Finite Group Databasebeta

← #15673390

Subgroups — #15673390

Order 2944.

272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×C4×Dic46C211yesmaximal, characteristic
2#13092441C211yesmaximal, characteristic
3C2×#10625006C212yesmaximal
4#13092185C212yesmaximal
5C23×#423C211yesmaximal, characteristic
6C22×Dic46C2211yescharacteristic
7C2×M16×C23C2212yes—
8C2×C42×C23C2211yescharacteristic
9C2×C4⋊Dic23C2211yescharacteristic
10C2×Dic23⋊C4C412yes—
11C2×C4×Dic23C412yes—
12C2×#67267C2212yes—
13C4×Dic46—21no—
14C4×Dic46—21no—
15C4×Dic46—21no—
16C4×Dic46—21no—
17C23×C4⋊C8—21no—
18C23×C4⋊C8—21no—
19#10625006—24no—
20C4⋊(C23⋊C8)—21no—
21C4⋊(C23⋊C8)—21no—
22C22×C4×C23C2×C411yescharacteristic
23C22×C4×C23C2×C411yescharacteristic
24C22×C4×C23C2311yescharacteristic
25C22×Dic23C2×C412yes—
26C22×Dic23C2×C412yes—
27C2×Dic46—21no—
28C2×Dic46—21no—
29C2×Dic46—21no—
30C2×Dic46—21no—
31C2×Dic46D412yes—
32C2×Dic46Q812yes—
33M16×C23—22no—
34M16×C23—22no—
35C2×C8×C23—22no—
36C42×C23D411yescharacteristic
37C42×C23D411yescharacteristic
38C42×C23D411yescharacteristic
39C42×C23D411yescharacteristic
40C4⋊Dic23—21no—
41C4⋊Dic23—21no—
42Dic23⋊C4—22no—
43Dic23⋊C4—22no—
44C4×Dic23—22no—
45C4×Dic23—22no—
46#67267—22no—
47#67267—22no—
48C2×C23⋊C8—22no—
49C23×C23C22×C411yescharacteristic
50C2×C4×C23—22no—
51C2×C4×C23—41no—
52C2×C4×C23C22⋊C411yescharacteristic
53C2×C4×C23C22⋊C411yescharacteristic
54C2×C4×C23C22⋊C411yescharacteristic
55C2×C4×C23C22⋊C411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×Q811yescharacteristic
60C2×C4×C23#4111yescharacteristic
61C2×C4×C23#4111yescharacteristic
62C2×Dic23—22no—
63C2×Dic23—22no—
64C2×Dic23—22no—
65C2×Dic23—42no—
66C2×Dic23C4⋊C414yes—
67Dic46—22no—
68Dic46—22no—
69Dic46—22no—
70Dic46—22no—
71C8×C23—42no—
72C23⋊C8—42no—
73#1801—231nomaximal, Sylow
74C22×C23—21no—
75C22×C23—21no—
76C22×C23C2×C22⋊C411yescharacteristic
77C22×C23C2×C4⋊C411yescharacteristic
78C22×C23#11711yescharacteristic
79C4×C23—21no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23#10112yescomplemented
83C4×C23#12111yescharacteristic
84C4×C23#12111yescharacteristic
85C4×C23C22⋊Q811yescharacteristic
86C4×C23C22⋊Q811yescharacteristic
87Dic23—24no—
88Dic23—42no—
89C2×C4×Q8—231no—
90#423—231no—
91#423D2311yescharacteristic
92C2×#101—232no—
93#343—232no—
94C2×C23—21no—
95C2×C23—21no—
96C2×C23#38011yescharacteristic
97C2×C23C2×#10111yescharacteristic
98C2×C23#41311yescharacteristic
99C22×Q8—231no—
100C2×M16—232no—
101C2×M16C2×D2312yes—
102C4×Q8—461no—
103C4×Q8—461no—
104C4×Q8—461no—
105C4×Q8—461no—
106C2×C4⋊C4—232no—
107C2×C4⋊C4—231no—
108C2×C42—232no—
109C2×C42C2×D2311yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—21no—
112C4⋊C8—461no—
113C4⋊C8—461no—
114#101—464no—
115C23#180111yescharacteristic, complemented, Sylow
116C2×Q8—232no—
117C2×Q8—232no—
118C2×Q8—461no—
119C2×Q8—461no—
120C2×Q8—461no—
121C2×Q8—461no—
122C22×C4—232no—
123C22×C4—232no—
124C22×C4C4×D2311yescharacteristic
125C22×C4C4×D2311yescharacteristic
126C22×C4C22×D2311yescharacteristic
127M16—22no—
128M16—22no—
129M16—462no—
130M16—462no—
131C2×C8—22no—
132C2×C8—462no—
133C4⋊C4—462no—
134C4⋊C4—462no—
135C4⋊C4—461no—
136C4⋊C4—461no—
137C42—462no—
138C42—462no—
139C42D9211yescharacteristic
140C42D9211yescharacteristic
141C42C22⋊D2311yescharacteristic
142C42C22⋊D2311yescharacteristic
143C23C2×C4×D2311yescharacteristic
144Q8—462no—
145Q8—462no—
146Q8—462no—
147Q8—462no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—234no—
151C2×C4—462no—
152C2×C4—462no—
153C2×C4—462no—
154C2×C4—922no—
155C2×C4(C2×D23)⋊C411yescharacteristic
156C2×C4(C2×D23)⋊C411yescharacteristic
157C2×C4(C2×D23)⋊C411yescharacteristic
158C2×C4(C2×D23)⋊C411yescharacteristic
159C2×C4C2×D9211yescharacteristic
160C2×C4D4×D2311yescharacteristic
161C2×C4#6729011yescharacteristic
162C2×C4Q8×D2311yescharacteristic
163C2×C4#6729211yescharacteristic
164C2×C4C2×C22⋊D2311yescharacteristic
165C8—42no—
166C8—922no—
167C22—21no—
168C22—21no—
169C22C4⋊C4×D2311yescharacteristic
170C22#1062506311yescharacteristic
171C22C2×(C2×D23)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—464no—
176C4—922no—
177C4#1062500612yescomplemented
178C4#1062506611yescharacteristic
179C4#1062506811yescharacteristic
180C4#1062510911yescharacteristic
181C4#1062511711yescharacteristic
182C2—21no—
183C2—21no—
184C2#1309227411yescharacteristic
185C2C2×#1062500611yescharacteristic
186C2#1309239911yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutator, prime radicalC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#423C2
socleC22×C23C2×C22⋊C4
cosocleC22×C4×C23C23
hypercenter#423D23
hypocenterC23#1801
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
82. C4×C23#101semidirect
115. C23#1801semidirect
177. C4#10625006semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic462
#130924412
C2×#106250062
#130921852
C23×#4232
#180123