Finite Group Databasebeta

← #14910772

Subgroups — #14910772

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#13080961C211yesmaximal, characteristic, complemented
2#13080354C211yesmaximal, characteristic, complemented
3#13070851C211yesmaximal, characteristic, complemented
4#13070820C211yesmaximal, characteristic, complemented
5#13070767C211yesmaximal, characteristic, complemented
6#13070730C211yesmaximal, characteristic, complemented
7#13070700C211yesmaximal, characteristic, complemented
8#13070670C211yesmaximal, characteristic, complemented
9#13070540C211yesmaximal, characteristic, complemented
10#13070535C211yesmaximal, characteristic, complemented
11#13070479C211yesmaximal, characteristic, complemented
12#13070438C211yesmaximal, characteristic, complemented
13#13070325C211yesmaximal, characteristic, complemented
14C2×#10622130C211yesmaximal, characteristic, complemented
15C11×#2232C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18#10623129—21no—
19#10623038—21no—
20C11×#466C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622768C2211yescharacteristic
23C2×#66890C2211yescharacteristic
24#10622728C2211yescharacteristic
25C8×C22⋊D11C2211yescharacteristic
26C22×C11⋊C16C2211yescharacteristic
27#10622653—21no—
28#10622580—21no—
29C2×#66864C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31C2×#66862C2211yescharacteristic
32#10622503—21no—
33#10622500C2211yescharacteristic
34#10622496C2211yescharacteristic
35#10622495—21no—
36D11×#107C2211yescharacteristic
37#10622487C2211yescharacteristic
38#10622486C2211yescharacteristic
39#10622485C2211yescharacteristic
40#10622396—21no—
41#10622380—21no—
42C11×#366C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46C11×C22⋊C16C2211yescharacteristic
47#10622200C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622140C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622129C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4341—21no—
60C2×#4339—41no—
61C22×Dic22—21no—
62C2×C11×D8C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#121—21no—
65C2×C11×C4⋊C4—21no—
66#66992—41no—
67#66989—21no—
68D4×Dic11—41no—
69C2×#4324—21no—
70C2×#4324—21no—
71#66983—21no—
72#66982—41no—
73C4×C22⋊D11D411yescharacteristic
74#66965—22no—
75#66965—41no—
76C2×Dic44—22no—
77C2×Dic44—21no—
78C2×Dic44—41no—
79C2×Dic44C2311yescharacteristic
80C2×Dic44C2311yescharacteristic
81C2×D88C2311yescharacteristic
82C2×C8×D11C2311yescharacteristic
83#66950—21no—
84#66949—41no—
85#66948—21no—
86#66947—41no—
87#66946—21no—
88C4⋊C4×D11—21no—
89#66941—21no—
90#66940—21no—
91#66938—41no—
92#66931—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107—21no—
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#102—21no—
100C22⋊(C11⋊C8)D411yescharacteristic
101#66890—41no—
102#66885—21no—
103(C2×D11)⋊C8D411yescharacteristic
104#66882C2311yescharacteristic
105Dic11⋊C8D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C2×C11⋊C16—41no—
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66874—21no—
111#66874—21no—
112#66873—21no—
113#66873—21no—
114#66871—21no—
115#66871—21no—
116#66864—22no—
117#66864—41no—
118#66862—41no—
119#33875—111nomaximal, Sylow
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11D811yescharacteristic
127C22×Dic11—41no—
128C22×Dic11—41no—
129#4341—42no—
130#4341—81no—
131#4339—84no—
132C2×D44—21no—
133C2×D44—41no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11C2×D411yescharacteristic
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—42no—
140C2×Dic22—41no—
141C2×Dic22—41no—
142C2×Dic22—81no—
143C11×D8—21no—
144C11×D8—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2411yescharacteristic
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—41no—
153C11×C22⋊C4—41no—
154C22⋊Dic11—41no—
155C22⋊Dic11—41no—
156C22⋊Dic11D811yescharacteristic
157#4324—42no—
158#4324—81no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4D811yescharacteristic
164C4⋊Dic11—21no—
165C4⋊Dic11—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4D811yescharacteristic
170C4×Dic11—41no—
171C4×Dic11C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174Dic44—21no—
175Dic44—21no—
176Dic44—21no—
177Dic44—42no—
178Dic44#4112yescomplemented
179D88—21no—
180D88—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#2232D1111yescharacteristic, complemented
192#2227—111no—
193#2220—111no—
194#2215—111no—
195#2210—111no—
196#2186—111no—
197#2185—111no—
198#2175—111no—
199#2168—111no—
200#2139—111no—
201C2×#358—111no—
202C23×C11—41no—
203C23×C11C2×D811yescharacteristic
204C22×D11—41no—
205C22×D11C2×D811yescharacteristic
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—82no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—82no—
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C22⋊D11—22no—
218C22⋊D11—82no—
219C22⋊D11—82no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—82no—
224C2×Dic11—82no—
225C2×Dic11C2×D811yescharacteristic
226C2×Dic11C2×D811yescharacteristic
227C2×Dic11C2×D811yescharacteristic
228D44—41no—
229D44—41no—
230D44—82no—
231C4×D11—21no—
232C4×D11—21no—
233C4×D11—82no—
234C4×D11—82no—
235Dic22—22no—
236Dic22—41no—
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×SD32—111no—
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#466C2×D1111yescharacteristic
264#464—221no—
265#452—221no—
266#448—221no—
267C4×Q16—111no—
268C4×D8—111no—
269C8×D4—111no—
270C2×#107—111no—
271C2×#107C2×D1111yescharacteristic
272#366—111no—
273#366C2×D1111yescharacteristic
274#366C2×D1111yescharacteristic
275C4⋊C16—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#358—111no—
280#358—111no—
281#358—111no—
282#357—111no—
283#357—111no—
284#357C2×D1111yescharacteristic
285#357C2×D1111yescharacteristic
286C22⋊C16—111no—
287C22⋊C16C2×D1111yescharacteristic
288#346—111no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11#50912yes—
295C22×C11C22×D811yescharacteristic
296C2×D11—21no—
297C2×D11—21no—
298C2×D11—21no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C4×C11—21no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11#54611yescharacteristic
307C4×C11#57711yescharacteristic
308Dic11—21no—
309Dic11—21no—
310Dic11—21no—
311Dic11—42no—
312Dic11—81no—
313Dic11—81no—
314C2×#41—221no—
315C2×#41—441no—
316C22×Q8—221no—
317#135—222no—
318#135—441no—
319C2×Q16—111no—
320C2×Q16—111no—
321C2×Q16—222no—
322C2×Q16—221no—
323C2×Q16—441no—
324C2×SD16—221no—
325C2×SD16—221no—
326C2×D8—111no—
327C2×D8C22×D1111yescharacteristic
328C22×C8—111no—
329C22×C8C22×D1111yescharacteristic
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—21no—
339#121—221no—
340#121—221no—
341#121—441no—
342C4×Q8—221no—
343C4×D4—111no—
344C4×D4—221no—
345C4×D4—441no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—221no—
348SD32—222no—
349SD32—441no—
350D16—441no—
351M32—441no—
352C2×C16—111no—
353C2×C16—111no—
354C2×C16—441no—
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357#107—21no—
358#107—111no—
359#107—221no—
360#107—221no—
361#107C22×D1111yescharacteristic
362#107C22×D1111yescharacteristic
363#107C22×D1111yescharacteristic
364C4⋊C8—111no—
365#103—221no—
366#103—221no—
367#102—21no—
368#102—221no—
369#102—221no—
370#102—221no—
371C22⋊C8—111no—
372C22⋊C8—111no—
373C4×C8—111no—
374C2×C11—22no—
375C2×C11—161no—
376C2×C11#329411yescharacteristic
377C2×C11C2×#50911yescharacteristic
378C2×C11#341711yescharacteristic
379D11—41no—
380D11—161no—
381#41—442no—
382#41—884no—
383#41—881no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—442no—
387C2×Q8—441no—
388C2×Q8—441no—
389C2×Q8—881no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—111no—
393C2×D4—221no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4—441no—
397C22×C4—41no—
398C22×C4—111no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4D4×D1111yescharacteristic
404Q16—112no—
405Q16—221no—
406Q16—221no—
407Q16—221no—
408Q16—442no—
409SD16—442no—
410SD16—881no—
411D8—21no—
412D8—21no—
413D8—221no—
414D8—221no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—111no—
418C2×C8—111no—
419C2×C8—221no—
420C2×C8—221no—
421C2×C8D4×D1111yescharacteristic
422C2×C8C23×D1111yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—111no—
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—111no—
443C42—441no—
444C16—21no—
445C16—21no—
446C16—221no—
447C16—221no—
448C11#3387511yescharacteristic, complemented, Sylow
449C23—41no—
450C23—111no—
451C23—441no—
452C23D8×D1111yescharacteristic
453Q8—222no—
454Q8—441no—
455Q8—441no—
456Q8—441no—
457Q8—882no—
458Q8—882no—
459D4—41no—
460D4—41no—
461D4—82no—
462D4—222no—
463D4—441no—
464D4—441no—
465D4—882no—
466D4—882no—
467D4—882no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—82no—
474C2×C4—111no—
475C2×C4—111no—
476C2×C4—111no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—882no—
483C2×C4—882no—
484C2×C4—882no—
485C2×C4—882no—
486C2×C4D8×D1111yescharacteristic
487C2×C4C2×D4×D1111yescharacteristic
488C8—21no—
489C8—221no—
490C8—221no—
491C8#41×D1111yescharacteristic
492C8#6704211yescharacteristic
493C22—21no—
494C22—21no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—221no—
499C22—221no—
500C22—221no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22#1062252412yes—
505C22C2×D8×D1111yescharacteristic
506C4—21no—
507C4—81no—
508C4—81no—
509C4—81no—
510C4—221no—
511C4—221no—
512C4—221no—
513C4—442no—
514C4—881no—
515C4—881no—
516C4#1062318511yescharacteristic
517C4#1062330911yescharacteristic
518C2—22no—
519C2—161no—
520C2—441no—
521C2—1761no—
522C2#1308042711yescharacteristic
523C2C2×#1062252411yescharacteristic
524C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2232C2
socleC22×C11C22×D8
hypercenter#2232D11
hypocenterC11#33875
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
1. #13080961C2semidirect
2. #13080354C2semidirect
3. #13070851C2semidirect
4. #13070820C2semidirect
5. #13070767C2semidirect
6. #13070730C2semidirect
7. #13070700C2semidirect
8. #13070670C2semidirect
9. #13070540C2semidirect
10. #13070535C2semidirect
11. #13070479C2semidirect
12. #13070438C2semidirect
13. #13070325C2semidirect
14. C2×#10622130C2semidirect
15. C11×#2232C2semidirect
178. Dic44#41semidirect
191. #2232D11semidirect
448. C11#33875semidirect

Maximal subgroups

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

subgroupindex
#130809612
#130803542
#130708512
#130708202
#130707672
#130707302
#130707002
#130706702
#130705402
#130705352
#130704792
#130704382
#130703252
C2×#106221302
C11×#22322
#3387511