Finite Group Databasebeta

← #14909593

Subgroups — #14909593

Order 2816.

592 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078197C212yesmaximal, complemented
2#13070825C212yesmaximal, complemented
3#13070808C212yesmaximal, complemented
4#13070729C212yesmaximal, complemented
5#13070724C211yesmaximal, characteristic, complemented
6#13070719C211yesmaximal, characteristic, complemented
7#13070558C212yesmaximal, complemented
8#13070541C212yesmaximal, complemented
9C11×#2112C211yesmaximal, characteristic, complemented
10C23×C8×C11C2211yescharacteristic
11#10623322—22no—
12C2×#66957C2212yes—
13C2×C11×M32C2211yescharacteristic
14C2×C11×M32C2211yescharacteristic
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#10622143C2211yescharacteristic, complemented
31#10622143C2211yescharacteristic, complemented
32#10622142C2212yescomplemented
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—
57C11×M32—41no—
58C11×M32—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#33763—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#2220—112no—
119#2219—111no—
120#2218—111no—
121#2189—112no—
122#2186—112no—
123#2112D1111yescharacteristic, complemented
124C23×C11—41no—
125C23×C11—42no—
126C23×C11C2×D812yes—
127C23×C11C2×D811yescharacteristic
128C22×D11—42no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11—41no—
135C2×C4×C11C2×D812yes—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C22×D411yescharacteristic
138C22⋊D11—84no—
139C22⋊D11—84no—
140C22⋊D11—84no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144D44—42no—
145D44—42no—
146C4×D11—84no—
147Dic22—42no—
148Dic22—42no—
149C8×C11—22no—
150C8×C11—21no—
151C8×C11H(5,𝔽2)11yescharacteristic
152C8×C11H(5,𝔽2)11yescharacteristic
153C2×#135—112no—
154C23×C8C2×D1111yescharacteristic
155#525—222no—
156C2×Q32—111no—
157C2×SD32—112no—
158C2×D16—111no—
159C2×M32C2×D1111yescharacteristic
160C2×M32C2×D1111yescharacteristic
161#467—112no—
162#467—112no—
163#466—112no—
164#466—112no—
165#465—222no—
166#465—222no—
167#427—112no—
168#416—222no—
169#367—111no—
170#367—111no—
171#366—112no—
172#358—112no—
173#358—112no—
174#357—112no—
175#357—112no—
176C22⋊C16C2×D1112yes—
177C22⋊C16C2×D1112yes—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—21no—
182C22×C11—22no—
183C22×C11—44no—
184C22×C11C22×D811yescharacteristic
185C2×D11—82no—
186C2×D11—82no—
187C2×D11—82no—
188C4×C11—21no—
189C4×C11—22no—
190C4×C11#53411yescharacteristic
191C4×C11#57511yescharacteristic
192Dic11—82no—
193Dic11—82no—
194Dic11—82no—
195C2×#41—222no—
196C23×C4D4411yescharacteristic
197#135—442no—
198#135—442no—
199C2×Q16—112no—
200C2×SD16—222no—
201C2×D8—112no—
202C22×C8—41no—
203C22×C8—41no—
204C22×C8D4412yes—
205C22×C8D4411yescharacteristic
206C22×C8C22×D1112yes—
207C22×C8C22×D1111yescharacteristic
208#123—442no—
209C22⋊Q8—222no—
210C22⋊Q8—222no—
211#121—222no—
212#121—222no—
213#120—442no—
214C4×D4—442no—
215C4×D4—442no—
216#117—222no—
217Q32—441no—
218SD32—442no—
219D16—441no—
220M32—41no—
221M32—41no—
222C2×C16C22×D1111yescharacteristic
223C2×C16C22×D1112yes—
224C2×C16C22×D1111yescharacteristic
225#107—112no—
226#107—112no—
227#106—222no—
228#103—222no—
229#103—222no—
230#102—222no—
231#102—222no—
232C2×C11—42no—
233C2×C11—41no—
234C2×C11#318611yescharacteristic
235C2×C11#341412yes—
236D11—162no—
237C24D8811yescharacteristic
238#41—444no—
239#41—444no—
240C2×Q8—222no—
241C2×D4—222no—
242C2×D4—442no—
243C2×D4—442no—
244C2×D4—442no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—442no—
248C22×C4D8811yescharacteristic
249C22×C4D8812yes—
250C22×C4C2×D4412yes—
251C22×C4C2×D4411yescharacteristic
252Q16—222no—
253Q16—222no—
254SD16—444no—
255D8—222no—
256D8—222no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—42no—
263C2×C8C2×D4411yescharacteristic
264C2×C8C2×D4412yes—
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—222no—
267C4⋊C4—222no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C42—442no—
276C16—21no—
277C16—22no—
278C16—21no—
279C11#3376311yescharacteristic, complemented, Sylow
280C23—41no—
281C23—42no—
282C23—442no—
283C23C2×D8812yes—
284C23C2×D8811yescharacteristic
285Q8—442no—
286Q8—442no—
287D4—442no—
288D4—442no—
289D4—884no—
290D4—884no—
291D4—884no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—884no—
302C2×C4C2×D8812yes—
303C2×C4C2×D8811yescharacteristic
304C2×C4C22×D4411yescharacteristic
305C8—22no—
306C8—21no—
307C8#6703711yescharacteristic
308C8#6703711yescharacteristic
309C22—22no—
310C22—21no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—44no—
315C22—882no—
316C22—882no—
317C22—882no—
318C22C22×D8811yescharacteristic
319C4—22no—
320C4—21no—
321C4—882no—
322C4—882no—
323C4—882no—
324C4#1062302411yescharacteristic
325C4#1062327911yescharacteristic
326C2—42no—
327C2—41no—
328C2—1762no—
329C2#1307936711yescharacteristic
330C2#1308175212yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2112C2
socleC22×C11C22×D8
hypercenter#2112D11
hypocenterC11#33763
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
1. #13078197C2semidirect
2. #13070825C2semidirect
3. #13070808C2semidirect
4. #13070729C2semidirect
5. #13070724C2semidirect
6. #13070719C2semidirect
7. #13070558C2semidirect
8. #13070541C2semidirect
9. C11×#2112C2semidirect
23. C2×Dic88C22semidirect
24. C2×#66864C22semidirect
25. C2×D176C22semidirect
28. #10622147C22semidirect
29. #10622147C22semidirect
30. #10622143C22semidirect
31. #10622143C22semidirect
32. #10622142C22semidirect
33. #10622141C22semidirect
34. #10622141C22semidirect
123. #2112D11semidirect
279. C11#33763semidirect

Maximal subgroups

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

subgroupindex
#130781972
#130708252
#130708082
#130707292
#130707242
#130707192
#130705582
#130705412
C11×#21122
#3376311