Finite Group Databasebeta

← #14664419

Subgroups — #14664419

Order 2816.

378 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 73 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#13073827C211yesmaximal, characteristic
2#13068411C211yesmaximal, characteristic
3#13066958C211yesmaximal, characteristic
4#13066644C211yesmaximal, characteristic
5#13066643C211yesmaximal, characteristic
6#13066642C211yesmaximal, characteristic
7C11×#1353C211yesmaximal, characteristic
8C2×#66941C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C11×#400C2211yescharacteristic
11C2×#66888—21no—
12M16×Dic11—21no—
13#10622599C2211yescharacteristic
14#10622595C411yescharacteristic
15#10622332—21no—
16#10622272C411yescharacteristic
17#10622263—21no—
18#10622262C411yescharacteristic
19#10622259—21no—
20#10622259—21no—
21#10622259—21no—
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×Dic22—21no—
28C22×Dic22D411yescharacteristic
29C2×C11×M16—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C4⋊Dic11C2×C411yescharacteristic
33C2×Dic11⋊C4—21no—
34C2×Dic11⋊C4—21no—
35C2×Dic11⋊C4C2×C411yescharacteristic
36C2×Dic11⋊C4D411yescharacteristic
37C2×C4×Dic11—21no—
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40C2×C4×Dic11D411yescharacteristic
41C2×#4318—21no—
42#66941—41no—
43#66941—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—24no—
59#66879—41no—
60#66879—41no—
61Dic11⋊C8—41no—
62C8×Dic11—41no—
63#11794—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—22no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—41no—
79C2×Dic22—44no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C11×M16—22no—
83C11×M16—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C4⋊Dic11—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—42no—
100#4318—22no—
101#4318—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2568—111no—
105C4×#101—111no—
106#1467—111no—
107#1353—111no—
108#1353—111no—
109#1353—111no—
110#1353D1111yescharacteristic
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—42no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11#13711yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—22no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11#9911yescharacteristic
139C2×Dic11#9911yescharacteristic
140C2×Dic11#10412yes—
141Dic22—42no—
142Dic22—42no—
143Dic22—82no—
144Dic22—82no—
145C8×C11—42no—
146C8×C11—81no—
147C11⋊C8—42no—
148C11⋊C8—81no—
149C2×C4⋊Q8—111no—
150C2×C4×Q8—111no—
151#432—221no—
152C2×#101—221no—
153C4×M16—221no—
154#400—111no—
155#400—111no—
156#400—111no—
157#400C2×D1111yescharacteristic
158#391—221no—
159#391—221no—
160#391—221no—
161#382—221no—
162C4×C4⋊C4—111no—
163#343—111no—
164#343C2×D1111yescharacteristic
165#324—111no—
166#324—221no—
167#324C2×D1111yescharacteristic
168C22×C11—21no—
169C22×C11—21no—
170C22×C11C2×#9911yescharacteristic
171C22×C11#41911yescharacteristic
172C22×C11C2×#10411yescharacteristic
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—81no—
178C4×C11—81no—
179Dic11—21no—
180Dic11—22no—
181Dic11—41no—
182Dic11—41no—
183Dic11—81no—
184Dic11—81no—
185Dic11#35512yes—
186C22×Q8—111no—
187C22×Q8—221no—
188C2×M16—21no—
189C2×M16—221no—
190C4⋊Q8—441no—
191C4⋊Q8—441no—
192C4×Q8—441no—
193C4×Q8—441no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
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—
204C2×C42—221no—
205C4⋊C8—441no—
206#101—224no—
207C22⋊C8—21no—
208C22⋊C8—221no—
209#97—441no—
210#97—441no—
211C4×C8—441no—
212#95—21no—
213#95—21no—
214#95—111no—
215#95—221no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95C4×D1111yescharacteristic
222C2×C11—21no—
223C2×C11—21no—
224C2×C11#150811yescharacteristic
225C2×C11#212311yescharacteristic
226C2×C11C2×#35511yescharacteristic
227C2×Q8—222no—
228C2×Q8—221no—
229C2×Q8—221no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8—441no—
233C2×Q8—444no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4C2×C4×D1111yescharacteristic
243C22×C4D4×D1111yescharacteristic
244C22×C4D4×D1111yescharacteristic
245M16—22no—
246M16—41no—
247M16—222no—
248M16—441no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—441no—
252C2×C8—441no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—442no—
259C4⋊C4—442no—
260C42—221no—
261C42—221no—
262C42—221no—
263C42—221no—
264C42—221no—
265C42—221no—
266C42—442no—
267C11#1179411yescharacteristic, complemented, Sylow
268C23C22⋊C4×D1111yescharacteristic
269Q8—442no—
270Q8—442no—
271Q8—882no—
272Q8—882no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—111no—
285C2×C4—111no—
286C2×C4—112no—
287C2×C4—222no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—442no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4#6696811yescharacteristic
301C2×C4#6697111yescharacteristic
302C8—42no—
303C8—81no—
304C8—442no—
305C8—881no—
306C22—21no—
307C22—21no—
308C22D11×#9911yescharacteristic
309C22#1062241511yescharacteristic
310C22D11×#10411yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—81no—
316C4—81no—
317C4—112no—
318C4—222no—
319C4—221no—
320C4—441no—
321C4—441no—
322C4—881no—
323C4—881no—
324C2—21no—
325C2—21no—
326C2#1306713411yescharacteristic
327C2#1307026811yescharacteristic
328C2D11×#35511yescharacteristic
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#11794
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
267. C11#11794semidirect

Maximal subgroups

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

subgroupindex
#130738272
#130684112
#130669582
#130666442
#130666432
#130666422
C11×#13532
#1179411