Finite Group Databasebeta

← #14664826

Subgroups — #14664826

Order 2816.

476 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 99 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#13073615C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic, complemented
3#13066618C214yesmaximal, complemented
4C11×#1801C211yesmaximal, characteristic, complemented
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#67000—21no—
7C2×#66927C411yescharacteristic
8C11×#423—21no—
9C2×C11×#101—21no—
10#10622604C412yes—
11#10622604C2212yes—
12#10622601—21no—
13#10622552—21no—
14#10622552—21no—
15C4×C4⋊Dic11C411yescharacteristic
16#10622538—21no—
17C11×#343C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×D44—21no—
22C22×D44—21no—
23C22×D44C2×C412yes—
24C2×C11×M16—22no—
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33#67000—42no—
34#67000—42no—
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—22no—
39C2×C4⋊Dic11—21no—
40C2×C4×Dic11—21no—
41#66927—41no—
42#66927—41no—
43C11×C4⋊C8—41no—
44C11×C4⋊C8—41no—
45C11×#101—42no—
46C11⋊#95C2×C412yes—
47C22⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)—41no—
49C4×C11⋊C8—41no—
50#11882—111nomaximal, Sylow
51C23×D11—22no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11D812yes—
55C2×Q8×C11SD1612yes—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—22no—
64C2×D44—42no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—42no—
68C2×D44—42no—
69C2×D44—41no—
70C2×D44—41no—
71C2×D44—42no—
72C2×D44—82no—
73C11×M16—42no—
74C11×M16—42no—
75C2×C8×C11—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85(C2×D11)⋊C4—44no—
86(C2×D11)⋊C4—42no—
87(C2×D11)⋊C4—42no—
88(C2×D11)⋊C4—82no—
89(C2×D11)⋊C4—82no—
90C4⋊Dic11—42no—
91C4×Dic11—42no—
92C2×C11⋊C8—42no—
93#2548—111no—
94#1801D1111yescharacteristic, complemented
95#1461—111no—
96#1345—114no—
97C23×C11C2×C22⋊C411yescharacteristic
98C22×D11—42no—
99C22×D11—42no—
100C22×D11—42no—
101C22×D11—42no—
102C22×D11—42no—
103C22×D11—42no—
104C22×D11—42no—
105Q8×C11—42no—
106Q8×C11—42no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11#9911yescharacteristic
121C2×C4×C11#9911yescharacteristic
122C2×C4×C11#10212yes—
123C2×C4×C11#10212yes—
124C2×C4×C11C2×D811yescharacteristic
125C2×C4×C11C2×SD1611yescharacteristic
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129D44—82no—
130D44—84no—
131D44—84no—
132D44—82no—
133C8×C11—82no—
134C11⋊C8—82no—
135C2×#127—111no—
136C2×#124—221no—
137C2×C4×Q8C2×D1111yescharacteristic
138#431—221no—
139#423—21no—
140C2×#101—21no—
141#394—112no—
142#394—112no—
143#390—221no—
144#390—221no—
145#390—221no—
146C4×C4⋊C4—111no—
147#343C2×D1112yes—
148#324—112no—
149#324—221no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11C2×#9911yescharacteristic
153C22×C11C2×#10211yescharacteristic
154C22×C11#42111yescharacteristic
155C2×D11—82no—
156C2×D11—82no—
157C2×D11—82no—
158C2×D11—82no—
159C2×D11—82no—
160C2×D11—82no—
161C2×D11—82no—
162C4×C11—21no—
163C4×C11—22no—
164C4×C11—22no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11#35512yes—
171Dic11—82no—
172C22×Q8C22⋊D1111yescharacteristic
173C22×D4—112no—
174C22×D4—221no—
175C22×D4—221no—
176C2×M16—22no—
177#127—441no—
178#127—441no—
179#124—442no—
180#124—442no—
181C4×Q8—41no—
182C4×Q8—41no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4C4×D1111yescharacteristic
185C2×C4⋊C4D4411yescharacteristic
186C2×C4⋊C4C22×D1111yescharacteristic
187C2×C22⋊C4—222no—
188C2×C22⋊C4—222no—
189C2×C22⋊C4—222no—
190C2×C22⋊C4—222no—
191C2×C42—221no—
192C2×C42C4×D1111yescharacteristic
193C2×C42D4411yescharacteristic
194C2×C42C22⋊D1111yescharacteristic
195C4⋊C8—41no—
196C4⋊C8—41no—
197C4⋊C8—441no—
198#101—42no—
199C22⋊C8—222no—
200C4×C8—441no—
201#95—112no—
202C2×C11—21no—
203C2×C11—21no—
204C2×C11#151911yescharacteristic
205C2×C11#212211yescharacteristic
206C2×C11C2×#35511yescharacteristic
207D11—162no—
208C24—222no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8#432312yes—
212C2×Q8#432512yes—
213C2×D4—442no—
214C2×D4—442no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4—441no—
219C2×D4—441no—
220C2×D4—442no—
221C2×D4—882no—
222C22×C4—222no—
223C22×C4(C2×D11)⋊C411yescharacteristic
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4(C2×D11)⋊C411yescharacteristic
226C22×C4(C2×D11)⋊C411yescharacteristic
227C22×C4C2×C4×D1111yescharacteristic
228C22×C4C2×D4411yescharacteristic
229C22×C4C2×C22⋊D1111yescharacteristic
230M16—42no—
231M16—42no—
232C2×C8—42no—
233C2×C8—442no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—442no—
238C22⋊C4—444no—
239C22⋊C4—442no—
240C22⋊C4—442no—
241C22⋊C4—882no—
242C22⋊C4—882no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—442no—
250C11#1188211yescharacteristic, complemented, Sylow
251C23—442no—
252C23—442no—
253C23—442no—
254C23—442no—
255C23—442no—
256C23—442no—
257C23—442no—
258C23C2×(C2×D11)⋊C411yescharacteristic
259Q8—42no—
260Q8—42no—
261D4—884no—
262D4—882no—
263D4—884no—
264D4—882no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4—442no—
281C2×C4#6687011yescharacteristic
282C2×C4#6687011yescharacteristic
283C2×C4#6687312yes—
284C2×C4#6687312yes—
285C2×C4C2×#432311yescharacteristic
286C2×C4C2×#432511yescharacteristic
287C8—82no—
288C8—882no—
289C22—21no—
290C22—21no—
291C22—882no—
292C22—882no—
293C22—882no—
294C22—882no—
295C22—882no—
296C22—882no—
297C22—882no—
298C22C2×#6687011yescharacteristic
299C22C2×#6687311yescharacteristic
300C22#1062261811yescharacteristic
301C4—21no—
302C4—22no—
303C4—22no—
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—882no—
310C4#1062211512yes—
311C2—21no—
312C2—21no—
313C2—1762no—
314C2#1306718311yescharacteristic
315C2#1307026711yescharacteristic
316C2C2×#1062211511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1801C2
socleC22×C11C2×#99
prime radicalC2×#66927C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1801D11
hypocenterC11#11882
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. #13066940C2semidirect
3. #13066618C2semidirect
4. C11×#1801C2semidirect
94. #1801D11semidirect
250. C11#11882semidirect

Maximal subgroups

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

subgroupindex
#130736152
#130669402
#130666182
C11×#18012
#1188211