Finite Group Databasebeta

← #14911141

Subgroups — #14911141

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081009C211yesmaximal, characteristic, complemented
2#13080964C211yesmaximal, characteristic
3#13070898C211yesmaximal, characteristic, complemented
4#13070814C212yesmaximal, complemented
5#13070802C212yesmaximal, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070759C211yesmaximal, characteristic, complemented
8#13070712C212yesmaximal, complemented
9C4×#66864C211yesmaximal, characteristic, complemented
10C2×#10622143C212yesmaximal, complemented
11D4×C11×C16C211yesmaximal, characteristic, complemented
12#10623086—21no—
13#10623074—21no—
14C22×C11×C16C2212yes—
15C8×D4×C11C2211yescharacteristic
16#10622729C2212yes—
17#10622728C2212yes—
18C2×#66882C2212yes—
19C2×#66882C2212yes—
20C2×#66864C2211yescharacteristic
21#10622463—21no—
22#10622459—21no—
23#10622349—22no—
24#10622335—22no—
25C4×Dic44C2211yescharacteristic
26C4×D88C2211yescharacteristic
27#10622295C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×C22⋊C16C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622147C2212yes—
33#10622147C2211yescharacteristic
34#10622143C2212yes—
35#10622143C2212yes—
36#10622143C2211yescharacteristic
37#10622143C2212yes—
38#10622143C2212yes—
39#10622141C2212yes—
40#10622141C2211yescharacteristic
41C2×#4341—41no—
42C22×C8×C11C2312yes—
43C4×D4×C11D411yescharacteristic
44D4×Dic11—41no—
45#66983—22no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11—22no—
48#66977—22no—
49C2×Dic44C2311yescharacteristic
50C2×D88C2311yescharacteristic
51#66950—41no—
52#66943—41no—
53#66939—42no—
54#66931—42no—
55C4×D44—21no—
56#66922—21no—
57#66922—21no—
58C4×Dic22—21no—
59C2×C11×C16—24no—
60C2×C11×C16C2312yes—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×C4⋊C8D411yescharacteristic
64C11×C22⋊C8D412yes—
65C4×C8×C11C2311yescharacteristic
66#66885—22no—
67#66885—21no—
68#66882—21no—
69#66882—21no—
70#66882—22no—
71#66882—22no—
72#66882C2312yes—
73#66882C2312yes—
74#66882C2311yescharacteristic
75#66882C2311yescharacteristic
76#66880—22no—
77#66880—21no—
78#66864—22no—
79#33902—111nomaximal, Sylow
80C2×D4×C11D811yescharacteristic
81C22×C4×C11C2×D412yes—
82C2×C22⋊D11—42no—
83C22×Dic11—42no—
84C22×Dic11—42no—
85#4341—84no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—21no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4D811yescharacteristic
97C11×C22⋊C4D812yes—
98C42×C11C2×D411yescharacteristic
99C22⋊Dic11—42no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—21no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—21no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11—42no—
109C4⋊Dic11—42no—
110Dic11⋊C4—41no—
111Dic11⋊C4—42no—
112C4×Dic11—41no—
113Dic44—21no—
114Dic44—21no—
115D88—21no—
116D88—21no—
117C11×C16—22no—
118C11×C16—21no—
119C11×C16#4112yescomplemented
120#3338—111no—
121#3334—111no—
122#2254—111no—
123#2235—112no—
124#2233—112no—
125#2226—111no—
126#2225—111no—
127#2217—112no—
128C4×SD32—111no—
129D4×C16D1111yescharacteristic, complemented
130C2×#367—112no—
131C23×C11C2×D812yes—
132C22×D11—41no—
133D4×C11SD3214yescomplemented
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11C2×D812yes—
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C22⋊D11—84no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11—84no—
147C2×Dic11—162no—
148D44—41no—
149D44—41no—
150C4×D11—82no—
151Dic22—41no—
152Dic22—41no—
153Dic22—82no—
154Dic22—161no—
155C8×C11—22no—
156C8×C11—21no—
157C8×C11C2×#4111yescharacteristic
158C8×C112−1+411yescharacteristic
159#554—221no—
160#547—221no—
161C2×SD32—111no—
162C22×C16C2×D1112yes—
163#500—111no—
164#500—111no—
165#484—222no—
166#480—222no—
167#477—221no—
168#474—221no—
169#467—112no—
170#466—112no—
171C4×Q16—111no—
172C4×D8—111no—
173C8×D4C2×D1111yescharacteristic
174C2×#107—112no—
175C2×#107—112no—
176#367—111no—
177#367—112no—
178#367—112no—
179#367—112no—
180#367—112no—
181C4⋊C16C2×D1111yescharacteristic
182#358—111no—
183#358—112no—
184#357—111no—
185#357—112no—
186C22⋊C16C2×D1112yes—
187C4×C16C2×D1111yescharacteristic
188C22×C11—22no—
189C22×C11—22no—
190C22×C11C2×SD3214yes—
191C22×C11C22×D811yescharacteristic
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C4×C11—22no—
196C4×C11—21no—
197C4×C11C2×SD3212yes—
198C4×C11#54711yescharacteristic
199C4×C11#57811yescharacteristic
200Dic11—81no—
201Dic11—82no—
202Dic11—81no—
203Dic11—82no—
204Dic11—81no—
205C2×#41—441no—
206C2×Q16—111no—
207C2×D8—111no—
208C22×C8C22×D1112yes—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211#125—441no—
212#123—442no—
213C22⋊Q8—222no—
214C22⋊Q8—441no—
215C22⋊Q8—442no—
216#121—222no—
217C4×Q8—221no—
218C4×D4—221no—
219C4×D4—441no—
220C4×D4D4411yescharacteristic
221C2×C4⋊C4—222no—
222C2×C4⋊C4—222no—
223SD32—222no—
224C2×C16—24no—
225C2×C16C22×D1111yescharacteristic
226C2×C16C22×D1112yes—
227C2×C16C22×D1111yescharacteristic
228#107—111no—
229#107—112no—
230#107—111no—
231#107—112no—
232#107—222no—
233#107—222no—
234#107—221no—
235#107—221no—
236C4⋊C8D4411yescharacteristic
237#103—221no—
238#103—222no—
239#102—221no—
240#102—222no—
241C22⋊C8D4412yes—
242C4×C8C22×D1111yescharacteristic
243C2×C11—24no—
244C2×C11#333411yescharacteristic
245C2×C11C22×SD3211yescharacteristic
246C2×C11#341611yescharacteristic
247D11—161no—
248#41—884no—
249C2×Q8—221no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×D4—221no—
253C2×D4—442no—
254C2×D4D8811yescharacteristic
255C22×C4—442no—
256C22×C4—442no—
257C22×C4—441no—
258C22×C4C2×D4412yes—
259Q16—221no—
260Q16—221no—
261D8—221no—
262D8—221no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8C2×D4411yescharacteristic
266C2×C8C2×D4412yes—
267C2×C8C23×D1111yescharacteristic
268C4⋊C4—221no—
269C4⋊C4—222no—
270C4⋊C4—221no—
271C4⋊C4—222no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—442no—
277C4⋊C4—441no—
278C4⋊C4D8811yescharacteristic
279C22⋊C4—442no—
280C22⋊C4—441no—
281C22⋊C4—442no—
282C22⋊C4D8812yes—
283C42—441no—
284C42C2×D4411yescharacteristic
285C16—22no—
286C16—21no—
287C16#434112yescomplemented
288C11#3390211yescharacteristic, complemented, Sylow
289C23—441no—
290C23C2×D8812yes—
291Q8—441no—
292Q8—441no—
293Q8—882no—
294Q8—1761no—
295D4—441no—
296D4—441no—
297D4—884no—
298D4#6686414yescomplemented
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—442no—
304C2×C4—441no—
305C2×C4—442no—
306C2×C4—884no—
307C2×C4—882no—
308C2×C4—1762no—
309C2×C4C2×D8811yescharacteristic
310C2×C4C2×D8812yes—
311C2×C4C2×D8811yescharacteristic
312C2×C4C22×D4411yescharacteristic
313C8—21no—
314C8—22no—
315C8C2×#434111yescharacteristic
316C8#6704311yescharacteristic
317C22—22no—
318C22—22no—
319C22—881no—
320C22—881no—
321C22—881no—
322C22C2×#6686414yes—
323C22C22×D8811yescharacteristic
324C4—22no—
325C4—21no—
326C4—881no—
327C4—882no—
328C4—881no—
329C4—881no—
330C4—882no—
331C4C2×#6686412yes—
332C4#1062308611yescharacteristic
333C4#1062328411yescharacteristic
334C2—24no—
335C2—1761no—
336C2#1308096411yescharacteristic
337C2C22×#6686411yescharacteristic
338C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×C16C2
socleC22×C11C22×D8
prime radical#13080964C2
hypercenterD4×C16D11
hypocenterC11#33902
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #13081009C2semidirect
3. #13070898C2semidirect
4. #13070814C2semidirect
5. #13070802C2semidirect
6. #13070764C2semidirect
7. #13070759C2semidirect
8. #13070712C2semidirect
9. C4×#66864C2semidirect
10. C2×#10622143C2semidirect
11. D4×C11×C16C2semidirect
119. C11×C16#41semidirect
129. D4×C16D11semidirect
133. D4×C11SD32semidirect
287. C16#4341semidirect
288. C11#33902semidirect
298. D4#66864semidirect

Maximal subgroups

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

subgroupindex
#130810092
#130809642
#130708982
#130708142
#130708022
#130707642
#130707592
#130707122
C4×#668642
C2×#106221432
D4×C11×C162
#3390211