Finite Group Databasebeta

← #14909538

Subgroups — #14909538

Order 2816.

598 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 131 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#13078195C212yesmaximal, complemented
2#13070826C212yesmaximal, complemented
3#13070805C212yesmaximal, complemented
4#13070710C212yesmaximal, complemented
5#13070707C211yesmaximal, characteristic, complemented
6#13070557C212yesmaximal, complemented
7#13070536C212yesmaximal, complemented
8C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
9C11×#2215C211yesmaximal, characteristic, complemented
10C2×#66965C2212yes—
11C22×C8×D11C2211yescharacteristic
12#10623137—22no—
13C2×C11×D16C2211yescharacteristic, complemented
14C22×C11×C16C2211yescharacteristic
15C11×#466C2212yes—
16#10622770C2212yes—
17C2×#66891C2212yescomplemented
18#10622729C2212yes—
19C22×C11⋊C16C2211yescharacteristic
20#10622654—22no—
21C2×Dic88C2211yescharacteristic, complemented
22#10622500C2212yes—
23#10622493C2212yes—
24#10622391—22no—
25#10622385—22no—
26C11×#366C2211yescharacteristic, complemented
27C11×#357C2212yescomplemented
28#10622200C2212yescomplemented
29(C2×D11)⋊C16C2212yes—
30(C2×D11)⋊C16C2212yes—
31#10622142C2211yescharacteristic, complemented
32#10622141C2212yescomplemented
33#10622130C2212yescomplemented
34#10622128C2212yescomplemented
35C2×#4341—22no—
36C22×C4×D11D411yescharacteristic
37C2×C11×D8C2312yes—
38C22×C8×C11C2311yescharacteristic
39C11×#121—22no—
40#66991—22no—
41#66990—42no—
42D4×Dic11—42no—
43C2×#4324—22no—
44#66977—22no—
45C22×C11⋊C8D411yescharacteristic
46#66965—42no—
47#66965—42no—
48C2×Dic44C2312yes—
49C2×C8×D11—41no—
50C2×C8×D11—41no—
51C2×C8×D11D412yes—
52C2×C8×D11C2312yes—
53#66950—22no—
54#66945—22no—
55#66936—42no—
56(C22⋊D11)⋊C4—42no—
57C11×D16—41no—
58C2×C11×C16—41no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107C2312yes—
62C11×#102—22no—
63#66896—22no—
64#66891—42no—
65#66882C2312yes—
66#66880—22no—
67C2×C11⋊C16—41no—
68C2×C11⋊C16C2312yes—
69#66874—22no—
70#66872—22no—
71Dic88—41no—
72#33757—111nomaximal, Sylow
73C23×D11D811yescharacteristic
74C2×D4×C11—22no—
75C2×D4×C11—42no—
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C22×Dic11—42no—
80C22×Dic11D811yescharacteristic
81#4341—44no—
82#4341—44no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11D812yes—
86C2×C4×D11C2×D412yes—
87C2×Dic22—22no—
88C11×D8—22no—
89C11×D8—22no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—22no—
95C11×C22⋊C4—42no—
96C22⋊Dic11—42no—
97C22⋊Dic11—42no—
98#4324—44no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101C4⋊Dic11—22no—
102C4⋊Dic11—42no—
103Dic11⋊C4—42no—
104C4×Dic11—42no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8C2×D412yes—
107Dic44—22no—
108Dic44—22no—
109C8×D11—22no—
110C8×D11—22no—
111C8×D11—42no—
112C11×C16—21no—
113C11×C16—21no—
114C11⋊C16—22no—
115#3050—112no—
116#2237—112no—
117#2234—112no—
118#2217—112no—
119#2216—111no—
120#2215D1111yescharacteristic, complemented
121#2189—112no—
122#2186—112no—
123C2×C22⋊C16—111no—
124C23×C11—42no—
125C23×C11C2×D811yescharacteristic
126C22×D11—22no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11C2×D812yes—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—84no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—42no—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C22×D411yescharacteristic
138C22⋊D11—84no—
139C22⋊D11—84no—
140C2×Dic11—41no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—84no—
144C2×Dic11C2×D812yes—
145C4×D11—22no—
146C4×D11—22no—
147C4×D11—42no—
148Dic22—42no—
149Dic22—42no—
150C8×C11—21no—
151C8×C11H(5,𝔽2)11yescharacteristic
152C8×C11H(5,𝔽2)11yescharacteristic
153C11⋊C8—22no—
154C2×#135—112no—
155C23×C8—111no—
156#525—222no—
157C2×Q32—111no—
158C2×SD32—112no—
159C2×D16C2×D1111yescharacteristic, complemented
160C22×C16—111no—
161C22×C16C2×D1111yescharacteristic
162#467—112no—
163#467—112no—
164#466—112no—
165#466C2×D1112yes—
166#465—222no—
167#465—222no—
168#427—112no—
169#416—222no—
170#367—112no—
171#366—111no—
172#366C2×D1111yescharacteristic, complemented
173#358—112no—
174#358—112no—
175#357—112no—
176#357C2×D1112yescomplemented
177C22⋊C16—112no—
178C22⋊C16—112no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11#50812yes—
185C22×C11C22×D811yescharacteristic
186C2×D11—22no—
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—44no—
190C4×C11—21no—
191C4×C11—82no—
192C4×C11#53411yescharacteristic
193C4×C11#57511yescharacteristic
194Dic11—22no—
195Dic11—82no—
196Dic11—82no—
197C2×#41—222no—
198C23×C4—111no—
199#135—442no—
200#135—442no—
201C2×Q16—112no—
202C2×SD16—222no—
203C2×D8C22×D1112yes—
204C22×C8—111no—
205C22×C8—112no—
206C22×C8—112no—
207C22×C8—441no—
208C22×C8—441no—
209C22×C8C22×D1111yescharacteristic
210#123—442no—
211C22⋊Q8—222no—
212C22⋊Q8—222no—
213#121—22no—
214#121—222no—
215#120—442no—
216C4×D4—442no—
217C4×D4—442no—
218#117—222no—
219Q32—441no—
220SD32—442no—
221D16—41no—
222C2×C16—41no—
223C2×C16—112no—
224C2×C16—441no—
225C2×C16C22×D1111yescharacteristic
226C2×C16C22×D1111yescharacteristic
227#107—112no—
228#107C22×D1112yes—
229#106—222no—
230#103—222no—
231#103—222no—
232#102—22no—
233#102—222no—
234C2×C11—22no—
235C2×C11—162no—
236C2×C11#318611yescharacteristic
237C2×C11C2×#50811yescharacteristic
238C2×C11#341411yescharacteristic
239D11—42no—
240C24—111no—
241#41—444no—
242#41—444no—
243C2×Q8—222no—
244C2×D4—22no—
245C2×D4—42no—
246C2×D4—442no—
247C2×D4—442no—
248C22×C4—111no—
249C22×C4—112no—
250C22×C4—112no—
251C22×C4—441no—
252C22×C4—441no—
253C22×C4—442no—
254C22×C4D4×D1111yescharacteristic
255Q16—222no—
256Q16—222no—
257SD16—444no—
258D8—22no—
259D8—22no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—112no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—442no—
266C2×C8—441no—
267C2×C8D4×D1111yescharacteristic
268C2×C8C23×D1111yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—222no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C22⋊C4—42no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C22⋊C4—442no—
278C42—442no—
279C16—21no—
280C16—21no—
281C16—222no—
282C11#3375711yescharacteristic, complemented, Sylow
283C23—42no—
284C23—112no—
285C23—222no—
286C23—441no—
287C23—441no—
288C23D8×D1111yescharacteristic
289Q8—442no—
290Q8—442no—
291D4—42no—
292D4—42no—
293D4—84no—
294D4—884no—
295D4—884no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—112no—
300C2×C4—222no—
301C2×C4—222no—
302C2×C4—442no—
303C2×C4—441no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4—884no—
307C2×C4D8×D1111yescharacteristic
308C2×C4C2×D4×D1111yescharacteristic
309C8—21no—
310C8—222no—
311C8#6703711yescharacteristic
312C8#6704211yescharacteristic
313C22—21no—
314C22—21no—
315C22—82no—
316C22—82no—
317C22—82no—
318C22—222no—
319C22—222no—
320C22—222no—
321C22—444no—
322C22#1062252512yes—
323C22C2×D8×D1111yescharacteristic
324C4—21no—
325C4—82no—
326C4—222no—
327C4—882no—
328C4—882no—
329C4#1062313611yescharacteristic
330C4#1062329911yescharacteristic
331C2—22no—
332C2—162no—
333C2—442no—
334C2#1307936311yescharacteristic
335C2C2×#1062252511yescharacteristic
336C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2215C2
socleC22×C11C22×D8
hypercenter#2215D11
hypocenterC11#33757
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. #13078195C2semidirect
2. #13070826C2semidirect
3. #13070805C2semidirect
4. #13070710C2semidirect
5. #13070707C2semidirect
6. #13070557C2semidirect
7. #13070536C2semidirect
8. C2×(C2×D11)⋊C16C2semidirect
9. C11×#2215C2semidirect
13. C2×C11×D16C22semidirect
17. C2×#66891C22semidirect
21. C2×Dic88C22semidirect
26. C11×#366C22semidirect
27. C11×#357C22semidirect
28. #10622200C22semidirect
31. #10622142C22semidirect
32. #10622141C22semidirect
33. #10622130C22semidirect
34. #10622128C22semidirect
120. #2215D11semidirect
159. C2×D16C2×D11semidirect
172. #366C2×D11semidirect
176. #357C2×D11semidirect
282. C11#33757semidirect

Maximal subgroups

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

subgroupindex
#130781952
#130708262
#130708052
#130707102
#130707072
#130705572
#130705362
C2×(C2×D11)⋊C162
C11×#22152
#3375711