Finite Group Databasebeta

← #14652181

Subgroups — #14652181

Order 2816.

370 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069565C211yesmaximal, characteristic
2#13069377C211yesmaximal, characteristic
3#13068483C211yesmaximal, characteristic
4C2×#10622184C211yesmaximal, characteristic
5#13066499C211yesmaximal, characteristic
6#13066451C211yesmaximal, characteristic
7C11×#1990C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×C8×C11C2211yescharacteristic
10C11×#384C2211yescharacteristic
11C2×#66879—21no—
12C2×#66872—21no—
13C4×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C11×#340—21no—
18C11×#340—21no—
19#10622188—21no—
20#10622184C414yescomplemented
21#10622167—21no—
22#10622167—21no—
23#10622167—21no—
24C22×Q8×C11—21no—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11D411yescharacteristic
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8C2×C412yes—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4×Dic11—21no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8—21no—
42C22×C11⋊C8—21no—
43C4×C8×C11—21no—
44C4×C8×C11—21no—
45C11⋊#95—21no—
46#66879—42no—
47#66872—42no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)C2×C412yes—
53C4⋊(C11⋊C8)C2×C412yes—
54#9575—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×Q8×C11—41no—
57C2×Q8×C11—81no—
58C2×Q8×C11—81no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×C8×C11—21no—
67C2×C8×C11—21no—
68C2×C8×C11—21no—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11SD1612yes—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—81no—
81C42×C11C22×C411yescharacteristic
82C42×C11#4111yescharacteristic
83C42×C11#4111yescharacteristic
84C42×C11#4111yescharacteristic
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4×Dic11—41no—
90C4×Dic11—41no—
91C2×C11⋊C8—22no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8—41no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100#1990D1111yescharacteristic
101#1987—111no—
102#1948—111no—
103#1770—111no—
104C2×#333—111no—
105#1296—111no—
106#1277—111no—
107C23×C11#12111yescharacteristic
108Q8×C11—82no—
109Q8×C11—82no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—42no—
113C2×C4×C11—81no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11#11711yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11C4×D411yescharacteristic
121C2×C4×C11#12311yescharacteristic
122C2×C4×C11#12411yescharacteristic
123C2×C4×C11#12611yescharacteristic
124C2×C4×C11C2×SD1611yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C8×C11—22no—
139C8×C11—41no—
140C11⋊C8—42no—
141C11⋊C8—42no—
142C11⋊C8—81no—
143C2×C4⋊Q8C2×D1111yescharacteristic
144C2×#106—221no—
145C2×C4⋊C8—111no—
146C2×C4⋊C8—111no—
147C2×C4⋊C8—111no—
148C2×#97—221no—
149C2×C4×C8C2×D1111yescharacteristic
150#384C2×D1111yescharacteristic
151C4×C4⋊C4—111no—
152#340—21no—
153#340—21no—
154#340—221no—
155#340—221no—
156#340—221no—
157#336—221no—
158#333—114no—
159C22×C11#38811yescharacteristic
160C22×C11#46111yescharacteristic
161C22×C11#46411yescharacteristic
162C22×C11#46811yescharacteristic
163C22×C11#47011yescharacteristic
164C22×C11#47111yescharacteristic
165C22×C11#47211yescharacteristic
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—82no—
169C4×C11—161no—
170C4×C11C4×SD1611yescharacteristic
171C4×C11#44011yescharacteristic
172C4×C11#44111yescharacteristic
173C4×C11#44111yescharacteristic
174C4×C11#48311yescharacteristic
175C4×C11#48511yescharacteristic
176C4×C11#48911yescharacteristic
177C4×C11#49111yescharacteristic
178Dic11—81no—
179Dic11—81no—
180C22×Q8—21no—
181C22×C8—221no—
182C22×C8—221no—
183C22×C8—221no—
184C22×C8C22⋊D1111yescharacteristic
185C22×C8C22⋊D1111yescharacteristic
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8C4×D1112yes—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C42—221no—
198C2×C42C22×D1111yescharacteristic
199#106—442no—
200C4⋊C8—112no—
201C4⋊C8—112no—
202C4⋊C8—221no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206#97—442no—
207C4×C8—21no—
208C4×C8—21no—
209#95—221no—
210C2×C11#169111yescharacteristic
211C2×C11#169511yescharacteristic
212C2×C11#169811yescharacteristic
213C2×C11#170411yescharacteristic
214C2×C11#192711yescharacteristic
215C2×C11#193111yescharacteristic
216C2×C11#193511yescharacteristic
217C2×Q8—22no—
218C2×Q8—41no—
219C2×Q8—81no—
220C2×Q8—81no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4D4×D1111yescharacteristic
226C22×C4#434111yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—222no—
234C2×C8—222no—
235C2×C8—441no—
236C2×C8—441no—
237C2×C8—441no—
238C2×C8—441no—
239C2×C8—441no—
240C2×C8—441no—
241C2×C8—441no—
242C2×C8#432512yes—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—81no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C42—441no—
257C42—441no—
258C42C2×C4×D1111yescharacteristic
259C42#433911yescharacteristic
260C42#434111yescharacteristic
261C42#434111yescharacteristic
262C11#957511yescharacteristic, complemented, Sylow
263C23#6699111yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4#6693011yescharacteristic
281C2×C4#6693211yescharacteristic
282C2×C4(C22⋊D11)⋊C411yescharacteristic
283C2×C4#6693811yescharacteristic
284C2×C4#6696711yescharacteristic
285C2×C4#6696811yescharacteristic
286C2×C4#6697111yescharacteristic
287C2×C4#6697111yescharacteristic
288C2×C4C4×C22⋊D1111yescharacteristic
289C2×C4#6698811yescharacteristic
290C2×C4C2×#432511yescharacteristic
291C2×C4#6699511yescharacteristic
292C2×C4#6700311yescharacteristic
293C2×C4#6700411yescharacteristic
294C8—22no—
295C8—41no—
296C8—442no—
297C8—442no—
298C8—881no—
299C22#1062255711yescharacteristic
300C22#1062266711yescharacteristic
301C22#1062269611yescharacteristic
302C22#1062277311yescharacteristic
303C22#1062278711yescharacteristic
304C22#1062279011yescharacteristic
305C22#1062280211yescharacteristic
306C4—21no—
307C4—21no—
308C4—82no—
309C4—161no—
310C4—881no—
311C4—881no—
312C4#1062240211yescharacteristic
313C4#1062240811yescharacteristic
314C4#1062241011yescharacteristic
315C4#1062243011yescharacteristic
316C4C4×#432511yescharacteristic
317C4#1062264311yescharacteristic
318C4#1062265611yescharacteristic
319C4#1062265811yescharacteristic
320C2#1306811211yescharacteristic
321C2#1306813611yescharacteristic
322C2#1306815311yescharacteristic
323C2#1306819511yescharacteristic
324C2#1306924711yescharacteristic
325C2#1306927511yescharacteristic
326C2#1306930311yescharacteristic
subgroupG/H
centerC23#66991
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1990C2
socle, prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1990D11
hypocenterC11#9575
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
20. #10622184C4semidirect
262. C11#9575semidirect

Maximal subgroups

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

subgroupindex
#130695652
#130693772
#130684832
C2×#106221842
#130664992
#130664512
C11×#19902
#957511