Finite Group Databasebeta

← #14670622

Subgroups — #14670622

Order 2816.

416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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#13070301C211yesmaximal, characteristic
2#13069000C211yesmaximal, characteristic
3#13068835C212yesmaximal, complemented
4#13066745C212yesmaximal, complemented
5C11×#2979C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7#10623350C2211yescharacteristic
8C11×#436—22no—
9C8×D4×C11—22no—
10C11×#431—21no—
11C11×#408—21no—
12C11×#408C2212yes—
13#10622853C2211yescharacteristic
14#10622850C2212yes—
15#10622849—21no—
16#10622737—22no—
17#10622190—22no—
18#10622186C412yescomplemented
19#10622180C412yescomplemented
20#10622161—21no—
21C2×C11×#41D411yescharacteristic
22C2×C11×#41C2311yescharacteristic
23C2×C11×M16—21no—
24C2×C11×M16D412yes—
25C22×C8×C11—21no—
26C22×C8×C11D412yes—
27C11×C4⋊Q8C2×C411yescharacteristic
28C11×#127Q811yescharacteristic
29C11×#124C2×C411yescharacteristic
30C11×#124Q811yescharacteristic
31C11×#121—22no—
32C4×D4×C11—22no—
33C2×C42×C11D411yescharacteristic
34#67001—42no—
35#66979—21no—
36C2×#4318—22no—
37C2×#4318—22no—
38C2×#4318—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C22⋊C8—22no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—22no—
44C4×C8×C11—22no—
45#66901—42no—
46#66900C2×C414yes—
47#66898—22no—
48#66897—22no—
49#66886—44no—
50#12975—111nomaximal, Sylow
51C11×#41—41no—
52C11×#41—41no—
53C11×#41—41no—
54C11×#41—41no—
55C2×Q8×C11C4⋊C411yescharacteristic
56C2×Q8×C11C22×C411yescharacteristic
57C2×D4×C11—22no—
58C2×D4×C11—21no—
59C2×D4×C11C4⋊C411yescharacteristic
60C2×D4×C11C2×Q811yescharacteristic
61C2×D4×C11#4112yes—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D412yes—
66C11×M16—42no—
67C11×M16—81no—
68C2×C8×C11—22no—
69C2×C8×C11—22no—
70C2×C8×C11—42no—
71C2×C8×C11—81no—
72C11×C4⋊C4—22no—
73C11×C22⋊C4—22no—
74C11×C22⋊C4—22no—
75C42×C11—21no—
76C42×C11C4⋊C411yescharacteristic
77C42×C11C4⋊C411yescharacteristic
78C22⋊Dic11—41no—
79C4⋊Dic11—41no—
80C4×Dic11—41no—
81#4318—24no—
82#4318—22no—
83#4318—24no—
84#4318—42no—
85#4318—41no—
86C2×C11⋊C8—42no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—41no—
89#2979D1111yescharacteristic
90#2132—111no—
91#1884—111no—
92#1858—112no—
93#1395—112no—
94C23×C11—21no—
95C23×C11C22⋊Q812yes—
96C23×C11#12311yescharacteristic
97Q8×C11—41no—
98Q8×C11—41no—
99D4×C11—41no—
100D4×C11—42no—
101D4×C11—41no—
102D4×C11—44no—
103D4×C11—81no—
104C2×C4×C11—21no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11C2×C4⋊C411yescharacteristic
115C2×C4×C11C4×D412yes—
116C2×C4×C11#12011yescharacteristic
117C2×Dic11—81no—
118C8×C11—42no—
119C8×C11—42no—
120C11⋊C8—44no—
121C11⋊C8—42no—
122#568—111no—
123#532C2×D1111yescharacteristic
124#436—22no—
125C8×D4—22no—
126#431—21no—
127#430—222no—
128#421—221no—
129#413—112no—
130#410—111no—
131#408—21no—
132#408C2×D1112yes—
133#356—112no—
134#355—112no—
135#341—222no—
136#339—221no—
137C22×C11—21no—
138C22×C11—22no—
139C22×C11—41no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11—41no—
143C22×C11#38511yescharacteristic
144C4×C11—22no—
145C4×C11—21no—
146C4×C11—22no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11B(4,𝔽2)11yescharacteristic
150C4×C11#45811yescharacteristic
151Dic11—161no—
152C2×#41C22⋊D1111yescharacteristic
153C2×#41C22×D1111yescharacteristic
154#131—442no—
155C2×M16—21no—
156C2×M16—221no—
157C2×M16—222no—
158C2×M16—222no—
159C2×M16C22⋊D1112yes—
160C22×C8—21no—
161C22×C8C22⋊D1112yes—
162C4⋊Q8C4×D1111yescharacteristic
163#127Dic2211yescharacteristic
164#124Dic2211yescharacteristic
165#124C4×D1111yescharacteristic
166#121—22no—
167C4×D4—22no—
168#117—221no—
169C2×C42C22⋊D1111yescharacteristic
170#108—444no—
171C4⋊C8—21no—
172C4⋊C8—21no—
173#104—442no—
174#101—114no—
175#100—222no—
176#99—222no—
177C22⋊C8—22no—
178C22⋊C8—22no—
179C22⋊C8—22no—
180C4×C8—22no—
181C2×C11—21no—
182C2×C11—41no—
183C2×C11—42no—
184C2×C11—81no—
185C2×C11#186711yescharacteristic
186#41—41no—
187#41—41no—
188#41—41no—
189#41—41no—
190C2×Q8Dic11⋊C411yescharacteristic
191C2×Q8C2×C4×D1111yescharacteristic
192C2×D4—22no—
193C2×D4—21no—
194C2×D4Dic11⋊C411yescharacteristic
195C2×D4C2×Dic2211yescharacteristic
196C2×D4#433912yes—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4C2×C22⋊D1111yescharacteristic
200C22×C4C2×C22⋊D1112yes—
201M16—42no—
202M16—81no—
203M16—222no—
204M16—224no—
205M16—224no—
206M16—442no—
207M16—441no—
208C2×C8—22no—
209C2×C8—22no—
210C2×C8—42no—
211C2×C8—81no—
212C2×C8—442no—
213C2×C8—441no—
214C2×C8—442no—
215C4⋊C4—22no—
216C4⋊C4—441no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—441no—
220C42—21no—
221C42—441no—
222C42Dic11⋊C411yescharacteristic
223C42Dic11⋊C411yescharacteristic
224C11#1297511yescharacteristic, complemented, Sylow
225C23—21no—
226C23#6697712yes—
227C23#6698211yescharacteristic
228Q8—41no—
229Q8—41no—
230D4—41no—
231D4—42no—
232D4—41no—
233D4—44no—
234D4—81no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—881no—
246C2×C4C2×Dic11⋊C411yescharacteristic
247C2×C4C4×C22⋊D1112yes—
248C2×C4#6700611yescharacteristic
249C8—42no—
250C8—42no—
251C8—444no—
252C8—442no—
253C22—21no—
254C22—22no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—41no—
259C22#1062282311yescharacteristic
260C4—22no—
261C4—22no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—1761no—
266C4#1062285611yescharacteristic
267C4#1062285711yescharacteristic
268C2—21no—
269C2—41no—
270C2—42no—
271C2—81no—
272C2#1306889711yescharacteristic
subgroupG/H
centerC4#10622857
commutatorC2×Q8×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#2979C2
socleC2×C11#1867
prime radicalC11×#532C22
cosocleC2×C11×#41C23
hypercenter#2979D11
hypocenterC11#12975
LCSG ▷ C2×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2979

Complements

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

NH ≅ G/Ntype
3. #13068835C2semidirect
4. #13066745C2semidirect
18. #10622186C4semidirect
19. #10622180C4semidirect
224. C11#12975semidirect

Maximal subgroups

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

subgroupindex
#130703012
#130690002
#130688352
#130667452
C11×#29792
#1297511