Finite Group Databasebeta

← #14743975

Subgroups — #14743975

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081535C211yesmaximal, characteristic
2#13081294C211yesmaximal, characteristic, complemented
3D4×#4326C211yesmaximal, characteristic
4#13068290C211yesmaximal, characteristic, complemented
5#13068119C211yesmaximal, characteristic, complemented
6#13068069C211yesmaximal, characteristic
7#13068010C211yesmaximal, characteristic, complemented
8#13067984C211yesmaximal, characteristic, complemented
9#13067865C211yesmaximal, characteristic
10#13067857C211yesmaximal, characteristic, complemented
11#13067837C211yesmaximal, characteristic, complemented
12#13067780C211yesmaximal, characteristic
13#13067466C211yesmaximal, characteristic, complemented
14SD16⋊(C11⋊C8)C211yesmaximal, characteristic
15Q8×C11×SD16C211yesmaximal, characteristic
16Q82×C11C2211yescharacteristic
17D4×Q8×C11C2211yescharacteristic
18C22×#4326—21no—
19#10623101C2211yescharacteristic
20D4×Dic22C2211yescharacteristic
21C11×#498—21no—
22C11×#498C2211yescharacteristic
23C11×#476—21no—
24C11×#476C2211yescharacteristic
25C11×#475—21no—
26C11×#475C2211yescharacteristic
27C8×Q8×C11C2211yescharacteristic
28C4×C11×SD16—21no—
29C4×C11×SD16C2211yescharacteristic
30#10622841—21no—
31#10622777—21no—
32#10622706—21no—
33#10622706C2211yescharacteristic
34#10622705C2211yescharacteristic
35#10622704—21no—
36#10622704C2211yescharacteristic
37#10622703C2211yescharacteristic
38#10622694C2211yescharacteristic
39#10622691C2211yescharacteristic
40#10622664—21no—
41#10622663—21no—
42#10622644—21no—
43#10622644C2211yescharacteristic
44#10622644C2211yescharacteristic
45C4×#4326—21no—
46C4×#4326C2211yescharacteristic
47Q8×C11⋊C8C2211yescharacteristic
48#10622633C2211yescharacteristic
49D4×C11⋊C8C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622469—21no—
52#10622407—21no—
53#10622379—21no—
54#10622295C2211yescharacteristic
55#10622292C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59Q8⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622124C2211yescharacteristic
62#10622124C2211yescharacteristic
63#10622122C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622096C2211yescharacteristic
66#10622093C2211yescharacteristic
67C22×Q8×C11—21no—
68C22×Dic22—21no—
69C2×C11×SD16D411yescharacteristic
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—41no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—41no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11C2311yescharacteristic
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84Q8×Dic11—21no—
85C2×#4326—21no—
86C2×#4326—21no—
87C2×#4326—21no—
88C2×#4326—21no—
89C2×#4326—21no—
90C2×#4326—44no—
91C2×#4326D411yescharacteristic
92D4×Dic11—21no—
93#66977—21no—
94C22×C11⋊C8—21no—
95#66943—21no—
96#66943—41no—
97#66941—21no—
98#66931—41no—
99#66922—21no—
100#66922C2311yescharacteristic
101#66922C2311yescharacteristic
102C4×Dic22—21no—
103C4×Dic22C2311yescharacteristic
104C11×#106—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106D411yescharacteristic
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#103D411yescharacteristic
113C11×#102—21no—
114C11×#102D411yescharacteristic
115C4×C8×C11—21no—
116C4×C8×C11C2311yescharacteristic
117#66899—21no—
118#66899—21no—
119#66899—41no—
120#66899D411yescharacteristic
121#66896—21no—
122C22⋊(C11⋊C8)—21no—
123#66882—21no—
124#66882—21no—
125#66879—21no—
126Dic11⋊C8—21no—
127#66874—21no—
128#66874—21no—
129#66874—21no—
130#66874—21no—
131#66874—21no—
132#66874D411yescharacteristic
133#66872—21no—
134#66871—21no—
135#66871—21no—
136#66871—41no—
137#66871D411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19812—111nomaximal, Sylow
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—41no—
149C2×Q8×C11—41no—
150C2×Q8×C11—42no—
151C2×Q8×C11—81no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—41no—
157C22×Dic11—41no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—41no—
161C2×Dic22—42no—
162C2×Dic22—81no—
163C2×Dic22C2×D411yescharacteristic
164C11×SD16Q1614yescomplemented
165C2×C8×C11—21no—
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×C4⋊C4—41no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—41no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—41no—
185C42×C11C2411yescharacteristic
186C22⋊Dic11—41no—
187#4326—22no—
188#4326—42no—
189#4326—42no—
190#4326—42no—
191#4326—42no—
192#4326—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—41no—
198C4⋊Dic11—41no—
199C4⋊Dic11C2×D411yescharacteristic
200Dic11⋊C4—21no—
201Dic11⋊C4—41no—
202Dic11⋊C4—41no—
203C4×Dic11—21no—
204C4×Dic11—41no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—42no—
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#3386—111no—
213Q8×SD16D1111yescharacteristic
214#3363—111no—
215D4×Q16—111no—
216#1723—111no—
217#1692—111no—
218#1683—111no—
219#1674—111no—
220#1670—111no—
221#1649—111no—
222#1648—111no—
223#1645—111no—
224#1637—111no—
225#1584—111no—
226SD16⋊C8—111no—
227C23×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—82no—
233Q8×C11—81no—
234Q8×C11—161no—
235Q8×C11C2×Q1612yescomplemented
236Q8×C11AGL(1,ℤ/8)12yes—
237D4×C11—21no—
238D4×C11C2×Q1612yes—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—82no—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—82no—
257Dic22—21no—
258Dic22—21no—
259Dic22—41no—
260Dic22—41no—
261Dic22—41no—
262Dic22—41no—
263Dic22—82no—
264C8×C11—21no—
265C8×C11—41no—
266C8×C11C2×Q1612yescomplemented
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C22×Q16—221no—
274Q82C2×D1111yescharacteristic
275#557—111no—
276D4×Q8—111no—
277D4×Q8C2×D1111yescharacteristic
278#501—221no—
279#500—111no—
280#500—111no—
281#498—21no—
282#498C2×D1111yescharacteristic
283#494—111no—
284#487—111no—
285#487—111no—
286#487—221no—
287#478—221no—
288#477—111no—
289#477—221no—
290#477—221no—
291#476—21no—
292#476C2×D1111yescharacteristic
293#475—21no—
294#475—111no—
295#475C2×D1111yescharacteristic
296#474—111no—
297#467—221no—
298#462—111no—
299#462—111no—
300#462—111no—
301#462—221no—
302#451—221no—
303#451—221no—
304#446—111no—
305C8×Q8—111no—
306C8×Q8C2×D1111yescharacteristic
307#440—221no—
308C4×Q16—111no—
309C4×Q16—221no—
310C4×SD16—21no—
311C4×SD16C2×D1111yescharacteristic
312C8×D4—111no—
313#335—111no—
314#335—111no—
315#333—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322D4⋊C8—111no—
323#322—111no—
324C22×C11—22no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11D4211yescharacteristic
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—21no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11C22×Q1611yescharacteristic
337C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
338C4×C11#57711yescharacteristic
339C4×C11#57811yescharacteristic
340Dic11—41no—
341Dic11—41no—
342Dic11—81no—
343Dic11—81no—
344C22×Q8—21no—
345C22×Q8—221no—
346C2×Q16—111no—
347C2×Q16—221no—
348C2×Q16—221no—
349C2×Q16—221no—
350C2×Q16—221no—
351C2×Q16—221no—
352C2×Q16—444no—
353C2×SD16C22⋊D1111yescharacteristic
354C22×C8—221no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—41no—
359C4⋊Q8—111no—
360C4⋊Q8—111no—
361C4⋊Q8—221no—
362C4⋊Q8—221no—
363C4⋊Q8C22×D1111yescharacteristic
364C4⋊Q8C22×D1111yescharacteristic
365#125—221no—
366#125—441no—
367C22⋊Q8—21no—
368C22⋊Q8—41no—
369C22⋊Q8—221no—
370C22⋊Q8—441no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—111no—
374C4×Q8—221no—
375C4×Q8—221no—
376C4×Q8C22×D1111yescharacteristic
377C4×Q8C22×D1111yescharacteristic
378C4×D4—21no—
379C4×D4—221no—
380C4×D4C22×D1111yescharacteristic
381#107—111no—
382#107—221no—
383#107—221no—
384#107—221no—
385#107—221no—
386#107—441no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—221no—
392#106C22⋊D1111yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8C22×D1111yescharacteristic
400#103—21no—
401#103—111no—
402#103—111no—
403#103—221no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—441no—
411#103C22⋊D1111yescharacteristic
412#102—21no—
413#102—221no—
414#102C22⋊D1111yescharacteristic
415C22⋊C8—221no—
416#97—221no—
417C4×C8—21no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—221no—
421C4×C8C22×D1111yescharacteristic
422C2×C11—42no—
423C2×C11#326511yescharacteristic
424C2×C11D4×Q1611yescharacteristic
425C2×C11#328911yescharacteristic
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—42no—
431C2×Q8—81no—
432C2×Q8—111no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—441no—
436C2×Q8—442no—
437C2×Q8—881no—
438C2×Q8D4×D1111yescharacteristic
439C2×Q8C2×C22⋊D1111yescharacteristic
440C2×D4C2×C22⋊D1111yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—441no—
444Q16—222no—
445Q16—442no—
446Q16—442no—
447Q16—442no—
448Q16—442no—
449Q16—881no—
450SD16#432614yescomplemented
451C2×C8—21no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—442no—
459C2×C8C2×C22⋊D1111yescharacteristic
460C2×C8C2×C22⋊D1111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—111no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—441no—
477C4⋊C4—441no—
478C4⋊C4—441no—
479C4⋊C4—441no—
480C4⋊C4D4×D1111yescharacteristic
481C4⋊C4C2×C22⋊D1111yescharacteristic
482C4⋊C4C2×C22⋊D1111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—441no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42—221no—
490C42—441no—
491C42C23×D1111yescharacteristic
492C11#1981211yescharacteristic, complemented, Sylow
493C23—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—82no—
499Q8—81no—
500Q8—161no—
501Q8—221no—
502Q8—221no—
503Q8—441no—
504Q8—441no—
505Q8—441no—
506Q8—441no—
507Q8—882no—
508Q8#6696712yes—
509Q8C2×#432612yescomplemented
510D4—21no—
511D4C2×#432612yes—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—882no—
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4#6703711yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C8—21no—
531C8—41no—
532C8—221no—
533C8—221no—
534C8—441no—
535C8—441no—
536C8—441no—
537C8—441no—
538C8C2×#432612yescomplemented
539C22—22no—
540C22—41no—
541C22—41no—
542C22D4×C22⋊D1111yescharacteristic
543C4—22no—
544C4—22no—
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—441no—
552C4—441no—
553C4—881no—
554C4—881no—
555C4C2×#6696711yescharacteristic
556C4#1062329311yescharacteristic
557C4C22×#432611yescharacteristic
558C4#1062336911yescharacteristic
559C2—42no—
560C2#1308011111yescharacteristic
561C2D4×#432611yescharacteristic
562C2#1308038911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingQ8×C11×SD16C2
socleC22×C11D42
prime radicalC2×D4×C11C2×D4
hypercenterQ8×SD16D11
hypocenterC11#19812
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ Q8×SD16

Complements

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

NH ≅ G/Ntype
2. #13081294C2semidirect
4. #13068290C2semidirect
5. #13068119C2semidirect
7. #13068010C2semidirect
8. #13067984C2semidirect
10. #13067857C2semidirect
11. #13067837C2semidirect
13. #13067466C2semidirect
164. C11×SD16Q16semidirect
235. Q8×C11C2×Q16semidirect
266. C8×C11C2×Q16semidirect
450. SD16#4326semidirect
492. C11#19812semidirect
509. Q8C2×#4326semidirect
538. C8C2×#4326semidirect

Maximal subgroups

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

subgroupindex
#130815352
#130812942
D4×#43262
#130682902
#130681192
#130680692
#130680102
#130679842
#130678652
#130678572
#130678372
#130677802
#130674662
SD16⋊(C11⋊C8)2
Q8×C11×SD162
#1981211