Finite Group Databasebeta

← #14668051

Subgroups — #14668051

Order 2816.

212 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 63 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#13070868C211yesmaximal, characteristic
2#13070521C211yesmaximal, characteristic
3#13067987C211yesmaximal, characteristic
4#13067983C211yesmaximal, characteristic
5#13066689C211yesmaximal, characteristic
6#13066666C211yesmaximal, characteristic
7C11×#1362C211yesmaximal, characteristic
8C11×#494C2211yescharacteristic
9C2×#66893—21no—
10C2×#66893—21no—
11#10622707—21no—
12#10622464—21no—
13#10622312C2211yescharacteristic
14C8×Dic22C2211yescharacteristic
15C11×C4⋊C16C2211yescharacteristic
16C11×#335C2211yescharacteristic
17#10622185—21no—
18#10622140—21no—
19Dic11⋊C16—21no—
20#10622124—21no—
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C11×C4⋊Q8—21no—
26C2×Dic44—21no—
27C2×Dic44—21no—
28#66922—21no—
29C4×Dic22D411yescharacteristic
30C2×C11×C16—21no—
31C11×C4⋊C8—21no—
32C4×C8×C11C2311yescharacteristic
33#66893—42no—
34#66893—42no—
35#66881—41no—
36#66880—41no—
37Dic11⋊C8—21no—
38C8×Dic11—21no—
39C2×C11⋊C16D411yescharacteristic
40C2×C11⋊C16D411yescharacteristic
41#66874—41no—
42#66872—41no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)D411yescharacteristic
45#12443—111nomaximal, Sylow
46C2×Q8×C11—41no—
47C2×Dic22—41no—
48C2×Dic22D811yescharacteristic
49C11×Q16—41no—
50C11×Q16—41no—
51C11×Q16—81no—
52C2×C8×C11—41no—
53C2×C8×C11C2×D411yescharacteristic
54C2×C8×C11#4111yescharacteristic
55C11×C4⋊C4—41no—
56C11×C4⋊C4—41no—
57C42×C11C2×D411yescharacteristic
58C4⋊Dic11—41no—
59C4⋊Dic11—41no—
60C4⋊Dic11D811yescharacteristic
61Dic11⋊C4—21no—
62C4×Dic11—21no—
63C2×C11⋊C8—21no—
64C2×C11⋊C8—41no—
65Dic44—41no—
66Dic44—41no—
67Dic44—81no—
68C11×C16—41no—
69C11⋊C16—21no—
70C11⋊C16SD1612yes—
71#2247—111no—
72#2183—111no—
73#1670—111no—
74#1670—111no—
75#1372—111no—
76#1362—111no—
77#1362D1111yescharacteristic
78Q8×C11—81no—
79Q8×C11—81no—
80C2×C4×C11—81no—
81C2×C4×C11#12111yescharacteristic
82C2×C4×C11C2×D811yescharacteristic
83C2×C4×C11#13511yescharacteristic
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—81no—
87Dic22—21no—
88Dic22—21no—
89Dic22—81no—
90Dic22—81no—
91C8×C11—21no—
92C8×C11—81no—
93C8×C11C2×SD1611yescharacteristic
94C8×C11AGL(1,ℤ/8)11yescharacteristic
95C11⋊C8—41no—
96C11⋊C8—81no—
97C2×Q32—221no—
98C2×Q32—221no—
99#494—111no—
100#494C2×D1111yescharacteristic
101#475—221no—
102#475—221no—
103C8×Q8—111no—
104C4⋊C16—221no—
105C4⋊C16C2×D1111yescharacteristic
106#346—221no—
107C4×C16—111no—
108#335—111no—
109#335C2×D1111yescharacteristic
110#332—221no—
111#332—221no—
112C22×C11#46611yescharacteristic
113C4×C11—21no—
114C4×C11—161no—
115C4×C11#46011yescharacteristic
116C4×C11#47211yescharacteristic
117C4×C11#51011yescharacteristic
118C4×C11#51011yescharacteristic
119Dic11—41no—
120Dic11—41no—
121Dic11—161no—
122C2×Q16—21no—
123C2×Q16—21no—
124C2×Q16—221no—
125C2×Q16—221no—
126C4⋊Q8—21no—
127C4⋊Q8—221no—
128C4×Q8—111no—
129Q32—442no—
130Q32—442no—
131C2×C16—21no—
132C2×C16—111no—
133C2×C16—111no—
134#106—441no—
135#106—441no—
136C4⋊C8—21no—
137C4⋊C8—111no—
138C4⋊C8—221no—
139C4⋊C8—221no—
140#103—441no—
141#103—441no—
142C4×C8—221no—
143C4×C8C22×D1111yescharacteristic
144C2×C11#166811yescharacteristic
145C2×C11#221911yescharacteristic
146C2×C11#222211yescharacteristic
147C2×Q8—41no—
148C2×Q8—111no—
149C2×Q8—441no—
150Q16—41no—
151Q16—41no—
152Q16—81no—
153Q16—441no—
154Q16—441no—
155Q16—881no—
156C2×C8—41no—
157C2×C8—221no—
158C2×C8—441no—
159C2×C8#433911yescharacteristic
160C2×C8D4×D1111yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—111no—
164C4⋊C4—221no—
165C4⋊C4—441no—
166C4⋊C4—441no—
167C42—221no—
168C42D4×D1111yescharacteristic
169C16—41no—
170C16—112no—
171C16—221no—
172C11#1244311yescharacteristic, complemented, Sylow
173Q8—81no—
174Q8—81no—
175Q8—221no—
176Q8—221no—
177Q8—881no—
178Q8—881no—
179C2×C4—81no—
180C2×C4—221no—
181C2×C4—221no—
182C2×C4—881no—
183C2×C4#6693711yescharacteristic
184C2×C4D8×D1111yescharacteristic
185C2×C4#6696911yescharacteristic
186C8—21no—
187C8—81no—
188C8—441no—
189C8—881no—
190C8#6696411yescharacteristic
191C8SD16×D1111yescharacteristic
192C22#1062238811yescharacteristic
193C4—21no—
194C4—161no—
195C4—441no—
196C4—441no—
197C4—1761no—
198C4#1062236211yescharacteristic
199C4#1062237511yescharacteristic
200C4#1062252811yescharacteristic
201C4#1062253111yescharacteristic
202C2#1306797511yescharacteristic
203C2#1307072311yescharacteristic
204C2#1307074011yescharacteristic
subgroupG/H
centerC22#10622388
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1362C2
socle, prime radicalC22×C11#466
hypercenter#1362D11
hypocenterC11#12443
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
172. C11#12443semidirect

Maximal subgroups

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

subgroupindex
#130708682
#130705212
#130679872
#130679832
#130666892
#130666662
C11×#13622
#1244311