Finite Group Databasebeta

← #14658524

Subgroups — #14658524

Order 2816.

350 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 119 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#13069552C211yesmaximal, characteristic
2#13068744C211yesmaximal, characteristic
3#13068622C212yesmaximal
4#13066500C212yesmaximal
5C11×#1277C211yesmaximal, characteristic
6C2×C4×Dic22C2211yescharacteristic
7C2×C11×C4⋊C8C2212yes—
8C2×C4×C8×C11C2211yescharacteristic
9C2×#66880—22no—
10#10622548C2212yes—
11C2×C4⋊(C11⋊C8)C2211yescharacteristic
12#10622189—22no—
13#10622189—22no—
14#10622188—22no—
15C22×Dic22D411yescharacteristic
16C22×C8×C11—22no—
17C22×C8×C11D412yes—
18C2×C42×C11C2311yescharacteristic
19C2×C4⋊Dic11—22no—
20C2×C4⋊Dic11—22no—
21C2×C4⋊Dic11—22no—
22C2×C4⋊Dic11D411yescharacteristic
23C2×Dic11⋊C4—21no—
24C2×C4×Dic11—21no—
25C22×C11⋊C8—21no—
26C4×Dic22—22no—
27C4×Dic22—22no—
28C11×C4⋊C8—22no—
29C11×C4⋊C8—22no—
30C4×C8×C11—22no—
31#66880—44no—
32C4⋊(C11⋊C8)—22no—
33#10624—111nomaximal, Sylow
34C22×C4×C11C2×D411yescharacteristic
35C22×C4×C11C2×D411yescharacteristic
36C22×C4×C11#4111yescharacteristic
37C22×Dic11—21no—
38C22×Dic11—21no—
39C22×Dic11—42no—
40C2×Dic22—22no—
41C2×Dic22—21no—
42C2×Dic22—22no—
43C2×Dic22Q1612yes—
44C2×C8×C11—22no—
45C2×C8×C11—22no—
46C2×C8×C11—22no—
47C2×C8×C11—42no—
48C2×C8×C11—42no—
49C2×C8×C11—42no—
50C42×C11#4112yes—
51C42×C11#4112yes—
52C4⋊Dic11—22no—
53C4⋊Dic11—42no—
54C4⋊Dic11—42no—
55C4⋊Dic11—42no—
56C4⋊Dic11—42no—
57C4⋊Dic11—82no—
58Dic11⋊C4—42no—
59C4×Dic11—41no—
60C4×Dic11—41no—
61C2×C11⋊C8—41no—
62C2×C11⋊C8—42no—
63#1984—111no—
64#1834—111no—
65#1803—112no—
66#1296—112no—
67#1277D1111yescharacteristic
68C23×C11#12111yescharacteristic
69C2×C4×C11—22no—
70C2×C4×C11#12312yes—
71C2×C4×C11#12311yescharacteristic
72C2×C4×C11#12411yescharacteristic
73C2×C4×C11#12612yes—
74C2×C4×C11C2×Q1611yescharacteristic
75C2×C4×C11#13512yes—
76C2×C4×C11#13511yescharacteristic
77C2×C4×C11AGL(1,ℤ/8)12yes—
78C2×C4×C11#13712yes—
79C2×Dic11—22no—
80C2×Dic11—41no—
81C2×Dic11—41no—
82C2×Dic11—41no—
83C2×Dic11—42no—
84C2×Dic11—82no—
85C2×Dic11—82no—
86C2×Dic11—82no—
87Dic22—24no—
88Dic22—42no—
89C8×C11—42no—
90C8×C11—82no—
91C11⋊C8—81no—
92C2×C4×Q8—111no—
93C2×C4⋊C8—111no—
94C2×C4⋊C8C2×D1112yes—
95C2×#103—222no—
96C2×C4×C8C2×D1111yescharacteristic
97#384—112no—
98#340—222no—
99#340—222no—
100#336—222no—
101C22×C11#39711yescharacteristic
102C22×C11#46412yes—
103C22×C11#46711yescharacteristic
104C22×C11#46911yescharacteristic
105C22×C11#47112yes—
106C4×C11—22no—
107C4×C11#48212yes—
108C4×C11#48412yes—
109C4×C11#48512yes—
110C4×C11#48811yescharacteristic
111C4×C11#49111yescharacteristic
112Dic11—42no—
113Dic11—81no—
114Dic11—162no—
115C22×Q8—111no—
116C22×C8—22no—
117C22×C8—221no—
118C22×C8D4412yes—
119C4×Q8—222no—
120C4×Q8—222no—
121C2×C4⋊C4—111no—
122C2×C4⋊C4—221no—
123C2×C4⋊C4—222no—
124C2×C4⋊C4—222no—
125C2×C4⋊C4—222no—
126C2×C42—221no—
127C2×C42C22×D1111yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—22no—
130C4⋊C8—222no—
131#103—444no—
132C4×C8—22no—
133C2×C11#168412yes—
134C2×C11#170212yes—
135C2×C11#207411yescharacteristic
136C2×C11#207611yescharacteristic
137C2×C11#207911yescharacteristic
138C2×Q8—112no—
139C2×Q8—221no—
140C2×Q8—222no—
141C2×Q8—222no—
142C22×C4—221no—
143C22×C4—221no—
144C22×C4—442no—
145C22×C4C2×D4411yescharacteristic
146C22×C4D4×D1111yescharacteristic
147C22×C4#434311yescharacteristic
148C2×C8—22no—
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—42no—
154C2×C8—441no—
155C2×C8—442no—
156C4⋊C4—222no—
157C4⋊C4—442no—
158C4⋊C4—442no—
159C4⋊C4—442no—
160C4⋊C4—442no—
161C4⋊C4—442no—
162C4⋊C4—882no—
163C42—441no—
164C42—441no—
165C42#433912yes—
166C42#434112yes—
167C11#1062411yescharacteristic, complemented, Sylow
168C23#6694811yescharacteristic
169Q8—224no—
170Q8—442no—
171C2×C4—22no—
172C2×C4—222no—
173C2×C4—441no—
174C2×C4—441no—
175C2×C4—442no—
176C2×C4—441no—
177C2×C4—882no—
178C2×C4—882no—
179C2×C4—882no—
180C2×C4#6692811yescharacteristic
181C2×C4#6693612yes—
182C2×C4#6693911yescharacteristic
183C2×C4#6695112yes—
184C2×C4#6695712yes—
185C2×C4#6696212yes—
186C2×C4#6696511yescharacteristic
187C2×C4#6696712yes—
188C2×C4Q16×D1111yescharacteristic
189C8—42no—
190C8—82no—
191C8—881no—
192C22#1062228711yescharacteristic
193C22#1062245812yes—
194C22#1062247811yescharacteristic
195C22#1062250011yescharacteristic
196C22#1062251112yes—
197C4—22no—
198C4—442no—
199C4—881no—
200C4—1762no—
201C4#1062231011yescharacteristic
202C4#1062231611yescharacteristic
203C4#1062233612yes—
204C4#1062239712yes—
205C4#1062242212yes—
206C2#1306807512yes—
207C2#1306818512yes—
208C2#1307003611yescharacteristic
209C2#1307004611yescharacteristic
210C2#1307006311yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socle, prime radicalC23×C11#121
hypercenter#1277D11
hypocenterC11#10624
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
167. C11#10624semidirect

Maximal subgroups

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

subgroupindex
#130695522
#130687442
#130686222
#130665002
C11×#12772
#1062411