Finite Group Databasebeta

← #22609204

Subgroups — #22609204

Order 9344.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#17989307C211yesmaximal, characteristic
2#17988985C211yesmaximal, characteristic, complemented
3#17988867C211yesmaximal, characteristic
4#17988798C211yesmaximal, characteristic, complemented
5#17988332C211yesmaximal, characteristic, complemented
6#17988319C211yesmaximal, characteristic, complemented
7D4⋊C8×C73C211yesmaximal, characteristic
8C2×Dic292—21no—
9#14556591C2211yescharacteristic
10#14556591C2211yescharacteristic
11#14556584—22no—
12#14556578—21no—
13#14556570—21no—
14C4×Dic146C2211yescharacteristic
15#14556556—21no—
16#14556550—21no—
17#14556524—21no—
18#14556523—22no—
19C4⋊#10596831C2211yescharacteristic
20#14556516—21no—
21#14556512—21no—
22C4×D4×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24C4×C8×C73C2211yescharacteristic
25C2×Dic146—21no—
26C2×Dic146—21no—
27C2×Dic146D411yescharacteristic
28Dic292—42no—
29C2×#10596831—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C4⋊Dic73—21no—
33C4⋊Dic73D411yescharacteristic
34C4⋊Dic73D412yes—
35#11924007—22no—
36#11924007—21no—
37C22⋊Dic73—22no—
38C22⋊Dic73—22no—
39C4×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×C73—21no—
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—
61Dic146—21no—
62Dic146—21no—
63Dic146—41no—
64Dic146—41no—
65Dic146—41no—
66Dic146—41no—
67C8×C73—22no—
68C8×C73—41no—
69#10596831—41no—
70C22×C73—41no—
71C22×C73—41no—
72C22×C73—41no—
73C22×C73#12011yescharacteristic
74C4×C73—21no—
75C4×C73—41no—
76C4×C73#13511yescharacteristic
77C4×C73#13511yescharacteristic
78C4×C73AGL(1,ℤ/8)11yescharacteristic
79C4×C73#13711yescharacteristic
80Dic73—41no—
81Dic73—42no—
82Dic73—41no—
83Dic73—81no—
84C2×C73—81no—
85C2×C73#44911yescharacteristic
86C2×C73#45211yescharacteristic
87C2×C73#45611yescharacteristic
88#1652—731nomaximal, Sylow
89C73#165211yescharacteristic, complemented, Sylow
90#556—731no—
91#498—731no—
92#474—731no—
93#462—731no—
94#332—731no—
95Q8⋊C8—731no—
96D4⋊C8D7311yescharacteristic
97C2×Q16—1461no—
98C4⋊Q8—731no—
99C4⋊Q8—731no—
100#126—1462no—
101#124—1461no—
102C22⋊Q8—1461no—
103C4×Q8—731no—
104C4×Q8—1461no—
105C4×D4C2×D7311yescharacteristic
106#117—1461no—
107#107—1461no—
108#106—1462no—
109C4⋊C8—731no—
110C4⋊C8C2×D7311yescharacteristic
111#103—1461no—
112#102—1461no—
113C4×C8C2×D7311yescharacteristic
114C2×Q8—731no—
115C2×Q8—1461no—
116C2×Q8—1461no—
117C2×D4D29211yescharacteristic
118C22×C4—21no—
119Q16—2922no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—1461no—
123C4⋊C4—731no—
124C4⋊C4—732no—
125C4⋊C4—1462no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C4⋊C4D29211yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—1462no—
133C22⋊C4—1462no—
134C42—1462no—
135C42—1461no—
136C42C22×D7311yescharacteristic
137C23—21no—
138Q8—2921no—
139Q8—2921no—
140Q8—2921no—
141Q8—2921no—
142Q8—1461no—
143Q8—1461no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—2921no—
150C2×C4—1461no—
151C2×C4—1462no—
152C2×C4—1461no—
153C2×C4D4×D7311yescharacteristic
154C2×C4D4×D7311yescharacteristic
155C2×C4C2×D29211yescharacteristic
156C8—22no—
157C8—41no—
158C8—2921no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1455656111yescharacteristic
163C4—21no—
164C4—41no—
165C4—2921no—
166C4—2922no—
167C4—2921no—
168C4—5841no—
169C4#1455661211yescharacteristic
170C4#1455661311yescharacteristic
171C4#1455661511yescharacteristic
172C4#1455662411yescharacteristic
173C2—81no—
174C2#1798873311yescharacteristic
175C2#1798875111yescharacteristic
176C2#1798877111yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
FittingD4⋊C8×C73C2
socleC22×C73#120
hypercenterD4⋊C8D73
hypocenterC73#1652
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. #17988985C2semidirect
4. #17988798C2semidirect
5. #17988332C2semidirect
6. #17988319C2semidirect
89. C73#1652semidirect