Finite Group Databasebeta

← #14910690

Subgroups — #14910690

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#13081020C211yesmaximal, characteristic, complemented
2#13080358C211yesmaximal, characteristic, complemented
3#13070848C211yesmaximal, characteristic, complemented
4#13070827C211yesmaximal, characteristic, complemented
5#13070803C211yesmaximal, characteristic, complemented
6#13070780C211yesmaximal, characteristic, complemented
7#13070711C211yesmaximal, characteristic, complemented
8#13070701C211yesmaximal, characteristic, complemented
9#13070671C211yesmaximal, characteristic, complemented
10#13070538C211yesmaximal, characteristic, complemented
11#13070531C211yesmaximal, characteristic, complemented
12C16×D44C211yesmaximal, characteristic, complemented
13#13070322C211yesmaximal, characteristic, complemented
14D11×#358C211yesmaximal, characteristic, complemented
15C4×C11×SD32C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18#10623107—21no—
19#10623089—21no—
20C2×C11×SD32C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22C4×C11×D8C2211yescharacteristic
23#10622770C2211yescharacteristic
24#10622770C2211yescharacteristic
25C2×#66891C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27#10622641—21no—
28#10622622—21no—
29C2×C16×D11C2211yescharacteristic
30C2×C16×D11C2211yescharacteristic
31#10622500C2211yescharacteristic
32#10622496C2211yescharacteristic
33#10622493C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622423—21no—
36#10622419—21no—
37#10622392—21no—
38#10622390—21no—
39#10622309C2211yescharacteristic
40C8×D44C2211yescharacteristic
41#10622296C2211yescharacteristic
42C11×#367C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C4×C11×C16C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×#4343—21no—
60C2×Q8×D11—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C4×Q8×C11—21no—
64C4×D4×C11—21no—
65C2×#4326—21no—
66C2×#4325—21no—
67#66991—21no—
68#66991—21no—
69#66982—41no—
70C4×C22⋊D11—41no—
71#66972—22no—
72#66972—41no—
73Q16×D11—22no—
74Q16×D11—41no—
75C2×Dic44C2311yescharacteristic
76C2×D88C2311yescharacteristic
77C2×#4314—21no—
78C2×C8×D11C2311yescharacteristic
79C2×C8×D11C2311yescharacteristic
80#66950—21no—
81#66950—41no—
82#66948—21no—
83#66948—41no—
84#66945—21no—
85C4⋊C4×D11—21no—
86#66937—41no—
87#66932—41no—
88#66928—21no—
89#66928—41no—
90C4×D44—41no—
91C4×D44D411yescharacteristic
92#66923—21no—
93C11×SD32—22no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99C11×#102—21no—
100C4×C8×C11C2311yescharacteristic
101#66896—21no—
102#66896—21no—
103#66891—41no—
104#66890—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#66873—21no—
114#66872—21no—
115#66871—21no—
116C4⋊(C11⋊C8)D411yescharacteristic
117C16×D11—41no—
118C16×D11—41no—
119#33868—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×D4×C11—21no—
122C22×C4×C11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125#4343—42no—
126#4343—81no—
127Q8×D11—42no—
128Q8×D11—81no—
129C2×D44—21no—
130C2×D44—41no—
131C2×D44—41no—
132C2×D44D811yescharacteristic
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11C2×D411yescharacteristic
137C2×C4×D11C2×D411yescharacteristic
138C2×Dic22—21no—
139C2×Dic22—41no—
140C11×Q16—21no—
141C11×Q16#4112yes—
142C11×D8—21no—
143C11×D8—21no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2411yescharacteristic
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—41no—
149C11×C22⋊C4—41no—
150C42×C11—41no—
151C42×C11C2×D411yescharacteristic
152C22⋊Dic11—41no—
153C22⋊Dic11—41no—
154#4326—42no—
155#4325—42no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4D811yescharacteristic
162(C2×D11)⋊C4D811yescharacteristic
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
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—
175D88—21no—
176D88—21no—
177#4314—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#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×SD32D1111yescharacteristic, complemented
198D4×C16—111no—
199#2138—111no—
200C2×#358—111no—
201C23×C11—41no—
202C22×D11—41no—
203C22×D11C2×D811yescharacteristic
204C22×D11C2×D811yescharacteristic
205Q8×C11—22no—
206Q8×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—161no—
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C22⋊D11—82no—
217C22⋊D11—161no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223D44—22no—
224D44—41no—
225D44—41no—
226D44—82no—
227D44—82no—
228C4×D11—21no—
229C4×D11—21no—
230C4×D11—21no—
231C4×D11—21no—
232C4×D11—82no—
233C4×D11—82no—
234C4×D11—161no—
235Dic22—41no—
236Dic22—41no—
237Dic22—82no—
238C8×C11—21no—
239C8×C11C2×#4111yescharacteristic
240C8×C11H(5,𝔽2)11yescharacteristic
241C11⋊C8—21no—
242C11⋊C8—21no—
243C2×#135—111no—
244C22×Q16—111no—
245#553—221no—
246#548—221no—
247C2×SD32—111no—
248C2×SD32C2×D1111yescharacteristic
249C2×D16—111no—
250C22×C16—111no—
251C22×C16—111no—
252#499—111no—
253#495—111no—
254#482—221no—
255#481—221no—
256#478—221no—
257#467—111no—
258#466—111no—
259#466—111no—
260#466—111no—
261#464—221no—
262#452—221no—
263#448—221no—
264C4×Q16C2×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#358C2×D1111yescharacteristic
279#357—111no—
280#357—111no—
281#357—111no—
282#357C2×D1111yescharacteristic
283C22⋊C16—111no—
284C22⋊C16—111no—
285C4×C16C2×D1111yescharacteristic
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11C22×D811yescharacteristic
290C2×D11—21no—
291C2×D11—21no—
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11#50812yes—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—42no—
302C4×C11—81no—
303C4×C11—81no—
304C4×C11#54611yescharacteristic
305C4×C11#57711yescharacteristic
306Dic11—21no—
307Dic11—21no—
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311C2×#41—221no—
312C22×Q8—221no—
313#135—222no—
314#135—441no—
315C2×Q16—111no—
316C2×Q16—221no—
317C2×Q16—222no—
318C2×Q16—441no—
319C2×Q16C22×D1111yescharacteristic
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8C22×D1111yescharacteristic
324C22×C8—111no—
325C22×C8—111no—
326#126—441no—
327#125—221no—
328#124—221no—
329#124—441no—
330#123—441no—
331C22⋊Q8—221no—
332C22⋊Q8—441no—
333#121—221no—
334#121—221no—
335#121—221no—
336#121—441no—
337#121—441no—
338C4×Q8—21no—
339C4×D4—21no—
340C4×D4—111no—
341C4×D4—441no—
342C4×D4—441no—
343#117—221no—
344C2×C4⋊C4—221no—
345SD32—22no—
346SD32—441no—
347D16—441no—
348C2×C16—111no—
349C2×C16—111no—
350C2×C16—441no—
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—21no—
363#103—221no—
364#102—21no—
365#102—221no—
366#102—221no—
367#102—221no—
368C22⋊C8—111no—
369C22⋊C8—111no—
370C4×C8C22×D1111yescharacteristic
371C2×C11—161no—
372C2×C11#329411yescharacteristic
373C2×C11C2×#50811yescharacteristic
374C2×C11#341611yescharacteristic
375D11—22no—
376D11—41no—
377D11—161no—
378#41—442no—
379#41—881no—
380C2×Q8—21no—
381C2×Q8—221no—
382C2×Q8—441no—
383C2×Q8—442no—
384C2×Q8—881no—
385C2×D4—21no—
386C2×D4—111no—
387C2×D4—221no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4—441no—
392C22×C4—41no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398Q16—21no—
399Q16—221no—
400Q16—221no—
401Q16—442no—
402Q16#433912yes—
403SD16—442no—
404SD16—881no—
405D8—21no—
406D8—21no—
407D8—221no—
408D8—221no—
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—41no—
420C4⋊C4—111no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C22⋊C4—41no—
428C22⋊C4—111no—
429C22⋊C4—111no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C42—41no—
438C42—441no—
439C42D4×D1111yescharacteristic
440C16—21no—
441C16—21no—
442C16—221no—
443C16—221no—
444C11#3386811yescharacteristic, complemented, Sylow
445C23—41no—
446C23—111no—
447C23—111no—
448C23—441no—
449Q8—22no—
450Q8—41no—
451Q8—441no—
452Q8—441no—
453Q8—882no—
454D4—41no—
455D4—41no—
456D4—222no—
457D4—441no—
458D4—441no—
459D4—882no—
460D4—882no—
461D4—882no—
462D4—1761no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—111no—
467C2×C4—111no—
468C2×C4—161no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—221no—
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—81no—
488C22—81no—
489C22—81no—
490C22—112no—
491C22—221no—
492C22—221no—
493C22—221no—
494C22—221no—
495C22—221no—
496C22—881no—
497C22—881no—
498C22—881no—
499C22C2×D8×D1111yescharacteristic
500C4—21no—
501C4—21no—
502C4—42no—
503C4—81no—
504C4—81no—
505C4—221no—
506C4—221no—
507C4—881no—
508C4—881no—
509C4—881no—
510C4#1062308111yescharacteristic
511C4#1062330111yescharacteristic
512C2—161no—
513C2—222no—
514C2—441no—
515C2—1761no—
516C2#1308043111yescharacteristic
517C2D11×#50811yescharacteristic
518C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
hypercenterC4×SD32D11
hypocenterC11#33868
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #13081020C2semidirect
2. #13080358C2semidirect
3. #13070848C2semidirect
4. #13070827C2semidirect
5. #13070803C2semidirect
6. #13070780C2semidirect
7. #13070711C2semidirect
8. #13070701C2semidirect
9. #13070671C2semidirect
10. #13070538C2semidirect
11. #13070531C2semidirect
12. C16×D44C2semidirect
13. #13070322C2semidirect
14. D11×#358C2semidirect
15. C4×C11×SD32C2semidirect
197. C4×SD32D11semidirect
444. C11#33868semidirect

Maximal subgroups

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

subgroupindex
#130810202
#130803582
#130708482
#130708272
#130708032
#130707802
#130707112
#130707012
#130706712
#130705382
#130705312
C16×D442
#130703222
D11×#3582
C4×C11×SD322
#3386811