Finite Group Databasebeta

← #22625169

Subgroups — #22625169

Order 9344.

332 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C2×C22⋊#10596833C212yesmaximal, complemented
2#17989433C212yesmaximal, complemented
3#17989431C212yesmaximal, complemented
4C2×#14556551C211yesmaximal, characteristic
5C22×#10596833—22no—
6C22⋊#10596833—22no—
7C22⋊#10596833C2214yes—
8C22×C22⋊D73C411yescharacteristic
9C23×Dic73C2211yescharacteristic
10C22×C4×D73C411yescharacteristic
11#14556551—22no—
12#14556551—22no—
13C2×#11924007C2211yescharacteristic
14C2×#11924005C2211yescharacteristic
15C2×C4×Dic73C411yescharacteristic
16C2×C22⋊C4×C73C411yescharacteristic
17C2×#10596833—24no—
18C2×#10596833—44no—
19C23×D73C2×C411yescharacteristic
20C2×C22⋊D73—22no—
21C2×C22⋊D73—22no—
22C2×C22⋊D73C814yescomplemented
23C22×Dic73—42no—
24C22×Dic73C2×C411yescharacteristic
25C22×Dic73C2×C411yescharacteristic
26C22×Dic73D412yes—
27C22×Dic73D412yes—
28C22×Dic73C2311yescharacteristic
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×C4×D73—42no—
32#11924007—22no—
33#11924005—22no—
34C4×Dic73—21no—
35C4×Dic73—21no—
36C24×C73C2×C411yescharacteristic
37C22×C4×C73C2×C411yescharacteristic
38C22×C4×C73C2×C411yescharacteristic
39C22⋊C4×C73—22no—
40C23×C73—41no—
41C23×C73—41no—
42C23×C73C22⋊C412yes—
43C23×C73C2×C812yes—
44C23×C73M1612yes—
45C23×C73C22×C411yescharacteristic
46C22×D73—21no—
47C22×D73—21no—
48C22×D73—41no—
49C22×D73—41no—
50C22×D73C2×C812yescomplemented
51C2×C4×C73—21no—
52C2×C4×C73—21no—
53C2×C4×C73—41no—
54C2×C4×C73—41no—
55C22⋊D73—28no—
56C2×Dic73—21no—
57C2×Dic73—21no—
58C2×Dic73—22no—
59C2×Dic73—24no—
60C2×Dic73—42no—
61C2×Dic73—41no—
62C2×Dic73C22⋊C411yescharacteristic
63C2×Dic73C22⋊C411yescharacteristic
64C2×Dic73C2×C812yescomplemented
65C2×Dic73C2×D412yes—
66C4×D73—42no—
67C4×D73—42no—
68#10596833—44no—
69C22×C73—21no—
70C22×C73—22no—
71C22×C73—21no—
72C22×C73—22no—
73C22×C73—42no—
74C22×C73—42no—
75C22×C73C22⋊C814yes—
76C22×C73C2×C22⋊C411yescharacteristic
77C22×C73C22×C811yescharacteristic
78C22×C73C2×M1611yescharacteristic
79C2×D73—22no—
80C2×D73—42no—
81C2×D73—41no—
82C2×D73—41no—
83C2×D73—42no—
84C4×C73—41no—
85C4×C73—41no—
86Dic73—22no—
87Dic73—22no—
88Dic73—21no—
89Dic73#9912yes—
90C2×C73—21no—
91C2×C73—21no—
92C2×C73—24no—
93C2×C73C2×C22⋊C811yescharacteristic
94C2×C73C2×#9911yescharacteristic
95C2×C73#41311yescharacteristic
96D73—42no—
97#1459—731nomaximal, Sylow
98C73#145911yescharacteristic, complemented, Sylow
99C2×C4×D4—731no—
100C2×C22⋊C8—732no—
101#324—732no—
102#323—732no—
103C22×D4—731no—
104C23×C4—731no—
105C23×C4—731no—
106C22×C8—1462no—
107C4×D4—1462no—
108C4×D4—1462no—
109C2×C4⋊C4—731no—
110C2×C22⋊C4—731no—
111C2×C22⋊C4#6440811yescharacteristic
112C2×C42—731no—
113C22⋊C8—734no—
114C22⋊C8—1462no—
115C24—731no—
116C24C2×#6440811yescharacteristic
117C2×D4—734no—
118C2×D4—1462no—
119C2×D4—1462no—
120C22×C4—2922no—
121C22×C4—2922no—
122C22×C4—732no—
123C22×C4—731no—
124C22×C4—732no—
125C22×C4—731no—
126C22×C4—731no—
127C22×C4—1461no—
128C22×C4—1461no—
129C22×C4C2×#6440811yescharacteristic
130C22×C4C2×#6440811yescharacteristic
131C2×C8—2924no—
132C2×C8—1464no—
133C4⋊C4—1462no—
134C22⋊C4—22no—
135C22⋊C4—1462no—
136C42—1461no—
137C42—1461no—
138C23—41no—
139C23—41no—
140C23—2921no—
141C23—2921no—
142C23—732no—
143C23—1461no—
144C23—1461no—
145C23C22⋊#6440812yes—
146C23#1192403612yes—
147C23#1192403812yes—
148C23C22×#6440811yescharacteristic
149D4—1468no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—2922no—
155C2×C4—2922no—
156C2×C4—2921no—
157C2×C4—2922no—
158C2×C4—731no—
159C2×C4—732no—
160C2×C4—731no—
161C2×C4—732no—
162C2×C4—1464no—
163C2×C4—1462no—
164C2×C4—1461no—
165C2×C4—1461no—
166C8—2924no—
167C22—21no—
168C22—22no—
169C22—21no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22—2922no—
174C22—2922no—
175C22—2921no—
176C22—2921no—
177C22—1462no—
178C22#1455664814yes—
179C22C2×C22⋊#6440811yescharacteristic
180C22C2×#1192403611yescharacteristic
181C22C2×#1192403811yescharacteristic
182C4—41no—
183C4—41no—
184C4—732no—
185C4—1462no—
186C4—1462no—
187C4—1461no—
188C2—21no—
189C2—21no—
190C2—24no—
191C2—2922no—
192C2C2×#1455664811yescharacteristic
193C2D73⋊#9911yescharacteristic
194C2#1798957411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC22×C73C22×C8
FrattiniC23C22×#64408
FittingC2×C22⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C22⋊C4#64408
hypocenterC73#1459
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊#10596833C2semidirect
2. #17989433C2semidirect
3. #17989431C2semidirect
22. C2×C22⋊D73C8semidirect
50. C22×D73C2×C8semidirect
64. C2×Dic73C2×C8semidirect
98. C73#1459semidirect