Finite Group Databasebeta

← #22611585

Subgroups — #22611585

Order 9344.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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#17988571C211yesmaximal, characteristic
2#17988561C211yesmaximal, characteristic
3#17988377C214yesmaximal, complemented
4#536×C73C211yesmaximal, characteristic
5C2×#11924012—21no—
6#14556550—21no—
7#14556510—21no—
8#14556508C2212yes—
9#14556506—21no—
10#14556506C2212yes—
11C2×#41×C73C2211yescharacteristic
12C22×Q8×C73C411yescharacteristic, complemented
13C4⋊Q8×C73—21no—
14#124×C73—21no—
15#123×C73C412yescomplemented
16#123×C73C2212yes—
17C22⋊Q8×C73—21no—
18C22⋊Q8×C73—21no—
19#117×C73C411yescharacteristic, complemented
20#11924012—22no—
21#11924012—41no—
22C2×#10596831—41no—
23C4⋊Dic73—41no—
24C22⋊Dic73—22no—
25C4×Dic73—41no—
26#41×C73—41no—
27#41×C73—41no—
28C2×Q8×C73—21no—
29C2×Q8×C73—21no—
30C2×Q8×C73—41no—
31C2×Q8×C73—41no—
32C2×Q8×C73D411yescharacteristic
33C2×D4×C73C2×C411yescharacteristic
34C2×D4×C73D411yescharacteristic
35C2×D4×C73C2311yescharacteristic
36C22×C4×C73C2×C411yescharacteristic
37C22×C4×C73C2×C412yes—
38C22×C4×C73D411yescharacteristic
39C22×C4×C73D411yescharacteristic
40C4⋊C4×C73—21no—
41C4⋊C4×C73—22no—
42C4⋊C4×C73—22no—
43C22⋊C4×C73—22no—
44C22⋊C4×C73—22no—
45C22⋊C4×C73C2×C412yes—
46C42×C73—21no—
47C23×C73C22⋊C411yescharacteristic
48C23×C73C22×C411yescharacteristic
49C23×C73C2×D411yescharacteristic
50Q8×C73—41no—
51Q8×C73—42no—
52Q8×C73—41no—
53Q8×C73—41no—
54D4×C73—41no—
55D4×C73—41no—
56D4×C73—41no—
57C2×C4×C73—21no—
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73—21no—
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—42no—
66C2×C4×C73C22⋊C411yescharacteristic
67C2×C4×C73C22⋊C411yescharacteristic
68C2×C4×C73C22⋊C411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×Dic73—42no—
71#10596831—42no—
72C22×C73—21no—
73C22×C73—21no—
74C22×C73—21no—
75C22×C73—41no—
76C22×C73—41no—
77C22×C73—41no—
78C22×C73C2×C22⋊C411yescharacteristic
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—21no—
82C4×C73—42no—
83C4×C73—42no—
84C4×C73#9911yescharacteristic
85C4×C73#9911yescharacteristic
86Dic73—82no—
87C2×C73—21no—
88C2×C73—41no—
89C2×C73—41no—
90C2×C73—41no—
91C2×C73C2×#9911yescharacteristic
92#2123—731nomaximal, Sylow
93C73#212311yescharacteristic, complemented, Sylow
94#536D7311yescharacteristic
95#413—731no—
96#410—731no—
97#352—734no—
98C2×#41C2×D7311yescharacteristic
99C22×Q8Dic7311yescharacteristic, complemented
100C2×M16—1461no—
101C4⋊Q8—21no—
102#124—21no—
103#123Dic7312yescomplemented
104#123C2×D7312yes—
105C22⋊Q8—21no—
106C22⋊Q8—21no—
107#117—1461no—
108#117Dic7311yescharacteristic, complemented
109#101—1461no—
110#100—732no—
111#99—732no—
112#99—1461no—
113#41—41no—
114#41—41no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—41no—
118C2×Q8—41no—
119C2×Q8C22⋊D7311yescharacteristic
120C2×D4C2×Dic7311yescharacteristic
121C2×D4C22⋊D7311yescharacteristic
122C2×D4C22×D7311yescharacteristic
123C22×C4C2×Dic7311yescharacteristic
124C22×C4C2×Dic7312yes—
125C22×C4C22⋊D7311yescharacteristic
126C22×C4C22⋊D7311yescharacteristic
127M16—2921no—
128M16—1462no—
129C2×C8—2921no—
130C4⋊C4—22no—
131C4⋊C4—21no—
132C4⋊C4—22no—
133C4⋊C4—2921no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—1462no—
137C22⋊C4C2×Dic7312yes—
138C42—21no—
139C42—2921no—
140C23C22⋊Dic7311yescharacteristic
141C23C22×Dic7311yescharacteristic
142C23C2×C22⋊D7311yescharacteristic
143Q8—41no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—2922no—
160C2×C4C22⋊Dic7311yescharacteristic
161C2×C4C22⋊Dic7311yescharacteristic
162C2×C4C22⋊Dic7311yescharacteristic
163C2×C4C2×C22⋊D7311yescharacteristic
164C8—2922no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×C22⋊Dic7311yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—42no—
176C4—42no—
177C4—5842no—
178C4#1455650611yescharacteristic
179C4#1455650611yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1455650611yescharacteristic
subgroupG/H
centerC2C2×#14556506
commutatorC23×C73C22×C4
FrattiniC2×D4C22×D73
Fitting#536×C73C2
socleC2×C73C2×#99
hypercenter#536D73
hypocenterC73#2123
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
3. #17988377C2semidirect
12. C22×Q8×C73C4semidirect
15. #123×C73C4semidirect
19. #117×C73C4semidirect
93. C73#2123semidirect
99. C22×Q8Dic73semidirect
103. #123Dic73semidirect
108. #117Dic73semidirect