Finite Group Databasebeta

← #22625339

Subgroups — #22625339

Order 9344.

274 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989559C211yesmaximal, characteristic
2#17989530C211yesmaximal, characteristic
3#17989440C214yesmaximal, complemented
4C2×#14556571C211yesmaximal, characteristic
5C2×#11924037—21no—
6C2×C22⋊#64408—21no—
7#14556648—21no—
8#14556648C2212yes—
9(C2×#64408)⋊C4—21no—
10(C2×#64408)⋊C4C2212yes—
11C22×Dic146C411yescharacteristic, complemented
12C22×C4×D73C2211yescharacteristic
13#14556571—21no—
14#14556571—21no—
15#14556571C412yescomplemented
16#14556571C2212yes—
17C2×C4⋊Dic73—21no—
18C2×#11924005—21no—
19C2×C4⋊C4×C73C411yescharacteristic, complemented
20C22×#64408—22no—
21#11924037—42no—
22C2×#10596833—22no—
23C22⋊#64408—42no—
24C23×D73D411yescharacteristic
25C2×Dic146—21no—
26C2×Dic146—42no—
27C2×Dic146C2×C412yes—
28C22×Dic73—21no—
29C22×Dic73D411yescharacteristic
30C2×C4×D73—42no—
31C2×C4×D73C2×C411yescharacteristic
32C2×C4×D73D411yescharacteristic
33C2×C4×D73D411yescharacteristic
34C2×C4×D73C2311yescharacteristic
35C4⋊Dic73—22no—
36C4⋊Dic73—22no—
37#11924005—22no—
38#11924005—22no—
39C22×C4×C73—21no—
40C22×C4×C73C2×C411yescharacteristic
41C4⋊C4×C73—21no—
42C4⋊C4×C73C2×C412yes—
43C23×C73C22⋊C411yescharacteristic
44C22×D73—22no—
45C22×D73—22no—
46C22×D73—41no—
47C22×D73C22⋊C411yescharacteristic
48C22×D73C2×D411yescharacteristic
49C2×#64408—42no—
50C2×#64408—42no—
51C2×#64408—42no—
52C2×C4×C73—22no—
53C2×C4×C73—22no—
54C2×C4×C73—42no—
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22×C411yescharacteristic
57C2×Dic73—22no—
58C2×Dic73—22no—
59C2×Dic73—42no—
60C2×Dic73C22⋊C411yescharacteristic
61C2×Dic73C2×D411yescharacteristic
62C4×D73—41no—
63C4×D73—41no—
64C4×D73—41no—
65C4×D73—41no—
66Dic146—42no—
67Dic146—42no—
68#10596833—42no—
69C22×C73—21no—
70C22×C73—21no—
71C22×C73#9912yes—
72C22×C73C2×C22⋊C411yescharacteristic
73C2×D73—21no—
74C2×D73—21no—
75C2×D73—21no—
76C2×D73—21no—
77C2×D73—21no—
78C2×D73—44no—
79C2×D73#13712yes—
80#64408—82no—
81C4×C73—21no—
82C4×C73—21no—
83C4×C73—42no—
84Dic73—21no—
85Dic73—21no—
86Dic73—42no—
87C2×C73—22no—
88C2×C73C2×#9911yescharacteristic
89C2×C73#41911yescharacteristic
90C2×C73#42111yescharacteristic
91D73—22no—
92D73—41no—
93#1511—731nomaximal, Sylow
94C73#151111yescharacteristic, complemented, Sylow
95C2×C22⋊Q8—731no—
96#407—731no—
97#381—731no—
98#328—734no—
99C22×Q8—731no—
100C23×C4—731no—
101C2×M16—1461no—
102C22⋊Q8—732no—
103C22⋊Q8—732no—
104C22⋊Q8—1461no—
105C22⋊Q8—1461no—
106C2×C4⋊C4—1461no—
107C2×C4⋊C4#6440811yescharacteristic, complemented
108C2×C22⋊C4—1461no—
109C2×C22⋊C4—1461no—
110C22⋊C8—732no—
111C22⋊C8—1461no—
112#95—732no—
113#95—1461no—
114C24—731no—
115C2×Q8—2922no—
116C2×Q8—732no—
117C2×Q8—1461no—
118C22×C4—21no—
119C22×C4—2922no—
120C22×C4—731no—
121C22×C4—731no—
122C22×C4—731no—
123C22×C4—731no—
124C22×C4—731no—
125C22×C4—1462no—
126C22×C4—1461no—
127C22×C4C2×#6440811yescharacteristic
128M16—2922no—
129C2×C8—1462no—
130C4⋊C4—21no—
131C4⋊C4—1462no—
132C4⋊C4—1462no—
133C4⋊C4C2×#6440812yes—
134C22⋊C4—2922no—
135C22⋊C4—1462no—
136C22⋊C4—1462no—
137C23—2921no—
138C23—731no—
139C23—731no—
140C23—1462no—
141C23—1462no—
142C23C22⋊#6440811yescharacteristic
143Q8—2922no—
144Q8—2922no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—42no—
148C2×C4—2921no—
149C2×C4—2921no—
150C2×C4—2921no—
151C2×C4—2921no—
152C2×C4—2922no—
153C2×C4—2922no—
154C2×C4—2922no—
155C2×C4—2922no—
156C2×C4—731no—
157C2×C4—731no—
158C2×C4—1462no—
159C2×C4—1462no—
160C2×C4C22⋊#6440811yescharacteristic
161C2×C4C22×#6440811yescharacteristic
162C8—2922no—
163C22—21no—
164C22—21no—
165C22—2924no—
166C22—732no—
167C22—1461no—
168C22—1461no—
169C22—1461no—
170C22—1461no—
171C22—1461no—
172C22#1455665012yes—
173C22C2×C22⋊#6440811yescharacteristic
174C4—21no—
175C4—21no—
176C4—42no—
177C4—2922no—
178C4—5842no—
179C4—1461no—
180C4—1461no—
181C2—22no—
182C2—2921no—
183C2—1462no—
184C2C2×#1455665011yescharacteristic
185C2#1798958011yescharacteristic
186C2#1798958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×C4⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73#1511
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #17989440C2semidirect
11. C22×Dic146C4semidirect
15. #14556571C4semidirect
19. C2×C4⋊C4×C73C4semidirect
94. C73#1511semidirect
107. C2×C4⋊C4#64408semidirect