Finite Group Databasebeta

← #14909571

Subgroups — #14909571

Order 2816.

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

normal subgroups only

This group has 584 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
1D11×#467C212yesmaximal
2#13070815C212yesmaximal, complemented
3#13070812C212yesmaximal, complemented
4#13070724C211yesmaximal, characteristic, complemented
5#13070722C212yesmaximal, complemented
6#13070551C212yesmaximal, complemented
7#13070548C212yesmaximal, complemented
8#13070226C211yesmaximal, characteristic
9C11×#2219C211yesmaximal, characteristic, complemented
10C2×Q16×D11C2212yes—
11C22×C8×D11C2211yescharacteristic
12D11×C22⋊Q8—22no—
13C2×C11×Q32C2211yescharacteristic, complemented
14C2×C11×M32C2211yescharacteristic
15C11×#467C2212yes—
16#10622801C2212yes—
17C2×#66893C2212yescomplemented
18#10622729C2212yes—
19C2×#66876C2211yescharacteristic
20#10622664—22no—
21C2×Dic88C2211yescharacteristic, complemented
22#10622500C2212yes—
23D11×#107C2212yes—
24#10622426—22no—
25D11×#103—22no—
26C11×#367C2211yescharacteristic, complemented
27C11×#358C2212yescomplemented
28#10622202C2212yescomplemented
29(C2×D11)⋊C16C2212yes—
30(C2×D11)⋊C16C2212yes—
31#10622143C2211yescharacteristic, complemented
32#10622141C2212yescomplemented
33#10622130C2212yescomplemented
34#10622128C2212yescomplemented
35C2×Q8×D11—22no—
36C22×C4×D11D411yescharacteristic
37C2×C11×Q16C2312yes—
38C22×C8×C11C2311yescharacteristic
39C11×C22⋊Q8—22no—
40#66999—22no—
41C2×#4326—22no—
42#66977—22no—
43C22×C11⋊C8D411yescharacteristic
44Q16×D11—42no—
45Q16×D11—42no—
46C2×Dic44C2312yes—
47C2×C8×D11—41no—
48C2×C8×D11—41no—
49C2×C8×D11D412yes—
50C2×C8×D11C2312yes—
51#66950—22no—
52#66949—42no—
53C4⋊C4×D11—22no—
54C4⋊C4×D11—42no—
55C22⋊C4×D11—42no—
56#66931—42no—
57C11×Q32—41no—
58C11×M32—41no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107C2312yes—
62C11×#103—22no—
63#66899—22no—
64#66893—42no—
65#66882C2312yes—
66#66880—22no—
67#66876—41no—
68C2×C11⋊C16C2312yes—
69#66874—22no—
70#66871—22no—
71Dic88—41no—
72#33761—111nomaximal, Sylow
73C23×D11D811yescharacteristic
74C2×Q8×C11—22no—
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11D811yescharacteristic
77Q8×D11—44no—
78Q8×D11—44no—
79C2×C4×D11—41no—
80C2×C4×D11—41no—
81C2×C4×D11—42no—
82C2×C4×D11—42no—
83C2×C4×D11D812yes—
84C2×C4×D11C2×D412yes—
85C2×Dic22—22no—
86C2×Dic22—42no—
87C11×Q16—22no—
88C11×Q16—22no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4—22no—
94C11×C4⋊C4—42no—
95C11×C22⋊C4—42no—
96C22⋊Dic11—42no—
97#4326—44no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100C4⋊Dic11—22no—
101C4⋊Dic11—42no—
102Dic11⋊C4—42no—
103Dic11⋊C4—42no—
104Dic11⋊C4—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—
115C2×#467—112no—
116#2235—112no—
117#2235—112no—
118#2219—111no—
119#2219—112no—
120#2219D1111yescharacteristic, complemented
121#2188—112no—
122#2188—112no—
123#2112—111no—
124C23×C11C2×D811yescharacteristic
125C22×D11—24no—
126C22×D11—41no—
127C22×D11C2×D812yes—
128Q8×C11—42no—
129Q8×C11—42no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C2×Dic11—41no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11C2×D812yes—
140C4×D11—22no—
141C4×D11—22no—
142C4×D11—42no—
143C4×D11—84no—
144C4×D11—84no—
145Dic22—42no—
146Dic22—42no—
147Dic22—84no—
148C8×C11—21no—
149C8×C11H(5,𝔽2)11yescharacteristic
150C8×C11H(5,𝔽2)11yescharacteristic
151C11⋊C8—22no—
152C22×Q16—112no—
153C23×C8—111no—
154C2×C22⋊Q8—222no—
155C2×Q32—112no—
156C2×Q32—111no—
157C2×Q32C2×D1111yescharacteristic, complemented
158C2×M32—111no—
159C2×M32C2×D1111yescharacteristic
160#467—112no—
161#467—112no—
162#467—112no—
163#467—222no—
164#467—222no—
165#467C2×D1112yes—
166C2×#107—112no—
167C2×#103—222no—
168#367—111no—
169#367—112no—
170#367C2×D1111yescharacteristic, complemented
171#358—112no—
172#358—112no—
173#358—112no—
174#358C2×D1112yescomplemented
175C22⋊C16—112no—
176C22⋊C16—112no—
177C22×C11—22no—
178C22×C11—21no—
179C22×C11C22×D811yescharacteristic
180C2×D11—22no—
181C2×D11—22no—
182C2×D11—44no—
183C2×D11#51014yes—
184C4×C11—21no—
185C4×C11—82no—
186C4×C11—82no—
187C4×C11#53411yescharacteristic
188C4×C11#57511yescharacteristic
189Dic11—22no—
190Dic11—82no—
191Dic11—82no—
192C22×Q8—222no—
193C23×C4—111no—
194C2×Q16—112no—
195C2×Q16—222no—
196C2×Q16—442no—
197C2×Q16—442no—
198C2×Q16C22×D1112yes—
199C22×C8—111no—
200C22×C8—112no—
201C22×C8—112no—
202C22×C8—441no—
203C22×C8—441no—
204C22×C8C22×D1111yescharacteristic
205C22⋊Q8—22no—
206C22⋊Q8—222no—
207C22⋊Q8—222no—
208C22⋊Q8—222no—
209C22⋊Q8—442no—
210C22⋊Q8—442no—
211C2×C4⋊C4—222no—
212C2×C4⋊C4—442no—
213C2×C22⋊C4—442no—
214Q32—41no—
215Q32—441no—
216Q32—442no—
217M32—41no—
218M32—441no—
219C2×C16—112no—
220C2×C16C22×D1111yescharacteristic
221C2×C16C22×D1111yescharacteristic
222#107—112no—
223#107—222no—
224#107C22×D1112yes—
225#103—22no—
226#103—222no—
227#103—222no—
228#103—222no—
229C2×C11—41no—
230C2×C11#318611yescharacteristic
231C2×C11C2×#51012yes—
232D11—24no—
233C24—111no—
234C2×Q8—22no—
235C2×Q8—222no—
236C2×Q8—442no—
237C2×Q8—444no—
238C2×Q8—444no—
239C22×C4—111no—
240C22×C4—112no—
241C22×C4—112no—
242C22×C4—441no—
243C22×C4—441no—
244C22×C4—442no—
245C22×C4—442no—
246C22×C4D4×D1111yescharacteristic
247Q16—22no—
248Q16—22no—
249Q16—222no—
250Q16—222no—
251Q16—444no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—112no—
255C2×C8—222no—
256C2×C8—222no—
257C2×C8—442no—
258C2×C8—441no—
259C2×C8D4×D1111yescharacteristic
260C2×C8C23×D1111yescharacteristic
261C4⋊C4—22no—
262C4⋊C4—42no—
263C4⋊C4—222no—
264C4⋊C4—442no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C4⋊C4—442no—
268C22⋊C4—42no—
269C22⋊C4—442no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C16—21no—
273C16—21no—
274C16—222no—
275C11#3376111yescharacteristic, complemented, Sylow
276C23—112no—
277C23—224no—
278C23—441no—
279C23D8×D1111yescharacteristic
280Q8—42no—
281Q8—42no—
282Q8—442no—
283Q8—442no—
284Q8—884no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—112no—
290C2×C4—222no—
291C2×C4—222no—
292C2×C4—442no—
293C2×C4—441no—
294C2×C4—442no—
295C2×C4—442no—
296C2×C4—884no—
297C2×C4—884no—
298C2×C4D8×D1111yescharacteristic
299C2×C4C2×D4×D1111yescharacteristic
300C8—21no—
301C8—222no—
302C8#6703711yescharacteristic
303C8#6704211yescharacteristic
304C22—21no—
305C22—22no—
306C22—114no—
307C22—222no—
308C22—222no—
309C22—444no—
310C22C2×D8×D1111yescharacteristic
311C4—21no—
312C4—82no—
313C4—82no—
314C4—222no—
315C4—882no—
316C4—882no—
317C4#1062313611yescharacteristic
318C4#1062329911yescharacteristic
319C2—41no—
320C2—224no—
321C2#1307936311yescharacteristic
322C2D11×#51012yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2219C2
socleC22×C11C22×D8
prime radicalC23×D11D8
hypercenter#2219D11
hypocenterC11#33761
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
2. #13070815C2semidirect
3. #13070812C2semidirect
4. #13070724C2semidirect
5. #13070722C2semidirect
6. #13070551C2semidirect
7. #13070548C2semidirect
9. C11×#2219C2semidirect
13. C2×C11×Q32C22semidirect
17. C2×#66893C22semidirect
21. C2×Dic88C22semidirect
26. C11×#367C22semidirect
27. C11×#358C22semidirect
28. #10622202C22semidirect
31. #10622143C22semidirect
32. #10622141C22semidirect
33. #10622130C22semidirect
34. #10622128C22semidirect
120. #2219D11semidirect
157. C2×Q32C2×D11semidirect
170. #367C2×D11semidirect
174. #358C2×D11semidirect
275. C11#33761semidirect

Maximal subgroups

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

subgroupindex
D11×#4672
#130708152
#130708122
#130707242
#130707222
#130705512
#130705482
#130702262
C11×#22192
#3376111