Finite Group Databasebeta

← #14645531

Subgroups — #14645531

Order 2816.

738 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068612C211yesmaximal, characteristic, complemented
2#13067297C212yesmaximal, complemented
3#13067041C212yesmaximal
4#13066940C211yesmaximal, characteristic, complemented
5C2×C11×#556C211yesmaximal, characteristic
6C11×#556—24no—
7C11×#556—24no—
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#126—22no—
10C2×C11×#124C412yes—
11C2×C11×C22⋊Q8—21no—
12C2×C4×Q8×C11C412yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117—21no—
16C2×#66900—21no—
17#10622538C2212yes—
18#10622537C2212yes—
19#10622184—24no—
20D4⋊(C11⋊C8)—24no—
21#10622168—21no—
22#10622166—22no—
23C22×Q8×C11C2×C412yes—
24C22×Q8×C11D411yescharacteristic
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11—21no—
27C11×C4⋊Q8—22no—
28C11×C4⋊Q8D414yes—
29C11×#126—216no—
30C11×#124—24no—
31C11×#124—24no—
32C11×C22⋊Q8—28no—
33C4×Q8×C11—24no—
34C4×Q8×C11—24no—
35C4×Q8×C11—22no—
36C4×Q8×C11—22no—
37C4×D4×C11—22no—
38C4×D4×C11D414yes—
39C11×#117—28no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4D412yes—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—21no—
49C2×C42×C11—22no—
50C2×C42×C11C2×C412yes—
51C2×C42×C11C2311yescharacteristic
52C2×#4318—22no—
53#66900—42no—
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58C4×C11⋊C8—22no—
59#8394—111nomaximal, Sylow
60C24×C11—21no—
61C2×Q8×C11—22no—
62C2×Q8×C11—22no—
63C2×Q8×C11—22no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—44no—
67C2×Q8×C11C22⋊C414yes—
68C2×D4×C11—21no—
69C2×D4×C11—42no—
70C2×D4×C11C22⋊C412yes—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—24no—
74C22×C4×C11—42no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C22⋊C412yes—
78C22×C4×C11C22⋊C412yes—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C11×C4⋊C4—28no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—24no—
85C11×C4⋊C4—24no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4C22⋊C412yes—
89C11×C22⋊C4—28no—
90C11×C22⋊C4—28no—
91C11×C22⋊C4—24no—
92C42×C11—28no—
93C42×C11—22no—
94C42×C11—22no—
95C42×C11C2×D412yes—
96C42×C11C2×D412yes—
97#4318—42no—
98#4318—42no—
99C2×C11⋊C8—42no—
100C2×C11⋊C8—42no—
101C2×#556D1111yescharacteristic
102#1801—111no—
103#1548—112no—
104#1486—112no—
105#1461—111no—
106C23×C11—22no—
107C23×C11—42no—
108C23×C11—42no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11C2×C22⋊C411yescharacteristic
112Q8×C11—44no—
113Q8×C11—44no—
114Q8×C11—42no—
115Q8×C11—42no—
116D4×C11—24no—
117D4×C11—42no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—24no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—44no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11—42no—
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C2×C22⋊C411yescharacteristic
134C2×C4×C11#12012yes—
135C2×C4×C11#12012yes—
136C2×C4×C11#13512yes—
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C11⋊C8—82no—
140C11⋊C8—82no—
141#556—24no—
142#556—24no—
143C2×C4⋊Q8C2×D1111yescharacteristic
144C2×#126—22no—
145C2×#124Dic1112yes—
146C2×C22⋊Q8—21no—
147C2×C4×Q8Dic1112yes—
148C2×C4×Q8C2×D1111yescharacteristic
149C2×C4×D4C2×D1111yescharacteristic
150C2×#117—21no—
151#431—112no—
152#423—112no—
153C2×#101—221no—
154#343—221no—
155#333—224no—
156D4⋊C8—224no—
157#324—222no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11—82no—
164C22×C11—82no—
165C22×C11#37911yescharacteristic
166C22×C11#41611yescharacteristic
167C22×C11#41711yescharacteristic
168C4×C11—22no—
169C4×C11—21no—
170C4×C11—42no—
171C4×C11—44no—
172C4×C11—42no—
173C4×C11—42no—
174C4×C11#41312yes—
175C4×C11#44912yes—
176C4×C11#45212yes—
177C22×Q8C2×Dic1112yes—
178C22×Q8C22⋊D1111yescharacteristic
179C22×D4C2×Dic1111yescharacteristic
180C23×C4—21no—
181C2×M16—222no—
182C4⋊Q8—22no—
183C4⋊Q8C22⋊D1114yes—
184#126—216no—
185#124—24no—
186#124—24no—
187C22⋊Q8—28no—
188C4×Q8—24no—
189C4×Q8—24no—
190C4×Q8—22no—
191C4×Q8—22no—
192C4×D4—22no—
193C4×D4C22⋊D1114yes—
194#117—28no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×Dic1111yescharacteristic
199C2×C4⋊C4C22⋊D1111yescharacteristic
200C2×C4⋊C4C22⋊D1112yes—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—21no—
204C2×C42—22no—
205C2×C42C2×Dic1112yes—
206C2×C42C22×D1111yescharacteristic
207C4⋊C8—222no—
208C4⋊C8—222no—
209C4⋊C8—222no—
210#101—442no—
211C22⋊C8—222no—
212C4×C8—222no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11—82no—
216C2×C11#178511yescharacteristic
217C2×C11#178811yescharacteristic
218C2×C11#179611yescharacteristic
219C24—21no—
220C2×Q8—21no—
221C2×Q8—22no—
222C2×Q8—21no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—44no—
226C2×Q8C22⋊Dic1114yes—
227C2×D4—21no—
228C2×D4—42no—
229C2×D4C22⋊Dic1112yes—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4—41no—
236C22×C4C22⋊Dic1112yes—
237C22×C4C22⋊Dic1112yes—
238C22×C4C22×Dic1111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241M16—442no—
242M16—442no—
243C2×C8—442no—
244C2×C8—442no—
245C4⋊C4—28no—
246C4⋊C4—21no—
247C4⋊C4—24no—
248C4⋊C4—24no—
249C4⋊C4—22no—
250C4⋊C4—24no—
251C4⋊C4C22⋊Dic1112yes—
252C22⋊C4—28no—
253C22⋊C4—28no—
254C22⋊C4—24no—
255C42—28no—
256C42—22no—
257C42—22no—
258C42C2×C22⋊D1112yes—
259C42C2×C22⋊D1112yes—
260C11#839411yescharacteristic, complemented, Sylow
261C23—22no—
262C23—42no—
263C23—42no—
264C23—41no—
265C23—41no—
266C23C2×C22⋊Dic1111yescharacteristic
267Q8—44no—
268Q8—44no—
269Q8—42no—
270Q8—42no—
271D4—24no—
272D4—42no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—44no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4#6700211yescharacteristic
288C2×C4#6700312yes—
289C2×C4#6700411yescharacteristic
290C2×C4C2×C22⋊Dic1111yescharacteristic
291C2×C4C2×C22⋊Dic1111yescharacteristic
292C2×C4#6700612yes—
293C2×C4#6700612yes—
294C8—882no—
295C8—882no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—82no—
302C22—82no—
303C22#1062284511yescharacteristic
304C22#1062284611yescharacteristic
305C22#1062286011yescharacteristic
306C4—21no—
307C4—22no—
308C4—44no—
309C4—42no—
310C4—42no—
311C4—42no—
312C4#1062285012yes—
313C4#1062285112yes—
314C4#1062285212yes—
315C2—21no—
316C2—21no—
317C2—82no—
318C2#1306854411yescharacteristic
319C2#1306855611yescharacteristic
320C2#1306859111yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#556C2
socleC22×C11#379
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC2×#556D11
hypocenterC11#8394
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #13068612C2semidirect
2. #13067297C2semidirect
4. #13066940C2semidirect
260. C11#8394semidirect

Maximal subgroups

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

subgroupindex
#130686122
#130672972
#130670412
#130669402
C2×C11×#5562
#839411