Finite Group Databasebeta

← #14667321

Subgroups — #14667321

Order 2816.

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

normal subgroups only

This group has 306 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#13081622C211yesmaximal, characteristic
2#13070868C211yesmaximal, characteristic
3#13070663C211yesmaximal, characteristic
4#13066664C211yesmaximal, characteristic
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic
6#13066579C211yesmaximal, characteristic
7C11×#1670C211yesmaximal, characteristic
8#10623101—21no—
9C11×#494C2211yescharacteristic
10C11×#475—21no—
11C8×Q8×C11C2211yescharacteristic
12C2×#66893—22no—
13C2×#66893—21no—
14#10622462—22no—
15#10622462—21no—
16#10622312—21no—
17#10622312C2211yescharacteristic
18C4×Dic44—21no—
19C4×Dic44C2211yescharacteristic
20C11×#335C2211yescharacteristic
21C11×#332—21no—
22#10622202—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C11×C4⋊Q8—21no—
28C4×Q8×C11D411yescharacteristic
29Q8×Dic11—41no—
30C2×Dic44—21no—
31C2×Dic44—22no—
32C2×Dic44D411yescharacteristic
33C2×Dic44D412yes—
34#66943—42no—
35#66943—41no—
36#66922—22no—
37#66922—21no—
38C4×Dic22—22no—
39C4×Dic22—21no—
40C11×#106—41no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×#103—41no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66893—44no—
48#66893—42no—
49#66882D411yescharacteristic
50#66880—22no—
51#66880—21no—
52C2×C11⋊C16—21no—
53C2×C11⋊C16—21no—
54#12334—111nomaximal, Sylow
55C2×Q8×C11—41no—
56C2×Q8×C11D811yescharacteristic
57C2×Dic22—21no—
58C2×Dic22—22no—
59C11×Q16—42no—
60C11×Q16—41no—
61C11×Q16—41no—
62C2×C8×C11—21no—
63C2×C8×C11—41no—
64C2×C8×C11C2×D411yescharacteristic
65C2×C8×C11C2×D411yescharacteristic
66C11×C4⋊C4—21no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4D811yescharacteristic
70C42×C11—21no—
71C42×C11C2×D411yescharacteristic
72C4⋊Dic11—21no—
73C4⋊Dic11—42no—
74C4⋊Dic11—42no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77Dic11⋊C4—42no—
78Dic11⋊C4—41no—
79C4×Dic11—42no—
80C4×Dic11—41no—
81Dic44—21no—
82Dic44—21no—
83Dic44—42no—
84Dic44—41no—
85Dic44—41no—
86Dic44—82no—
87C11⋊C16—22no—
88C11⋊C16—41no—
89#3395—111no—
90#2247—111no—
91#2209—111no—
92#1670D1111yescharacteristic
93#1362—111no—
94Q8⋊C16—111no—
95#1332—111no—
96Q8×C11—21no—
97Q8×C11—81no—
98Q8×C11—81no—
99Q8×C11Q3212yescomplemented
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—81no—
103C2×C4×C11#12011yescharacteristic
104C2×C4×C11C2×D811yescharacteristic
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C2×Dic11—41no—
107C2×Dic11—42no—
108C2×Dic11—41no—
109Dic22—41no—
110Dic22—42no—
111Dic22—42no—
112Dic22—41no—
113C8×C11—21no—
114C8×C11—41no—
115C8×C11—81no—
116C8×C11#13511yescharacteristic
117C8×C11AGL(1,ℤ/8)11yescharacteristic
118#557—221no—
119C2×Q32—221no—
120C2×Q32—222no—
121#494—111no—
122#494—221no—
123#494C2×D1111yescharacteristic
124#475—21no—
125#462—222no—
126#462—221no—
127C8×Q8C2×D1111yescharacteristic
128C4×Q16—111no—
129C4×Q16—221no—
130C4⋊C16—111no—
131#358—221no—
132C4×C16—111no—
133#335C2×D1111yescharacteristic
134#332—21no—
135C22×C11#44711yescharacteristic
136C4×C11—22no—
137C4×C11—21no—
138C4×C11—41no—
139C4×C11—161no—
140C4×C11#44911yescharacteristic
141C4×C11#45311yescharacteristic
142C4×C11C2×Q3211yescharacteristic
143C4×C11#51011yescharacteristic
144Dic11—81no—
145Dic11—82no—
146Dic11—81no—
147C2×Q16—21no—
148C2×Q16—21no—
149C2×Q16—111no—
150C2×Q16—112no—
151C2×Q16—222no—
152C2×Q16—221no—
153C4⋊Q8—21no—
154C4⋊Q8—222no—
155C4⋊Q8—221no—
156#125—442no—
157#125—441no—
158C4×Q8—222no—
159C4×Q8—221no—
160C4×Q8—441no—
161C4×Q8C22⋊D1111yescharacteristic
162Q32—444no—
163Q32—442no—
164C2×C16—221no—
165C2×C16—221no—
166#107—111no—
167#106—41no—
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8C22⋊D1111yescharacteristic
171#103—41no—
172#103—222no—
173#103—221no—
174C4×C8—21no—
175C4×C8C22×D1111yescharacteristic
176C2×C11#162111yescharacteristic
177C2×C11#218811yescharacteristic
178C2×C11#219511yescharacteristic
179C2×Q8—41no—
180C2×Q8—221no—
181C2×Q8—222no—
182C2×Q8#432311yescharacteristic
183Q16—42no—
184Q16—41no—
185Q16—41no—
186Q16—221no—
187Q16—221no—
188Q16—442no—
189Q16—441no—
190Q16—441no—
191Q16—882no—
192C2×C8—21no—
193C2×C8—41no—
194C2×C8D4×D1111yescharacteristic
195C2×C8D4×D1111yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—221no—
200C4⋊C4—442no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C4⋊C4—441no—
204C4⋊C4—441no—
205C4⋊C4—441no—
206C4⋊C4#432311yescharacteristic
207C42—21no—
208C42—442no—
209C42—441no—
210C42C2×C22⋊D1111yescharacteristic
211C16—222no—
212C16—441no—
213C11#1233411yescharacteristic, complemented, Sylow
214Q8—21no—
215Q8—81no—
216Q8—81no—
217Q8—441no—
218Q8—442no—
219Q8—442no—
220Q8—441no—
221Q8#6689312yescomplemented
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—81no—
225C2×C4—441no—
226C2×C4—442no—
227C2×C4—441no—
228C2×C4C2×#432311yescharacteristic
229C2×C4#6699011yescharacteristic
230C2×C4#6700211yescharacteristic
231C8—21no—
232C8—41no—
233C8—81no—
234C8#6696711yescharacteristic
235C8#6696911yescharacteristic
236C22#1062264911yescharacteristic
237C4—21no—
238C4—22no—
239C4—41no—
240C4—161no—
241C4—881no—
242C4—881no—
243C4—882no—
244C4#1062278511yescharacteristic
245C4C2×#6689311yescharacteristic
246C4#1062280811yescharacteristic
247C4#1062281111yescharacteristic
248C2#1306767911yescharacteristic
249C2#1307054911yescharacteristic
250C2#1307059211yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1670C2
socle, prime radicalC22×C11#447
hypercenter#1670D11
hypocenterC11#12334
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

Complements

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

NH ≅ G/Ntype
99. Q8×C11Q32semidirect
213. C11#12334semidirect
221. Q8#66893semidirect

Maximal subgroups

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

subgroupindex
#130816222
#130708682
#130706632
#130666642
Q8⋊(C11⋊C16)2
#130665792
C11×#16702
#1233411