Finite Group Databasebeta

← #22610874

Subgroups — #22610874

Order 9344.

260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 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#17989144C211yesmaximal, characteristic
2C4×#11924012C211yesmaximal, characteristic
3#17988347C214yesmaximal
4C4×C4⋊C4×C73C211yesmaximal, characteristic
5C2×#11924012C2212yes—
6#14556591C411yescharacteristic, complemented
7#14556591C411yescharacteristic, complemented
8#14556583C412yescomplemented
9#14556570—21no—
10#14556570—21no—
11C4×Dic146—21no—
12C4×Dic146—21no—
13#14556550C2212yes—
14#14556502—21no—
15C4×#10596831—21no—
16C2×C4⋊C4×C73—21no—
17C2×C42×C73C2212yes—
18C2×C42×C73C2211yescharacteristic
19#95×C73—21no—
20C2×Dic146—21no—
21C2×Dic146—21no—
22#11924012—22no—
23#11924012Q814yescomplemented
24C2×#10596831—22no—
25C4⋊Dic73—21no—
26C4⋊Dic73—21no—
27C4⋊Dic73C2×C412yes—
28C4⋊Dic73C2×C412yes—
29#11924007—22no—
30#11924007—22no—
31C22⋊Dic73—22no—
32C4×Dic73—22no—
33C22×C4×C73—22no—
34C22×C4×C73D411yescharacteristic
35C22×C4×C73D411yescharacteristic
36C22×C4×C73C2311yescharacteristic
37C4⋊C4×C73—24no—
38C42×C73—24no—
39C42×C73C2×C411yescharacteristic
40C42×C73C2×C411yescharacteristic
41C42×C73D411yescharacteristic
42C42×C73D411yescharacteristic
43C23×C73C2×D411yescharacteristic
44C2×C4×C73—22no—
45C2×C4×C73—24no—
46C2×C4×C73—41no—
47C2×C4×C73—42no—
48C2×C4×C73—42no—
49C2×C4×C73C22⋊C411yescharacteristic
50C2×C4×C73C22⋊C411yescharacteristic
51C2×C4×C73C22⋊C411yescharacteristic
52C2×C4×C73C22⋊C411yescharacteristic
53C2×C4×C73C22×C411yescharacteristic
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×Q812yes—
56C2×C4×C73#4112yes—
57C2×Dic73—22no—
58C2×Dic73—22no—
59Dic146—42no—
60Dic146—42no—
61#10596831—24no—
62C22×C73—21no—
63C22×C73—21no—
64C22×C73C2×C22⋊C411yescharacteristic
65C22×C73#12411yescharacteristic
66C22×C73C4⋊Q811yescharacteristic
67C4×C73—21no—
68C4×C73—21no—
69C4×C73—21no—
70C4×C73—44no—
71C4×C73#10412yes—
72C4×C73C4×Q812yes—
73C4×C73C22⋊Q812yes—
74Dic73—42no—
75Dic73—42no—
76C2×C73—21no—
77C2×C73—21no—
78C2×C73#39111yescharacteristic
79C2×C73C2×#10411yescharacteristic
80C2×C73#42111yescharacteristic
81#1986—731nomaximal, Sylow
82C73#198611yescharacteristic, complemented, Sylow
83#533—731no—
84C4×M16—731no—
85C4×C4⋊C4D7311yescharacteristic
86#339—734no—
87C2×M16—732no—
88C4⋊Q8—731no—
89C4⋊Q8—731no—
90#125—732no—
91C22⋊Q8—1461no—
92C22⋊Q8—1461no—
93C4×Q8—1461no—
94C4×Q8—1461no—
95#117—732no—
96C2×C4⋊C4—21no—
97C2×C42C2×D7312yes—
98C2×C42C2×D7311yescharacteristic
99#97—1461no—
100C4×C8—1461no—
101#95—21no—
102C2×Q8—1461no—
103C2×Q8—1461no—
104C22×C4—22no—
105C22×C4C22⋊D7311yescharacteristic
106C22×C4C22⋊D7311yescharacteristic
107C22×C4C22×D7311yescharacteristic
108M16—734no—
109M16—1462no—
110C2×C8—1462no—
111C4⋊C4—24no—
112C4⋊C4—732no—
113C4⋊C4—732no—
114C4⋊C4—1462no—
115C4⋊C4—1462no—
116C4⋊C4—1461no—
117C4⋊C4—1461no—
118C22⋊C4—1462no—
119C42—24no—
120C42—1462no—
121C42C4×D7311yescharacteristic
122C42C4×D7311yescharacteristic
123C42D29211yescharacteristic
124C42D29211yescharacteristic
125C23C2×C22⋊D7311yescharacteristic
126Q8—2922no—
127Q8—2922no—
128C2×C4—22no—
129C2×C4—24no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—1462no—
134C2×C4—1462no—
135C2×C4#1192400511yescharacteristic
136C2×C4#1192400511yescharacteristic
137C2×C4#1192400511yescharacteristic
138C2×C4#1192400511yescharacteristic
139C2×C4C2×C4×D7311yescharacteristic
140C2×C4C2×D29211yescharacteristic
141C2×C4Q8×D7312yes—
142C2×C4#1192402712yes—
143C8—1464no—
144C22—21no—
145C22—21no—
146C22C2×#1192400511yescharacteristic
147C22#1455657811yescharacteristic
148C22#1455658911yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—44no—
153C4—2922no—
154C4—2922no—
155C4#1455651912yes—
156C4#1455655612yes—
157C4#1455657112yes—
158C2—21no—
159C2—21no—
160C2#1798849211yescharacteristic
161C2C2×#1455651911yescharacteristic
162C2#1798860511yescharacteristic
subgroupG/H
centerC2×C4C2×D292
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC4×C4⋊C4×C73C2
socleC22×C73C2×C22⋊C4
hypercenterC4×C4⋊C4D73
hypocenterC73#1986
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #14556591C4semidirect
7. #14556591C4semidirect
8. #14556583C4semidirect
23. #11924012Q8semidirect
82. C73#1986semidirect