Finite Group Databasebeta

← #14910179

Subgroups — #14910179

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079275C211yesmaximal, characteristic, complemented
2#13079255C211yesmaximal, characteristic
3#13070781C211yesmaximal, characteristic, complemented
4#13070774C211yesmaximal, characteristic, complemented
5#13070769C211yesmaximal, characteristic, complemented
6#13070759C211yesmaximal, characteristic, complemented
7#13070729C211yesmaximal, characteristic
8#13070724C211yesmaximal, characteristic, complemented
9#13070712C211yesmaximal, characteristic
10#13070707C211yesmaximal, characteristic, complemented
11#13070679C211yesmaximal, characteristic, complemented
12#13070679C211yesmaximal, characteristic, complemented
13#13070667C211yesmaximal, characteristic, complemented
14#13070662C211yesmaximal, characteristic, complemented
15C11×#2151C211yesmaximal, characteristic, complemented
16#10623065—21no—
17#10623049—21no—
18C2×C11×M32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C11×#405C2211yescharacteristic
21#10622750—21no—
22#10622747—21no—
23#10622729C2211yescharacteristic
24#10622729C2211yescharacteristic
25#10622729C2211yescharacteristic
26#10622728C2211yescharacteristic
27C2×Dic88C2211yescharacteristic
28C2×Dic88C2211yescharacteristic
29C2×#66864C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31#10622329—21no—
32#10622327—21no—
33#10622323—21no—
34#10622316—21no—
35#10622312C2211yescharacteristic
36C4×Dic44C2211yescharacteristic
37C4×Dic44C2211yescharacteristic
38C4×Dic44C2211yescharacteristic
39#10622309C2211yescharacteristic
40C4×D88C2211yescharacteristic
41#10622296C2211yescharacteristic
42#10622295C2211yescharacteristic
43C11×C4⋊C16C2211yescharacteristic
44C11×C4⋊C16C2211yescharacteristic
45C11×C4⋊C16C2211yescharacteristic
46C11×C4⋊C16C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×C11×M16D411yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#117D411yescharacteristic
62#66983—21no—
63#66977—21no—
64#66977—21no—
65#66977—21no—
66C2×Dic44—21no—
67C2×Dic44C2311yescharacteristic
68C2×Dic44C2311yescharacteristic
69C2×Dic44C2311yescharacteristic
70C2×D88C2311yescharacteristic
71C2×#4314—21no—
72#66951—41no—
73#66949—41no—
74#66942—41no—
75#66942—41no—
76#66938—41no—
77#66936—41no—
78#66932—41no—
79#66932—41no—
80#66928—21no—
81C4×D44—21no—
82#66923—21no—
83#66922—21no—
84#66922—21no—
85C4×Dic22—21no—
86C4×Dic22—21no—
87C4×Dic22—21no—
88C11×M32—41no—
89C2×C11×C16—41no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#97D411yescharacteristic
95C11×#97D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97C4×C8×C11C2311yescharacteristic
98#66885—21no—
99#66885—21no—
100#66882—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106#66880—21no—
107#66880—21no—
108#66880—21no—
109#66880—21no—
110#66880—21no—
111#66880—21no—
112Dic88—41no—
113Dic88—41no—
114#66864—41no—
115#66864—41no—
116#33824—111nomaximal, Sylow
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—41no—
119C2×D44—21no—
120C2×C4×D11—41no—
121C2×Dic22—21no—
122C2×Dic22—21no—
123C2×Dic22—21no—
124C2×Dic22—41no—
125C11×M16—41no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4D811yescharacteristic
133C11×C4⋊C4D811yescharacteristic
134C11×C22⋊C4D811yescharacteristic
135C11×C22⋊C4D811yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163Dic44—21no—
164Dic44—21no—
165Dic44—21no—
166Dic44—21no—
167Dic44—21no—
168Dic44—21no—
169Dic44—42no—
170D88—21no—
171D88—21no—
172#4314—42no—
173C11×C16—21no—
174C11×C16—21no—
175C11×C16—21no—
176C11×C16—21no—
177#3177—111no—
178#3175—111no—
179#2229—111no—
180#2228—111no—
181#2227—111no—
182#2225—111no—
183#2220—111no—
184#2219—111no—
185#2217—111no—
186#2216—111no—
187#2211—111no—
188#2211—111no—
189#2209—111no—
190#2208—111no—
191#2151D1111yescharacteristic, complemented
192C23×C11C2×D811yescharacteristic
193C22×D11—41no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C22⋊D11—161no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210D44—41no—
211D44—41no—
212C4×D11—161no—
213Dic22—41no—
214Dic22—41no—
215Dic22—41no—
216Dic22—41no—
217Dic22—41no—
218Dic22—41no—
219Dic22—161no—
220C8×C11—21no—
221C8×C11—21no—
222C8×C11—21no—
223C8×C11H(5,𝔽2)11yescharacteristic
224C8×C112−1+411yescharacteristic
225#542—221no—
226#541—221no—
227C2×Q32—111no—
228C2×Q32—111no—
229C2×SD32—111no—
230C2×SD32—111no—
231C2×M32C2×D1111yescharacteristic
232C22×C16C2×D1111yescharacteristic
233#500—111no—
234#499—111no—
235#495—111no—
236#494—111no—
237#491—221no—
238#489—221no—
239#470—221no—
240#468—221no—
241#467—111no—
242#467—111no—
243#467—111no—
244#466—111no—
245#441—221no—
246#440—221no—
247C4×Q16—111no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×D8—111no—
251#405C2×D1111yescharacteristic
252#367—111no—
253#367—111no—
254#366—111no—
255#366—111no—
256C4⋊C16C2×D1111yescharacteristic
257C4⋊C16C2×D1111yescharacteristic
258C4⋊C16C2×D1111yescharacteristic
259C4⋊C16C2×D1111yescharacteristic
260#358—111no—
261#358—111no—
262#358—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#357—111no—
267#357—111no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11C22×D811yescharacteristic
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11#53711yescharacteristic
281C4×C11#57511yescharacteristic
282Dic11—81no—
283Dic11—81no—
284Dic11—81no—
285Dic11—81no—
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289C2×Q16—111no—
290C2×Q16—111no—
291C2×Q16—111no—
292C2×Q16—221no—
293C2×SD16—221no—
294C2×D8—111no—
295C2×M16D4411yescharacteristic
296C22×C8C22×D1111yescharacteristic
297C4⋊Q8—221no—
298C4⋊Q8—221no—
299#126—441no—
300#126—441no—
301#126—441no—
302#125—221no—
303#125—441no—
304#125—441no—
305#124—221no—
306#124—441no—
307#123—441no—
308C22⋊Q8—221no—
309C22⋊Q8—221no—
310C22⋊Q8—221no—
311C22⋊Q8—441no—
312#121—221no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×D4—221no—
317#117D4411yescharacteristic
318Q32—441no—
319Q32—441no—
320SD32—441no—
321SD32—441no—
322M32—41no—
323C2×C16—41no—
324C2×C16C22×D1111yescharacteristic
325C2×C16C22×D1111yescharacteristic
326C2×C16C22×D1111yescharacteristic
327C2×C16C22×D1111yescharacteristic
328#107—111no—
329#107—111no—
330#107—111no—
331#107—111no—
332#107—221no—
333#106—221no—
334#103—221no—
335#103—221no—
336#103—221no—
337#103—221no—
338#103—221no—
339#103—221no—
340#102—221no—
341#102—221no—
342#97D4411yescharacteristic
343#97D4411yescharacteristic
344C4×C8C22×D1111yescharacteristic
345C4×C8C22×D1111yescharacteristic
346C2×C11—41no—
347C2×C11#324511yescharacteristic
348C2×C11#341611yescharacteristic
349C2×C11#341711yescharacteristic
350D11—161no—
351C2×Q8—221no—
352C2×Q8—221no—
353C2×Q8—221no—
354C2×Q8—441no—
355C2×D4—221no—
356C2×D4—441no—
357C22×C4—441no—
358C22×C4C2×D4411yescharacteristic
359Q16—221no—
360Q16—221no—
361Q16—221no—
362Q16—221no—
363Q16—221no—
364Q16—221no—
365Q16—442no—
366SD16—442no—
367D8—221no—
368D8—221no—
369M16—41no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8C2×D4411yescharacteristic
373C2×C8C2×D4411yescharacteristic
374C2×C8C2×D4411yescharacteristic
375C2×C8C23×D1111yescharacteristic
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4D8811yescharacteristic
392C4⋊C4D8811yescharacteristic
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4D8811yescharacteristic
401C22⋊C4D8811yescharacteristic
402C42—441no—
403C42—441no—
404C42—441no—
405C42C2×D4411yescharacteristic
406C42C2×D4411yescharacteristic
407C16—21no—
408C16—21no—
409C16—21no—
410C16—21no—
411C11#3382411yescharacteristic, complemented, Sylow
412C23—441no—
413C23C2×D8811yescharacteristic
414Q8—441no—
415Q8—441no—
416Q8—441no—
417Q8—441no—
418Q8—441no—
419Q8—441no—
420Q8—1761no—
421D4—441no—
422D4—441no—
423D4—1761no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—1761no—
434C2×C4C2×D8811yescharacteristic
435C2×C4C2×D8811yescharacteristic
436C2×C4C2×D8811yescharacteristic
437C2×C4C2×D8811yescharacteristic
438C2×C4C2×D8811yescharacteristic
439C2×C4C22×D4411yescharacteristic
440C8—21no—
441C8—21no—
442C8—21no—
443C8#6703711yescharacteristic
444C8#6704011yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—881no—
449C22—881no—
450C22—881no—
451C22C22×D8811yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—881no—
458C4—881no—
459C4—881no—
460C4—881no—
461C4—881no—
462C4—881no—
463C4—881no—
464C4#1062304111yescharacteristic
465C4#1062327911yescharacteristic
466C2—41no—
467C2—1761no—
468C2#1307992611yescharacteristic
469C2#1308176411yescharacteristic
470C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2151C2
socleC22×C11C22×D8
prime radical#10622728C22
hypercenter#2151D11
hypocenterC11#33824
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2151

Complements

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

NH ≅ G/Ntype
1. #13079275C2semidirect
3. #13070781C2semidirect
4. #13070774C2semidirect
5. #13070769C2semidirect
6. #13070759C2semidirect
8. #13070724C2semidirect
10. #13070707C2semidirect
11. #13070679C2semidirect
12. #13070679C2semidirect
13. #13070667C2semidirect
14. #13070662C2semidirect
15. C11×#2151C2semidirect
191. #2151D11semidirect
411. C11#33824semidirect

Maximal subgroups

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

subgroupindex
#130792752
#130792552
#130707812
#130707742
#130707692
#130707592
#130707292
#130707242
#130707122
#130707072
#130706792
#130706672
#130706622
C11×#21512
#3382411