Finite Group Databasebeta

← #22625313

Subgroups — #22625313

Order 9344.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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#17989605C211yesmaximal, characteristic
2C4×C4⋊#64408C211yesmaximal, characteristic
3#17989441C212yesmaximal
4#17989440C212yesmaximal
5#17989141C211yesmaximal, characteristic
6C2×C4⋊#64408—21no—
7C2×C4×#64408—21no—
8#14556658—21no—
9#14556648C2212yes—
10C4×#10596833—21no—
11(C2×#64408)⋊C4C2212yes—
12#14556590C411yescharacteristic, complemented
13#14556589C411yescharacteristic, complemented
14#14556581—21no—
15#14556571C2211yescharacteristic
16#14556569—21no—
17#14556567C2211yescharacteristic
18C4×Dic146—21no—
19C4×Dic146C411yescharacteristic, complemented
20#14556548—21no—
21C42×D73C2211yescharacteristic
22C4×Q8×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C2×#10596833—22no—
25C4⋊#64408—24no—
26C4×#64408—42no—
27C2×Dic146—21no—
28C2×Dic146C2×C411yescharacteristic
29C2×C4×D73D411yescharacteristic
30C2×C4×D73D411yescharacteristic
31C2×C4×D73C2311yescharacteristic
32C4⋊Dic73—21no—
33C4⋊Dic73C2×C411yescharacteristic
34#11924007—21no—
35#11924007—21no—
36#11924007—21no—
37#11924007—21no—
38#11924007—21no—
39#11924005—21no—
40#11924005—21no—
41C4×Dic73—21no—
42C4×Dic73C2×C411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73D411yescharacteristic
45C2×Q8×C73C2×C411yescharacteristic
46C4⋊C4×C73—21no—
47C4⋊C4×C73C2×C411yescharacteristic
48C42×C73—21no—
49C42×C73C2×C411yescharacteristic
50C22×D73C2×D411yescharacteristic
51C2×#64408—24no—
52C2×#64408—42no—
53C2×#64408—42no—
54Q8×C73—41no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C2×Dic73—21no—
61C2×Dic73—21no—
62C2×Dic73C22⋊C411yescharacteristic
63C2×Dic73C22⋊C411yescharacteristic
64C2×Dic73C2×D411yescharacteristic
65C4×D73—22no—
66C4×D73—41no—
67C4×D73SD1612yes—
68C4×D73Q1612yes—
69Dic146—42no—
70Dic146—41no—
71#10596833—42no—
72C22×C73C2×C22⋊C411yescharacteristic
73C2×D73—21no—
74C2×D73—21no—
75C2×D73C2×SD1611yescharacteristic
76C2×D73C2×Q1611yescharacteristic
77#64408—44no—
78C4×C73—21no—
79C4×C73—21no—
80C4×C73—41no—
81C4×C73—41no—
82C4×C73#10312yes—
83Dic73—21no—
84Dic73—41no—
85Dic73—41no—
86Dic73#10312yes—
87Dic73#10412yes—
88C2×C73#41011yescharacteristic
89C2×C73C2×#10311yescharacteristic
90C2×C73C2×#10411yescharacteristic
91D73—21no—
92D73—21no—
93#1503—731nomaximal, Sylow
94C73#150311yescharacteristic, complemented, Sylow
95#533—731no—
96#431—731no—
97C4×C4⋊C4—731no—
98#328—732no—
99#328—732no—
100C4⋊Q8—731no—
101C4⋊Q8—731no—
102#125—1461no—
103C22⋊Q8—731no—
104C22⋊Q8—731no—
105C22⋊Q8—1461no—
106C4×Q8—731no—
107C4×Q8—1461no—
108C4×Q8#6440811yescharacteristic, complemented
109#117—1461no—
110C2×C4⋊C4—1461no—
111C2×C42—731no—
112C2×C42—1461no—
113C4⋊C8—1461no—
114C22⋊C8—732no—
115C4×C8—1461no—
116#95—732no—
117C2×Q8—731no—
118C2×Q8—1461no—
119C2×Q8C2×#6440811yescharacteristic
120C22×C4—731no—
121C22×C4—731no—
122C22×C4—731no—
123C22×C4—1462no—
124C2×C8—1462no—
125C4⋊C4—21no—
126C4⋊C4—731no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4—1461no—
132C4⋊C4—1464no—
133C4⋊C4—1461no—
134C4⋊C4C2×#6440811yescharacteristic
135C22⋊C4—1461no—
136C22⋊C4—1461no—
137C42—21no—
138C42—2922no—
139C42—731no—
140C42—731no—
141C42—731no—
142C42—1461no—
143C42C2×#6440811yescharacteristic
144C23—731no—
145Q8—41no—
146Q8—2921no—
147Q8—2922no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—2921no—
151C2×C4—2922no—
152C2×C4—2922no—
153C2×C4—731no—
154C2×C4—731no—
155C2×C4—732no—
156C2×C4—732no—
157C2×C4—731no—
158C2×C4—1462no—
159C2×C4—1464no—
160C2×C4—1461no—
161C2×C4—1461no—
162C2×C4C22⋊#6440811yescharacteristic
163C2×C4C22⋊#6440811yescharacteristic
164C2×C4C22×#6440811yescharacteristic
165C8—2922no—
166C22—731no—
167C22—731no—
168C22—1461no—
169C22—1461no—
170C22C2×C22⋊#6440811yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—2924no—
176C4—2921no—
177C4—2921no—
178C4—732no—
179C4—732no—
180C4—1461no—
181C4#1455665412yes—
182C2—1461no—
183C2—1461no—
184C2#1798956611yescharacteristic
185C2C2×#1455665411yescharacteristic
186C2D73⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×Q8#64408
hypocenterC73#1503
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #14556590C4semidirect
13. #14556589C4semidirect
19. C4×Dic146C4semidirect
22. C4×Q8×C73C4semidirect
94. C73#1503semidirect
108. C4×Q8#64408semidirect