392C2semidirect
6. #13113383C2semidirect
7. #13113374C2semidirect
8. #13113365C2semidirect
9. #13113361C2semidirect
10. #13113344C2semidirect
11. #13113340C2semidirect
12. #13113331C2semidirect
13. #13113322C2semidirect
14. C2×#11718129C2semidirect
24. C13×#544C4semidirect
25. C13×#542C4semidirect
26. C13×#542C4semidirect
27. C13×#540C4semidirect
28. C13×#540C4semidirect
29. C13×#535C4semidirect
36. C13×#520C4semidirect
37. C13×#518C4semidirect
51. #11718598C22semidirect
52. #11718597C22semidirect
53. C4×C4⋊Dic13C22semidirect
54. #11718593C22semidirect
55. #11718587C22semidirect
56. #11718587C22semidirect
57. #11718586C22semidirect
58. #11718586C22semidirect
59. #11718130C22semidirect
60. #11718130C22semidirect
61. #11718130C22semidirect
62. #11718130C22semidirect
71. #11718129C22semidirect
72. #11718129C22semidirect
73. #11718129C22semidirect
74. #11718129C22semidirect
83. C13×C4⋊Q8C2×C4semidirect
84. C13×C4⋊Q8C2×C4semidirect
85. C13×#127C2×C4semidirect
86. C13×#127C2×C4semidirect
92. C13×#125C2×C4semidirect
93. C13×#125C2×C4semidirect
98. C13×#124C2×C4semidirect
99. C13×#124C2×C4semidirect
134. C4×Q8×C13C2×C4semidirect
135. C4×Q8×C13C2×C4semidirect
146. C4×D4×C13C2×C4semidirect
147. C4×D4×C13C2×C4semidirect
148. C4×D4×C13C2×C4semidirect
149. C4×D4×C13C2×C4semidirect
150. C4×D4×C13C2×C4semidirect
151. C4×D4×C13C2×C4semidirect
444. #544Dic13semidirect
445. #542Dic13semidirect
446. #542Dic13semidirect
447. #540Dic13semidirect
448. #540Dic13semidirect
449. #535Dic13semidirect
456. #520Dic13semidirect
457. #518Dic13semidirect
549. C4⋊Q8C2×Dic13semidirect
550. C4⋊Q8C2×Dic13semidirect
551. #127C2×Dic13semidirect
552. #127C2×Dic13semidirect
558. #125C2×Dic13semidirect
559. #125C2×Dic13semidirect
564. #124C2×Dic13semidirect
565. #124C2×Dic13semidirect
600. C4×Q8C2×Dic13semidirect
601. C4×Q8C2×Dic13semidirect
612. C4×D4C2×Dic13semidirect
613. C4×D4C2×Dic13semidirect
614. C4×D4C2×Dic13semidirect
615. C4×D4C2×Dic13semidirect
616. C4×D4C2×Dic13semidirect
617. C4×D4C2×Dic13semidirect
806. C13#17604semidirect

Maximal subgroups

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

subgroupindex
#131234942
#131176962
#131134132
#131133962
#131133922
#131133832
#131133742
#131133652
#131133612
#131133442
#131133402
#131133312
#131133222
C2×#117181292
C13×#34942
#1760413