Finite Group Databasebeta

← #15672462

Subgroups — #15672462

Order 2944.

278 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 61 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#13092793C211yesmaximal, characteristic, complemented
2#13092617C211yesmaximal, characteristic, complemented
3#13092612C211yesmaximal, characteristic, complemented
4#13092161C211yesmaximal, characteristic, complemented
5Q8⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
7C23×#550C211yesmaximal, characteristic, complemented
8C2×#41×C23—21no—
9C23×#127—21no—
10C23×#127C2211yescharacteristic
11C23×#121—22no—
12C23×#121—21no—
13C4×Q8×C23C2211yescharacteristic
14C4×D4×C23—21no—
15C4×D4×C23C2211yescharacteristic
16C2×#67274—21no—
17C2×#67272—21no—
18C2×#67272—22no—
19#10625045C2211yescharacteristic
20#10624991—21no—
21#10624991—21no—
22C4⋊(C23⋊C8)C2211yescharacteristic
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4×C23⋊C8C2211yescharacteristic
25#41×C23—42no—
26#41×C23—42no—
27C2×Q8×C23D411yescharacteristic
28C2×D4×C23—22no—
29C2×D4×C23—22no—
30C2×D4×C23—21no—
31C2×D4×C23—21no—
32C2×D4×C23D411yescharacteristic
33C2×D4×C23D412yes—
34C22×C4×C23—22no—
35C22×C4×C23—21no—
36C2×D92—21no—
37C2×D92—21no—
38C2×D92—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23D411yescharacteristic
41C4⋊C4×C23D411yescharacteristic
42C22⋊C4×C23—22no—
43C22⋊C4×C23—21no—
44C42×C23—21no—
45C42×C23C2311yescharacteristic
46#67274—42no—
47#67272—44no—
48#67272—42no—
49C2×C23⋊C8—21no—
50C2×C23⋊C8—21no—
51C2×C23⋊C8—21no—
52C23×C23—21no—
53C23×C23—22no—
54C22×D23—41no—
55Q8×C23—21no—
56Q8×C23D812yescomplemented
57D4×C23—21no—
58D4×C23—21no—
59D4×C23—42no—
60D4×C23—44no—
61D4×C23—41no—
62D4×C23—41no—
63D4×C23—41no—
64D4×C23—41no—
65D4×C23—82no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23—21no—
69C2×C4×C23—44no—
70C2×C4×C23—41no—
71C2×C4×C23—41no—
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2×D411yescharacteristic
74C2×C4×C23C2×D411yescharacteristic
75D92—42no—
76D92—41no—
77D92—41no—
78D92—41no—
79D92—41no—
80C23⋊C8—22no—
81C23⋊C8—41no—
82C23⋊C8—41no—
83#1621—231nomaximal, Sylow
84C22×C23—42no—
85C22×C23—41no—
86C22×C23—41no—
87C22×C23—42no—
88C22×C23—42no—
89C22×C23—41no—
90C22×C23#12011yescharacteristic
91C2×D23—81no—
92C2×D23—81no—
93C2×D23—81no—
94C4×C23—22no—
95C4×C23—21no—
96C4×C23—41no—
97C4×C23—41no—
98C4×C23C2×D811yescharacteristic
99C4×C23#13511yescharacteristic
100C4×C23AGL(1,ℤ/8)11yescharacteristic
101C4×C23AGL(1,ℤ/8)11yescharacteristic
102#550D2311yescharacteristic, complemented
103#493—231no—
104#460—231no—
105#459—231no—
106#331—231no—
107Q8⋊C8—231no—
108D4⋊C8—231no—
109C2×C23—81no—
110C2×C23—82no—
111C2×C23#44711yescharacteristic
112C2×C23#44911yescharacteristic
113C2×C23#45311yescharacteristic
114D23—161no—
115C2×#41—21no—
116C2×SD16—461no—
117C2×D8—461no—
118C2×D8—462no—
119#127—21no—
120#127—231no—
121#127C2×D2311yescharacteristic
122#121—22no—
123#121—21no—
124C4×Q8C2×D2311yescharacteristic
125C4×D4—21no—
126C4×D4C2×D2311yescharacteristic
127C4⋊C8—231no—
128C4⋊C8—231no—
129#102—461no—
130#102—461no—
131C4×C8—231no—
132C23#162111yescharacteristic, complemented, Sylow
133#41—42no—
134#41—42no—
135C2×Q8C22⋊D2311yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—461no—
141C2×D4—461no—
142C2×D4—461no—
143C2×D4C22⋊D2311yescharacteristic
144C2×D4C22⋊D2312yes—
145C22×C4—22no—
146C22×C4—21no—
147SD16—922no—
148D8—924no—
149D8—922no—
150C2×C8—461no—
151C2×C8—461no—
152C2×C8—461no—
153C4⋊C4—21no—
154C4⋊C4C22⋊D2311yescharacteristic
155C4⋊C4C22⋊D2311yescharacteristic
156C22⋊C4—22no—
157C22⋊C4—21no—
158C42—21no—
159C42C22×D2311yescharacteristic
160C23—21no—
161C23—22no—
162C23—921no—
163Q8—21no—
164Q8#6727212yescomplemented
165D4—21no—
166D4—21no—
167D4—42no—
168D4—44no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—82no—
174D4—922no—
175D4—921no—
176D4—921no—
177D4—921no—
178D4—921no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—44no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4C2×C22⋊D2311yescharacteristic
186C2×C4C2×C22⋊D2311yescharacteristic
187C2×C4C2×C22⋊D2311yescharacteristic
188C8—462no—
189C8—921no—
190C8—921no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22—42no—
195C22—42no—
196C22—41no—
197C22—1841no—
198C22—1841no—
199C22—1841no—
200C22#1062512411yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4C2×#6727211yescharacteristic
206C4#1062510311yescharacteristic
207C4#1062512011yescharacteristic
208C4#1062512111yescharacteristic
209C2—81no—
210C2—82no—
211C2—3681no—
212C2#1309255111yescharacteristic
213C2#1309256211yescharacteristic
214C2#1309258511yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#550C2
socleC22×C23#120
hypercenter#550D23
hypocenterC23#1621
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #13092793C2semidirect
2. #13092617C2semidirect
3. #13092612C2semidirect
4. #13092161C2semidirect
5. Q8⋊(C23⋊C8)C2semidirect
6. D4⋊(C23⋊C8)C2semidirect
7. C23×#550C2semidirect
56. Q8×C23D8semidirect
102. #550D23semidirect
132. C23#1621semidirect
164. Q8#67272semidirect

Maximal subgroups

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

subgroupindex
#130927932
#130926172
#130926122
#130921612
Q8⋊(C23⋊C8)2
D4⋊(C23⋊C8)2
C23×#5502
#162123