Finite Group Databasebeta

← #14764092

Subgroups — #14764092

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C212yesmaximal
2#13068823C218yesmaximal, complemented
3#13068654C214yesmaximal, complemented
4C22×C11×C22⋊C8C211yesmaximal, characteristic
5C24×C4×C11C2211yescharacteristic
6C23×C8×C11C2212yes—
7C22×#4318C2214yes—
8C2×C11×C22⋊C8C414yes—
9C2×C11×C22⋊C8C412yes—
10C2×C11×C22⋊C8C412yes—
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×C412yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D412yes—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11Q811yescharacteristic
29C23×C4×C11Q812yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C22×C8×C11—44no—
33C22×C8×C11C2×C414yes—
34C22×C8×C11C2×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#21948—111nomaximal, Sylow
48C24×C11—24no—
49C24×C11—42no—
50C24×C11—42no—
51C24×C11C4⋊C412yes—
52C24×C11C4⋊C411yescharacteristic
53C24×C11C4⋊C411yescharacteristic
54C24×C11C2×Q811yescharacteristic
55C24×C11C2×Q812yes—
56C22×C4×C11—28no—
57C22×C4×C11—24no—
58C22×C4×C11—42no—
59C22×C4×C11—44no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—44no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—44no—
66C22×C4×C11C4⋊C412yes—
67C22×C4×C11C4⋊C412yes—
68C22×C4×C11C4⋊C411yescharacteristic
69C22×C4×C11C4⋊C412yes—
70C22×C4×C11C4⋊C412yes—
71C22×C4×C11C4⋊C411yescharacteristic
72C22×C4×C11C4⋊C412yes—
73C22×C4×C11C22×C412yes—
74C22×C4×C11C22×C412yes—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×D412yes—
81C22×C4×C11C2×Q812yes—
82C22×C4×C11C2×Q811yescharacteristic
83C22×C4×C11C2411yescharacteristic
84C2×C8×C11—28no—
85C2×C8×C11—44no—
86C2×C8×C11—44no—
87C2×C8×C11C22×C418yes—
88#4318—216no—
89#4318—48no—
90C2×C11⋊C8—28no—
91C2×C11⋊C8—48no—
92C2×#407—112no—
93C22×C22⋊C8D1111yescharacteristic
94#1855—118no—
95#1810—114no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11—24no—
100C23×C11—24no—
101C23×C11—22no—
102C23×C11—24no—
103C23×C11—24no—
104C23×C11—41no—
105C23×C11—42no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—42no—
110C23×C11—416no—
111C23×C11#10814yescomplemented
112C23×C11C2×C4⋊C412yes—
113C23×C11C2×C4⋊C412yes—
114C23×C11C2×C4⋊C411yescharacteristic
115C23×C11C2×C4⋊C411yescharacteristic
116C23×C11C22×Q811yescharacteristic
117C2×C4×C11—24no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—24no—
122C2×C4×C11—24no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11C2×C4⋊C412yes—
135C2×C4×C11C2×C4⋊C412yes—
136C2×C4×C11C2×C4⋊C411yescharacteristic
137C2×C4×C11C2×C4⋊C411yescharacteristic
138C2×C4×C11C23×C411yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×C4×C11H(5,𝔽2)14yes—
141C8×C11—28no—
142C11⋊C8—48no—
143C24×C4C2×D1111yescharacteristic
144C22×M16—114no—
145C23×C8C2×D1112yes—
146C2×#108—118no—
147#407—114no—
148#407—114no—
149#407—222no—
150#407—222no—
151C2×C22⋊C8—222no—
152C2×C22⋊C8—222no—
153C2×C22⋊C8Dic1114yes—
154C2×C22⋊C8Dic1112yes—
155C2×C22⋊C8Dic1112yes—
156C2×C22⋊C8C2×D1114yes—
157#341—118no—
158C22×C11—28no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—22no—
166C22×C11—21no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—22no—
170C22×C11—44no—
171C22×C11—48no—
172C22×C11—48no—
173C22×C11—44no—
174C22×C11C2×#10812yes—
175C22×C11C2×#10814yes—
176C22×C11#43012yes—
177C22×C11C22×C4⋊C411yescharacteristic
178C22×C11#54312yes—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11#51812yes—
184C4×C11#53412yes—
185C25Dic2211yescharacteristic
186C23×C4—44no—
187C23×C4Dic2211yescharacteristic
188C23×C4Dic2212yes—
189C23×C4D4411yescharacteristic
190C23×C4D4412yes—
191C23×C4D4411yescharacteristic
192C23×C4C2×Dic1112yes—
193C23×C4C2×Dic1111yescharacteristic
194C23×C4C2×Dic1111yescharacteristic
195C23×C4C22×D1111yescharacteristic
196C23×C4C22×D1112yes—
197C2×M16—118no—
198C2×M16—224no—
199C2×M16—448no—
200C22×C8—44no—
201C22×C8—224no—
202C22×C8C2×Dic1114yes—
203C22×C8C2×Dic1114yes—
204C22×C8C22×D1114yes—
205#108—448no—
206C22⋊C8—224no—
207C22⋊C8—224no—
208C22⋊C8—224no—
209C22⋊C8—224no—
210C22⋊C8C2×Dic1118yes—
211C22⋊C8C2×Dic1118yes—
212C2×C11—22no—
213C2×C11—22no—
214C2×C11—22no—
215C2×C11—24no—
216C2×C11—42no—
217C2×C11#231511yescharacteristic
218C2×C11C22×#10811yescharacteristic
219C2×C11C2×#43011yescharacteristic
220C24—24no—
221C24—42no—
222C24—42no—
223C24C4⋊Dic1112yes—
224C24C4⋊Dic1111yescharacteristic
225C24C4⋊Dic1111yescharacteristic
226C24C2×Dic2211yescharacteristic
227C24C2×Dic2212yes—
228C22×C4—24no—
229C22×C4—28no—
230C22×C4—42no—
231C22×C4—44no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—44no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—44no—
238C22×C4C4⋊Dic1112yes—
239C22×C4C4⋊Dic1112yes—
240C22×C4C4⋊Dic1112yes—
241C22×C4C4⋊Dic1111yescharacteristic
242C22×C4C4⋊Dic1112yes—
243C22×C4C4⋊Dic1111yescharacteristic
244C22×C4C4⋊Dic1112yes—
245C22×C4C2×Dic2211yescharacteristic
246C22×C4C2×Dic2212yes—
247C22×C4C2×D4411yescharacteristic
248C22×C4C2×D4411yescharacteristic
249C22×C4C2×D4412yes—
250C22×C4C2×D4412yes—
251C22×C4C22×Dic1112yes—
252C22×C4C22×Dic1112yes—
253C22×C4C22×Dic1111yescharacteristic
254C22×C4C22×Dic1111yescharacteristic
255C22×C4C23×D1111yescharacteristic
256M16—2216no—
257M16—448no—
258C2×C8—28no—
259C2×C8—44no—
260C2×C8—44no—
261C2×C8—228no—
262C2×C8—448no—
263C2×C8C22×Dic1118yes—
264C11#2194811yescharacteristic, complemented, Sylow
265C23—22no—
266C23—22no—
267C23—22no—
268C23—24no—
269C23—22no—
270C23—24no—
271C23—24no—
272C23—24no—
273C23—41no—
274C23—42no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—42no—
279C23—416no—
280C23#6688314yescomplemented
281C23C2×C4⋊Dic1112yes—
282C23C2×C4⋊Dic1111yescharacteristic
283C23C2×C4⋊Dic1112yes—
284C23C2×C4⋊Dic1111yescharacteristic
285C23C22×Dic2211yescharacteristic
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×C4⋊Dic1111yescharacteristic
304C2×C4C2×C4⋊Dic1111yescharacteristic
305C2×C4C2×C4⋊Dic1112yes—
306C2×C4C2×C4⋊Dic1112yes—
307C2×C4C22×D4411yescharacteristic
308C2×C4#6703714yes—
309C2×C4C23×Dic1111yescharacteristic
310C8—28no—
311C8—448no—
312C22—28no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—22no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—44no—
325C22—48no—
326C22—48no—
327C22—44no—
328C22C2×#6688312yes—
329C22C2×#6688314yes—
330C22#1062273812yes—
331C22#1062301412yes—
332C22C22×C4⋊Dic1111yescharacteristic
333C4—22no—
334C4—22no—
335C4—21no—
336C4—21no—
337C4#1062302412yes—
338C4#1062332912yes—
339C2—22no—
340C2—22no—
341C2—22no—
342C2—24no—
343C2—42no—
344C2#1307123011yescharacteristic
345C2C22×#6688311yescharacteristic
346C2C2×#1062273811yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊C8C2
socleC22×C11C22×C4⋊C4
prime radicalC25×C11Q8
cosocleC22×C4×C11C24
hypercenterC22×C22⋊C8D11
hypocenterC11#21948
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #13068823C2semidirect
3. #13068654C2semidirect
18. C2×#66883C22semidirect
19. #10622190C22semidirect
111. C23×C11#108semidirect
264. C11#21948semidirect
280. C23#66883semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130688232
#130686542
C22×C11×C22⋊C82
#2194811