Finite Group Databasebeta

← #22625180

Subgroups — #22625180

Order 9344.

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

normal subgroups only

This group has 312 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#17989558C212yesmaximal
2#17989433C212yesmaximal, complemented
3#17989432C212yesmaximal, complemented
4C2×C4⋊C4×D73C211yesmaximal, characteristic
5C2×#11924038—22no—
6#14556648—22no—
7C22⋊#10596833C2214yes—
8C22×C4×D73C411yescharacteristic
9C22×C4×D73C411yescharacteristic
10C22×C4×D73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007C411yescharacteristic
13C2×#11924007C2211yescharacteristic
14C4⋊C4×D73—22no—
15C4⋊C4×D73—22no—
16C2×C4⋊C4×C73C411yescharacteristic
17#11924038—44no—
18C2×#10596833—24no—
19C23×D73C2×C411yescharacteristic
20C22×Dic73C2×C411yescharacteristic
21C22×Dic73C2×C411yescharacteristic
22C22×Dic73C2311yescharacteristic
23C2×C4×D73—21no—
24C2×C4×D73—21no—
25C2×C4×D73—22no—
26C2×C4×D73—22no—
27C2×C4×D73—21no—
28C2×C4×D73—21no—
29C2×C4×D73—42no—
30C2×C4×D73—42no—
31C2×C4×D73D412yes—
32C2×C4×D73D412yes—
33C4⋊Dic73—22no—
34#11924007—22no—
35#11924007—22no—
36C22×C4×C73C2×C411yescharacteristic
37C22×C4×C73C2×C411yescharacteristic
38C22×C4×C73C2×C411yescharacteristic
39C4⋊C4×C73—22no—
40C23×C73C22×C411yescharacteristic
41C22×D73—21no—
42C22×D73—21no—
43C22×D73—22no—
44C22×D73—22no—
45C22×D73C22⋊C411yescharacteristic
46C22×D73C22⋊C411yescharacteristic
47C2×C4×C73—21no—
48C2×C4×C73—21no—
49C2×C4×C73—21no—
50C2×C4×C73—41no—
51C2×C4×C73—41no—
52C2×C4×C73C22⋊C412yes—
53C2×C4×C73M1612yescomplemented
54C2×Dic73—21no—
55C2×Dic73—21no—
56C2×Dic73—21no—
57C2×Dic73—41no—
58C2×Dic73—41no—
59C2×Dic73M1612yescomplemented
60C2×Dic73C2×D412yes—
61C4×D73—24no—
62C4×D73—24no—
63C4×D73—24no—
64C4×D73—42no—
65C4×D73—42no—
66C4×D73—42no—
67#10596833—44no—
68C22×C73—21no—
69C22×C73—21no—
70C22×C73C2×C22⋊C411yescharacteristic
71C22×C73C2×M1611yescharacteristic
72C22×C73C2×M1611yescharacteristic
73C2×D73—24no—
74C2×D73—24no—
75C2×D73—21no—
76C2×D73—21no—
77C2×D73—21no—
78C2×D73—21no—
79C2×D73#9912yes—
80C2×D73#10112yes—
81C4×C73—22no—
82C4×C73—22no—
83C4×C73—41no—
84Dic73—22no—
85Dic73—22no—
86Dic73—41no—
87C2×C73—21no—
88C2×C73—21no—
89C2×C73#40711yescharacteristic
90C2×C73C2×#9911yescharacteristic
91C2×C73C2×#10111yescharacteristic
92D73—22no—
93D73—22no—
94#1463—731nomaximal, Sylow
95C73#146311yescharacteristic, complemented, Sylow
96C22×C4⋊C4—731no—
97#407—732no—
98#324—732no—
99#324—732no—
100C23×C4—731no—
101C23×C4—731no—
102C23×C4—731no—
103C2×M16—1462no—
104C2×C4⋊C4—731no—
105C2×C4⋊C4—731no—
106C2×C4⋊C4—731no—
107C2×C4⋊C4—1462no—
108C2×C4⋊C4—1462no—
109C2×C4⋊C4#6440811yescharacteristic
110C22⋊C8—734no—
111C22⋊C8—1462no—
112C24—731no—
113C22×C4—2922no—
114C22×C4—2922no—
115C22×C4—731no—
116C22×C4—732no—
117C22×C4—731no—
118C22×C4—731no—
119C22×C4—732no—
120C22×C4—1461no—
121C22×C4—1461no—
122C22×C4—1462no—
123C22×C4—1461no—
124C22×C4—1461no—
125C22×C4—1462no—
126C22×C4C2×#6440811yescharacteristic
127C22×C4C2×#6440811yescharacteristic
128C22×C4C2×#6440811yescharacteristic
129M16—2924no—
130C2×C8—1464no—
131C4⋊C4—22no—
132C4⋊C4—1462no—
133C4⋊C4—1462no—
134C4⋊C4—1462no—
135C23—731no—
136C23—731no—
137C23—1462no—
138C23—1462no—
139C23—1461no—
140C23—1461no—
141C23C22×#6440811yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—2922no—
148C2×C4—2922no—
149C2×C4—2922no—
150C2×C4—2921no—
151C2×C4—2921no—
152C2×C4—732no—
153C2×C4—732no—
154C2×C4—1464no—
155C2×C4—1464no—
156C2×C4—1464no—
157C2×C4—1461no—
158C2×C4—1461no—
159C2×C4—1461no—
160C2×C4C22⋊#6440812yes—
161C2×C4#1192403812yescomplemented
162C8—2924no—
163C22—21no—
164C22—21no—
165C22—732no—
166C22—732no—
167C22—1464no—
168C22—1464no—
169C22—1461no—
170C22—1461no—
171C22—1461no—
172C22—1461no—
173C22C2×C22⋊#6440811yescharacteristic
174C22D73⋊M1611yescharacteristic
175C22C2×#1192403811yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—2921no—
180C4—1462no—
181C4—1462no—
182C2—21no—
183C2—21no—
184C2—1462no—
185C2—1462no—
186C2#1798955811yescharacteristic
187C2D73⋊#9911yescharacteristic
188C2D73⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C4⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73#1463
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #17989433C2semidirect
3. #17989432C2semidirect
53. C2×C4×C73M16semidirect
59. C2×Dic73M16semidirect
95. C73#1463semidirect
161. C2×C4#11924038semidirect