Finite Group Databasebeta

← #14764299

Subgroups — #14764299

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
1C2×#10622538C211yesmaximal, characteristic
2C2×#10622549C211yesmaximal, characteristic
3#13069384C214yesmaximal, complemented
4#13068808C212yesmaximal
5#13068803C212yesmaximal
6#13068778C212yesmaximal, complemented
7#13068746C212yesmaximal, complemented
8C11×#2283C211yesmaximal, characteristic
9C22×C42×C11C2211yescharacteristic
10C22×C4⋊Dic11C2212yes—
11C11×#383—21no—
12C11×#382C2211yescharacteristic
13C11×#382C2211yescharacteristic
14C11×#381—21no—
15C11×#380C2212yes—
16C4×C11×C4⋊C4C2212yes—
17C4×C11×C22⋊C4—21no—
18C11×#376—21no—
19C2×C11⋊#95—21no—
20C2×C11⋊#95—21no—
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×#66872C2214yes—
24C2×#66871C2214yes—
25#10622549—21no—
26#10622549—21no—
27#10622549C2212yes—
28#10622549C2212yes—
29#10622538C418yescomplemented
30C2×C4⋊(C11⋊C8)C2212yes—
31C2×C4×C11⋊C8C2212yes—
32#10622167C2214yes—
33#10622167C2214yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—22no—
38C2×C11×C4⋊C4C2312yes—
39C2×C11×C4⋊C4C2312yes—
40C2×C11×C22⋊C4—22no—
41C2×C42×C11—22no—
42C2×C42×C11C2×C414yes—
43C2×C42×C11D411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C42×C11Q814yes—
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11—44no—
50C2×C4⋊Dic11C2314yes—
51C22×C11⋊C8C2312yes—
52C22×C11⋊C8C2312yes—
53C11×#95—22no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—22no—
59C11⋊#95—22no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C22⋊(C11⋊C8)C2×C414yes—
64C22⋊(C11⋊C8)C2×C414yes—
65#66872—44no—
66#66871—44no—
67C4⋊(C11⋊C8)C2×C418yescomplemented
68C4×C11⋊C8C2×C418yescomplemented
69#21983—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C22×C4×C11—24no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—42no—
77C22×C4×C11C4⋊C414yes—
78C22×C4×C11C4⋊C414yes—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×Q812yes—
86C22×C4×C11C2411yescharacteristic
87C22×Dic11—24no—
88C22×Dic11—44no—
89C22×Dic11—44no—
90C22×Dic11—44no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C22⋊C4—44no—
94C42×C11—44no—
95C42×C11C4⋊C414yes—
96C42×C11C4⋊C414yes—
97C42×C11C22×C412yes—
98C42×C11C22×C412yes—
99C42×C11C2×Q812yes—
100C42×C11C2×Q812yes—
101C4⋊Dic11—24no—
102C4⋊Dic11—24no—
103C4⋊Dic11—44no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8C22×C414yes—
109C2×C11⋊C8C22×C414yes—
110C2×#431—111no—
111#2283D1111yescharacteristic
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×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11C2×C4⋊C412yes—
141C2×C4×C11C2×C4⋊C412yes—
142C2×C4×C11C2×C4⋊C412yes—
143C2×C4×C11C2×C4⋊C412yes—
144C2×C4×C11C2×C4⋊C412yes—
145C2×C4×C11C23×C411yescharacteristic
146C2×C4×C11C22×Q811yescharacteristic
147C2×C4×C11H(5,𝔽2)12yes—
148C2×C4×C112−1+412yes—
149C2×Dic11—44no—
150C2×Dic11—44no—
151C2×Dic11—44no—
152C2×Dic11—88no—
153C11⋊C8—24no—
154C11⋊C8—24no—
155C22×C4⋊C4—112no—
156C22×C42C2×D1111yescharacteristic
157#431—118no—
158C2×#107—114no—
159C2×#106—114no—
160C2×C4⋊C8—112no—
161C2×C22⋊C8—111no—
162C2×C22⋊C8—111no—
163C2×C4×C8—112no—
164#383—21no—
165#382—112no—
166#382—112no—
167#382—221no—
168#382—221no—
169#382C2×D1111yescharacteristic
170#382C2×D1111yescharacteristic
171#381—21no—
172#380C2×D1112yes—
173C4×C4⋊C4C2×D1112yes—
174C4×C22⋊C4—21no—
175#376—21no—
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—82no—
196C4×C11—82no—
197C4×C11#52012yes—
198C4×C11#54412yes—
199Dic11—84no—
200C23×C4—222no—
201C23×C4C22⋊D1111yescharacteristic
202C23×C4C22⋊D1111yescharacteristic
203C23×C4C22×D1111yescharacteristic
204C22×C8—112no—
205C22×C8—112no—
206C2×C4⋊C4—114no—
207C2×C4⋊C4—222no—
208C2×C4⋊C4—444no—
209C2×C4⋊C4C22×D1112yes—
210C2×C4⋊C4C22×D1112yes—
211C2×C22⋊C4—22no—
212C2×C42—22no—
213C2×C42Dic2214yes—
214C2×C42C4×D1114yes—
215C2×C42C22⋊D1111yescharacteristic
216C2×C42C22⋊D1111yescharacteristic
217C2×C42C22×D1111yescharacteristic
218C2×C42C22×D1111yescharacteristic
219#107—444no—
220#106—444no—
221C4⋊C8—118no—
222C22⋊C8—114no—
223C22⋊C8—114no—
224C4×C8—118no—
225#95—22no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—22no—
231#95—222no—
232#95—222no—
233#95—222no—
234#95—222no—
235C2×C11—24no—
236C2×C11#231711yescharacteristic
237C2×C11C2×#42711yescharacteristic
238C2×C11#291111yescharacteristic
239C2×C11#321112yes—
240C2×C11#323212yes—
241C24C2×C22⋊D1111yescharacteristic
242C22×C4—24no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—42no—
248C22×C4—224no—
249C22×C4—444no—
250C22×C4—444no—
251C22×C4—444no—
252C22×C4Dic11⋊C414yes—
253C22×C4Dic11⋊C414yes—
254C22×C4C2×Dic2212yes—
255C22×C4C2×C4×D1112yes—
256C22×C4C2×C22⋊D1111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261C22×C4C23×D1111yescharacteristic
262C2×C8—114no—
263C2×C8—114no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—222no—
267C2×C8—222no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—224no—
271C4⋊C4—224no—
272C4⋊C4—444no—
273C22⋊C4—44no—
274C42—44no—
275C42Dic11⋊C414yes—
276C42Dic11⋊C414yes—
277C42C2×Dic2212yes—
278C42C2×Dic2212yes—
279C42C2×C4×D1112yes—
280C42C2×C4×D1112yes—
281C11#2198311yescharacteristic, complemented, Sylow
282C23—22no—
283C23—21no—
284C23—21no—
285C23C2×Dic11⋊C412yes—
286C23#6700314yes—
287C23C22×C22⋊D1111yescharacteristic
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—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—444no—
305C2×C4—444no—
306C2×C4—444no—
307C2×C4—888no—
308C2×C4C2×Dic11⋊C412yes—
309C2×C4C2×Dic11⋊C412yes—
310C2×C4C2×Dic11⋊C412yes—
311C2×C4C2×Dic11⋊C412yes—
312C2×C4C2×Dic11⋊C412yes—
313C2×C4C22×Dic2211yescharacteristic
314C2×C4C22×C4×D1111yescharacteristic
315C2×C4#6704212yes—
316C2×C4#6704312yes—
317C8—224no—
318C8—224no—
319C22—24no—
320C22—22no—
321C22—22no—
322C22—24no—
323C22#1062261114yes—
324C22C22×Dic11⋊C411yescharacteristic
325C22C2×#6700312yes—
326C22#1062335312yes—
327C22#1062335611yescharacteristic
328C22#1062336111yescharacteristic
329C4—22no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—22no—
334C4—82no—
335C4—82no—
336C4—884no—
337C4#1062305012yes—
338C4#1062305412yes—
339C2—24no—
340C2#1307123611yescharacteristic
341C2C2×#1062261111yescharacteristic
342C2#1307720511yescharacteristic
343C2#1307957712yes—
344C2#1307978012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2283C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2283D11
hypocenterC11#21983
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
3. #13069384C2semidirect
6. #13068778C2semidirect
7. #13068746C2semidirect
29. #10622538C4semidirect
67. C4⋊(C11⋊C8)C2×C4semidirect
68. C4×C11⋊C8C2×C4semidirect
281. C11#21983semidirect

Maximal subgroups

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

subgroupindex
C2×#106225382
C2×#106225492
#130693842
#130688082
#130688032
#130687782
#130687462
C11×#22832
#2198311