Finite Group Databasebeta

← #22608243

Subgroups — #22608243

Order 9344.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14556548C211yesmaximal, characteristic
2#17988640C211yesmaximal, characteristic, complemented
3#17988312C212yesmaximal, complemented
4#17988310C212yesmaximal
5#431×C73C211yesmaximal, characteristic, complemented
6C22×C4×D73C411yescharacteristic
7#14556548—21no—
8#14556548—21no—
9#14556548—21no—
10#14556548—21no—
11C2×#11924007C411yescharacteristic
12C2×#11924007C2211yescharacteristic
13C2×#11924005C411yescharacteristic
14C2×#11924005C2211yescharacteristic
15C2×C4×Dic73C411yescharacteristic
16C4⋊#10596831—21no—
17C22⋊#10596831C2212yes—
18C4×#10596831—21no—
19C2×C42×C73C2211yescharacteristic
20C4⋊C8×C73—21no—
21C22⋊C8×C73C2212yes—
22C4×C8×C73—21no—
23C23×D73C2×C411yescharacteristic
24C22×Dic73C2×C411yescharacteristic
25C22×Dic73C2×C411yescharacteristic
26C22×Dic73C2×C411yescharacteristic
27C2×C4×D73—21no—
28C2×C4×D73—21no—
29C2×C4×D73—22no—
30C2×C4×D73C814yescomplemented
31C2×#10596831—22no—
32#11924007—21no—
33#11924007—21no—
34#11924007—21no—
35#11924007—21no—
36#11924005—21no—
37#11924005—21no—
38#11924005—21no—
39#11924005—21no—
40C4×Dic73—21no—
41C4×Dic73—21no—
42C22×C4×C73C2×C411yescharacteristic
43C22×C4×C73C2×C411yescharacteristic
44C22×C4×C73C2311yescharacteristic
45C2×C8×C73—22no—
46C42×C73D411yescharacteristic
47C42×C73D411yescharacteristic
48C42×C73D411yescharacteristic
49C42×C73D411yescharacteristic
50C23×C73C22×C411yescharacteristic
51C22×D73—21no—
52C22×D73—21no—
53C22×D73—41no—
54C22×D73—41no—
55C22×D73C2×C812yes—
56C2×C4×C73—41no—
57C2×C4×C73—41no—
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22⋊C411yescharacteristic
62C2×C4×C73C2×C812yes—
63C2×C4×C73M1612yes—
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73—41no—
71C2×Dic73—41no—
72C2×Dic73C2×C812yes—
73C4×D73—24no—
74C4×D73—24no—
75C8×C73—42no—
76#10596831—42no—
77C22×C73—21no—
78C22×C73—21no—
79C22×C73C2×C22⋊C411yescharacteristic
80C22×C73C22×C811yescharacteristic
81C22×C73C2×M1611yescharacteristic
82C2×D73—22no—
83C2×D73—42no—
84C2×D73—41no—
85C2×D73—41no—
86C2×D73—42no—
87C4×C73—21no—
88C4×C73—21no—
89C4×C73—21no—
90C4×C73—21no—
91C4×C73C22⋊C812yes—
92C4×C73C22⋊C812yes—
93Dic73—22no—
94Dic73—41no—
95Dic73—41no—
96C2×C73—21no—
97C2×C73—21no—
98C2×C73C2×C22⋊C811yescharacteristic
99C2×C73#41011yescharacteristic
100C2×C73#41311yescharacteristic
101D73—42no—
102#1458—731nomaximal, Sylow
103C73#145811yescharacteristic, complemented, Sylow
104C2×#117—731no—
105#431—731no—
106#431D7311yescharacteristic, complemented
107#324—732no—
108#323—732no—
109C23×C4—731no—
110#117—1461no—
111#117—1461no—
112#117—1461no—
113#117—1461no—
114C2×C4⋊C4—731no—
115C2×C4⋊C4—731no—
116C2×C22⋊C4—731no—
117C2×C22⋊C4—731no—
118C2×C42—731no—
119C2×C42C2×D7311yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—1461no—
122C22⋊C8—732no—
123C22⋊C8C2×D7312yes—
124C4×C8—21no—
125C4×C8—1461no—
126C24—731no—
127C22×C4—731no—
128C22×C4—731no—
129C22×C4—731no—
130C22×C4—734no—
131C22×C4—1461no—
132C22×C4—1461no—
133C22×C4—1462no—
134C22×C4C4×D7311yescharacteristic
135C22×C4C4×D7311yescharacteristic
136C22×C4C22×D7311yescharacteristic
137C2×C8—22no—
138C2×C8—1462no—
139C4⋊C4—1461no—
140C4⋊C4—1461no—
141C4⋊C4—1461no—
142C4⋊C4—1461no—
143C22⋊C4—1461no—
144C22⋊C4—1461no—
145C22⋊C4—1461no—
146C22⋊C4—1461no—
147C42—1461no—
148C42—1461no—
149C42D29211yescharacteristic
150C42D29211yescharacteristic
151C42C22⋊D7311yescharacteristic
152C42C22⋊D7311yescharacteristic
153C23—2921no—
154C23—2921no—
155C23—732no—
156C23—1461no—
157C23—1461no—
158C23C2×C4×D7311yescharacteristic
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—2921no—
162C2×C4—2921no—
163C2×C4—732no—
164C2×C4—1461no—
165C2×C4—1461no—
166C2×C4—1461no—
167C2×C4—1461no—
168C2×C4—1464no—
169C2×C4—1464no—
170C2×C4#1192400511yescharacteristic
171C2×C4#1192400511yescharacteristic
172C2×C4#1192400511yescharacteristic
173C2×C4#1192400511yescharacteristic
174C2×C4C8×D7312yes—
175C2×C4#1192401112yes—
176C2×C4C2×C22⋊D7311yescharacteristic
177C2×C4C2×D29211yescharacteristic
178C8—42no—
179C8—2922no—
180C22—21no—
181C22—21no—
182C22—2922no—
183C22—2922no—
184C22—2921no—
185C22—2921no—
186C22—1462no—
187C22C2×#1192400511yescharacteristic
188C22C2×C8×D7311yescharacteristic
189C22C2×#1192401111yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—2921no—
195C4—2921no—
196C4—1462no—
197C4#1455650312yes—
198C4#1455650312yes—
199C2—21no—
200C2—21no—
201C2—2922no—
202C2C2×#1455650311yescharacteristic
203C2#1798856011yescharacteristic
204C2#1798856911yescharacteristic
subgroupG/H
centerC2×C4#11924005
commutatorC22×C73C22×C8
FrattiniC22×C4C22×D73
Fitting#431×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#431D73
hypocenterC73#1458
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #17988640C2semidirect
3. #17988312C2semidirect
5. #431×C73C2semidirect
30. C2×C4×D73C8semidirect
103. C73#1458semidirect
106. #431D73semidirect