Finite Group Databasebeta

← #14910650

Subgroups — #14910650

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080965C211yesmaximal, characteristic
2Q16×D44C211yesmaximal, characteristic, complemented
3#13070844C211yesmaximal, characteristic, complemented
4#13070815C212yesmaximal, complemented
5#13070758C211yesmaximal, characteristic, complemented
6#13070711C212yesmaximal, complemented
7#13070661C211yesmaximal, characteristic, complemented
8#13070531C212yesmaximal, complemented
9C16×D44C211yesmaximal, characteristic, complemented
10D11×#358C212yesmaximal, complemented
11C4×C11×SD32C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2212yes—
13Q8×D44—21no—
14#10623082—21no—
15C2×C11×SD32C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C4×C11×D8C2211yescharacteristic
18#10622770C2212yes—
19C2×#66891C2212yes—
20#10622644—21no—
21#10622620—21no—
22C2×C16×D11C2212yes—
23#10622500C2212yes—
24D11×#107C2212yes—
25#10622421—22no—
26#10622387—22no—
27#10622312C2211yescharacteristic
28C8×D44C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×#367C2211yescharacteristic
31C11×#358C2211yescharacteristic
32C11×#357C2211yescharacteristic
33C4×C11×C16C2211yescharacteristic
34#10622202C2212yes—
35(C2×D11)⋊C16C2212yes—
36#10622141C2212yes—
37#10622141C2212yes—
38#10622130C2212yes—
39#10622128C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×Q8×D11—22no—
42C2×#4339—41no—
43C2×C11×Q16C2311yescharacteristic
44C2×C11×D8C2311yescharacteristic
45C4×Q8×C11—21no—
46C4×D4×C11—21no—
47C2×#4326—22no—
48#66991—22no—
49#66977—41no—
50Q16×D11—24no—
51Q16×D11—42no—
52C2×Dic44—21no—
53C2×Dic44C2312yes—
54C2×C8×D11C2312yes—
55#66950—22no—
56#66950—42no—
57C4⋊C4×D11—22no—
58#66936—42no—
59C4×D44—41no—
60C4×D44D411yescharacteristic
61#66922—21no—
62#66922—21no—
63#66922—41no—
64C11×SD32—22no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2311yescharacteristic
67C11×#107C2311yescharacteristic
68C11×#107C2311yescharacteristic
69C11×#103—21no—
70C11×#102—21no—
71C4×C8×C11C2311yescharacteristic
72#66896—22no—
73#66891—42no—
74(C2×D11)⋊C8D412yes—
75#66882—21no—
76#66882C2312yes—
77C2×C11⋊C16C2312yes—
78#66874—22no—
79#66871—22no—
80C4⋊(C11⋊C8)D411yescharacteristic
81C16×D11—42no—
82#33865—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×D4×C11—21no—
85C22×C4×C11—41no—
86C2×C22⋊D11—42no—
87Q8×D11—44no—
88Q8×D11—82no—
89#4339—84no—
90C2×D44D811yescharacteristic
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×C4×D11C2×D412yes—
94C2×Dic22—22no—
95C2×Dic22—42no—
96C2×Dic22—41no—
97C11×Q16—21no—
98C11×Q16#4112yescomplemented
99C11×D8—21no—
100C11×D8—21no—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11C2×D411yescharacteristic
109C22⋊Dic11—42no—
110#4326—44no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4D812yes—
113C4⋊Dic11—22no—
114C4⋊Dic11—42no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11D811yescharacteristic
119Dic11⋊C4—42no—
120C2×C11⋊C8C2×D412yes—
121Dic44—22no—
122Dic44—22no—
123Dic44—81no—
124C8×D11—22no—
125C8×D11—22no—
126C11×C16—21no—
127C11×C16—21no—
128C11⋊C16—22no—
129#3334—111no—
130D4×Q16—111no—
131#2241—111no—
132#2235—112no—
133#2225—111no—
134#2217—112no—
135#2208—111no—
136#2185—112no—
137C4×SD32D1111yescharacteristic, complemented
138D4×C16—111no—
139C2×#358—112no—
140C23×C11—41no—
141C22×D11C2×D812yes—
142Q8×C11—22no—
143Q8×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—82no—
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C22⋊D11—84no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11C2×D812yes—
157D44SD3214yescomplemented
158C4×D11—22no—
159C4×D11—22no—
160C4×D11—84no—
161C4×D11—84no—
162Dic22—42no—
163Dic22—42no—
164Dic22—84no—
165Dic22—82no—
166C8×C11—21no—
167C8×C11C2×#4111yescharacteristic
168C8×C11H(5,𝔽2)11yescharacteristic
169C11⋊C8—22no—
170C22×Q16—112no—
171D4×Q8—221no—
172#547—221no—
173C2×SD32—112no—
174C2×SD32C2×D1111yescharacteristic
175C22×C16—112no—
176#500—111no—
177#494—111no—
178#480—222no—
179#474—221no—
180#467—112no—
181#466—112no—
182#462—221no—
183#451—222no—
184C4×Q16C2×D1111yescharacteristic
185C4×D8C2×D1111yescharacteristic
186C8×D4—111no—
187C2×#107—112no—
188#367—112no—
189#367C2×D1111yescharacteristic
190C4⋊C16—111no—
191#358—112no—
192#358—112no—
193#358—112no—
194#358—112no—
195#358C2×D1111yescharacteristic
196#357C2×D1111yescharacteristic
197C22⋊C16—112no—
198C4×C16C2×D1111yescharacteristic
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11C22×D811yescharacteristic
203C2×D11—22no—
204C2×D11—22no—
205C2×D11C2×SD3214yes—
206C4×C11—21no—
207C4×C11—42no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11C2×SD3212yes—
211C4×C11#54611yescharacteristic
212C4×C11#57711yescharacteristic
213Dic11—22no—
214Dic11—82no—
215Dic11—82no—
216C2×#41—441no—
217C22×Q8—222no—
218C2×Q16—112no—
219C2×Q16—222no—
220C2×Q16—224no—
221C2×Q16—221no—
222C2×Q16—442no—
223C2×Q16C22×D1111yescharacteristic
224C2×D8C22×D1111yescharacteristic
225C22×C8—112no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8—441no—
229#123—442no—
230C22⋊Q8—222no—
231C22⋊Q8—442no—
232C22⋊Q8—441no—
233#121—222no—
234C4×Q8—21no—
235C4×D4—21no—
236C4×D4—111no—
237C4×D4—441no—
238C2×C4⋊C4—222no—
239SD32—22no—
240SD32—442no—
241C2×C16—112no—
242C2×C16—442no—
243C2×C16C22×D1111yescharacteristic
244C2×C16C22×D1111yescharacteristic
245#107—112no—
246#107—222no—
247#107—221no—
248#107C22×D1111yescharacteristic
249#107C22×D1111yescharacteristic
250C4⋊C8—111no—
251#103—21no—
252#103—222no—
253#102—21no—
254#102—222no—
255C22⋊C8—112no—
256C4×C8C22×D1111yescharacteristic
257C2×C11—161no—
258C2×C11#329411yescharacteristic
259C2×C11C22×SD3211yescharacteristic
260C2×C11#341711yescharacteristic
261D11—24no—
262#41—884no—
263C2×Q8—21no—
264C2×Q8—222no—
265C2×Q8—442no—
266C2×Q8—444no—
267C2×Q8—441no—
268C2×Q8—882no—
269C2×D4—21no—
270C2×D4—111no—
271C2×D4—442no—
272C22×C4—41no—
273C22×C4—112no—
274C22×C4—442no—
275C22×C4—442no—
276Q16—21no—
277Q16—222no—
278Q16—222no—
279Q16—444no—
280Q16—881no—
281Q16#433912yescomplemented
282D8—21no—
283D8—21no—
284C2×C8—112no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8D4×D1111yescharacteristic
288C2×C8C23×D1111yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—111no—
293C4⋊C4—222no—
294C4⋊C4—442no—
295C4⋊C4—442no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C22⋊C4—41no—
300C22⋊C4—112no—
301C22⋊C4—442no—
302C22⋊C4—442no—
303C42—41no—
304C42D4×D1111yescharacteristic
305C16—21no—
306C16—21no—
307C16—222no—
308C11#3386511yescharacteristic, complemented, Sylow
309C23—41no—
310C23—112no—
311Q8—22no—
312Q8—41no—
313Q8—442no—
314Q8—442no—
315Q8—884no—
316Q8—882no—
317D4—41no—
318D4—41no—
319D4—114no—
320D4—884no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—82no—
325C2×C4—112no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—884no—
331C2×C4—884no—
332C2×C4D8×D1111yescharacteristic
333C2×C4D8×D1111yescharacteristic
334C2×C4C2×D4×D1111yescharacteristic
335C8—21no—
336C8—222no—
337C8C2×#433911yescharacteristic
338C8#6704211yescharacteristic
339C22—81no—
340C22—81no—
341C22—81no—
342C22—114no—
343C22—222no—
344C22—222no—
345C22C2×D8×D1111yescharacteristic
346C4—21no—
347C4—42no—
348C4—81no—
349C4—81no—
350C4—222no—
351C4—882no—
352C4—882no—
353C4D11×SD3212yes—
354C4#1062308111yescharacteristic
355C4#1062330111yescharacteristic
356C2—161no—
357C2—224no—
358C2#1308043111yescharacteristic
359C2C2×D11×SD3211yescharacteristic
360C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13080965C2
hypercenterC4×SD32D11
hypocenterC11#33865
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. Q16×D44C2semidirect
3. #13070844C2semidirect
4. #13070815C2semidirect
5. #13070758C2semidirect
6. #13070711C2semidirect
7. #13070661C2semidirect
8. #13070531C2semidirect
9. C16×D44C2semidirect
10. D11×#358C2semidirect
11. C4×C11×SD32C2semidirect
98. C11×Q16#41semidirect
137. C4×SD32D11semidirect
157. D44SD32semidirect
281. Q16#4339semidirect
308. C11#33865semidirect

Maximal subgroups

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

subgroupindex
#130809652
Q16×D442
#130708442
#130708152
#130707582
#130707112
#130706612
#130705312
C16×D442
D11×#3582
C4×C11×SD322
#3386511