Finite Group Databasebeta

← #14764303

Subgroups — #14764303

Order 2816.

834 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071014C211yesmaximal, characteristic
2C2×#10622549C211yesmaximal, characteristic
3#13069386C214yesmaximal, complemented
4#13068811C212yesmaximal
5#13068806C212yesmaximal
6#13068780C212yesmaximal, complemented
7#13068747C212yesmaximal, complemented
8C2×C11×#431C211yesmaximal, characteristic
9C22×C42×C11C2211yescharacteristic
10C22×C4⋊Dic11C2212yes—
11C11×#431C418yescomplemented
12C2×C11×C4⋊C8C2212yes—
13C2×C11×C22⋊C8C2211yescharacteristic
14C2×C11×C22⋊C8C2211yescharacteristic
15C2×C4×C8×C11C2212yes—
16#10622825C2212yes—
17#10622824—21no—
18C4×C22⋊Dic11—21no—
19C2×C11⋊#95—21no—
20C2×C11⋊#95—21no—
21C2×#66882C2214yes—
22C2×#66881C2214yes—
23#10622550—21no—
24#10622549—21no—
25#10622549—21no—
26#10622549C2212yes—
27#10622549C2212yes—
28#10622549C2211yescharacteristic
29#10622549C2211yescharacteristic
30C4×C4⋊Dic11C2212yes—
31#10622545—21no—
32#10622189C2214yes—
33#10622189C2214yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—22no—
38C22×C8×C11C2312yes—
39C22×C8×C11C2312yes—
40C2×C42×C11C2×C414yes—
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11Q814yes—
44C2×C42×C11C2311yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11—22no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11—44no—
49C2×C4⋊Dic11C2312yes—
50C2×C4⋊Dic11C2312yes—
51C2×C4⋊Dic11C2314yes—
52C2×C4×Dic11—22no—
53C11×C4⋊C8C2×C418yescomplemented
54C11×C22⋊C8C2×C414yes—
55C11×C22⋊C8C2×C414yes—
56C4×C8×C11C2×C418yescomplemented
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—22no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67#66882—44no—
68#66881—44no—
69#21983—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C22×C4×C11—24no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—42no—
75C22×C4×C11C4⋊C414yes—
76C22×C4×C11C4⋊C414yes—
77C22×C4×C11C22×C412yes—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×Q812yes—
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—22no—
86C22×Dic11—22no—
87C22×Dic11—24no—
88C22×Dic11—44no—
89C22×Dic11—44no—
90C22×Dic11—44no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11C22×C414yes—
96C2×C8×C11C22×C414yes—
97C42×C11C4⋊C414yes—
98C42×C11C4⋊C414yes—
99C42×C11C22×C412yes—
100C42×C11C22×C412yes—
101C42×C11C2×Q812yes—
102C42×C11C2×Q812yes—
103C22⋊Dic11—44no—
104C4⋊Dic11—24no—
105C4⋊Dic11—24no—
106C4⋊Dic11—24no—
107C4⋊Dic11—24no—
108C4⋊Dic11—44no—
109C4×Dic11—44no—
110C2×#431D1111yescharacteristic
111#2283—111no—
112C2×#382—111no—
113#1949—114no—
114#1853—112no—
115#1852—112no—
116#1846—112no—
117#1835—112no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—22no—
121C23×C11C2×C4⋊C412yes—
122C23×C11#13514yes—
123C23×C11C22×D411yescharacteristic
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—28no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—44no—
134C2×C4×C11C2×C4⋊C412yes—
135C2×C4×C11C2×C4⋊C412yes—
136C2×C4×C11C2×C4⋊C412yes—
137C2×C4×C11C2×C4⋊C412yes—
138C2×C4×C11C2×C4⋊C412yes—
139C2×C4×C11C23×C411yescharacteristic
140C2×C4×C11C22×Q811yescharacteristic
141C2×C4×C11H(5,𝔽2)12yes—
142C2×C4×C112−1+412yes—
143C2×Dic11—44no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—44no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—44no—
152C2×Dic11—88no—
153C8×C11—24no—
154C8×C11—24no—
155C22×C4⋊C4—112no—
156C22×C42C2×D1111yescharacteristic
157#431Dic1118yescomplemented
158C2×#107—114no—
159C2×#106—114no—
160C2×C4⋊C8C2×D1112yes—
161C2×C22⋊C8C2×D1111yescharacteristic
162C2×C22⋊C8C2×D1111yescharacteristic
163C2×C4×C8C2×D1112yes—
164#383—221no—
165#382—111no—
166#382—112no—
167#382—111no—
168#382—112no—
169#382—221no—
170#382—221no—
171#381—221no—
172#380—112no—
173C4×C4⋊C4—112no—
174C4×C22⋊C4—221no—
175#376—221no—
176C2×#95—221no—
177C2×#95—221no—
178#340—114no—
179#340—114no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—24no—
183C22×C11—24no—
184C22×C11#42714yes—
185C22×C11C22×C4⋊C411yescharacteristic
186C22×C11#53511yescharacteristic
187C22×C11#53611yescharacteristic
188C22×C11C2×#13512yes—
189C22×C11#57512yes—
190C4×C11—22no—
191C4×C11—22no—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11#52012yes—
196C4×C11#54412yes—
197Dic11—82no—
198Dic11—84no—
199Dic11—82no—
200C23×C4—222no—
201C23×C4D4411yescharacteristic
202C23×C4D4411yescharacteristic
203C23×C4C22×D1111yescharacteristic
204C22×C8C22×D1112yes—
205C22×C8C22×D1112yes—
206C2×C4⋊C4—114no—
207C2×C4⋊C4—112no—
208C2×C4⋊C4—112no—
209C2×C4⋊C4—222no—
210C2×C4⋊C4—444no—
211C2×C22⋊C4—222no—
212C2×C42—222no—
213C2×C42Dic2214yes—
214C2×C42D4411yescharacteristic
215C2×C42D4411yescharacteristic
216C2×C42C2×Dic1114yes—
217C2×C42C22×D1111yescharacteristic
218C2×C42C22×D1111yescharacteristic
219#107—444no—
220#106—444no—
221C4⋊C8C2×Dic1118yescomplemented
222C22⋊C8C2×Dic1114yes—
223C22⋊C8C2×Dic1114yes—
224C4×C8C2×Dic1118yescomplemented
225#95—222no—
226#95—222no—
227#95—222no—
228#95—222no—
229#95—222no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—222no—
235C2×C11—24no—
236C2×C11#231711yescharacteristic
237C2×C11C2×#42711yescharacteristic
238C2×C11#291111yescharacteristic
239C2×C11#321112yes—
240C2×C11#323212yes—
241C24C2×D4411yescharacteristic
242C22×C4—24no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—42no—
246C22×C4—222no—
247C22×C4—222no—
248C22×C4—224no—
249C22×C4—444no—
250C22×C4—444no—
251C22×C4—444no—
252C22×C4C4⋊Dic1114yes—
253C22×C4C4⋊Dic1114yes—
254C22×C4C2×Dic2212yes—
255C22×C4C2×D4411yescharacteristic
256C22×C4C2×D4411yescharacteristic
257C22×C4C2×D4411yescharacteristic
258C22×C4C2×D4411yescharacteristic
259C22×C4C2×D4411yescharacteristic
260C22×C4C22×Dic1112yes—
261C22×C4C23×D1111yescharacteristic
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8C22×Dic1114yes—
267C2×C8C22×Dic1114yes—
268C4⋊C4—224no—
269C4⋊C4—224no—
270C4⋊C4—224no—
271C4⋊C4—224no—
272C4⋊C4—444no—
273C22⋊C4—444no—
274C42—444no—
275C42C4⋊Dic1114yes—
276C42C4⋊Dic1114yes—
277C42C2×Dic2212yes—
278C42C2×Dic2212yes—
279C42C22×Dic1112yes—
280C42C22×Dic1112yes—
281C11#2198311yescharacteristic, complemented, Sylow
282C23—22no—
283C23—21no—
284C23—21no—
285C23#6695714yes—
286C23C2×C4⋊Dic1112yes—
287C23C22×D4411yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—28no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—44no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—444no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—444no—
304C2×C4—444no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—888no—
308C2×C4C2×C4⋊Dic1112yes—
309C2×C4C2×C4⋊Dic1112yes—
310C2×C4C2×C4⋊Dic1112yes—
311C2×C4C2×C4⋊Dic1112yes—
312C2×C4C2×C4⋊Dic1112yes—
313C2×C4C22×Dic2211yescharacteristic
314C2×C4#6704212yes—
315C2×C4#6704312yes—
316C2×C4C23×Dic1111yescharacteristic
317C8—24no—
318C8—24no—
319C22—24no—
320C22—22no—
321C22—22no—
322C22—24no—
323C22#1062271914yes—
324C22#1062305611yescharacteristic
325C22#1062305711yescharacteristic
326C22C2×#6695712yes—
327C22#1062327912yes—
328C22C22×C4⋊Dic1111yescharacteristic
329C4—22no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—22no—
334C4—884no—
335C4—882no—
336C4—882no—
337C4#1062305012yes—
338C4#1062335812yes—
339C2—24no—
340C2#1307123911yescharacteristic
341C2C2×#1062271911yescharacteristic
342C2#1307720611yescharacteristic
343C2#1307958312yes—
344C2#1307978612yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#431C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#431D11
hypocenterC11#21983
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. #13069386C2semidirect
6. #13068780C2semidirect
7. #13068747C2semidirect
11. C11×#431C4semidirect
53. C11×C4⋊C8C2×C4semidirect
56. C4×C8×C11C2×C4semidirect
157. #431Dic11semidirect
221. C4⋊C8C2×Dic11semidirect
224. C4×C8C2×Dic11semidirect
281. C11#21983semidirect

Maximal subgroups

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

subgroupindex
#130710142
C2×#106225492
#130693862
#130688112
#130688062
#130687802
#130687472
C2×C11×#4312
#2198311