Finite Group Databasebeta

← #14642011

Subgroups — #14642011

Order 2816.

434 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 101 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#13071087C211yesmaximal, characteristic
2#13068468C211yesmaximal, characteristic
3#13068363C211yesmaximal, characteristic
4#13066441C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic
6#13066439C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C2×#66940C411yescharacteristic
9C11×#389C2211yescharacteristic
10C2×#66879—21no—
11C2×#66879—21no—
12C2×Dic11⋊C8—21no—
13#10622598C411yescharacteristic
14#10622591—21no—
15C4⋊C4×Dic11—21no—
16C4⋊C4×Dic11C411yescharacteristic
17#10622587C411yescharacteristic
18C42×Dic11C2211yescharacteristic
19#10622542C2211yescharacteristic
20#10622268—21no—
21#10622261—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Dic22C2×C411yescharacteristic
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×C4×Dic11—21no—
38C2×C4×Dic11—21no—
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11C2×C411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C22×C11⋊C8—21no—
46C22×C11⋊C8—21no—
47#66940—22no—
48#66940—22no—
49C11×#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#66879—24no—
57#66879—42no—
58Dic11⋊C8—24no—
59#7630—111nomaximal, Sylow
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67C22×Dic11C22⋊C411yescharacteristic
68C22×Dic11C22⋊C411yescharacteristic
69C22×Dic11C22⋊C411yescharacteristic
70C22×Dic11C22⋊C411yescharacteristic
71C2×Dic22—21no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×Dic22M1612yes—
75C2×C8×C11—22no—
76C2×C8×C11—22no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4M1612yes—
86C42×C11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—42no—
89Dic11⋊C4—24no—
90C4×Dic11—24no—
91C4×Dic11—22no—
92C4×Dic11—22no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—41no—
100C4×Dic11—42no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2295—111no—
108#1767—111no—
109#1745—111no—
110#1272—111no—
111#1272—111no—
112#1271—111no—
113#1271D1111yescharacteristic
114C23×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11C2×M1611yescharacteristic
128C2×C4×C11C2×M1611yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—22no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11#10412yes—
150C2×Dic11#10412yes—
151Dic22—42no—
152Dic22—42no—
153C8×C11—42no—
154C8×C11—42no—
155C11⋊C8—42no—
156C11⋊C8—42no—
157C2×C4×Q8—111no—
158C2×C4⋊C8—221no—
159C2×#97—221no—
160C2×#97—221no—
161#391—111no—
162#391—111no—
163#389—111no—
164#389C2×D1111yescharacteristic
165#387—221no—
166#387—221no—
167C4×C4⋊C4—111no—
168C4×C4⋊C4—221no—
169#376—221no—
170C43—111no—
171#336—111no—
172#336—111no—
173#336—221no—
174#336C2×D1111yescharacteristic
175#336C2×D1111yescharacteristic
176C22×C11#40711yescharacteristic
177C22×C11#41011yescharacteristic
178C22×C11#41311yescharacteristic
179C22×C11#41711yescharacteristic
180C22×C11#41911yescharacteristic
181C22×C11C2×#10411yescharacteristic
182C22×C11C2×#10411yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—42no—
190C4×C11—81no—
191Dic11—22no—
192Dic11—22no—
193Dic11—41no—
194Dic11—42no—
195Dic11—41no—
196Dic11—81no—
197C22×Q8—111no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—221no—
201C22×C8—221no—
202C4×Q8—222no—
203C4×Q8—222no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C4×D1111yescharacteristic
209C2×C4⋊C4C4×D1111yescharacteristic
210C2×C42—111no—
211C2×C42—111no—
212C2×C42—111no—
213C2×C42—111no—
214C2×C42—111no—
215C2×C42—111no—
216C2×C42—221no—
217C2×C42—221no—
218C2×C42C22×D1111yescharacteristic
219C4⋊C8—224no—
220#97—224no—
221#97—442no—
222#95—21no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229C2×C11#146411yescharacteristic
230C2×C11#148911yescharacteristic
231C2×C11#149111yescharacteristic
232C2×C11#150611yescharacteristic
233C2×C11#150911yescharacteristic
234C2×C11#152411yescharacteristic
235C2×C11#155911yescharacteristic
236C2×Q8—112no—
237C2×Q8—221no—
238C2×Q8—441no—
239C2×Q8—441no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—111no—
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4C2×C4×D1111yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—222no—
258C2×C8—222no—
259C2×C8—441no—
260C2×C8—441no—
261C2×C8—441no—
262C2×C8—441no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—224no—
268C4⋊C4—441no—
269C4⋊C4—442no—
270C4⋊C4#431312yes—
271C42—41no—
272C42—222no—
273C42—222no—
274C42—224no—
275C42—221no—
276C42—221no—
277C42—221no—
278C42—221no—
279C42—221no—
280C42—221no—
281C42—441no—
282C42—442no—
283C11#763011yescharacteristic, complemented, Sylow
284C23C22⋊C4×D1111yescharacteristic
285Q8—442no—
286Q8—442no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—112no—
300C2×C4—112no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—222no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4C2×#431311yescharacteristic
318C2×C4M16×D1111yescharacteristic
319C2×C4#6696411yescharacteristic
320C2×C4#6696811yescharacteristic
321C2×C4#6696811yescharacteristic
322C2×C4#6697111yescharacteristic
323C8—42no—
324C8—42no—
325C8—442no—
326C8—442no—
327C22#1062233911yescharacteristic
328C22#1062235311yescharacteristic
329C22#1062236411yescharacteristic
330C22#1062238411yescharacteristic
331C22#1062241511yescharacteristic
332C22D11×#10411yescharacteristic
333C22D11×#10411yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—81no—
342C4—222no—
343C4—222no—
344C4—441no—
345C4—441no—
346C4—442no—
347C4—881no—
348C2#1306694911yescharacteristic
349C2#1306705211yescharacteristic
350C2#1306706111yescharacteristic
351C2#1306712611yescharacteristic
352C2#1306713811yescharacteristic
353C2#1306720311yescharacteristic
354C2#1306734511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1271D11
hypocenterC11#7630
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
283. C11#7630semidirect

Maximal subgroups

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

subgroupindex
#130710872
#130684682
#130683632
#130664412
#130664392
C11×#12712
#763011