Finite Group Databasebeta

← D23×#353 #15675053

Subgroups — D23×#353 #15675053

Order 2944.

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

normal subgroups only

This group has 368 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#127×D23C211yesmaximal, characteristic
2#99×D23C212yesmaximal, complemented
3#13092210C211yesmaximal, characteristic, complemented
4#13092209C212yesmaximal, complemented
5C23×#353C211yesmaximal, characteristic, complemented
6C2×D4×D23—22no—
7C2×D4×D23C411yescharacteristic, complemented
8C2×D4×D23C2211yescharacteristic
9C23×#127C2211yescharacteristic
10#10625111—22no—
11#10625111C411yescharacteristic, complemented
12#10625111C2211yescharacteristic
13C22⋊C4×D23—22no—
14#10625045C411yescharacteristic, complemented
15C42×D23C411yescharacteristic, complemented
16C23×#99C2212yescomplemented
17#10625016C2212yescomplemented
18#10624988—22no—
19C23×D23—21no—
20C23×D23D412yes—
21C2×D4×C23—22no—
22C2×D4×C23C2×C411yescharacteristic, complemented
23C2×D4×C23C2311yescharacteristic
24C2×C22⋊D23—22no—
25C2×C22⋊D23—22no—
26C2×C22⋊D23—21no—
27C2×C22⋊D23D412yes—
28D4×D23—41no—
29D4×D23—41no—
30D4×D23—41no—
31D4×D23—41no—
32D4×D23—48no—
33C2×D92—22no—
34C2×D92C2×C411yescharacteristic
35C2×D92C2×C411yescharacteristic, complemented
36C2×C4×D23—21no—
37C2×C4×D23—42no—
38C2×C4×D23C2×C411yescharacteristic
39C22⋊C4×C23—22no—
40C42×C23C2×C411yescharacteristic, complemented
41C22⋊Dic23—22no—
42(C2×D23)⋊C4—42no—
43C4×Dic23—21no—
44C4×Dic23C2×C411yescharacteristic, complemented
45C23×C23—21no—
46C23×C23C2×D412yes—
47C22×D23—22no—
48C22×D23—22no—
49C22×D23—21no—
50C22×D23—44no—
51C22×D23—44no—
52C22×D23—41no—
53C22×D23—41no—
54C22×D23C22⋊C411yescharacteristic
55C22×D23C22⋊C412yes—
56D4×C23—41no—
57D4×C23—41no—
58D4×C23—44no—
59C2×C4×C23—21no—
60C2×C4×C23—42no—
61C2×C4×C23C22×C411yescharacteristic
62C22⋊D23—42no—
63C22⋊D23—44no—
64C22⋊D23—44no—
65C22⋊D23—42no—
66C2×Dic23—21no—
67C2×Dic23—42no—
68C2×Dic23C22⋊C411yescharacteristic
69D92—41no—
70D92—41no—
71D92—44no—
72C4×D23—24no—
73C4×D23—21no—
74C4×D23—21no—
75C4×D23—84no—
76C2×#353—231nomaximal, Sylow
77C22×C23—22no—
78C22×C23—42no—
79C22×C23—42no—
80C22×C23—41no—
81C22×C23C2×C22⋊C411yescharacteristic
82C2×D23—22no—
83C2×D23—22no—
84C2×D23—44no—
85C2×D23—42no—
86C2×D23—42no—
87C2×D23—41no—
88C2×D23—82no—
89C2×D23—82no—
90C2×D23—82no—
91C2×D23#9911yescharacteristic
92C2×D23#9911yescharacteristic
93C4×C23—22no—
94C4×C23—21no—
95C4×C23—82no—
96Dic23—22no—
97Dic23—21no—
98Dic23—82no—
99C2×#127—231no—
100C2×#99—232no—
101#353—231no—
102#353—232no—
103#353D2311yescharacteristic, direct product factor
104C2×C23—21no—
105C2×C23—42no—
106C2×C23—81no—
107C2×C23C2×#9911yescharacteristic
108D23—21no—
109D23—42no—
110D23—81no—
111D23#35312yesdirect product factor
112C22×D4—231no—
113C22×D4—231no—
114C22×D4—462no—
115#127—231no—
116#127—231no—
117#127—231no—
118#127—462no—
119#127C2×D2311yescharacteristic
120C2×C22⋊C4—462no—
121C2×C42—231no—
122#99—232no—
123#99—462no—
124#99C2×D2312yescomplemented
125C23C2×#35311yescharacteristic, complemented, Sylow
126C24—232no—
127C24—461no—
128C2×D4—22no—
129C2×D4—232no—
130C2×D4—231no—
131C2×D4—231no—
132C2×D4—462no—
133C2×D4—461no—
134C2×D4—462no—
135C2×D4—462no—
136C2×D4—921no—
137C2×D4—921no—
138C2×D4—921no—
139C2×D4—921no—
140C2×D4—928no—
141C2×D4C4×D2311yescharacteristic, complemented
142C2×D4C22×D2311yescharacteristic
143C22×C4—231no—
144C22×C4—461no—
145C22×C4—922no—
146C22⋊C4—22no—
147C22⋊C4—462no—
148C22⋊C4—922no—
149C42—231no—
150C42—461no—
151C42C4×D2311yescharacteristic, complemented
152C23—21no—
153C23—231no—
154C23—232no—
155C23—462no—
156C23—462no—
157C23—461no—
158C23—921no—
159C23—921no—
160C23—924no—
161C23—924no—
162C23D4×D2312yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—921no—
167D4—921no—
168D4—924no—
169D4—922no—
170D4—924no—
171D4—924no—
172D4—922no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—231no—
176C2×C4—461no—
177C2×C4—461no—
178C2×C4—464no—
179C2×C4—461no—
180C2×C4—922no—
181C2×C4—1844no—
182C2×C4C2×C4×D2311yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—231no—
188C22—231no—
189C22—462no—
190C22—462no—
191C22—922no—
192C22—922no—
193C22—924no—
194C22—921no—
195C22—1842no—
196C22—1842no—
197C22—1842no—
198C22C22⋊C4×D2311yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—462no—
203C4—461no—
204C4—1842no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—232no—
209C2—461no—
210C2—922no—
211C2—1841no—
212C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC2×C4×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#353C2
socleC2×C23C2×#99
prime radical#127×D23C2
cosocleC2×D4×C23C23
hypercenter#353D23
hypocenterC23C2×#353
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D23C2semidirect
3. #13092210C2semidirect
4. #13092209C2semidirect
5. C23×#353C2semidirect
7. C2×D4×D23C4semidirect
11. #10625111C4semidirect
14. #10625045C4semidirect
15. C42×D23C4semidirect
16. C23×#99C22semidirect
17. #10625016C22semidirect
22. C2×D4×C23C2×C4semidirect
35. C2×D92C2×C4semidirect
40. C42×C23C2×C4semidirect
44. C4×Dic23C2×C4semidirect
103. #353D23direct (N × H)
111. D23#353direct (N × H)
124. #99C2×D23semidirect
125. C23C2×#353semidirect
141. C2×D4C4×D23semidirect
151. C42C4×D23semidirect

Maximal subgroups

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

subgroupindex
#127×D232
#99×D232
#130922102
#130922092
C23×#3532
C2×#35323