Finite Group Databasebeta

← #22621139

Subgroups — #22621139

Order 9344.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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#17989144C211yesmaximal, characteristic
2C2×#14556583C211yesmaximal, characteristic
3#17988996C212yesmaximal, complemented
4#17988956C212yesmaximal, complemented
5#17988923C212yesmaximal
6#17988918C212yesmaximal
7#17988895C214yesmaximal, complemented
8#432×C73C211yesmaximal, characteristic
9#14556591C2211yescharacteristic
10#14556591C2211yescharacteristic
11#14556583—21no—
12#14556583—21no—
13#14556583—21no—
14#14556583C2212yes—
15#14556583C2212yes—
16#14556570—21no—
17#14556570C2212yes—
18C4×Dic146—21no—
19C4×Dic146C2212yes—
20#14556550—21no—
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×#11924007—21no—
24C2×#11924007—21no—
25#14556525C2214yes—
26#14556523C2214yes—
27#14556516C2214yes—
28#14556516C2214yes—
29C2×C42×C73C2211yescharacteristic
30C4⋊C8×C73C2212yes—
31C22⋊C8×C73C2212yes—
32#97×C73C2212yes—
33C2×Dic146—21no—
34C2×Dic146C2312yes—
35C22×Dic73—21no—
36C22×Dic73—21no—
37C4⋊Dic73—21no—
38C4⋊Dic73—21no—
39C4⋊Dic73—21no—
40C4⋊Dic73—21no—
41C4⋊Dic73—21no—
42C4⋊Dic73C2312yes—
43C4⋊Dic73C2312yes—
44C4⋊Dic73C2312yes—
45#11924007—22no—
46#11924007—22no—
47#11924007—22no—
48#11924007—22no—
49#11924007—22no—
50#11924007—22no—
51C22⋊Dic73—22no—
52C4×Dic73—22no—
53C22×C4×C73D411yescharacteristic
54C22×C4×C73D411yescharacteristic
55C22×C4×C73C2311yescharacteristic
56C2×C8×C73C2314yes—
57C42×C73D411yescharacteristic
58C42×C73D411yescharacteristic
59C42×C73C2311yescharacteristic
60C42×C73C2311yescharacteristic
61C23×C73C2×D411yescharacteristic
62C2×C4×C73—22no—
63C2×C4×C73—22no—
64C2×C4×C73—41no—
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2411yescharacteristic
71C2×Dic73—22no—
72C2×Dic73—22no—
73C2×Dic73—22no—
74C2×Dic73—22no—
75C2×Dic73—42no—
76C2×Dic73—42no—
77Dic146—24no—
78Dic146—42no—
79C8×C73—24no—
80C22×C73—21no—
81C22×C73—21no—
82C22×C73#13712yes—
83C22×C73C22×D411yescharacteristic
84C4×C73—21no—
85C4×C73—21no—
86C4×C73—21no—
87C4×C73—21no—
88C4×C73—21no—
89C4×C732−1+412yes—
90Dic73—42no—
91Dic73—42no—
92Dic73—42no—
93Dic73—42no—
94C2×C73—22no—
95C2×C73#53611yescharacteristic
96C2×C73C2×#13711yescharacteristic
97C2×C73#57511yescharacteristic
98#3236—731nomaximal, Sylow
99C73#323611yescharacteristic, complemented, Sylow
100#533—731no—
101C2×#125—731no—
102#501—732no—
103#491—732no—
104#484—732no—
105#483—732no—
106#479—734no—
107#432D7311yescharacteristic
108C4⋊Q8—731no—
109C4⋊Q8—731no—
110#125—732no—
111#125—732no—
112#125—1461no—
113#125—1461no—
114#125—1461no—
115C22⋊Q8—732no—
116C22⋊Q8—1461no—
117C4×Q8—732no—
118C4×Q8—1461no—
119#117—1461no—
120C2×C4⋊C4—731no—
121C2×C4⋊C4—731no—
122C2×C4⋊C4—1461no—
123C2×C4⋊C4—1461no—
124C2×C42C2×D7311yescharacteristic
125#107—734no—
126#106—734no—
127C4⋊C8C2×D7312yes—
128#103—734no—
129#103—734no—
130C22⋊C8C2×D7312yes—
131#97C2×D7312yes—
132C2×Q8—732no—
133C2×Q8—1461no—
134C22×C4—1461no—
135C22×C4—1461no—
136C22×C4D29211yescharacteristic
137C22×C4D29211yescharacteristic
138C22×C4C22×D7311yescharacteristic
139C2×C8C22×D7314yes—
140C4⋊C4—732no—
141C4⋊C4—732no—
142C4⋊C4—732no—
143C4⋊C4—1462no—
144C4⋊C4—1462no—
145C4⋊C4—1462no—
146C4⋊C4—1462no—
147C4⋊C4—1462no—
148C4⋊C4—1462no—
149C4⋊C4—1461no—
150C4⋊C4—1461no—
151C4⋊C4—1461no—
152C4⋊C4—1461no—
153C4⋊C4—1461no—
154C22⋊C4—1462no—
155C42—1462no—
156C42D29211yescharacteristic
157C42D29211yescharacteristic
158C42C22×D7311yescharacteristic
159C42C22×D7311yescharacteristic
160C23C2×D29211yescharacteristic
161Q8—2922no—
162Q8—1464no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—2922no—
167C2×C4—2922no—
168C2×C4—1462no—
169C2×C4—1462no—
170C2×C4—1462no—
171C2×C4—1462no—
172C2×C4C2×D29211yescharacteristic
173C2×C4C2×D29211yescharacteristic
174C2×C4C2×D29211yescharacteristic
175C2×C4C2×D29211yescharacteristic
176C2×C4C2×D29211yescharacteristic
177C2×C4C23×D7311yescharacteristic
178C8—24no—
179C22—21no—
180C22—21no—
181C22#1455662412yes—
182C22C22×D29211yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—2922no—
189C4—2922no—
190C4—2922no—
191C4—2922no—
192C4#1455663812yes—
193C2—22no—
194C2#1798916311yescharacteristic
195C2C2×#1455662411yescharacteristic
196C2#1798938711yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#432×C73C2
socleC22×C73C22×D4
hypercenter#432D73
hypocenterC73#3236
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
3. #17988996C2semidirect
4. #17988956C2semidirect
7. #17988895C2semidirect
99. C73#3236semidirect