Finite Group Databasebeta

← #15675084

Subgroups — #15675084

Order 2944.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#13092991C211yesmaximal, characteristic
2C2×#10625018C211yesmaximal, characteristic, complemented
3#13092215C212yesmaximal, complemented
4#13092213C212yesmaximal, complemented
5C2×C23×#101C211yesmaximal, characteristic, complemented
6C22×Q8×C23C2211yescharacteristic
7C2×#67288C411yescharacteristic
8C2×M16×C23—21no—
9#10625118C411yescharacteristic
10#10625118C2211yescharacteristic
11#10625117—21no—
12#10625117—21no—
13#10625115C411yescharacteristic
14#10625115C2211yescharacteristic
15#10625100—21no—
16#10625100—21no—
17#10625097C411yescharacteristic
18C2×#67267—21no—
19C23×#101—21no—
20C23×#101C2212yes—
21#10625018—21no—
22#10625018C2212yes—
23C2×Q8×C23—41no—
24C2×Q8×C23—41no—
25C2×Q8×C23C2×C411yescharacteristic
26C2×Q8×C23D411yescharacteristic
27C2×Q8×C23D411yescharacteristic
28C2×Q8×C23C2311yescharacteristic
29C22×C4×C23C2×C411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23D411yescharacteristic
32C2×C22⋊D23—21no—
33#67288—41no—
34#67288—41no—
35C2×D92C2×C411yescharacteristic
36C2×C4×D23—21no—
37C2×Dic46C2×C411yescharacteristic
38M16×C23—22no—
39M16×C23—41no—
40C2×C8×C23—41no—
41C22⋊Dic23—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45(C2×D23)⋊C4—21no—
46C4⋊Dic23—21no—
47Dic23⋊C4—21no—
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51C4×Dic23C2×C411yescharacteristic
52C4×Dic23C2×C411yescharacteristic
53#67267—22no—
54#67267—41no—
55C2×C23⋊C8—41no—
56C23×C23C22⋊C411yescharacteristic
57C22×D23—21no—
58Q8×C23—41no—
59Q8×C23—41no—
60Q8×C23—41no—
61Q8×C23—41no—
62C2×C4×C23—21no—
63C2×C4×C23—21no—
64C2×C4×C23—21no—
65C2×C4×C23—21no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23C22⋊C411yescharacteristic
69C2×C4×C23C22⋊C411yescharacteristic
70C2×C4×C23C22⋊C411yescharacteristic
71C2×C4×C23C22×C411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2×D411yescharacteristic
74C22⋊D23—41no—
75C22⋊D23—41no—
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79D92—41no—
80C4×D23—42no—
81Dic46—41no—
82C8×C23—42no—
83C23⋊C8—42no—
84#2133—231nomaximal, Sylow
85C22×C23—41no—
86C22×C23#9911yescharacteristic
87C22×C23#9911yescharacteristic
88C22×C23C2×C22⋊C411yescharacteristic
89C2×D23—42no—
90C2×D23—41no—
91C4×C23—21no—
92C4×C23—21no—
93C4×C23—21no—
94C4×C23—21no—
95C4×C23—21no—
96C4×C23—21no—
97Dic23—41no—
98Dic23—41no—
99Dic23—41no—
100#536—231no—
101C2×#101—231no—
102C2×#101D2311yescharacteristic, complemented
103#356—232no—
104#355—232no—
105C2×C23—21no—
106C2×C23—21no—
107C2×C23—21no—
108C2×C23C2×#9911yescharacteristic
109D23—81no—
110C2×#41—231no—
111C22×Q8C2×D2311yescharacteristic
112C2×M16—21no—
113C2×M16—461no—
114C4⋊Q8—231no—
115C4⋊Q8—231no—
116#124—231no—
117#124—231no—
118#123—461no—
119#123—461no—
120C22⋊Q8—461no—
121C22⋊Q8—461no—
122#117—231no—
123#101—21no—
124#101—232no—
125#101—461no—
126#101C2×D2312yes—
127C23#213311yescharacteristic, complemented, Sylow
128#41—921no—
129#41—921no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—231no—
133C2×Q8C4×D2311yescharacteristic
134C2×Q8D9211yescharacteristic
135C2×Q8C22⋊D2311yescharacteristic
136C2×Q8C22×D2311yescharacteristic
137C2×D4—231no—
138C2×D4—461no—
139C22×C4—461no—
140C22×C4C4×D2311yescharacteristic
141C22×C4D9211yescharacteristic
142C22×C4C22⋊D2311yescharacteristic
143M16—22no—
144M16—41no—
145M16—462no—
146M16—921no—
147C2×C8—41no—
148C2×C8—921no—
149C4⋊C4—461no—
150C4⋊C4—461no—
151C4⋊C4—461no—
152C4⋊C4—461no—
153C4⋊C4—461no—
154C22⋊C4—461no—
155C22⋊C4—461no—
156C22⋊C4—461no—
157C22⋊C4—461no—
158C22⋊C4—461no—
159C42—231no—
160C42—231no—
161C23—461no—
162C23(C2×D23)⋊C411yescharacteristic
163Q8—41no—
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—921no—
168D4—921no—
169D4—921no—
170D4—921no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—461no—
178C2×C4—461no—
179C2×C4—461no—
180C2×C4—922no—
181C2×C4(C2×D23)⋊C411yescharacteristic
182C2×C4(C2×D23)⋊C411yescharacteristic
183C2×C4(C2×D23)⋊C411yescharacteristic
184C2×C4C2×C4×D2311yescharacteristic
185C2×C4C2×D9211yescharacteristic
186C2×C4C2×C22⋊D2311yescharacteristic
187C8—42no—
188C8—922no—
189C22—41no—
190C22—922no—
191C22—921no—
192C22#1062498811yescharacteristic
193C22#1062498811yescharacteristic
194C22C2×(C2×D23)⋊C411yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—21no—
199C4—21no—
200C4—21no—
201C4—921no—
202C4—921no—
203C4—921no—
204C2—21no—
205C2—21no—
206C2—21no—
207C2—1841no—
208C2C2×#1062498811yescharacteristic
subgroupG/H
centerC2C2×#10624988
commutatorC2×C4×C23C22×C4
FrattiniC2×Q8C22×D23
FittingC2×C23×#101C2
socleC2×C23C2×#99
prime radicalC2×#67288C4
cosocleC2×Q8×C23C23
hypercenterC2×#101D23
hypocenterC23#2133
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#10625018C2semidirect
3. #13092215C2semidirect
4. #13092213C2semidirect
5. C2×C23×#101C2semidirect
102. C2×#101D23semidirect
127. C23#2133semidirect

Maximal subgroups

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

subgroupindex
#130929912
C2×#106250182
#130922152
#130922132
C2×C23×#1012
#213323