Finite Group Databasebeta

← #14910764

Subgroups — #14910764

Order 2816.

554 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#13081020C211yesmaximal, characteristic, complemented
2#13080337C211yesmaximal, characteristic, complemented
3#13070862C211yesmaximal, characteristic, complemented
4#13070827C211yesmaximal, characteristic, complemented
5#13070815C211yesmaximal, characteristic, complemented
6#13070773C211yesmaximal, characteristic, complemented
7#13070728C211yesmaximal, characteristic, complemented
8#13070711C211yesmaximal, characteristic, complemented
9#13070661C211yesmaximal, characteristic, complemented
10#13070536C211yesmaximal, characteristic, complemented
11#13070536C211yesmaximal, characteristic, complemented
12#13070443C211yesmaximal, characteristic, complemented
13#13070325C211yesmaximal, characteristic, complemented
14#13070320C211yesmaximal, characteristic, complemented
15C11×#2177C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C2×#66965C2211yescharacteristic
18#10623089—21no—
19#10623086—21no—
20C2×C11×D16C2211yescharacteristic
21C4×C11×D8C2211yescharacteristic
22C4×C11×D8C2211yescharacteristic
23#10622770C2211yescharacteristic
24#10622770C2211yescharacteristic
25C2×#66891C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27#10622632—21no—
28#10622622—21no—
29C2×#66862C2211yescharacteristic
30C2×C16×D11C2211yescharacteristic
31#10622500C2211yescharacteristic
32#10622500C2211yescharacteristic
33#10622493C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622396—21no—
36#10622396—21no—
37#10622392—21no—
38#10622390—21no—
39#10622312C2211yescharacteristic
40C8×D44C2211yescharacteristic
41#10622296C2211yescharacteristic
42C11×#367C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#346C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×#4341—21no—
60C2×#4341—21no—
61C2×C11×D8C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65#66991—21no—
66#66991—21no—
67C2×#4324—21no—
68C2×#4324—21no—
69#66983—41no—
70#66982—41no—
71C4×C22⋊D11—41no—
72C2×C4⋊Dic11—41no—
73#66965—22no—
74#66965—22no—
75#66965—41no—
76#66965—41no—
77C2×Dic44—21no—
78C2×Dic44C2311yescharacteristic
79C2×Dic44C2311yescharacteristic
80C2×C8×D11C2311yescharacteristic
81C2×C8×D11C2311yescharacteristic
82#66950—21no—
83#66950—21no—
84#66945—21no—
85C4⋊C4×D11—21no—
86#66939—41no—
87#66939—41no—
88#66937—41no—
89#66932—41no—
90C4×D44D411yescharacteristic
91#66923—21no—
92#66922—21no—
93C11×D16—22no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#102—21no—
99C11×#102—21no—
100C4×C8×C11C2311yescharacteristic
101#66896—21no—
102#66896—21no—
103#66891—41no—
104#66891—41no—
105(C2×D11)⋊C8D411yescharacteristic
106(C2×D11)⋊C8D411yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66881—21no—
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112#66874—21no—
113#66874—21no—
114#66872—21no—
115#66871—21no—
116C4⋊(C11⋊C8)D411yescharacteristic
117#66862—41no—
118C16×D11—41no—
119#33874—111nomaximal, Sylow
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C22×Dic11—41no—
129C22×Dic11—41no—
130#4341—42no—
131#4341—42no—
132#4341—81no—
133#4341—81no—
134C2×D44D811yescharacteristic
135C2×C4×D11—41no—
136C2×C4×D11C2×D411yescharacteristic
137C2×C4×D11C2×D411yescharacteristic
138C2×Dic22—21no—
139C2×Dic22—21no—
140C11×D8—21no—
141C11×D8—21no—
142C11×D8—21no—
143C11×D8#4112yes—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2411yescharacteristic
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C42×C11C2×D411yescharacteristic
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153#4324—42no—
154#4324—42no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4D811yescharacteristic
159(C2×D11)⋊C4D811yescharacteristic
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—41no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166C4⋊Dic11D811yescharacteristic
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170C4×Dic11—41no—
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173Dic44—21no—
174Dic44—21no—
175Dic44—21no—
176Dic44—21no—
177Dic44—81no—
178C8×D11—21no—
179C8×D11—21no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3339—111no—
187#3283—111no—
188#2245—111no—
189#2237—111no—
190#2235—111no—
191#2228—111no—
192#2220—111no—
193#2217—111no—
194#2208—111no—
195#2186—111no—
196#2186—111no—
197#2177D1111yescharacteristic, complemented
198#2168—111no—
199#2139—111no—
200#2138—111no—
201C23×C11—41no—
202C23×C11—41no—
203C22×D11C2×D811yescharacteristic
204C22×D11C2×D811yescharacteristic
205D4×C11—22no—
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—82no—
212C2×C4×C11—161no—
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C22⋊D11—82no—
217C22⋊D11—82no—
218C22⋊D11—82no—
219C22⋊D11—161no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—82no—
225C2×Dic11—82no—
226C2×Dic11C2×D811yescharacteristic
227C2×Dic11C2×D811yescharacteristic
228D44—41no—
229C4×D11—21no—
230C4×D11—21no—
231C4×D11—21no—
232C4×D11—21no—
233C4×D11—161no—
234Dic22—41no—
235Dic22—41no—
236Dic22—41no—
237Dic22—41no—
238C8×C11—21no—
239C8×C11C2×#4111yescharacteristic
240C8×C11H(5,𝔽2)11yescharacteristic
241C11⋊C8—21no—
242C11⋊C8—21no—
243C2×#135—111no—
244C2×#135—111no—
245#553—221no—
246#547—221no—
247C2×SD32—111no—
248C2×SD32—111no—
249C2×D16C2×D1111yescharacteristic
250C2×M32—111no—
251C22×C16—111no—
252#499—111no—
253#494—111no—
254#482—221no—
255#481—221no—
256#478—221no—
257#467—111no—
258#467—111no—
259#466—111no—
260#466—111no—
261#461—221no—
262#452—221no—
263#452—221no—
264C4×D8C2×D1111yescharacteristic
265C4×D8C2×D1111yescharacteristic
266C8×D4—111no—
267#427—111no—
268C2×#107—111no—
269#367—111no—
270#367C2×D1111yescharacteristic
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#357C2×D1111yescharacteristic
282#357C2×D1111yescharacteristic
283C22⋊C16—111no—
284C22⋊C16—111no—
285#346C2×D1111yescharacteristic
286C22×C11—42no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11C22×D811yescharacteristic
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—21no—
296C2×D11—21no—
297C2×D11—21no—
298C2×D11—21no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—81no—
302C4×C11—81no—
303C4×C11#54611yescharacteristic
304C4×C11#57711yescharacteristic
305Dic11—21no—
306Dic11—21no—
307Dic11—81no—
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311C2×#41—221no—
312C2×#41—221no—
313#135—222no—
314#135—222no—
315#135—441no—
316#135—441no—
317C2×Q16—111no—
318C2×Q16—111no—
319C2×Q16—221no—
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8C22×D1111yescharacteristic
323C2×D8C22×D1111yescharacteristic
324C22×C8—111no—
325C22×C8—111no—
326C4⋊Q8—221no—
327#126—441no—
328#125—221no—
329#123—441no—
330#123—441no—
331#123—441no—
332C22⋊Q8—221no—
333C22⋊Q8—221no—
334#121—221no—
335#121—221no—
336#121—441no—
337#121—441no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—111no—
341C4×D4—441no—
342#117—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—441no—
345SD32—441no—
346SD32—441no—
347D16—22no—
348M32—441no—
349C2×C16—111no—
350C2×C16—111no—
351C2×C16—441no—
352C2×C16C22×D1111yescharacteristic
353C2×C16C22×D1111yescharacteristic
354#107—111no—
355#107—111no—
356#107—221no—
357#107C22×D1111yescharacteristic
358#107C22×D1111yescharacteristic
359#106—221no—
360#106—221no—
361C4⋊C8—111no—
362#103—221no—
363#103—221no—
364#102—21no—
365#102—21no—
366#102—221no—
367#102—221no—
368C22⋊C8—111no—
369C22⋊C8—111no—
370C4×C8C22×D1111yescharacteristic
371C2×C11—82no—
372C2×C11—161no—
373C2×C11#329411yescharacteristic
374C2×C11#341411yescharacteristic
375C2×C11#341611yescharacteristic
376D11—41no—
377D11—41no—
378#41—442no—
379#41—442no—
380#41—881no—
381#41—881no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—111no—
387C2×D4—441no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4—441no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398Q16—221no—
399Q16—221no—
400Q16—221no—
401Q16—221no—
402Q16—881no—
403SD16—442no—
404SD16—442no—
405D8—21no—
406D8—21no—
407D8—21no—
408D8#433912yes—
409C2×C8—111no—
410C2×C8—111no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8—221no—
415C2×C8D4×D1111yescharacteristic
416C2×C8C23×D1111yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—111no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—111no—
432C22⋊C4—111no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C42—441no—
439C42D4×D1111yescharacteristic
440C16—21no—
441C16—21no—
442C16—221no—
443C16—221no—
444C11#3387411yescharacteristic, complemented, Sylow
445C23—41no—
446C23—41no—
447C23—111no—
448C23—111no—
449Q8—441no—
450Q8—441no—
451Q8—441no—
452Q8—441no—
453D4—22no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—441no—
458D4—882no—
459D4—882no—
460D4—882no—
461D4—1761no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—82no—
465C2×C4—111no—
466C2×C4—111no—
467C2×C4—161no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—882no—
477C2×C4—882no—
478C2×C4—1761no—
479C2×C4D8×D1111yescharacteristic
480C2×C4D8×D1111yescharacteristic
481C2×C4C2×D4×D1111yescharacteristic
482C8—21no—
483C8—221no—
484C8—221no—
485C8C2×#433911yescharacteristic
486C8#6704211yescharacteristic
487C22—42no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—221no—
494C22—221no—
495C22—221no—
496C22—221no—
497C22—221no—
498C22—221no—
499C22C2×D8×D1111yescharacteristic
500C4—21no—
501C4—21no—
502C4—81no—
503C4—81no—
504C4—221no—
505C4—221no—
506C4—881no—
507C4—881no—
508C4—881no—
509C4—881no—
510C4#1062308111yescharacteristic
511C4#1062330111yescharacteristic
512C2—82no—
513C2—161no—
514C2—441no—
515C2—441no—
516C2#1308043111yescharacteristic
517C2#1308174811yescharacteristic
518C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2177C2
socleC22×C11C22×D8
hypercenter#2177D11
hypocenterC11#33874
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2177

Complements

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

NH ≅ G/Ntype
1. #13081020C2semidirect
2. #13080337C2semidirect
3. #13070862C2semidirect
4. #13070827C2semidirect
5. #13070815C2semidirect
6. #13070773C2semidirect
7. #13070728C2semidirect
8. #13070711C2semidirect
9. #13070661C2semidirect
10. #13070536C2semidirect
11. #13070536C2semidirect
12. #13070443C2semidirect
13. #13070325C2semidirect
14. #13070320C2semidirect
15. C11×#2177C2semidirect
197. #2177D11semidirect
444. C11#33874semidirect

Maximal subgroups

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

subgroupindex
#130810202
#130803372
#130708622
#130708272
#130708152
#130707732
#130707282
#130707112
#130706612
#130705362
#130704432
#130703252
#130703202
C11×#21772
#3387411