Finite Group Databasebeta

← #15675065

Subgroups — #15675065

Order 2944.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#13092985C211yesmaximal, characteristic
2#99×D23C212yesmaximal, complemented
3#13092212C211yesmaximal, characteristic, complemented
4#13092209C212yesmaximal, complemented
5C23×#354C211yesmaximal, characteristic, complemented
6C2×#67292C411yescharacteristic, complemented
7C2×D4×D23C2211yescharacteristic
8C23×#124C2211yescharacteristic
9#10625118C411yescharacteristic, complemented
10#10625111C2211yescharacteristic
11#10625055—22no—
12#10625053—22no—
13C22⋊C4×D23—22no—
14#10625045C411yescharacteristic, complemented
15#10625043C411yescharacteristic, complemented
16C23×#99C2212yes—
17#10625016C2212yes—
18#10624988—22no—
19C23×D23D412yes—
20C2×Q8×C23C2×C411yescharacteristic, complemented
21C2×D4×C23C2311yescharacteristic
22C2×C22⋊D23—22no—
23C2×C22⋊D23D412yes—
24#67292—42no—
25D4×D23—42no—
26C2×D92—21no—
27C2×D92—22no—
28C2×D92C2×C411yescharacteristic
29C2×D92C2×C411yescharacteristic, complemented
30C2×C4×D23—21no—
31C2×C4×D23—42no—
32C2×C4×D23C2×C411yescharacteristic
33C22⋊C4×C23—22no—
34C22⋊C4×C23—22no—
35C42×C23C2×C411yescharacteristic, complemented
36C22⋊Dic23—22no—
37(C2×D23)⋊C4—21no—
38(C2×D23)⋊C4—22no—
39(C2×D23)⋊C4—42no—
40Dic23⋊C4—21no—
41C4×Dic23C2×C411yescharacteristic, complemented
42C23×C23C2×D412yes—
43C22×D23—22no—
44C22×D23—22no—
45C22×D23—21no—
46C22×D23—82no—
47C22×D23C22⋊C412yes—
48C22×D23C22⋊C411yescharacteristic
49Q8×C23—41no—
50D4×C23—41no—
51C2×C4×C23—21no—
52C2×C4×C23—21no—
53C2×C4×C23—42no—
54C2×C4×C23C22×C411yescharacteristic
55C22⋊D23—42no—
56C22⋊D23—82no—
57C2×Dic23—21no—
58C2×Dic23—42no—
59C2×Dic23C22⋊C411yescharacteristic
60D92—41no—
61D92—41no—
62D92—42no—
63D92—82no—
64C4×D23—22no—
65C4×D23—42no—
66C4×D23—84no—
67#2127—231nomaximal, Sylow
68C22×C23—22no—
69C22×C23—42no—
70C22×C23C2×C22⋊C411yescharacteristic
71C2×D23—22no—
72C2×D23—41no—
73C2×D23—44no—
74C2×D23—42no—
75C2×D23—42no—
76C2×D23—41no—
77C2×D23—82no—
78C2×D23#9912yes—
79C4×C23—21no—
80C4×C23—41no—
81C4×C23—41no—
82C4×C23—82no—
83Dic23—21no—
84Dic23—41no—
85Dic23—82no—
86#535—231no—
87C2×#99—232no—
88#354—231no—
89#354D2311yescharacteristic, complemented
90#353—232no—
91C2×C23—21no—
92C2×C23—42no—
93C2×C23C2×#9911yescharacteristic
94D23—22no—
95D23—42no—
96D23—81no—
97C2×#41—231no—
98C22×D4—231no—
99#127—231no—
100#127—231no—
101#124—231no—
102#124C2×D2311yescharacteristic
103#121—462no—
104#120—462no—
105#117—231no—
106C2×C22⋊C4—462no—
107#99—232no—
108#99—462no—
109#99C2×D2312yes—
110C23#212711yescharacteristic, complemented, Sylow
111C24—232no—
112#41—922no—
113C2×Q8C4×D2311yescharacteristic, complemented
114C2×D4—232no—
115C2×D4—231no—
116C2×D4—231no—
117C2×D4—461no—
118C2×D4—462no—
119C2×D4—462no—
120C2×D4—922no—
121C2×D4C22×D2311yescharacteristic
122C22×C4—231no—
123C22×C4—461no—
124C22×C4—922no—
125C4⋊C4—461no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—461no—
129C22⋊C4—462no—
130C22⋊C4—462no—
131C22⋊C4—922no—
132C42—231no—
133C42C4×D2311yescharacteristic, complemented
134C23—231no—
135C23—232no—
136C23—462no—
137C23—462no—
138C23—461no—
139C23—1842no—
140C23D4×D2312yes—
141Q8—41no—
142D4—41no—
143D4—921no—
144D4—921no—
145D4—922no—
146D4—922no—
147D4—1842no—
148D4—1842no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—231no—
153C2×C4—462no—
154C2×C4—461no—
155C2×C4—922no—
156C2×C4—922no—
157C2×C4—1844no—
158C2×C4C2×C4×D2311yescharacteristic
159C22—22no—
160C22—42no—
161C22—232no—
162C22—462no—
163C22—921no—
164C22—922no—
165C22—922no—
166C22—924no—
167C22—921no—
168C22—1842no—
169C22C22⋊C4×D2311yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—461no—
175C4—921no—
176C4—1842no—
177C2—21no—
178C2—42no—
179C2—462no—
180C2—922no—
181C2—1841no—
182C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC2×C4×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#354C2
socleC2×C23C2×#99
prime radical#13092985C2
cosocleC2×D4×C23C23
hypercenter#354D23
hypocenterC23#2127
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
2. #99×D23C2semidirect
3. #13092212C2semidirect
4. #13092209C2semidirect
5. C23×#354C2semidirect
6. C2×#67292C4semidirect
9. #10625118C4semidirect
14. #10625045C4semidirect
15. #10625043C4semidirect
20. C2×Q8×C23C2×C4semidirect
29. C2×D92C2×C4semidirect
35. C42×C23C2×C4semidirect
41. C4×Dic23C2×C4semidirect
89. #354D23semidirect
110. C23#2127semidirect
113. C2×Q8C4×D23semidirect
133. C42C4×D23semidirect

Maximal subgroups

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

subgroupindex
#130929852
#99×D232
#130922122
#130922092
C23×#3542
#212723