Finite Group Databasebeta

← #14910889

Subgroups — #14910889

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081005C211yesmaximal, characteristic, complemented
2#13080360C211yesmaximal, characteristic
3#13070854C211yesmaximal, characteristic, complemented
4#13070811C211yesmaximal, characteristic, complemented
5#13070803C211yesmaximal, characteristic, complemented
6#13070757C211yesmaximal, characteristic, complemented
7#13070715C211yesmaximal, characteristic, complemented
8#13070680C211yesmaximal, characteristic, complemented
9#13070554C211yesmaximal, characteristic, complemented
10#13070548C211yesmaximal, characteristic, complemented
11#13070484C211yesmaximal, characteristic, complemented
12#13070439C211yesmaximal, characteristic, complemented
13#13070329C211yesmaximal, characteristic, complemented
14D11×#358C211yesmaximal, characteristic, complemented
15C11×#2219C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18#10623166—21no—
19#10623164—21no—
20C2×C11×Q32C2211yescharacteristic
21C2×C11×M32C2211yescharacteristic
22C11×#467C2211yescharacteristic
23C11×#467C2211yescharacteristic
24#10622804C2211yescharacteristic
25#10622801C2211yescharacteristic
26Q16×Dic11C2211yescharacteristic
27C2×#66893C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C8×C22⋊D11C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31#10622660—21no—
32#10622657—21no—
33C2×C16×D11C2211yescharacteristic
34#10622496C2211yescharacteristic
35D11×#107C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622422—21no—
39#10622419—21no—
40#10622411—21no—
41#10622407—21no—
42C11×#367C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622140C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×#4339—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66#67000—21no—
67#66999—21no—
68Q8×Dic11—21no—
69C2×#4326—21no—
70C2×#4325—21no—
71C4×C22⋊D11D411yescharacteristic
72C2×C4⋊Dic11—21no—
73Q16×D11—22no—
74Q16×D11—41no—
75C2×Dic44C2311yescharacteristic
76#66957—22no—
77#66957—41no—
78C2×D88C2311yescharacteristic
79C2×#4314—21no—
80C2×C8×D11C2311yescharacteristic
81#66950—41no—
82#66949—41no—
83#66948—21no—
84#66946—41no—
85C4⋊C4×D11—21no—
86#66942—41no—
87#66941—21no—
88#66940—21no—
89#66938—41no—
90#66937—41no—
91(C22⋊D11)⋊C4—41no—
92#66931—41no—
93C11×Q32—41no—
94C11×M32—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#103—21no—
100C11×#103—21no—
101#66899—21no—
102#66899—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66893—22no—
105#66892—41no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110Dic11⋊C8D411yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66874—21no—
115#66873—21no—
116#66871—21no—
117#66871—21no—
118C16×D11—41no—
119#33883—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C22×C4×C11C2×D411yescharacteristic
123C2×C22⋊D11—41no—
124C2×C22⋊D11D811yescharacteristic
125C22×Dic11—41no—
126Q8×D11—42no—
127Q8×D11—81no—
128#4339—42no—
129#4339—81no—
130C2×D44—21no—
131C2×D44—41no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11C2×D411yescharacteristic
136C2×Dic22—21no—
137C2×Dic22—41no—
138C2×Dic22—41no—
139C11×Q16—21no—
140C11×Q16—21no—
141C11×Q16—21no—
142C11×Q16—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C22⋊Dic11D811yescharacteristic
154#4326—42no—
155#4325—81no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4D811yescharacteristic
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4D811yescharacteristic
170C4×Dic11—41no—
171C4×Dic11—41no—
172C4×Dic11C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175Dic44—21no—
176Dic44#4112yes—
177D88—21no—
178D88—21no—
179#4314—42no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3338—111no—
187#3285—111no—
188#2243—111no—
189#2235—111no—
190#2233—111no—
191#2225—111no—
192#2219D1111yescharacteristic, complemented
193#2217—111no—
194#2211—111no—
195#2189—111no—
196#2188—111no—
197#2176—111no—
198#2168—111no—
199#2139—111no—
200C2×#358—111no—
201C23×C11C2×D811yescharacteristic
202C22×D11—41no—
203C22×D11C2×D811yescharacteristic
204Q8×C11—41no—
205Q8×C11—41no—
206Q8×C11—41no—
207Q8×C11—41no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C22⋊D11—22no—
217C22⋊D11—82no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—161no—
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225D44—41no—
226D44—41no—
227D44—82no—
228C4×D11—21no—
229C4×D11—21no—
230C4×D11—82no—
231C4×D11—82no—
232C4×D11—161no—
233Dic22—22no—
234Dic22—41no—
235Dic22—82no—
236Dic22—161no—
237C8×C11—21no—
238C8×C11C2×#4111yescharacteristic
239C8×C11H(5,𝔽2)11yescharacteristic
240C11⋊C8—21no—
241C11⋊C8—21no—
242C2×#135—111no—
243C22×Q16—111no—
244#554—221no—
245#548—221no—
246C2×Q32—111no—
247C2×Q32C2×D1111yescharacteristic
248C2×SD32—111no—
249C2×M32C2×D1111yescharacteristic
250C22×C16—111no—
251#500—111no—
252#495—111no—
253#484—221no—
254#484—221no—
255#477—221no—
256#467—111no—
257#467C2×D1111yescharacteristic
258#467C2×D1111yescharacteristic
259#466—111no—
260#464—221no—
261#452—221no—
262#448—221no—
263C4×Q16—111no—
264C4×Q16—111no—
265C8×D4—111no—
266C2×#107—111no—
267C2×#107—111no—
268#367—111no—
269#367—111no—
270#367C2×D1111yescharacteristic
271C4⋊C16—111no—
272#358—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#358C2×D1111yescharacteristic
278#358C2×D1111yescharacteristic
279#357—111no—
280#357—111no—
281#357—111no—
282C22⋊C16—111no—
283C22⋊C16—111no—
284#346—111no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11C22×D811yescharacteristic
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—81no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11#51012yes—
295C4×C11—21no—
296C4×C11—81no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11—81no—
300C4×C11#54611yescharacteristic
301C4×C11#57711yescharacteristic
302Dic11—21no—
303Dic11—21no—
304Dic11—21no—
305Dic11—42no—
306Dic11—81no—
307Dic11—81no—
308C2×#41—221no—
309C22×Q8—221no—
310#135—222no—
311#135—441no—
312C2×Q16—111no—
313C2×Q16—221no—
314C2×Q16—222no—
315C2×Q16—441no—
316C2×Q16C22×D1111yescharacteristic
317C2×Q16C22×D1111yescharacteristic
318C2×SD16—221no—
319C2×SD16—221no—
320C2×D8—111no—
321C22×C8—111no—
322C22×C8C22×D1111yescharacteristic
323C4⋊Q8—221no—
324#125—441no—
325#124—221no—
326#124—441no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—221no—
330C22⋊Q8—441no—
331C22⋊Q8—441no—
332C22⋊Q8—441no—
333#121—221no—
334#121—441no—
335C4×Q8—221no—
336C4×Q8—221no—
337C4×D4—111no—
338C4×D4—441no—
339C4×D4—441no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342Q32—41no—
343Q32—222no—
344SD32—441no—
345M32—41no—
346C2×C16—111no—
347C2×C16—111no—
348C2×C16—441no—
349C2×C16C22×D1111yescharacteristic
350C2×C16C22×D1111yescharacteristic
351#107—111no—
352#107—111no—
353#107—221no—
354#107—221no—
355#107—221no—
356#107C22×D1111yescharacteristic
357#107C22×D1111yescharacteristic
358C4⋊C8—111no—
359#103—21no—
360#103—21no—
361#103—221no—
362#103—221no—
363#103—221no—
364#102—221no—
365C22⋊C8—111no—
366C22⋊C8—111no—
367C4×C8—111no—
368C2×C11—41no—
369C2×C11#329411yescharacteristic
370C2×C11C2×#51011yescharacteristic
371C2×C11#341611yescharacteristic
372D11—22no—
373D11—161no—
374#41—442no—
375#41—881no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—221no—
379C2×Q8—441no—
380C2×Q8—441no—
381C2×Q8—442no—
382C2×Q8—881no—
383C2×D4—111no—
384C2×D4—221no—
385C2×D4—441no—
386C2×D4—441no—
387C22×C4—111no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4D4×D1111yescharacteristic
393Q16—21no—
394Q16—21no—
395Q16—21no—
396Q16—21no—
397Q16—112no—
398Q16—221no—
399Q16—442no—
400SD16—442no—
401SD16—881no—
402D8—221no—
403D8—221no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—111no—
407C2×C8—111no—
408C2×C8—221no—
409C2×C8—221no—
410C2×C8D4×D1111yescharacteristic
411C2×C8C23×D1111yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—111no—
417C4⋊C4—221no—
418C4⋊C4—221no—
419C4⋊C4—441no—
420C4⋊C4—441no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—111no—
428C22⋊C4—111no—
429C22⋊C4—441no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C42—111no—
434C42—441no—
435C42—441no—
436C16—21no—
437C16—21no—
438C16—221no—
439C16—221no—
440C11#3388311yescharacteristic, complemented, Sylow
441C23—111no—
442C23—441no—
443C23D8×D1111yescharacteristic
444Q8—41no—
445Q8—41no—
446Q8—41no—
447Q8—41no—
448Q8—222no—
449Q8—441no—
450Q8—882no—
451Q8—1761no—
452D4—222no—
453D4—441no—
454D4—441no—
455D4—882no—
456D4—882no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—111no—
464C2×C4—111no—
465C2×C4—111no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—882no—
472C2×C4—882no—
473C2×C4—1761no—
474C2×C4—1761no—
475C2×C4D8×D1111yescharacteristic
476C2×C4C2×D4×D1111yescharacteristic
477C8—21no—
478C8—221no—
479C8—221no—
480C8#6703711yescharacteristic
481C8#41×D1111yescharacteristic
482C22—21no—
483C22—21no—
484C22—21no—
485C22—112no—
486C22—221no—
487C22—221no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22C2×D8×D1111yescharacteristic
492C4—21no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—221no—
498C4—221no—
499C4—221no—
500C4—442no—
501C4—881no—
502C4—881no—
503C4#1062314111yescharacteristic
504C4#1062330111yescharacteristic
505C2—41no—
506C2—222no—
507C2—1761no—
508C2#1308042411yescharacteristic
509C2D11×#51011yescharacteristic
510C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2219C2
socleC22×C11C22×D8
prime radical#13080360C2
hypercenter#2219D11
hypocenterC11#33883
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
1. #13081005C2semidirect
3. #13070854C2semidirect
4. #13070811C2semidirect
5. #13070803C2semidirect
6. #13070757C2semidirect
7. #13070715C2semidirect
8. #13070680C2semidirect
9. #13070554C2semidirect
10. #13070548C2semidirect
11. #13070484C2semidirect
12. #13070439C2semidirect
13. #13070329C2semidirect
14. D11×#358C2semidirect
15. C11×#2219C2semidirect
192. #2219D11semidirect
440. C11#33883semidirect

Maximal subgroups

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

subgroupindex
#130810052
#130803602
#130708542
#130708112
#130708032
#130707572
#130707152
#130706802
#130705542
#130705482
#130704842
#130704392
#130703292
D11×#3582
C11×#22192
#3388311