Finite Group Databasebeta

← #22609067

Subgroups — #22609067

Order 9344.

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

normal subgroups only

This group has 214 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#17989294C211yesmaximal, characteristic
2#17988967C211yesmaximal, characteristic, complemented
3#17988883C211yesmaximal, characteristic, complemented
4#17988877C211yesmaximal, characteristic
5#17988335C211yesmaximal, characteristic, complemented
6#17988319C211yesmaximal, characteristic, complemented
7D4⋊C8×C73C211yesmaximal, characteristic
8C2×Dic292—22no—
9#14556591C2211yescharacteristic
10#14556591C2211yescharacteristic
11#14556582—21no—
12#14556570—21no—
13#14556568—22no—
14C4×Dic146C2211yescharacteristic
15D4×Dic73—21no—
16C2×C4⋊Dic73—21no—
17#14556525—21no—
18#14556522—21no—
19C4⋊#10596831C2211yescharacteristic
20#14556516—21no—
21#14556512—21no—
22C4×D4×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24C4×C8×C73C2211yescharacteristic
25C2×Dic146—21no—
26C2×Dic146D411yescharacteristic
27C2×Dic146D412yes—
28C22×Dic73—22no—
29Dic292—44no—
30C2×#10596831—21no—
31C4⋊Dic73—22no—
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73D411yescharacteristic
37#11924007—22no—
38#11924007—21no—
39C22⋊Dic73—22no—
40C4×Dic73—21no—
41C2×D4×C73D411yescharacteristic
42C22×C4×C73—21no—
43C2×C8×C73—21no—
44C2×C8×C73—21no—
45C4⋊C4×C73D411yescharacteristic
46C22⋊C4×C73—21no—
47C42×C73C2311yescharacteristic
48C23×C73—21no—
49D4×C73—21no—
50D4×C73Q1612yescomplemented
51C2×C4×C73—21no—
52C2×C4×C73—41no—
53C2×C4×C73—41no—
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×D411yescharacteristic
57C2×Dic73—21no—
58C2×Dic73—21no—
59C2×Dic73—22no—
60C2×Dic73—41no—
61C2×Dic73—82no—
62Dic146—21no—
63Dic146—21no—
64Dic146—42no—
65Dic146—42no—
66C8×C73—22no—
67C8×C73—41no—
68#10596831—41no—
69C22×C73—22no—
70C22×C73—41no—
71C22×C73—41no—
72C22×C73#12011yescharacteristic
73C4×C73—21no—
74C4×C73—41no—
75C4×C73C2×Q1611yescharacteristic
76C4×C73#13511yescharacteristic
77C4×C73#13711yescharacteristic
78C4×C73#13711yescharacteristic
79Dic73—41no—
80Dic73—42no—
81Dic73—41no—
82Dic73—81no—
83C2×C73—42no—
84C2×C73#45111yescharacteristic
85C2×C73#45211yescharacteristic
86C2×C73#45311yescharacteristic
87#1632—731nomaximal, Sylow
88C73#163211yescharacteristic, complemented, Sylow
89#554—731no—
90#494—731no—
91#477—731no—
92#476—731no—
93#333—731no—
94Q8⋊C8—731no—
95D4⋊C8D7311yescharacteristic
96C2×Q16—1462no—
97C4⋊Q8—731no—
98C4⋊Q8—731no—
99#125—1461no—
100C22⋊Q8—1462no—
101C22⋊Q8—1461no—
102C4×Q8—731no—
103C4×D4—1461no—
104C4×D4C2×D7311yescharacteristic
105C2×C4⋊C4—1461no—
106#107—1461no—
107#106—1461no—
108C4⋊C8—731no—
109C4⋊C8C2×D7311yescharacteristic
110#103—1461no—
111#102—1461no—
112C4×C8C2×D7311yescharacteristic
113C2×Q8—732no—
114C2×Q8—731no—
115C2×Q8—1461no—
116C2×D4D29211yescharacteristic
117C22×C4—21no—
118C22×C4—1462no—
119Q16—2924no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—1461no—
123C4⋊C4—731no—
124C4⋊C4—1462no—
125C4⋊C4—1462no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4D29211yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—1462no—
134C42—1461no—
135C42C22×D7311yescharacteristic
136C23—21no—
137Q8—2922no—
138Q8—2922no—
139Q8—1461no—
140Q8—1461no—
141D4—21no—
142D4Dic29212yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—2921no—
147C2×C4—5842no—
148C2×C4—1461no—
149C2×C4—1461no—
150C2×C4—1462no—
151C2×C4D4×D7311yescharacteristic
152C2×C4D4×D7311yescharacteristic
153C2×C4C2×D29211yescharacteristic
154C8—22no—
155C8—41no—
156C8—2921no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1455656111yescharacteristic
161C4—21no—
162C4—41no—
163C4—2921no—
164C4—2921no—
165C4—2922no—
166C4—5841no—
167C4C2×Dic29211yescharacteristic
168C4#1455661011yescharacteristic
169C4#1455662011yescharacteristic
170C4#1455662411yescharacteristic
171C2—42no—
172C2#1798874511yescharacteristic
173C2#1798875011yescharacteristic
174C2#1798875611yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
FittingD4⋊C8×C73C2
socleC22×C73#120
hypercenterD4⋊C8D73
hypocenterC73#1632
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #17988967C2semidirect
3. #17988883C2semidirect
5. #17988335C2semidirect
6. #17988319C2semidirect
50. D4×C73Q16semidirect
88. C73#1632semidirect
142. D4Dic292semidirect