Finite Group Databasebeta

← #22608268

Subgroups — #22608268

Order 9344.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14556553C211yesmaximal, characteristic
2#17988549C212yesmaximal, complemented
3#17988313C211yesmaximal, characteristic, complemented
4#17988310C212yesmaximal, complemented
5#324×C73C211yesmaximal, characteristic, complemented
6C22×D292C411yescharacteristic
7C22×C4×D73C411yescharacteristic
8C22×C4×D73C2211yescharacteristic
9C2×#11924011—22no—
10#14556553—22no—
11#14556553—22no—
12C2×#11924005C411yescharacteristic
13C2×#11924005C2211yescharacteristic
14C2×C4×Dic73C411yescharacteristic
15C22⋊#10596831C2212yes—
16#14556503—22no—
17C2×C4⋊C4×C73C2211yescharacteristic
18C22⋊C8×C73C2212yes—
19C23×D73C2×C411yescharacteristic
20C23×D73C2×C411yescharacteristic
21C2×D292—22no—
22C2×D292—22no—
23C2×D292—22no—
24C22×Dic73C2×C411yescharacteristic
25C22×Dic73C2×C411yescharacteristic
26C2×C4×D73—21no—
27C2×C4×D73—21no—
28C2×C4×D73—42no—
29C2×C4×D73—42no—
30C2×C4×D73D412yes—
31C2×C4×D73D412yes—
32#11924011—44no—
33C2×#10596831—22no—
34#11924005—22no—
35#11924005—22no—
36C4×Dic73—21no—
37C4×Dic73—21no—
38C22×C4×C73C2×C411yescharacteristic
39C22×C4×C73C2×C411yescharacteristic
40C22×C4×C73C2311yescharacteristic
41C2×C8×C73—22no—
42C4⋊C4×C73—22no—
43C23×C73C22×C411yescharacteristic
44C22×D73—21no—
45C22×D73—21no—
46C22×D73—21no—
47C22×D73—21no—
48C22×D73—41no—
49C22×D73—41no—
50C22×D73—41no—
51C22×D73—41no—
52C22×D73C22⋊C412yes—
53C22×D73M1612yescomplemented
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73—41no—
58C2×C4×C73—41no—
59C2×C4×C73M1612yescomplemented
60C2×C4×C73C2×D412yes—
61C2×Dic73—22no—
62C2×Dic73—21no—
63C2×Dic73—41no—
64C2×Dic73C22⋊C411yescharacteristic
65C2×Dic73C22⋊C411yescharacteristic
66D292—28no—
67C4×D73—24no—
68C4×D73—42no—
69C4×D73—42no—
70C4×D73—42no—
71C8×C73—42no—
72#10596831—42no—
73C22×C73—21no—
74C22×C73—21no—
75C22×C73C2×C22⋊C411yescharacteristic
76C22×C73C2×M1611yescharacteristic
77C22×C73C2×M1611yescharacteristic
78C2×D73—22no—
79C2×D73—22no—
80C2×D73—22no—
81C2×D73—22no—
82C2×D73—42no—
83C2×D73—42no—
84C2×D73—42no—
85C2×D73—41no—
86C2×D73—41no—
87C2×D73—42no—
88C4×C73—22no—
89C4×C73—22no—
90C4×C73—41no—
91Dic73—21no—
92Dic73—41no—
93Dic73#9912yes—
94C2×C73—21no—
95C2×C73—21no—
96C2×C73#40711yescharacteristic
97C2×C73C2×#9911yescharacteristic
98C2×C73#41311yescharacteristic
99D73—42no—
100D73—42no—
101#1465—731nomaximal, Sylow
102C73#146511yescharacteristic, complemented, Sylow
103C2×C4×D4—731no—
104#407—732no—
105#324—731no—
106#324D7311yescharacteristic, complemented
107#323—732no—
108C22×D4—731no—
109C23×C4—731no—
110C23×C4—731no—
111C2×M16—1462no—
112C4×D4—1462no—
113C4×D4—1462no—
114C2×C4⋊C4C2×D7311yescharacteristic
115C2×C22⋊C4—731no—
116C2×C22⋊C4—731no—
117C2×C42—731no—
118C22⋊C8—732no—
119C22⋊C8—1462no—
120C22⋊C8C2×D7312yes—
121C24—731no—
122C24—731no—
123C2×D4—1462no—
124C2×D4—1462no—
125C2×D4—1462no—
126C22×C4—2922no—
127C22×C4—2922no—
128C22×C4—732no—
129C22×C4—731no—
130C22×C4—731no—
131C22×C4—732no—
132C22×C4—1461no—
133C22×C4—1461no—
134C22×C4C4×D7311yescharacteristic
135C22×C4C4×D7311yescharacteristic
136C22×C4C22×D7311yescharacteristic
137M16—2924no—
138C2×C8—22no—
139C2×C8—1462no—
140C4⋊C4—22no—
141C22⋊C4—1462no—
142C22⋊C4—1462no—
143C42—1461no—
144C42—1461no—
145C23—2921no—
146C23—2921no—
147C23—2921no—
148C23—2921no—
149C23—732no—
150C23—732no—
151C23—1461no—
152C23—1461no—
153C23—1461no—
154C23—1461no—
155C23C2×C4×D7311yescharacteristic
156D4—1468no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—2922no—
163C2×C4—2922no—
164C2×C4—2922no—
165C2×C4—2921no—
166C2×C4—731no—
167C2×C4—731no—
168C2×C4—1464no—
169C2×C4—1461no—
170C2×C4—1462no—
171C2×C4#1192401112yescomplemented
172C2×C4D4×D7312yes—
173C8—42no—
174C8—2922no—
175C22—21no—
176C22—21no—
177C22—2922no—
178C22—2922no—
179C22—2922no—
180C22—2922no—
181C22—2921no—
182C22—2921no—
183C22—1462no—
184C22—1462no—
185C22—1462no—
186C22—1462no—
187C22C22⋊C4×D7311yescharacteristic
188C22M16×D7311yescharacteristic
189C22C2×#1192401111yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—2921no—
194C4—732no—
195C4—1461no—
196C2—21no—
197C2—21no—
198C2—2922no—
199C2—2922no—
200C2#1798854911yescharacteristic
201C2#99×D7311yescharacteristic
202C2#1798857011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC23×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#324×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#324D73
hypocenterC73#1465
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #17988549C2semidirect
3. #17988313C2semidirect
4. #17988310C2semidirect
5. #324×C73C2semidirect
53. C22×D73M16semidirect
59. C2×C4×C73M16semidirect
102. C73#1465semidirect
106. #324D73semidirect
171. C2×C4#11924011semidirect