Finite Group Databasebeta

← #14667657

Subgroups — #14667657

Order 2816.

294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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#13081602C211yesmaximal, characteristic
2#13070845C211yesmaximal, characteristic, complemented
3#13068007C211yesmaximal, characteristic, complemented
4#13066666C211yesmaximal, characteristic, complemented
5#13066594C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic
7C11×#2224C211yesmaximal, characteristic
8#10623073—21no—
9C11×#500C2211yescharacteristic
10C4×C11×D8C2211yescharacteristic
11#10622768—21no—
12#10622703—21no—
13#10622632—21no—
14#10622486—21no—
15#10622380—22no—
16#10622312C2211yescharacteristic
17C8×Dic22C2211yescharacteristic
18C11×#366—21no—
19C11×C4⋊C16C2211yescharacteristic
20C11×#357—21no—
21#10622185—21no—
22#10622130—22no—
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×D8D411yescharacteristic
26C11×C4⋊Q8—21no—
27C4×D4×C11—21no—
28C2×#4326—41no—
29#66989—22no—
30C2×#4324—22no—
31#66979—41no—
32#66977—41no—
33C2×Dic44—21no—
34C2×Dic44D412yes—
35#66940—22no—
36#66932—42no—
37#66922—21no—
38C4×Dic22D411yescharacteristic
39C2×C11×C16—21no—
40C11×#107—21no—
41C11×#107—21no—
42C11×#107D411yescharacteristic
43C11×#102—21no—
44C4×C8×C11C2311yescharacteristic
45#66899—41no—
46Dic11⋊C8—21no—
47C8×Dic11—21no—
48C2×C11⋊C16—21no—
49#66874—22no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)D411yescharacteristic
52#12383—111nomaximal, Sylow
53C2×Q8×C11—41no—
54C2×D4×C11—21no—
55C22×C4×C11—41no—
56C2×Dic22—22no—
57C2×Dic22D811yescharacteristic
58C11×D8—21no—
59C11×D8—21no—
60C2×C8×C11C2×D411yescharacteristic
61C2×C8×C11C2×D411yescharacteristic
62C11×C4⋊C4—21no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C22⋊C4—41no—
66C42×C11C2×D411yescharacteristic
67C22⋊Dic11—42no—
68C22⋊Dic11—42no—
69#4326—82no—
70#4324—82no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C4⋊Dic11D811yescharacteristic
74Dic11⋊C4—21no—
75Dic11⋊C4—42no—
76C4×Dic11—21no—
77C4×Dic11—42no—
78C2×C11⋊C8—21no—
79C2×C11⋊C8—41no—
80Dic44—42no—
81Dic44—41no—
82Dic44—41no—
83C11×C16—41no—
84C11⋊C16—41no—
85#3393—111no—
86#2241—111no—
87#2224D1111yescharacteristic
88#1674—111no—
89#1362—111no—
90Q8⋊C16—111no—
91#1331—111no—
92C23×C11—41no—
93Q8×C11—81no—
94Q8×C11—81no—
95D4×C11—41no—
96D4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11—81no—
99C2×C4×C11—81no—
100C2×C4×C11—81no—
101C2×C4×C11#12011yescharacteristic
102C2×C4×C11C2×D811yescharacteristic
103C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—42no—
107Dic22—21no—
108Dic22—21no—
109Dic22—42no—
110Dic22—42no—
111C8×C11—21no—
112C8×C11#13511yescharacteristic
113C8×C11#13711yescharacteristic
114C11⋊C8—41no—
115C11⋊C8—81no—
116#556—221no—
117#500C2×D1111yescharacteristic
118#495—221no—
119#494—111no—
120#464—222no—
121#462—221no—
122#461—221no—
123C8×Q8—111no—
124C4×Q16—221no—
125C4×D8C2×D1111yescharacteristic
126#366—21no—
127C4⋊C16C2×D1111yescharacteristic
128#358—222no—
129#357—21no—
130C4×C16—111no—
131#335—111no—
132#332—221no—
133C22×C11—81no—
134C22×C11—81no—
135C22×C11—81no—
136C22×C11#44711yescharacteristic
137C4×C11—21no—
138C4×C11—81no—
139C4×C11—161no—
140C4×C11#45211yescharacteristic
141C4×C11#45511yescharacteristic
142C4×C11#50811yescharacteristic
143C4×C11#50911yescharacteristic
144Dic11—41no—
145Dic11—41no—
146Dic11—82no—
147C2×Q16—112no—
148C2×Q16—221no—
149C2×Q16—441no—
150C2×SD16—222no—
151C2×D8C22⋊D1111yescharacteristic
152C4⋊Q8—21no—
153C4⋊Q8—221no—
154#126—442no—
155#124—222no—
156C22⋊Q8—441no—
157C4×Q8—111no—
158C4×Q8—222no—
159C4×D4—21no—
160#117—441no—
161C2×C16—21no—
162C2×C16—221no—
163#107—21no—
164#107—21no—
165#107C22⋊D1111yescharacteristic
166C4⋊C8—111no—
167C4⋊C8—221no—
168C4⋊C8—221no—
169#103—222no—
170#103—441no—
171#102—21no—
172C4×C8—221no—
173C4×C8C22×D1111yescharacteristic
174C2×C11—161no—
175C2×C11#164111yescharacteristic
176C2×C11#218611yescharacteristic
177C2×C11#219511yescharacteristic
178C2×Q8—41no—
179C2×Q8—111no—
180C2×Q8—222no—
181C2×D4—21no—
182C22×C4—41no—
183Q16—442no—
184Q16—441no—
185Q16—441no—
186Q16—882no—
187SD16—882no—
188D8—21no—
189D8—21no—
190C2×C8—221no—
191C2×C8—441no—
192C2×C8D4×D1111yescharacteristic
193C2×C8C2×C22⋊D1111yescharacteristic
194C4⋊C4—21no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—111no—
198C4⋊C4—221no—
199C4⋊C4—442no—
200C4⋊C4—441no—
201C4⋊C4—441no—
202C22⋊C4—41no—
203C22⋊C4—442no—
204C22⋊C4—442no—
205C42—221no—
206C42—442no—
207C42D4×D1111yescharacteristic
208C16—41no—
209C16—441no—
210C11#1238311yescharacteristic, complemented, Sylow
211C23—41no—
212Q8—81no—
213Q8—81no—
214Q8—221no—
215Q8—221no—
216Q8—442no—
217Q8—442no—
218D4—41no—
219D4—41no—
220C2×C4—41no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—442no—
227C2×C4D8×D1111yescharacteristic
228C2×C4#6696411yescharacteristic
229C2×C4#6699011yescharacteristic
230C8—21no—
231C8—441no—
232C8—881no—
233C8#6699511yescharacteristic
234C8#6700311yescharacteristic
235C22—81no—
236C22—81no—
237C22—81no—
238C22#1062276911yescharacteristic
239C4—21no—
240C4—81no—
241C4—161no—
242C4—441no—
243C4—441no—
244C4—882no—
245C4#1062252411yescharacteristic
246C4#1062252511yescharacteristic
247C4#1062266011yescharacteristic
248C4#1062281511yescharacteristic
249C2—161no—
250C2#1306780811yescharacteristic
251C2#1307053611yescharacteristic
252C2#1307059111yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2224C2
socleC22×C11#447
prime radicalC2×C11×D8D4
hypercenter#2224D11
hypocenterC11#12383
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
2. #13070845C2semidirect
3. #13068007C2semidirect
4. #13066666C2semidirect
5. #13066594C2semidirect
210. C11#12383semidirect

Maximal subgroups

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

subgroupindex
#130816022
#130708452
#130680072
#130666662
#130665942
#130665772
C11×#22242
#1238311