Finite Group Databasebeta

← #15672464

Subgroups — #15672464

Order 2944.

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

normal subgroups only

This group has 278 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#13093089C211yesmaximal, characteristic, complemented
2#13092794C211yesmaximal, characteristic, complemented
3#13092617C211yesmaximal, characteristic, complemented
4#13092613C211yesmaximal, characteristic, complemented
5#13092160C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#67292—21no—
9C4×Q8×C23C2211yescharacteristic
10C2×#67274—21no—
11C2×D184—21no—
12C2×D184—22no—
13#10625066—22no—
14#10625066—21no—
15#10625045—21no—
16#10625045C2211yescharacteristic
17#10625045C2211yescharacteristic
18C4×D92—21no—
19C4×D92C2211yescharacteristic
20C23×C4⋊C8C2211yescharacteristic
21C4×C8×C23C2211yescharacteristic
22#10625003—21no—
23#10624991—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23D411yescharacteristic
26#67292—42no—
27#67292—42no—
28C2×D92—22no—
29C2×D92—21no—
30C2×D92—21no—
31C2×D92—21no—
32C2×D92—21no—
33C2×D92—21no—
34C2×D92—22no—
35C2×D92D411yescharacteristic
36C2×D92D412yes—
37C2×C4×D23—22no—
38C2×C4×D23—21no—
39C2×C8×C23—21no—
40C2×C8×C23—21no—
41C4⋊C4×C23—21no—
42C4⋊C4×C23D411yescharacteristic
43C42×C23—21no—
44C42×C23C2311yescharacteristic
45#67274—42no—
46(C2×D23)⋊C4—22no—
47(C2×D23)⋊C4—21no—
48C4⋊Dic23D411yescharacteristic
49C2×C23⋊C8—21no—
50D184—44no—
51D184—42no—
52C22×D23—21no—
53C22×D23—22no—
54C22×D23—41no—
55Q8×C23—21no—
56Q8×C23D812yescomplemented
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C2×Dic23—21no—
63D92—21no—
64D92—21no—
65D92—42no—
66D92—44no—
67D92—42no—
68D92—41no—
69D92—41no—
70D92—41no—
71D92—41no—
72D92—41no—
73D92—41no—
74D92—41no—
75D92—41no—
76D92—82no—
77C4×D23—44no—
78C4×D23—41no—
79C4×D23—41no—
80C8×C23—22no—
81C8×C23—41no—
82C23⋊C8—41no—
83#1621—231nomaximal, Sylow
84C22×C23#12011yescharacteristic
85C2×D23—42no—
86C2×D23—41no—
87C2×D23—41no—
88C2×D23—42no—
89C2×D23—42no—
90C2×D23—41no—
91C2×D23—81no—
92C2×D23—81no—
93C2×D23—81no—
94C4×C23—22no—
95C4×C23—21no—
96C4×C23—41no—
97C4×C23C2×D811yescharacteristic
98C4×C23#13511yescharacteristic
99C4×C23AGL(1,ℤ/8)11yescharacteristic
100C4×C23AGL(1,ℤ/8)11yescharacteristic
101Dic23—41no—
102#550—231no—
103#493—231no—
104#460—231no—
105#459—231no—
106#331—231no—
107Q8⋊C8D2311yescharacteristic, complemented
108D4⋊C8—231no—
109C2×C23#44711yescharacteristic
110C2×C23#44911yescharacteristic
111C2×C23#45311yescharacteristic
112D23—81no—
113D23—82no—
114D23—161no—
115C2×#41—461no—
116C2×SD16—461no—
117C2×D8—461no—
118C2×D8—462no—
119#127—231no—
120#127—231no—
121#127—461no—
122#121—462no—
123#121—461no—
124C4×Q8C2×D2311yescharacteristic
125C4×D4—231no—
126C4×D4—461no—
127C4⋊C8—231no—
128C4⋊C8C2×D2311yescharacteristic
129#102—461no—
130#102—461no—
131C4×C8C2×D2311yescharacteristic
132C23#162111yescharacteristic, complemented, Sylow
133#41—922no—
134#41—922no—
135C2×Q8D9211yescharacteristic
136C2×D4—231no—
137C2×D4—232no—
138C2×D4—462no—
139C2×D4—462no—
140C2×D4—461no—
141C2×D4—461no—
142C2×D4—461no—
143C2×D4—461no—
144C2×D4—461no—
145C22×C4—462no—
146C22×C4—461no—
147SD16—922no—
148D8—924no—
149D8—922no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—461no—
153C4⋊C4—21no—
154C4⋊C4—231no—
155C4⋊C4D9211yescharacteristic
156C22⋊C4—462no—
157C22⋊C4—461no—
158C42—21no—
159C42C22×D2311yescharacteristic
160C23—461no—
161C23—462no—
162C23—921no—
163Q8—21no—
164Q8D18412yescomplemented
165D4—461no—
166D4—461no—
167D4—922no—
168D4—924no—
169D4—922no—
170D4—921no—
171D4—921no—
172D4—921no—
173D4—921no—
174D4—921no—
175D4—921no—
176D4—921no—
177D4—921no—
178D4—1842no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—461no—
182C2×C4—924no—
183C2×C4—921no—
184C2×C4—921no—
185C2×C4C2×D9211yescharacteristic
186C2×C4D4×D2311yescharacteristic
187C2×C4D4×D2311yescharacteristic
188C8—22no—
189C8—41no—
190C8—921no—
191C22—922no—
192C22—921no—
193C22—921no—
194C22—922no—
195C22—922no—
196C22—921no—
197C22—1841no—
198C22—1841no—
199C22—1841no—
200C22#1062505311yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—921no—
205C4C2×D18411yescharacteristic
206C4#1062507911yescharacteristic
207C4#1062508511yescharacteristic
208C4#1062509011yescharacteristic
209C2—3681no—
210C2—1841no—
211C2—1842no—
212C2#1309255311yescharacteristic
213C2#1309256511yescharacteristic
214C2#1309258611yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×Q8⋊C8C2
socleC22×C23#120
hypercenterQ8⋊C8D23
hypocenterC23#1621
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. #13093089C2semidirect
2. #13092794C2semidirect
3. #13092617C2semidirect
4. #13092613C2semidirect
5. #13092160C2semidirect
6. #13092146C2semidirect
7. C23×Q8⋊C8C2semidirect
56. Q8×C23D8semidirect
107. Q8⋊C8D23semidirect
132. C23#1621semidirect
164. Q8D184semidirect

Maximal subgroups

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

subgroupindex
#130930892
#130927942
#130926172
#130926132
#130921602
#130921462
C23×Q8⋊C82
#162123