Finite Group Databasebeta

← #14737179

Subgroups — #14737179

Order 2816.

596 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#13079791C211yesmaximal, characteristic, complemented
2#13079171C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068120C211yesmaximal, characteristic, complemented
5#13068113C211yesmaximal, characteristic, complemented
6#13068086C211yesmaximal, characteristic, complemented
7#13068079C211yesmaximal, characteristic, complemented
8#13068048C211yesmaximal, characteristic, complemented
9#13068041C211yesmaximal, characteristic, complemented
10#13068030C211yesmaximal, characteristic, complemented
11#13068023C211yesmaximal, characteristic, complemented
12#13067362C211yesmaximal, characteristic, complemented
13#13067324C211yesmaximal, characteristic, complemented
14#13067321C211yesmaximal, characteristic, complemented
15C11×#3212C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#495—21no—
20C11×#488—21no—
21C11×#462C2211yescharacteristic
22C11×#461C2211yescharacteristic
23C11×#460C2211yescharacteristic
24C11×#459C2211yescharacteristic
25C11×#452—21no—
26C11×#449—21no—
27C11×#431C2211yescharacteristic
28#10622706C2211yescharacteristic
29#10622692C2211yescharacteristic
30#10622689C2211yescharacteristic
31#10622683C2211yescharacteristic
32#10622677—21no—
33#10622669—21no—
34#10622658—21no—
35#10622654—21no—
36#10622654—21no—
37#10622648—21no—
38#10622637C2211yescharacteristic
39Q8×C11⋊C8C2211yescharacteristic
40#10622634C2211yescharacteristic
41#10622633C2211yescharacteristic
42C4×#4324—21no—
43C4×#4324—21no—
44#10622625C2211yescharacteristic
45#10622624—21no—
46D4×C11⋊C8—21no—
47D4×C11⋊C8C2211yescharacteristic
48#10622621C2211yescharacteristic
49#10622620C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53#10622538C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×Q16—21no—
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×D8—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#126—21no—
75C11×#125D411yescharacteristic
76C11×#124—21no—
77C11×#124D411yescharacteristic
78C11×#123—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×#121—21no—
81C11×#121—21no—
82C11×#121D411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4324—21no—
91C2×#4324—21no—
92#66979—21no—
93#66977—21no—
94#66977—21no—
95C2×#4318—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8D411yescharacteristic
98C22×C11⋊C8D411yescharacteristic
99#66923—21no—
100#66922C2311yescharacteristic
101#66922C2311yescharacteristic
102C4×Dic22—21no—
103C4×Dic22—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103—21no—
107C11×#103—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×C22⋊C8—21no—
111C4×C8×C11—21no—
112#66899—21no—
113#66899—21no—
114#66896—21no—
115#66896—21no—
116#66896—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66874—21no—
123#66874—21no—
124#66872—21no—
125#66872—21no—
126#66872—21no—
127#66872—21no—
128#66871—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19224—111nomaximal, Sylow
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—41no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C11×Q16—81no—
163C11×SD16—81no—
164C11×SD16—81no—
165C11×D8—81no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
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⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C42×C11—21no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189#4324—42no—
190#4324—42no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195Dic11⋊C4—41no—
196Dic11⋊C4—41no—
197C4×Dic11—41no—
198#4318—42no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—41no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3233—111no—
211#3212D1111yescharacteristic
212#3167—111no—
213#2966—111no—
214#1692—111no—
215#1691—111no—
216#1686—111no—
217#1685—111no—
218#1680—111no—
219#1679—111no—
220#1678—111no—
221#1677—111no—
222#1564—111no—
223#1554—111no—
224#1553—111no—
225C23×C11—21no—
226C23×C11—41no—
227C23×C11#12111yescharacteristic
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—41no—
231Q8×C11—41no—
232D4×C11—21no—
233D4×C11—21no—
234D4×C11—42no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—81no—
240D4×C11—82no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—82no—
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×Dic11—41no—
260C2×Dic11—41no—
261Dic22—41no—
262Dic22—41no—
263Dic22—81no—
264C8×C11—41no—
265C8×C11—41no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8#13512yes—
274#533—111no—
275#532C2×D1111yescharacteristic
276#529C2×D1111yescharacteristic
277#499—221no—
278#498—111no—
279#495—21no—
280#492—111no—
281#488—21no—
282#488—221no—
283#487—111no—
284#486—111no—
285#485—221no—
286#482—221no—
287#477—111no—
288#476—111no—
289#475—111no—
290#474—111no—
291#465—221no—
292#465—221no—
293#462C2×D1111yescharacteristic
294#461C2×D1111yescharacteristic
295#460C2×D1111yescharacteristic
296#459C2×D1111yescharacteristic
297#452—21no—
298#449—21no—
299#446—111no—
300C8×Q8—111no—
301C4×SD16—221no—
302C4×SD16—221no—
303#436—111no—
304#435—221no—
305C8×D4—111no—
306C8×D4—221no—
307#433—221no—
308#432—111no—
309#431—111no—
310#431C2×D1111yescharacteristic
311#405—221no—
312C2×C4×C8—111no—
313#335—111no—
314#335—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—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11C2×#12111yescharacteristic
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—81no—
343C4×C11C2×#13511yescharacteristic
344C4×C11#57511yescharacteristic
345C4×C11#57711yescharacteristic
346C4×C11#57711yescharacteristic
347Dic11—81no—
348Dic11—81no—
349C2×#41—21no—
350C2×Q16—21no—
351C2×SD16—21no—
352C2×SD16—21no—
353C2×SD16—221no—
354C2×SD16—221no—
355C2×D8—21no—
356C2×M16—221no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—221no—
360C4⋊Q8—111no—
361C4⋊Q8—111no—
362C4⋊Q8C22×D1111yescharacteristic
363#127C22×D1111yescharacteristic
364#126—21no—
365#125—221no—
366#125C22⋊D1111yescharacteristic
367#124—21no—
368#124C22⋊D1111yescharacteristic
369#123—21no—
370C22⋊Q8—221no—
371C22⋊Q8—221no—
372C22⋊Q8C22⋊D1111yescharacteristic
373#121—21no—
374#121—21no—
375#121C22⋊D1111yescharacteristic
376C4×Q8—221no—
377C4×Q8—221no—
378C4×Q8C22×D1111yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C22×D1111yescharacteristic
383#117—21no—
384#117—221no—
385C2×C42C22×D1111yescharacteristic
386#107—221no—
387#107—221no—
388#106—221no—
389#106—221no—
390#106—221no—
391#106—221no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8C22×D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400#103—21no—
401#103—21no—
402#103—221no—
403#103—221no—
404#103—221no—
405#103—221no—
406#102—21no—
407#102—21no—
408#102—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412C22⋊C8—21no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417#97—221no—
418#97—221no—
419C4×C8—21no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—221no—
425C4×C8—221no—
426C2×C11—41no—
427C2×C11—81no—
428C2×C11—161no—
429C2×C11#303511yescharacteristic
430C2×C11#305711yescharacteristic
431C2×C11#306711yescharacteristic
432#41—81no—
433#41—81no—
434C2×Q8—21no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8C2×C22⋊D1111yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4C2×C22⋊D1111yescharacteristic
444C22×C4—21no—
445C22×C4—41no—
446C22×C4D4×D1111yescharacteristic
447C22×C4#434111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449Q16—81no—
450SD16—81no—
451SD16—81no—
452SD16—442no—
453SD16—442no—
454D8—81no—
455M16—442no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—222no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—441no—
468C2×C8—442no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—441no—
480C4⋊C4—441no—
481C4⋊C4C2×C22⋊D1111yescharacteristic
482C4⋊C4C2×C22⋊D1111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—441no—
491C42—21no—
492C42—441no—
493C42D4×D1111yescharacteristic
494C42#434111yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C42C23×D1111yescharacteristic
497C11#1922411yescharacteristic, complemented, Sylow
498C23—21no—
499C23—41no—
500C23#6699211yescharacteristic
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—441no—
506Q8—441no—
507Q8—881no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—82no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4#6699211yescharacteristic
532C2×C4#6699211yescharacteristic
533C2×C4#6699211yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4C2×#434111yescharacteristic
536C2×C4C22×C22⋊D1111yescharacteristic
537C8—41no—
538C8—41no—
539C8—112no—
540C8—221no—
541C8—221no—
542C8—221no—
543C8—441no—
544C8—441no—
545C8—441no—
546C8—441no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22C2×#6699211yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—881no—
566C4—881no—
567C4D11×#13511yescharacteristic
568C4#1062329911yescharacteristic
569C4#1062336711yescharacteristic
570C4#1062336711yescharacteristic
571C2—41no—
572C2—81no—
573C2—161no—
574C2#1307806711yescharacteristic
575C2#1307825211yescharacteristic
576C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3212C2
socleC22×C11C2×#121
hypercenter#3212D11
hypocenterC11#19224
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3212

Complements

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

NH ≅ G/Ntype
1. #13079791C2semidirect
2. #13079171C2semidirect
3. #13077592C2semidirect
4. #13068120C2semidirect
5. #13068113C2semidirect
6. #13068086C2semidirect
7. #13068079C2semidirect
8. #13068048C2semidirect
9. #13068041C2semidirect
10. #13068030C2semidirect
11. #13068023C2semidirect
12. #13067362C2semidirect
13. #13067324C2semidirect
14. #13067321C2semidirect
497. C11#19224semidirect

Maximal subgroups

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

subgroupindex
#130797912
#130791712
#130775922
#130681202
#130681132
#130680862
#130680792
#130680482
#130680412
#130680302
#130680232
#130673622
#130673242
#130673212
C11×#32122
#1922411