Finite Group Databasebeta

← #14656884

Subgroups — #14656884

Order 2816.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#13077001C211yesmaximal, characteristic
2#13069594C211yesmaximal, characteristic
3#13067180C211yesmaximal, characteristic
4#13066475C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic
6#13066448C211yesmaximal, characteristic
7C11×#1518C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#382C2211yescharacteristic
11#10622598—21no—
12#10622586—21no—
13#10622549C2211yescharacteristic
14C42×Dic11C2211yescharacteristic
15#10622538C2211yescharacteristic
16#10622537C2211yescharacteristic
17#10622268—22no—
18#10622267—22no—
19C11×#328—22no—
20#10622176—22no—
21#10622170—21no—
22#10622170—21no—
23C11×C4⋊Q8Q811yescharacteristic
24C11×C4⋊Q8Q811yescharacteristic
25C11×#125—21no—
26C11×C22⋊Q8—21no—
27C11×C22⋊Q8—21no—
28C4×Q8×C11—21no—
29C4×Q8×C11—21no—
30C11×#117—21no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11—21no—
37C2×C4×Dic11—21no—
38C2×C4×Dic11D411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40C2×#4318—21no—
41C11×C4⋊C8—21no—
42C11×C22⋊C8—21no—
43C4×C8×C11—21no—
44C11×#95—21no—
45C11×#95D412yes—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C11⋊#95D412yes—
50C22⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4×C11⋊C8—21no—
55#10367—111nomaximal, Sylow
56C2×Q8×C11—21no—
57C2×Q8×C11—21no—
58C22×C4×C11—22no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—21no—
63C22×Dic11—21no—
64C22×Dic11—22no—
65C2×C8×C11—41no—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C22⋊C4—41no—
75C42×C11—41no—
76C42×C11C2×Q811yescharacteristic
77C42×C11#4111yescharacteristic
78C42×C11#4111yescharacteristic
79C42×C11#4111yescharacteristic
80C4⋊Dic11—44no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83Dic11⋊C4—44no—
84C4×Dic11—21no—
85C4×Dic11—21no—
86C4×Dic11—21no—
87C4×Dic11—21no—
88C4×Dic11—42no—
89C4×Dic11—42no—
90#4318—41no—
91#4318—41no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8—41no—
94#2864—111no—
95#1994—111no—
96#1518—111no—
97#1518D1111yescharacteristic
98#1286—111no—
99#1286—111no—
100#1276—111no—
101C23×C11#12011yescharacteristic
102Q8×C11—81no—
103Q8×C11—81no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11C22⋊Q811yescharacteristic
112C2×C4×C11C22⋊Q811yescharacteristic
113C2×C4×C11C22⋊Q811yescharacteristic
114C2×C4×C11#12411yescharacteristic
115C2×C4×C11#12411yescharacteristic
116C2×C4×C11#12411yescharacteristic
117C2×C4×C11#13511yescharacteristic
118C2×C4×C11#13511yescharacteristic
119C2×C4×C11#13711yescharacteristic
120C2×C4×C11#13711yescharacteristic
121C2×Dic11—22no—
122C2×Dic11—22no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C8×C11—81no—
131C11⋊C8—81no—
132C11⋊C8—81no—
133#533C2×D1111yescharacteristic
134#431—111no—
135#431C2×D1111yescharacteristic
136#423—111no—
137#389—221no—
138#389—221no—
139#387—222no—
140#387—222no—
141#382—111no—
142#382C2×D1111yescharacteristic
143C43—111no—
144#339—221no—
145#339—221no—
146#328—22no—
147#328—222no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11#39311yescharacteristic
151C22×C11#45211yescharacteristic
152C22×C11#45211yescharacteristic
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—82no—
158C4×C11—81no—
159C4×C11—81no—
160C4×C11#47911yescharacteristic
161C4×C11#47911yescharacteristic
162C4×C11#48811yescharacteristic
163C4×C11#49111yescharacteristic
164Dic11—42no—
165Dic11—42no—
166Dic11—82no—
167C2×M16—221no—
168C4⋊Q8Dic2211yescharacteristic
169C4⋊Q8Dic2211yescharacteristic
170#125—21no—
171C22⋊Q8—21no—
172C22⋊Q8—21no—
173C4×Q8—21no—
174C4×Q8—21no—
175#117—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—222no—
178C2×C4⋊C4—222no—
179C2×C4⋊C4—221no—
180C2×C42—111no—
181C2×C42—111no—
182C2×C42—221no—
183C2×C42—221no—
184C2×C42C22×D1111yescharacteristic
185C4⋊C8—21no—
186C4⋊C8—221no—
187C4⋊C8—221no—
188C4⋊C8—221no—
189C22⋊C8—21no—
190C22⋊C8—221no—
191C4×C8—21no—
192C4×C8—221no—
193#95—21no—
194#95—112no—
195#95—222no—
196#95—222no—
197#95—221no—
198#95C22⋊D1112yes—
199C2×C11—21no—
200C2×C11—21no—
201C2×C11#202611yescharacteristic
202C2×C11#203111yescharacteristic
203C2×C11#203111yescharacteristic
204C2×Q8—21no—
205C2×Q8—21no—
206C22×C4—22no—
207C22×C4—221no—
208C22×C4—221no—
209C22×C4—222no—
210C22×C4D4×D1111yescharacteristic
211C22×C4D4×D1111yescharacteristic
212C22×C4C2×C22⋊D1111yescharacteristic
213M16—441no—
214M16—441no—
215C2×C8—41no—
216C2×C8—441no—
217C2×C8—441no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—444no—
227C4⋊C4—444no—
228C4⋊C4—441no—
229C4⋊C4—441no—
230C22⋊C4—41no—
231C42—41no—
232C42—221no—
233C42—221no—
234C42—221no—
235C42—221no—
236C42—442no—
237C42—442no—
238C42C2×Dic2211yescharacteristic
239C42#433911yescharacteristic
240C42#434111yescharacteristic
241C42#434111yescharacteristic
242C11#1036711yescharacteristic, complemented, Sylow
243C23#6699011yescharacteristic
244Q8—81no—
245Q8—81no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—441no—
256C2×C4—441no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4—442no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4#6693111yescharacteristic
263C2×C4#6693111yescharacteristic
264C2×C4#6693811yescharacteristic
265C2×C4#6693811yescharacteristic
266C2×C4#6696811yescharacteristic
267C2×C4#6696911yescharacteristic
268C2×C4#6697111yescharacteristic
269C2×C4#6697211yescharacteristic
270C2×C4#6697711yescharacteristic
271C2×C4#6698911yescharacteristic
272C8—81no—
273C8—881no—
274C8—881no—
275C22—21no—
276C22—21no—
277C22#1062256011yescharacteristic
278C22#1062278611yescharacteristic
279C22#1062280011yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—82no—
285C4—81no—
286C4—81no—
287C4—442no—
288C4—442no—
289C4—882no—
290C4#1062240911yescharacteristic
291C4#1062241011yescharacteristic
292C4#1062241211yescharacteristic
293C4#1062241311yescharacteristic
294C2—21no—
295C2—21no—
296C2#1306976511yescharacteristic
297C2#1306978611yescharacteristic
298C2#1306979011yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1518C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1518D11
hypocenterC11#10367
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
242. C11#10367semidirect

Maximal subgroups

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

subgroupindex
#130770012
#130695942
#130671802
#130664752
#130664742
#130664482
C11×#15182
#1036711