Finite Group Databasebeta

← #14910779

Subgroups — #14910779

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080965C211yesmaximal, characteristic, complemented
2#13080358C211yesmaximal, characteristic, complemented
3#13070853C211yesmaximal, characteristic, complemented
4#13070820C211yesmaximal, characteristic, complemented
5#13070798C211yesmaximal, characteristic, complemented
6#13070768C211yesmaximal, characteristic, complemented
7#13070728C211yesmaximal, characteristic, complemented
8#13070701C211yesmaximal, characteristic, complemented
9#13070671C211yesmaximal, characteristic, complemented
10#13070538C211yesmaximal, characteristic, complemented
11#13070531C211yesmaximal, characteristic, complemented
12#13070443C211yesmaximal, characteristic, complemented
13#13070327C211yesmaximal, characteristic, complemented
14D11×#358C211yesmaximal, characteristic, complemented
15C11×#2175C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18#10623107—21no—
19#10623082—21no—
20C2×C11×SD32C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22C4×C11×D8C2211yescharacteristic
23#10622770C2211yescharacteristic
24#10622770C2211yescharacteristic
25C2×#66891C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27#10622641—21no—
28#10622620—21no—
29C2×#66862C2211yescharacteristic
30C2×C16×D11C2211yescharacteristic
31#10622500C2211yescharacteristic
32#10622496C2211yescharacteristic
33D11×#107C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622423—21no—
36#10622419—21no—
37#10622387—21no—
38#10622387—21no—
39#10622309C2211yescharacteristic
40C8×D44C2211yescharacteristic
41#10622295C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#346C2211yescharacteristic
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#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×#4343—21no—
60C2×Q8×D11—21no—
61C2×#4339—41no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C4×Q8×C11—21no—
65C4×D4×C11—21no—
66C2×#4326—21no—
67C2×#4325—21no—
68#66991—21no—
69#66991—21no—
70#66977—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—
84C4⋊C4×D11—21no—
85C4⋊C4×D11—21no—
86#66936—41no—
87#66936—41no—
88#66928—21no—
89#66928—41no—
90C4×D44—41no—
91C4×D44D411yescharacteristic
92#66922—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#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112#66874—21no—
113#66873—21no—
114#66871—21no—
115#66871—21no—
116C4⋊(C11⋊C8)D411yescharacteristic
117#66862—41no—
118C16×D11—41no—
119#33875—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—
129#4339—84no—
130C2×D44—21no—
131C2×D44—41no—
132C2×D44—41no—
133C2×D44D811yescharacteristic
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11C2×D411yescharacteristic
139C2×C4×D11C2×D411yescharacteristic
140C2×Dic22—21no—
141C2×Dic22—41no—
142C2×Dic22—41no—
143C11×Q16—21no—
144C11×Q16#4112yescomplemented
145C11×D8—21no—
146C11×D8—21no—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2411yescharacteristic
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—41no—
152C11×C22⋊C4—41no—
153C42×C11—41no—
154C42×C11C2×D411yescharacteristic
155C22⋊Dic11—41no—
156C22⋊Dic11—41no—
157#4326—42no—
158#4325—42no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4D811yescharacteristic
164(C2×D11)⋊C4D811yescharacteristic
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—41no—
168C4⋊Dic11—41no—
169C4⋊Dic11D811yescharacteristic
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174Dic44—21no—
175Dic44—21no—
176D88—21no—
177D88—21no—
178#4314—81no—
179C8×D11—21no—
180C8×D11—21no—
181C8×D11—21no—
182C8×D11—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3334—111no—
188#3285—111no—
189#2243—111no—
190#2236—111no—
191#2232—111no—
192#2227—111no—
193#2220—111no—
194#2215—111no—
195#2210—111no—
196#2186—111no—
197#2185—111no—
198#2175D1111yescharacteristic, complemented
199#2168—111no—
200#2139—111no—
201C2×#358—111no—
202C23×C11—41no—
203C22×D11—41no—
204C22×D11C2×D811yescharacteristic
205C22×D11C2×D811yescharacteristic
206Q8×C11—22no—
207Q8×C11—41no—
208D4×C11—41no—
209D4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—82no—
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C22⋊D11—82no—
218C22⋊D11—82no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224D44—22no—
225D44—41no—
226D44—41no—
227D44—82no—
228D44—82no—
229C4×D11—21no—
230C4×D11—21no—
231C4×D11—21no—
232C4×D11—21no—
233C4×D11—82no—
234C4×D11—82no—
235C4×D11—82no—
236C4×D11—82no—
237Dic22—41no—
238Dic22—41no—
239Dic22—82no—
240Dic22—82no—
241C8×C11—21no—
242C8×C11C2×#4111yescharacteristic
243C8×C11H(5,𝔽2)11yescharacteristic
244C11⋊C8—21no—
245C11⋊C8—21no—
246C2×#135—111no—
247C22×Q16—111no—
248#548—221no—
249#547—221no—
250C2×SD32—111no—
251C2×SD32C2×D1111yescharacteristic
252C2×D16—111no—
253C2×M32—111no—
254C22×C16—111no—
255#500—111no—
256#495—111no—
257#480—221no—
258#480—221no—
259#474—221no—
260#467—111no—
261#466—111no—
262#466—111no—
263#466—111no—
264#464—221no—
265#452—221no—
266#448—221no—
267C4×Q16C2×D1111yescharacteristic
268C4×D8C2×D1111yescharacteristic
269C8×D4—111no—
270C2×#107—111no—
271C2×#107—111no—
272#366—111no—
273#366—111no—
274#366C2×D1111yescharacteristic
275C4⋊C16—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#358—111no—
280#358—111no—
281#358C2×D1111yescharacteristic
282#357—111no—
283#357—111no—
284#357—111no—
285#357C2×D1111yescharacteristic
286C22⋊C16—111no—
287C22⋊C16—111no—
288#346C2×D1111yescharacteristic
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—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11#50912yes—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—42no—
305C4×C11—81no—
306C4×C11—81no—
307C4×C11#54611yescharacteristic
308C4×C11#57711yescharacteristic
309Dic11—21no—
310Dic11—21no—
311Dic11—81no—
312Dic11—81no—
313Dic11—81no—
314C2×#41—221no—
315C2×#41—441no—
316C22×Q8—221no—
317#135—222no—
318#135—441no—
319C2×Q16—111no—
320C2×Q16—221no—
321C2×Q16—222no—
322C2×Q16—441no—
323C2×Q16C22×D1111yescharacteristic
324C2×SD16—221no—
325C2×SD16—221no—
326C2×D8—111no—
327C2×D8C22×D1111yescharacteristic
328C22×C8—111no—
329C22×C8—111no—
330C4⋊Q8—221no—
331#124—221no—
332#124—441no—
333#123—441no—
334#123—441no—
335C22⋊Q8—221no—
336C22⋊Q8—441no—
337C22⋊Q8—441no—
338#121—221no—
339#121—221no—
340#121—221no—
341#121—441no—
342C4×Q8—21no—
343C4×D4—21no—
344C4×D4—111no—
345C4×D4—441no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348SD32—22no—
349SD32—441no—
350D16—441no—
351M32—441no—
352C2×C16—111no—
353C2×C16—111no—
354C2×C16—441no—
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357#107—111no—
358#107—111no—
359#107—221no—
360#107—221no—
361#107—221no—
362#107C22×D1111yescharacteristic
363#107C22×D1111yescharacteristic
364C4⋊C8—111no—
365#103—21no—
366#103—221no—
367#102—21no—
368#102—221no—
369#102—221no—
370#102—221no—
371C22⋊C8—111no—
372C22⋊C8—111no—
373C4×C8C22×D1111yescharacteristic
374C2×C11—161no—
375C2×C11#329411yescharacteristic
376C2×C11C2×#50911yescharacteristic
377C2×C11#341711yescharacteristic
378D11—22no—
379D11—41no—
380D11—161no—
381#41—442no—
382#41—884no—
383#41—881no—
384C2×Q8—21no—
385C2×Q8—221no—
386C2×Q8—441no—
387C2×Q8—442no—
388C2×Q8—441no—
389C2×Q8—881no—
390C2×D4—21no—
391C2×D4—111no—
392C2×D4—221no—
393C2×D4—441no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4—441no—
397C22×C4—41no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—441no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4—441no—
404Q16—21no—
405Q16—221no—
406Q16—221no—
407Q16—442no—
408Q16#433912yescomplemented
409SD16—442no—
410SD16—881no—
411D8—21no—
412D8—21no—
413D8—221no—
414D8—221no—
415C2×C8—111no—
416C2×C8—111no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—221no—
420C2×C8—221no—
421C2×C8D4×D1111yescharacteristic
422C2×C8C23×D1111yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—41no—
426C4⋊C4—111no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C22⋊C4—41no—
434C22⋊C4—111no—
435C22⋊C4—111no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C22⋊C4—441no—
442C42—41no—
443C42D4×D1111yescharacteristic
444C16—21no—
445C16—21no—
446C16—221no—
447C16—221no—
448C11#3387511yescharacteristic, complemented, Sylow
449C23—41no—
450C23—111no—
451C23—111no—
452C23—441no—
453Q8—22no—
454Q8—41no—
455Q8—441no—
456Q8—441no—
457Q8—882no—
458Q8—882no—
459D4—41no—
460D4—41no—
461D4—222no—
462D4—441no—
463D4—441no—
464D4—882no—
465D4—882no—
466D4—882no—
467D4—882no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—111no—
473C2×C4—111no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—882no—
482C2×C4—882no—
483C2×C4—882no—
484C2×C4—882no—
485C2×C4D8×D1111yescharacteristic
486C2×C4D8×D1111yescharacteristic
487C2×C4C2×D4×D1111yescharacteristic
488C8—21no—
489C8—221no—
490C8—221no—
491C8C2×#433911yescharacteristic
492C8#6704211yescharacteristic
493C22—81no—
494C22—81no—
495C22—81no—
496C22—112no—
497C22—221no—
498C22—221no—
499C22—221no—
500C22—221no—
501C22—221no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22C2×D8×D1111yescharacteristic
506C4—21no—
507C4—21no—
508C4—42no—
509C4—81no—
510C4—81no—
511C4—221no—
512C4—221no—
513C4—881no—
514C4—881no—
515C4—881no—
516C4#1062308111yescharacteristic
517C4#1062330111yescharacteristic
518C2—161no—
519C2—222no—
520C2—441no—
521C2—1761no—
522C2#1308043111yescharacteristic
523C2D11×#50911yescharacteristic
524C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2175C2
socleC22×C11C22×D8
hypercenter#2175D11
hypocenterC11#33875
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. #13080965C2semidirect
2. #13080358C2semidirect
3. #13070853C2semidirect
4. #13070820C2semidirect
5. #13070798C2semidirect
6. #13070768C2semidirect
7. #13070728C2semidirect
8. #13070701C2semidirect
9. #13070671C2semidirect
10. #13070538C2semidirect
11. #13070531C2semidirect
12. #13070443C2semidirect
13. #13070327C2semidirect
14. D11×#358C2semidirect
15. C11×#2175C2semidirect
144. C11×Q16#41semidirect
198. #2175D11semidirect
408. Q16#4339semidirect
448. C11#33875semidirect

Maximal subgroups

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

subgroupindex
#130809652
#130803582
#130708532
#130708202
#130707982
#130707682
#130707282
#130707012
#130706712
#130705382
#130705312
#130704432
#130703272
D11×#3582
C11×#21752
#3387511