Finite Group Databasebeta

← #15671834

Subgroups — #15671834

Order 2944.

266 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C4×#67288C211yesmaximal, characteristic
2C4×#67267C211yesmaximal, characteristic, complemented
3#13092147C212yesmaximal, complemented
4#13092144C212yesmaximal, complemented
5C23×#423C211yesmaximal, characteristic, complemented
6C2×#67288C411yescharacteristic
7C2×M16×C23—21no—
8C2×C42×C23C2211yescharacteristic
9C4×C22⋊D23—21no—
10C4×C22⋊D23—21no—
11#10625097C411yescharacteristic
12C2×#67267—21no—
13C4×D92C411yescharacteristic
14C4×D92C2211yescharacteristic
15#10625043—21no—
16C42×D23—21no—
17C4×Dic46C411yescharacteristic
18C4×Dic46C2211yescharacteristic
19C23×C4⋊C8—21no—
20C23×C4⋊C8C2212yes—
21#10624985—21no—
22C4×C23⋊C8C2212yes—
23C22×C4×C23C2×C411yescharacteristic
24C22×C4×C23D411yescharacteristic
25C22×C4×C23D411yescharacteristic
26C2×C22⋊D23—21no—
27#67288—22no—
28#67288—22no—
29C2×D92C2×C411yescharacteristic
30C2×C4×D23—21no—
31C2×C4×D23—21no—
32C2×C4×D23—21no—
33C2×Dic46C2×C411yescharacteristic
34M16×C23—42no—
35C2×C8×C23—22no—
36C42×C23C2×C411yescharacteristic
37C42×C23D411yescharacteristic
38C42×C23D411yescharacteristic
39C42×C23C2311yescharacteristic
40C22⋊Dic23—21no—
41(C2×D23)⋊C4—21no—
42(C2×D23)⋊C4—21no—
43C4⋊Dic23C2×C411yescharacteristic
44C4⋊Dic23C2×C411yescharacteristic
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47C4×Dic23—21no—
48C4×Dic23—21no—
49C4×Dic23—21no—
50#67267—24no—
51C2×C23⋊C8—22no—
52C23×C23C22⋊C411yescharacteristic
53C22×D23—21no—
54C2×C4×C23—22no—
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23C22⋊C411yescharacteristic
60C2×C4×C23C22⋊C411yescharacteristic
61C2×C4×C23C22⋊C411yescharacteristic
62C2×C4×C23C22×C411yescharacteristic
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C22⋊D23—24no—
66C2×Dic23—21no—
67C2×Dic23—21no—
68C2×Dic23—21no—
69D92—21no—
70D92M1612yescomplemented
71C4×D23—24no—
72C4×D23—42no—
73C4×D23—41no—
74C4×D23—41no—
75Dic46—21no—
76Dic46M1612yescomplemented
77C8×C23—42no—
78C23⋊C8—24no—
79#1489—231nomaximal, Sylow
80C22×C23—21no—
81C22×C23—21no—
82C22×C23—21no—
83C22×C23C2×C22⋊C411yescharacteristic
84C2×D23—22no—
85C2×D23—41no—
86C2×D23—41no—
87C4×C23—21no—
88C4×C23—21no—
89C4×C23—21no—
90C4×C23#10412yes—
91C4×C23C2×M1611yescharacteristic
92C4×C23C2×M1611yescharacteristic
93C4×C23AGL(1,ℤ/8)11yescharacteristic
94C4×C23#13711yescharacteristic
95Dic23—22no—
96Dic23—41no—
97Dic23—41no—
98C4×#41—231no—
99#423D2311yescharacteristic, complemented
100C4×M16—231no—
101Q8⋊C8—232no—
102D4⋊C8—232no—
103C2×C23—41no—
104C2×C23#40711yescharacteristic
105C2×C23#41711yescharacteristic
106C2×C23C2×#10411yescharacteristic
107D23—42no—
108C2×#41—231no—
109C2×M16—21no—
110C2×M16—461no—
111C4×Q8—231no—
112C4×Q8—231no—
113C4×D4—231no—
114C4×D4—231no—
115C4×D4—461no—
116C4×D4—461no—
117#117—231no—
118#117—461no—
119C2×C42—461no—
120C2×C42C2×D2311yescharacteristic
121C4⋊C8—21no—
122C4⋊C8C2×D2312yes—
123#97—461no—
124C4×C8—232no—
125C23#148911yescharacteristic, complemented, Sylow
126#41—462no—
127#41—462no—
128C2×Q8—231no—
129C2×D4—231no—
130C2×D4—461no—
131C22×C4—461no—
132C22×C4—461no—
133C22×C4—461no—
134C22×C4C4×D2311yescharacteristic
135C22×C4D9211yescharacteristic
136C22×C4C22⋊D2311yescharacteristic
137M16—42no—
138M16—464no—
139C2×C8—22no—
140C2×C8—462no—
141C4⋊C4—231no—
142C4⋊C4—231no—
143C4⋊C4—461no—
144C4⋊C4—461no—
145C22⋊C4—461no—
146C22⋊C4—461no—
147C22⋊C4—461no—
148C42—461no—
149C42—461no—
150C42—461no—
151C42C4×D2311yescharacteristic
152C42D9211yescharacteristic
153C42C22⋊D2311yescharacteristic
154C42C22×D2311yescharacteristic
155C23—461no—
156C23(C2×D23)⋊C411yescharacteristic
157Q8—232no—
158Q8—461no—
159D4—232no—
160D4—464no—
161D4—461no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—464no—
168C2×C4—461no—
169C2×C4—461no—
170C2×C4—461no—
171C2×C4—921no—
172C2×C4—921no—
173C2×C4—922no—
174C2×C4(C2×D23)⋊C411yescharacteristic
175C2×C4(C2×D23)⋊C411yescharacteristic
176C2×C4(C2×D23)⋊C411yescharacteristic
177C2×C4C2×C4×D2311yescharacteristic
178C2×C4C2×D9211yescharacteristic
179C2×C4C2×C22⋊D2311yescharacteristic
180C8—42no—
181C8—464no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—462no—
186C22—921no—
187C22—921no—
188C22C2×(C2×D23)⋊C411yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—462no—
193C4—921no—
194C4—921no—
195C4#1062500712yes—
196C4M16×D2311yescharacteristic
197C4M16×D2311yescharacteristic
198C4#1062510311yescharacteristic
199C4#1062511311yescharacteristic
200C2—41no—
201C2—922no—
202C2#1309238011yescharacteristic
203C2#1309241611yescharacteristic
204C2C2×#1062500711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#423C2
socleC22×C23C2×C22⋊C4
prime radicalC2×#67288C4
cosocleC42×C23C23
hypercenter#423D23
hypocenterC23#1489
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C4×#67267C2semidirect
3. #13092147C2semidirect
4. #13092144C2semidirect
5. C23×#423C2semidirect
70. D92M16semidirect
76. Dic46M16semidirect
99. #423D23semidirect
125. C23#1489semidirect

Maximal subgroups

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

subgroupindex
C4×#672882
C4×#672672
#130921472
#130921442
C23×#4232
#148923