Finite Group Databasebeta

← #14645501

Subgroups — #14645501

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068612C211yesmaximal, characteristic, complemented
2#13067288C212yesmaximal, complemented
3#13067041C212yesmaximal
4#13066940C211yesmaximal, characteristic, complemented
5C2×D4×Q8×C11C211yesmaximal, characteristic
6C23×Q8×C11—21no—
7D4×Q8×C11—24no—
8D4×Q8×C11—24no—
9C2×C11×C4⋊Q8C412yes—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C22⋊Q8—21no—
12C2×C11×C22⋊Q8—22no—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C412yes—
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66900—21no—
17#10622538C2212yes—
18#10622537C2212yes—
19#10622185—24no—
20D4⋊(C11⋊C8)—24no—
21#10622168—21no—
22#10622166—22no—
23C22×Q8×C11—28no—
24C22×Q8×C11—22no—
25C22×Q8×C11—21no—
26C22×Q8×C11—44no—
27C22×Q8×C11—42no—
28C22×Q8×C11—42no—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11—22no—
32C23×C4×C11—21no—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8—24no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8D414yes—
37C11×C22⋊Q8—28no—
38C11×C22⋊Q8—216no—
39C4×Q8×C11—22no—
40C4×Q8×C11—22no—
41C4×D4×C11—24no—
42C4×D4×C11—24no—
43C4×D4×C11—22no—
44C4×D4×C11D414yes—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4C2×C412yes—
48C2×C11×C4⋊C4C2×C411yescharacteristic
49C2×C11×C4⋊C4D412yes—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2×C412yes—
54C2×C42×C11C2311yescharacteristic
55C2×#4318—22no—
56#66900—42no—
57C22⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)—22no—
60C4⋊(C11⋊C8)—22no—
61C4×C11⋊C8—22no—
62#8388—111nomaximal, Sylow
63C24×C11—21no—
64C2×Q8×C11—28no—
65C2×Q8×C11—22no—
66C2×Q8×C11—24no—
67C2×Q8×C11—22no—
68C2×Q8×C11—44no—
69C2×Q8×C11—416no—
70C2×Q8×C11—416no—
71C2×Q8×C11—44no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—42no—
75C2×Q8×C11D812yes—
76C2×Q8×C11SD1612yes—
77C2×D4×C11—24no—
78C2×D4×C11—21no—
79C2×D4×C11C22⋊C412yes—
80C22×C4×C11—28no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—24no—
84C22×C4×C11—44no—
85C22×C4×C11—44no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—42no—
89C22×C4×C11C22⋊C412yes—
90C22×C4×C11C22⋊C412yes—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×C4⋊C4—28no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4C22⋊C414yes—
101C11×C4⋊C4C22⋊C412yes—
102C11×C22⋊C4—28no—
103C11×C22⋊C4—24no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11C2×D412yes—
107C42×C11C2×D412yes—
108#4318—42no—
109#4318—42no—
110C2×C11⋊C8—42no—
111C2×C11⋊C8—42no—
112C2×D4×Q8D1111yescharacteristic
113#1801—111no—
114#1546—112no—
115#1486—112no—
116#1461—111no—
117C23×C11—24no—
118C23×C11—22no—
119C23×C11—42no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11C2×C22⋊C411yescharacteristic
123Q8×C11—24no—
124Q8×C11—24no—
125Q8×C11—416no—
126Q8×C11—44no—
127Q8×C11—44no—
128D4×C11—24no—
129D4×C11—22no—
130D4×C11#10114yescomplemented
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—416no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—44no—
144C2×C4×C11—44no—
145C2×C4×C11—42no—
146C2×C4×C11#10214yes—
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11#12012yes—
150C2×C4×C11#12012yes—
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)12yes—
154C11⋊C8—82no—
155C11⋊C8—82no—
156C23×Q8—21no—
157D4×Q8—24no—
158D4×Q8—24no—
159C2×C4⋊Q8Dic1112yes—
160C2×C4⋊Q8C2×D1111yescharacteristic
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—22no—
163C2×C4×Q8C2×D1111yescharacteristic
164C2×C4×D4Dic1112yes—
165C2×C4×D4C2×D1111yescharacteristic
166#431—112no—
167#423—112no—
168C2×#101—221no—
169#343—221no—
170#332—224no—
171D4⋊C8—224no—
172#324—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—24no—
176C22×C11—44no—
177C22×C11—44no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11#37911yescharacteristic
181C22×C11C2×#10211yescharacteristic
182C22×C11#41811yescharacteristic
183C4×C11—22no—
184C4×C11—21no—
185C4×C11—24no—
186C4×C11—42no—
187C4×C11—44no—
188C4×C11—42no—
189C4×C11C2×#10112yes—
190C4×C11#44712yes—
191C4×C11#45012yes—
192C22×Q8—28no—
193C22×Q8—22no—
194C22×Q8—21no—
195C22×Q8—44no—
196C22×Q8—42no—
197C22×Q8—42no—
198C22×Q8C22⋊D1111yescharacteristic
199C22×D4C2×Dic1111yescharacteristic
200C23×C4—22no—
201C23×C4—21no—
202C2×M16—222no—
203C4⋊Q8—24no—
204C4⋊Q8—24no—
205C4⋊Q8—22no—
206C4⋊Q8C22⋊D1114yes—
207C22⋊Q8—28no—
208C22⋊Q8—216no—
209C4×Q8—22no—
210C4×Q8—22no—
211C4×D4—24no—
212C4×D4—24no—
213C4×D4—22no—
214C4×D4C22⋊D1114yes—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C2×Dic1112yes—
218C2×C4⋊C4C2×Dic1111yescharacteristic
219C2×C4⋊C4C22⋊D1112yes—
220C2×C4⋊C4C22⋊D1111yescharacteristic
221C2×C22⋊C4—22no—
222C2×C22⋊C4—21no—
223C2×C42C2×Dic1112yes—
224C2×C42C22×D1111yescharacteristic
225C4⋊C8—222no—
226C4⋊C8—222no—
227C4⋊C8—222no—
228#101—442no—
229C22⋊C8—222no—
230C4×C8—222no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11—44no—
234C2×C11#178411yescharacteristic
235C2×C11#178611yescharacteristic
236C2×C11#179611yescharacteristic
237C24—21no—
238C2×Q8—28no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—24no—
242C2×Q8—44no—
243C2×Q8—416no—
244C2×Q8—416no—
245C2×Q8—44no—
246C2×Q8—41no—
247C2×Q8—42no—
248C2×Q8—41no—
249C2×Q8#432312yes—
250C2×Q8#432412yes—
251C2×D4—24no—
252C2×D4—21no—
253C2×D4C22⋊Dic1112yes—
254C22×C4—28no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—24no—
258C22×C4—44no—
259C22×C4—44no—
260C22×C4—41no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4C22⋊Dic1112yes—
264C22×C4C22⋊Dic1112yes—
265C22×C4C22×Dic1111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268M16—442no—
269M16—442no—
270C2×C8—442no—
271C2×C8—442no—
272C4⋊C4—28no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—22no—
278C4⋊C4C22⋊Dic1114yes—
279C4⋊C4C22⋊Dic1112yes—
280C22⋊C4—28no—
281C22⋊C4—24no—
282C42—22no—
283C42—22no—
284C42C2×C22⋊D1112yes—
285C42C2×C22⋊D1112yes—
286C11#838811yescharacteristic, complemented, Sylow
287C23—24no—
288C23—22no—
289C23—42no—
290C23—41no—
291C23—41no—
292C23C2×C22⋊Dic1111yescharacteristic
293Q8—24no—
294Q8—24no—
295Q8—416no—
296Q8—44no—
297Q8—44no—
298D4—24no—
299D4—22no—
300D4#6690014yescomplemented
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—416no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4#6689614yes—
317C2×C4C2×#432311yescharacteristic
318C2×C4#6698512yes—
319C2×C4C2×#432411yescharacteristic
320C2×C4C2×C22⋊Dic1111yescharacteristic
321C2×C4C2×C22⋊Dic1111yescharacteristic
322C2×C4#6700612yes—
323C2×C4#6700612yes—
324C8—882no—
325C8—882no—
326C22—21no—
327C22—21no—
328C22—24no—
329C22—44no—
330C22—44no—
331C22—42no—
332C22—42no—
333C22C2×#6689611yescharacteristic
334C22#1062282811yescharacteristic
335C22#1062286011yescharacteristic
336C4—24no—
337C4—22no—
338C4—21no—
339C4—44no—
340C4—42no—
341C4—42no—
342C4#1062283012yes—
343C4#1062283112yes—
344C4C2×#6690012yes—
345C2—21no—
346C2—21no—
347C2—44no—
348C2#1306854011yescharacteristic
349C2#1306854711yescharacteristic
350C2#1306859111yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×D4×Q8×C11C2
socleC22×C11#379
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC2×D4×Q8D11
hypocenterC11#8388
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #13068612C2semidirect
2. #13067288C2semidirect
4. #13066940C2semidirect
130. D4×C11#101semidirect
286. C11#8388semidirect
300. D4#66900semidirect

Maximal subgroups

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

subgroupindex
#130686122
#130672882
#130670412
#130669402
C2×D4×Q8×C112
#838811