Finite Group Databasebeta

← #14745650

Subgroups — #14745650

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081535C211yesmaximal, characteristic
2#13081294C211yesmaximal, characteristic, complemented
3#13080486C211yesmaximal, characteristic
4#13068225C211yesmaximal, characteristic, complemented
5#13068141C211yesmaximal, characteristic, complemented
6#13068134C211yesmaximal, characteristic, complemented
7#13068076C211yesmaximal, characteristic, complemented
8#13068069C211yesmaximal, characteristic
9#13067837C211yesmaximal, characteristic, complemented
10#13067830C211yesmaximal, characteristic
11#13067780C211yesmaximal, characteristic
12#13067773C211yesmaximal, characteristic, complemented
13#13067511C211yesmaximal, characteristic, complemented
14SD16×C11⋊C8C211yesmaximal, characteristic
15C11×#3385C211yesmaximal, characteristic
16Q82×C11C2211yescharacteristic
17C11×#554C2211yescharacteristic
18#10623101C2211yescharacteristic
19D4×Dic22C2211yescharacteristic
20C11×#501—21no—
21C11×#500C2211yescharacteristic
22C11×#479—21no—
23C11×#477C2211yescharacteristic
24C11×#476C2211yescharacteristic
25C11×#474—21no—
26C11×#446C2211yescharacteristic
27C11×#440—21no—
28C4×C11×SD16C2211yescharacteristic
29#10622777—21no—
30#10622706—21no—
31#10622706C2211yescharacteristic
32#10622706C2211yescharacteristic
33#10622704—21no—
34#10622704C2211yescharacteristic
35#10622704C2211yescharacteristic
36#10622694C2211yescharacteristic
37#10622694C2211yescharacteristic
38#10622664—21no—
39#10622663—21no—
40#10622644—21no—
41#10622644C2211yescharacteristic
42#10622644C2211yescharacteristic
43C4×#4326—21no—
44C4×#4326C2211yescharacteristic
45Q8×C11⋊C8C2211yescharacteristic
46#10622633C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622583—21no—
50C2×#66874—21no—
51#10622469—21no—
52#10622407—21no—
53#10622379—21no—
54#10622295C2211yescharacteristic
55#10622292C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622184C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59Q8⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622124C2211yescharacteristic
62#10622124C2211yescharacteristic
63#10622122C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622095C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Dic22—21no—
68C2×C11×SD16D411yescharacteristic
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—41no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#125—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—41no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11C2311yescharacteristic
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11C2311yescharacteristic
83C2×C11×C4⋊C4—21no—
84Q8×Dic11—21no—
85C2×#4326—21no—
86C2×#4326—21no—
87C2×#4326D411yescharacteristic
88D4×Dic11—21no—
89#66977—21no—
90C22×C11⋊C8—21no—
91#66943—21no—
92#66943—41no—
93#66941—21no—
94#66931—41no—
95#66922—21no—
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98C4×Dic22—21no—
99C4×Dic22C2311yescharacteristic
100C11×#107—21no—
101C11×#107—21no—
102C11×#107—21no—
103C11×#106—21no—
104C11×#106D411yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×#103—21no—
108C11×#103D411yescharacteristic
109C11×#102—21no—
110C11×#102D411yescharacteristic
111C11×#97—21no—
112C4×C8×C11C2311yescharacteristic
113#66899—21no—
114#66899—41no—
115#66899—41no—
116#66899D411yescharacteristic
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119#66882—21no—
120#66882—21no—
121#66879—21no—
122Dic11⋊C8—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66874—21no—
127#66874—21no—
128#66874—21no—
129#66874—21no—
130#66874—21no—
131#66874D411yescharacteristic
132#66872—21no—
133#66871—21no—
134#66871—21no—
135#66871—21no—
136#66871D411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19929—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—41no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11C2×D411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—41no—
153C22×Dic11—41no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—41no—
157C2×Dic22—42no—
158C2×Dic22—81no—
159C2×Dic22C2×D411yescharacteristic
160C11×SD16Q1614yescomplemented
161C2×C8×C11—21no—
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—41no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—41no—
182C42×C11C2411yescharacteristic
183C22⋊Dic11—41no—
184#4326—41no—
185#4326—42no—
186#4326—81no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—41no—
192C4⋊Dic11—41no—
193C4⋊Dic11C2×D411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—41no—
196Dic11⋊C4—41no—
197C4×Dic11—21no—
198C4×Dic11—41no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206#3386—111no—
207#3385D1111yescharacteristic
208#3363—111no—
209#3299—111no—
210#1710—111no—
211#1696—111no—
212#1694—111no—
213#1684—111no—
214#1683—111no—
215#1645—111no—
216#1644—111no—
217#1637—111no—
218#1636—111no—
219#1591—111no—
220C8×SD16—111no—
221C23×C11—21no—
222Q8×C11—21no—
223Q8×C11—21no—
224Q8×C11—21no—
225Q8×C11—81no—
226Q8×C11—81no—
227Q8×C11—161no—
228Q8×C11C2×Q1612yes—
229D4×C11—21no—
230D4×C11C2×Q1612yes—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—161no—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—82no—
249Dic22—21no—
250Dic22—21no—
251Dic22—41no—
252Dic22—41no—
253Dic22—41no—
254Dic22—41no—
255Dic22—82no—
256C8×C11—21no—
257C8×C11—41no—
258C8×C11C2×Q1612yes—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265Q82C2×D1111yescharacteristic
266#557—111no—
267#554C2×D1111yescharacteristic
268D4×Q8—111no—
269#501—21no—
270#501—221no—
271#500—111no—
272#500C2×D1111yescharacteristic
273#487—111no—
274#487—111no—
275#487—111no—
276#487—111no—
277#487—221no—
278#484—221no—
279#479—21no—
280#478—221no—
281#477—111no—
282#477—111no—
283#477—221no—
284#477—221no—
285#477C2×D1111yescharacteristic
286#476C2×D1111yescharacteristic
287#475—111no—
288#474—21no—
289#474—111no—
290#467—221no—
291#462—111no—
292#462—111no—
293#462—221no—
294#451—221no—
295#446—111no—
296#446C2×D1111yescharacteristic
297C8×Q8—111no—
298#440—21no—
299#440—221no—
300C4×Q16—111no—
301C4×Q16—221no—
302C4×SD16C2×D1111yescharacteristic
303C8×D4—111no—
304C2×#103—221no—
305#335—111no—
306#334—111no—
307#333—111no—
308#333—111no—
309#332—111no—
310#332—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314D4⋊C8—111no—
315C82—111no—
316C22×C11—22no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11D4211yescharacteristic
320C4×C11—22no—
321C4×C11—21no—
322C4×C11—41no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—81no—
327C4×C11—81no—
328C4×C11C22×Q1611yescharacteristic
329C4×C11#57511yescharacteristic
330C4×C11#57711yescharacteristic
331C4×C11#57811yescharacteristic
332Dic11—41no—
333Dic11—41no—
334Dic11—81no—
335Dic11—81no—
336C22×Q8—221no—
337C2×Q16—111no—
338C2×Q16—221no—
339C2×Q16—221no—
340C2×SD16C22⋊D1111yescharacteristic
341C22×C8—221no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—41no—
345C4⋊Q8—111no—
346C4⋊Q8—111no—
347C4⋊Q8—221no—
348C4⋊Q8—221no—
349C4⋊Q8C22×D1111yescharacteristic
350C4⋊Q8C22×D1111yescharacteristic
351#125—21no—
352#125—221no—
353#125—441no—
354C22⋊Q8—21no—
355C22⋊Q8—41no—
356C22⋊Q8—221no—
357C22⋊Q8—441no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—111no—
361C4×Q8—221no—
362C4×Q8—221no—
363C4×Q8C22×D1111yescharacteristic
364C4×Q8C22×D1111yescharacteristic
365C4×D4—21no—
366C4×D4—221no—
367C4×D4C22×D1111yescharacteristic
368C2×C4⋊C4—21no—
369#107—21no—
370#107—21no—
371#107—21no—
372#107—111no—
373#107—221no—
374#107—221no—
375#107—221no—
376#107—221no—
377#107—221no—
378#106—21no—
379#106—221no—
380#106C22⋊D1111yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8C22×D1111yescharacteristic
388#103—21no—
389#103—111no—
390#103—111no—
391#103—221no—
392#103—221no—
393#103—221no—
394#103—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—441no—
401#103—441no—
402#103C22⋊D1111yescharacteristic
403#102—21no—
404#102—221no—
405#102C22⋊D1111yescharacteristic
406C22⋊C8—221no—
407#97—21no—
408#97—221no—
409C4×C8—111no—
410C4×C8—111no—
411C4×C8—221no—
412C4×C8C22×D1111yescharacteristic
413C2×C11—42no—
414C2×C11#327511yescharacteristic
415C2×C11D4×Q1611yescharacteristic
416C2×C11#329011yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—41no—
420C2×Q8—111no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—441no—
424C2×Q8—442no—
425C2×Q8—881no—
426C2×Q8D4×D1111yescharacteristic
427C2×Q8C2×C22⋊D1111yescharacteristic
428C2×D4C2×C22⋊D1111yescharacteristic
429C22×C4—21no—
430C22×C4—41no—
431C22×C4—441no—
432Q16—441no—
433Q16—442no—
434Q16—881no—
435SD16#432614yescomplemented
436C2×C8—21no—
437C2×C8—111no—
438C2×C8—111no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—881no—
444C2×C8C2×C22⋊D1111yescharacteristic
445C2×C8C2×C22⋊D1111yescharacteristic
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—111no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—441no—
463C4⋊C4—441no—
464C4⋊C4—441no—
465C4⋊C4—441no—
466C4⋊C4D4×D1111yescharacteristic
467C4⋊C4C2×C22⋊D1111yescharacteristic
468C4⋊C4C2×C22⋊D1111yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—41no—
471C22⋊C4—441no—
472C42—21no—
473C42—21no—
474C42—41no—
475C42—221no—
476C42—441no—
477C42C23×D1111yescharacteristic
478C11#1992911yescharacteristic, complemented, Sylow
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—81no—
484Q8—81no—
485Q8—161no—
486Q8—221no—
487Q8—221no—
488Q8—441no—
489Q8—441no—
490Q8—441no—
491Q8—441no—
492Q8—882no—
493Q8C2×#432612yes—
494D4—21no—
495D4C2×#432612yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—161no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—882no—
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4#6703711yescharacteristic
513C2×C4C22×C22⋊D1111yescharacteristic
514C8—21no—
515C8—41no—
516C8—221no—
517C8—221no—
518C8—441no—
519C8—441no—
520C8—441no—
521C8—441no—
522C8C2×#432612yes—
523C22—22no—
524C22—41no—
525C22—41no—
526C22D4×C22⋊D1111yescharacteristic
527C4—22no—
528C4—21no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—81no—
534C4—81no—
535C4—441no—
536C4—441no—
537C4—881no—
538C4—881no—
539C4#1062330811yescharacteristic
540C4#1062330911yescharacteristic
541C4C22×#432611yescharacteristic
542C4#1062336911yescharacteristic
543C2—42no—
544C2#1308024111yescharacteristic
545C2D4×#432611yescharacteristic
546C2#1308039811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3385C2
socleC22×C11D42
prime radicalC2×D4×C11C2×D4
hypercenter#3385D11
hypocenterC11#19929
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3385

Complements

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

NH ≅ G/Ntype
2. #13081294C2semidirect
4. #13068225C2semidirect
5. #13068141C2semidirect
6. #13068134C2semidirect
7. #13068076C2semidirect
9. #13067837C2semidirect
12. #13067773C2semidirect
13. #13067511C2semidirect
160. C11×SD16Q16semidirect
435. SD16#4326semidirect
478. C11#19929semidirect

Maximal subgroups

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

subgroupindex
#130815352
#130812942
#130804862
#130682252
#130681412
#130681342
#130680762
#130680692
#130678372
#130678302
#130677802
#130677732
#130675112
SD16×C11⋊C82
C11×#33852
#1992911