Finite Group Databasebeta

← #14644734

Subgroups — #14644734

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068469C211yesmaximal, characteristic
2#13068469C211yesmaximal, characteristic
3C2×#10622185C212yesmaximal
4#13066499C212yesmaximal
5C4×C11×C4⋊Q8C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8×C11—21no—
8C11×#391—21no—
9C11×#389—21no—
10C11×#389C412yes—
11C11×#384C2211yescharacteristic
12C4×C11×C4⋊C4—21no—
13C4×C11×C4⋊C4C412yes—
14C43×C11C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2212yes—
16C2×C4⋊(C11⋊C8)C2212yes—
17C2×#66867—21no—
18C2×#66867—21no—
19#10622185C418yescomplemented
20#10622162—21no—
21#10622162—21no—
22C22×Q8×C11—21no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8C2×C414yes—
25C4×Q8×C11—44no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C42×C11—22no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C22×C11⋊C8—22no—
41C22×C11⋊C8—22no—
42C11×#95—22no—
43C11×#95—22no—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)C2×C414yes—
47C4⋊(C11⋊C8)C2×C414yes—
48#66867—42no—
49#66867—42no—
50#8233—111nomaximal, Sylow
51C2×Q8×C11—24no—
52C2×Q8×C11—42no—
53C2×Q8×C11—41no—
54C2×Q8×C11—41no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C11×C4⋊C4—22no—
65C11×C4⋊C4—24no—
66C11×C4⋊C4—44no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4C4214yes—
72C42×C11—22no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—22no—
76C42×C11—22no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—41no—
80C42×C11—44no—
81C42×C11C22×C412yes—
82C42×C11#4112yes—
83C2×C11⋊C8—24no—
84C2×C11⋊C8—24no—
85C2×C11⋊C8—42no—
86C2×C11⋊C8—42no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89C4×C4⋊Q8D1111yescharacteristic
90#1767—111no—
91#1767—111no—
92C2×#332—112no—
93#1296—112no—
94C23×C11C2×C22⋊C411yescharacteristic
95Q8×C11—44no—
96Q8×C11—44no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—24no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11#10112yes—
117C2×C4×C11C2×C4211yescharacteristic
118C2×C4×C11#11711yescharacteristic
119C2×C4×C11C4×D412yes—
120C2×C4×C11C4×D412yes—
121C2×C4×C11AGL(1,ℤ/8)12yes—
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C11#13712yes—
125C2×C4×C11#13711yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C11⋊C8—44no—
128C11⋊C8—44no—
129C2×C4⋊Q8C2×D1111yescharacteristic
130C2×C4×Q8—21no—
131C2×C4⋊C8—112no—
132C2×C4⋊C8—112no—
133C2×#97—221no—
134C2×#97—221no—
135#391—21no—
136#389—21no—
137#389Dic1112yes—
138#384C2×D1111yescharacteristic
139C4×C4⋊C4—21no—
140C4×C4⋊C4Dic1112yes—
141C43C2×D1111yescharacteristic
142#336—221no—
143#336—221no—
144#332—118no—
145C22×C11C4×C22⋊C411yescharacteristic
146C22×C11C2×#10111yescharacteristic
147C22×C11#41311yescharacteristic
148C22×C11#41711yescharacteristic
149C22×C11#41711yescharacteristic
150C22×C11#41811yescharacteristic
151C22×C11#41911yescharacteristic
152C4×C11—22no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11—44no—
159C4×C11—82no—
160C4×C11#44012yes—
161C4×C11#44012yes—
162C4×C11#44112yes—
163C4×C11#44212yes—
164C22×Q8—21no—
165C22×C8—222no—
166C22×C8—222no—
167C4⋊Q8—22no—
168C4⋊Q8C4×D1114yes—
169C4×Q8—44no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4C2×Dic1112yes—
175C2×C4⋊C4C2×Dic1112yes—
176C2×C42—22no—
177C2×C42C2×Dic1111yescharacteristic
178C2×C42C2×Dic1111yescharacteristic
179C2×C42C22⋊D1111yescharacteristic
180C2×C42C22⋊D1111yescharacteristic
181C2×C42C22⋊D1111yescharacteristic
182C2×C42C22⋊D1111yescharacteristic
183C2×C42C22×D1111yescharacteristic
184C4⋊C8—114no—
185C4⋊C8—114no—
186C4⋊C8—222no—
187C4⋊C8—222no—
188#97—442no—
189#97—442no—
190#95—22no—
191#95—22no—
192C2×C11#155611yescharacteristic
193C2×C11#155711yescharacteristic
194C2×C11#155911yescharacteristic
195C2×C11#156111yescharacteristic
196C2×C11C4×#10111yescharacteristic
197C2×C11#176211yescharacteristic
198C2×C11#176311yescharacteristic
199C2×Q8—24no—
200C2×Q8—42no—
201C2×Q8—41no—
202C2×Q8—41no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4C22⋊Dic1111yescharacteristic
206C22×C4C22⋊Dic1111yescharacteristic
207C22×C4C22⋊Dic1111yescharacteristic
208C22×C4C22⋊Dic1111yescharacteristic
209C22×C4C22×Dic1111yescharacteristic
210C22×C4C2×C22⋊D1111yescharacteristic
211C22×C4C2×C22⋊D1111yescharacteristic
212C2×C8—224no—
213C2×C8—224no—
214C2×C8—442no—
215C2×C8—442no—
216C2×C8—442no—
217C2×C8—442no—
218C4⋊C4—22no—
219C4⋊C4—24no—
220C4⋊C4—42no—
221C4⋊C4—44no—
222C4⋊C4—42no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4C4×Dic1114yes—
226C42—22no—
227C42—22no—
228C42—22no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—41no—
234C42—44no—
235C42C2×C4×D1112yes—
236C42#433912yes—
237C11#823311yescharacteristic, complemented, Sylow
238C23C2×C22⋊Dic1111yescharacteristic
239Q8—44no—
240Q8—44no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—24no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4#6690012yes—
261C2×C4C2×C4×Dic1111yescharacteristic
262C2×C4#6697911yescharacteristic
263C2×C4C4×C22⋊D1112yes—
264C2×C4C4×C22⋊D1112yes—
265C2×C4#6698512yes—
266C2×C4#6699512yes—
267C2×C4#6700211yescharacteristic
268C2×C4#6700211yescharacteristic
269C2×C4#6700411yescharacteristic
270C2×C4#6700411yescharacteristic
271C8—444no—
272C8—444no—
273C22C4×C22⋊Dic1111yescharacteristic
274C22#1062282811yescharacteristic
275C22#1062283811yescharacteristic
276C22C2×#6690011yescharacteristic
277C22#1062284511yescharacteristic
278C22#1062284511yescharacteristic
279C22#1062285011yescharacteristic
280C4—22no—
281C4—21no—
282C4—21no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—44no—
287C4—82no—
288C4#1062262712yes—
289C4#1062263112yes—
290C4#1062263912yes—
291C4#1062264312yes—
292C2#1306733311yescharacteristic
293C2#1306733811yescharacteristic
294C2#1306734611yescharacteristic
295C2#1306735411yescharacteristic
296C2C4×#6690011yescharacteristic
297C2#1306844111yescharacteristic
298C2#1306844611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC4×C11×C4⋊Q8C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC4×C4⋊Q8D11
hypocenterC11#8233
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
19. #10622185C4semidirect
237. C11#8233semidirect

Maximal subgroups

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

subgroupindex
#130684692
C2×#106221852
#130664992
C4×C11×C4⋊Q82
#823311