Finite Group Databasebeta

← #22608492

Subgroups — #22608492

Order 9344.

264 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 85 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#17989137C211yesmaximal, characteristic
2#17988453C211yesmaximal, characteristic, complemented
3#17988322C214yesmaximal, complemented
4#431×C73C211yesmaximal, characteristic, complemented
5C2×#11924028—21no—
6#14556591C411yescharacteristic, complemented
7#14556588C411yescharacteristic, complemented
8#14556579—21no—
9#14556565—21no—
10#14556565C2212yes—
11C4×D292—21no—
12C4×D292C412yescomplemented
13C2×C4⋊Dic73—21no—
14#14556498—21no—
15#14556498C2212yes—
16C2×C42×C73C2211yescharacteristic
17C4⋊C8×C73—21no—
18C22⋊C8×C73C2212yes—
19C4×C8×C73—21no—
20#11924028—42no—
21#11924028—42no—
22C2×Dic146—21no—
23C2×D292—21no—
24C2×D292—21no—
25C2×D292C2×C412yes—
26C2×C22⋊D73—22no—
27C22×Dic73—22no—
28C2×C4×D73—22no—
29C4⋊Dic73—21no—
30C4⋊Dic73—42no—
31C4⋊Dic73C2×C412yes—
32#11924005—22no—
33#11924005—22no—
34C22×C4×C73D411yescharacteristic
35C22×C4×C73D411yescharacteristic
36C22×C4×C73C2311yescharacteristic
37C2×C8×C73—22no—
38C42×C73C2×C411yescharacteristic
39C42×C73C2×C411yescharacteristic
40C42×C73D411yescharacteristic
41C42×C73D411yescharacteristic
42C23×C73C2×D411yescharacteristic
43C22×D73—22no—
44C2×C4×C73—41no—
45C2×C4×C73—41no—
46C2×C4×C73C22⋊C411yescharacteristic
47C2×C4×C73C22⋊C411yescharacteristic
48C2×C4×C73C22⋊C411yescharacteristic
49C2×C4×C73C22⋊C411yescharacteristic
50C2×C4×C73D812yes—
51C2×C4×C73SD1612yes—
52C2×C4×C73C22×C411yescharacteristic
53C2×C4×C73C2×D411yescharacteristic
54C22⋊D73—42no—
55C22⋊D73—42no—
56C2×Dic73—22no—
57C2×Dic73—42no—
58C2×Dic73—42no—
59C2×Dic73—42no—
60D292—42no—
61D292—42no—
62D292—42no—
63C4×D73—44no—
64Dic146—42no—
65C8×C73—42no—
66C22×C73—21no—
67C22×C73—21no—
68C22×C73C2×C22⋊C411yescharacteristic
69C22×C73C2×D811yescharacteristic
70C22×C73C2×SD1611yescharacteristic
71C2×D73—42no—
72C2×D73—42no—
73C2×D73—42no—
74C4×C73—21no—
75C4×C73—21no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73#10212yes—
79C4×C73#10212yes—
80Dic73—42no—
81Dic73—82no—
82C2×C73—21no—
83C2×C73—21no—
84C2×C73#41011yescharacteristic
85C2×C73C2×#10211yescharacteristic
86C2×C73#42111yescharacteristic
87D73—82no—
88#1517—731nomaximal, Sylow
89C73#151711yescharacteristic, complemented, Sylow
90#532—731no—
91#431D7311yescharacteristic, complemented
92#382—731no—
93#327—734no—
94C2×#41—1461no—
95C4⋊Q8—731no—
96#127—731no—
97#124—1461no—
98#121—732no—
99#121—1461no—
100C4×D4—732no—
101C4×D4—1461no—
102C2×C4⋊C4—1461no—
103C2×C42C2×D7311yescharacteristic
104C4⋊C8—21no—
105C22⋊C8C2×D7312yes—
106C4×C8—21no—
107#95—732no—
108#95—1461no—
109#41—2922no—
110#41—2922no—
111C2×Q8—1461no—
112C2×D4—732no—
113C2×D4—1462no—
114C2×D4—1461no—
115C2×D4—1461no—
116C22×C4—1462no—
117C22×C4—1462no—
118C22×C4D29211yescharacteristic
119C22×C4D29211yescharacteristic
120C22×C4C22×D7311yescharacteristic
121C2×C8—22no—
122C4⋊C4—2922no—
123C4⋊C4—732no—
124C4⋊C4—1461no—
125C22⋊C4—1462no—
126C22⋊C4—1462no—
127C42C4×D7311yescharacteristic
128C42C4×D7311yescharacteristic
129C42C22⋊D7311yescharacteristic
130C42C22⋊D7311yescharacteristic
131C23—1462no—
132C23C2×D29211yescharacteristic
133Q8—2922no—
134D4—2922no—
135D4—2922no—
136D4—2922no—
137D4—2922no—
138D4—2922no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—2924no—
142C2×C4—2922no—
143C2×C4—2922no—
144C2×C4—2922no—
145C2×C4—1462no—
146C2×C4#1192400511yescharacteristic
147C2×C4#1192400511yescharacteristic
148C2×C4#1192400511yescharacteristic
149C2×C4#1192400511yescharacteristic
150C2×C4D58412yes—
151C2×C4#1192401712yes—
152C2×C4C2×C4×D7311yescharacteristic
153C2×C4C2×C22⋊D7311yescharacteristic
154C8—42no—
155C22—21no—
156C22—21no—
157C22—2922no—
158C22—2922no—
159C22—2922no—
160C22C2×#1192400511yescharacteristic
161C22C2×D58411yescharacteristic
162C22C2×#1192401711yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—2922no—
168C4—5842no—
169C4#1455651312yes—
170C4#1455651312yes—
171C2—21no—
172C2—21no—
173C2—5842no—
174C2#1798856011yescharacteristic
175C2C2×#1455651311yescharacteristic
176C2#1798860311yescharacteristic
subgroupG/H
centerC22C2×#11924005
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#431×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#431D73
hypocenterC73#1517
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #17988453C2semidirect
3. #17988322C2semidirect
4. #431×C73C2semidirect
6. #14556591C4semidirect
7. #14556588C4semidirect
12. C4×D292C4semidirect
89. C73#1517semidirect
91. #431D73semidirect