Finite Group Databasebeta

← #14667468

Subgroups — #14667468

Order 2816.

312 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 69 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#13081484C211yesmaximal, characteristic, complemented
2#13070839C211yesmaximal, characteristic, complemented
3#13070648C211yesmaximal, characteristic
4#13066675C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066576C211yesmaximal, characteristic, complemented
7C11×#1668C211yesmaximal, characteristic, complemented
8#10623110—21no—
9C11×#493C2211yescharacteristic
10C11×#460—21no—
11C8×Q8×C11C2211yescharacteristic
12C2×#66890—21no—
13#10622460—22no—
14#10622455—21no—
15C4×D88—21no—
16C4×D88C2211yescharacteristic
17#10622296—21no—
18#10622295C2211yescharacteristic
19C11×#335C2211yescharacteristic
20C11×#331—21no—
21#10622200—21no—
22#10622200—22no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×SD16—41no—
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C11×#127—21no—
29C4×Q8×C11D411yescharacteristic
30#66999—41no—
31C2×D88D411yescharacteristic
32#66949—42no—
33C4⋊C4×D11—41no—
34C4×D44—22no—
35C4×D44—21no—
36#66923—22no—
37#66922—21no—
38C11×C4⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×#102—41no—
42C4×C8×C11—21no—
43C4×C8×C11C2311yescharacteristic
44#66890—42no—
45#66885—22no—
46#66885—21no—
47#66882—21no—
48#66882D412yes—
49#66882D411yescharacteristic
50#66881—22no—
51C2×C11⋊C16—21no—
52C2×C11⋊C16—21no—
53#12355—111nomaximal, Sylow
54C2×Q8×C11D811yescharacteristic
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D44—21no—
59C2×C4×D11—42no—
60C2×C4×D11—41no—
61C2×Dic22—41no—
62C11×SD16—82no—
63C11×D8—42no—
64C11×D8—41no—
65C11×D8—41no—
66C2×C8×C11—21no—
67C2×C8×C11—41no—
68C2×C8×C11C2×D411yescharacteristic
69C2×C8×C11C2×D411yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4D811yescharacteristic
72C42×C11—21no—
73C42×C11C2×D411yescharacteristic
74(C2×D11)⋊C4—42no—
75(C2×D11)⋊C4—41no—
76C4⋊Dic11—21no—
77C4⋊Dic11—22no—
78C4⋊Dic11—41no—
79Dic11⋊C4—42no—
80Dic11⋊C4—42no—
81D88—21no—
82D88SD1612yescomplemented
83C11⋊C16—41no—
84C11⋊C16—41no—
85#3380—111no—
86#2240—111no—
87#2206—111no—
88#1668D1111yescharacteristic, complemented
89#1365—111no—
90Q8⋊C16—111no—
91#1331—111no—
92C23×C11—81no—
93C22×D11—41no—
94Q8×C11—21no—
95Q8×C11—21no—
96D4×C11—81no—
97D4×C11—81no—
98D4×C11—81no—
99D4×C11—81no—
100D4×C11—161no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11#12011yescharacteristic
104C2×C4×C11C2×D811yescharacteristic
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C2×Dic11—41no—
107C2×Dic11—42no—
108D44—22no—
109D44—41no—
110C4×D11—81no—
111C4×D11—81no—
112C4×D11—162no—
113Dic22—161no—
114C8×C11—21no—
115C8×C11—41no—
116C8×C11—81no—
117C8×C11C2×SD1611yescharacteristic
118C8×C11#13711yescharacteristic
119#554—221no—
120C2×D16—221no—
121#500—111no—
122#499—221no—
123#493C2×D1111yescharacteristic
124#478—222no—
125#476—221no—
126#460—21no—
127C8×Q8C2×D1111yescharacteristic
128C4×D8—111no—
129C4×D8—221no—
130C4⋊C16—111no—
131#357—221no—
132#357—222no—
133C4×C16—111no—
134#335C2×D1111yescharacteristic
135#331—21no—
136C22×C11—161no—
137C22×C11—161no—
138C22×C11—161no—
139C22×C11#44711yescharacteristic
140C2×D11—42no—
141C2×D11—81no—
142C2×D11—81no—
143C4×C11—21no—
144C4×C11—41no—
145C4×C11—41no—
146C4×C11#44811yescharacteristic
147C4×C11#45411yescharacteristic
148C4×C11#50811yescharacteristic
149C4×C11#50911yescharacteristic
150Dic11—81no—
151Dic11—82no—
152C2×SD16—41no—
153C2×D8—21no—
154C2×D8—21no—
155C2×D8—111no—
156C4⋊Q8—221no—
157#127—21no—
158#125—222no—
159C22⋊Q8—442no—
160C22⋊Q8—441no—
161C4×Q8C22⋊D1111yescharacteristic
162C4×D4—222no—
163C4×D4—221no—
164C2×C4⋊C4—441no—
165D16—442no—
166C2×C16—221no—
167C2×C16—221no—
168#107—111no—
169#107—112no—
170#107—221no—
171#106—222no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8C22⋊D1111yescharacteristic
175#102—41no—
176#102—222no—
177#102—221no—
178C4×C8—21no—
179C4×C8C22×D1111yescharacteristic
180C2×C11—321no—
181C2×C11#162711yescharacteristic
182C2×C11#218611yescharacteristic
183C2×C11#219211yescharacteristic
184D11—82no—
185C2×Q8—441no—
186C2×Q8#432311yescharacteristic
187C2×D4—41no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—221no—
191C22×C4—442no—
192C22×C4—441no—
193SD16—82no—
194D8—42no—
195D8—41no—
196D8—41no—
197D8—112no—
198D8—221no—
199C2×C8—21no—
200C2×C8—41no—
201C2×C8D4×D1111yescharacteristic
202C2×C8D4×D1111yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—221no—
205C4⋊C4—222no—
206C4⋊C4—442no—
207C4⋊C4—442no—
208C4⋊C4—441no—
209C4⋊C4#432311yescharacteristic
210C22⋊C4—442no—
211C22⋊C4—441no—
212C42—21no—
213C42C2×C22⋊D1111yescharacteristic
214C16—441no—
215C16—441no—
216C11#1235511yescharacteristic, complemented, Sylow
217C23—81no—
218C23—441no—
219Q8—21no—
220Q8—21no—
221Q8—1761no—
222D4—81no—
223D4—81no—
224D4—81no—
225D4—81no—
226D4—161no—
227D4—222no—
228D4—441no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—441no—
232C2×C4—442no—
233C2×C4—881no—
234C2×C4—881no—
235C2×C4—1762no—
236C2×C4C2×#432311yescharacteristic
237C2×C4#6699011yescharacteristic
238C2×C4#6700211yescharacteristic
239C8—21no—
240C8—41no—
241C8—81no—
242C8SD16×D1111yescharacteristic
243C8#6696811yescharacteristic
244C22—161no—
245C22—161no—
246C22—161no—
247C22—442no—
248C22—881no—
249C22—881no—
250C22#1062264911yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—881no—
255C4—882no—
256C4#1062276011yescharacteristic
257C4#1062278311yescharacteristic
258C4#1062280711yescharacteristic
259C4#1062281411yescharacteristic
260C2—321no—
261C2—882no—
262C2#1306771711yescharacteristic
263C2#1307053711yescharacteristic
264C2#1307057111yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1668C2
socleC22×C11#447
prime radical#13070648C2
hypercenter#1668D11
hypocenterC11#12355
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1668

Complements

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

NH ≅ G/Ntype
1. #13081484C2semidirect
2. #13070839C2semidirect
4. #13066675C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
6. #13066576C2semidirect
7. C11×#1668C2semidirect
82. D88SD16semidirect
88. #1668D11semidirect
216. C11#12355semidirect

Maximal subgroups

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

subgroupindex
#130814842
#130708392
#130706482
#130666752
Q8⋊(C11⋊C16)2
#130665762
C11×#16682
#1235511