Finite Group Databasebeta

← #22610641

Subgroups — #22610641

Order 9344.

222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#14556517C211yesmaximal, characteristic
2#17988581C211yesmaximal, characteristic
3#17988553C211yesmaximal, characteristic
4C2×#14556501C211yesmaximal, characteristic, complemented
5#17988351C211yesmaximal, characteristic, complemented
6#17988346C211yesmaximal, characteristic, complemented
7#424×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10C22×#10596831C2211yescharacteristic
11C2×C4×Dic73C2211yescharacteristic
12#14556517—22no—
13#14556514C412yescomplemented
14#14556511C412yescomplemented
15#14556503—22no—
16#14556501—22no—
17C2×M16×C73C2211yescharacteristic
18C22×C8×C73C2211yescharacteristic
19#117×C73C2211yescharacteristic
20C4⋊C8×C73—22no—
21#11924028—21no—
22#11924028—21no—
23#11924028—21no—
24#11924028—21no—
25C2×Dic146C2×C411yescharacteristic
26C2×D292C2×C411yescharacteristic
27C2×C22⋊D73—21no—
28C22×Dic73—21no—
29C2×C4×D73—21no—
30#11924012—21no—
31#11924012—21no—
32C2×#10596831—21no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C2×#10596831C2×C412yes—
36C4×Dic73—21no—
37C4×Dic73D412yes—
38C22×C4×C73C2311yescharacteristic
39M16×C73—21no—
40M16×C73—21no—
41C2×C8×C73—21no—
42C2×C8×C73—21no—
43C2×C8×C73—21no—
44C2×C8×C73D412yes—
45C4⋊C4×C73C2×C412yes—
46C22⋊C4×C73—21no—
47C42×C73—21no—
48C23×C73#4111yescharacteristic
49C22×D73—21no—
50C2×C4×C73—22no—
51C2×C4×C73C22×C411yescharacteristic
52C2×C4×C73C2×D411yescharacteristic
53C2×C4×C73C2×D411yescharacteristic
54C2×C4×C73#4111yescharacteristic
55C2×C4×C73#4111yescharacteristic
56C2×C4×C73#4111yescharacteristic
57C22⋊D73—41no—
58C22⋊D73—41no—
59C2×Dic73—21no—
60C2×Dic73—22no—
61C2×Dic73—42no—
62D292—21no—
63D292—21no—
64C4×D73—41no—
65C4×D73—41no—
66Dic146—21no—
67Dic146—21no—
68C8×C73—22no—
69C8×C73—41no—
70#10596831—22no—
71#10596831—41no—
72C22×C73—22no—
73C22×C73C4×D411yescharacteristic
74C22×C73#12311yescharacteristic
75C22×C73#12611yescharacteristic
76C2×D73—41no—
77C2×D73—42no—
78C4×C73—42no—
79C4×C73#11711yescharacteristic
80C4×C73C4×D411yescharacteristic
81C4×C73#12111yescharacteristic
82C4×C73#12411yescharacteristic
83Dic73—42no—
84Dic73—41no—
85C2×C73—21no—
86C2×C73—21no—
87C2×C73#38811yescharacteristic
88C2×C73#44412yes—
89D73—81no—
90#1938—731nomaximal, Sylow
91C73#193811yescharacteristic, complemented, Sylow
92#424D7311yescharacteristic, complemented
93C2×#104—731no—
94#416—731no—
95#408—731no—
96C2×#97—731no—
97#341—731no—
98#339—731no—
99C2×#41—731no—
100C2×M16—731no—
101C2×M16C2×D7311yescharacteristic
102C22×C8—731no—
103C22×C8C2×D7311yescharacteristic
104#117C2×D7311yescharacteristic
105C2×C42—731no—
106C4⋊C8—22no—
107#104—1462no—
108#103—732no—
109#102—732no—
110C22⋊C8—1462no—
111#97—1462no—
112#41—1461no—
113#41—1461no—
114#41—1461no—
115#41—1461no—
116C2×Q8—731no—
117C2×D4—731no—
118C2×D4—1461no—
119C22×C4—1461no—
120C22×C4—1461no—
121C22×C4C22×D7311yescharacteristic
122M16—21no—
123M16—21no—
124M16—1461no—
125M16—1461no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—732no—
130C2×C8—1461no—
131C2×C8—1461no—
132C2×C8—1461no—
133C2×C8C22⋊D7312yes—
134C4⋊C4C4×D7312yes—
135C22⋊C4—21no—
136C42—21no—
137C42—732no—
138C42—1461no—
139C23—1461no—
140C23#1192402811yescharacteristic
141Q8—1461no—
142Q8—1461no—
143D4—2921no—
144D4—2921no—
145D4—1461no—
146D4—1461no—
147C2×C4—22no—
148C2×C4—2922no—
149C2×C4—2921no—
150C2×C4—2921no—
151C2×C4—1461no—
152C2×C4—1462no—
153C2×C4C2×C4×D7311yescharacteristic
154C2×C4D4×D7311yescharacteristic
155C2×C4C2×C22⋊D7311yescharacteristic
156C2×C4#1192402711yescharacteristic
157C2×C4#1192402911yescharacteristic
158C2×C4#1192402911yescharacteristic
159C8—22no—
160C8—41no—
161C8—2921no—
162C8—1462no—
163C22—22no—
164C22—2922no—
165C22—2921no—
166C22C4×C22⋊D7311yescharacteristic
167C22#1455657611yescharacteristic
168C22#1455658611yescharacteristic
169C4—42no—
170C4—2922no—
171C4—2921no—
172C4#1455654911yescharacteristic
173C4#1455655311yescharacteristic
174C4#1455656311yescharacteristic
175C4#1455658011yescharacteristic
176C2—21no—
177C2—21no—
178C2—5841no—
179C2#1798847711yescharacteristic
180C2#1798870712yes—
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#424×C73C2
socleC22×C73C4×D4
hypercenter#424D73
hypocenterC73#1938
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
4. C2×#14556501C2semidirect
5. #17988351C2semidirect
6. #17988346C2semidirect
7. #424×C73C2semidirect
13. #14556514C4semidirect
14. #14556511C4semidirect
91. C73#1938semidirect
92. #424D73semidirect