Finite Group Databasebeta

← #14738659

Subgroups — #14738659

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079983C211yesmaximal, characteristic, complemented
2#13079972C211yesmaximal, characteristic
3#13077591C211yesmaximal, characteristic, complemented
4#13068195C211yesmaximal, characteristic, complemented
5#13068188C211yesmaximal, characteristic, complemented
6#13068181C211yesmaximal, characteristic, complemented
7#13068174C211yesmaximal, characteristic, complemented
8#13068043C211yesmaximal, characteristic, complemented
9#13068036C211yesmaximal, characteristic, complemented
10#13068029C211yesmaximal, characteristic, complemented
11#13068022C211yesmaximal, characteristic, complemented
12#13067372C211yesmaximal, characteristic, complemented
13#13067346C211yesmaximal, characteristic, complemented
14#13067338C211yesmaximal, characteristic, complemented
15C11×#3131C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#488—21no—
20C11×#488—21no—
21C11×#487C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#486C2211yescharacteristic
24C11×#486C2211yescharacteristic
25C11×#416—21no—
26C11×#416—21no—
27C2×C4×C8×C11C2211yescharacteristic
28#10622724—21no—
29C8×C22⋊D11—21no—
30#10622707C2211yescharacteristic
31#10622704C2211yescharacteristic
32#10622703C2211yescharacteristic
33#10622700C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622696C2211yescharacteristic
36#10622688C2211yescharacteristic
37#10622685C2211yescharacteristic
38#10622665—21no—
39#10622662—21no—
40#10622655—21no—
41#10622652—21no—
42#10622641—21no—
43#10622635—21no—
44#10622629—21no—
45#10622622—21no—
46#10622539C2211yescharacteristic
47#10622537C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622303—21no—
50#10622302—21no—
51#10622301C2211yescharacteristic
52C8×D44C2211yescharacteristic
53#10622292C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622184C2211yescharacteristic
60#10622184C2211yescharacteristic
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622095C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41—21no—
68C22×C8×C11D411yescharacteristic
69C22×C8×C11D411yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#125—21no—
75C11×#124—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×#121—21no—
79C11×#121—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C11×#117—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4326—21no—
87C2×#4325—21no—
88C2×#4324—21no—
89C2×#4323—21no—
90#66983D411yescharacteristic
91#66982—21no—
92C4×C22⋊D11—21no—
93#66977D411yescharacteristic
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4313—21no—
97C2×C8×D11—21no—
98#66929—21no—
99#66928D411yescharacteristic
100C4×D44C2311yescharacteristic
101#66925—21no—
102#66923D411yescharacteristic
103C4×Dic22C2311yescharacteristic
104C11×#103—21no—
105C11×#103—21no—
106C11×#103—21no—
107C11×#103—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×#102—21no—
112C4×C8×C11D411yescharacteristic
113C4×C8×C11D411yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120C22⋊(C11⋊C8)—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123#66879—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126C8×Dic11—21no—
127#66874—21no—
128#66874—21no—
129#66873—21no—
130#66873—21no—
131#66872—21no—
132#66872—21no—
133#66871—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#19366—111nomaximal, Sylow
145C11×#41—42no—
146C11×#41—42no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×C22⋊D11—21no—
159C2×D44C2×D411yescharacteristic
160C2×C4×D11—21no—
161C2×Dic22C2×D411yescharacteristic
162C2×C8×C11—41no—
163C2×C8×C11—41no—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4—41no—
179C42×C11—41no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11—21no—
185#4326—81no—
186#4325—81no—
187#4324—81no—
188#4323—81no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11C2×D411yescharacteristic
194C4⋊Dic11C2×D411yescharacteristic
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199C4×Dic11—21no—
200#4318—81no—
201#4318—81no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208#4313—42no—
209C8×D11—42no—
210#3252—111no—
211#3251—111no—
212#3131D1111yescharacteristic, complemented
213#2966—111no—
214#1704—111no—
215#1703—111no—
216#1702—111no—
217#1701—111no—
218#1680—111no—
219#1679—111no—
220#1678—111no—
221#1677—111no—
222#1566—111no—
223#1559—111no—
224#1557—111no—
225C23×C11—41no—
226C23×C11#12111yescharacteristic
227C22×D11—21no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—81no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—81no—
238D4×C11—82no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—82no—
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C22⋊D11—42no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258D44—21no—
259D44—21no—
260C4×D11—41no—
261C4×D11—41no—
262Dic22—21no—
263Dic22—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274#533C2×D1111yescharacteristic
275#532C2×D1111yescharacteristic
276#529—111no—
277#488—21no—
278#488—21no—
279#487C2×D1111yescharacteristic
280#487C2×D1111yescharacteristic
281#486C2×D1111yescharacteristic
282#486C2×D1111yescharacteristic
283#479—221no—
284#478—221no—
285#477—111no—
286#476—111no—
287#475—111no—
288#474—111no—
289#470—221no—
290#469—221no—
291#468—221no—
292#468—221no—
293#464—221no—
294#463—221no—
295#462—111no—
296#461—111no—
297#460—111no—
298#459—111no—
299#446—111no—
300C8×Q8—111no—
301#436—111no—
302#435—221no—
303C8×D4—111no—
304C8×D4—221no—
305#433—221no—
306#432—111no—
307#423—111no—
308#423—111no—
309#416—21no—
310#416—21no—
311#405—221no—
312C2×C4×C8C2×D1111yescharacteristic
313#334—111no—
314#334—111no—
315#334—111no—
316#334—111no—
317#333—111no—
318#333—111no—
319#332—111no—
320#332—111no—
321#332—111no—
322#332—111no—
323#331—111no—
324#331—111no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11C2×#12111yescharacteristic
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11#57511yescharacteristic
343C4×C11#57511yescharacteristic
344C4×C11#57711yescharacteristic
345C4×C11#57711yescharacteristic
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349C2×#41—21no—
350C2×Q16—221no—
351C2×SD16—221no—
352C2×SD16—221no—
353C2×D8—221no—
354C2×M16—221no—
355C2×M16—221no—
356C2×M16—221no—
357C22×C8—221no—
358C22×C8C22⋊D1111yescharacteristic
359C22×C8C22⋊D1111yescharacteristic
360C4⋊Q8C22×D1111yescharacteristic
361C4⋊Q8C22×D1111yescharacteristic
362C4⋊Q8C22×D1111yescharacteristic
363#127C22×D1111yescharacteristic
364#126—221no—
365#125—21no—
366#125—111no—
367#124—21no—
368#124—111no—
369#123—221no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—111no—
373#121—21no—
374#121—21no—
375#121—111no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—111no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—111no—
382C4×D4—221no—
383#117—21no—
384#117—221no—
385C2×C42C22×D1111yescharacteristic
386#107—221no—
387#107—221no—
388#106—221no—
389#106—221no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—221no—
413#102—221no—
414#102—221no—
415#102—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—221no—
420#97—221no—
421C4×C8—221no—
422C4×C8C22⋊D1111yescharacteristic
423C4×C8C22⋊D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C4×C8C22×D1111yescharacteristic
426C2×C11—41no—
427C2×C11—161no—
428C2×C11#304011yescharacteristic
429C2×C11#306011yescharacteristic
430C2×C11#306711yescharacteristic
431D11—81no—
432#41—42no—
433#41—42no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—111no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—111no—
443C2×D4—221no—
444C22×C4—41no—
445C22×C4—221no—
446C22×C4D4×D1111yescharacteristic
447C22×C4#434111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449Q16—881no—
450SD16—881no—
451SD16—881no—
452D8—881no—
453M16—442no—
454M16—881no—
455M16—881no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—442no—
465C2×C8C2×C22⋊D1111yescharacteristic
466C2×C8C2×C22⋊D1111yescharacteristic
467C2×C8C2×C22⋊D1111yescharacteristic
468C2×C8C2×C22⋊D1111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—111no—
478C4⋊C4—111no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C42—41no—
492C42—221no—
493C42D4×D1111yescharacteristic
494C42#434111yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C42C23×D1111yescharacteristic
497C11#1936611yescharacteristic, complemented, Sylow
498C23—41no—
499C23—221no—
500C23#6699111yescharacteristic
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—221no—
507Q8—221no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—81no—
513D4—82no—
514D4—221no—
515D4—221no—
516D4—442no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4#6699111yescharacteristic
532C2×C4#6699111yescharacteristic
533C2×C4#6699111yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4C2×#434111yescharacteristic
536C2×C4C22×C22⋊D1111yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C8—441no—
546C8—441no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22C2×#6699111yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—441no—
565C4—441no—
566C4—441no—
567C4#1062330111yescharacteristic
568C4#1062330111yescharacteristic
569C4#1062335311yescharacteristic
570C4#1062335311yescharacteristic
571C2—41no—
572C2—161no—
573C2—881no—
574C2#1307810611yescharacteristic
575C2#1307827411yescharacteristic
576C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3131C2
socleC22×C11C2×#121
prime radical#13079972C2
hypercenter#3131D11
hypocenterC11#19366
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #13079983C2semidirect
3. #13077591C2semidirect
4. #13068195C2semidirect
5. #13068188C2semidirect
6. #13068181C2semidirect
7. #13068174C2semidirect
8. #13068043C2semidirect
9. #13068036C2semidirect
10. #13068029C2semidirect
11. #13068022C2semidirect
12. #13067372C2semidirect
13. #13067346C2semidirect
14. #13067338C2semidirect
15. C11×#3131C2semidirect
212. #3131D11semidirect
497. C11#19366semidirect

Maximal subgroups

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

subgroupindex
#130799832
#130799722
#130775912
#130681952
#130681882
#130681812
#130681742
#130680432
#130680362
#130680292
#130680222
#130673722
#130673462
#130673382
C11×#31312
#1936611