Finite Group Databasebeta

← #14656768

Subgroups — #14656768

Order 2816.

640 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 107 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#13074586C211yesmaximal, characteristic
2#13068551C212yesmaximal
3#13066495C212yesmaximal
4#13066459C211yesmaximal, characteristic
5C11×#1446C211yesmaximal, characteristic
6C23×Q8×C11C2211yescharacteristic
7C2×C11×#95—22no—
8C2×C11×#95C2211yescharacteristic
9C2×C11×#95C2211yescharacteristic
10C2×#66899—22no—
11C2×#66899—22no—
12#10622825C2212yes—
13#10622823—22no—
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622273—22no—
16#10622270—22no—
17C22×Q8×C11—21no—
18C22×Q8×C11—22no—
19C22×Q8×C11—22no—
20C22×Q8×C11—44no—
21C22×Q8×C11Q812yes—
22C23×C4×C11—21no—
23C23×C4×C11—21no—
24C23×C4×C11D412yes—
25C23×C4×C11C2311yescharacteristic
26C2×C22⋊Dic11—22no—
27C2×C4⋊Dic11D412yes—
28C2×C4⋊Dic11D412yes—
29C2×Dic11⋊C4—22no—
30C2×Dic11⋊C4—22no—
31C22×C11⋊C8—22no—
32C11×#95—22no—
33C11×#95—22no—
34C11×#95—44no—
35#66899—44no—
36#66899—44no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40C22⋊(C11⋊C8)—22no—
41C22⋊(C11⋊C8)—22no—
42#10345—111nomaximal, Sylow
43C24×C11C2×D411yescharacteristic
44C2×Q8×C11—24no—
45C2×Q8×C11—24no—
46C2×Q8×C11—24no—
47C2×Q8×C11—44no—
48C2×Q8×C11—42no—
49C2×Q8×C11—42no—
50C2×Q8×C11—44no—
51C2×Q8×C11—48no—
52C2×Q8×C11—42no—
53C22×C4×C11—24no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—42no—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×Q811yescharacteristic
71C22×C4×C11#4112yes—
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—22no—
74C22×Dic11—22no—
75C22⋊Dic11—42no—
76C22⋊Dic11—42no—
77C4⋊Dic11—42no—
78C4⋊Dic11—42no—
79Dic11⋊C4—82no—
80Dic11⋊C4—82no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84#2646—111no—
85#1787—112no—
86#1446D1111yescharacteristic
87#1294—112no—
88#1280—111no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—22no—
92C23×C11#12011yescharacteristic
93C23×C11C22⋊Q811yescharacteristic
94C23×C11#12411yescharacteristic
95C23×C11#13512yes—
96C23×C11#13712yes—
97Q8×C11—28no—
98Q8×C11—44no—
99Q8×C11—44no—
100Q8×C11—44no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—24no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—44no—
109C2×C4×C11—42no—
110C2×C4×C11—44no—
111C2×C4×C11—44no—
112C2×C4×C11—42no—
113C2×C4×C11—44no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—82no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11—82no—
121C2×C4×C11C22⋊Q812yes—
122C2×C4×C11#12412yes—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C11⋊C8—82no—
130C23×Q8C2×D1111yescharacteristic
131C2×#103—222no—
132C2×#103—222no—
133C2×C22⋊C8—112no—
134#400—222no—
135#398—222no—
136#385—222no—
137#380—112no—
138C2×#95—22no—
139C2×#95C2×D1111yescharacteristic
140C2×#95C2×D1111yescharacteristic
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11#39311yescharacteristic
150C22×C11#45212yes—
151C22×C11#45511yescharacteristic
152C22×C11#45611yescharacteristic
153C22×C11B(4,𝔽2)12yes—
154C22×C11#47912yes—
155C22×C11#48811yescharacteristic
156C22×C11#49111yescharacteristic
157C4×C11—22no—
158C4×C11—22no—
159C4×C11—44no—
160C4×C11—82no—
161C4×C11—82no—
162Dic11—82no—
163Dic11—82no—
164C22×Q8—21no—
165C22×Q8—22no—
166C22×Q8—22no—
167C22×Q8—44no—
168C22×Q8Dic2212yes—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4C22⋊D1112yes—
172C23×C4C22×D1111yescharacteristic
173C22×C8—222no—
174C2×C4⋊C4—112no—
175C2×C4⋊C4—112no—
176C2×C4⋊C4—222no—
177C2×C4⋊C4—222no—
178C2×C22⋊C4—222no—
179#103—444no—
180#103—444no—
181C22⋊C8—222no—
182C22⋊C8—222no—
183#95—22no—
184#95—22no—
185#95—44no—
186#95—222no—
187#95—222no—
188#95—222no—
189C2×C11—21no—
190C2×C11—22no—
191C2×C11—21no—
192C2×C11#160312yes—
193C2×C11#160612yes—
194C2×C11#202611yescharacteristic
195C2×C11#202811yescharacteristic
196C2×C11#202911yescharacteristic
197C24C2×C22⋊D1111yescharacteristic
198C2×Q8—24no—
199C2×Q8—24no—
200C2×Q8—24no—
201C2×Q8—44no—
202C2×Q8—42no—
203C2×Q8—42no—
204C2×Q8—44no—
205C2×Q8—48no—
206C2×Q8—42no—
207C22×C4—24no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—42no—
223C22×C4—222no—
224C22×C4—222no—
225C22×C4C2×Dic2211yescharacteristic
226C22×C4#433911yescharacteristic
227C22×C4D4×D1112yes—
228C22×C4#434112yes—
229C2×C8—442no—
230C2×C8—442no—
231C2×C8—442no—
232C4⋊C4—442no—
233C4⋊C4—442no—
234C4⋊C4—882no—
235C4⋊C4—882no—
236C22⋊C4—442no—
237C22⋊C4—442no—
238C11#1034511yescharacteristic, complemented, Sylow
239C23—22no—
240C23—21no—
241C23—21no—
242C23#6697711yescharacteristic
243C23#6698911yescharacteristic
244C23#6699011yescharacteristic
245C23#6699512yes—
246C23#6700312yes—
247Q8—28no—
248Q8—44no—
249Q8—44no—
250Q8—44no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—82no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—82no—
271C2×C4—442no—
272C2×C4—442no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4—442no—
277C2×C4#6693112yes—
278C2×C4#6693812yes—
279C8—882no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22#1062256011yescharacteristic
289C22#1062263512yes—
290C22#1062264512yes—
291C22#1062266012yes—
292C22#1062266911yescharacteristic
293C22#1062267411yescharacteristic
294C22#1062269511yescharacteristic
295C22#1062270811yescharacteristic
296C4—22no—
297C4—22no—
298C4—44no—
299C4—82no—
300C4—82no—
301C4—882no—
302C4—882no—
303C2—21no—
304C2—22no—
305C2—21no—
306C2#1306757712yes—
307C2#1306759412yes—
308C2#1306976711yescharacteristic
309C2#1306977711yescharacteristic
310C2#1306978011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1446C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1446D11
hypocenterC11#10345
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1446

Complements

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

NH ≅ G/Ntype
238. C11#10345semidirect

Maximal subgroups

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

subgroupindex
#130745862
#130685512
#130664952
#130664592
C11×#14462
#1034511