Finite Group Databasebeta

← #14911575

Subgroups — #14911575

Order 2816.

520 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#13081629C211yesmaximal, characteristic, complemented
2#13070855C212yesmaximal, complemented
3#13070841C211yesmaximal, characteristic, complemented
4#13070760C212yesmaximal, complemented
5#13070755C211yesmaximal, characteristic, complemented
6#13070671C212yesmaximal, complemented
7#13070651C211yesmaximal, characteristic
8#13070525C211yesmaximal, characteristic, complemented
9#13070490C212yesmaximal, complemented
10C4×#66891C211yesmaximal, characteristic, complemented
11Q8×C11×D8C211yesmaximal, characteristic, complemented
12D4×Q8×C11—21no—
13#10623116—21no—
14C11×#500C2212yes—
15C11×#500C2211yescharacteristic
16C11×#474—22no—
17C11×#474—21no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C4×C11×D8C2212yes—
21C2×#66891C2211yescharacteristic
22C2×#66890C2212yes—
23#10622461—21no—
24#10622457—22no—
25C4×Dic44C2211yescharacteristic
26#10622309C2212yes—
27#10622308C2211yescharacteristic
28C4×D88C2212yes—
29#10622200C2211yescharacteristic
30#10622130C2211yescharacteristic
31#10622130C2212yes—
32#10622129C2212yes—
33#10622129C2212yes—
34#10622129C2212yes—
35#10622128C2211yescharacteristic
36#10622128C2212yes—
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39#10622099C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C22×Q8×C11—41no—
42C2×C11×D8C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—22no—
45C11×C22⋊Q8—41no—
46C11×C22⋊Q8—42no—
47C4×Q8×C11D411yescharacteristic
48C4×D4×C11—21no—
49C4×D4×C11—22no—
50#67000—41no—
51C2×Dic44C2311yescharacteristic
52C2×D88—21no—
53C2×D88C2312yes—
54C2×#4314—22no—
55#66947—42no—
56#66946—41no—
57#66928—22no—
58#66927—21no—
59C4×D44—22no—
60C4×Dic22—21no—
61C11×#107—21no—
62C11×#107—22no—
63C11×#107C2311yescharacteristic
64C11×#107C2312yes—
65C11×C4⋊C8D412yes—
66C11×C4⋊C8D411yescharacteristic
67C11×#102—21no—
68C11×#102—22no—
69C4×C8×C11C2312yes—
70C4×C8×C11C2311yescharacteristic
71#66891—22no—
72#66890—24no—
73#66885—22no—
74#66882C2311yescharacteristic
75#66880—21no—
76C2×C11⋊C16C2312yes—
77C2×C11⋊C16C2311yescharacteristic
78C2×C11⋊C16C2311yescharacteristic
79#33940—111nomaximal, Sylow
80C2×Q8×C11—42no—
81C2×Q8×C11—41no—
82C2×Q8×C11—84no—
83C2×Q8×C11D811yescharacteristic
84C2×D4×C11—21no—
85C22×C4×C11—42no—
86C22×C4×C11—41no—
87C2×D44—22no—
88C2×D44—41no—
89C2×D44—41no—
90C2×C4×D11—42no—
91C2×Dic22—21no—
92C11×D8—21no—
93C11×D8#4112yes—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D412yes—
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4D811yescharacteristic
102C11×C4⋊C4D812yes—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—42no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D412yes—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—21no—
111Dic11⋊C4—41no—
112C4×Dic11—41no—
113Dic44—21no—
114Dic44—21no—
115D88—22no—
116D88—22no—
117D88—81no—
118#4314—82no—
119C11⋊C16—22no—
120C11⋊C16—21no—
121C11⋊C16—21no—
122#3396—111no—
123Q8×D8D1111yescharacteristic, complemented
124#2243—112no—
125#2240—111no—
126#2226—112no—
127#2225—111no—
128#2210—112no—
129#2206—111no—
130#2183—111no—
131#2177—112no—
132C4×SD32—111no—
133C23×C11—41no—
134C22×D11—42no—
135Q8×C11—22no—
136Q8×C11—84no—
137Q8×C11—82no—
138D4×C11—22no—
139D4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—84no—
143C2×C4×C11—82no—
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C2×D812yes—
146C2×C4×C11C2×D812yes—
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×Dic11—41no—
150C2×Dic11—41no—
151D44—42no—
152D44—42no—
153D44—82no—
154D44—161no—
155C4×D11—162no—
156Dic22—41no—
157Dic22—41no—
158C8×C11—22no—
159C8×C11—21no—
160C8×C11C2×#4111yescharacteristic
161C8×C112−1+411yescharacteristic
162#559—221no—
163D4×Q8—21no—
164C2×SD32—111no—
165C2×D16—112no—
166#500C2×D1111yescharacteristic
167#500C2×D1112yes—
168#495—112no—
169#493—111no—
170#474—21no—
171#474—22no—
172#463—222no—
173#460—221no—
174C8×Q8C2×D1111yescharacteristic
175C4×Q16—111no—
176C4×D8—112no—
177C4×D8C2×D1111yescharacteristic
178C4×D8C2×D1112yes—
179#367—111no—
180#367—112no—
181C4⋊C16—111no—
182C4⋊C16—112no—
183#358—111no—
184#358—112no—
185#357—111no—
186#357—112no—
187#357—112no—
188#357—112no—
189#346—112no—
190C4×C16—111no—
191C22×C11—42no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11C22×D811yescharacteristic
195C2×D11—82no—
196C2×D11—82no—
197C2×D11—82no—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11—82no—
202C4×C11—81no—
203C4×C11#50912yes—
204C4×C11#54811yescharacteristic
205C4×C11#57711yescharacteristic
206Dic11—81no—
207Dic11—81no—
208C22×Q8—41no—
209C2×Q16—111no—
210C2×SD16—222no—
211C2×D8—112no—
212C2×D8—221no—
213C2×D8C22×D1111yescharacteristic
214C4⋊Q8—22no—
215C4⋊Q8—21no—
216#127—221no—
217#124—222no—
218#124—441no—
219#123—442no—
220C22⋊Q8—41no—
221C22⋊Q8—42no—
222C4×Q8—221no—
223C4×Q8C22⋊D1111yescharacteristic
224C4×D4—22no—
225C4×D4—21no—
226C4×D4—222no—
227C4×D4—441no—
228SD32—222no—
229D16—224no—
230C2×C16—111no—
231C2×C16—111no—
232C2×C16—112no—
233#107—22no—
234#107—21no—
235#107—111no—
236#107C22×D1112yes—
237#107C22×D1111yescharacteristic
238C4⋊C8C22⋊D1111yescharacteristic
239C4⋊C8C22⋊D1112yes—
240#103—221no—
241#102—22no—
242#102—21no—
243#102—222no—
244C4×C8C22×D1111yescharacteristic
245C4×C8C22×D1112yes—
246C2×C11—82no—
247C2×C11#335811yescharacteristic
248C2×C11C2×#50911yescharacteristic
249C2×C11#341611yescharacteristic
250D11—162no—
251C2×Q8—42no—
252C2×Q8—41no—
253C2×Q8—84no—
254C2×Q8—221no—
255C2×Q8#432311yescharacteristic
256C2×D4—21no—
257C2×D4—222no—
258C2×D4—441no—
259C2×D4—441no—
260C22×C4—42no—
261C22×C4—41no—
262C22×C4—442no—
263Q16—221no—
264Q16—221no—
265SD16—882no—
266D8—21no—
267D8—222no—
268D8—222no—
269D8—881no—
270D8#434312yes—
271C2×C8C2×C22⋊D1112yes—
272C2×C8C2×C22⋊D1111yescharacteristic
273C2×C8C23×D1111yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—21no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—221no—
279C4⋊C4—441no—
280C4⋊C4#432311yescharacteristic
281C4⋊C4#432312yes—
282C22⋊C4—42no—
283C22⋊C4—41no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C42—441no—
288C42C2×C22⋊D1112yes—
289C42C2×C22⋊D1111yescharacteristic
290C16—222no—
291C16—221no—
292C16—221no—
293C11#3394011yescharacteristic, complemented, Sylow
294C23—41no—
295C23—442no—
296Q8—22no—
297Q8—84no—
298Q8—82no—
299Q8—441no—
300Q8—441no—
301D4—22no—
302D4—41no—
303D4—442no—
304D4—442no—
305D4—882no—
306D4—1761no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—84no—
310C2×C4—82no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—1762no—
314C2×C4C2×#432312yes—
315C2×C4C2×#432311yescharacteristic
316C2×C4C2×#432312yes—
317C2×C4C2×#432311yescharacteristic
318C2×C4C22×C22⋊D1111yescharacteristic
319C8—21no—
320C8—22no—
321C8C2×#434311yescharacteristic
322C8#6704011yescharacteristic
323C22—42no—
324C22—81no—
325C22—81no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22C22×#432311yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—82no—
334C4—81no—
335C4—881no—
336C4—881no—
337C4#1062276012yes—
338C4#1062334811yescharacteristic
339C4#1062336811yescharacteristic
340C2—82no—
341C2—1762no—
342C2#1308125111yescharacteristic
343C2C2×#1062276011yescharacteristic
344C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingQ8×C11×D8C2
socleC22×C11C22×D8
prime radical#13070651C2
hypercenterQ8×D8D11
hypocenterC11#33940
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ Q8×D8

Complements

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

NH ≅ G/Ntype
1. #13081629C2semidirect
2. #13070855C2semidirect
3. #13070841C2semidirect
4. #13070760C2semidirect
5. #13070755C2semidirect
6. #13070671C2semidirect
8. #13070525C2semidirect
9. #13070490C2semidirect
10. C4×#66891C2semidirect
11. Q8×C11×D8C2semidirect
123. Q8×D8D11semidirect
293. C11#33940semidirect

Maximal subgroups

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

subgroupindex
#130816292
#130708552
#130708412
#130707602
#130707552
#130706712
#130706512
#130705252
#130704902
C4×#668912
Q8×C11×D82
#3394011