Finite Group Databasebeta

← #14657015

Subgroups — #14657015

Order 2816.

594 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 75 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#13074286C211yesmaximal, characteristic, complemented
2#13068560C212yesmaximal
3#13066524C211yesmaximal, characteristic, complemented
4#13066468C212yesmaximal, complemented
5C11×#1782C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C2×C11×#99—22no—
8C11×#381C2211yescharacteristic
9C11×#381C2211yescharacteristic
10C2×#66901—22no—
11C2×#66901—22no—
12C4×C22⋊Dic11C2212yes—
13#10622820C2212yes—
14#10622561—22no—
15#10622267—22no—
16#10622260—22no—
17C2×C11×#41—22no—
18C2×C11×#41—22no—
19C2×C11×#41—44no—
20C22×Q8×C11Q811yescharacteristic
21C22×D4×C11—21no—
22C22×D4×C11Q811yescharacteristic
23C23×C4×C11—21no—
24C23×C4×C11C2311yescharacteristic
25C2×C11×C22⋊C4—21no—
26C2×C11×C22⋊C4D412yes—
27C2×C22⋊Dic11—22no—
28C2×C4⋊Dic11—22no—
29C2×Dic11⋊C4—22no—
30C2×Dic11⋊C4—22no—
31C2×C4×Dic11D412yes—
32C2×C4×Dic11D412yes—
33C2×#4318—22no—
34C11×#99—44no—
35C11×#95—22no—
36C11×#95—22no—
37#66901—44no—
38#66901—44no—
39C11⋊#95—22no—
40C11⋊#95—22no—
41C22⋊(C11⋊C8)—22no—
42C22⋊(C11⋊C8)—22no—
43#10388—111nomaximal, Sylow
44C24×C11—21no—
45C24×C11C2×D411yescharacteristic
46C11×#41—24no—
47C11×#41—24no—
48C11×#41—42no—
49C11×#41—42no—
50C11×#41—44no—
51C11×#41—44no—
52C2×Q8×C11—22no—
53C2×Q8×C11—42no—
54C2×D4×C11—24no—
55C2×D4×C11—22no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—41no—
67C22×C4×C11C2×D412yes—
68C22×C4×C11C2×Q811yescharacteristic
69C22×C4×C11#4112yes—
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—22no—
72C22×Dic11—22no—
73C11×C22⋊C4—42no—
74C11×C22⋊C4—42no—
75C22⋊Dic11—44no—
76C4⋊Dic11—44no—
77Dic11⋊C4—44no—
78Dic11⋊C4—82no—
79C4×Dic11—42no—
80C4×Dic11—42no—
81#4318—42no—
82#4318—42no—
83C2×C11⋊C8—42no—
84#2608—111no—
85#1789—112no—
86#1782D1111yescharacteristic
87#1306—111no—
88#1284—112no—
89C23×C11—22no—
90C23×C11—22no—
91C23×C11—42no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11—82no—
95C23×C11#12011yescharacteristic
96C23×C11C22⋊Q811yescharacteristic
97C23×C11#12411yescharacteristic
98Q8×C11—24no—
99Q8×C11—42no—
100D4×C11—24no—
101D4×C11—42no—
102D4×C11—44no—
103D4×C11—44no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—44no—
111C2×C4×C11—44no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—81no—
118C2×C4×C11—82no—
119C2×C4×C11C22⋊Q812yes—
120C2×C4×C11#12412yes—
121C2×Dic11—24no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C11⋊C8—82no—
128C22×#41C2×D1111yescharacteristic
129C2×#104—222no—
130C2×#104—222no—
131C2×#99—22no—
132#407—112no—
133#396—222no—
134#389—222no—
135#387—222no—
136#381C2×D1111yescharacteristic
137#381C2×D1111yescharacteristic
138C4×C22⋊C4—112no—
139C22×C11—22no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—42no—
145C22×C11—82no—
146C22×C11—82no—
147C22×C11—82no—
148C22×C11—82no—
149C22×C11#39311yescharacteristic
150C22×C11B(4,𝔽2)12yes—
151C4×C11—22no—
152C4×C11—22no—
153C4×C11—42no—
154C4×C11—82no—
155C4×C11—161no—
156Dic11—44no—
157Dic11—82no—
158C2×#41—22no—
159C2×#41—22no—
160C2×#41—44no—
161C22×Q8Dic2211yescharacteristic
162C22×D4—21no—
163C22×D4Dic2211yescharacteristic
164C23×C4—21no—
165C23×C4C22×D1111yescharacteristic
166C2×M16—222no—
167C2×C4⋊C4—222no—
168C2×C4⋊C4—222no—
169C2×C4⋊C4—222no—
170C2×C22⋊C4—21no—
171C2×C22⋊C4—222no—
172C2×C22⋊C4C22⋊D1112yes—
173C2×C42—112no—
174C2×C42—112no—
175#104—444no—
176#104—444no—
177#99—44no—
178C22⋊C8—222no—
179C22⋊C8—222no—
180#95—22no—
181#95—22no—
182#95—222no—
183#95—222no—
184C2×C11—22no—
185C2×C11—41no—
186C2×C11—41no—
187C2×C11—82no—
188C2×C11#202911yescharacteristic
189C2×C11#203112yes—
190C24—21no—
191C24C2×C22⋊D1111yescharacteristic
192#41—24no—
193#41—24no—
194#41—42no—
195#41—42no—
196#41—44no—
197#41—44no—
198C2×Q8—22no—
199C2×Q8—42no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—41no—
205C2×D4—41no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—222no—
214C22×C4—222no—
215C22×C4C2×Dic2211yescharacteristic
216C22×C4#433911yescharacteristic
217C22×C4D4×D1112yes—
218C22×C4#434112yes—
219M16—442no—
220M16—442no—
221C2×C8—442no—
222C4⋊C4—444no—
223C4⋊C4—444no—
224C4⋊C4—882no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C22⋊C4—444no—
228C42—442no—
229C42—442no—
230C11#1038811yescharacteristic, complemented, Sylow
231C23—22no—
232C23—22no—
233C23—42no—
234C23—41no—
235C23—41no—
236C23—82no—
237C23#6697711yescharacteristic
238C23#6698911yescharacteristic
239C23#6699011yescharacteristic
240Q8—24no—
241Q8—42no—
242D4—24no—
243D4—42no—
244D4—44no—
245D4—44no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—44no—
253C2×C4—44no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—81no—
260C2×C4—82no—
261C2×C4—224no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4#6693112yes—
268C2×C4#6693812yes—
269C8—882no—
270C22—22no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22#1062256011yescharacteristic
281C22#1062264512yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—82no—
286C4—161no—
287C4—444no—
288C4—882no—
289C2—22no—
290C2—41no—
291C2—41no—
292C2—82no—
293C2#1306978011yescharacteristic
294C2#1306979012yes—
subgroupG/H
centerC22#10622560
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1782C2
socleC22×C11#393
prime radicalC22×C11×#41C22
hypercenter#1782D11
hypocenterC11#10388
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
1. #13074286C2semidirect
3. #13066524C2semidirect
4. #13066468C2semidirect
230. C11#10388semidirect

Maximal subgroups

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

subgroupindex
#130742862
#130685602
#130665242
#130664682
C11×#17822
#1038811