Finite Group Databasebeta

← #14667467

Subgroups — #14667467

Order 2816.

312 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081485C211yesmaximal, characteristic, complemented
2#13070648C211yesmaximal, characteristic
3#13067973C211yesmaximal, characteristic, complemented
4#13066674C211yesmaximal, characteristic, complemented
5#13066596C211yesmaximal, characteristic, complemented
6#13066578C211yesmaximal, characteristic, complemented
7C11×#2240C211yesmaximal, characteristic, complemented
8#10623261—21no—
9C11×#500C2211yescharacteristic
10C11×#493C2211yescharacteristic
11C2×#66890—21no—
12#10622697—21no—
13#10622688—21no—
14#10622504—22no—
15#10622491—21no—
16#10622485—21no—
17C4×D88C2211yescharacteristic
18C8×Dic22C2211yescharacteristic
19C11×#357—22no—
20C4×C11×C16C2211yescharacteristic
21#10622200—21no—
22#10622182—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×D8—21no—
26C2×C11×D8—21no—
27C11×C4⋊Q8—21no—
28C11×#127—21no—
29#66999—42no—
30C2×#4324—41no—
31C2×D88D411yescharacteristic
32#66950—41no—
33#66946—22no—
34C4⋊C4×D11—41no—
35#66943—22no—
36C4×D44—21no—
37C4×Dic22D411yescharacteristic
38C2×C11×C16—21no—
39C11×#107—21no—
40C11×#107D412yes—
41C4×C8×C11C2311yescharacteristic
42#66896—41no—
43#66890—42no—
44#66885—21no—
45#66882D411yescharacteristic
46Dic11⋊C8—21no—
47C8×Dic11—21no—
48C2×C11⋊C16—21no—
49#66873—22no—
50#66872—22no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12355—111nomaximal, Sylow
54C2×Q8×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D44—21no—
59C2×C4×D11—42no—
60C2×C4×D11—41no—
61C2×Dic22D811yescharacteristic
62C11×D8—42no—
63C11×D8—41no—
64C11×D8—41no—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4—22no—
68C11×C4⋊C4—41no—
69C42×C11C2×D411yescharacteristic
70#4324—82no—
71(C2×D11)⋊C4—42no—
72(C2×D11)⋊C4—41no—
73C4⋊Dic11—21no—
74C4⋊Dic11—42no—
75C4⋊Dic11D811yescharacteristic
76Dic11⋊C4—21no—
77Dic11⋊C4—42no—
78C4×Dic11—21no—
79C2×C11⋊C8—21no—
80C2×C11⋊C8—41no—
81D88—21no—
82D88SD1612yescomplemented
83C11×C16—41no—
84C11⋊C16—41no—
85#3380—111no—
86#2240D1111yescharacteristic, complemented
87#2206—111no—
88#1668—111no—
89#1365—111no—
90Q8⋊C16—111no—
91#1331—111no—
92C23×C11—81no—
93C22×D11—41no—
94Q8×C11—161no—
95D4×C11—81no—
96D4×C11—81no—
97D4×C11—81no—
98D4×C11—81no—
99D4×C11—161no—
100C2×C4×C11—42no—
101C2×C4×C11#12011yescharacteristic
102C2×C4×C11C2×D811yescharacteristic
103C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—41no—
107D44—22no—
108D44—41no—
109C4×D11—81no—
110C4×D11—81no—
111C4×D11—162no—
112Dic22—21no—
113Dic22—21no—
114C8×C11—21no—
115C8×C11C2×SD1611yescharacteristic
116C8×C11#13711yescharacteristic
117C11⋊C8—41no—
118C11⋊C8—81no—
119#554—221no—
120C2×D16—221no—
121#500C2×D1111yescharacteristic
122#499—221no—
123#493C2×D1111yescharacteristic
124#478—222no—
125#476—221no—
126#460—221no—
127C8×Q8—111no—
128C4×D8—111no—
129C4×D8—221no—
130C4⋊C16—111no—
131#357—22no—
132#357—221no—
133C4×C16C2×D1111yescharacteristic
134#335—111no—
135#331—221no—
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—82no—
145C4×C11#44811yescharacteristic
146C4×C11#45411yescharacteristic
147C4×C11#50811yescharacteristic
148C4×C11#50911yescharacteristic
149Dic11—41no—
150Dic11—41no—
151Dic11—81no—
152C2×SD16—441no—
153C2×D8—21no—
154C2×D8—21no—
155C2×D8—111no—
156C4⋊Q8—21no—
157#127—21no—
158#125—222no—
159C22⋊Q8—441no—
160C22⋊Q8—442no—
161C4×Q8—111no—
162C4×D4—222no—
163C4×D4—221no—
164C2×C4⋊C4—441no—
165D16—442no—
166C2×C16—21no—
167C2×C16—221no—
168#107—21no—
169#107—111no—
170#107C22⋊D1112yes—
171#106—222no—
172C4⋊C8—111no—
173C4⋊C8—221no—
174C4⋊C8—221no—
175#102—222no—
176#102—221no—
177#102—441no—
178C4×C8—221no—
179C4×C8C22×D1111yescharacteristic
180C2×C11—321no—
181C2×C11#162711yescharacteristic
182C2×C11#218611yescharacteristic
183C2×C11#219211yescharacteristic
184D11—82no—
185C2×Q8—41no—
186C2×Q8—111no—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—221no—
191C22×C4—442no—
192C22×C4—441no—
193SD16—882no—
194D8—42no—
195D8—41no—
196D8—41no—
197D8—112no—
198D8—221no—
199C2×C8—221no—
200C2×C8—441no—
201C2×C8D4×D1111yescharacteristic
202C2×C8C2×C22⋊D1111yescharacteristic
203C4⋊C4—22no—
204C4⋊C4—41no—
205C4⋊C4—111no—
206C4⋊C4—221no—
207C4⋊C4—221no—
208C4⋊C4—442no—
209C4⋊C4—442no—
210C22⋊C4—442no—
211C22⋊C4—441no—
212C42—221no—
213C42D4×D1111yescharacteristic
214C16—41no—
215C16—441no—
216C11#1235511yescharacteristic, complemented, Sylow
217C23—81no—
218C23—441no—
219Q8—161no—
220Q8—221no—
221Q8—221no—
222D4—81no—
223D4—81no—
224D4—81no—
225D4—81no—
226D4—161no—
227D4—222no—
228D4—441no—
229C2×C4—42no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—441no—
233C2×C4—881no—
234C2×C4—881no—
235C2×C4—1762no—
236C2×C4D8×D1111yescharacteristic
237C2×C4#6696411yescharacteristic
238C2×C4#6699011yescharacteristic
239C8—21no—
240C8—441no—
241C8—881no—
242C8SD16×D1111yescharacteristic
243C8#6696811yescharacteristic
244C22—161no—
245C22—161no—
246C22—161no—
247C22—442no—
248C22—881no—
249C22—881no—
250C22#1062276911yescharacteristic
251C4—21no—
252C4—82no—
253C4—441no—
254C4—441no—
255C4—881no—
256C4#1062252711yescharacteristic
257C4#1062252911yescharacteristic
258C4#1062267511yescharacteristic
259C4#1062278311yescharacteristic
260C2—321no—
261C2—882no—
262C2#1306771611yescharacteristic
263C2#1307053811yescharacteristic
264C2#1307057211yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2240C2
socleC22×C11#447
prime radical#13070648C2
hypercenter#2240D11
hypocenterC11#12355
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. #13081485C2semidirect
3. #13067973C2semidirect
4. #13066674C2semidirect
5. #13066596C2semidirect
6. #13066578C2semidirect
7. C11×#2240C2semidirect
82. D88SD16semidirect
86. #2240D11semidirect
216. C11#12355semidirect

Maximal subgroups

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

subgroupindex
#130814852
#130706482
#130679732
#130666742
#130665962
#130665782
C11×#22402
#1235511