Finite Group Databasebeta

← #14735318

Subgroups — #14735318

Order 2816.

884 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#13079834C211yesmaximal, characteristic, complemented
2#13078998C211yesmaximal, characteristic, complemented
3C2×#10622668C211yesmaximal, characteristic, complemented
4#13067950C214yesmaximal, complemented
5#13067939C214yesmaximal, complemented
6#13067231C211yesmaximal, characteristic, complemented
7#13067214C211yesmaximal, characteristic, complemented
8#13067204C211yesmaximal, characteristic, complemented
9C11×#3561C211yesmaximal, characteristic
10C11×#563C2212yes—
11C11×#562C2212yes—
12C11×#556—21no—
13C11×#551—22no—
14D4×Q8×C11—21no—
15C11×#548—21no—
16C11×#546—21no—
17C11×#543—21no—
18C11×#542—21no—
19C11×#542—22no—
20C11×#538—21no—
21C11×#536—21no—
22C11×#533C2211yescharacteristic
23C11×#529C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×#66899—21no—
27C2×#66896—21no—
28#10622706—21no—
29#10622706—21no—
30#10622682C2214yescomplemented
31#10622678C2212yescomplemented
32#10622668—22no—
33#10622668C2214yes—
34#10622668C2212yescomplemented
35#10622656—21no—
36#10622646—21no—
37#10622634—21no—
38#10622621—21no—
39#10622617—22no—
40#10622539C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43#10622181C2214yescomplemented
44#10622181C2212yescomplemented
45#10622178C2214yes—
46#10622178C2212yescomplemented
47C2×C11×#41—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11D411yescharacteristic
51C22×Dic22—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×#126—22no—
57C11×#126—22no—
58C11×#126—22no—
59C11×#126—21no—
60C11×#125C2311yescharacteristic
61C11×#125C2312yes—
62C11×#124—21no—
63C11×#124—22no—
64C11×#124—22no—
65C11×#124—21no—
66C11×#124—21no—
67C11×#124D412yes—
68C11×#124C2312yes—
69C11×#124C2311yescharacteristic
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—21no—
73C11×#123—22no—
74C11×#123—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8D411yescharacteristic
86C11×#121—21no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121D411yescharacteristic
90C11×#120—22no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11D411yescharacteristic
95C4×D4×C11—22no—
96C4×D4×C11—21no—
97C4×D4×C11—22no—
98C4×D4×C11—21no—
99C4×D4×C11D411yescharacteristic
100C11×#117—22no—
101C11×#117—21no—
102C11×#117D412yes—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C42×C11C2311yescharacteristic
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×#4318—21no—
110C22×C11⋊C8—21no—
111#66922—21no—
112#66922—21no—
113#66922—21no—
114#66922C2312yes—
115#66899—24no—
116#66899—22no—
117#66896—24no—
118#66896—22no—
119C22⋊(C11⋊C8)—21no—
120#66874—24no—
121#66874—24no—
122#66872—22no—
123#66871—22no—
124C4⋊(C11⋊C8)—21no—
125#66867—21no—
126#66867C2312yes—
127#66867C2312yes—
128#66867C2312yes—
129C4×C11⋊C8—21no—
130#19027—111nomaximal, Sylow
131C24×C11—21no—
132C11×#41—82no—
133C2×Q8×C11—22no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—42no—
138C2×Q8×C11—82no—
139C2×Q8×C11C2×D411yescharacteristic
140C2×Q8×C11C2×D412yes—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—21no—
145C2×D4×C11—42no—
146C2×D4×C11C2×D411yescharacteristic
147C2×D4×C11C2×D412yes—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×Dic11—41no—
157C2×Dic22—22no—
158C2×Dic22—44no—
159C2×Dic22—41no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
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—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C4⋊C4C2×D412yes—
175C11×C4⋊C4C2×D412yes—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—21no—
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11C2411yescharacteristic
198C4⋊Dic11—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11—41no—
201C4⋊Dic11—41no—
202#4318—42no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—42no—
207#3561D1111yescharacteristic
208#3238—111no—
209#3139—111no—
210C2×#489—111no—
211#1664—114no—
212#1662—114no—
213#1531—111no—
214#1527—111no—
215#1524—111no—
216C23×C11—22no—
217C23×C11—21no—
218C23×C11—42no—
219C23×C11—81no—
220C23×C11—81no—
221C23×C11#12011yescharacteristic
222Q8×C11—42no—
223Q8×C11—41no—
224Q8×C11—42no—
225Q8×C11—42no—
226Q8×C11—81no—
227Q8×C11—82no—
228D4×C11—42no—
229D4×C11—41no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—82no—
233D4×C11—82no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—81no—
245C2×C4×C11—82no—
246C2×C4×C11—82no—
247C2×C4×C11—82no—
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#12011yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×Dic11—42no—
255C2×Dic11—82no—
256Dic22—44no—
257Dic22—82no—
258C11⋊C8—42no—
259C11⋊C8—42no—
260C11⋊C8—42no—
261#563C2×D1112yes—
262#562C2×D1112yes—
263#556—21no—
264#551—22no—
265D4×Q8—21no—
266#548—21no—
267#546—21no—
268#543—21no—
269#542—21no—
270#542—22no—
271#538—21no—
272#536—21no—
273#533C2×D1111yescharacteristic
274C2×C4⋊Q8—111no—
275#529C2×D1111yescharacteristic
276C2×#124C2×D1111yescharacteristic
277#501—112no—
278#491—114no—
279#489—114no—
280#489—112no—
281#489—222no—
282#487—221no—
283#487—221no—
284#483—221no—
285#480—221no—
286#477—221no—
287#476—221no—
288#432—111no—
289#419—222no—
290C2×#103—221no—
291C2×#102—221no—
292C4×M16—111no—
293C2×#97—111no—
294#330—114no—
295#330—112no—
296#329—112no—
297#329—114no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—41no—
301C22×C11—42no—
302C22×C11—41no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—41no—
306C22×C11—162no—
307C22×C11#45412yes—
308C22×C11C2×#12011yescharacteristic
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—41no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—41no—
318C4×C11—41no—
319C4×C11—42no—
320C4×C11#45512yes—
321Dic11—82no—
322C2×#41—21no—
323C22×Q8—21no—
324C22×Q8—221no—
325C22×Q8C22⋊D1111yescharacteristic
326C22×D4C22⋊D1111yescharacteristic
327C2×M16—221no—
328C22×C8—221no—
329C4⋊Q8—21no—
330C4⋊Q8—22no—
331C4⋊Q8—112no—
332C4⋊Q8—221no—
333C4⋊Q8—221no—
334C4⋊Q8—221no—
335C4⋊Q8C22⋊D1111yescharacteristic
336C4⋊Q8C22⋊D1111yescharacteristic
337#126—22no—
338#126—22no—
339#126—22no—
340#126—21no—
341#125C22×D1111yescharacteristic
342#125C22×D1112yes—
343#124—21no—
344#124—22no—
345#124—22no—
346#124—21no—
347#124—21no—
348#124C22⋊D1112yes—
349#124C22×D1112yes—
350#124C22×D1111yescharacteristic
351#123—22no—
352#123—22no—
353#123—21no—
354#123—22no—
355#123—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—21no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8C22⋊D1111yescharacteristic
367#121—21no—
368#121—22no—
369#121—22no—
370#121C22⋊D1111yescharacteristic
371#120—22no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C22⋊D1111yescharacteristic
376C4×D4—22no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4C22⋊D1111yescharacteristic
381#117—22no—
382#117—21no—
383#117C22⋊D1112yes—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C42C22×D1111yescharacteristic
390#107—222no—
391#106—222no—
392C4⋊C8—221no—
393#103—224no—
394#103—222no—
395#103—224no—
396#103—224no—
397#102—224no—
398#102—222no—
399C22⋊C8—221no—
400#97—112no—
401#97—112no—
402#97—112no—
403#97—221no—
404C4×C8—221no—
405C2×C11—22no—
406C2×C11—81no—
407C2×C11—82no—
408C2×C11C2×#45511yescharacteristic
409C2×C11C2×#45411yescharacteristic
410C2×C11#302211yescharacteristic
411C24—21no—
412#41—82no—
413C2×Q8—22no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—42no—
418C2×Q8—82no—
419C2×Q8—222no—
420C2×Q8—444no—
421C2×Q8—441no—
422C2×Q8C2×C22⋊D1111yescharacteristic
423C2×Q8C2×C22⋊D1112yes—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—42no—
429C2×D4C2×C22⋊D1111yescharacteristic
430C2×D4C2×C22⋊D1112yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—441no—
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440M16—442no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—442no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4—441no—
460C4⋊C4—441no—
461C4⋊C4C2×C22⋊D1112yes—
462C4⋊C4C2×C22⋊D1112yes—
463C4⋊C4C2×C22⋊D1111yescharacteristic
464C4⋊C4C2×C22⋊D1111yescharacteristic
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—21no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C42—22no—
481C42—22no—
482C42—21no—
483C42C2×C22⋊D1111yescharacteristic
484C42C2×C22⋊D1111yescharacteristic
485C42C2×C22⋊D1111yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1902711yescharacteristic, complemented, Sylow
488C23—22no—
489C23—21no—
490C23—42no—
491C23—81no—
492C23—81no—
493C23#6700611yescharacteristic
494Q8—42no—
495Q8—41no—
496Q8—42no—
497Q8—42no—
498Q8—81no—
499Q8—82no—
500Q8—444no—
501Q8—882no—
502D4—42no—
503D4—41no—
504D4—42no—
505D4—42no—
506D4—82no—
507D4—82no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—81no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—442no—
523C2×C4—882no—
524C2×C4#6700611yescharacteristic
525C2×C4#6700611yescharacteristic
526C2×C4#6700611yescharacteristic
527C2×C4C22×C22⋊D1111yescharacteristic
528C2×C4C22×C22⋊D1111yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C8—442no—
531C8—442no—
532C8—442no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—42no—
537C22—41no—
538C22—42no—
539C22—42no—
540C22—41no—
541C22—162no—
542C22#1062285812yes—
543C22C2×#6700611yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—42no—
551C4—42no—
552C4—41no—
553C4—41no—
554C4—42no—
555C4—882no—
556C4#1062285512yes—
557C2—22no—
558C2—82no—
559C2—81no—
560C2C2×#1062285511yescharacteristic
561C2C2×#1062285811yescharacteristic
562C2#1307799511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3561C2
socleC22×C11C2×#120
hypercenter#3561D11
hypocenterC11#19027
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3561

Complements

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

NH ≅ G/Ntype
1. #13079834C2semidirect
2. #13078998C2semidirect
3. C2×#10622668C2semidirect
4. #13067950C2semidirect
5. #13067939C2semidirect
6. #13067231C2semidirect
7. #13067214C2semidirect
8. #13067204C2semidirect
30. #10622682C22semidirect
31. #10622678C22semidirect
34. #10622668C22semidirect
43. #10622181C22semidirect
44. #10622181C22semidirect
46. #10622178C22semidirect
487. C11#19027semidirect

Maximal subgroups

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

subgroupindex
#130798342
#130789982
C2×#106226682
#130679502
#130679392
#130672312
#130672142
#130672042
C11×#35612
#1902711