Finite Group Databasebeta

← #15831064

Subgroups — #15831064

Order 3328.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123850C211yesmaximal, characteristic, complemented
2#13123487C211yesmaximal, characteristic, complemented
3#13113471C211yesmaximal, characteristic, complemented
4#13113467C211yesmaximal, characteristic, complemented
5#13113467C211yesmaximal, characteristic, complemented
6#13113460C211yesmaximal, characteristic, complemented
7#13113456C211yesmaximal, characteristic, complemented
8#13113456C211yesmaximal, characteristic, complemented
9#13113447C211yesmaximal, characteristic, complemented
10#13113443C211yesmaximal, characteristic, complemented
11#13113434C211yesmaximal, characteristic, complemented
12#13113434C211yesmaximal, characteristic, complemented
13#13113424C211yesmaximal, characteristic, complemented
14C2×#11718132C211yesmaximal, characteristic, complemented
15C13×#3514C211yesmaximal, characteristic
16C13×#559C411yescharacteristic
17C13×#556C411yescharacteristic
18C13×#555—21no—
19C13×#551—21no—
20C13×#551—21no—
21D4×Q8×C13C411yescharacteristic
22C13×#548C411yescharacteristic
23C13×#548C411yescharacteristic
24C13×#546—21no—
25C13×#546C411yescharacteristic
26C13×#546C411yescharacteristic
27D42×C13C411yescharacteristic
28C13×#542—21no—
29C13×#538—21no—
30C13×#538—21no—
31C13×#532C2211yescharacteristic
32C13×#529C2211yescharacteristic
33C13×#529C2211yescharacteristic
34C13×#529C2211yescharacteristic
35C2×C13×#124C2211yescharacteristic
36C2×C13×#124C2211yescharacteristic
37C13×#518—21no—
38C4×C13×#41C2211yescharacteristic
39#11718895—21no—
40#11718685—21no—
41#11718672—21no—
42#11718672—21no—
43D4×#1055—21no—
44#11718661—21no—
45#11718661—21no—
46#11718660—21no—
47#11718587C2211yescharacteristic, complemented
48#11718587C2211yescharacteristic, complemented
49#11718587C2211yescharacteristic, complemented
50#11718587C2211yescharacteristic, complemented
51#11718587C2211yescharacteristic, complemented
52#11718587C2211yescharacteristic, complemented
53#11718587C2211yescharacteristic, complemented
54C4×#6099C2211yescharacteristic, complemented
55C4×#6099C2211yescharacteristic, complemented
56C2×#88043C2211yescharacteristic, complemented
57C2×#88043C2211yescharacteristic, complemented
58C2×#88043C2211yescharacteristic, complemented
59#11718135C2211yescharacteristic, complemented
60#11718135C2211yescharacteristic, complemented
61#11718135C2211yescharacteristic, complemented
62#11718135C2211yescharacteristic, complemented
63#11718132C2211yescharacteristic
64#11718132C2211yescharacteristic
65#11718132C2211yescharacteristic
66#11718132C2211yescharacteristic
67#11718132C2211yescharacteristic, complemented
68#11718132C2211yescharacteristic, complemented
69#11718132C2211yescharacteristic, complemented
70#11718132C2211yescharacteristic, complemented
71#11718132C2211yescharacteristic, complemented
72#11718132C2211yescharacteristic, complemented
73#11718132C2211yescharacteristic, complemented
74#11718132C2211yescharacteristic, complemented
75C2×C13×#41C2×C411yescharacteristic
76C2×C13×#41C2×C411yescharacteristic
77C2×C13×#41D411yescharacteristic
78C22×Q8×C13C2×C411yescharacteristic
79C22×Q8×C13C2×C411yescharacteristic
80C22×D4×C13—21no—
81C22×D4×C13C2×C411yescharacteristic
82C22×D4×C13C2×C411yescharacteristic
83C13×C4⋊Q8—21no—
84C13×C4⋊Q8C2×C411yescharacteristic
85C13×#127C2×C411yescharacteristic
86C13×#126—21no—
87C13×#126—21no—
88C13×#126—21no—
89C13×#126—21no—
90C13×#126—21no—
91C13×#125C2311yescharacteristic
92C13×#124—21no—
93C13×#124—21no—
94C13×#124—21no—
95C13×#124—21no—
96C13×#124—21no—
97C13×#124—21no—
98C13×#124—21no—
99C13×#124C2×C411yescharacteristic
100C13×#124C2×C411yescharacteristic
101C13×#124C2×C411yescharacteristic
102C13×#124C2×C411yescharacteristic
103C13×#124C2311yescharacteristic
104C13×#124C2311yescharacteristic
105C13×#124C2311yescharacteristic
106C13×#123—21no—
107C13×#123—21no—
108C13×#123—21no—
109C13×#123—21no—
110C13×#123—21no—
111C13×#123—21no—
112C13×#123—21no—
113C13×C22⋊Q8—21no—
114C13×C22⋊Q8—21no—
115C13×C22⋊Q8—21no—
116C13×C22⋊Q8—21no—
117C13×C22⋊Q8—21no—
118C13×C22⋊Q8C2×C411yescharacteristic
119C13×C22⋊Q8C2×C411yescharacteristic
120C13×C22⋊Q8C2×C411yescharacteristic
121C13×#121—21no—
122C13×#121—21no—
123C13×#121—21no—
124C13×#121—21no—
125C13×#121—21no—
126C13×#121—21no—
127C13×#121—21no—
128C13×#121C2×C411yescharacteristic
129C13×#121C2×C411yescharacteristic
130C13×#121C2×C411yescharacteristic
131C13×#120—21no—
132C13×#120—21no—
133C13×#120—21no—
134C13×#120—21no—
135C4×Q8×C13C2×C411yescharacteristic
136C4×Q8×C13C2×C411yescharacteristic
137C4×Q8×C13C2×C411yescharacteristic
138C4×Q8×C13C2×C411yescharacteristic
139C4×Q8×C13D411yescharacteristic
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×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
154C4×D4×C13C2×C411yescharacteristic
155C4×D4×C13D411yescharacteristic
156C4×D4×C13D411yescharacteristic
157C4×D4×C13D411yescharacteristic
158C13×#117—21no—
159C13×#117—21no—
160C13×#117—21no—
161C13×#117—21no—
162C13×#117D411yescharacteristic
163C13×#117D411yescharacteristic
164C13×#117D411yescharacteristic
165C2×C13×C22⋊C4—21no—
166C2×C13×C22⋊C4—21no—
167C2×C13×C22⋊C4—21no—
168C2×C13×C22⋊C4—21no—
169C2×C13×C22⋊C4—21no—
170C2×C13×C22⋊C4—21no—
171C2×C42×C13C2311yescharacteristic
172C2×C42×C13C2311yescharacteristic
173C2×C42×C13C2311yescharacteristic
174C2×#6099—21no—
175C2×#6099—21no—
176C22×#1055—21no—
177C22×#1055—21no—
178C22×#1055—21no—
179C22⋊#1055—21no—
180C22⋊#1055—21no—
181C22⋊#1055—21no—
182C22⋊#1055—21no—
183C22⋊#1055—21no—
184C22⋊#1055—21no—
185C22⋊#1055—21no—
186C4⋊#1055—21no—
187C4⋊#1055—21no—
188C4⋊#1055—21no—
189C4⋊#1055—21no—
190C4⋊#1055—21no—
191C4⋊#1055—21no—
192C4⋊#1055—21no—
193#88043—21no—
194#88043—21no—
195#88043—21no—
196#88043C2311yescharacteristic
197#88043C2311yescharacteristic
198#88043C2311yescharacteristic
199#88043C2311yescharacteristic
200#88043C2311yescharacteristic
201#88043C2311yescharacteristic
202#88043C2311yescharacteristic
203#88043C2311yescharacteristic
204C4×#1055—21no—
205C4×#1055—21no—
206#17679—131nomaximal, Sylow
207C24×C13—21no—
208C24×C13—21no—
209C13×#41—42no—
210C13×#41—81no—
211C13×#41—81no—
212C2×Q8×C13—21no—
213C2×Q8×C13—21no—
214C2×Q8×C13—81no—
215C2×Q8×C13—81no—
216C2×Q8×C13C22⋊C411yescharacteristic
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—21no—
226C2×D4×C13—21no—
227C2×D4×C13—21no—
228C2×D4×C13—21no—
229C2×D4×C13—44no—
230C2×D4×C13—81no—
231C2×D4×C13—81no—
232C2×D4×C13C22⋊C411yescharacteristic
233C2×D4×C13C22⋊C411yescharacteristic
234C2×D4×C13C22⋊C411yescharacteristic
235C2×D4×C13C22×C411yescharacteristic
236C2×D4×C13C22×C411yescharacteristic
237C2×D4×C13C22×C411yescharacteristic
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13C22×C411yescharacteristic
246C22×C4×C13C22×C411yescharacteristic
247C22×C4×C13C22×C411yescharacteristic
248C22×C4×C13C2×D411yescharacteristic
249C22×C4×C13C2×D411yescharacteristic
250C22×C4×C13C2×D411yescharacteristic
251C22×C4×C13C2×D411yescharacteristic
252C22×C4×C13C2×D411yescharacteristic
253C22×C4×C13C2×D411yescharacteristic
254C13×C4⋊C4—21no—
255C13×C4⋊C4—21no—
256C13×C4⋊C4—21no—
257C13×C4⋊C4—21no—
258C13×C4⋊C4—21no—
259C13×C4⋊C4—21no—
260C13×C4⋊C4—21no—
261C13×C4⋊C4—21no—
262C13×C4⋊C4—21no—
263C13×C4⋊C4—21no—
264C13×C4⋊C4C22⋊C411yescharacteristic
265C13×C4⋊C4C22⋊C411yescharacteristic
266C13×C4⋊C4C22⋊C411yescharacteristic
267C13×C4⋊C4C22⋊C411yescharacteristic
268C13×C4⋊C4C22⋊C411yescharacteristic
269C13×C4⋊C4C22⋊C411yescharacteristic
270C13×C4⋊C4C22×C411yescharacteristic
271C13×C4⋊C4C22×C411yescharacteristic
272C13×C22⋊C4—21no—
273C13×C22⋊C4—21no—
274C13×C22⋊C4—21no—
275C13×C22⋊C4—21no—
276C13×C22⋊C4—21no—
277C13×C22⋊C4—21no—
278C13×C22⋊C4—21no—
279C13×C22⋊C4—21no—
280C13×C22⋊C4—21no—
281C13×C22⋊C4—21no—
282C13×C22⋊C4—21no—
283C13×C22⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
296C13×C22⋊C4C22⋊C411yescharacteristic
297C13×C22⋊C4C22⋊C411yescharacteristic
298C13×C22⋊C4C22⋊C411yescharacteristic
299C13×C22⋊C4C22⋊C411yescharacteristic
300C13×C22⋊C4C22⋊C411yescharacteristic
301C42×C13—21no—
302C42×C13—21no—
303C42×C13—21no—
304C42×C13C22×C411yescharacteristic
305C42×C13C22×C411yescharacteristic
306C42×C13C22×C411yescharacteristic
307C42×C13C2×D411yescharacteristic
308C42×C13C2×D411yescharacteristic
309C42×C13C2×D411yescharacteristic
310C42×C13C2×D411yescharacteristic
311C42×C13C2×D411yescharacteristic
312C42×C13C2×D411yescharacteristic
313C42×C13C2411yescharacteristic
314#6099—42no—
315#6099—42no—
316C2×#1055—21no—
317C2×#1055—21no—
318C2×#1055—21no—
319C2×#1055—21no—
320C2×#1055—21no—
321C2×#1055—21no—
322C2×#1055—21no—
323C2×#1055—21no—
324C2×#1055—42no—
325C2×#1055—42no—
326C2×#1055—42no—
327#3514D1311yescharacteristic
328#2970—131no—
329#2923—131no—
330#1536—131no—
331#1535—131no—
332#1535—131no—
333#1533—131no—
334#1532—131no—
335#1532—131no—
336#1530—131no—
337#1529—131no—
338#1527—131no—
339#1527—131no—
340#1524—131no—
341C2×#329—131no—
342C23×C13—21no—
343C23×C13—21no—
344C23×C13—21no—
345C23×C13—42no—
346C23×C13—42no—
347C23×C13—81no—
348C23×C13—81no—
349C23×C13—81no—
350C23×C13—81no—
351C23×C13C2×C22⋊C411yescharacteristic
352C23×C13C2×C22⋊C411yescharacteristic
353C23×C13C2×C22⋊C411yescharacteristic
354Q8×C13—41no—
355Q8×C13—41no—
356Q8×C13—41no—
357Q8×C13—41no—
358Q8×C13—81no—
359Q8×C13—81no—
360D4×C13—22no—
361D4×C13—22no—
362D4×C13—41no—
363D4×C13—42no—
364D4×C13—41no—
365D4×C13—41no—
366D4×C13—41no—
367D4×C13—42no—
368D4×C13—42no—
369D4×C13—81no—
370D4×C13—81no—
371D4×C13—81no—
372D4×C13—81no—
373D4×C13—81no—
374D4×C13—81no—
375C2×C4×C13—22no—
376C2×C4×C13—21no—
377C2×C4×C13—21no—
378C2×C4×C13—21no—
379C2×C4×C13—21no—
380C2×C4×C13—21no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—42no—
390C2×C4×C13—81no—
391C2×C4×C13—81no—
392C2×C4×C13—81no—
393C2×C4×C13—81no—
394C2×C4×C13—81no—
395C2×C4×C13—81no—
396C2×C4×C13C2×C22⋊C411yescharacteristic
397C2×C4×C13C2×C22⋊C411yescharacteristic
398C2×C4×C13C2×C22⋊C411yescharacteristic
399C2×C4×C13C2×C22⋊C411yescharacteristic
400C2×C4×C13C2×C22⋊C411yescharacteristic
401C2×C4×C13C2×C22⋊C411yescharacteristic
402C2×C4×C13C2×C22⋊C411yescharacteristic
403C2×C4×C13C2×C22⋊C411yescharacteristic
404C2×C4×C13C2×C22⋊C411yescharacteristic
405C2×C4×C13C23×C411yescharacteristic
406C2×C4×C13C22×D411yescharacteristic
407C2×C4×C13C22×D411yescharacteristic
408#1055—22no—
409#1055—41no—
410#1055—41no—
411#1055—41no—
412#1055—41no—
413#1055—41no—
414#1055—41no—
415#1055—41no—
416#559Dic1311yescharacteristic
417#556Dic1311yescharacteristic
418#555—21no—
419#551—21no—
420#551—21no—
421D4×Q8Dic1311yescharacteristic
422#548Dic1311yescharacteristic
423#548Dic1311yescharacteristic
424#546—21no—
425#546Dic1311yescharacteristic
426#546Dic1311yescharacteristic
427D42Dic1311yescharacteristic
428#542—21no—
429#538—21no—
430#538—21no—
431#532C2×D1311yescharacteristic
432#529C2×D1311yescharacteristic
433#529C2×D1311yescharacteristic
434#529C2×D1311yescharacteristic
435C2×#124C2×D1311yescharacteristic
436C2×#124C2×D1311yescharacteristic
437#518—21no—
438C4×#41C2×D1311yescharacteristic
439#446—261no—
440#435—261no—
441#435—261no—
442C8×D4—261no—
443#433—261no—
444#433—261no—
445#432—131no—
446#432—131no—
447#432—131no—
448#432—131no—
449#432—131no—
450#432—131no—
451#432—131no—
452#424—261no—
453#408—261no—
454C4×M16—131no—
455C4×M16—131no—
456C2×#97—131no—
457C2×#97—131no—
458C2×#97—131no—
459#330—131no—
460#330—131no—
461#330—131no—
462#330—131no—
463#329—131no—
464#329—131no—
465#329—131no—
466#329—131no—
467#329—131no—
468#329—131no—
469#329—131no—
470#329—131no—
471#329—131no—
472#329—131no—
473#329—131no—
474#329—131no—
475C22×C13—21no—
476C22×C13—21no—
477C22×C13—21no—
478C22×C13—21no—
479C22×C13—21no—
480C22×C13—21no—
481C22×C13—21no—
482C22×C13—21no—
483C22×C13—41no—
484C22×C13—41no—
485C22×C13—41no—
486C22×C13—41no—
487C22×C13—41no—
488C22×C13—41no—
489C22×C13—41no—
490C22×C13—41no—
491C22×C13—41no—
492C22×C13—162no—
493C22×C13—162no—
494C22×C13#42112yes—
495C22×C13C22×C22⋊C411yescharacteristic
496C4×C13—21no—
497C4×C13—21no—
498C4×C13—21no—
499C4×C13—21no—
500C4×C13—21no—
501C4×C13—21no—
502C4×C13—21no—
503C4×C13—21no—
504C4×C13—21no—
505C4×C13—21no—
506C4×C13—21no—
507C4×C13—21no—
508C4×C13—41no—
509C4×C13—41no—
510C4×C13—41no—
511C4×C13—41no—
512C4×C13—41no—
513C2×#41C2×Dic1311yescharacteristic
514C2×#41C2×Dic1311yescharacteristic
515C2×#41C22⋊D1311yescharacteristic
516C22×Q8C2×Dic1311yescharacteristic
517C22×Q8C2×Dic1311yescharacteristic
518C22×D4—21no—
519C22×D4C2×Dic1311yescharacteristic
520C22×D4C2×Dic1311yescharacteristic
521C2×M16—261no—
522C2×M16—261no—
523C22×C8—261no—
524C22×C8—261no—
525C22×C8—261no—
526C4⋊Q8—21no—
527C4⋊Q8C2×Dic1311yescharacteristic
528#127C2×Dic1311yescharacteristic
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#125C22×D1311yescharacteristic
535#124—21no—
536#124—21no—
537#124—21no—
538#124—21no—
539#124—21no—
540#124—21no—
541#124—21no—
542#124C2×Dic1311yescharacteristic
543#124C2×Dic1311yescharacteristic
544#124C2×Dic1311yescharacteristic
545#124C2×Dic1311yescharacteristic
546#124C22×D1311yescharacteristic
547#124C22×D1311yescharacteristic
548#124C22×D1311yescharacteristic
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8C2×Dic1311yescharacteristic
562C22⋊Q8C2×Dic1311yescharacteristic
563C22⋊Q8C2×Dic1311yescharacteristic
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121C2×Dic1311yescharacteristic
572#121C2×Dic1311yescharacteristic
573#121C2×Dic1311yescharacteristic
574#120—21no—
575#120—21no—
576#120—21no—
577#120—21no—
578C4×Q8C2×Dic1311yescharacteristic
579C4×Q8C2×Dic1311yescharacteristic
580C4×Q8C2×Dic1311yescharacteristic
581C4×Q8C2×Dic1311yescharacteristic
582C4×Q8C22⋊D1311yescharacteristic
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4C2×Dic1311yescharacteristic
593C4×D4C2×Dic1311yescharacteristic
594C4×D4C2×Dic1311yescharacteristic
595C4×D4C2×Dic1311yescharacteristic
596C4×D4C2×Dic1311yescharacteristic
597C4×D4C2×Dic1311yescharacteristic
598C4×D4C22⋊D1311yescharacteristic
599C4×D4C22⋊D1311yescharacteristic
600C4×D4C22⋊D1311yescharacteristic
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605#117C22⋊D1311yescharacteristic
606#117C22⋊D1311yescharacteristic
607#117C22⋊D1311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C42C22×D1311yescharacteristic
615C2×C42C22×D1311yescharacteristic
616C2×C42C22×D1311yescharacteristic
617C4⋊C8—261no—
618C4⋊C8—261no—
619C4⋊C8—261no—
620C4⋊C8—261no—
621C4⋊C8—261no—
622C4⋊C8—261no—
623C4⋊C8—261no—
624C22⋊C8—261no—
625C22⋊C8—261no—
626C22⋊C8—261no—
627C22⋊C8—261no—
628C22⋊C8—261no—
629C22⋊C8—261no—
630C22⋊C8—261no—
631#97—131no—
632#97—131no—
633#97—131no—
634#97—131no—
635#97—131no—
636#97—131no—
637#97—131no—
638#97—131no—
639#97—261no—
640#97—261no—
641#97—261no—
642C4×C8—261no—
643C4×C8—261no—
644C2×C13—22no—
645C2×C13—41no—
646C2×C13—41no—
647C2×C13—81no—
648C2×C13—81no—
649C2×C13—81no—
650C2×C13#288811yescharacteristic
651C2×C13C2×#42111yescharacteristic
652C2×C13#290111yescharacteristic
653C24—21no—
654C24—21no—
655#41—42no—
656#41—81no—
657#41—81no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8—81no—
662C2×Q8C22⋊Dic1311yescharacteristic
663C2×Q8C22×Dic1311yescharacteristic
664C2×Q8C22×Dic1311yescharacteristic
665C2×Q8C22×Dic1311yescharacteristic
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—44no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4C22⋊Dic1311yescharacteristic
679C2×D4C22⋊Dic1311yescharacteristic
680C2×D4C22⋊Dic1311yescharacteristic
681C2×D4C22×Dic1311yescharacteristic
682C2×D4C22×Dic1311yescharacteristic
683C2×D4C22×Dic1311yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4C22×Dic1311yescharacteristic
692C22×C4C22×Dic1311yescharacteristic
693C22×C4C22×Dic1311yescharacteristic
694C22×C4C2×C22⋊D1311yescharacteristic
695C22×C4C2×C22⋊D1311yescharacteristic
696C22×C4C2×C22⋊D1311yescharacteristic
697C22×C4C2×C22⋊D1311yescharacteristic
698C22×C4C2×C22⋊D1311yescharacteristic
699C22×C4C2×C22⋊D1311yescharacteristic
700M16—522no—
701M16—522no—
702C2×C8—261no—
703C2×C8—261no—
704C2×C8—261no—
705C2×C8—261no—
706C2×C8—261no—
707C2×C8—261no—
708C2×C8—261no—
709C2×C8—261no—
710C2×C8—522no—
711C2×C8—522no—
712C2×C8—522no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4C22⋊Dic1311yescharacteristic
724C4⋊C4C22⋊Dic1311yescharacteristic
725C4⋊C4C22⋊Dic1311yescharacteristic
726C4⋊C4C22⋊Dic1311yescharacteristic
727C4⋊C4C22⋊Dic1311yescharacteristic
728C4⋊C4C22⋊Dic1311yescharacteristic
729C4⋊C4C22×Dic1311yescharacteristic
730C4⋊C4C22×Dic1311yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4C22⋊Dic1311yescharacteristic
755C22⋊C4C22⋊Dic1311yescharacteristic
756C22⋊C4C22⋊Dic1311yescharacteristic
757C22⋊C4C22⋊Dic1311yescharacteristic
758C22⋊C4C22⋊Dic1311yescharacteristic
759C22⋊C4C22⋊Dic1311yescharacteristic
760C42—21no—
761C42—21no—
762C42—21no—
763C42C22×Dic1311yescharacteristic
764C42C22×Dic1311yescharacteristic
765C42C22×Dic1311yescharacteristic
766C42C2×C22⋊D1311yescharacteristic
767C42C2×C22⋊D1311yescharacteristic
768C42C2×C22⋊D1311yescharacteristic
769C42C2×C22⋊D1311yescharacteristic
770C42C2×C22⋊D1311yescharacteristic
771C42C2×C22⋊D1311yescharacteristic
772C42C23×D1311yescharacteristic
773C13#1767911yescharacteristic, complemented, Sylow
774C23—21no—
775C23—21no—
776C23—21no—
777C23—42no—
778C23—42no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23C2×C22⋊Dic1311yescharacteristic
784C23C2×C22⋊Dic1311yescharacteristic
785C23C2×C22⋊Dic1311yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4C2×C22⋊Dic1311yescharacteristic
829C2×C4C2×C22⋊Dic1311yescharacteristic
830C2×C4C2×C22⋊Dic1311yescharacteristic
831C2×C4C2×C22⋊Dic1311yescharacteristic
832C2×C4C2×C22⋊Dic1311yescharacteristic
833C2×C4C2×C22⋊Dic1311yescharacteristic
834C2×C4C2×C22⋊Dic1311yescharacteristic
835C2×C4C2×C22⋊Dic1311yescharacteristic
836C2×C4C2×C22⋊Dic1311yescharacteristic
837C2×C4C23×Dic1311yescharacteristic
838C2×C4C22×C22⋊D1311yescharacteristic
839C2×C4C22×C22⋊D1311yescharacteristic
840C8—262no—
841C8—521no—
842C8—521no—
843C8—521no—
844C8—521no—
845C8—521no—
846C8—521no—
847C8—521no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—162no—
866C22—162no—
867C22#1171889712yes—
868C22C22×C22⋊Dic1311yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—41no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—81no—
890C2—81no—
891C2—81no—
892C2#1312331511yescharacteristic
893C2C2×#1171889711yescharacteristic
894C2#1312338311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
Fitting, prime radicalC13×#3514C2
socleC22×C13C22×C22⋊C4
cosocleC42×C13C24
hypercenter#3514D13
hypocenterC13#17679
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3514

Complements

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

NH ≅ G/Ntype
1. #13123850C2semidirect
2. #13123487C2semidirect
3. #13113471C2semidirect
4. #13113467C2semidirect
5. #13113467C2semidirect
6. #13113460C2semidirect
7. #13113456C2semidirect
8. #13113456C2semidirect
9. #13113447C2semidirect
10. #13113443C2semidirect
11. #13113434C2semidirect
12. #13113434C2semidirect
13. #13113424C2semidirect
14. C2×#11718132C2semidirect
47. #11718587C22semidirect
48. #11718587C22semidirect
49. #11718587C22semidirect
50. #11718587C22semidirect
51. #11718587C22semidirect
52. #11718587C22semidirect
53. #11718587C22semidirect
54. C4×#6099C22semidirect
55. C4×#6099C22semidirect
56. C2×#88043C22semidirect
57. C2×#88043C22semidirect
58. C2×#88043C22semidirect
59. #11718135C22semidirect
60. #11718135C22semidirect
61. #11718135C22semidirect
62. #11718135C22semidirect
67. #11718132C22semidirect
68. #11718132C22semidirect
69. #11718132C22semidirect
70. #11718132C22semidirect
71. #11718132C22semidirect
72. #11718132C22semidirect
73. #11718132C22semidirect
74. #11718132C22semidirect
773. C13#17679semidirect

Maximal subgroups

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

subgroupindex
#131238502
#131234872
#131134712
#131134672
#131134602
#131134562
#131134472
#131134432
#131134342
#131134242
C2×#117181322
C13×#35142
#1767913