Finite Group Databasebeta

← #14738751

Subgroups — #14738751

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080007C211yesmaximal, characteristic, complemented
2#13079330C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13068182C211yesmaximal, characteristic, complemented
5#13068172C211yesmaximal, characteristic, complemented
6#13068132C211yesmaximal, characteristic, complemented
7#13068086C211yesmaximal, characteristic, complemented
8#13068058C211yesmaximal, characteristic, complemented
9#13068048C211yesmaximal, characteristic, complemented
10#13068008C211yesmaximal, characteristic, complemented
11#13067962C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067317C211yesmaximal, characteristic, complemented
14#13067293C211yesmaximal, characteristic
15C11×#3216C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#497—21no—
20C11×#489—21no—
21C11×#462C2211yescharacteristic
22C11×#462C2211yescharacteristic
23C11×#460C2211yescharacteristic
24C11×#460C2211yescharacteristic
25C11×#452—21no—
26C11×#452—21no—
27C11×#432C2211yescharacteristic
28#10622707—21no—
29#10622706C2211yescharacteristic
30#10622703—21no—
31#10622691C2211yescharacteristic
32#10622689C2211yescharacteristic
33#10622683C2211yescharacteristic
34#10622665—21no—
35#10622665—21no—
36#10622655—21no—
37#10622655—21no—
38#10622644C2211yescharacteristic
39#10622644C2211yescharacteristic
40#10622637—21no—
41#10622637—21no—
42#10622637C2211yescharacteristic
43#10622637C2211yescharacteristic
44Q8×C11⋊C8C2211yescharacteristic
45Q8×C11⋊C8C2211yescharacteristic
46#10622633C2211yescharacteristic
47#10622633C2211yescharacteristic
48#10622631—21no—
49#10622631—21no—
50#10622612—21no—
51#10622610—21no—
52#10622537C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C11×C4⋊Q8D411yescharacteristic
73C11×C4⋊Q8D411yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#127C2311yescharacteristic
76C11×#125—21no—
77C11×#124—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×C22⋊Q8D411yescharacteristic
81C11×#121—21no—
82C11×#121—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11C2311yescharacteristic
85C4×Q8×C11C2311yescharacteristic
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4326—21no—
91C2×#4326—21no—
92C2×#4324—21no—
93C2×#4324—21no—
94#66979—21no—
95#66977—21no—
96#66977—21no—
97C2×#4318—21no—
98C2×#4318D411yescharacteristic
99C2×#4318D411yescharacteristic
100C22×C11⋊C8—21no—
101#66923—21no—
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104C4×Dic22—21no—
105C4×Dic22—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#103—21no—
109C11×#103—21no—
110C11×#102—21no—
111C11×#102—21no—
112C11×C22⋊C8—21no—
113C11×#97—21no—
114#66899—21no—
115#66899—21no—
116#66896—21no—
117#66896—21no—
118#66874—21no—
119#66874—21no—
120#66874—21no—
121#66874—21no—
122#66872—21no—
123#66872—21no—
124#66871—21no—
125#66871—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—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—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19372—111nomaximal, Sylow
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C2×Dic22—21no—
160C2×Dic22—21no—
161C11×Q16—81no—
162C11×Q16—81no—
163C11×SD16—81no—
164C11×SD16—81no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C11×C4⋊C4—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⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—41no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189#4326—81no—
190#4326—81no—
191#4324—42no—
192#4324—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197Dic11⋊C4—41no—
198Dic11⋊C4—41no—
199C4×Dic11—41no—
200#4318—22no—
201#4318—41no—
202#4318—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—42no—
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#3255—111no—
213#3216D1111yescharacteristic
214#3182—111no—
215#2962—111no—
216#1702—111no—
217#1700—111no—
218#1694—111no—
219#1686—111no—
220#1682—111no—
221#1680—111no—
222#1674—111no—
223#1666—111no—
224#1569—111no—
225#1552—111no—
226#1547—111no—
227C23×C11—41no—
228C23×C11#12111yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—81no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—81no—
241D4×C11—82no—
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—21no—
249C2×C4×C11—21no—
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—41no—
264Dic22—41no—
265C8×C11—41no—
266C8×C11—41no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8#13712yes—
275#533—111no—
276#533C2×D1111yescharacteristic
277#532C2×D1111yescharacteristic
278#500—111no—
279#497—21no—
280#492—111no—
281#489—21no—
282#487—111no—
283#486—111no—
284#475—111no—
285#475—111no—
286#475—221no—
287#470—221no—
288#470—221no—
289#468—221no—
290#468—221no—
291#462—111no—
292#462—111no—
293#462—221no—
294#462C2×D1111yescharacteristic
295#462C2×D1111yescharacteristic
296#460C2×D1111yescharacteristic
297#460C2×D1111yescharacteristic
298#452—21no—
299#452—21no—
300#446—111no—
301#446—111no—
302#446—221no—
303#446—221no—
304C8×Q8—111no—
305C8×Q8—111no—
306#440—221no—
307#440—221no—
308#432C2×D1111yescharacteristic
309#424—221no—
310#423—111no—
311C2×C4⋊C8—111no—
312#405—221no—
313C4×M16—111no—
314#335—111no—
315#335—111no—
316#334—111no—
317#334—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321#332—111no—
322#332—111no—
323#332—111no—
324#331—111no—
325#331—111no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11C2×#12111yescharacteristic
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11C2×#13711yescharacteristic
343C4×C11#57511yescharacteristic
344C4×C11#57611yescharacteristic
345C4×C11#57711yescharacteristic
346Dic11—81no—
347Dic11—81no—
348C2×#41—21no—
349C2×Q16—21no—
350C2×Q16—21no—
351C2×Q16—221no—
352C2×Q16—221no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—221no—
356C2×SD16—221no—
357C2×M16—111no—
358C2×M16—111no—
359C2×M16—221no—
360C22×C8—221no—
361C4⋊Q8—111no—
362C4⋊Q8—111no—
363C4⋊Q8C22⋊D1111yescharacteristic
364C4⋊Q8C22⋊D1111yescharacteristic
365C4⋊Q8C22×D1111yescharacteristic
366#127C22×D1111yescharacteristic
367#125—21no—
368#125—221no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—221no—
372C22⋊Q8—221no—
373C22⋊Q8C22⋊D1111yescharacteristic
374C22⋊Q8C22⋊D1111yescharacteristic
375#121—21no—
376#121—21no—
377C4×Q8—21no—
378C4×Q8—221no—
379C4×Q8—221no—
380C4×Q8C22×D1111yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384#117—21no—
385#117—221no—
386C2×C42C22×D1111yescharacteristic
387#107—221no—
388#107—221no—
389#106—221no—
390#106—221no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400C4⋊C8—221no—
401C4⋊C8C22×D1111yescharacteristic
402C4⋊C8C22×D1111yescharacteristic
403#103—21no—
404#103—21no—
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#102—21no—
412#102—21no—
413#102—221no—
414#102—221no—
415C22⋊C8—21no—
416#97—21no—
417#97—111no—
418#97—111no—
419#97—221no—
420#97—221no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8—221no—
425C2×C11—41no—
426C2×C11—161no—
427C2×C11#303711yescharacteristic
428C2×C11#306211yescharacteristic
429C2×C11#306911yescharacteristic
430#41—81no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8C2×C22⋊D1111yescharacteristic
437C2×Q8C2×C22⋊D1111yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C22×C4—41no—
443C22×C4D4×D1111yescharacteristic
444C22×C4#434111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446Q16—81no—
447Q16—81no—
448Q16—881no—
449Q16—881no—
450SD16—81no—
451SD16—81no—
452SD16—442no—
453SD16—442no—
454M16—222no—
455M16—441no—
456M16—881no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—442no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C4⋊C4C2×C22⋊D1111yescharacteristic
484C4⋊C4C2×C22⋊D1111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—441no—
490C42—21no—
491C42—21no—
492C42—441no—
493C42D4×D1111yescharacteristic
494C42#434111yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C42C23×D1111yescharacteristic
497C11#1937211yescharacteristic, complemented, Sylow
498C23—41no—
499C23#6699211yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—441no—
508Q8—441no—
509Q8—441no—
510Q8—441no—
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—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4#6699211yescharacteristic
531C2×C4#6699211yescharacteristic
532C2×C4#6699211yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4C2×#434111yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C8—41no—
537C8—41no—
538C8—112no—
539C8—221no—
540C8—221no—
541C8—221no—
542C8—441no—
543C8—441no—
544C8—441no—
545C8—441no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22C2×#6699211yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—881no—
563C4—881no—
564C4D11×#13711yescharacteristic
565C4#1062330811yescharacteristic
566C4#1062336611yescharacteristic
567C4#1062336711yescharacteristic
568C2—41no—
569C2—161no—
570C2#1307808511yescharacteristic
571C2#1307829211yescharacteristic
572C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3216C2
socleC22×C11C2×#121
prime radicalC11×#532C22
hypercenter#3216D11
hypocenterC11#19372
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3216

Complements

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

NH ≅ G/Ntype
1. #13080007C2semidirect
3. #13077565C2semidirect
4. #13068182C2semidirect
5. #13068172C2semidirect
6. #13068132C2semidirect
7. #13068086C2semidirect
8. #13068058C2semidirect
9. #13068048C2semidirect
10. #13068008C2semidirect
11. #13067962C2semidirect
12. #13067384C2semidirect
13. #13067317C2semidirect
497. C11#19372semidirect

Maximal subgroups

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

subgroupindex
#130800072
#130793302
#130775652
#130681822
#130681722
#130681322
#130680862
#130680582
#130680482
#130680082
#130679622
#130673842
#130673172
#130672932
C11×#32162
#1937211