Finite Group Databasebeta

← #14908846

Subgroups — #14908846

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic, complemented
2C4×#66972C211yesmaximal, characteristic, complemented
3#13070810C211yesmaximal, characteristic, complemented
4#13070806C211yesmaximal, characteristic, complemented
5#13070756C211yesmaximal, characteristic, complemented
6#13070752C211yesmaximal, characteristic, complemented
7#13070654C211yesmaximal, characteristic, complemented
8#13070650C211yesmaximal, characteristic, complemented
9#13070542C211yesmaximal, characteristic, complemented
10#13070538C211yesmaximal, characteristic, complemented
11#13070493C211yesmaximal, characteristic, complemented
12#13070490C211yesmaximal, characteristic, complemented
13#13070478C211yesmaximal, characteristic, complemented
14#13070417C211yesmaximal, characteristic, complemented
15C11×#2175C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C4×#4343—21no—
18#10623079—21no—
19C2×C11×SD32C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21C4×C11×D8C2211yescharacteristic
22Q16×Dic11C2211yescharacteristic
23C2×#66892C2211yescharacteristic
24#10622770C2211yescharacteristic
25#10622764C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27C4×#4325—21no—
28C4×#4323—21no—
29C2×D176C2211yescharacteristic
30#10622496C2211yescharacteristic
31#10622493C2211yescharacteristic
32#10622487C2211yescharacteristic
33#10622485C2211yescharacteristic
34#10622417—21no—
35#10622401—21no—
36#10622388—21no—
37#10622373—21no—
38C4×D88C2211yescharacteristic
39C4×D88C2211yescharacteristic
40C4×C8×D11C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#346C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622143C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×#4343—21no—
60C2×#4339—41no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C4×Q8×C11—21no—
64C4×D4×C11—21no—
65Q8×Dic11—21no—
66C2×#4325—21no—
67#66993—21no—
68#66991—21no—
69C2×#4323—21no—
70C4×C22⋊D11—41no—
71#66972—22no—
72#66972—22no—
73C2×D88C2311yescharacteristic
74C2×D88C2311yescharacteristic
75C2×C8×D11D411yescharacteristic
76C2×C8×D11C2311yescharacteristic
77#66948—21no—
78#66946—21no—
79#66946—41no—
80#66945—21no—
81#66945—41no—
82#66941—21no—
83#66938—41no—
84#66937—41no—
85C4×D44—21no—
86C4×D44—21no—
87C4×D44—41no—
88C42×D11—41no—
89C42×D11D411yescharacteristic
90C11×SD32—22no—
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#103—21no—
96C11×#102—21no—
97C4×C8×C11C2311yescharacteristic
98#66899—21no—
99#66896—21no—
100#66892—22no—
101#66890—22no—
102#66885—21no—
103#66885—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106C8×Dic11D411yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66873—21no—
111#66873—21no—
112#66872—21no—
113#66871—21no—
114C4×C11⋊C8D411yescharacteristic
115D176—22no—
116#33675—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C22×C4×C11—41no—
120C2×C22⋊D11—41no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123#4343—24no—
124#4343—42no—
125#4339—84no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—41no—
129C2×D44—41no—
130C2×C4×D11—41no—
131C2×C4×D11—41no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11D811yescharacteristic
135C2×C4×D11D811yescharacteristic
136C2×C4×D11C2×D411yescharacteristic
137C2×Dic22—41no—
138C11×Q16—21no—
139C11×Q16#4112yescomplemented
140C11×D8—21no—
141C11×D8—21no—
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2411yescharacteristic
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—41no—
147C11×C22⋊C4—41no—
148C42×C11—41no—
149C42×C11C2×D411yescharacteristic
150C22⋊Dic11—41no—
151#4325—24no—
152#4323—42no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11D811yescharacteristic
165C4×Dic11D811yescharacteristic
166C4×Dic11C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169D88—21no—
170D88—21no—
171D88—21no—
172D88#4112yescomplemented
173C8×D11—21no—
174C8×D11—21no—
175C8×D11—41no—
176C11×C16—21no—
177C11×C16—21no—
178C11⋊C16—21no—
179C11⋊C16—21no—
180#3169—111no—
181C4×#135—111no—
182#2234—111no—
183#2234—111no—
184#2225—111no—
185#2224—111no—
186#2207—111no—
187#2206—111no—
188#2186—111no—
189#2186—111no—
190#2177—111no—
191#2177—111no—
192#2175—111no—
193#2175D1111yescharacteristic, complemented
194#2163—111no—
195C23×C11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11C2×D811yescharacteristic
199Q8×C11—22no—
200Q8×C11—41no—
201D4×C11—41no—
202D4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—82no—
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C22⋊D11—82no—
211C22⋊D11—82no—
212C22⋊D11—82no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218D44—22no—
219D44—44no—
220D44—41no—
221D44—41no—
222D44—41no—
223D44—82no—
224C4×D11—21no—
225C4×D11—21no—
226C4×D11—22no—
227C4×D11—41no—
228C4×D11—44no—
229C4×D11—82no—
230C4×D11—82no—
231C4×D11—82no—
232Dic22—82no—
233C8×C11—21no—
234C8×C11C2×#4111yescharacteristic
235C8×C11C2×#4111yescharacteristic
236C11⋊C8—21no—
237C11⋊C8—21no—
238C2×#135—111no—
239#532—221no—
240C4×#41—221no—
241C2×SD32—111no—
242C2×SD32C2×D1111yescharacteristic
243C2×D16—111no—
244C2×D16—111no—
245#500—111no—
246#493—111no—
247#486—221no—
248#466—111no—
249#466—111no—
250#466—221no—
251C4×Q16—111no—
252C4×Q16C2×D1111yescharacteristic
253C4×SD16—221no—
254C4×SD16—221no—
255C4×D8—111no—
256C4×D8—111no—
257C4×D8—111no—
258C4×D8—221no—
259C4×D8C2×D1111yescharacteristic
260#427—111no—
261#416—221no—
262C2×C4×C8—111no—
263#367—111no—
264#367—111no—
265#366—111no—
266#366C2×D1111yescharacteristic
267C4⋊C16—111no—
268C4⋊C16—111no—
269#358—111no—
270#358C2×D1111yescharacteristic
271#357—111no—
272#357—111no—
273#357—111no—
274#357—111no—
275#357—111no—
276#357C2×D1111yescharacteristic
277C22⋊C16—111no—
278C22⋊C16—111no—
279#346—111no—
280#346C2×D1111yescharacteristic
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11C22×D811yescharacteristic
285C2×D11—21no—
286C2×D11—21no—
287C2×D11—21no—
288C2×D11—42no—
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—81no—
292C2×D11—81no—
293C2×D11—81no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—42no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11#52511yescharacteristic
300C4×C11#57511yescharacteristic
301Dic11—21no—
302Dic11—21no—
303Dic11—81no—
304Dic11—81no—
305Dic11#50912yes—
306C2×#41—221no—
307C2×#41—441no—
308#135—222no—
309#135—222no—
310C2×Q16C22×D1111yescharacteristic
311C2×SD16—221no—
312C2×D8—111no—
313C2×D8—111no—
314C2×D8—221no—
315C2×D8C22×D1111yescharacteristic
316C22×C8—111no—
317C22×C8—111no—
318C4⋊Q8—221no—
319#127—221no—
320#124—441no—
321#121—221no—
322#121—221no—
323#121—441no—
324C4×Q8—21no—
325C4×Q8—221no—
326C4×D4—21no—
327C4×D4—221no—
328C4×D4—221no—
329C4×D4—221no—
330C4×D4—441no—
331C4×D4—441no—
332C4×D4—441no—
333#117—221no—
334#117—441no—
335C2×C42—111no—
336C2×C42—441no—
337SD32—22no—
338SD32—222no—
339D16—222no—
340D16—222no—
341C2×C16—111no—
342C2×C16—111no—
343C2×C16C22×D1111yescharacteristic
344C2×C16C22×D1111yescharacteristic
345#107—111no—
346#107—111no—
347#107—221no—
348#107C22×D1111yescharacteristic
349#107C22×D1111yescharacteristic
350#106—221no—
351#103—21no—
352#103—221no—
353#102—21no—
354#102—221no—
355#102—221no—
356#102—221no—
357#102—221no—
358#102—221no—
359C4×C8—111no—
360C4×C8—111no—
361C4×C8—111no—
362C4×C8C22×D1111yescharacteristic
363C2×C11—161no—
364C2×C11#310011yescharacteristic
365C2×C11C2×#50911yescharacteristic
366C2×C11#341411yescharacteristic
367D11—41no—
368D11—82no—
369D11—161no—
370#41—224no—
371#41—442no—
372#41—884no—
373C2×Q8—21no—
374C2×Q8—441no—
375C2×D4—21no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—441no—
379C2×D4—441no—
380C2×D4—441no—
381C2×D4—441no—
382C2×D4—441no—
383C22×C4—41no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391Q16—21no—
392Q16#433912yescomplemented
393SD16—224no—
394D8—21no—
395D8—21no—
396D8—112no—
397D8—221no—
398D8—221no—
399D8—221no—
400D8—442no—
401C2×C8—111no—
402C2×C8—111no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8—441no—
406C2×C8D4×D1111yescharacteristic
407C2×C8C23×D1111yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C22⋊C4—41no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—441no—
422C42—41no—
423C42—111no—
424C42—111no—
425C42—111no—
426C42—441no—
427C42—441no—
428C42D4×D1111yescharacteristic
429C16—21no—
430C16—21no—
431C16—221no—
432C16—221no—
433C11#3367511yescharacteristic, complemented, Sylow
434C23—41no—
435C23—111no—
436C23—441no—
437C23—441no—
438Q8—22no—
439Q8—41no—
440Q8—882no—
441D4—41no—
442D4—41no—
443D4—222no—
444D4—444no—
445D4—441no—
446D4—441no—
447D4—441no—
448D4—882no—
449D4—882no—
450D4—882no—
451D4—882no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—82no—
456C2×C4—111no—
457C2×C4—111no—
458C2×C4—111no—
459C2×C4—222no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—441no—
463C2×C4—444no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—882no—
467C2×C4—882no—
468C2×C4—882no—
469C2×C4D8×D1111yescharacteristic
470C2×C4D8×D1111yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C8—21no—
473C8—221no—
474C8—221no—
475C8C2×#433911yescharacteristic
476C8#41×D1111yescharacteristic
477C22—81no—
478C22—81no—
479C22—81no—
480C22—221no—
481C22—221no—
482C22—221no—
483C22—442no—
484C22—881no—
485C22—881no—
486C22—881no—
487C22—881no—
488C22—881no—
489C22C2×D8×D1111yescharacteristic
490C4—21no—
491C4—21no—
492C4—42no—
493C4—81no—
494C4—81no—
495C4—112no—
496C4—221no—
497C4—221no—
498C4—881no—
499C4—881no—
500C4#1062307811yescharacteristic
501C4#1062329911yescharacteristic
502C2—161no—
503C2—441no—
504C2—882no—
505C2—1761no—
506C2#1307861411yescharacteristic
507C2D11×#50911yescharacteristic
508C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2175C2
socleC22×C11C22×D8
hypercenter#2175D11
hypocenterC11#33675
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. #13079192C2semidirect
2. C4×#66972C2semidirect
3. #13070810C2semidirect
4. #13070806C2semidirect
5. #13070756C2semidirect
6. #13070752C2semidirect
7. #13070654C2semidirect
8. #13070650C2semidirect
9. #13070542C2semidirect
10. #13070538C2semidirect
11. #13070493C2semidirect
12. #13070490C2semidirect
13. #13070478C2semidirect
14. #13070417C2semidirect
15. C11×#2175C2semidirect
139. C11×Q16#41semidirect
172. D88#41semidirect
193. #2175D11semidirect
392. Q16#4339semidirect
433. C11#33675semidirect

Maximal subgroups

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

subgroupindex
#130791922
C4×#669722
#130708102
#130708062
#130707562
#130707522
#130706542
#130706502
#130705422
#130705382
#130704932
#130704902
#130704782
#130704172
C11×#21752
#3367511