Finite Group Databasebeta

← #14651868

Subgroups — #14651868

Order 2816.

428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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#13078716C211yesmaximal, characteristic
2#13077713C211yesmaximal, characteristic, complemented
3#13067344C211yesmaximal, characteristic, complemented
4#13067040C211yesmaximal, characteristic
5#13066956C211yesmaximal, characteristic
6#13066479C211yesmaximal, characteristic, complemented
7C11×#1307C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622539C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622459—21no—
16#10622454—21no—
17#10622444—21no—
18#10622443—21no—
19#10622344C412yes—
20#10622335C412yes—
21#10622333—22no—
22#10622323—22no—
23#10622314—22no—
24#10622121—21no—
25#10622121—21no—
26#10622120—21no—
27#10622119—21no—
28#10622106—22no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—21no—
31C2×C11×M16—21no—
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34#66979—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36#66977—21no—
37#66977C2×C412yes—
38C2×#4314—22no—
39C4×D44—21no—
40C4×D44—21no—
41C4×D44—21no—
42C4×D44—21no—
43#66923—21no—
44#66922D411yescharacteristic
45#66922D411yescharacteristic
46C4×Dic22—21no—
47C4×Dic22D412yes—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8C2×C412yes—
53C11×C22⋊C8D412yes—
54C11×#97—21no—
55C11×#97—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66885—22no—
59#66882—22no—
60#66880—22no—
61#66879—22no—
62Dic11⋊C8—22no—
63Dic11⋊C8—22no—
64C8×Dic11—22no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67#66867—21no—
68C4×C11⋊C8D411yescharacteristic
69C4×C11⋊C8D411yescharacteristic
70#9530—111nomaximal, Sylow
71C23×D11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×Dic11—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—42no—
79C2×C4×D11—41no—
80C2×C4×D11—41no—
81C2×C4×D11—81no—
82C2×C4×D11—81no—
83C2×Dic22—21no—
84C2×Dic22C22⋊C412yes—
85C11×M16—81no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C22⋊Dic11—22no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11C22⋊C412yes—
102Dic11⋊C4—22no—
103Dic11⋊C4—22no—
104C4×Dic11—22no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—41no—
108#4314—44no—
109#3110—111no—
110#2985—111no—
111#1559—111no—
112#1486—111no—
113#1466—111no—
114#1307D1111yescharacteristic, complemented
115#1287—111no—
116C23×C11C4×D411yescharacteristic
117C22×D11—22no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—81no—
121C22×D11—81no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×Dic11—22no—
133C2×Dic11—22no—
134C2×Dic11—41no—
135C2×Dic11—81no—
136D44—22no—
137D44—22no—
138D44—41no—
139D44—41no—
140C4×D11—82no—
141C4×D11—81no—
142C4×D11—81no—
143Dic22—41no—
144Dic22—41no—
145Dic22—42no—
146C8×C11—42no—
147C8×C11—42no—
148C8×C11—81no—
149C11⋊C8—41no—
150C11⋊C8—41no—
151C11⋊C8—81no—
152#533—111no—
153C2×C4×D4—111no—
154#484—112no—
155#474—221no—
156#461—221no—
157#450—112no—
158#446—221no—
159#446—222no—
160C8×Q8—221no—
161#440—222no—
162#433—222no—
163#432—111no—
164#432C2×D1111yescharacteristic
165#432C2×D1111yescharacteristic
166#431—111no—
167#423C2×D1111yescharacteristic
168#333—221no—
169#332—221no—
170D4⋊C8—221no—
171D4⋊C8—221no—
172#323—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11#38611yescharacteristic
177C2×D11—42no—
178C2×D11—82no—
179C2×D11—81no—
180C2×D11—81no—
181C2×D11—82no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11#47111yescharacteristic
188C4×C11#47211yescharacteristic
189Dic11—42no—
190Dic11—42no—
191Dic11—81no—
192C22×D4—111no—
193C23×C4—221no—
194C2×SD16—222no—
195C2×M16—21no—
196C4⋊Q8—111no—
197C4⋊Q8—111no—
198#125—221no—
199C22⋊Q8—112no—
200C22⋊Q8—221no—
201C4×Q8—112no—
202C4×Q8—221no—
203C4×D4—221no—
204C4×D4—221no—
205C4×D4—221no—
206C4×D4—221no—
207#117—221no—
208C2×C4⋊C4—111no—
209C2×C22⋊C4—221no—
210C2×C42C22×D1111yescharacteristic
211#107—222no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—222no—
217C4⋊C8—222no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220#103—222no—
221#102—222no—
222C22⋊C8—221no—
223C22⋊C8—221no—
224C22⋊C8C4×D1112yes—
225C22⋊C8D4412yes—
226#97—21no—
227#97—21no—
228#97—222no—
229#97—221no—
230C4×C8—111no—
231C4×C8—111no—
232C4×C8—222no—
233C2×C11—41no—
234C2×C11#189111yescharacteristic
235C2×C11#190511yescharacteristic
236C2×C11#190711yescharacteristic
237D11—82no—
238C24—221no—
239C2×Q8—112no—
240C2×Q8—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—442no—
244C22×C4—221no—
245C22×C4—441no—
246C22×C4—441no—
247C22×C4—881no—
248C22×C4—881no—
249C22×C4C2×C4×D1111yescharacteristic
250C22×C4C2×D4411yescharacteristic
251C22×C4#433911yescharacteristic
252SD16—444no—
253M16—81no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—221no—
258C2×C8—221no—
259C2×C8—441no—
260C4⋊C4—112no—
261C4⋊C4—221no—
262C4⋊C4—222no—
263C4⋊C4—222no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C22⋊C4—222no—
269C22⋊C4—441no—
270C22⋊C4—441no—
271C42—222no—
272C42D4×D1111yescharacteristic
273C42D4×D1111yescharacteristic
274C42D4×D1111yescharacteristic
275C42#434311yescharacteristic
276C11#953011yescharacteristic, complemented, Sylow
277C23—222no—
278C23—441no—
279C23—441no—
280C23—881no—
281C23—881no—
282C23C4×D4411yescharacteristic
283Q8—442no—
284Q8—441no—
285Q8—441no—
286D4—222no—
287D4—222no—
288D4—441no—
289D4—441no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—441no—
297C2×C4—882no—
298C2×C4—881no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4C22⋊C4×D1111yescharacteristic
302C2×C4#6693511yescharacteristic
303C2×C4#6693711yescharacteristic
304C2×C4#6694611yescharacteristic
305C2×C4#6694711yescharacteristic
306C2×C4#6694811yescharacteristic
307C8—42no—
308C8—42no—
309C8—81no—
310C8—441no—
311C8—441no—
312C8—881no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—442no—
317C22—882no—
318C22—882no—
319C22—881no—
320C22—881no—
321C22#1062227811yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—442no—
328C4—442no—
329C4—881no—
330C4#1062236211yescharacteristic
331C4#1062236711yescharacteristic
332C2—41no—
333C2—882no—
334C2#1306903311yescharacteristic
335C2#1306910911yescharacteristic
336C2#1306912511yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1307C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1307D11
hypocenterC11#9530
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
2. #13077713C2semidirect
3. #13067344C2semidirect
6. #13066479C2semidirect
7. C11×#1307C2semidirect
114. #1307D11semidirect
276. C11#9530semidirect

Maximal subgroups

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

subgroupindex
#130787162
#130777132
#130673442
#130670402
#130669562
#130664792
C11×#13072
#953011