Finite Group Databasebeta

← #14664608

Subgroups — #14664608

Order 2816.

340 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 69 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#13074498C211yesmaximal, characteristic
2#13068611C211yesmaximal, characteristic
3#13066958C211yesmaximal, characteristic
4#13066643C211yesmaximal, characteristic
5#13066623C211yesmaximal, characteristic
6#13066621C211yesmaximal, characteristic
7C11×#1353C211yesmaximal, characteristic
8C2×#66943C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C11×#400C2211yescharacteristic
11C2×#66888—21no—
12#10622731—21no—
13#10622596C2211yescharacteristic
14#10622595C411yescharacteristic
15#10622332—21no—
16#10622274C411yescharacteristic
17#10622273—21no—
18#10622269—21no—
19#10622267—21no—
20#10622265—21no—
21#10622264C411yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×Dic22D411yescharacteristic
28C2×C11×M16—21no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×Dic11⋊C4—21no—
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4C2×C411yescharacteristic
37C2×Dic11⋊C4D411yescharacteristic
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40C2×C4×Dic11D411yescharacteristic
41C2×#4318—21no—
42#66943—41no—
43#66943—41no—
44#66940—41no—
45#66940—41no—
46C11×C22⋊C8—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95C2×C411yescharacteristic
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58#66888—42no—
59#66879—41no—
60Dic11⋊C8—41no—
61Dic11⋊C8—41no—
62Dic11⋊C8—41no—
63#11835—111nomaximal, Sylow
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2634—111no—
105#1801—111no—
106#1467—111no—
107#1353—111no—
108#1353D1111yescharacteristic
109#1346—111no—
110#1346—111no—
111C23×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11#9911yescharacteristic
141C2×Dic11#9911yescharacteristic
142Dic22—42no—
143Dic22—42no—
144C8×C11—81no—
145C8×C11—81no—
146C11⋊C8—81no—
147C11⋊C8—81no—
148C2×#125—111no—
149C2×C4×Q8—111no—
150#432—221no—
151#423—221no—
152C2×#101—221no—
153#400—111no—
154#400—221no—
155#400C2×D1111yescharacteristic
156#398—111no—
157#398—111no—
158#395—221no—
159#387—221no—
160#387—221no—
161#383—111no—
162#343—111no—
163#343C2×D1111yescharacteristic
164#324—111no—
165#324—221no—
166#324C2×D1111yescharacteristic
167C22×C11—21no—
168C22×C11—21no—
169C22×C11C2×#9911yescharacteristic
170C22×C11#41711yescharacteristic
171C22×C11#42111yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—81no—
177C4×C11—81no—
178Dic11—21no—
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182Dic11—41no—
183Dic11—81no—
184Dic11—81no—
185C22×Q8—111no—
186C2×M16—21no—
187C2×M16—221no—
188#125—441no—
189#125—441no—
190C4×Q8—441no—
191C4×Q8—441no—
192C2×C4⋊C4—111no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4C4×D1111yescharacteristic
200C2×C4⋊C4C22×D1111yescharacteristic
201C2×C42—111no—
202C2×C42—111no—
203C2×C42—111no—
204C4⋊C8—441no—
205C4⋊C8—441no—
206C4⋊C8—441no—
207#101—442no—
208C22⋊C8—21no—
209C22⋊C8—221no—
210#97—441no—
211#95—21no—
212#95—21no—
213#95—111no—
214#95—221no—
215#95—221no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95C4×D1111yescharacteristic
221C2×C11—21no—
222C2×C11—21no—
223C2×C11#151311yescharacteristic
224C2×C11#212311yescharacteristic
225C2×C11#213311yescharacteristic
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8—441no—
229C2×Q8—441no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4C2×C4×D1111yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241M16—41no—
242M16—41no—
243M16—441no—
244M16—441no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—442no—
257C4⋊C4—442no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C42—221no—
261C42—221no—
262C42—221no—
263C42—221no—
264C42—221no—
265C42—221no—
266C11#1183511yescharacteristic, complemented, Sylow
267C23C22⋊C4×D1111yescharacteristic
268Q8—442no—
269Q8—442no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—111no—
282C2×C4—111no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4#6696711yescharacteristic
299C2×C4#6697111yescharacteristic
300C8—81no—
301C8—81no—
302C8—881no—
303C8—881no—
304C22—21no—
305C22—21no—
306C22D11×#9911yescharacteristic
307C22#1062241611yescharacteristic
308C22#1062243411yescharacteristic
309C4—21no—
310C4—21no—
311C4—41no—
312C4—41no—
313C4—81no—
314C4—81no—
315C4—221no—
316C4—221no—
317C4—441no—
318C4—441no—
319C4—441no—
320C4—881no—
321C4—881no—
322C2—21no—
323C2—21no—
324C2#1306715811yescharacteristic
325C2#1307026811yescharacteristic
326C2#1307030211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1353C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1353D11
hypocenterC11#11835
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
266. C11#11835semidirect

Maximal subgroups

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

subgroupindex
#130744982
#130686112
#130669582
#130666432
#130666232
#130666212
C11×#13532
#1183511