Finite Group Databasebeta

← #14657012

Subgroups — #14657012

Order 2816.

594 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 77 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#13068561C212yesmaximal
2#13068533C211yesmaximal, characteristic
3#13066524C211yesmaximal, characteristic, complemented
4#13066469C212yesmaximal, complemented
5C11×#2608C211yesmaximal, characteristic, complemented
6C22×#4339C2211yescharacteristic
7C11×#396—22no—
8C11×#389—22no—
9C11×#387—22no—
10C11×#381C2211yescharacteristic
11C4×C11×C22⋊C4C2212yes—
12#10622824C2211yescharacteristic
13#10622820C2212yes—
14C2×#66870—22no—
15C2×#66869—22no—
16C2×#66869—22no—
17C23×C4×C11C2311yescharacteristic
18C22×C22⋊D11—21no—
19C2×#4339—22no—
20C2×#4339—22no—
21C2×#4339—44no—
22C22×D44Q811yescharacteristic
23C22×C4×D11—21no—
24C22×Dic22Q811yescharacteristic
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4D412yes—
30C2×C42×C11D412yes—
31C2×C42×C11D412yes—
32C2×C22⋊Dic11—21no—
33C2×#4318—22no—
34C11×#95—22no—
35C11×#95—22no—
36C11×#95—22no—
37C11⋊#95—22no—
38C22⋊(C11⋊C8)—22no—
39C22⋊(C11⋊C8)—22no—
40#66870—44no—
41#66869—44no—
42#66869—44no—
43#10388—111nomaximal, Sylow
44C24×C11C2×D411yescharacteristic
45C23×D11—21no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—42no—
50C22×C4×C11C2×D412yes—
51C22×C4×C11C2×Q811yescharacteristic
52C22×C4×C11#4112yes—
53C22×C4×C11#4111yescharacteristic
54C2×C22⋊D11—24no—
55C2×C22⋊D11—42no—
56C2×C22⋊D11—41no—
57C2×C22⋊D11—41no—
58C22×Dic11—21no—
59C22×Dic11—41no—
60#4339—24no—
61#4339—24no—
62#4339—42no—
63#4339—42no—
64#4339—44no—
65#4339—44no—
66C2×D44—22no—
67C2×D44—42no—
68C2×C4×D11—42no—
69C2×C4×D11—42no—
70C2×C4×D11—42no—
71C2×Dic22—22no—
72C2×Dic22—42no—
73C11×C4⋊C4—44no—
74C11×C4⋊C4—44no—
75C11×C4⋊C4—82no—
76C11×C22⋊C4—44no—
77C11×C22⋊C4—42no—
78C42×C11—42no—
79C42×C11—42no—
80C22⋊Dic11—42no—
81#4318—42no—
82#4318—42no—
83C2×C11⋊C8—42no—
84#2608D1111yescharacteristic, complemented
85#1789—112no—
86#1782—111no—
87#1306—111no—
88#1284—112no—
89C23×C11—22no—
90C23×C11—42no—
91C23×C11#12011yescharacteristic
92C23×C11C22⋊Q811yescharacteristic
93C23×C11#12411yescharacteristic
94C22×D11—22no—
95C22×D11—41no—
96C22×D11—41no—
97C22×D11—82no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—24no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11C22⋊Q812yes—
113C2×C4×C11#12412yes—
114C22⋊D11—44no—
115C22⋊D11—44no—
116C2×Dic11—22no—
117C2×Dic11—41no—
118C2×Dic11—41no—
119C2×Dic11—81no—
120C2×Dic11—82no—
121D44—24no—
122D44—42no—
123C4×D11—44no—
124C4×D11—44no—
125Dic22—24no—
126Dic22—42no—
127C11⋊C8—82no—
128C22×#41—111no—
129C2×#104—222no—
130C2×#104—222no—
131C2×#99—222no—
132#407—112no—
133#396—22no—
134#389—22no—
135#387—22no—
136#381—111no—
137#381C2×D1111yescharacteristic
138C4×C22⋊C4C2×D1112yes—
139C22×C11—22no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—82no—
145C22×C11#39311yescharacteristic
146C22×C11B(4,𝔽2)12yes—
147C2×D11—42no—
148C2×D11—82no—
149C2×D11—82no—
150C2×D11—82no—
151C4×C11—22no—
152C4×C11—22no—
153C4×C11—44no—
154C4×C11—82no—
155C4×C11—82no—
156Dic11—42no—
157Dic11—161no—
158C2×#41—222no—
159C2×#41—222no—
160C2×#41—444no—
161C22×Q8—111no—
162C22×D4—111no—
163C22×D4—221no—
164C23×C4—221no—
165C23×C4C22×D1111yescharacteristic
166C2×M16—222no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—221no—
172C2×C22⋊C4C22⋊D1112yes—
173C2×C42C22⋊D1112yes—
174C2×C42C22⋊D1112yes—
175#104—444no—
176#104—444no—
177#99—444no—
178C22⋊C8—222no—
179C22⋊C8—222no—
180#95—22no—
181#95—22no—
182#95—22no—
183#95—222no—
184C2×C11—22no—
185C2×C11—41no—
186C2×C11—41no—
187C2×C11#202911yescharacteristic
188C2×C11#203112yes—
189D11—82no—
190C24—221no—
191C24C2×C22⋊D1111yescharacteristic
192#41—224no—
193#41—224no—
194#41—442no—
195#41—442no—
196#41—444no—
197#41—444no—
198C2×Q8—222no—
199C2×Q8—442no—
200C2×D4—224no—
201C2×D4—222no—
202C2×D4—442no—
203C2×D4—442no—
204C2×D4—441no—
205C2×D4—441no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—221no—
211C22×C4—442no—
212C22×C4—442no—
213C22×C4—442no—
214C22×C4—441no—
215C22×C4Q8×D1111yescharacteristic
216C22×C4#434312yes—
217C22×C4#434311yescharacteristic
218C22×C4C2×C22⋊D1112yes—
219M16—442no—
220M16—442no—
221C2×C8—442no—
222C4⋊C4—44no—
223C4⋊C4—44no—
224C4⋊C4—82no—
225C22⋊C4—44no—
226C22⋊C4—42no—
227C22⋊C4—442no—
228C42—42no—
229C42—42no—
230C11#1038811yescharacteristic, complemented, Sylow
231C23—22no—
232C23—42no—
233C23—222no—
234C23—441no—
235C23—441no—
236C23—882no—
237C23#6699911yescharacteristic
238C23#6700011yescharacteristic
239C23#6700611yescharacteristic
240Q8—224no—
241Q8—442no—
242D4—224no—
243D4—442no—
244D4—444no—
245D4—444no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—222no—
261C2×C4—444no—
262C2×C4—444no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—881no—
266C2×C4—882no—
267C2×C4#6699912yes—
268C2×C4#6700012yes—
269C8—882no—
270C22—22no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—22no—
275C22—82no—
276C22—442no—
277C22—882no—
278C22—882no—
279C22—882no—
280C22#1062284411yescharacteristic
281C22#1062285712yes—
282C4—22no—
283C4—22no—
284C4—44no—
285C4—82no—
286C4—82no—
287C4—442no—
288C4—1761no—
289C2—22no—
290C2—41no—
291C2—41no—
292C2—882no—
293C2#1306977911yescharacteristic
294C2#1306978512yes—
subgroupG/H
centerC22#10622844
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2608C2
socleC22×C11#393
prime radicalC22×#4339C22
hypercenter#2608D11
hypocenterC11#10388
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2608

Complements

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

NH ≅ G/Ntype
3. #13066524C2semidirect
4. #13066469C2semidirect
5. C11×#2608C2semidirect
84. #2608D11semidirect
230. C11#10388semidirect

Maximal subgroups

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

subgroupindex
#130685612
#130685332
#130665242
#130664692
C11×#26082
#1038811