Finite Group Databasebeta

← #15672502

Subgroups — #15672502

Order 2944.

250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×D92C211yesmaximal, characteristic, complemented
2#13092764C211yesmaximal, characteristic, complemented
3#13092617C211yesmaximal, characteristic, complemented
4#13092613C211yesmaximal, characteristic
5#13092162C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×Q8×D23—21no—
9C4×Q8×C23C2211yescharacteristic
10C2×#67274—21no—
11C2×D184—21no—
12#10625068—21no—
13#10625068—22no—
14#10625045C2211yescharacteristic
15C4×D92—21no—
16C4×D92C2211yescharacteristic
17#10625040—21no—
18#10625040C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C4×C8×C23C2211yescharacteristic
21#10625003—21no—
22#10625003—22no—
23#10624991—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23D411yescharacteristic
26Q8×D23—42no—
27Q8×D23—42no—
28C2×D92—21no—
29C2×D92—21no—
30C2×D92—21no—
31C2×D92D411yescharacteristic
32C2×C4×D23—22no—
33C2×C4×D23—21no—
34C2×Dic46—22no—
35C2×Dic46—21no—
36C2×C8×C23—21no—
37C2×C8×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23D411yescharacteristic
40C42×C23—21no—
41C42×C23C2311yescharacteristic
42#67274—42no—
43(C2×D23)⋊C4—22no—
44(C2×D23)⋊C4—21no—
45C4⋊Dic23—22no—
46C4⋊Dic23—21no—
47C4⋊Dic23D411yescharacteristic
48C4⋊Dic23D412yes—
49C2×C23⋊C8—21no—
50D184—42no—
51C22×D23—21no—
52C22×D23—41no—
53Q8×C23—21no—
54Q8×C23D812yescomplemented
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C2×Dic23—21no—
61C2×Dic23—22no—
62D92—21no—
63D92—42no—
64D92—41no—
65D92—41no—
66D92—41no—
67D92—41no—
68D92SD1612yescomplemented
69C4×D23—44no—
70C4×D23—41no—
71C4×D23—41no—
72Dic46—44no—
73Dic46—41no—
74Dic46—41no—
75C8×C23—41no—
76C8×C23—41no—
77C23⋊C8—41no—
78#1627—231nomaximal, Sylow
79C22×C23#12011yescharacteristic
80C2×D23—22no—
81C2×D23—41no—
82C2×D23—41no—
83C2×D23—81no—
84C2×D23—81no—
85C2×D23—81no—
86C4×C23—22no—
87C4×C23—21no—
88C4×C23—41no—
89C4×C23C2×D811yescharacteristic
90C4×C23C2×SD1611yescharacteristic
91C4×C23AGL(1,ℤ/8)11yescharacteristic
92C4×C23#13711yescharacteristic
93Dic23—41no—
94Dic23—42no—
95D4×Q8—231no—
96#486—231no—
97#460—231no—
98#459—231no—
99#332—231no—
100Q8⋊C8D2311yescharacteristic, complemented
101D4⋊C8—231no—
102C2×C23#44711yescharacteristic
103C2×C23#44811yescharacteristic
104C2×C23#45411yescharacteristic
105D23—42no—
106D23—161no—
107C22×Q8—461no—
108C2×SD16—461no—
109C2×D8—461no—
110C4⋊Q8—231no—
111C4⋊Q8—461no—
112#127—231no—
113C22⋊Q8—462no—
114C22⋊Q8—461no—
115C4×Q8C2×D2311yescharacteristic
116C4×D4—231no—
117C4×D4—461no—
118C4⋊C8—231no—
119C4⋊C8C2×D2311yescharacteristic
120#102—461no—
121#102—462no—
122#102—461no—
123C4×C8C2×D2311yescharacteristic
124C23#162711yescharacteristic, complemented, Sylow
125C2×Q8—462no—
126C2×Q8—461no—
127C2×Q8—922no—
128C2×Q8—922no—
129C2×Q8D9211yescharacteristic
130C2×D4—231no—
131C2×D4—461no—
132C2×D4—461no—
133C2×D4—461no—
134C22×C4—462no—
135C22×C4—461no—
136SD16—922no—
137D8—922no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—461no—
141C4⋊C4—21no—
142C4⋊C4—231no—
143C4⋊C4—232no—
144C4⋊C4—462no—
145C4⋊C4—461no—
146C4⋊C4D9211yescharacteristic
147C22⋊C4—462no—
148C22⋊C4—461no—
149C42—21no—
150C42C22×D2311yescharacteristic
151C23—461no—
152C23—921no—
153Q8—21no—
154Q8—924no—
155Q8—921no—
156Q8—921no—
157Q8D18412yescomplemented
158D4—232no—
159D4—461no—
160D4—922no—
161D4—921no—
162D4—921no—
163D4—921no—
164D4—921no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—462no—
168C2×C4—461no—
169C2×C4—924no—
170C2×C4—921no—
171C2×C4—921no—
172C2×C4C2×D9211yescharacteristic
173C2×C4D4×D2311yescharacteristic
174C2×C4D4×D2311yescharacteristic
175C8—41no—
176C8—41no—
177C8—921no—
178C22—462no—
179C22—921no—
180C22—921no—
181C22—1841no—
182C22—1841no—
183C22—1841no—
184C22#1062505311yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—922no—
189C4—921no—
190C4C2×D18411yescharacteristic
191C4#1062507911yescharacteristic
192C4SD16×D2311yescharacteristic
193C4#1062508911yescharacteristic
194C2—922no—
195C2—3681no—
196C2#1309255311yescharacteristic
197C2#1309255711yescharacteristic
198C2#1309259111yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×Q8⋊C8C2
socleC22×C23#120
prime radical#13092613C2
hypercenterQ8⋊C8D23
hypocenterC23#1627
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. Q8×D92C2semidirect
2. #13092764C2semidirect
3. #13092617C2semidirect
5. #13092162C2semidirect
6. #13092146C2semidirect
7. C23×Q8⋊C8C2semidirect
54. Q8×C23D8semidirect
68. D92SD16semidirect
100. Q8⋊C8D23semidirect
124. C23#1627semidirect
157. Q8D184semidirect

Maximal subgroups

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

subgroupindex
Q8×D922
#130927642
#130926172
#130926132
#130921622
#130921462
C23×Q8⋊C82
#162723