Finite Group Databasebeta

← #22610910

Subgroups — #22610910

Order 9344.

244 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 83 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#17989140C211yesmaximal, characteristic
2#17988610C211yesmaximal, characteristic
3#17988433C211yesmaximal, characteristic
4#17988348C211yesmaximal, characteristic
5#17988347C211yesmaximal, characteristic
6#17988346C211yesmaximal, characteristic
7#339×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9#14556590C412yescomplemented
10#14556582C412yescomplemented
11#14556568—22no—
12C4×Dic146—22no—
13#14556550C2211yescharacteristic
14C2×C4×Dic73C2211yescharacteristic
15C2×C4×Dic73C2211yescharacteristic
16#14556520—22no—
17#14556498—22no—
18C2×M16×C73C2211yescharacteristic
19#117×C73C2211yescharacteristic
20C2×C42×C73C2211yescharacteristic
21C2×Dic146—22no—
22C22×Dic73—21no—
23C22×Dic73D412yes—
24#11924012—21no—
25#11924012—21no—
26C2×#10596831—21no—
27C4⋊Dic73—22no—
28C4⋊Dic73C2×C412yes—
29#11924007—22no—
30#11924007—22no—
31C22⋊Dic73—21no—
32C4×Dic73—21no—
33C4×Dic73—21no—
34C4×Dic73C2×C411yescharacteristic
35C4×Dic73C2×C411yescharacteristic
36C4×Dic73D412yes—
37C4×Dic73Q812yescomplemented
38C22×C4×C73—21no—
39C22×C4×C73C2311yescharacteristic
40M16×C73—21no—
41M16×C73—21no—
42C2×C8×C73—21no—
43C4⋊C4×C73C2×C412yes—
44C22⋊C4×C73—21no—
45C42×C73—21no—
46C42×C73—21no—
47C42×C73Q812yescomplemented
48C23×C73C2×D411yescharacteristic
49C2×C4×C73—22no—
50C2×C4×C73—22no—
51C2×C4×C73—42no—
52C2×C4×C73C22×C411yescharacteristic
53C2×C4×C73C2×D411yescharacteristic
54C2×C4×C73C2×Q811yescharacteristic
55C2×C4×C73C2×Q811yescharacteristic
56C2×C4×C73#4111yescharacteristic
57C2×C4×C73#4111yescharacteristic
58C2×Dic73—22no—
59C2×Dic73—22no—
60C2×Dic73—42no—
61C2×Dic73—42no—
62C2×Dic73C22⋊C412yes—
63C2×Dic73C22⋊C412yes—
64Dic146—44no—
65C8×C73—41no—
66#10596831—41no—
67C22×C73—22no—
68C22×C73C2×C22⋊C411yescharacteristic
69C22×C73C22⋊Q811yescharacteristic
70C22×C73C22⋊Q811yescharacteristic
71C4×C73—42no—
72C4×C73—42no—
73C4×C73C4×Q811yescharacteristic
74C4×C73C4×Q811yescharacteristic
75C4×C73#12411yescharacteristic
76C4×C73C4⋊Q811yescharacteristic
77Dic73—22no—
78Dic73—22no—
79Dic73—42no—
80Dic73—42no—
81C2×C73—21no—
82C2×C73—21no—
83C2×C73#39111yescharacteristic
84C2×C73#42112yes—
85#1995—731nomaximal, Sylow
86C73#199511yescharacteristic, complemented, Sylow
87#533—731no—
88#423—731no—
89#376—731no—
90#339—731no—
91#339—731no—
92#339—731no—
93#339D7311yescharacteristic
94C2×M16—731no—
95C2×M16C2×D7311yescharacteristic
96C4⋊Q8—732no—
97#125—732no—
98C22⋊Q8—1462no—
99C4×Q8—1462no—
100#117—731no—
101#117C2×D7311yescharacteristic
102C2×C42—731no—
103C2×C42—731no—
104C2×C42C2×D7311yescharacteristic
105C4⋊C8—1462no—
106#95—1462no—
107C2×Q8—1462no—
108C22×C4—21no—
109C22×C4—732no—
110C22×C4—1461no—
111C22×C4C22×D7311yescharacteristic
112M16—21no—
113M16—21no—
114M16—1461no—
115M16—1461no—
116C2×C8—21no—
117C2×C8—1461no—
118C4⋊C4—732no—
119C4⋊C4—1462no—
120C4⋊C4—1462no—
121C4⋊C4—1462no—
122C4⋊C4C4×D7312yes—
123C22⋊C4—21no—
124C22⋊C4—1461no—
125C42—21no—
126C42—21no—
127C42—731no—
128C42—731no—
129C42—732no—
130C42—732no—
131C42—1461no—
132C42—1461no—
133C42Dic14612yescomplemented
134C23D4×D7311yescharacteristic
135Q8—2924no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—2922no—
140C2×C4—2922no—
141C2×C4—732no—
142C2×C4—732no—
143C2×C4—1462no—
144C2×C4—1462no—
145C2×C4C2×C4×D7311yescharacteristic
146C2×C4D4×D7311yescharacteristic
147C2×C4Q8×D7311yescharacteristic
148C2×C4C2×Dic14611yescharacteristic
149C2×C4#1192402711yescharacteristic
150C2×C4#1192402811yescharacteristic
151C8—41no—
152C8—2921no—
153C22—22no—
154C22C22⋊C4×D7311yescharacteristic
155C22#1455656811yescharacteristic
156C22#1455656911yescharacteristic
157C4—42no—
158C4—42no—
159C4—2922no—
160C4—2922no—
161C4—1462no—
162C4—1462no—
163C4#1455655611yescharacteristic
164C4C4×Dic14611yescharacteristic
165C4#1455657711yescharacteristic
166C4#1455659011yescharacteristic
167C2—21no—
168C2—21no—
169C2#1798849111yescharacteristic
170C2#1798860212yes—
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#339×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#339D73
hypocenterC73#1995
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #14556590C4semidirect
10. #14556582C4semidirect
37. C4×Dic73Q8semidirect
47. C42×C73Q8semidirect
86. C73#1995semidirect
133. C42Dic146semidirect