Finite Group Databasebeta

← #15870773

Subgroups — #15870773

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124626C211yesmaximal, characteristic
2#13123776C211yesmaximal, characteristic, complemented
3#13123261C211yesmaximal, characteristic
4#13115779C211yesmaximal, characteristic, complemented
5#13115612C211yesmaximal, characteristic, complemented
6#13115436C211yesmaximal, characteristic, complemented
7#13115436C211yesmaximal, characteristic, complemented
8#13115114C211yesmaximal, characteristic
9#13115114C211yesmaximal, characteristic
10#13114857C211yesmaximal, characteristic
11#13114720C211yesmaximal, characteristic, complemented
12#13114715C211yesmaximal, characteristic, complemented
13#13114680C211yesmaximal, characteristic
14#13114673C211yesmaximal, characteristic
15C13×#1771C211yesmaximal, characteristic, complemented
16C2×#88155C2211yescharacteristic
17C2×#88155C2211yescharacteristic
18C4×#6127C2211yescharacteristic
19#11719175C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×#97C2211yescharacteristic
22C2×C13×#97C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25#11718774C2211yescharacteristic
26#11718774C2211yescharacteristic
27C2×#88059C2211yescharacteristic
28C2×#88059C2211yescharacteristic
29#11718767C2211yescharacteristic
30#11718767C2211yescharacteristic
31#11718763C2211yescharacteristic
32#11718763C2211yescharacteristic
33#11718762C2211yescharacteristic
34#11718762C2211yescharacteristic
35#11718762C2211yescharacteristic
36#11718762C2211yescharacteristic
37C2×#88045C2211yescharacteristic
38C2×#88045C2211yescharacteristic
39#11718585C2211yescharacteristic
40C4×#6099C2211yescharacteristic
41#11718512C411yescharacteristic, complemented
42#11718511C411yescharacteristic, complemented
43#11718508C411yescharacteristic, complemented
44#11718508C411yescharacteristic, complemented
45#11718507C411yescharacteristic, complemented
46#11718503C411yescharacteristic, complemented
47#11718490C411yescharacteristic, complemented
48#11718490C411yescharacteristic, complemented
49#11718369—21no—
50#11718369—21no—
51#11718368—21no—
52D13×#97—21no—
53#11718362—21no—
54#11718362—21no—
55#11718362—21no—
56#11718362—21no—
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59#11718144C2211yescharacteristic
60#11718144C2211yescharacteristic
61#11718115C2211yescharacteristic
62#11718115C2211yescharacteristic
63#11718115C2211yescharacteristic
64#11718115C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C2×#6127C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C2×C13×C4⋊C4—21no—
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C4×C22⋊D13—21no—
77C4×C22⋊D13—21no—
78#88180C2311yescharacteristic
79#88180C2311yescharacteristic
80#88180C2311yescharacteristic
81#88178—21no—
82#88178—21no—
83C2×#6099C2311yescharacteristic
84C2×#6099C2311yescharacteristic
85C2×#6099C2311yescharacteristic
86C2×#6099C2311yescharacteristic
87#88155—22no—
88#88155—22no—
89#88155—22no—
90#88155Q814yescomplemented
91C2×#6094—21no—
92C2×#6094—21no—
93C2×C8×D13—21no—
94C2×C8×D13—21no—
95C4×D52C2×C411yescharacteristic
96C4×D52C2×C411yescharacteristic
97#88126—21no—
98C42×D13—21no—
99#88124C2×C411yescharacteristic
100#88124C2×C411yescharacteristic
101#88123C2×C411yescharacteristic
102#88123C2×C411yescharacteristic
103C4×Dic26—21no—
104C4×Dic26—21no—
105C4×Dic26C2×C411yescharacteristic
106C4×Dic26C2×C411yescharacteristic
107C13×C4⋊C8C2×C411yescharacteristic
108C13×C4⋊C8C2×C411yescharacteristic
109C13×C4⋊C8C2×C411yescharacteristic
110C13×C4⋊C8C2×C411yescharacteristic
111C13×#97—22no—
112C13×#97D411yescharacteristic
113C13×#97D411yescharacteristic
114C13×#97D411yescharacteristic
115C13×#97D411yescharacteristic
116C4×C8×C13—22no—
117C13×#95—21no—
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88059—22no—
123#88059—22no—
124#88058C2×C411yescharacteristic
125#88058C2×C411yescharacteristic
126#88058C2×C411yescharacteristic
127#88058C2×C411yescharacteristic
128#88057C2×C411yescharacteristic
129#88057C2×C411yescharacteristic
130#88057C2×C411yescharacteristic
131#88057C2×C411yescharacteristic
132#88056C2×C411yescharacteristic
133#88056C2×C411yescharacteristic
134#88056C2×C411yescharacteristic
135#88056C2×C411yescharacteristic
136#88055—21no—
137#88055—21no—
138#88055—21no—
139#88055—21no—
140#88054—21no—
141#88054—21no—
142#88054—21no—
143#88054—21no—
144C8×Dic13—21no—
145C8×Dic13—21no—
146C8×Dic13—21no—
147C8×Dic13—21no—
148#88045—22no—
149#88045—22no—
150C4⋊#1055—21no—
151C4⋊#1055—21no—
152#88043—21no—
153C4×#1055—21no—
154#21629—131nomaximal, Sylow
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13#4111yescharacteristic
158C22×C4×C13#4111yescharacteristic
159C22×C4×C13C2411yescharacteristic
160C2×C22⋊D13—21no—
161#6127—21no—
162#6127—21no—
163#6127C2×Q812yes—
164#6127#4112yes—
165C2×D52C22×C411yescharacteristic
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—21no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26C22×C411yescharacteristic
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13C22×C411yescharacteristic
179C2×C8×C13C22×C411yescharacteristic
180C2×C8×C13C22×C411yescharacteristic
181C2×C8×C13C22×C411yescharacteristic
182C2×C8×C13C2×D411yescharacteristic
183C2×C8×C13C2×D411yescharacteristic
184C2×C8×C13C2×D411yescharacteristic
185C2×C8×C13C2×D411yescharacteristic
186C2×C8×C13C2×Q812yes—
187C2×C8×C13#4112yes—
188C13×C4⋊C4—42no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13C22×C411yescharacteristic
194C42×C13C22×C411yescharacteristic
195C42×C13C2×D411yescharacteristic
196C42×C13C2×D411yescharacteristic
197C22⋊Dic13—21no—
198C22⋊Dic13—21no—
199C22⋊Dic13—21no—
200#6103—21no—
201#6103—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13C22×C411yescharacteristic
205C4⋊Dic13C22×C411yescharacteristic
206C4⋊Dic13C22×C411yescharacteristic
207C4⋊Dic13C22×C411yescharacteristic
208C4⋊Dic13C22×C411yescharacteristic
209C4⋊Dic13C22×C411yescharacteristic
210#6101—21no—
211#6101—21no—
212#6101—21no—
213#6101—21no—
214#6101—21no—
215#6101—21no—
216C4×Dic13—21no—
217C4×Dic13—21no—
218C4×Dic13—21no—
219C4×Dic13—21no—
220C4×Dic13—21no—
221#6099—21no—
222#6099—21no—
223#6099—21no—
224#6099—21no—
225#6099—21no—
226#6099—21no—
227#6099C2×Q812yes—
228#6099#4112yes—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233#6094—24no—
234#6094—24no—
235C8×D13—24no—
236C8×D13—24no—
237#3076—131no—
238#2961—131no—
239#2875—131no—
240#1986—131no—
241#1950—131no—
242#1922—131no—
243#1922—131no—
244#1866—131no—
245#1866—131no—
246#1806—131no—
247#1773—131no—
248#1772—131no—
249#1771D1311yescharacteristic, complemented
250#1765—131no—
251#1764—131no—
252C23×C13C2×#4111yescharacteristic
253C22×D13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13C4×D411yescharacteristic
263C2×C4×C13C4×D411yescharacteristic
264C2×C4×C13C4×D411yescharacteristic
265C2×C4×C13C4×D411yescharacteristic
266C2×C4×C13C23×C411yescharacteristic
267C2×C4×C13C22×D411yescharacteristic
268C2×C4×C13C22×Q811yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C22⋊D13—22no—
273C22⋊D13—22no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281D52—21no—
282D52C4×Q812yes—
283C4×D13—22no—
284C4×D13—22no—
285C4×D13—81no—
286C4×D13—81no—
287Dic26—21no—
288Dic26—81no—
289Dic26—81no—
290Dic26C4×Q812yes—
291C8×C13—21no—
292C8×C13—21no—
293C8×C13—21no—
294C8×C13—21no—
295C8×C13—21no—
296C8×C13—21no—
297C8×C13C22⋊Q812yes—
298C8×C13C22⋊Q812yes—
299#1055—22no—
300#1055—22no—
301#1055—41no—
302#1055—41no—
303C2×#131—131no—
304C2×#131—131no—
305#533—131no—
306C4×#41—131no—
307#479—131no—
308#479—131no—
309#478—131no—
310#478—131no—
311#477—131no—
312#476—131no—
313#475—131no—
314#474—131no—
315#446—261no—
316#446—261no—
317#446—261no—
318#446—261no—
319C2×#108—131no—
320C2×#108—131no—
321#427—131no—
322#427—131no—
323#424—131no—
324#424—131no—
325#423—131no—
326C2×C4⋊C8C2×D1311yescharacteristic
327C2×#104—131no—
328C2×#104—131no—
329#416—131no—
330#416—131no—
331#405—131no—
332#405—131no—
333#405—131no—
334#405—131no—
335#405—261no—
336#405—261no—
337C4×M16—131no—
338C4×M16—261no—
339C2×#97—261no—
340C2×#97C2×D1311yescharacteristic
341C2×#97C2×D1311yescharacteristic
342C2×C4×C8C2×D1311yescharacteristic
343C4×C4⋊C4C2×D1311yescharacteristic
344#341—131no—
345#341—131no—
346#339—131no—
347#339—131no—
348#339—131no—
349#339—131no—
350#339—131no—
351#339—131no—
352#336C2×D1311yescharacteristic
353#336C2×D1311yescharacteristic
354C22×C13—21no—
355C22×C13—21no—
356C22×C13C2×C4×D411yescharacteristic
357C22×C13#52911yescharacteristic
358C22×C13#53311yescharacteristic
359C2×D13—22no—
360C2×D13—41no—
361C2×D13—41no—
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—21no—
366C4×C13—42no—
367C4×C13—81no—
368C4×C13C2×C4×Q811yescharacteristic
369C4×C13C4×#4111yescharacteristic
370C4×C13C2×C22⋊Q811yescharacteristic
371C4×C13#52511yescharacteristic
372Dic13—22no—
373Dic13—41no—
374Dic13—41no—
375Dic13—41no—
376Dic13—41no—
377Dic13—41no—
378Dic13—41no—
379C2×#41—131no—
380#131—134no—
381#131—262no—
382#131—262no—
383#131—262no—
384C2×M16—131no—
385C2×M16—131no—
386C2×M16—131no—
387C2×M16—131no—
388C2×M16—261no—
389C2×M16—261no—
390C22×C8—261no—
391C22×C8—261no—
392C22×C8C22×D1311yescharacteristic
393C22×C8C22×D1311yescharacteristic
394C22×C8C22×D1311yescharacteristic
395C22×C8C22×D1311yescharacteristic
396C4⋊Q8—131no—
397C4⋊Q8—131no—
398#125—131no—
399#125—131no—
400C22⋊Q8—261no—
401C22⋊Q8—261no—
402C4×Q8—131no—
403C4×Q8—131no—
404C4×Q8—261no—
405C4×Q8—261no—
406C4×D4—131no—
407C4×D4—131no—
408C4×D4—261no—
409C4×D4—261no—
410#117—131no—
411#117—131no—
412#117—131no—
413#117—261no—
414C2×C4⋊C4—21no—
415C2×C42—261no—
416C2×C42C22×D1311yescharacteristic
417C2×C42C22×D1311yescharacteristic
418C2×C42C22×D1311yescharacteristic
419#108—262no—
420#108—262no—
421#107—131no—
422#107—131no—
423#107—131no—
424#107—131no—
425#106—131no—
426#106—131no—
427#106—131no—
428#106—131no—
429C4⋊C8—261no—
430C4⋊C8—261no—
431C4⋊C8—261no—
432C4⋊C8—261no—
433C4⋊C8—261no—
434C4⋊C8—261no—
435C4⋊C8C4×D1311yescharacteristic
436C4⋊C8C4×D1311yescharacteristic
437C4⋊C8C4×D1311yescharacteristic
438C4⋊C8C4×D1311yescharacteristic
439#104—262no—
440#104—262no—
441#103—131no—
442#103—131no—
443#103—131no—
444#103—131no—
445#102—131no—
446#102—131no—
447#102—131no—
448#102—131no—
449#97—22no—
450#97—261no—
451#97—261no—
452#97—261no—
453#97—261no—
454#97—261no—
455#97D5211yescharacteristic
456#97D5211yescharacteristic
457#97D5211yescharacteristic
458#97D5211yescharacteristic
459C4×C8—22no—
460C4×C8—261no—
461C4×C8—261no—
462C4×C8—261no—
463C4×C8—261no—
464C4×C8—261no—
465#95—21no—
466C2×C13—21no—
467C2×C13—21no—
468C2×C13C4×C22⋊Q811yescharacteristic
469C2×C13#295611yescharacteristic
470C2×C13#295711yescharacteristic
471D13—42no—
472#41—132no—
473#41—132no—
474#41—261no—
475#41—261no—
476C2×Q8—131no—
477C2×Q8—261no—
478C2×Q8—261no—
479C2×D4—131no—
480C2×D4—261no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4#612711yescharacteristic
487C22×C4#612711yescharacteristic
488C22×C4C23×D1311yescharacteristic
489M16—132no—
490M16—132no—
491M16—264no—
492M16—261no—
493M16—261no—
494M16—264no—
495M16—261no—
496M16—261no—
497M16—261no—
498M16—261no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—264no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—264no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8C2×C4×D1311yescharacteristic
512C2×C8C2×C4×D1311yescharacteristic
513C2×C8C2×C4×D1311yescharacteristic
514C2×C8C2×C4×D1311yescharacteristic
515C2×C8C2×D5211yescharacteristic
516C2×C8C2×D5211yescharacteristic
517C2×C8C2×D5211yescharacteristic
518C2×C8C2×D5211yescharacteristic
519C2×C8#612912yes—
520C2×C8Q8×D1312yes—
521C4⋊C4—42no—
522C4⋊C4—131no—
523C4⋊C4—131no—
524C4⋊C4—131no—
525C4⋊C4—131no—
526C4⋊C4—131no—
527C4⋊C4—131no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—261no—
535C4⋊C4—261no—
536C22⋊C4—261no—
537C22⋊C4—261no—
538C22⋊C4—261no—
539C22⋊C4—261no—
540C22⋊C4—261no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—261no—
546C42—261no—
547C42—261no—
548C42—261no—
549C42—261no—
550C42C2×C4×D1311yescharacteristic
551C42C2×C4×D1311yescharacteristic
552C42C2×D5211yescharacteristic
553C42C2×D5211yescharacteristic
554C13#2162911yescharacteristic, complemented, Sylow
555C23—261no—
556C23C2×#612711yescharacteristic
557Q8—132no—
558Q8—261no—
559Q8—1041no—
560Q8—1041no—
561D4—132no—
562D4—262no—
563D4—262no—
564D4—261no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—261no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—1041no—
583C2×C4—1041no—
584C2×C4C4×D5211yescharacteristic
585C2×C4C4×D5211yescharacteristic
586C2×C4C4×D5211yescharacteristic
587C2×C4C4×D5211yescharacteristic
588C2×C4C22×C4×D1311yescharacteristic
589C2×C4C22×D5211yescharacteristic
590C2×C4C2×#612911yescharacteristic
591C2×C4C2×Q8×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#41×D1311yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—21no—
599C8—21no—
600C8—262no—
601C8—262no—
602C8—521no—
603C8—521no—
604C8#8815112yes—
605C8#8815112yes—
606C22—21no—
607C22—21no—
608C22—262no—
609C22—521no—
610C22—521no—
611C22C2×C4×D5211yescharacteristic
612C22#1171926211yescharacteristic
613C22#1171928311yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—81no—
620C4—262no—
621C4—521no—
622C4—521no—
623C4—521no—
624C4—521no—
625C4—521no—
626C4—521no—
627C4C2×#8815111yescharacteristic
628C4#1171922911yescharacteristic
629C4C4×#612911yescharacteristic
630C4C4×Q8×D1311yescharacteristic
631C2—21no—
632C2—21no—
633C2—522no—
634C2C4×#8815111yescharacteristic
635C2#1312374711yescharacteristic
636C2#1312375411yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1771C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C23
cosocleC22×C4×C13C24
hypercenter#1771D13
hypocenterC13#21629
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #13123776C2semidirect
4. #13115779C2semidirect
5. #13115612C2semidirect
6. #13115436C2semidirect
7. #13115436C2semidirect
11. #13114720C2semidirect
12. #13114715C2semidirect
15. C13×#1771C2semidirect
41. #11718512C4semidirect
42. #11718511C4semidirect
43. #11718508C4semidirect
44. #11718508C4semidirect
45. #11718507C4semidirect
46. #11718503C4semidirect
47. #11718490C4semidirect
48. #11718490C4semidirect
90. #88155Q8semidirect
249. #1771D13semidirect
554. C13#21629semidirect

Maximal subgroups

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

subgroupindex
#131246262
#131237762
#131232612
#131157792
#131156122
#131154362
#131151142
#131148572
#131147202
#131147152
#131146802
#131146732
C13×#17712
#2162913