Finite Group Databasebeta

← #14667681

Subgroups — #14667681

Order 2816.

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

normal subgroups only

This group has 282 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#13070844C211yesmaximal, characteristic
3#13070769C211yesmaximal, characteristic
4#13068020C211yesmaximal, characteristic
5#13066666C211yesmaximal, characteristic
6#13066581C211yesmaximal, characteristic
7C11×Q8⋊C16C211yesmaximal, characteristic
8#10623101—21no—
9C8×Q8×C11C2211yescharacteristic
10#10622634—21no—
11#10622462—22no—
12#10622462—21no—
13#10622312—21no—
14#10622312C2211yescharacteristic
15C4×Dic44—21no—
16C4×Dic44C2211yescharacteristic
17#10622295C2211yescharacteristic
18C11×C4⋊C16C2211yescharacteristic
19C4×C11×C16C2211yescharacteristic
20#10622142—21no—
21#10622141—21no—
22#10622141—22no—
23#10622119—21no—
24#10622096C2211yescharacteristic
25C4×Q8×C11D411yescharacteristic
26Q8×Dic11—41no—
27C2×Dic44—21no—
28C2×Dic44—22no—
29C2×Dic44D411yescharacteristic
30C2×Dic44D412yes—
31#66943—42no—
32#66943—41no—
33#66922—22no—
34#66922—21no—
35#66922—21no—
36C4×Dic22—22no—
37C4×Dic22—21no—
38C2×C11×C16—21no—
39C2×C11×C16—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8D411yescharacteristic
42C4×C8×C11—21no—
43C4×C8×C11C2311yescharacteristic
44#66899—41no—
45#66882—21no—
46#66882—21no—
47#66882D411yescharacteristic
48#66880—22no—
49#66880—21no—
50#66871—41no—
51C4⋊(C11⋊C8)—21no—
52#12386—111nomaximal, Sylow
53C2×Q8×C11D811yescharacteristic
54C2×Dic22—21no—
55C2×Dic22—22no—
56C2×Dic22—41no—
57C2×C8×C11—21no—
58C2×C8×C11C2×D411yescharacteristic
59C2×C8×C11C2×D411yescharacteristic
60C11×C4⋊C4—21no—
61C11×C4⋊C4D811yescharacteristic
62C42×C11—21no—
63C42×C11C2×D411yescharacteristic
64C4⋊Dic11—21no—
65C4⋊Dic11—42no—
66C4⋊Dic11—42no—
67C4⋊Dic11—41no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71Dic11⋊C4—42no—
72Dic11⋊C4—41no—
73C4×Dic11—42no—
74C4×Dic11—41no—
75C2×C11⋊C8—41no—
76Dic44—21no—
77Dic44—21no—
78Dic44—42no—
79Dic44—41no—
80Dic44—41no—
81Dic44—82no—
82C11×C16—41no—
83C11×C16—41no—
84#3395—111no—
85#2241—111no—
86#2227—111no—
87#1676—111no—
88#1362—111no—
89Q8⋊C16D1111yescharacteristic
90#1332—111no—
91Q8×C11—21no—
92Q8×C11Q3212yes—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11C2×D811yescharacteristic
97C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
98C2×Dic11—41no—
99C2×Dic11—42no—
100C2×Dic11—41no—
101C2×Dic11—81no—
102Dic22—41no—
103Dic22—42no—
104Dic22—42no—
105Dic22—41no—
106Dic22—161no—
107C8×C11—21no—
108C8×C11—41no—
109C8×C11#13511yescharacteristic
110C8×C11#13711yescharacteristic
111C11⋊C8—81no—
112#557—221no—
113#500—111no—
114#494—111no—
115#494—221no—
116#477—221no—
117#462—222no—
118#462—221no—
119C8×Q8C2×D1111yescharacteristic
120C4×Q16—111no—
121C4×Q16—221no—
122#366—221no—
123C4⋊C16C2×D1111yescharacteristic
124#358—221no—
125#358—222no—
126C4×C16C2×D1111yescharacteristic
127#335—111no—
128#333—221no—
129C22×C11#44711yescharacteristic
130C4×C11—22no—
131C4×C11—21no—
132C4×C11—41no—
133C4×C11#45211yescharacteristic
134C4×C11#45511yescharacteristic
135C4×C11C2×Q3211yescharacteristic
136C4×C11#51011yescharacteristic
137Dic11—81no—
138Dic11—82no—
139Dic11—81no—
140Dic11—161no—
141C2×Q16—111no—
142C2×Q16—112no—
143C2×Q16—222no—
144C2×Q16—221no—
145C4⋊Q8—222no—
146C4⋊Q8—221no—
147C4⋊Q8—221no—
148#125—442no—
149#125—441no—
150C4×Q8—222no—
151C4×Q8—221no—
152C4×Q8—441no—
153C4×Q8D4411yescharacteristic
154C2×C16—21no—
155C2×C16—21no—
156#107—111no—
157#107—221no—
158#107—221no—
159#107—441no—
160C4⋊C8—21no—
161C4⋊C8—221no—
162C4⋊C8D4411yescharacteristic
163#103—222no—
164#103—221no—
165#103—441no—
166C4×C8—21no—
167C4×C8C22×D1111yescharacteristic
168C2×C11#164111yescharacteristic
169C2×C11#218811yescharacteristic
170C2×C11#219311yescharacteristic
171C2×Q8—221no—
172C2×Q8—222no—
173C2×Q8—441no—
174C2×Q8D8811yescharacteristic
175Q16—221no—
176Q16—221no—
177Q16—442no—
178Q16—441no—
179Q16—441no—
180Q16—882no—
181C2×C8—21no—
182C2×C8—441no—
183C2×C8D4×D1111yescharacteristic
184C2×C8D4×D1111yescharacteristic
185C4⋊C4—21no—
186C4⋊C4—221no—
187C4⋊C4—442no—
188C4⋊C4—442no—
189C4⋊C4—442no—
190C4⋊C4—441no—
191C4⋊C4—441no—
192C4⋊C4—441no—
193C4⋊C4—441no—
194C4⋊C4—441no—
195C4⋊C4D8811yescharacteristic
196C42—21no—
197C42—442no—
198C42—441no—
199C42C2×D4411yescharacteristic
200C16—41no—
201C16—41no—
202C11#1238611yescharacteristic, complemented, Sylow
203Q8—21no—
204Q8—441no—
205Q8—442no—
206Q8—442no—
207Q8—441no—
208Q8—1761no—
209Q8Dic8812yes—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—441no—
213C2×C4—442no—
214C2×C4—441no—
215C2×C4—881no—
216C2×C4#6693511yescharacteristic
217C2×C4C2×D8811yescharacteristic
218C2×C4#6696111yescharacteristic
219C8—21no—
220C8—41no—
221C8—881no—
222C8#6696911yescharacteristic
223C8#6697111yescharacteristic
224C22#1062234511yescharacteristic
225C4—22no—
226C4—21no—
227C4—41no—
228C4—881no—
229C4—882no—
230C4—881no—
231C4—1761no—
232C4#1062242311yescharacteristic
233C4#1062243811yescharacteristic
234C4C2×Dic8811yescharacteristic
235C4#1062252211yescharacteristic
236C2#1306781111yescharacteristic
237C2#1307055211yescharacteristic
238C2#1307058211yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×Q8⋊C16C2
socle, prime radicalC22×C11#447
hypercenterQ8⋊C16D11
hypocenterC11#12386
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
202. C11#12386semidirect

Maximal subgroups

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

subgroupindex
#130816222
#130708442
#130707692
#130680202
#130666662
#130665812
C11×Q8⋊C162
#1238611