Finite Group Databasebeta

← D23×#354 #15675056

Subgroups — D23×#354 #15675056

Order 2944.

284 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D23C211yesmaximal, characteristic
2#99×D23C212yesmaximal
3#13092212C211yesmaximal, characteristic, complemented
4#13092211C212yesmaximal, complemented
5C23×#354C211yesmaximal, characteristic, complemented
6C2×Q8×D23C411yescharacteristic, complemented
7C2×D4×D23C2211yescharacteristic
8C23×#124C2211yescharacteristic
9#10625118C411yescharacteristic, complemented
10#10625107C2211yescharacteristic
11#10625056—22no—
12C22⋊C4×D23—22no—
13C22⋊C4×D23—22no—
14#10625046C411yescharacteristic, complemented
15C42×D23C411yescharacteristic, complemented
16C23×#99C2212yes—
17#10625016C2212yes—
18#10624988—22no—
19C23×D23D412yes—
20C2×Q8×C23C2×C411yescharacteristic, complemented
21C2×D4×C23C2311yescharacteristic
22C2×C22⋊D23D412yes—
23Q8×D23—41no—
24Q8×D23—41no—
25D4×D23—41no—
26D4×D23—41no—
27C2×D92C2×C411yescharacteristic
28C2×C4×D23—21no—
29C2×C4×D23—21no—
30C2×C4×D23—42no—
31C2×C4×D23C2×C411yescharacteristic
32C2×Dic46—21no—
33C2×Dic46C2×C411yescharacteristic, complemented
34C22⋊C4×C23—22no—
35C22⋊C4×C23—22no—
36C42×C23C2×C411yescharacteristic, complemented
37C22⋊Dic23—22no—
38C22⋊Dic23—22no—
39(C2×D23)⋊C4—22no—
40(C2×D23)⋊C4—22no—
41(C2×D23)⋊C4—42no—
42C4×Dic23—21no—
43C4×Dic23C2×C411yescharacteristic, complemented
44C23×C23C2×D412yes—
45C22×D23—22no—
46C22×D23—22no—
47C22×D23—44no—
48C22×D23C22⋊C411yescharacteristic
49C22×D23C22⋊C412yes—
50Q8×C23—41no—
51D4×C23—41no—
52C2×C4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23—42no—
55C2×C4×C23C22×C411yescharacteristic
56C22⋊D23—42no—
57C2×Dic23—21no—
58C2×Dic23—21no—
59C2×Dic23—42no—
60C2×Dic23C22⋊C411yescharacteristic
61D92—41no—
62C4×D23—21no—
63C4×D23—21no—
64C4×D23—42no—
65C4×D23—41no—
66C4×D23—41no—
67C4×D23—84no—
68Dic46—42no—
69Dic46—41no—
70C2×#354—231nomaximal, Sylow
71C22×C23—22no—
72C22×C23—42no—
73C22×C23C2×C22⋊C411yescharacteristic
74C2×D23—22no—
75C2×D23—22no—
76C2×D23—44no—
77C2×D23—42no—
78C2×D23—82no—
79C2×D23#9911yescharacteristic
80C2×D23#9911yescharacteristic
81C4×C23—21no—
82C4×C23—41no—
83C4×C23—41no—
84C4×C23—82no—
85Dic23—21no—
86Dic23—41no—
87Dic23—41no—
88Dic23—82no—
89C2×#124—231no—
90C2×#99—232no—
91#354—231no—
92#354—232no—
93#354D2311yescharacteristic, direct product factor
94C2×C23—21no—
95C2×C23—42no—
96C2×C23C2×#9911yescharacteristic
97D23—21no—
98D23—42no—
99D23#35412yesdirect product factor
100C22×Q8—231no—
101C22×D4—231no—
102#124—231no—
103#124—231no—
104#124—231no—
105#124—462no—
106#124C2×D2311yescharacteristic
107C2×C22⋊C4—462no—
108C2×C22⋊C4—462no—
109C2×C42—231no—
110#99—232no—
111#99—462no—
112#99C2×D2312yes—
113C23C2×#35411yescharacteristic, complemented, Sylow
114C24—232no—
115C2×Q8—231no—
116C2×Q8—461no—
117C2×Q8—921no—
118C2×Q8—921no—
119C2×Q8C4×D2311yescharacteristic, complemented
120C2×D4—232no—
121C2×D4—231no—
122C2×D4—921no—
123C2×D4—921no—
124C2×D4C22×D2311yescharacteristic
125C22×C4—231no—
126C22×C4—461no—
127C22×C4—461no—
128C22×C4—922no—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—462no—
132C22⋊C4—462no—
133C22⋊C4—462no—
134C22⋊C4—462no—
135C22⋊C4—922no—
136C42—231no—
137C42—461no—
138C42C4×D2311yescharacteristic, complemented
139C23—231no—
140C23—232no—
141C23—462no—
142C23—462no—
143C23—924no—
144C23D4×D2312yes—
145Q8—41no—
146Q8—921no—
147Q8—922no—
148D4—41no—
149D4—921no—
150D4—922no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—231no—
155C2×C4—461no—
156C2×C4—461no—
157C2×C4—461no—
158C2×C4—461no—
159C2×C4—921no—
160C2×C4—921no—
161C2×C4—922no—
162C2×C4—922no—
163C2×C4—1844no—
164C2×C4C2×C4×D2311yescharacteristic
165C22—22no—
166C22—42no—
167C22—231no—
168C22—231no—
169C22—462no—
170C22—462no—
171C22—922no—
172C22—924no—
173C22—1842no—
174C22C22⋊C4×D2311yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—461no—
180C4—921no—
181C4—921no—
182C4—1842no—
183C2—21no—
184C2—42no—
185C2—232no—
186C2—461no—
187C2—922no—
188C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC2×C4×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#354C2
socleC2×C23C2×#99
prime radicalC2×D4×D23C22
cosocleC2×D4×C23C23
hypercenter#354D23
hypocenterC23C2×#354
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #13092212C2semidirect
4. #13092211C2semidirect
5. C23×#354C2semidirect
6. C2×Q8×D23C4semidirect
9. #10625118C4semidirect
14. #10625046C4semidirect
15. C42×D23C4semidirect
20. C2×Q8×C23C2×C4semidirect
33. C2×Dic46C2×C4semidirect
36. C42×C23C2×C4semidirect
43. C4×Dic23C2×C4semidirect
93. #354D23direct (N × H)
99. D23#354direct (N × H)
113. C23C2×#354semidirect
119. C2×Q8C4×D23semidirect
138. C42C4×D23semidirect

Maximal subgroups

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

subgroupindex
#124×D232
#99×D232
#130922122
#130922112
C23×#3542
C2×#35423