Finite Group Databasebeta

← #14909544

Subgroups — #14909544

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078197C212yesmaximal, complemented
2#13070825C212yesmaximal, complemented
3#13070808C212yesmaximal, complemented
4#13070712C212yesmaximal, complemented
5#13070707C211yesmaximal, characteristic, complemented
6#13070702C211yesmaximal, characteristic, complemented
7#13070558C212yesmaximal, complemented
8#13070541C212yesmaximal, complemented
9C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
10C23×C8×C11C2211yescharacteristic
11#10623322—22no—
12C2×#66957C2212yes—
13C22×C11×C16C2211yescharacteristic
14C22×C11×C16C2211yescharacteristic
15#10622729C2212yes—
16#10622729C2212yes—
17#10622728C2212yes—
18#10622728C2212yes—
19#10622727—22no—
20#10622727—22no—
21#10622726—22no—
22#10622719C2212yes—
23C2×Dic88C2211yescharacteristic, complemented
24C2×#66864C2212yescomplemented
25C2×D176C2211yescharacteristic, complemented
26C11×C22⋊C16C2212yes—
27C11×C22⋊C16C2212yes—
28#10622147C2212yescomplemented
29#10622147C2212yescomplemented
30#10622143C2212yescomplemented
31#10622142C2211yescharacteristic, complemented
32#10622142C2211yescharacteristic, complemented
33#10622141C2212yescomplemented
34#10622141C2212yescomplemented
35C23×C4×C11D411yescharacteristic
36C2×#4339—22no—
37C22×C8×C11—41no—
38C22×C8×C11—41no—
39C22×C8×C11D412yes—
40C22×C8×C11D411yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C22×C8×C11C2312yes—
43#67006—42no—
44#66983—22no—
45#66983—22no—
46#66982—42no—
47C4×C22⋊D11—42no—
48C4×C22⋊D11—42no—
49#66979—22no—
50#66977—22no—
51#66977—22no—
52C2×Dic44C2312yes—
53#66957—42no—
54#66957—42no—
55C2×D88C2312yes—
56C2×#4314—22no—
57C2×C11×C16—41no—
58C2×C11×C16—41no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2312yes—
61C2×C11×C16C2311yescharacteristic
62#66885—22no—
63#66885—22no—
64#66882C2312yes—
65#66882C2312yes—
66#66881—22no—
67#66880—22no—
68#66880—22no—
69Dic88—41no—
70#66864—42no—
71D176—41no—
72#33757—111nomaximal, Sylow
73C24×C11D811yescharacteristic
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11D811yescharacteristic
77C22×C4×C11D812yes—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D412yes—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—42no—
83#4339—44no—
84#4339—44no—
85C2×D44—22no—
86C2×C4×D11—42no—
87C2×Dic22—22no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—42no—
93C2×C8×C11—41no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D412yes—
96C2×C8×C11C2411yescharacteristic
97C22⋊Dic11—42no—
98C22⋊Dic11—42no—
99C22⋊Dic11—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106C4×Dic11—42no—
107Dic44—22no—
108Dic44—22no—
109D88—22no—
110D88—22no—
111#4314—44no—
112C11×C16—21no—
113C11×C16—22no—
114C11×C16—21no—
115#3050—112no—
116#2237—112no—
117#2234—112no—
118#2217—112no—
119#2216—111no—
120#2215—111no—
121#2189—112no—
122#2186—112no—
123C2×C22⋊C16D1111yescharacteristic, complemented
124C23×C11—22no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11C2×D812yes—
128C23×C11C2×D811yescharacteristic
129C22×D11—42no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—21no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11C2×D812yes—
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C22⋊D11—84no—
140C22⋊D11—84no—
141C22⋊D11—84no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145D44—42no—
146D44—42no—
147C4×D11—84no—
148Dic22—42no—
149Dic22—42no—
150C8×C11—22no—
151C8×C11—21no—
152C8×C11H(5,𝔽2)11yescharacteristic
153C8×C11H(5,𝔽2)11yescharacteristic
154C2×#135—112no—
155C23×C8C2×D1111yescharacteristic
156#525—222no—
157C2×Q32—111no—
158C2×SD32—112no—
159C2×D16—111no—
160C22×C16C2×D1111yescharacteristic
161C22×C16C2×D1111yescharacteristic
162#467—112no—
163#467—112no—
164#466—112no—
165#466—112no—
166#465—222no—
167#465—222no—
168#427—112no—
169#416—222no—
170#367—112no—
171#366—111no—
172#366—111no—
173#358—112no—
174#358—112no—
175#357—112no—
176#357—112no—
177C22⋊C16C2×D1112yes—
178C22⋊C16C2×D1112yes—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11—44no—
185C22×C11#50812yes—
186C22×C11C22×D811yescharacteristic
187C2×D11—82no—
188C2×D11—82no—
189C2×D11—82no—
190C4×C11—21no—
191C4×C11—22no—
192C4×C11#53411yescharacteristic
193C4×C11#57511yescharacteristic
194Dic11—82no—
195Dic11—82no—
196Dic11—82no—
197C2×#41—222no—
198C23×C4D4411yescharacteristic
199#135—442no—
200#135—442no—
201C2×Q16—112no—
202C2×SD16—222no—
203C2×D8—112no—
204C22×C8—41no—
205C22×C8—41no—
206C22×C8D4412yes—
207C22×C8D4411yescharacteristic
208C22×C8C22×D1112yes—
209C22×C8C22×D1111yescharacteristic
210#123—442no—
211C22⋊Q8—222no—
212C22⋊Q8—222no—
213#121—222no—
214#121—222no—
215#120—442no—
216C4×D4—442no—
217C4×D4—442no—
218#117—222no—
219Q32—441no—
220SD32—442no—
221D16—441no—
222C2×C16—41no—
223C2×C16—41no—
224C2×C16C22×D1111yescharacteristic
225C2×C16C22×D1112yes—
226C2×C16C22×D1111yescharacteristic
227#107—112no—
228#107—112no—
229#106—222no—
230#103—222no—
231#103—222no—
232#102—222no—
233#102—222no—
234C2×C11—22no—
235C2×C11—42no—
236C2×C11#318611yescharacteristic
237C2×C11C2×#50811yescharacteristic
238C2×C11#341411yescharacteristic
239D11—162no—
240C24D8811yescharacteristic
241#41—444no—
242#41—444no—
243C2×Q8—222no—
244C2×D4—222no—
245C2×D4—442no—
246C2×D4—442no—
247C2×D4—442no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—442no—
251C22×C4D8811yescharacteristic
252C22×C4D8812yes—
253C22×C4C2×D4412yes—
254C22×C4C2×D4411yescharacteristic
255Q16—222no—
256Q16—222no—
257SD16—444no—
258D8—222no—
259D8—222no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—42no—
266C2×C8C2×D4411yescharacteristic
267C2×C8C2×D4412yes—
268C2×C8C23×D1111yescharacteristic
269C4⋊C4—222no—
270C4⋊C4—222no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C22⋊C4—442no—
278C42—442no—
279C16—21no—
280C16—22no—
281C16—21no—
282C11#3375711yescharacteristic, complemented, Sylow
283C23—22no—
284C23—41no—
285C23—41no—
286C23—442no—
287C23C2×D8812yes—
288C23C2×D8811yescharacteristic
289Q8—442no—
290Q8—442no—
291D4—442no—
292D4—442no—
293D4—884no—
294D4—884no—
295D4—884no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—884no—
306C2×C4C2×D8812yes—
307C2×C4C2×D8811yescharacteristic
308C2×C4C22×D4411yescharacteristic
309C8—22no—
310C8—21no—
311C8#6703711yescharacteristic
312C8#6703711yescharacteristic
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—44no—
319C22—882no—
320C22—882no—
321C22—882no—
322C22#1062251712yes—
323C22C22×D8811yescharacteristic
324C4—22no—
325C4—21no—
326C4—882no—
327C4—882no—
328C4—882no—
329C4#1062302411yescharacteristic
330C4#1062327911yescharacteristic
331C2—22no—
332C2—42no—
333C2—1762no—
334C2#1307936711yescharacteristic
335C2C2×#1062251711yescharacteristic
336C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×C22⋊C16C2
socleC22×C11C22×D8
hypercenterC2×C22⋊C16D11
hypocenterC11#33757
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
1. #13078197C2semidirect
2. #13070825C2semidirect
3. #13070808C2semidirect
4. #13070712C2semidirect
5. #13070707C2semidirect
6. #13070702C2semidirect
7. #13070558C2semidirect
8. #13070541C2semidirect
9. C2×C11×C22⋊C16C2semidirect
23. C2×Dic88C22semidirect
24. C2×#66864C22semidirect
25. C2×D176C22semidirect
28. #10622147C22semidirect
29. #10622147C22semidirect
30. #10622143C22semidirect
31. #10622142C22semidirect
32. #10622142C22semidirect
33. #10622141C22semidirect
34. #10622141C22semidirect
123. C2×C22⋊C16D11semidirect
282. C11#33757semidirect

Maximal subgroups

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

subgroupindex
#130781972
#130708252
#130708082
#130707122
#130707072
#130707022
#130705582
#130705412
C2×C11×C22⋊C162
#3375711