Finite Group Databasebeta

← #14658759

Subgroups — #14658759

Order 2816.

320 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 95 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#13069557C211yesmaximal, characteristic
2#13068790C211yesmaximal, characteristic
3#13067392C211yesmaximal, characteristic
4#13067391C211yesmaximal, characteristic
5#13067045C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1487C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×#66886—22no—
12#10622538C2211yescharacteristic
13#10622537C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×#66867C2211yescharacteristic
16C11×Q8⋊C8—22no—
17Q8⋊(C11⋊C8)—22no—
18#10622162—22no—
19#10622117—22no—
20#10622096—22no—
21C22×Q8×C11Q811yescharacteristic
22C2×C11×M16—21no—
23C4×Q8×C11—21no—
24C4×Q8×C11—21no—
25C4×Q8×C11—21no—
26C4×Q8×C11—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4Q811yescharacteristic
29C2×C42×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C2×#4318—21no—
32C22×C11⋊C8—21no—
33C22×C11⋊C8D412yes—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11D412yes—
39C22⋊(C11⋊C8)—21no—
40#66886—44no—
41C4⋊(C11⋊C8)—21no—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46#66867—21no—
47#66867—21no—
48C4×C11⋊C8D412yes—
49#10662—111nomaximal, Sylow
50C2×Q8×C11—21no—
51C2×Q8×C11—21no—
52C2×Q8×C11—42no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×Q811yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C11×M16—42no—
59C2×C8×C11—22no—
60C2×C8×C11—41no—
61C11×C4⋊C4—21no—
62C11×C4⋊C4—21no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C42×C11—41no—
66C42×C11—41no—
67C42×C11C2×D411yescharacteristic
68C42×C11C2×D411yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4111yescharacteristic
71#4318—42no—
72C2×C11⋊C8—22no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8—41no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8Q1614yes—
79#1985—111no—
80#1849—111no—
81#1571—111no—
82#1571—111no—
83#1487—111no—
84#1487D1111yescharacteristic
85#1275—111no—
86C23×C11C22⋊Q811yescharacteristic
87Q8×C11—22no—
88Q8×C11—22no—
89Q8×C11—41no—
90Q8×C11—41no—
91C2×C4×C11—22no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—42no—
97C2×C4×C11—41no—
98C2×C4×C11C22⋊Q811yescharacteristic
99C2×C4×C11C22⋊Q811yescharacteristic
100C2×C4×C11#12311yescharacteristic
101C2×C4×C11#12311yescharacteristic
102C2×C4×C11#12311yescharacteristic
103C2×C4×C11#12711yescharacteristic
104C2×C4×C11C2×Q1612yes—
105C2×C4×C11AGL(1,ℤ/8)12yes—
106C8×C11—42no—
107C8×C11—81no—
108C11⋊C8—24no—
109C11⋊C8—42no—
110C11⋊C8—81no—
111C11⋊C8—81no—
112C2×C4×Q8C2×D1111yescharacteristic
113#431—111no—
114#431C2×D1111yescharacteristic
115C2×#108—222no—
116#423—111no—
117#423C2×D1111yescharacteristic
118C2×C4⋊C8—111no—
119C2×#97—111no—
120#336—222no—
121#335—222no—
122#335—222no—
123Q8⋊C8—22no—
124Q8⋊C8—222no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11#39911yescharacteristic
128C22×C11#47712yes—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11—21no—
133C4×C11—42no—
134C4×C11—81no—
135C4×C11#48412yes—
136C4×C11#49411yescharacteristic
137C4×C11#49611yescharacteristic
138C22×Q8Dic2211yescharacteristic
139C2×M16—21no—
140C2×M16—221no—
141C22×C8—112no—
142C22×C8—221no—
143C4×Q8—21no—
144C4×Q8—21no—
145C4×Q8—21no—
146C4×Q8—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4Dic2211yescharacteristic
149C2×C42—21no—
150C2×C42C22×D1111yescharacteristic
151#108—444no—
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—221no—
156C4⋊C8—221no—
157C4⋊C8—221no—
158C4⋊C8—221no—
159C4⋊C8—221no—
160C22⋊C8—21no—
161C22⋊C8—221no—
162#97—221no—
163#97—221no—
164C4×C8—112no—
165C4×C8C22⋊D1112yes—
166C2×C11—22no—
167C2×C11#209111yescharacteristic
168C2×C11#209511yescharacteristic
169C2×C11#209811yescharacteristic
170C2×Q8—21no—
171C2×Q8—21no—
172C2×Q8—42no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4C2×Dic2211yescharacteristic
176C22×C4D4×D1111yescharacteristic
177C22×C4#434111yescharacteristic
178M16—42no—
179M16—442no—
180C2×C8—22no—
181C2×C8—41no—
182C2×C8—114no—
183C2×C8—222no—
184C2×C8—222no—
185C2×C8—222no—
186C2×C8—442no—
187C2×C8—441no—
188C2×C8—441no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C42—41no—
194C42—41no—
195C42#433911yescharacteristic
196C42D4×D1111yescharacteristic
197C42#434111yescharacteristic
198C42C2×C22⋊D1111yescharacteristic
199C11#1066211yescharacteristic, complemented, Sylow
200C23#6693111yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—41no—
204Q8—41no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4#6693111yescharacteristic
213C2×C4#6693611yescharacteristic
214C2×C4#6693611yescharacteristic
215C2×C4#6696712yes—
216C2×C4Q16×D1112yes—
217C2×C4#6697711yescharacteristic
218C2×C4#6698811yescharacteristic
219C2×C4#6699311yescharacteristic
220C8—42no—
221C8—81no—
222C8—224no—
223C8—442no—
224C8—881no—
225C8—881no—
226C22—21no—
227C22—21no—
228C22#1062240712yes—
229C22#1062256211yescharacteristic
230C4—21no—
231C4—21no—
232C4—21no—
233C4—21no—
234C4—42no—
235C4—81no—
236C4#1062242212yes—
237C4#1062278911yescharacteristic
238C4#1062279411yescharacteristic
239C2—22no—
240C2#1307013211yescharacteristic
241C2#1307015211yescharacteristic
242C2#1307017111yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1487C2
socleC22×C11#399
prime radicalC23×C11C22⋊Q8
hypercenter#1487D11
hypocenterC11#10662
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
199. C11#10662semidirect

Maximal subgroups

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

subgroupindex
#130695572
#130687902
#130673922
#130673912
#130670452
#130664462
C11×#14872
#1066211