Finite Group Databasebeta

← #15672578

Subgroups — #15672578

Order 2944.

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

normal subgroups only

This group has 308 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
1D4×D92C211yesmaximal, characteristic
2#13092764C211yesmaximal, characteristic, complemented
3#13092698C211yesmaximal, characteristic, complemented
4#13092622C211yesmaximal, characteristic, complemented
5#13092160C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×D4×D23—21no—
9C22×D92—21no—
10C4×D4×C23C2211yescharacteristic
11C2×#67273—21no—
12#10625101—21no—
13#10625066—21no—
14#10625053—22no—
15#10625045C2211yescharacteristic
16C4×D92C2211yescharacteristic
17#10625040C2211yescharacteristic, complemented
18C23×C4⋊C8C2211yescharacteristic, complemented
19C4×C8×C23C2211yescharacteristic, complemented
20#10625003—21no—
21#10625003—22no—
22#10625000—21no—
23#10624992—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic, complemented
25C23×D23—22no—
26C2×D4×C23D411yescharacteristic
27C22×C4×C23—21no—
28C2×C22⋊D23—22no—
29D4×D23—42no—
30D4×D23—42no—
31C2×D92—22no—
32C2×D92—21no—
33C2×D92—21no—
34C2×D92—42no—
35C2×D92—42no—
36C2×D92D411yescharacteristic
37C2×D92D412yes—
38C2×C4×D23—21no—
39C2×Dic46—21no—
40C2×C8×C23—21no—
41C2×C8×C23—21no—
42C4⋊C4×C23D411yescharacteristic
43C22⋊C4×C23—21no—
44C42×C23C2311yescharacteristic
45#67273—42no—
46(C2×D23)⋊C4—22no—
47(C2×D23)⋊C4—21no—
48C4⋊Dic23—21no—
49C4⋊Dic23—21no—
50C4⋊Dic23D411yescharacteristic
51C2×C23⋊C8—21no—
52C23×C23—21no—
53C22×D23—21no—
54C22×D23—22no—
55C22×D23—44no—
56C22×D23—44no—
57C22×D23—82no—
58D4×C23—21no—
59D4×C23D812yes—
60C2×C4×C23—21no—
61C2×C4×C23—41no—
62C2×C4×C23—41no—
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C22⋊D23—44no—
67C2×Dic23—21no—
68C2×Dic23—41no—
69D92—21no—
70D92—42no—
71D92—44no—
72D92—41no—
73D92—41no—
74D92—41no—
75D92—41no—
76D92SD1612yescomplemented
77C4×D23—41no—
78C4×D23—41no—
79Dic46—41no—
80Dic46—41no—
81C8×C23—41no—
82C8×C23—41no—
83C23⋊C8—41no—
84#1639—231nomaximal, Sylow
85C22×C23—22no—
86C22×C23—41no—
87C22×C23—41no—
88C22×C23#12011yescharacteristic
89C2×D23—22no—
90C2×D23—41no—
91C2×D23—41no—
92C2×D23—42no—
93C2×D23—42no—
94C2×D23—42no—
95C2×D23—88no—
96C4×C23—21no—
97C4×C23—41no—
98C4×C23C2×D811yescharacteristic
99C4×C23C2×SD1611yescharacteristic
100C4×C23AGL(1,ℤ/8)11yescharacteristic
101C4×C23AGL(1,ℤ/8)11yescharacteristic
102Dic23—41no—
103Dic23—81no—
104D42—231no—
105#486—231no—
106#474—231no—
107#461—231no—
108#331—231no—
109D4⋊C8—231no—
110D4⋊C8D2311yescharacteristic, complemented
111C2×C23—42no—
112C2×C23#44711yescharacteristic
113C2×C23#45011yescharacteristic
114C2×C23#45511yescharacteristic
115D23—42no—
116D23—82no—
117C22×D4—461no—
118C22×D4—461no—
119C2×SD16—461no—
120C4⋊Q8—231no—
121#127—231no—
122#121—461no—
123#121—461no—
124#120—462no—
125C4×D4—231no—
126C4×D4C2×D2311yescharacteristic
127#107—461no—
128C4⋊C8—231no—
129C4⋊C8C2×D2311yescharacteristic, complemented
130#103—461no—
131#102—461no—
132#102—462no—
133C4×C8C2×D2311yescharacteristic, complemented
134C23#163911yescharacteristic, complemented, Sylow
135C24—462no—
136C2×Q8—461no—
137C2×D4—231no—
138C2×D4—232no—
139C2×D4—462no—
140C2×D4—462no—
141C2×D4—461no—
142C2×D4—461no—
143C2×D4—922no—
144C2×D4—922no—
145C2×D4—922no—
146C2×D4—922no—
147C2×D4D9211yescharacteristic
148C22×C4—21no—
149C22×C4—461no—
150SD16—922no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—461no—
154C4⋊C4—231no—
155C4⋊C4—461no—
156C4⋊C4—461no—
157C4⋊C4D9211yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—462no—
160C22⋊C4—461no—
161C42C22×D2311yescharacteristic
162C23—21no—
163C23—461no—
164C23—462no—
165C23—924no—
166C23—924no—
167C23—1842no—
168Q8—921no—
169Q8—921no—
170D4—21no—
171D4—232no—
172D4—461no—
173D4—922no—
174D4—924no—
175D4—924no—
176D4—921no—
177D4—921no—
178D4—921no—
179D4—921no—
180D4D18412yes—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—461no—
185C2×C4—921no—
186C2×C4—921no—
187C2×C4—921no—
188C2×C4C2×D9211yescharacteristic
189C2×C4D4×D2311yescharacteristic
190C2×C4D4×D2311yescharacteristic
191C8—41no—
192C8—41no—
193C8—921no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—462no—
198C22—921no—
199C22—921no—
200C22—922no—
201C22—922no—
202C22—922no—
203C22—1848no—
204C22#1062505311yescharacteristic
205C4—21no—
206C4—41no—
207C4—921no—
208C4—1841no—
209C4C2×D18411yescharacteristic
210C4#1062507911yescharacteristic
211C4#1062508211yescharacteristic
212C4SD16×D2311yescharacteristic
213C2—42no—
214C2—922no—
215C2—1842no—
216C2#1309255311yescharacteristic
217C2#1309256911yescharacteristic
218C2#1309259611yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×D4⋊C8C2
socleC22×C23#120
prime radicalD4×D92C2
hypercenterD4⋊C8D23
hypocenterC23#1639
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13092764C2semidirect
3. #13092698C2semidirect
4. #13092622C2semidirect
5. #13092160C2semidirect
6. #13092146C2semidirect
7. C23×D4⋊C8C2semidirect
17. #10625040C22semidirect
18. C23×C4⋊C8C22semidirect
19. C4×C8×C23C22semidirect
24. C4⋊(C23⋊C8)C22semidirect
76. D92SD16semidirect
110. D4⋊C8D23semidirect
129. C4⋊C8C2×D23semidirect
133. C4×C8C2×D23semidirect
134. C23#1639semidirect

Maximal subgroups

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

subgroupindex
D4×D922
#130927642
#130926982
#130926222
#130921602
#130921462
C23×D4⋊C82
#163923