Finite Group Databasebeta

← #14764096

Subgroups — #14764096

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C212yesmaximal
2#13068823C218yesmaximal, complemented
3#13068658C214yesmaximal, complemented
4C2×C11×#407C211yesmaximal, characteristic
5C24×C4×C11C2211yescharacteristic
6C22×C11×M16C2212yes—
7C22×#4318C2214yes—
8C11×#407C412yes—
9C11×#407C414yes—
10C11×#407C412yes—
11C2×C11×C22⋊C8C2214yes—
12#10622820—22no—
13#10622820—22no—
14#10622820C2214yes—
15#10622820C2214yes—
16C2×C22⋊(C11⋊C8)—22no—
17C2×C22⋊(C11⋊C8)—22no—
18C2×#66883C2218yescomplemented
19#10622190C2218yescomplemented
20C25×C11Q811yescharacteristic
21C23×C4×C11—44no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11C2×C412yes—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D412yes—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11Q812yes—
29C23×C4×C11Q811yescharacteristic
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C2×C11×M16—44no—
33C2×C11×M16C2×C414yes—
34C2×C11×M16C2×C414yes—
35C22×C8×C11C2314yes—
36C2×#4318—24no—
37C2×#4318—48no—
38C2×#4318C2318yes—
39C22×C11⋊C8—24no—
40C11×C22⋊C8C2×C418yes—
41C11×C22⋊C8C2×C418yes—
42C22⋊(C11⋊C8)—24no—
43C22⋊(C11⋊C8)—24no—
44C22⋊(C11⋊C8)—24no—
45C22⋊(C11⋊C8)—24no—
46#66883—48no—
47#21949—111nomaximal, Sylow
48C24×C11—42no—
49C24×C11—44no—
50C24×C11C4⋊C411yescharacteristic
51C24×C11C4⋊C412yes—
52C24×C11C4⋊C411yescharacteristic
53C24×C11C2×Q812yes—
54C24×C11C2×Q811yescharacteristic
55C22×C4×C11—28no—
56C22×C4×C11—24no—
57C22×C4×C11—42no—
58C22×C4×C11—44no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11—44no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—44no—
65C22×C4×C11C4⋊C411yescharacteristic
66C22×C4×C11C4⋊C412yes—
67C22×C4×C11C4⋊C412yes—
68C22×C4×C11C4⋊C411yescharacteristic
69C22×C4×C11C4⋊C412yes—
70C22×C4×C11C4⋊C412yes—
71C22×C4×C11C4⋊C412yes—
72C22×C4×C11C22×C412yes—
73C22×C4×C11C22×C412yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×Q812yes—
81C22×C4×C11C2×Q811yescharacteristic
82C22×C4×C11C2411yescharacteristic
83C11×M16—44no—
84C11×M16—44no—
85C2×C8×C11—28no—
86C2×C8×C11C22×C418yes—
87#4318—216no—
88#4318—48no—
89C2×C11⋊C8—28no—
90C2×C11⋊C8—48no—
91C2×#407—112no—
92C2×#407D1111yescharacteristic
93#1855—118no—
94#1811—114no—
95C23×C11—24no—
96C23×C11—22no—
97C23×C11—24no—
98C23×C11—24no—
99C23×C11—24no—
100C23×C11—41no—
101C23×C11—42no—
102C23×C11—41no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11—416no—
108C23×C11C2×C4⋊C412yes—
109C23×C11C2×C4⋊C411yescharacteristic
110C23×C11C2×C4⋊C411yescharacteristic
111C23×C11C2×C4⋊C412yes—
112C23×C11C22×Q811yescharacteristic
113C2×C4×C11—24no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—24no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11C2×C4⋊C412yes—
131C2×C4×C11C2×C4⋊C412yes—
132C2×C4×C11C2×C4⋊C411yescharacteristic
133C2×C4×C11C2×C4⋊C411yescharacteristic
134C2×C4×C11C23×C411yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11H(5,𝔽2)14yes—
137C8×C11—28no—
138C11⋊C8—48no—
139C24×C4C2×D1111yescharacteristic
140C22×M16—114no—
141C22×M16C2×D1112yes—
142C2×#108—118no—
143#407—114no—
144#407—114no—
145#407—222no—
146#407—222no—
147#407Dic1112yes—
148#407Dic1114yes—
149#407Dic1112yes—
150C2×C22⋊C8—222no—
151C2×C22⋊C8—222no—
152C2×C22⋊C8C2×D1114yes—
153#341—118no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—48no—
165C22×C11—44no—
166C22×C11—44no—
167C22×C11—48no—
168C22×C11—44no—
169C22×C11#43014yes—
170C22×C11C22×C4⋊C411yescharacteristic
171C22×C11#54312yes—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11#51812yes—
177C4×C11#53412yes—
178C25Dic2211yescharacteristic
179C23×C4—44no—
180C23×C4Dic2212yes—
181C23×C4Dic2211yescharacteristic
182C23×C4D4411yescharacteristic
183C23×C4D4412yes—
184C23×C4D4411yescharacteristic
185C23×C4C2×Dic1111yescharacteristic
186C23×C4C2×Dic1112yes—
187C23×C4C2×Dic1111yescharacteristic
188C23×C4C22×D1112yes—
189C23×C4C22×D1111yescharacteristic
190C2×M16—44no—
191C2×M16—118no—
192C2×M16—224no—
193C2×M16—448no—
194C2×M16C2×Dic1114yes—
195C2×M16C2×Dic1114yes—
196C22×C8—224no—
197C22×C8C22×D1114yes—
198#108—448no—
199C22⋊C8—224no—
200C22⋊C8—224no—
201C22⋊C8—224no—
202C22⋊C8—224no—
203C22⋊C8C2×Dic1118yes—
204C22⋊C8C2×Dic1118yes—
205C2×C11—22no—
206C2×C11—24no—
207C2×C11—41no—
208C2×C11—42no—
209C2×C11—41no—
210C2×C11#231511yescharacteristic
211C2×C11C2×#43012yes—
212C24—42no—
213C24—44no—
214C24C4⋊Dic1111yescharacteristic
215C24C4⋊Dic1112yes—
216C24C4⋊Dic1111yescharacteristic
217C24C2×Dic2212yes—
218C24C2×Dic2211yescharacteristic
219C22×C4—24no—
220C22×C4—28no—
221C22×C4—42no—
222C22×C4—44no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—44no—
226C22×C4—42no—
227C22×C4—44no—
228C22×C4—42no—
229C22×C4C4⋊Dic1111yescharacteristic
230C22×C4C4⋊Dic1112yes—
231C22×C4C4⋊Dic1112yes—
232C22×C4C4⋊Dic1112yes—
233C22×C4C4⋊Dic1111yescharacteristic
234C22×C4C4⋊Dic1112yes—
235C22×C4C4⋊Dic1112yes—
236C22×C4C2×Dic2212yes—
237C22×C4C2×Dic2211yescharacteristic
238C22×C4C2×D4411yescharacteristic
239C22×C4C2×D4411yescharacteristic
240C22×C4C2×D4412yes—
241C22×C4C2×D4412yes—
242C22×C4C22×Dic1112yes—
243C22×C4C22×Dic1112yes—
244C22×C4C22×Dic1111yescharacteristic
245C22×C4C22×Dic1111yescharacteristic
246C22×C4C23×D1111yescharacteristic
247M16—44no—
248M16—44no—
249M16—2216no—
250M16—448no—
251C2×C8—28no—
252C2×C8—228no—
253C2×C8—448no—
254C2×C8C22×Dic1118yes—
255C11#2194911yescharacteristic, complemented, Sylow
256C23—24no—
257C23—24no—
258C23—24no—
259C23—24no—
260C23—22no—
261C23—41no—
262C23—42no—
263C23—41no—
264C23—42no—
265C23—42no—
266C23—42no—
267C23—42no—
268C23—416no—
269C23C2×C4⋊Dic1111yescharacteristic
270C23C2×C4⋊Dic1111yescharacteristic
271C23C2×C4⋊Dic1112yes—
272C23C2×C4⋊Dic1112yes—
273C23C22×Dic2211yescharacteristic
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4C2×C4⋊Dic1111yescharacteristic
292C2×C4C2×C4⋊Dic1111yescharacteristic
293C2×C4C2×C4⋊Dic1112yes—
294C2×C4C2×C4⋊Dic1112yes—
295C2×C4C22×D4411yescharacteristic
296C2×C4#6703714yes—
297C2×C4C23×Dic1111yescharacteristic
298C8—28no—
299C8—448no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—21no—
305C22—21no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—44no—
311C22—48no—
312C22—48no—
313C22—44no—
314C22—44no—
315C22#1062273814yes—
316C22#1062301412yes—
317C22C22×C4⋊Dic1111yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4#1062302412yes—
323C4#1062332912yes—
324C2—24no—
325C2—22no—
326C2—42no—
327C2—41no—
328C2—41no—
329C2#1307123011yescharacteristic
330C2C2×#1062273812yes—
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC22×C11C22×C4⋊C4
prime radicalC25×C11Q8
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#21949
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #13068823C2semidirect
3. #13068658C2semidirect
18. C2×#66883C22semidirect
19. #10622190C22semidirect
255. C11#21949semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130688232
#130686582
C2×C11×#4072
#2194911