Finite Group Databasebeta

← #14910679

Subgroups — #14910679

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080359C211yesmaximal, characteristic, complemented
2#13070850C211yesmaximal, characteristic, complemented
3#13070824C211yesmaximal, characteristic, complemented
4#13070801C211yesmaximal, characteristic, complemented
5#13070777C211yesmaximal, characteristic, complemented
6#13070710C211yesmaximal, characteristic, complemented
7#13070700C211yesmaximal, characteristic, complemented
8#13070671C211yesmaximal, characteristic, complemented
9#13070537C211yesmaximal, characteristic, complemented
10#13070532C211yesmaximal, characteristic, complemented
11C4×#66891C211yesmaximal, characteristic, complemented
12D4×C11⋊C16C211yesmaximal, characteristic, complemented
13#13070321C211yesmaximal, characteristic, complemented
14C2×#10622130C211yesmaximal, characteristic, complemented
15C11×#3339C211yesmaximal, characteristic, complemented
16C11×#553—21no—
17C22×Dic44C2211yescharacteristic
18C2×#66957C2211yescharacteristic
19#10623083—21no—
20C11×#499C2211yescharacteristic
21C11×#482—21no—
22C11×#481—21no—
23C11×#478—21no—
24C11×#466C2211yescharacteristic
25C11×#466C2211yescharacteristic
26C4×C11×D8C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C11×#427C2211yescharacteristic
29C2×C11×#107C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31C2×#66891C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622729C2211yescharacteristic
34#10622728C2211yescharacteristic
35C22×C11⋊C16C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622458—21no—
38#10622351—21no—
39#10622346—21no—
40C4×Dic44C2211yescharacteristic
41#10622309C2211yescharacteristic
42#10622200C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622130C2211yescharacteristic
46#10622130C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622130C2211yescharacteristic
49#10622130C2211yescharacteristic
50#10622130C2211yescharacteristic
51#10622129C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×#4339—21no—
60C22×Dic22—21no—
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#126—41no—
65C11×#125—21no—
66C11×#123—41no—
67C11×#121—21no—
68C11×#121—21no—
69C11×#121—41no—
70C4×D4×C11—21no—
71C4×D4×C11—41no—
72C4×D4×C11D411yescharacteristic
73C11×#117—21no—
74C2×C11×C4⋊C4—21no—
75#66992—41no—
76#66983—21no—
77#66977—21no—
78C2×Dic44—22no—
79C2×Dic44—21no—
80C2×Dic44—41no—
81C2×Dic44C2311yescharacteristic
82C2×Dic44C2311yescharacteristic
83#66957—22no—
84#66957—41no—
85C2×D88C2311yescharacteristic
86C2×#4314—21no—
87C2×#4314—21no—
88#66949—41no—
89#66938—41no—
90(C22⋊D11)⋊C4—41no—
91#66928—21no—
92C4×Dic22—21no—
93C11×#107—21no—
94C11×#107C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#106—21no—
98C11×#106—21no—
99C11×C4⋊C8D411yescharacteristic
100C11×#102—21no—
101C11×#102—21no—
102C11×#102—21no—
103C11×C22⋊C8D411yescharacteristic
104C11×C22⋊C8D411yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66891—22no—
107#66891—41no—
108#66890—41no—
109#66885—21no—
110#66882C2311yescharacteristic
111#66880—21no—
112#66880—21no—
113C2×C11⋊C16—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33868—111nomaximal, Sylow
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11D811yescharacteristic
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C22×Dic11—41no—
131#4339—42no—
132#4339—81no—
133C2×D44—21no—
134C2×C4×D11—41no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—42no—
138C2×Dic22—41no—
139C2×Dic22—81no—
140C11×D8—21no—
141C11×D8—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2411yescharacteristic
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4D811yescharacteristic
157C11×C22⋊C4—41no—
158C11×C22⋊C4—41no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C11×C22⋊C4D811yescharacteristic
162C11×C22⋊C4D811yescharacteristic
163C42×C11—41no—
164C42×C11C2×D411yescharacteristic
165C22⋊Dic11—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169C4⋊Dic11—21no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172C4×Dic11—41no—
173Dic44—21no—
174Dic44—21no—
175Dic44—21no—
176Dic44—42no—
177Dic44#4112yes—
178D88—21no—
179D88—21no—
180#4314—42no—
181#4314—81no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3339D1111yescharacteristic, complemented
187#3285—111no—
188#2242—111no—
189#2237—111no—
190#2233—111no—
191#2229—111no—
192#2217—111no—
193#2215—111no—
194#2210—111no—
195#2186—111no—
196#2185—111no—
197C4×SD32—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#358—111no—
201C23×C11—41no—
202C23×C11C2×D811yescharacteristic
203C23×C11C2×D811yescharacteristic
204C22×D11—41no—
205D4×C11—22no—
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—82no—
209D4×C11—161no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—161no—
218C2×C4×C11—161no—
219C2×C4×C11C2×D811yescharacteristic
220C2×C4×C11C2×D811yescharacteristic
221C2×C4×C11C2×D811yescharacteristic
222C2×C4×C11C2×D811yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C22⋊D11—82no—
225C22⋊D11—82no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—82no—
230D44—41no—
231D44—41no—
232C4×D11—82no—
233Dic22—22no—
234Dic22—41no—
235Dic22—41no—
236Dic22—41no—
237Dic22—82no—
238C8×C11—21no—
239C8×C11—21no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C2×#135—111no—
244C22×Q16—111no—
245#553—21no—
246#548—221no—
247C2×SD32—111no—
248C2×SD32—111no—
249C2×D16—111no—
250C22×C16—111no—
251C22×C16—111no—
252#499C2×D1111yescharacteristic
253#495—111no—
254#482—21no—
255#481—21no—
256#478—21no—
257#467—111no—
258#466—111no—
259#466C2×D1111yescharacteristic
260#466C2×D1111yescharacteristic
261#464—221no—
262#452—221no—
263#448—221no—
264C4×Q16—111no—
265C4×D8C2×D1111yescharacteristic
266C8×D4C2×D1111yescharacteristic
267#427C2×D1111yescharacteristic
268C2×#107C2×D1111yescharacteristic
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283C22⋊C16—111no—
284C22⋊C16—111no—
285C4×C16—111no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11#50812yes—
295C22×C11C22×D811yescharacteristic
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11#54611yescharacteristic
307C4×C11#57711yescharacteristic
308Dic11—42no—
309Dic11—81no—
310Dic11—81no—
311C2×#41—221no—
312C22×Q8—221no—
313#135—222no—
314#135—441no—
315C2×Q16—111no—
316C2×Q16—111no—
317C2×Q16—222no—
318C2×Q16—221no—
319C2×Q16—441no—
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8C22×D1111yescharacteristic
324C22×C8C22×D1111yescharacteristic
325C22×C8C22×D1111yescharacteristic
326#126—41no—
327#125—21no—
328#124—221no—
329#124—441no—
330#123—41no—
331C22⋊Q8—221no—
332C22⋊Q8—441no—
333#121—21no—
334#121—21no—
335#121—41no—
336#121—221no—
337#121—441no—
338C4×Q8—221no—
339C4×D4—21no—
340C4×D4—41no—
341C4×D4—441no—
342C4×D4C22⋊D1111yescharacteristic
343#117—21no—
344C2×C4⋊C4—21no—
345SD32—222no—
346SD32—441no—
347D16—441no—
348C2×C16—111no—
349C2×C16—111no—
350C2×C16—111no—
351C2×C16—111no—
352C2×C16—441no—
353C2×C16—441no—
354#107—21no—
355#107—111no—
356#107C22×D1111yescharacteristic
357#107C22×D1111yescharacteristic
358#107C22×D1111yescharacteristic
359#106—21no—
360#106—21no—
361C4⋊C8C22⋊D1111yescharacteristic
362#103—221no—
363#103—221no—
364#102—21no—
365#102—21no—
366#102—21no—
367#102—221no—
368C22⋊C8C22⋊D1111yescharacteristic
369C22⋊C8C22⋊D1111yescharacteristic
370C4×C8C22×D1111yescharacteristic
371C2×C11—22no—
372C2×C11—41no—
373C2×C11—161no—
374C2×C11#329411yescharacteristic
375C2×C11C2×#50811yescharacteristic
376C2×C11#341611yescharacteristic
377D11—161no—
378#41—442no—
379#41—881no—
380C2×Q8—221no—
381C2×Q8—221no—
382C2×Q8—442no—
383C2×Q8—441no—
384C2×Q8—881no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—221no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4#432311yescharacteristic
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398Q16—112no—
399Q16—221no—
400Q16—221no—
401Q16—221no—
402Q16—442no—
403SD16—442no—
404SD16—881no—
405D8—21no—
406D8—21no—
407D8—221no—
408D8—221no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×C22⋊D1111yescharacteristic
414C2×C8C2×C22⋊D1111yescharacteristic
415C2×C8C2×C22⋊D1111yescharacteristic
416C2×C8C23×D1111yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—221no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4#432311yescharacteristic
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4#432311yescharacteristic
436C22⋊C4#432311yescharacteristic
437C42—41no—
438C42—441no—
439C42C2×C22⋊D1111yescharacteristic
440C16—221no—
441C16—221no—
442C16—221no—
443C16—221no—
444C11#3386811yescharacteristic, complemented, Sylow
445C23—41no—
446C23—441no—
447C23C2×#432311yescharacteristic
448C23C2×#432311yescharacteristic
449Q8—222no—
450Q8—441no—
451Q8—441no—
452Q8—441no—
453Q8—882no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—82no—
458D4—161no—
459D4—441no—
460D4—441no—
461D4—882no—
462D4—882no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—161no—
471C2×C4—161no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—882no—
476C2×C4—882no—
477C2×C4C2×#432311yescharacteristic
478C2×C4C2×#432311yescharacteristic
479C2×C4C2×#432311yescharacteristic
480C2×C4C2×#432311yescharacteristic
481C2×C4C22×C22⋊D1111yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8#41×D1111yescharacteristic
486C8#6704211yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22#1062280712yes—
499C22C22×#432311yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—442no—
508C4—881no—
509C4—881no—
510C4#1062336011yescharacteristic
511C4#1062336811yescharacteristic
512C2—22no—
513C2—41no—
514C2—161no—
515C2—1761no—
516C2#1308042311yescharacteristic
517C2C2×#1062280711yescharacteristic
518C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3339C2
socleC22×C11C22×D8
hypercenter#3339D11
hypocenterC11#33868
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #13080359C2semidirect
2. #13070850C2semidirect
3. #13070824C2semidirect
4. #13070801C2semidirect
5. #13070777C2semidirect
6. #13070710C2semidirect
7. #13070700C2semidirect
8. #13070671C2semidirect
9. #13070537C2semidirect
10. #13070532C2semidirect
11. C4×#66891C2semidirect
12. D4×C11⋊C16C2semidirect
13. #13070321C2semidirect
14. C2×#10622130C2semidirect
15. C11×#3339C2semidirect
186. #3339D11semidirect
444. C11#33868semidirect

Maximal subgroups

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

subgroupindex
#130803592
#130708502
#130708242
#130708012
#130707772
#130707102
#130707002
#130706712
#130705372
#130705322
C4×#668912
D4×C11⋊C162
#130703212
C2×#106221302
C11×#33392
#3386811