Finite Group Databasebeta

← #14909587

Subgroups — #14909587

Order 2816.

592 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 127 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#13070827C212yesmaximal, complemented
3#13070806C212yesmaximal, complemented
4#13070727C212yesmaximal, complemented
5#13070724C211yesmaximal, characteristic, complemented
6#13070557C212yesmaximal, complemented
7#13070536C212yesmaximal, complemented
8#13070226C211yesmaximal, characteristic, complemented
9C11×#2218C211yesmaximal, characteristic, complemented
10C2×#66965C2212yes—
11C22×C8×D11C2211yescharacteristic
12#10623137—22no—
13C2×C11×D16C2211yescharacteristic, complemented
14C2×C11×M32C2211yescharacteristic
15C11×#466C2212yes—
16#10622770C2212yes—
17C2×#66891C2212yescomplemented
18#10622729C2212yes—
19C2×#66876C2211yescharacteristic
20#10622654—22no—
21C2×Dic88C2211yescharacteristic, complemented
22#10622500C2212yes—
23#10622493C2212yes—
24#10622391—22no—
25#10622385—22no—
26C11×#367C2211yescharacteristic, complemented
27C11×#357C2212yescomplemented
28#10622200C2212yescomplemented
29(C2×D11)⋊C16C2212yes—
30(C2×D11)⋊C16C2212yes—
31#10622143C2211yescharacteristic, complemented
32#10622141C2212yescomplemented
33#10622130C2212yescomplemented
34#10622127C2212yescomplemented
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—
58C11×M32—41no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107C2312yes—
62C11×#102—22no—
63#66896—22no—
64#66891—42no—
65#66882C2312yes—
66#66880—22no—
67#66876—41no—
68C2×C11⋊C16C2312yes—
69#66874—22no—
70#66872—22no—
71Dic88—41no—
72#33763—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#2220—112no—
119#2219—111no—
120#2218D1111yescharacteristic, complemented
121#2189—112no—
122#2186—112no—
123#2112—111no—
124C23×C11—42no—
125C23×C11C2×D811yescharacteristic
126C22×D11—41no—
127C22×D11—42no—
128C22×D11C2×D812yes—
129D4×C11—42no—
130D4×C11—42no—
131D4×C11—84no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—42no—
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11C22×D411yescharacteristic
137C22⋊D11—84no—
138C22⋊D11—84no—
139C2×Dic11—41no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—84no—
143C2×Dic11C2×D812yes—
144C4×D11—22no—
145C4×D11—22no—
146C4×D11—42no—
147Dic22—42no—
148Dic22—42no—
149C8×C11—21no—
150C8×C11H(5,𝔽2)11yescharacteristic
151C8×C11H(5,𝔽2)11yescharacteristic
152C11⋊C8—22no—
153C2×#135—112no—
154C23×C8—111no—
155#525—222no—
156C2×Q32—111no—
157C2×SD32—112no—
158C2×D16C2×D1111yescharacteristic, complemented
159C2×M32—111no—
160C2×M32C2×D1111yescharacteristic
161#467—112no—
162#467—112no—
163#466—112no—
164#466C2×D1112yes—
165#465—222no—
166#465—222no—
167#427—112no—
168#416—222no—
169#367—111no—
170#367C2×D1111yescharacteristic, complemented
171#366—112no—
172#358—112no—
173#358—112no—
174#357—112no—
175#357C2×D1112yescomplemented
176C22⋊C16—112no—
177C22⋊C16—112no—
178C22×C11—22no—
179C22×C11—21no—
180C22×C11—82no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11C22×D811yescharacteristic
184C2×D11—22no—
185C2×D11—22no—
186C2×D11—22no—
187C2×D11—44no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11#53411yescharacteristic
191C4×C11#57511yescharacteristic
192Dic11—22no—
193Dic11—82no—
194Dic11—82no—
195C2×#41—222no—
196C23×C4—111no—
197#135—442no—
198#135—442no—
199C2×Q16—112no—
200C2×SD16—222no—
201C2×D8C22×D1112yes—
202C22×C8—111no—
203C22×C8—112no—
204C22×C8—112no—
205C22×C8—441no—
206C22×C8—441no—
207C22×C8C22×D1111yescharacteristic
208#123—442no—
209C22⋊Q8—222no—
210C22⋊Q8—222no—
211#121—22no—
212#121—222no—
213#120—442no—
214C4×D4—442no—
215C4×D4—442no—
216#117—222no—
217Q32—441no—
218SD32—442no—
219D16—41no—
220M32—41no—
221M32—441no—
222C2×C16—112no—
223C2×C16C22×D1111yescharacteristic
224C2×C16C22×D1111yescharacteristic
225#107—112no—
226#107C22×D1112yes—
227#106—222no—
228#103—222no—
229#103—222no—
230#102—22no—
231#102—222no—
232C2×C11—41no—
233C2×C11—162no—
234C2×C11#318611yescharacteristic
235C2×C11#341412yes—
236D11—42no—
237C24—111no—
238#41—444no—
239#41—444no—
240C2×Q8—222no—
241C2×D4—22no—
242C2×D4—42no—
243C2×D4—442no—
244C2×D4—442no—
245C22×C4—111no—
246C22×C4—112no—
247C22×C4—112no—
248C22×C4—441no—
249C22×C4—441no—
250C22×C4—442no—
251C22×C4D4×D1111yescharacteristic
252Q16—222no—
253Q16—222no—
254SD16—444no—
255D8—22no—
256D8—22no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—112no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8—442no—
263C2×C8—441no—
264C2×C8D4×D1111yescharacteristic
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—222no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C22⋊C4—42no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C42—442no—
276C16—21no—
277C16—21no—
278C16—222no—
279C11#3376311yescharacteristic, complemented, Sylow
280C23—42no—
281C23—112no—
282C23—441no—
283C23—442no—
284C23D8×D1111yescharacteristic
285Q8—442no—
286Q8—442no—
287D4—42no—
288D4—42no—
289D4—84no—
290D4—884no—
291D4—884no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—112no—
296C2×C4—222no—
297C2×C4—222no—
298C2×C4—442no—
299C2×C4—441no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4—884no—
303C2×C4D8×D1111yescharacteristic
304C2×C4C2×D4×D1111yescharacteristic
305C8—21no—
306C8—222no—
307C8#6703711yescharacteristic
308C8#6704211yescharacteristic
309C22—21no—
310C22—22no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—222no—
315C22—222no—
316C22—222no—
317C22—444no—
318C22C2×D8×D1111yescharacteristic
319C4—21no—
320C4—82no—
321C4—222no—
322C4—882no—
323C4—882no—
324C4#1062313611yescharacteristic
325C4#1062329911yescharacteristic
326C2—41no—
327C2—162no—
328C2—442no—
329C2#1307936311yescharacteristic
330C2#1308174812yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2218C2
socleC22×C11C22×D8
hypercenter#2218D11
hypocenterC11#33763
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. #13078195C2semidirect
2. #13070827C2semidirect
3. #13070806C2semidirect
4. #13070727C2semidirect
5. #13070724C2semidirect
6. #13070557C2semidirect
7. #13070536C2semidirect
8. #13070226C2semidirect
9. C11×#2218C2semidirect
13. C2×C11×D16C22semidirect
17. C2×#66891C22semidirect
21. C2×Dic88C22semidirect
26. C11×#367C22semidirect
27. C11×#357C22semidirect
28. #10622200C22semidirect
31. #10622143C22semidirect
32. #10622141C22semidirect
33. #10622130C22semidirect
34. #10622127C22semidirect
120. #2218D11semidirect
158. C2×D16C2×D11semidirect
170. #367C2×D11semidirect
175. #357C2×D11semidirect
279. C11#33763semidirect

Maximal subgroups

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

subgroupindex
#130781952
#130708272
#130708062
#130707272
#130707242
#130705572
#130705362
#130702262
C11×#22182
#3376311