Finite Group Databasebeta

← #14667658

Subgroups — #14667658

Order 2816.

294 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 71 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#13070843C211yesmaximal, characteristic, complemented
2#13070753C211yesmaximal, characteristic
3#13068010C211yesmaximal, characteristic, complemented
4#13066665C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic
7C11×#3393C211yesmaximal, characteristic
8C11×#556—21no—
9C11×#495—21no—
10C11×#494C2211yescharacteristic
11C11×#464—22no—
12C11×#461—21no—
13C8×Q8×C11C2211yescharacteristic
14C4×C11×Q16—21no—
15C4×C11×D8C2211yescharacteristic
16#10622644—21no—
17#10622295C2211yescharacteristic
18#10622202—22no—
19#10622200—21no—
20#10622127—21no—
21#10622124—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16D412yes—
27C2×C11×SD16—22no—
28C2×C11×D8D411yescharacteristic
29C11×C4⋊Q8—21no—
30C11×#126—42no—
31C11×#124—22no—
32C11×C22⋊Q8—41no—
33C4×Q8×C11—22no—
34C4×Q8×C11D411yescharacteristic
35C4×D4×C11—21no—
36C11×#117—41no—
37C2×#4326—41no—
38#66922—21no—
39C11×#107D411yescharacteristic
40C11×C4⋊C8—21no—
41C11×C4⋊C8D411yescharacteristic
42C11×#103—22no—
43C11×#102—21no—
44C4×C8×C11—21no—
45C4×C8×C11C2311yescharacteristic
46#66882—21no—
47#66882—21no—
48C2×C11⋊C16—21no—
49C2×C11⋊C16—21no—
50#66874—41no—
51C4⋊(C11⋊C8)—21no—
52#12383—111nomaximal, Sylow
53C2×Q8×C11—22no—
54C2×Q8×C11D811yescharacteristic
55C2×D4×C11—21no—
56C22×C4×C11—41no—
57C2×Dic22—41no—
58C11×Q16—41no—
59C11×Q16—41no—
60C11×Q16—42no—
61C11×SD16—82no—
62C11×D8—21no—
63C11×D8—21no—
64C2×C8×C11—21no—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4D811yescharacteristic
73C11×C22⋊C4—42no—
74C11×C22⋊C4—42no—
75C11×C22⋊C4—41no—
76C42×C11—21no—
77C42×C11—42no—
78C42×C11C2×D411yescharacteristic
79#4326—82no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82C2×C11⋊C8—41no—
83C11⋊C16—41no—
84C11⋊C16—41no—
85#3393D1111yescharacteristic
86#2241—111no—
87#2224—111no—
88#1674—111no—
89#1362—111no—
90Q8⋊C16—111no—
91#1331—111no—
92C23×C11—41no—
93Q8×C11—21no—
94Q8×C11—21no—
95Q8×C11—42no—
96Q8×C11—42no—
97D4×C11—41no—
98D4×C11—41no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—81no—
104C2×C4×C11—81no—
105C2×C4×C11#12011yescharacteristic
106C2×C4×C11C2×D811yescharacteristic
107C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
108C2×Dic11—81no—
109Dic22—81no—
110Dic22—81no—
111C8×C11—21no—
112C8×C11—41no—
113C8×C11#13511yescharacteristic
114C8×C11#13711yescharacteristic
115C11⋊C8—81no—
116#556—21no—
117#500—111no—
118#495—21no—
119#494C2×D1111yescharacteristic
120#464—22no—
121#462—221no—
122#461—21no—
123C8×Q8C2×D1111yescharacteristic
124C4×Q16—21no—
125C4×D8C2×D1111yescharacteristic
126#366—221no—
127C4⋊C16—111no—
128#358—222no—
129#357—221no—
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—41no—
139C4×C11—41no—
140C4×C11—82no—
141C4×C11—81no—
142C4×C11#45211yescharacteristic
143C4×C11#45511yescharacteristic
144C4×C11#50811yescharacteristic
145C4×C11#50911yescharacteristic
146Dic11—161no—
147C2×Q16—21no—
148C2×Q16—441no—
149C2×Q16C22⋊D1112yes—
150C2×SD16—22no—
151C2×D8C22⋊D1111yescharacteristic
152C4⋊Q8—21no—
153C4⋊Q8—221no—
154#126—42no—
155#124—22no—
156C22⋊Q8—41no—
157C4×Q8—22no—
158C4×Q8C22⋊D1111yescharacteristic
159C4×D4—21no—
160#117—41no—
161C2×C16—221no—
162C2×C16—221no—
163#107—221no—
164#107—221no—
165#107C22⋊D1111yescharacteristic
166C4⋊C8—21no—
167C4⋊C8—221no—
168C4⋊C8C22⋊D1111yescharacteristic
169#103—22no—
170#103—441no—
171#102—21no—
172C4×C8—21no—
173C4×C8C22×D1111yescharacteristic
174C2×C11—161no—
175C2×C11#164111yescharacteristic
176C2×C11#218611yescharacteristic
177C2×C11#219511yescharacteristic
178C2×Q8—22no—
179C2×Q8—441no—
180C2×Q8#432311yescharacteristic
181C2×D4—21no—
182C22×C4—41no—
183Q16—42no—
184Q16—41no—
185Q16—41no—
186Q16—882no—
187SD16—82no—
188D8—21no—
189D8—21no—
190C2×C8—21no—
191C2×C8—441no—
192C2×C8C2×C22⋊D1111yescharacteristic
193C2×C8C2×C22⋊D1111yescharacteristic
194C4⋊C4—21no—
195C4⋊C4—21no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—441no—
200C4⋊C4—441no—
201C4⋊C4#432311yescharacteristic
202C22⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—41no—
205C42—21no—
206C42—42no—
207C42C2×C22⋊D1111yescharacteristic
208C16—441no—
209C16—441no—
210C11#1238311yescharacteristic, complemented, Sylow
211C23—41no—
212Q8—21no—
213Q8—21no—
214Q8—42no—
215Q8—42no—
216Q8—881no—
217Q8—881no—
218D4—41no—
219D4—41no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—881no—
227C2×C4C2×#432311yescharacteristic
228C2×C4#6698511yescharacteristic
229C2×C4#6700611yescharacteristic
230C8—21no—
231C8—41no—
232C8—881no—
233C8#6700311yescharacteristic
234C8#6700411yescharacteristic
235C22—81no—
236C22—81no—
237C22—81no—
238C22#1062283011yescharacteristic
239C4—21no—
240C4—41no—
241C4—41no—
242C4—82no—
243C4—81no—
244C4—1761no—
245C4#1062280611yescharacteristic
246C4#1062280711yescharacteristic
247C4#1062285211yescharacteristic
248C4#1062285511yescharacteristic
249C2—161no—
250C2#1306780911yescharacteristic
251C2#1307053911yescharacteristic
252C2#1307059411yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3393C2
socleC22×C11#447
prime radicalC2×C11×D8D4
hypercenter#3393D11
hypocenterC11#12383
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. #13070843C2semidirect
3. #13068010C2semidirect
4. #13066665C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
210. C11#12383semidirect

Maximal subgroups

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

subgroupindex
#130708432
#130707532
#130680102
#130666652
Q8⋊(C11⋊C16)2
#130665772
C11×#33932
#1238311