Finite Group Databasebeta

← #15870775

Subgroups — #15870775

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#13124620C211yesmaximal, characteristic
2#13123774C211yesmaximal, characteristic, complemented
3#13123262C211yesmaximal, characteristic
4#13115778C211yesmaximal, characteristic, complemented
5#13115610C211yesmaximal, characteristic, complemented
6#13115438C211yesmaximal, characteristic, complemented
7#13115434C211yesmaximal, characteristic, complemented
8#13115113C211yesmaximal, characteristic
9#13115109C211yesmaximal, characteristic
10#13114854C211yesmaximal, characteristic
11#13114720C211yesmaximal, characteristic, complemented
12#13114716C211yesmaximal, characteristic, complemented
13#13114712C211yesmaximal, characteristic, complemented
14#13114671C211yesmaximal, characteristic
15C13×#1765C211yesmaximal, characteristic
16C2×C13×#131C2211yescharacteristic
17#41×Dic13C2211yescharacteristic
18C2×#88202C2211yescharacteristic
19#11719222C2211yescharacteristic
20C2×C13×#104C2211yescharacteristic
21C13×#416C2211yescharacteristic
22C13×#405C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C2×#88077C2211yescharacteristic
25#11718894C2211yescharacteristic
26C2×#88062C2211yescharacteristic
27#11718783—21no—
28#11718783C2211yescharacteristic
29#11718780C2211yescharacteristic
30#11718779C2211yescharacteristic
31M16×Dic13—21no—
32M16×Dic13C2211yescharacteristic
33C2×#88059C2211yescharacteristic
34#11718767C2211yescharacteristic
35#11718762—21no—
36#11718762C2211yescharacteristic
37#11718762C2211yescharacteristic
38C2×#88055—21no—
39C2×#88055C2211yescharacteristic
40C2×#88054C2211yescharacteristic
41C2×C8×Dic13C2211yescharacteristic
42#11718660C2211yescharacteristic
43#11718659C2211yescharacteristic
44C4×#6101C2211yescharacteristic
45#11718460C411yescharacteristic, complemented
46#11718457C411yescharacteristic, complemented
47#11718455C411yescharacteristic, complemented
48#11718452C411yescharacteristic, complemented
49#11718427C411yescharacteristic, complemented
50#11718424C411yescharacteristic, complemented
51#11718422C411yescharacteristic, complemented
52#11718420C411yescharacteristic, complemented
53#11718362—21no—
54#11718362—21no—
55#11718340—21no—
56#11718340—21no—
57C13×#341C2211yescharacteristic
58C13×#339C2211yescharacteristic
59#11718150C2211yescharacteristic
60#11718147C2211yescharacteristic
61#11718147C2211yescharacteristic
62#11718142C2211yescharacteristic
63#11718124C2211yescharacteristic
64#11718116C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C2×C13×#41C2311yescharacteristic
68C13×#131—22no—
69C13×#131Q814yescomplemented
70C2×C13×M16—21no—
71C2×C13×M16C2311yescharacteristic
72C2×C13×M16C2311yescharacteristic
73C22×C8×C13—21no—
74C22×C8×C13C2311yescharacteristic
75C22×C8×C13C2311yescharacteristic
76C13×#117C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78#88202—22no—
79#88202—22no—
80Q8×Dic13C2×C411yescharacteristic
81Q8×Dic13C2×C411yescharacteristic
82D4×Dic13—21no—
83D4×Dic13—21no—
84D4×Dic13C2×C411yescharacteristic
85D4×Dic13C2×C411yescharacteristic
86#88180—21no—
87#88180C2311yescharacteristic
88#88180C2311yescharacteristic
89C2×#6101—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13C2311yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×#6099—21no—
94C2×#6099C2311yescharacteristic
95C2×#6099C2311yescharacteristic
96C22×#1055—21no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88144C2×C411yescharacteristic
100#88144C2×C411yescharacteristic
101#88142C2×C411yescharacteristic
102#88142C2×C411yescharacteristic
103#88132—21no—
104#88132—21no—
105C4×Dic26—21no—
106C4×Dic26—21no—
107C13×#104—22no—
108C13×#103C2×C411yescharacteristic
109C13×#103C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×#102C2×C411yescharacteristic
112C13×#97—21no—
113C13×#97—22no—
114C4×C8×C13—21no—
115#88077—22no—
116#88075C2×C411yescharacteristic
117#88075C2×C411yescharacteristic
118#88072C2×C411yescharacteristic
119#88072C2×C411yescharacteristic
120#88071—21no—
121#88062—22no—
122#88059—22no—
123#88058C2×C411yescharacteristic
124#88058C2×C411yescharacteristic
125#88057C2×C411yescharacteristic
126#88057C2×C411yescharacteristic
127#88055—21no—
128#88055—21no—
129#88055—21no—
130#88055—21no—
131#88055D411yescharacteristic
132#88055D411yescharacteristic
133#88055D411yescharacteristic
134#88055D411yescharacteristic
135#88054—21no—
136#88054—21no—
137#88054—21no—
138#88054—21no—
139#88054C2×C411yescharacteristic
140#88054C2×C411yescharacteristic
141#88054C2×C411yescharacteristic
142#88054C2×C411yescharacteristic
143C8×Dic13—21no—
144C8×Dic13—21no—
145C8×Dic13—22no—
146C8×Dic13—21no—
147C8×Dic13—21no—
148#88048C2×C411yescharacteristic
149#88048C2×C411yescharacteristic
150#88047C2×C411yescharacteristic
151#88047C2×C411yescharacteristic
152C4⋊#1055—21no—
153C4⋊#1055—21no—
154#21629—131nomaximal, Sylow
155C13×#41—21no—
156C13×#41—21no—
157C13×#41C2×Q812yes—
158C13×#41#4112yes—
159C2×Q8×C13C22×C411yescharacteristic
160C2×D4×C13—21no—
161C2×D4×C13C22×C411yescharacteristic
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13C2411yescharacteristic
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13#4111yescharacteristic
169C22×Dic13#4111yescharacteristic
170C2×Dic26—21no—
171C2×Dic26—21no—
172C13×M16—21no—
173C13×M16—24no—
174C13×M16—21no—
175C13×M16—21no—
176C13×M16C2×Q812yes—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—24no—
181C2×C8×C13—21no—
182C2×C8×C13C22×C411yescharacteristic
183C2×C8×C13C22×C411yescharacteristic
184C2×C8×C13C2×D411yescharacteristic
185C2×C8×C13C2×D411yescharacteristic
186C2×C8×C13C2×Q812yes—
187C2×C8×C13#4112yes—
188C13×C4⋊C4C22×C411yescharacteristic
189C13×C4⋊C4C22×C411yescharacteristic
190C13×C22⋊C4—21no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13—21no—
194C22⋊Dic13—21no—
195C22⋊Dic13—21no—
196C22⋊Dic13—21no—
197C22⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13C22×C411yescharacteristic
203C4⋊Dic13C22×C411yescharacteristic
204C4⋊Dic13C22×C411yescharacteristic
205C4⋊Dic13C22×C411yescharacteristic
206#6101—21no—
207#6101—21no—
208#6101—21no—
209#6101—21no—
210#6101—42no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213C4×Dic13—21no—
214C4×Dic13—21no—
215C4×Dic13—21no—
216C4×Dic13—21no—
217C4×Dic13C22×C411yescharacteristic
218C4×Dic13C22×C411yescharacteristic
219C4×Dic13C2×D411yescharacteristic
220C4×Dic13C2×D411yescharacteristic
221#6099—24no—
222#6099—21no—
223#6099—21no—
224#6099—21no—
225#6099#4112yes—
226C2×#1055—24no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055C22×C411yescharacteristic
234C2×#1055C22×C411yescharacteristic
235C2×#1055C2×D411yescharacteristic
236C2×#1055C2×D411yescharacteristic
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#1771—131no—
250#1765D1311yescharacteristic
251#1764—131no—
252C23×C13—21no—
253C23×C13C2×#4111yescharacteristic
254Q8×C13—21no—
255Q8×C13C4×Q812yes—
256D4×C13—22no—
257D4×C13—22no—
258D4×C13—21no—
259D4×C13C4×Q812yes—
260C2×C4×C13—21no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13C23×C411yescharacteristic
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C22×Q811yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×Dic13—22no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—81no—
284C2×Dic13—81no—
285C2×Dic13C4×D411yescharacteristic
286C2×Dic13C4×D411yescharacteristic
287C2×Dic13C4×D411yescharacteristic
288C2×Dic13C4×D411yescharacteristic
289Dic26—81no—
290Dic26—81no—
291C8×C13—21no—
292C8×C13—21no—
293C8×C13—22no—
294C8×C13—41no—
295C8×C13C22⋊Q812yes—
296C8×C13C22⋊Q812yes—
297#1055—21no—
298#1055—21no—
299#1055—21no—
300#1055—22no—
301#1055—21no—
302#1055—41no—
303C2×#131—131no—
304C2×#131C2×D1311yescharacteristic
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⋊C8—131no—
327C2×#104—131no—
328C2×#104C2×D1311yescharacteristic
329#416—131no—
330#416C2×D1311yescharacteristic
331#405—131no—
332#405—131no—
333#405—131no—
334#405—261no—
335#405—261no—
336#405C2×D1311yescharacteristic
337C4×M16—131no—
338C4×M16—261no—
339C2×#97—131no—
340C2×#97—261no—
341C2×#97C2×D1311yescharacteristic
342C2×C4×C8—131no—
343C4×C4⋊C4—131no—
344#341—131no—
345#341C2×D1311yescharacteristic
346#339—131no—
347#339—131no—
348#339—131no—
349#339—131no—
350#339—131no—
351#339C2×D1311yescharacteristic
352#336—131no—
353#336—131no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13—22no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13C2×C4×D411yescharacteristic
360C22×C13#52911yescharacteristic
361C22×C13#53311yescharacteristic
362C4×C13—22no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—81no—
366C4×C13C2×C4×Q811yescharacteristic
367C4×C13C4×#4111yescharacteristic
368C4×C13C2×C22⋊Q811yescharacteristic
369C4×C13#52511yescharacteristic
370Dic13—21no—
371Dic13—21no—
372Dic13—21no—
373Dic13—21no—
374Dic13—42no—
375Dic13—41no—
376Dic13—41no—
377Dic13—41no—
378Dic13—41no—
379C2×#41C22×D1311yescharacteristic
380#131—22no—
381#131—262no—
382#131—262no—
383#131Dic2614yescomplemented
384C2×M16—21no—
385C2×M16—131no—
386C2×M16—131no—
387C2×M16—261no—
388C2×M16C22×D1311yescharacteristic
389C2×M16C22×D1311yescharacteristic
390C22×C8—21no—
391C22×C8—131no—
392C22×C8—131no—
393C22×C8—261no—
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—261no—
413#117C22×D1311yescharacteristic
414C2×C4⋊C4—261no—
415C2×C42—131no—
416C2×C42—131no—
417C2×C42—261no—
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—131no—
430C4⋊C8—131no—
431C4⋊C8—131no—
432C4⋊C8—131no—
433C4⋊C8—261no—
434C4⋊C8—261no—
435C4⋊C8—261no—
436C4⋊C8—261no—
437C4⋊C8—261no—
438C4⋊C8—261no—
439#104—22no—
440#104—262no—
441#103—131no—
442#103—131no—
443#103C4×D1311yescharacteristic
444#103C4×D1311yescharacteristic
445#102—131no—
446#102—131no—
447#102C4×D1311yescharacteristic
448#102C4×D1311yescharacteristic
449#97—21no—
450#97—22no—
451#97—131no—
452#97—131no—
453#97—131no—
454#97—131no—
455#97—261no—
456#97—261no—
457#97—261no—
458#97—261no—
459C4×C8—21no—
460C4×C8—261no—
461C4×C8—261no—
462C4×C8—261no—
463C4×C8—261no—
464C4×C8—262no—
465#95—261no—
466C2×C13—21no—
467C2×C13—21no—
468C2×C13—42no—
469C2×C13C4×C22⋊Q811yescharacteristic
470C2×C13#295611yescharacteristic
471C2×C13#295711yescharacteristic
472#41—21no—
473#41—21no—
474#41C2×Dic2612yes—
475#41#612712yes—
476C2×Q8—261no—
477C2×Q8—261no—
478C2×Q8C2×C4×D1311yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D1311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4C23×D1311yescharacteristic
489M16—21no—
490M16—24no—
491M16—21no—
492M16—21no—
493M16—132no—
494M16—264no—
495M16—261no—
496M16—261no—
497M16—261no—
498M16C2×Dic2612yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—24no—
503C2×C8—21no—
504C2×C8—131no—
505C2×C8—131no—
506C2×C8—131no—
507C2×C8—131no—
508C2×C8—264no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8C2×Dic2612yes—
516C2×C8C2×C4×D1311yescharacteristic
517C2×C8C2×C4×D1311yescharacteristic
518C2×C8D4×D1311yescharacteristic
519C2×C8D4×D1311yescharacteristic
520C2×C8#612912yes—
521C4⋊C4—131no—
522C4⋊C4—131no—
523C4⋊C4—131no—
524C4⋊C4—131no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—522no—
534C4⋊C4C2×C4×D1311yescharacteristic
535C4⋊C4C2×C4×D1311yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—261no—
538C22⋊C4—261no—
539C22⋊C4—261no—
540C22⋊C4—261no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—131no—
545C42—131no—
546C42—131no—
547C42—131no—
548C42—261no—
549C42—261no—
550C42—261no—
551C42—261no—
552C42—261no—
553C42—261no—
554C13#2162911yescharacteristic, complemented, Sylow
555C23—21no—
556C23#41×D1311yescharacteristic
557Q8—21no—
558Q8—1041no—
559Q8—1041no—
560Q8C4×Dic2612yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4C4×Dic2612yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—131no—
574C2×C4—131no—
575C2×C4—131no—
576C2×C4—131no—
577C2×C4—262no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—1041no—
587C2×C4—1041no—
588C2×C4C22×Dic2611yescharacteristic
589C2×C4C22×C4×D1311yescharacteristic
590C2×C4C2×#612711yescharacteristic
591C2×C4C2×D4×D1311yescharacteristic
592C2×C4C2×#612911yescharacteristic
593C2×C4#41×D1311yescharacteristic
594C8—22no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—261no—
599C8—261no—
600C8—261no—
601C8—261no—
602C8—262no—
603C8—521no—
604C8#8813212yes—
605C8#8813212yes—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22#1171922211yescharacteristic
612C22#1171924311yescharacteristic
613C22C4×D4×D1311yescharacteristic
614C4—22no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—261no—
619C4—261no—
620C4—261no—
621C4—261no—
622C4—522no—
623C4—521no—
624C4—521no—
625C4—521no—
626C4—521no—
627C4C2×C4×Dic2611yescharacteristic
628C4C2×#8813211yescharacteristic
629C4C4×#612911yescharacteristic
630C4#1171925211yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2C4×#8813211yescharacteristic
635C2#1312374411yescharacteristic
636C2#1312375011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1765C2
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C23
cosocleC22×C4×C13C24
hypercenter#1765D13
hypocenterC13#21629
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
2. #13123774C2semidirect
4. #13115778C2semidirect
5. #13115610C2semidirect
6. #13115438C2semidirect
7. #13115434C2semidirect
11. #13114720C2semidirect
12. #13114716C2semidirect
13. #13114712C2semidirect
45. #11718460C4semidirect
46. #11718457C4semidirect
47. #11718455C4semidirect
48. #11718452C4semidirect
49. #11718427C4semidirect
50. #11718424C4semidirect
51. #11718422C4semidirect
52. #11718420C4semidirect
69. C13×#131Q8semidirect
383. #131Dic26semidirect
554. C13#21629semidirect

Maximal subgroups

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

subgroupindex
#131246202
#131237742
#131232622
#131157782
#131156102
#131154382
#131154342
#131151132
#131151092
#131148542
#131147202
#131147162
#131147122
#131146712
C13×#17652
#2162913