Finite Group Databasebeta

← #14911508

Subgroups — #14911508

Order 2816.

518 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081508C211yesmaximal, characteristic, complemented
2#13070857C212yesmaximal, complemented
3#13070839C211yesmaximal, characteristic, complemented
4#13070773C212yesmaximal, complemented
5#13070753C211yesmaximal, characteristic, complemented
6#13070653C212yesmaximal, complemented
7#13070653C211yesmaximal, characteristic, complemented
8#13070525C211yesmaximal, characteristic, complemented
9#13070480C212yesmaximal, complemented
10C4×#66891C211yesmaximal, characteristic, complemented
11C11×#3391C211yesmaximal, characteristic
12C11×#550—21no—
13#10623098—21no—
14C11×#493C2212yes—
15C11×#493C2211yescharacteristic
16C11×#459—21no—
17C11×#459—22no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C4×C11×D8C2212yes—
21C2×#66891C2211yescharacteristic
22C2×#66891C2212yes—
23#10622464—21no—
24#10622442—22no—
25C4×Dic44C2211yescharacteristic
26C4×Dic44C2212yes—
27#10622296C2212yes—
28#10622295C2211yescharacteristic
29#10622200C2211yescharacteristic
30#10622200C2212yes—
31#10622200C2212yes—
32#10622200C2212yes—
33#10622200C2212yes—
34#10622130C2211yescharacteristic
35#10622128C2211yescharacteristic
36#10622127C2212yes—
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39#10622099C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—41no—
42C2×C11×D8—22no—
43C2×C11×D8—21no—
44C2×C11×D8C2311yescharacteristic
45C2×C11×D8C2312yes—
46C11×#127—21no—
47C11×#127—22no—
48C11×#121—41no—
49C11×#121—42no—
50C4×Q8×C11D411yescharacteristic
51C4×D4×C11—21no—
52C4×D4×C11—22no—
53#66997—41no—
54C2×Dic44C2311yescharacteristic
55#66942—42no—
56#66940—41no—
57#66923—22no—
58#66922—21no—
59C4×Dic22—21no—
60C4×Dic22—22no—
61C11×#107C2311yescharacteristic
62C11×C4⋊C8D411yescharacteristic
63C11×C4⋊C8D412yes—
64C11×#102—22no—
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66891—22no—
69#66891—24no—
70#66882—21no—
71#66882C2312yes—
72#66882C2311yescharacteristic
73#66881—22no—
74#66880—22no—
75#66880—21no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33935—111nomaximal, Sylow
80C11×#41—84no—
81C2×Q8×C11D811yescharacteristic
82C2×D4×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—42no—
85C2×D4×C11—41no—
86C2×D4×C11—42no—
87C2×D4×C11—41no—
88C22×C4×C11—42no—
89C22×C4×C11—41no—
90C2×Dic22—21no—
91C2×Dic22—41no—
92C11×D8—21no—
93C11×D8—22no—
94C11×D8—21no—
95C11×D8—22no—
96C11×D8—82no—
97C11×D8—81no—
98C2×C8×C11C2×D412yes—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2411yescharacteristic
101C11×C4⋊C4—21no—
102C11×C4⋊C4D811yescharacteristic
103C11×C4⋊C4D812yes—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D412yes—
108C4⋊Dic11—21no—
109C4⋊Dic11—22no—
110C4⋊Dic11—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—42no—
113Dic11⋊C4—42no—
114Dic11⋊C4—42no—
115C4×Dic11—42no—
116C4×Dic11—41no—
117Dic44—21no—
118Dic44#4112yescomplemented
119C11⋊C16—21no—
120C11⋊C16—22no—
121C11⋊C16—21no—
122#3391D1111yescharacteristic
123#3383—111no—
124#2244—112no—
125#2240—111no—
126#2228—112no—
127#2224—111no—
128#2207—112no—
129#2207—111no—
130#2183—111no—
131#2175—112no—
132C4×SD32—111no—
133C23×C11—42no—
134C23×C11—41no—
135Q8×C11—22no—
136D4×C11—41no—
137D4×C11—42no—
138D4×C11—41no—
139D4×C11—42no—
140D4×C11—84no—
141D4×C11—82no—
142D4×C11—162no—
143D4×C11—161no—
144C2×C4×C11—41no—
145C2×C4×C11—84no—
146C2×C4×C11—82no—
147C2×C4×C11C2×D812yes—
148C2×C4×C11C2×D812yes—
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155Dic22—22no—
156Dic22—41no—
157Dic22—82no—
158C8×C11—22no—
159C8×C11—21no—
160C8×C11C2×#4111yescharacteristic
161C8×C112−1+411yescharacteristic
162#557—221no—
163#550—21no—
164C2×SD32—111no—
165C2×SD32—112no—
166#500—111no—
167#499—112no—
168#493C2×D1111yescharacteristic
169#493C2×D1112yes—
170#479—222no—
171#475—221no—
172#459—21no—
173#459—22no—
174C8×Q8C2×D1111yescharacteristic
175C4×Q16—111no—
176C4×Q16—112no—
177C4×D8C2×D1111yescharacteristic
178C4×D8C2×D1112yes—
179#367—111no—
180#366—112no—
181C4⋊C16—111no—
182C4⋊C16—112no—
183#358—111no—
184#357—111no—
185#357—112no—
186#357—112no—
187#357—112no—
188#357—112no—
189#346—112no—
190C4×C16—111no—
191C22×C11—82no—
192C22×C11—81no—
193C22×C11—82no—
194C22×C11—81no—
195C22×C11—82no—
196C22×C11—81no—
197C22×C11C22×D811yescharacteristic
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11—81no—
202C4×C11#50912yes—
203C4×C11#54811yescharacteristic
204C4×C11#57711yescharacteristic
205Dic11—42no—
206Dic11—82no—
207Dic11—81no—
208C2×#41—41no—
209C2×Q16—111no—
210C2×D8—22no—
211C2×D8—21no—
212C2×D8C22×D1111yescharacteristic
213C2×D8C22×D1112yes—
214C4⋊Q8—221no—
215C4⋊Q8—441no—
216#127—22no—
217#127—21no—
218#125—222no—
219#125—442no—
220#121—41no—
221#121—42no—
222C4×Q8—221no—
223C4×Q8—222no—
224C4×Q8—441no—
225C4×Q8C22⋊D1111yescharacteristic
226C4×D4—22no—
227C4×D4—21no—
228SD32—222no—
229SD32—224no—
230C2×C16—111no—
231C2×C16—111no—
232C2×C16—112no—
233#107—112no—
234#107—111no—
235#107—221no—
236#107C22×D1111yescharacteristic
237#106—222no—
238C4⋊C8C22⋊D1111yescharacteristic
239C4⋊C8C22⋊D1112yes—
240#103—222no—
241#103—221no—
242#102—22no—
243#102—21no—
244C4×C8C22×D1111yescharacteristic
245C4×C8C22×D1112yes—
246C2×C11—162no—
247C2×C11—161no—
248C2×C11#335811yescharacteristic
249C2×C11C2×#50911yescharacteristic
250C2×C11#341611yescharacteristic
251#41—84no—
252C2×Q8—221no—
253C2×Q8—441no—
254C2×Q8#432311yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—42no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4—41no—
261C22×C4—42no—
262C22×C4—41no—
263Q16—112no—
264Q16—221no—
265D8—21no—
266D8—22no—
267D8—21no—
268D8—22no—
269D8—82no—
270D8—81no—
271C2×C8C2×C22⋊D1112yes—
272C2×C8C2×C22⋊D1111yescharacteristic
273C2×C8C23×D1111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—221no—
276C4⋊C4—222no—
277C4⋊C4—441no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—442no—
281C4⋊C4—441no—
282C4⋊C4#432311yescharacteristic
283C4⋊C4#432312yes—
284C22⋊C4—42no—
285C22⋊C4—41no—
286C42—442no—
287C42—441no—
288C42C2×C22⋊D1112yes—
289C42C2×C22⋊D1111yescharacteristic
290C16—221no—
291C16—222no—
292C16—221no—
293C11#3393511yescharacteristic, complemented, Sylow
294C23—42no—
295C23—41no—
296Q8—22no—
297Q8—222no—
298Q8—441no—
299Q8—882no—
300D4—41no—
301D4—42no—
302D4—41no—
303D4—42no—
304D4—84no—
305D4—82no—
306D4—162no—
307D4—161no—
308C2×C4—41no—
309C2×C4—84no—
310C2×C4—82no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—442no—
314C2×C4C2×#432312yes—
315C2×C4C2×#432311yescharacteristic
316C2×C4C2×#432312yes—
317C2×C4C2×#432311yescharacteristic
318C2×C4C22×C22⋊D1111yescharacteristic
319C8—22no—
320C8—21no—
321C8#41×D1111yescharacteristic
322C8#6704311yescharacteristic
323C22—82no—
324C22—81no—
325C22—82no—
326C22—81no—
327C22—82no—
328C22—81no—
329C22C22×#432311yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—81no—
334C4—442no—
335C4—882no—
336C4—881no—
337C4#1062276012yes—
338C4#1062336211yescharacteristic
339C4#1062336711yescharacteristic
340C2—162no—
341C2—161no—
342C2#1308124711yescharacteristic
343C2C2×#1062276011yescharacteristic
344C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3391C2
socleC22×C11C22×D8
hypercenter#3391D11
hypocenterC11#33935
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3391

Complements

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

NH ≅ G/Ntype
1. #13081508C2semidirect
2. #13070857C2semidirect
3. #13070839C2semidirect
4. #13070773C2semidirect
5. #13070753C2semidirect
6. #13070653C2semidirect
7. #13070653C2semidirect
8. #13070525C2semidirect
9. #13070480C2semidirect
10. C4×#66891C2semidirect
118. Dic44#41semidirect
293. C11#33935semidirect

Maximal subgroups

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

subgroupindex
#130815082
#130708572
#130708392
#130707732
#130707532
#130706532
#130705252
#130704802
C4×#668912
C11×#33912
#3393511