Finite Group Databasebeta

← #14667325

Subgroups — #14667325

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#13070869C211yesmaximal, characteristic
3#13070667C211yesmaximal, characteristic
4#13067986C211yesmaximal, characteristic
5#13066666C211yesmaximal, characteristic
6#13066581C211yesmaximal, characteristic
7C11×Q8⋊C16C211yesmaximal, characteristic
8#10623101—21no—
9C8×Q8×C11C2211yescharacteristic
10#10622633—21no—
11C2×Dic88—22no—
12C2×Dic88—21no—
13#10622462—22no—
14#10622462—21no—
15#10622312—21no—
16#10622312C2211yescharacteristic
17#10622312C2211yescharacteristic
18C4×Dic44—21no—
19C4×Dic44C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C4×C11×C16C2211yescharacteristic
22#10622141—21no—
23#10622120—21no—
24#10622096C2211yescharacteristic
25C4×Q8×C11D411yescharacteristic
26Q8×Dic11—41no—
27C2×Dic44—21no—
28C2×Dic44—21no—
29C2×Dic44—21no—
30C2×Dic44—22no—
31C2×Dic44D411yescharacteristic
32C2×Dic44D412yes—
33#66943—42no—
34#66943—41no—
35#66922—22no—
36#66922—21no—
37#66922—21no—
38C4×Dic22—22no—
39C4×Dic22—21no—
40C2×C11×C16—21no—
41C2×C11×C16—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C4×C8×C11—21no—
45C4×C8×C11C2311yescharacteristic
46#66899—41no—
47#66882D411yescharacteristic
48#66880—22no—
49#66880—21no—
50#66872—41no—
51C4⋊(C11⋊C8)—21no—
52Dic88—44no—
53Dic88—42no—
54#12334—111nomaximal, Sylow
55C2×Q8×C11D811yescharacteristic
56C2×Dic22—21no—
57C2×Dic22—22no—
58C2×Dic22—41no—
59C2×C8×C11—21no—
60C2×C8×C11C2×D411yescharacteristic
61C2×C8×C11C2×D411yescharacteristic
62C11×C4⋊C4—21no—
63C11×C4⋊C4D811yescharacteristic
64C42×C11—21no—
65C42×C11C2×D411yescharacteristic
66C4⋊Dic11—21no—
67C4⋊Dic11—42no—
68C4⋊Dic11—42no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73Dic11⋊C4—42no—
74Dic11⋊C4—41no—
75C4×Dic11—42no—
76C4×Dic11—41no—
77C2×C11⋊C8—41no—
78Dic44—21no—
79Dic44—21no—
80Dic44—42no—
81Dic44—42no—
82Dic44—41no—
83Dic44—41no—
84Dic44—41no—
85Dic44—41no—
86Dic44—82no—
87C11×C16—22no—
88C11×C16—41no—
89#3395—111no—
90#2247—111no—
91#2209—111no—
92#1670—111no—
93#1362—111no—
94Q8⋊C16D1111yescharacteristic
95#1332—111no—
96Q8×C11—21no—
97Q8×C11Q3212yescomplemented
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11C2×D811yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C2×Dic11—41no—
104C2×Dic11—42no—
105C2×Dic11—41no—
106C2×Dic11—81no—
107Dic22—41no—
108Dic22—42no—
109Dic22—42no—
110Dic22—41no—
111Dic22—81no—
112Dic22—81no—
113C8×C11—21no—
114C8×C11—41no—
115C8×C11#13511yescharacteristic
116C8×C11AGL(1,ℤ/8)11yescharacteristic
117C11⋊C8—81no—
118#557—221no—
119C2×Q32—221no—
120C2×Q32—222no—
121#494—111no—
122#494—111no—
123#494—221no—
124#475—221no—
125#462—222no—
126#462—221no—
127C8×Q8C2×D1111yescharacteristic
128C4×Q16—111no—
129C4×Q16—221no—
130C4⋊C16C2×D1111yescharacteristic
131#358—221no—
132C4×C16C2×D1111yescharacteristic
133#335—111no—
134#332—221no—
135C22×C11#44711yescharacteristic
136C4×C11—22no—
137C4×C11—21no—
138C4×C11—41no—
139C4×C11#44911yescharacteristic
140C4×C11#45311yescharacteristic
141C4×C11C2×Q3211yescharacteristic
142C4×C11#51011yescharacteristic
143Dic11—81no—
144Dic11—82no—
145Dic11—81no—
146Dic11—161no—
147C2×Q16—111no—
148C2×Q16—112no—
149C2×Q16—222no—
150C2×Q16—221no—
151C2×Q16—221no—
152C2×Q16—221no—
153C4⋊Q8—222no—
154C4⋊Q8—221no—
155C4⋊Q8—221no—
156#125—442no—
157#125—441no—
158C4×Q8—222no—
159C4×Q8—221no—
160C4×Q8—441no—
161C4×Q8D4411yescharacteristic
162Q32—444no—
163Q32—442no—
164C2×C16—21no—
165C2×C16—21no—
166#107—111no—
167#106—441no—
168C4⋊C8—21no—
169C4⋊C8—221no—
170C4⋊C8D4411yescharacteristic
171#103—222no—
172#103—221no—
173#103—441no—
174C4×C8—21no—
175C4×C8C22×D1111yescharacteristic
176C2×C11#162111yescharacteristic
177C2×C11#218811yescharacteristic
178C2×C11#219511yescharacteristic
179C2×Q8—221no—
180C2×Q8—222no—
181C2×Q8—441no—
182C2×Q8D8811yescharacteristic
183Q16—221no—
184Q16—221no—
185Q16—442no—
186Q16—442no—
187Q16—441no—
188Q16—441no—
189Q16—441no—
190Q16—441no—
191Q16—882no—
192C2×C8—21no—
193C2×C8—441no—
194C2×C8D4×D1111yescharacteristic
195C2×C8D4×D1111yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—221no—
198C4⋊C4—442no—
199C4⋊C4—442no—
200C4⋊C4—442no—
201C4⋊C4—441no—
202C4⋊C4—441no—
203C4⋊C4—441no—
204C4⋊C4—441no—
205C4⋊C4—441no—
206C4⋊C4D8811yescharacteristic
207C42—21no—
208C42—442no—
209C42—441no—
210C42C2×D4411yescharacteristic
211C16—22no—
212C16—41no—
213C11#1233411yescharacteristic, complemented, Sylow
214Q8—21no—
215Q8—441no—
216Q8—442no—
217Q8—442no—
218Q8—441no—
219Q8—881no—
220Q8—881no—
221Q8Dic8812yescomplemented
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—441no—
225C2×C4—442no—
226C2×C4—441no—
227C2×C4—881no—
228C2×C4#6693511yescharacteristic
229C2×C4C2×D8811yescharacteristic
230C2×C4#6696111yescharacteristic
231C8—21no—
232C8—41no—
233C8—881no—
234C8#6696711yescharacteristic
235C8#6697211yescharacteristic
236C22#1062234511yescharacteristic
237C4—21no—
238C4—22no—
239C4—41no—
240C4—881no—
241C4—881no—
242C4—882no—
243C4—1761no—
244C4#1062242411yescharacteristic
245C4#1062243511yescharacteristic
246C4C2×Dic8811yescharacteristic
247C4#1062252211yescharacteristic
248C2#1306768311yescharacteristic
249C2#1307055211yescharacteristic
250C2#1307059611yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×Q8⋊C16C2
socle, prime radicalC22×C11#447
hypercenterQ8⋊C16D11
hypocenterC11#12334
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
97. Q8×C11Q32semidirect
213. C11#12334semidirect
221. Q8Dic88semidirect

Maximal subgroups

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

subgroupindex
#130816222
#130708692
#130706672
#130679862
#130666662
#130665812
C11×Q8⋊C162
#1233411