Finite Group Databasebeta

← #14911380

Subgroups — #14911380

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081040C211yesmaximal, characteristic, complemented
2#13080965C211yesmaximal, characteristic, complemented
3#13070898C211yesmaximal, characteristic, complemented
4#13070806C212yesmaximal, complemented
5#13070800C212yesmaximal, complemented
6#13070763C211yesmaximal, characteristic, complemented
7#13070753C211yesmaximal, characteristic, complemented
8#13070716C212yesmaximal, complemented
9#13070449C211yesmaximal, characteristic, complemented
10#13070401C212yesmaximal, complemented
11C4×C11×D16C211yesmaximal, characteristic, complemented
12#10623094—21no—
13#10623082—21no—
14C2×C11×D16C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622770C2212yes—
18#10622770C2212yes—
19#10622621—21no—
20#10622620—21no—
21C2×#66862C2212yes—
22#10622493C2212yes—
23D11×#107C2212yes—
24#10622397—22no—
25#10622387—22no—
26C8×D44C2211yescharacteristic
27#10622295C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#366C2211yescharacteristic
30C11×#357C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622200C2212yes—
34#10622200C2212yes—
35(C2×D11)⋊C16C2212yes—
36#10622143C2212yes—
37#10622143C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4339—41no—
42C2×C11×D8C2311yescharacteristic
43C2×C11×D8C2311yescharacteristic
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46#66991—22no—
47#66991—22no—
48#66983—41no—
49#66979—41no—
50#66977—41no—
51C2×C8×D11C2312yes—
52#66945—22no—
53C4⋊C4×D11—22no—
54#66938—42no—
55#66936—42no—
56C4×D44D411yescharacteristic
57#66922—21no—
58#66922—21no—
59C11×D16—22no—
60C2×C11×C16C2311yescharacteristic
61C2×C11×C16C2311yescharacteristic
62C11×#107C2311yescharacteristic
63C11×#107C2311yescharacteristic
64C11×#102—21no—
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67#66896—22no—
68#66896—22no—
69(C2×D11)⋊C8D412yes—
70#66882—21no—
71#66882—21no—
72#66882C2312yes—
73#66882C2312yes—
74C2×C11⋊C16C2312yes—
75#66872—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66862—24no—
79#33921—111nomaximal, Sylow
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86#4339—84no—
87C2×D44D811yescharacteristic
88C2×C4×D11—42no—
89C2×C4×D11C2×D412yes—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C11×D8—21no—
93C11×D8—21no—
94C11×D8—21no—
95C11×D8—21no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C22⋊Dic11—42no—
104C22⋊Dic11—42no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4D812yes—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11D811yescharacteristic
112Dic11⋊C4—42no—
113C4×Dic11—42no—
114C2×C11⋊C8C2×D412yes—
115C8×D11—22no—
116C8×D11—22no—
117C11×C16—21no—
118C11×C16#4112yescomplemented
119C11⋊C16—22no—
120#3341—111no—
121#3334—111no—
122#2254—111no—
123#2234—112no—
124#2233—112no—
125#2226—111no—
126#2224—111no—
127#2218—112no—
128C4×D16D1111yescharacteristic, complemented
129#2169—111no—
130#2159—112no—
131C23×C11—41no—
132C23×C11—41no—
133C22×D11C2×D812yes—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—41no—
137D4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—82no—
141C2×C4×C11—82no—
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C22⋊D11—84no—
146C22⋊D11—162no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11C2×D812yes—
150D44—22no—
151C4×D11—22no—
152C4×D11—22no—
153C4×D11—84no—
154Dic22—82no—
155Dic22—161no—
156C8×C11—21no—
157C8×C11C2×#4111yescharacteristic
158C8×C112−1+411yescharacteristic
159C11⋊C8—22no—
160#555—221no—
161#547—221no—
162C2×D16C2×D1111yescharacteristic
163C2×M32—112no—
164#500—111no—
165#500—111no—
166#482—222no—
167#480—222no—
168#476—221no—
169#474—221no—
170#466—112no—
171#466—112no—
172C4×D8C2×D1111yescharacteristic
173C4×D8C2×D1111yescharacteristic
174C8×D4—111no—
175#427—112no—
176C2×#107—112no—
177#367—112no—
178#367—112no—
179#367—112no—
180#366—112no—
181#366C2×D1111yescharacteristic
182C4⋊C16—111no—
183#357—112no—
184#357—112no—
185#357C2×D1111yescharacteristic
186#357C2×D1111yescharacteristic
187C22⋊C16—112no—
188C4×C16C2×D1111yescharacteristic
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11C22×D811yescharacteristic
196C2×D11—22no—
197C2×D11—22no—
198C2×D11—22no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11#50912yes—
203C4×C11#54711yescharacteristic
204C4×C11#57811yescharacteristic
205Dic11—22no—
206Dic11—82no—
207Dic11—82no—
208C2×#41—441no—
209C2×D8C22×D1111yescharacteristic
210C2×D8C22×D1111yescharacteristic
211C22×C8—112no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214#124—442no—
215#123—442no—
216C22⋊Q8—441no—
217#121—222no—
218#121—222no—
219#121—441no—
220C4×D4—21no—
221C4×D4—21no—
222C4×D4—111no—
223#117—222no—
224#117—441no—
225C2×C4⋊C4—222no—
226D16—22no—
227M32—224no—
228C2×C16—112no—
229C2×C16C22×D1111yescharacteristic
230C2×C16C22×D1111yescharacteristic
231#107—112no—
232#107—112no—
233#107—222no—
234#107—221no—
235#107—221no—
236#107C22×D1111yescharacteristic
237#107C22×D1111yescharacteristic
238#106—222no—
239C4⋊C8—111no—
240#102—21no—
241#102—21no—
242#102—222no—
243#102—222no—
244C22⋊C8—112no—
245C4×C8C22×D1111yescharacteristic
246C2×C11—161no—
247C2×C11—161no—
248C2×C11#333411yescharacteristic
249C2×C11C2×#50911yescharacteristic
250C2×C11#341611yescharacteristic
251D11—42no—
252#41—884no—
253C2×Q8—441no—
254C2×Q8—441no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—111no—
258C2×D4—442no—
259C2×D4—442no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—112no—
263C22×C4—442no—
264D8—21no—
265D8—21no—
266D8—21no—
267D8—21no—
268C2×C8—112no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8D4×D1111yescharacteristic
272C2×C8C23×D1111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—111no—
276C4⋊C4—222no—
277C4⋊C4—222no—
278C4⋊C4—442no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—112no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C42—442no—
288C42D4×D1111yescharacteristic
289C16—21no—
290C16—222no—
291C16#433912yescomplemented
292C11#3392111yescharacteristic, complemented, Sylow
293C23—41no—
294C23—41no—
295C23—112no—
296Q8—882no—
297Q8—1761no—
298D4—41no—
299D4—41no—
300D4—41no—
301D4—41no—
302D4—222no—
303D4—884no—
304D4—1762no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—112no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—884no—
315C2×C4D8×D1111yescharacteristic
316C2×C4D8×D1111yescharacteristic
317C2×C4C2×D4×D1111yescharacteristic
318C8—21no—
319C8—222no—
320C8C2×#433911yescharacteristic
321C8#6704311yescharacteristic
322C22—81no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—222no—
329C22—222no—
330C22—222no—
331C22C2×D8×D1111yescharacteristic
332C4—21no—
333C4—81no—
334C4—81no—
335C4—222no—
336C4—882no—
337C4—882no—
338C4#1062252412yes—
339C4#1062308211yescharacteristic
340C4#1062330211yescharacteristic
341C2—161no—
342C2—161no—
343C2—442no—
344C2#1308096511yescharacteristic
345C2C2×#1062252411yescharacteristic
346C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×D16C2
socleC22×C11C22×D8
hypercenterC4×D16D11
hypocenterC11#33921
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #13081040C2semidirect
2. #13080965C2semidirect
3. #13070898C2semidirect
4. #13070806C2semidirect
5. #13070800C2semidirect
6. #13070763C2semidirect
7. #13070753C2semidirect
8. #13070716C2semidirect
9. #13070449C2semidirect
10. #13070401C2semidirect
11. C4×C11×D16C2semidirect
118. C11×C16#41semidirect
128. C4×D16D11semidirect
291. C16#4339semidirect
292. C11#33921semidirect

Maximal subgroups

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

subgroupindex
#130810402
#130809652
#130708982
#130708062
#130708002
#130707632
#130707532
#130707162
#130704492
#130704012
C4×C11×D162
#3392111