Finite Group Databasebeta

← #14656901

Subgroups — #14656901

Order 2816.

454 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 99 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#13071909C211yesmaximal, characteristic, complemented
2#13067111C212yesmaximal
3#13066517C212yesmaximal, complemented
4#13066445C211yesmaximal, characteristic, complemented
5C11×#1963C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C2×C4×Dic22—21no—
8C11×#423C2211yescharacteristic
9C2×C11×#104—21no—
10C2×C11×#104—21no—
11C11×#376C2211yescharacteristic
12C4×C4⋊Dic11—21no—
13C4×C4⋊Dic11C2212yes—
14#10622538C2212yes—
15#10622274—22no—
16#10622269—22no—
17#10622175—22no—
18#10622175—22no—
19C2×C11×#41—21no—
20C22×Dic22—21no—
21C2×C11×M16—21no—
22C11×C4⋊Q8Q811yescharacteristic, complemented
23C11×#127Q811yescharacteristic, complemented
24C11×#124—21no—
25C11×#121—22no—
26C4×D4×C11—22no—
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—22no—
32C2×C4⋊Dic11—22no—
33C2×Dic11⋊C4—22no—
34C2×C4×Dic11—22no—
35C4×Dic22—42no—
36C4×Dic22—42no—
37C11×C4⋊C8—22no—
38C11×#104—42no—
39C11×#104—42no—
40C11×#95—22no—
41C11⋊#95—21no—
42C11⋊#95—21no—
43C11⋊#95D412yes—
44C11⋊#95D412yes—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—22no—
47C4×C11⋊C8—22no—
48#10370—111nomaximal, Sylow
49C11×#41—41no—
50C11×#41—41no—
51C11×#41—41no—
52C11×#41—41no—
53C2×Q8×C11—21no—
54C2×D4×C11—21no—
55C2×D4×C11—22no—
56C2×D4×C11—41no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—41no—
60C22×C4×C11C2×D412yes—
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—22no—
63C22×Dic11—22no—
64C2×Dic22—42no—
65C2×Dic22—44no—
66C11×M16—41no—
67C11×M16—41no—
68C2×C8×C11—41no—
69C11×C4⋊C4—22no—
70C11×C22⋊C4—42no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11D812yes—
74C42×C11SD1612yes—
75C42×C11C2×Q811yescharacteristic
76C42×C11#4111yescharacteristic
77C42×C11#4112yes—
78C4⋊Dic11—42no—
79C4⋊Dic11—44no—
80C4⋊Dic11—44no—
81Dic11⋊C4—44no—
82C4×Dic11—42no—
83C4×Dic11—42no—
84C2×C11⋊C8—42no—
85#2399—111no—
86#1963D1111yescharacteristic
87#1502—112no—
88#1303—112no—
89#1274—111no—
90C23×C11—41no—
91C23×C11#12011yescharacteristic
92Q8×C11—41no—
93Q8×C11—41no—
94D4×C11—41no—
95D4×C11—41no—
96D4×C11—82no—
97D4×C11—81no—
98D4×C11—81no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11—81no—
106C2×C4×C11—81no—
107C2×C4×C11C22⋊Q812yes—
108C2×C4×C11C22⋊Q811yescharacteristic
109C2×C4×C11#12412yes—
110C2×C4×C11#12411yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11C2×SD1611yescharacteristic
113C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C11#13711yescharacteristic
115C2×Dic11—24no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121Dic22—48no—
122C8×C11—81no—
123C11⋊C8—82no—
124#532C2×D1111yescharacteristic
125C2×C4×Q8—221no—
126#431—112no—
127#423C2×D1111yescharacteristic
128C2×#104—21no—
129C2×#104—21no—
130#398—222no—
131#395—222no—
132C4×C4⋊C4—112no—
133C4×C4⋊C4—221no—
134#376C2×D1111yescharacteristic
135#327—222no—
136#327—222no—
137C22×C11—22no—
138C22×C11—81no—
139C22×C11—82no—
140C22×C11#39311yescharacteristic
141C22×C11#44711yescharacteristic
142C22×C11#44811yescharacteristic
143C4×C11—22no—
144C4×C11—22no—
145C4×C11—42no—
146C4×C11—42no—
147C4×C11—81no—
148C4×C11#47411yescharacteristic
149C4×C11#47611yescharacteristic
150C4×C11#48611yescharacteristic
151C4×C11#48911yescharacteristic
152Dic11—44no—
153Dic11—82no—
154C2×#41—21no—
155C22×Q8—221no—
156C2×M16—21no—
157C4⋊Q8Dic2211yescharacteristic, complemented
158#127Dic2211yescharacteristic, complemented
159#124—21no—
160#121—22no—
161C4×Q8—442no—
162C4×Q8—442no—
163C4×D4—22no—
164C2×C4⋊C4—222no—
165C2×C4⋊C4—221no—
166C2×C4⋊C4—222no—
167C2×C4⋊C4—222no—
168C2×C42—222no—
169C2×C42C22⋊D1111yescharacteristic
170C2×C42C22⋊D1111yescharacteristic
171C2×C42C22×D1111yescharacteristic
172C4⋊C8—22no—
173C4⋊C8—222no—
174#104—42no—
175#104—42no—
176C22⋊C8—222no—
177C4×C8—222no—
178#95—22no—
179#95—112no—
180#95—112no—
181#95—221no—
182#95—221no—
183C2×C11—21no—
184C2×C11—21no—
185C2×C11—161no—
186C2×C11#202311yescharacteristic
187C2×C11#203112yes—
188#41—41no—
189#41—41no—
190#41—41no—
191#41—41no—
192C2×Q8—21no—
193C2×Q8—442no—
194C2×Q8—444no—
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—41no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4—222no—
202C22×C4—222no—
203C22×C4D4×D1112yes—
204C22×C4C2×C22⋊D1111yescharacteristic
205M16—41no—
206M16—41no—
207C2×C8—41no—
208C2×C8—442no—
209C4⋊C4—22no—
210C4⋊C4—444no—
211C4⋊C4—442no—
212C4⋊C4—444no—
213C4⋊C4—444no—
214C22⋊C4—42no—
215C42—21no—
216C42—21no—
217C42—442no—
218C42—442no—
219C42#432312yes—
220C42#432412yes—
221C42C2×Dic2211yescharacteristic
222C42#433911yescharacteristic
223C42#434112yes—
224C11#1037011yescharacteristic, complemented, Sylow
225C23—41no—
226C23#6699011yescharacteristic
227Q8—41no—
228Q8—41no—
229Q8—448no—
230D4—41no—
231D4—41no—
232D4—82no—
233D4—81no—
234D4—81no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—224no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—442no—
249C2×C4#6693112yes—
250C2×C4#6693812yes—
251C2×C4#6697711yescharacteristic
252C2×C4C2×#432311yescharacteristic
253C2×C4C2×#432411yescharacteristic
254C2×C4#6698911yescharacteristic
255C2×C4#6700211yescharacteristic
256C2×C4#6700411yescharacteristic
257C8—81no—
258C8—882no—
259C22—22no—
260C22—81no—
261C22—82no—
262C22#1062256011yescharacteristic
263C22#1062264911yescharacteristic
264C22#1062265311yescharacteristic
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—81no—
270C4—444no—
271C4—882no—
272C4#1062262011yescharacteristic
273C4#1062262111yescharacteristic
274C4#1062266811yescharacteristic
275C4#1062268311yescharacteristic
276C2—21no—
277C2—21no—
278C2—161no—
279C2#1306975211yescharacteristic
280C2#1306978612yes—
subgroupG/H
centerC2×C4#66989
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1963C2
socleC22×C11#393
prime radicalC11×#532C22
hypercenter#1963D11
hypocenterC11#10370
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
1. #13071909C2semidirect
3. #13066517C2semidirect
4. #13066445C2semidirect
22. C11×C4⋊Q8Q8semidirect
23. C11×#127Q8semidirect
157. C4⋊Q8Dic22semidirect
158. #127Dic22semidirect
224. C11#10370semidirect

Maximal subgroups

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

subgroupindex
#130719092
#130671112
#130665172
#130664452
C11×#19632
#1037011