Finite Group Databasebeta

← #14909883

Subgroups — #14909883

Order 2816.

504 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079130C211yesmaximal, characteristic, complemented
2#13070896C211yesmaximal, characteristic, complemented
3#13070889C211yesmaximal, characteristic, complemented
4#13070839C211yesmaximal, characteristic, complemented
5#13070839C211yesmaximal, characteristic, complemented
6#13070804C214yesmaximal, complemented
7#13070773C214yesmaximal, complemented
8#13070415C211yesmaximal, characteristic, complemented
9C11×#3169C211yesmaximal, characteristic
10C11×#532—21no—
11#10623001—21no—
12C11×#500C2211yescharacteristic
13C11×#493C2211yescharacteristic
14C11×#486—21no—
15C11×#466—21no—
16C11×#466C2212yes—
17C4×C11×D8—21no—
18C4×C11×D8C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20#10622719—21no—
21#10622719C2212yes—
22#10622296—21no—
23#10622296C2212yes—
24#10622295C2211yescharacteristic
25#10622295C2211yescharacteristic
26#10622293—21no—
27#10622200C2214yes—
28#10622200C2214yes—
29C22⋊(C11⋊C16)C2212yes—
30#10622128C2214yes—
31#10622127C2214yes—
32C4⋊(C11⋊C16)C2212yes—
33C4×C11⋊C16C2211yescharacteristic
34C4×C11⋊C16C2211yescharacteristic
35C2×C11×#41—41no—
36C2×C11×D8—21no—
37C2×C11×D8C2312yes—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11C2311yescharacteristic
40C11×C4⋊Q8—21no—
41C11×#127—21no—
42C11×#124—41no—
43C11×#121—22no—
44C11×#121—41no—
45C4×D4×C11—22no—
46C4×D4×C11—41no—
47C2×C42×C11D411yescharacteristic
48#66979—22no—
49#66977—41no—
50#66977—41no—
51#66923—22no—
52#66922—21no—
53#66922—21no—
54C4×Dic22—41no—
55C4×Dic22—41no—
56C11×#107—21no—
57C11×#107C2312yes—
58C11×#102—22no—
59C11×#102—22no—
60C4×C8×C11D411yescharacteristic
61C4×C8×C11D411yescharacteristic
62C4×C8×C11C2311yescharacteristic
63C4×C8×C11C2311yescharacteristic
64#66882—21no—
65#66882—21no—
66#66882C2312yes—
67#66882C2312yes—
68#66881—22no—
69#66881—22no—
70C2×C11⋊C16C2312yes—
71C2×C11⋊C16C2312yes—
72#33794—111nomaximal, Sylow
73C11×#41—84no—
74C2×Q8×C11—41no—
75C2×D4×C11—22no—
76C2×D4×C11—42no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C22×C4×C11—42no—
80C22×C4×C11D811yescharacteristic
81C22×C4×C11D811yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C2×Dic22—41no—
84C2×Dic22—41no—
85C11×D8—24no—
86C11×D8—42no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4—22no—
94C11×C4⋊C4—41no—
95C11×C22⋊C4—42no—
96C11×C22⋊C4—42no—
97C42×C11D811yescharacteristic
98C42×C11D811yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C22⋊Dic11—42no—
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108C4×Dic11—42no—
109C11⋊C16—22no—
110C11⋊C16—22no—
111#3169D1111yescharacteristic
112#3160—111no—
113#2254—111no—
114#2252—111no—
115#2240—111no—
116#2240—111no—
117#2234—114no—
118#2228—114no—
119#2162—111no—
120C23×C11—42no—
121C23×C11C2×D811yescharacteristic
122Q8×C11—82no—
123D4×C11—42no—
124D4×C11—42no—
125D4×C11—84no—
126D4×C11—82no—
127D4×C11—82no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—42no—
133C2×C4×C11—84no—
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×Dic11—42no—
141C2×Dic11—42no—
142Dic22—82no—
143Dic22—82no—
144C8×C11—21no—
145C8×C11—21no—
146C8×C11#13712yes—
147C8×C112−1+412yes—
148#533—221no—
149#532—21no—
150#500—111no—
151#500—111no—
152#500C2×D1111yescharacteristic
153#499—112no—
154#499—221no—
155#498—221no—
156#493C2×D1111yescharacteristic
157#486—21no—
158#466—21no—
159#466C2×D1112yes—
160C4×D8—21no—
161C4×D8C2×D1112yes—
162#427—112no—
163#427—221no—
164C2×C4×C8C2×D1111yescharacteristic
165#367—114no—
166#366—114no—
167C4⋊C16—112no—
168#357—114no—
169#357—114no—
170C22⋊C16—112no—
171C4×C16—111no—
172C4×C16—111no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—82no—
177C22×C11—82no—
178C22×C11—82no—
179C22×C11C22×D811yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—82no—
184C4×C11#50812yes—
185C4×C11#50912yes—
186C4×C11#53611yescharacteristic
187C4×C11C2×#13711yescharacteristic
188Dic11—82no—
189Dic11—82no—
190C2×#41—41no—
191C2×D8—21no—
192C2×D8C22×D1112yes—
193C22×C8C22⋊D1111yescharacteristic
194C22×C8C22×D1111yescharacteristic
195C4⋊Q8—21no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198#127—21no—
199#125—222no—
200#124—41no—
201C22⋊Q8—441no—
202C22⋊Q8—441no—
203#121—22no—
204#121—41no—
205C4×Q8—441no—
206C4×Q8—441no—
207C4×D4—22no—
208C4×D4—41no—
209#117—222no—
210C2×C42C22⋊D1111yescharacteristic
211C2×C16—112no—
212C2×C16—112no—
213#107—21no—
214#107—112no—
215#107—112no—
216#107—221no—
217#107—221no—
218#107C22×D1112yes—
219#106—222no—
220#106—222no—
221#102—22no—
222#102—22no—
223C4×C8C22⋊D1111yescharacteristic
224C4×C8C22⋊D1111yescharacteristic
225C4×C8C22×D1111yescharacteristic
226C4×C8C22×D1111yescharacteristic
227C2×C11—41no—
228C2×C11—162no—
229C2×C11#322611yescharacteristic
230C2×C11C2×#50811yescharacteristic
231C2×C11C2×#50911yescharacteristic
232#41—84no—
233C2×Q8—41no—
234C2×Q8—441no—
235C2×Q8—441no—
236C2×D4—22no—
237C2×D4—42no—
238C2×D4—41no—
239C2×D4—41no—
240C22×C4—42no—
241C22×C4#432311yescharacteristic
242C22×C4#432311yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244D8—24no—
245D8—42no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8C2×C22⋊D1111yescharacteristic
249C2×C8C2×C22⋊D1111yescharacteristic
250C2×C8C2×C22⋊D1111yescharacteristic
251C2×C8C23×D1111yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—222no—
255C4⋊C4—222no—
256C4⋊C4—442no—
257C4⋊C4—442no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—442no—
263C42—442no—
264C42#432311yescharacteristic
265C42#432311yescharacteristic
266C42C2×C22⋊D1111yescharacteristic
267C42C2×C22⋊D1111yescharacteristic
268C16—222no—
269C16—222no—
270C11#3379411yescharacteristic, complemented, Sylow
271C23—42no—
272C23C2×#432311yescharacteristic
273Q8—82no—
274Q8—882no—
275Q8—882no—
276D4—42no—
277D4—42no—
278D4—84no—
279D4—82no—
280D4—82no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—84no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4C2×#432311yescharacteristic
290C2×C4C2×#432311yescharacteristic
291C2×C4C2×#432311yescharacteristic
292C2×C4C2×#432311yescharacteristic
293C2×C4C2×#432311yescharacteristic
294C2×C4C22×C22⋊D1111yescharacteristic
295C8—21no—
296C8—21no—
297C8#6700412yes—
298C8#6704312yes—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—82no—
303C22—82no—
304C22—82no—
305C22C22×#432311yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—82no—
310C4—882no—
311C4—882no—
312C4#1062276012yes—
313C4#1062280712yes—
314C4C2×#6700411yescharacteristic
315C4#1062335611yescharacteristic
316C2—41no—
317C2—162no—
318C2#1307973411yescharacteristic
319C2C2×#1062280711yescharacteristic
320C2C2×#1062276011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3169C2
socleC22×C11C22×D8
hypercenter#3169D11
hypocenterC11#33794
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13079130C2semidirect
2. #13070896C2semidirect
3. #13070889C2semidirect
4. #13070839C2semidirect
5. #13070839C2semidirect
6. #13070804C2semidirect
7. #13070773C2semidirect
8. #13070415C2semidirect
270. C11#33794semidirect

Maximal subgroups

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

subgroupindex
#130791302
#130708962
#130708892
#130708392
#130708042
#130707732
#130704152
C11×#31692
#3379411