Finite Group Databasebeta

← #14909522

Subgroups — #14909522

Order 2816.

590 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 139 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#13070820C212yesmaximal, complemented
3#13070817C212yesmaximal, complemented
4#13070707C211yesmaximal, characteristic, complemented
5#13070705C212yesmaximal, complemented
6#13070551C212yesmaximal, complemented
7#13070548C212yesmaximal, complemented
8C2×(C2×D11)⋊C16C211yesmaximal, characteristic
9C11×#2216C211yesmaximal, characteristic, complemented
10C2×Q16×D11C2212yes—
11C22×C8×D11C2211yescharacteristic
12D11×C22⋊Q8—22no—
13C2×C11×Q32C2211yescharacteristic, complemented
14C22×C11×C16C2211yescharacteristic
15C11×#467C2212yes—
16#10622801C2212yes—
17C2×#66893C2212yescomplemented
18#10622729C2212yes—
19C22×C11⋊C16C2211yescharacteristic
20#10622664—22no—
21C2×Dic88C2211yescharacteristic, complemented
22#10622500C2212yes—
23D11×#107C2212yes—
24#10622426—22no—
25D11×#103—22no—
26C11×#366C2211yescharacteristic, complemented
27C11×#358C2212yescomplemented
28#10622202C2212yescomplemented
29(C2×D11)⋊C16C2212yes—
30(C2×D11)⋊C16C2212yes—
31#10622142C2211yescharacteristic, complemented
32#10622141C2212yescomplemented
33#10622130C2212yescomplemented
34#10622127C2212yescomplemented
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—
58C2×C11×C16—41no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107C2312yes—
62C11×#103—22no—
63#66899—22no—
64#66893—42no—
65#66882C2312yes—
66#66880—22no—
67C2×C11⋊C16—41no—
68C2×C11⋊C16C2312yes—
69#66874—22no—
70#66871—22no—
71Dic88—41no—
72#33755—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#2236—112no—
117#2236—112no—
118#2216—111no—
119#2216—112no—
120#2216D1111yescharacteristic, complemented
121#2188—112no—
122#2188—112no—
123C2×C22⋊C16—111no—
124C23×C11C2×D811yescharacteristic
125C22×D11—41no—
126C22×D11—41no—
127C22×D11Q3214yescomplemented
128C22×D11C2×D812yes—
129Q8×C11—42no—
130Q8×C11—42no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11C22×D411yescharacteristic
137C2×Dic11—41no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11C2×D812yes—
141C4×D11—22no—
142C4×D11—22no—
143C4×D11—42no—
144C4×D11—84no—
145C4×D11—84no—
146Dic22—42no—
147Dic22—42no—
148Dic22—84no—
149C8×C11—21no—
150C8×C11H(5,𝔽2)11yescharacteristic
151C8×C11H(5,𝔽2)11yescharacteristic
152C11⋊C8—22no—
153C22×Q16—112no—
154C23×C8—111no—
155C2×C22⋊Q8—222no—
156C2×Q32—112no—
157C2×Q32—111no—
158C2×Q32C2×D1111yescharacteristic, complemented
159C22×C16—111no—
160C22×C16C2×D1111yescharacteristic
161#467—112no—
162#467—112no—
163#467—112no—
164#467—222no—
165#467—222no—
166#467C2×D1112yes—
167C2×#107—112no—
168C2×#103—222no—
169#366—111no—
170#366—112no—
171#366C2×D1111yescharacteristic, complemented
172#358—112no—
173#358—112no—
174#358—112no—
175#358C2×D1112yescomplemented
176C22⋊C16—112no—
177C22⋊C16—112no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11C2×Q3212yes—
181C22×C11C22×D811yescharacteristic
182C2×D11—22no—
183C2×D11—22no—
184C2×D11—44no—
185C2×D11C2×Q3214yes—
186C4×C11—21no—
187C4×C11—82no—
188C4×C11—82no—
189C4×C11#53411yescharacteristic
190C4×C11#57511yescharacteristic
191Dic11—22no—
192Dic11—82no—
193Dic11—82no—
194C22×Q8—222no—
195C23×C4—111no—
196C2×Q16—112no—
197C2×Q16—222no—
198C2×Q16—442no—
199C2×Q16—442no—
200C2×Q16C22×D1112yes—
201C22×C8—111no—
202C22×C8—112no—
203C22×C8—112no—
204C22×C8—441no—
205C22×C8—441no—
206C22×C8C22×D1111yescharacteristic
207C22⋊Q8—22no—
208C22⋊Q8—222no—
209C22⋊Q8—222no—
210C22⋊Q8—222no—
211C22⋊Q8—442no—
212C22⋊Q8—442no—
213C2×C4⋊C4—222no—
214C2×C4⋊C4—442no—
215C2×C22⋊C4—442no—
216Q32—41no—
217Q32—441no—
218Q32—442no—
219C2×C16—41no—
220C2×C16—112no—
221C2×C16—441no—
222C2×C16C22×D1111yescharacteristic
223C2×C16C22×D1111yescharacteristic
224#107—112no—
225#107—222no—
226#107C22×D1112yes—
227#103—22no—
228#103—222no—
229#103—222no—
230#103—222no—
231C2×C11—22no—
232C2×C11#318611yescharacteristic
233C2×C11C22×Q3211yescharacteristic
234C2×C11#341411yescharacteristic
235D11—24no—
236C24—111no—
237C2×Q8—22no—
238C2×Q8—222no—
239C2×Q8—442no—
240C2×Q8—444no—
241C2×Q8—444no—
242C22×C4—111no—
243C22×C4—112no—
244C22×C4—112no—
245C22×C4—441no—
246C22×C4—441no—
247C22×C4—442no—
248C22×C4—442no—
249C22×C4D4×D1111yescharacteristic
250Q16—22no—
251Q16—22no—
252Q16—222no—
253Q16—222no—
254Q16—444no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—112no—
258C2×C8—222no—
259C2×C8—222no—
260C2×C8—442no—
261C2×C8—441no—
262C2×C8D4×D1111yescharacteristic
263C2×C8C23×D1111yescharacteristic
264C4⋊C4—22no—
265C4⋊C4—42no—
266C4⋊C4—222no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C22⋊C4—42no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C16—21no—
276C16—21no—
277C16—222no—
278C11#3375511yescharacteristic, complemented, Sylow
279C23—112no—
280C23—114no—
281C23—441no—
282C23—441no—
283C23D8×D1111yescharacteristic
284Q8—42no—
285Q8—42no—
286Q8—442no—
287Q8—442no—
288Q8—884no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—112no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—442no—
297C2×C4—441no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—884no—
301C2×C4—884no—
302C2×C4D8×D1111yescharacteristic
303C2×C4C2×D4×D1111yescharacteristic
304C8—21no—
305C8—222no—
306C8#6703711yescharacteristic
307C8#6704211yescharacteristic
308C22—21no—
309C22—21no—
310C22—114no—
311C22—222no—
312C22—222no—
313C22—444no—
314C22D11×Q3212yes—
315C22C2×D8×D1111yescharacteristic
316C4—21no—
317C4—82no—
318C4—82no—
319C4—222no—
320C4—882no—
321C4—882no—
322C4#1062313611yescharacteristic
323C4#1062329911yescharacteristic
324C2—22no—
325C2—224no—
326C2#1307936311yescharacteristic
327C2C2×D11×Q3211yescharacteristic
328C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2216C2
socleC22×C11C22×D8
prime radicalC23×D11D8
hypercenter#2216D11
hypocenterC11#33755
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

Complements

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

NH ≅ G/Ntype
2. #13070820C2semidirect
3. #13070817C2semidirect
4. #13070707C2semidirect
5. #13070705C2semidirect
6. #13070551C2semidirect
7. #13070548C2semidirect
9. C11×#2216C2semidirect
13. C2×C11×Q32C22semidirect
17. C2×#66893C22semidirect
21. C2×Dic88C22semidirect
26. C11×#366C22semidirect
27. C11×#358C22semidirect
28. #10622202C22semidirect
31. #10622142C22semidirect
32. #10622141C22semidirect
33. #10622130C22semidirect
34. #10622127C22semidirect
120. #2216D11semidirect
127. C22×D11Q32semidirect
158. C2×Q32C2×D11semidirect
171. #366C2×D11semidirect
175. #358C2×D11semidirect
278. C11#33755semidirect

Maximal subgroups

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

subgroupindex
D11×#4672
#130708202
#130708172
#130707072
#130707052
#130705512
#130705482
C2×(C2×D11)⋊C162
C11×#22162
#3375511