Finite Group Databasebeta

← #14655634

Subgroups — #14655634

Order 2816.

510 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079541C211yesmaximal, characteristic
2#13079010C211yesmaximal, characteristic
3C2×#10622694C211yesmaximal, characteristic, complemented
4#13067298C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622840—22no—
14C2×#66899—22no—
15#10622746—22no—
16#10622698—21no—
17#10622696—22no—
18#10622694—22no—
19#10622694—21no—
20#10622694—22no—
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622327—22no—
24#10622307—21no—
25#10622294—21no—
26C11×#343—22no—
27#10622121—22no—
28#10622119—22no—
29C22×Q8×C11D412yes—
30C2×#4339—21no—
31C22×Dic22—21no—
32C2×C11×M16—21no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4325—24no—
42#66983—21no—
43#66983—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C22×C11⋊C8—21no—
47#66928—21no—
48#66927D411yescharacteristic
49C4×D44—21no—
50C4×D44—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55#66922D411yescharacteristic
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×#97—21no—
59C4×C8×C11—21no—
60#66899—28no—
61#66899—24no—
62C22⋊(C11⋊C8)—21no—
63#66885—24no—
64#66880—24no—
65C4⋊(C11⋊C8)D412yes—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yes—
69#10162—111nomaximal, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—22no—
72C2×Q8×C11—44no—
73C22×C4×C11—22no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C2×C22⋊D11—41no—
78C22×Dic11—41no—
79#4339—42no—
80#4339—42no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×C4×D11—41no—
85C2×Dic22—21no—
86C2×Dic22—22no—
87C2×Dic22—41no—
88C2×Dic22—82no—
89C11×M16—22no—
90C11×M16—22no—
91C11×M16—42no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102#4325—84no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—42no—
114#3206—111no—
115#3141—111no—
116C2×#487—111no—
117#1997D1111yescharacteristic, complemented
118#1548—111no—
119#1492—111no—
120#1278—111no—
121C23×C11#12111yescharacteristic
122C22×D11—41no—
123Q8×C11—44no—
124Q8×C11—44no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—42no—
128C2×C4×C11—82no—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12711yescharacteristic
135C2×C4×C11#13512yes—
136C2×C4×C11#13712yes—
137C22⋊D11—82no—
138C2×Dic11—42no—
139C2×Dic11—41no—
140C2×Dic11—82no—
141D44—42no—
142D44—42no—
143D44—42no—
144C4×D11—81no—
145C4×D11—81no—
146Dic22—42no—
147Dic22—82no—
148Dic22—82no—
149C8×C11—42no—
150C8×C11—81no—
151C11⋊C8—42no—
152C11⋊C8—42no—
153#532—111no—
154C2×C4⋊Q8—111no—
155C2×C4⋊Q8C2×D1111yescharacteristic
156#492—221no—
157#489—222no—
158#487—221no—
159#487—222no—
160#487—222no—
161#487—221no—
162#486—221no—
163#461—222no—
164#448—222no—
165#431—111no—
166#423C2×D1111yescharacteristic
167#417—222no—
168C2×#103—222no—
169C4×M16C2×D1111yescharacteristic
170C2×C4×C8—111no—
171#343—22no—
172#333—222no—
173D4⋊C8—222no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11#39211yescharacteristic
177C22×C11#46412yes—
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—81no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—82no—
184C4×C11#45212yes—
185C4×C11#45512yes—
186C4×C11#47112yes—
187C4×C11#49511yescharacteristic
188C4×C11#49711yescharacteristic
189Dic11—81no—
190Dic11—82no—
191C2×#41—221no—
192C22×Q8—221no—
193C22×Q8D4412yes—
194C2×SD16—224no—
195C2×M16—21no—
196C2×M16C22⋊D1112yes—
197C22×C8—221no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—112no—
203C4⋊Q8—111no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207#127—111no—
208#124—221no—
209#121—221no—
210#121—221no—
211C4×D4—221no—
212C4×D4—221no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C42C22×D1111yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—112no—
221#103—224no—
222#103—228no—
223#103—224no—
224#102—224no—
225C22⋊C8—221no—
226#97—21no—
227C4×C8—21no—
228C4×C8—112no—
229C4×C8—221no—
230C4×C8—221no—
231C2×C11—22no—
232C2×C11#200411yescharacteristic
233C2×C11#201511yescharacteristic
234C2×C11#201911yescharacteristic
235D11—161no—
236#41—442no—
237#41—442no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—44no—
241C2×Q8—222no—
242C2×Q8—221no—
243C2×Q8—441no—
244C2×Q8—882no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—221no—
248C2×D4—441no—
249C22×C4—22no—
250C22×C4—441no—
251C22×C4—441no—
252C22×C4C2×D4411yescharacteristic
253C22×C4#433911yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255SD16—884no—
256M16—22no—
257M16—22no—
258M16—42no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—222no—
262C2×C8—222no—
263C2×C8—442no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—222no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—222no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C22⋊C4—441no—
275C22⋊C4—441no—
276C42D4×D1111yescharacteristic
277C42D4×D1111yescharacteristic
278C42D4×D1111yescharacteristic
279C42D4×D1111yescharacteristic
280C11#1016211yescharacteristic, complemented, Sylow
281C23—441no—
282C23#6698311yescharacteristic
283Q8—44no—
284Q8—44no—
285Q8—442no—
286Q8—882no—
287Q8—882no—
288D4—442no—
289D4—442no—
290D4—442no—
291D4—882no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—441no—
297C2×C4—442no—
298C2×C4—882no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4#6693511yescharacteristic
302C2×C4#6693511yescharacteristic
303C2×C4#6693711yescharacteristic
304C2×C4#6693711yescharacteristic
305C2×C4#6699011yescharacteristic
306C2×C4#6699311yescharacteristic
307C2×C4#6699512yes—
308C2×C4#6700312yes—
309C8—42no—
310C8—81no—
311C8—442no—
312C8—442no—
313C22—21no—
314C22—21no—
315C22—881no—
316C22—881no—
317C22—881no—
318C22#1062257311yescharacteristic
319C22#1062264112yes—
320C4—21no—
321C4—21no—
322C4—82no—
323C4—881no—
324C4—882no—
325C4#1062235912yes—
326C4#1062236712yes—
327C4#1062266012yes—
328C4#1062267211yescharacteristic
329C4#1062269911yescharacteristic
330C2—22no—
331C2—1761no—
332C2#1306964711yescharacteristic
333C2#1306970911yescharacteristic
334C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1997C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1997D11
hypocenterC11#10162
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
3. C2×#10622694C2semidirect
4. #13067298C2semidirect
6. #13066454C2semidirect
7. C11×#1997C2semidirect
117. #1997D11semidirect
280. C11#10162semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130790102
C2×#106226942
#130672982
#130670662
#130664542
C11×#19972
#1016211