Finite Group Databasebeta

← #14906985

Subgroups — #14906985

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×M32C212yesmaximal, complemented
2C2×C8×D44C211yesmaximal, characteristic
3#13070447C212yesmaximal, complemented
4#13070440C214yesmaximal, complemented
5#13070435C212yesmaximal, complemented
6#13070226C212yesmaximal, complemented
7C4×#66876C211yesmaximal, characteristic, complemented
8C11×#2150C211yesmaximal, characteristic, complemented
9C22×C8×D11C2212yes—
10C2×C4×D44C411yescharacteristic
11C2×C11×M32C2212yes—
12C2×C4×C8×C11C2211yescharacteristic
13C2×(C2×D11)⋊C8C412yes—
14C2×#66876C2211yescharacteristic
15C2×#66876C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C411yescharacteristic
17D11×M32—28no—
18C2×#66862C2214yescomplemented
19C2×C16×D11C2214yescomplemented
20C8×D44C411yescharacteristic
21C8×D44C412yes—
22C8×D44C411yescharacteristic
23C8×D44C2211yescharacteristic
24C8×D44C2212yes—
25C8×D44C2211yescharacteristic
26C11×C4⋊C16C2212yescomplemented
27C11×C4⋊C16C2212yescomplemented
28(C2×D11)⋊C16C2214yescomplemented
29(C2×D11)⋊C16C2214yescomplemented
30#10622099C2212yescomplemented
31C4×C11⋊C16C2212yescomplemented
32C22×D44C811yescharacteristic
33C22×C4×D11C2×C412yes—
34C22×C8×C11C2×C411yescharacteristic
35C22×C8×C11C2311yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×(C2×D11)⋊C4C812yes—
38C2×C4⋊Dic11C811yescharacteristic
39C22×C11⋊C8C2×C412yes—
40C2×C8×D11—24no—
41C2×C8×D11—24no—
42C2×C8×D11C2×C412yes—
43C2×C8×D11C2×C412yes—
44C2×C8×D11C2312yes—
45C2×C8×D11C2312yes—
46C4×D44C812yes—
47C4×D44C811yescharacteristic
48C4×D44C811yescharacteristic
49C4×D44C2×C412yes—
50C4×D44C2×C411yescharacteristic
51C4×D44C2×C411yescharacteristic
52C11×M32—24no—
53C2×C11×C16C2314yes—
54C4×C8×C11C2×C411yescharacteristic
55C4×C8×C11C2×C411yescharacteristic
56C4×C8×C11C2311yescharacteristic
57C4×C8×C11C2311yescharacteristic
58(C2×D11)⋊C8C2×C412yes—
59(C2×D11)⋊C8C2×C412yes—
60(C2×D11)⋊C8C2×C412yes—
61(C2×D11)⋊C8C2×C412yes—
62#66876—22no—
63#66876D414yescomplemented
64C2×C11⋊C16C2312yes—
65C2×C11⋊C16C2312yes—
66C4⋊(C11⋊C8)C2×C411yescharacteristic
67C4⋊(C11⋊C8)C2×C412yes—
68C4⋊(C11⋊C8)C2×C411yescharacteristic
69#66862—28no—
70C16×D11—28no—
71D4×M32—111nomaximal, Sylow
72C23×D11C2×C812yes—
73C22×C4×C11C2×C811yescharacteristic
74C22×C4×C11C2×C811yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×Dic11C2×C812yes—
77C2×D44—24no—
78C2×D44C2×C812yes—
79C2×D44C2×C811yescharacteristic
80C2×D44C2×C811yescharacteristic
81C2×C4×D11—24no—
82C2×C4×D11—24no—
83C2×C4×D11C2×C812yes—
84C2×C4×D11C2×C812yes—
85C2×C4×D11C22×C412yes—
86C2×C4×D11C22×C412yes—
87C2×C8×C11—22no—
88C2×C8×C11C22×C411yescharacteristic
89C2×C8×C11C22×C411yescharacteristic
90C2×C8×C11C22×C411yescharacteristic
91C2×C8×C11C2×D412yes—
92C2×C8×C11#4112yes—
93C2×C8×C11C2411yescharacteristic
94C42×C11C2×C811yescharacteristic
95C42×C11C2×C811yescharacteristic
96C42×C11C22×C411yescharacteristic
97C42×C11C22×C411yescharacteristic
98(C2×D11)⋊C4C2×C812yes—
99(C2×D11)⋊C4C2×C812yes—
100(C2×D11)⋊C4C2×C812yes—
101(C2×D11)⋊C4C2×C812yes—
102C4⋊Dic11C2×C812yes—
103C4⋊Dic11C2×C811yescharacteristic
104C4⋊Dic11C2×C811yescharacteristic
105C2×C11⋊C8—24no—
106C2×C11⋊C8C22×C412yes—
107C2×C11⋊C8C22×C412yes—
108C8×D11—24no—
109C8×D11—24no—
110C8×D11—22no—
111C8×D11—22no—
112C8×D11—22no—
113C8×D11—22no—
114C11×C16—24no—
115C11⋊C16—22no—
116C11⋊C16C2×D414yescomplemented
117C22×M32—112no—
118C2×C8×D4—111no—
119#2169—112no—
120#2168—114no—
121D4×C16—112no—
122#2150D1111yescharacteristic, complemented
123#2112—112no—
124C4×M32—111no—
125C23×C11C22×C811yescharacteristic
126C22×D11—24no—
127C22×D11—24no—
128C22×D11—42no—
129C22×D11C22×C812yes—
130C22×D11C22×C812yes—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11C4×D412yes—
134C2×C4×C11C22×C811yescharacteristic
135C2×C4×C11C22×C811yescharacteristic
136C2×C4×C11C22×C811yescharacteristic
137C2×C4×C11C22×C811yescharacteristic
138C2×C4×C11C22×C811yescharacteristic
139C2×C4×C11#13112yes—
140C2×C4×C11C23×C411yescharacteristic
141C2×Dic11—24no—
142C2×Dic11C22×C812yes—
143C2×Dic11C22×C812yes—
144D44—24no—
145D44—22no—
146D44M3214yescomplemented
147C4×D11—22no—
148C4×D11—22no—
149C4×D11—22no—
150C4×D11—22no—
151C4×D11—24no—
152C4×D11—24no—
153C8×C11—21no—
154C8×C11—21no—
155C8×C11C4×D412yes—
156C8×C11C22×D411yescharacteristic
157C8×C11C2×#4111yescharacteristic
158C11⋊C8—22no—
159C11⋊C8—22no—
160C23×C8—112no—
161C2×C4×D4—111no—
162C2×M32—111no—
163C2×M32—111no—
164C2×M32—114no—
165C2×M32—228no—
166C2×M32C2×D1112yes—
167C22×C16—114no—
168C8×D4—111no—
169C8×D4—112no—
170C8×D4—111no—
171C8×D4—112no—
172C8×D4—111no—
173C8×D4—111no—
174C2×C4⋊C8—111no—
175C2×C22⋊C8—112no—
176C2×C4×C8C2×D1111yescharacteristic
177C4⋊C16C2×D1112yescomplemented
178C4⋊C16C2×D1112yescomplemented
179C22⋊C16—114no—
180C22⋊C16—114no—
181#346—112no—
182C4×C16—112no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11C8×D412yes—
186C22×C11C23×C811yescharacteristic
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—22no—
190C2×D11—22no—
191C2×D11—22no—
192C2×D11—48no—
193C2×D11C2×M3214yescomplemented
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11C8×D412yes—
198C4×C11C2×M3212yescomplemented
199C4×C11C2×C4×D411yescharacteristic
200C4×C11C2×#13111yescharacteristic
201Dic11—22no—
202Dic11—22no—
203C22×D4—111no—
204C23×C4—112no—
205C22×C8—112no—
206C22×C8—112no—
207C22×C8—112no—
208C22×C8—112no—
209C22×C8—112no—
210C22×C8—224no—
211C22×C8—224no—
212C22×C8C4×D1111yescharacteristic
213C22×C8C22×D1111yescharacteristic
214C4×D4—111no—
215C4×D4—112no—
216C4×D4—111no—
217C4×D4—111no—
218C4×D4—112no—
219C4×D4—111no—
220C2×C4⋊C4—111no—
221C2×C22⋊C4—112no—
222C2×C42C4×D1111yescharacteristic
223M32—24no—
224M32—114no—
225M32—228no—
226M32—222no—
227C2×C16—112no—
228C2×C16—112no—
229C2×C16—228no—
230C2×C16C22×D1114yes—
231C4⋊C8—111no—
232C4⋊C8—112no—
233C4⋊C8—111no—
234C22⋊C8—112no—
235C22⋊C8—112no—
236C22⋊C8—112no—
237C22⋊C8—112no—
238C4×C8C4×D1111yescharacteristic
239C4×C8C4×D1111yescharacteristic
240C4×C8C22×D1111yescharacteristic
241C4×C8C22×D1111yescharacteristic
242C2×C11—22no—
243C2×C11C2×C8×D411yescharacteristic
244C2×C11C22×M3211yescharacteristic
245C2×C11#340711yescharacteristic
246D11—24no—
247D11—42no—
248C24—112no—
249C2×D4—111no—
250C2×D4—112no—
251C2×D4—111no—
252C2×D4—224no—
253C22×C4—112no—
254C22×C4—112no—
255C22×C4—112no—
256C22×C4—112no—
257C22×C4—112no—
258C22×C4—224no—
259C22×C4—224no—
260C22×C4C8×D1111yescharacteristic
261C22×C4C8×D1111yescharacteristic
262C22×C4C2×C4×D1111yescharacteristic
263C2×C8—22no—
264C2×C8—112no—
265C2×C8—112no—
266C2×C8—224no—
267C2×C8—224no—
268C2×C8—224no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8—222no—
273C2×C8C2×C4×D1111yescharacteristic
274C2×C8C2×C4×D1111yescharacteristic
275C2×C8C2×C4×D1111yescharacteristic
276C2×C8D4×D1112yes—
277C2×C8#434312yes—
278C2×C8C23×D1111yescharacteristic
279C4⋊C4—112no—
280C4⋊C4—111no—
281C4⋊C4—111no—
282C22⋊C4—112no—
283C22⋊C4—112no—
284C22⋊C4—112no—
285C22⋊C4—112no—
286C42C8×D1111yescharacteristic
287C42C8×D1111yescharacteristic
288C42C2×C4×D1111yescharacteristic
289C42C2×C4×D1111yescharacteristic
290C16—24no—
291C16—114no—
292C16—222no—
293C11D4×M3211yescharacteristic, complemented, Sylow
294C23—112no—
295C23—112no—
296C23—224no—
297C23—224no—
298C23—442no—
299C23C2×C8×D1111yescharacteristic
300D4—114no—
301D4—224no—
302D4—222no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—112no—
306C2×C4—112no—
307C2×C4—224no—
308C2×C4—222no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4—224no—
313C2×C4—224no—
314C2×C4#6694612yes—
315C2×C4C2×C8×D1111yescharacteristic
316C2×C4C2×C8×D1111yescharacteristic
317C2×C4C2×C8×D1111yescharacteristic
318C2×C4C2×C8×D1111yescharacteristic
319C2×C4C2×C8×D1111yescharacteristic
320C2×C4#6696012yes—
321C2×C4C22×C4×D1111yescharacteristic
322C8—21no—
323C8—21no—
324C8—222no—
325C8—222no—
326C8#6694612yes—
327C8C2×D4×D1111yescharacteristic
328C8C2×#434311yescharacteristic
329C22—21no—
330C22—21no—
331C22—114no—
332C22—222no—
333C22—222no—
334C22—222no—
335C22—222no—
336C22—222no—
337C22—448no—
338C22#1062244712yes—
339C22C22×C8×D1111yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—222no—
344C4—222no—
345C4#1062244712yes—
346C4D11×M3212yescomplemented
347C4C2×#6694611yescharacteristic
348C4C2×#6696011yescharacteristic
349C2—22no—
350C2—224no—
351C2—442no—
352C2C2×#1062244711yescharacteristic
353C2C2×D11×M3211yescharacteristic
354C2#1308171811yescharacteristic
subgroupG/H
center, FrattiniC2×C8C23×D11
commutator, socleC22×C11C23×C8
FittingC11×#2150C2
prime radicalC22×D44C8
cosocleC2×C8×C11C24
hypercenter#2150D11
hypocenterC11D4×M32
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ #2150

Complements

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

NH ≅ G/Ntype
1. C2×D11×M32C2semidirect
3. #13070447C2semidirect
4. #13070440C2semidirect
5. #13070435C2semidirect
6. #13070226C2semidirect
7. C4×#66876C2semidirect
8. C11×#2150C2semidirect
18. C2×#66862C22semidirect
19. C2×C16×D11C22semidirect
26. C11×C4⋊C16C22semidirect
27. C11×C4⋊C16C22semidirect
28. (C2×D11)⋊C16C22semidirect
29. (C2×D11)⋊C16C22semidirect
30. #10622099C22semidirect
31. C4×C11⋊C16C22semidirect
63. #66876D4semidirect
116. C11⋊C16C2×D4semidirect
122. #2150D11semidirect
146. D44M32semidirect
177. C4⋊C16C2×D11semidirect
178. C4⋊C16C2×D11semidirect
193. C2×D11C2×M32semidirect
198. C4×C11C2×M32semidirect
293. C11D4×M32semidirect
346. C4D11×M32semidirect

Maximal subgroups

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

subgroupindex
C2×D11×M322
C2×C8×D442
#130704472
#130704402
#130704352
#130702262
C4×#668762
C11×#21502
D4×M3211