Finite Group Databasebeta

← #22621131

Subgroups — #22621131

Order 9344.

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

normal subgroups only

This group has 366 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, complemented
2#17989137C211yesmaximal, characteristic
3#17988996C212yesmaximal, complemented
4#17988952C212yesmaximal, complemented
5#17988912C214yesmaximal, complemented
6#17988878C212yesmaximal, complemented
7#17988868C212yesmaximal, complemented
8#432×C73C211yesmaximal, characteristic, complemented
9C2×#11924028—21no—
10#14556591C2211yescharacteristic
11#14556591C2211yescharacteristic
12#14556591C2211yescharacteristic
13#14556588C2211yescharacteristic
14#14556583C2212yes—
15#14556579—21no—
16#14556570—21no—
17#14556570—21no—
18#14556565—21no—
19#14556565C2212yes—
20C4×Dic146—21no—
21C4×Dic146—21no—
22C4×D292—21no—
23C4×D292C2212yes—
24#14556550C2212yes—
25#14556525C2214yes—
26#14556523C2214yes—
27#14556513C2214yes—
28#14556513C2214yes—
29C2×C42×C73C2211yescharacteristic
30C4⋊C8×C73C2212yes—
31C22⋊C8×C73C2212yes—
32#97×C73C2212yes—
33#11924028—44no—
34C2×Dic146—21no—
35C2×Dic146—21no—
36C2×Dic146—21no—
37C2×D292—21no—
38C2×D292—21no—
39C2×D292C2312yes—
40C2×C22⋊D73—22no—
41C2×C4×D73—22no—
42C4⋊Dic73—21no—
43C4⋊Dic73—21no—
44C4⋊Dic73—21no—
45C4⋊Dic73C2312yes—
46C4⋊Dic73C2312yes—
47C4⋊Dic73C2312yes—
48#11924007—22no—
49#11924007—22no—
50C22⋊Dic73—22no—
51#11924005—22no—
52#11924005—22no—
53C4×Dic73—22no—
54C22×C4×C73D411yescharacteristic
55C22×C4×C73D411yescharacteristic
56C22×C4×C73C2311yescharacteristic
57C2×C8×C73C2314yes—
58C42×C73D411yescharacteristic
59C42×C73D411yescharacteristic
60C42×C73C2311yescharacteristic
61C42×C73C2311yescharacteristic
62C23×C73C2×D411yescharacteristic
63C22×D73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—41no—
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2411yescharacteristic
73C22⋊D73—44no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—22no—
77D292—24no—
78D292—42no—
79D292—42no—
80C4×D73—44no—
81Dic146—42no—
82Dic146—42no—
83Dic146—42no—
84C8×C73—24no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73C22×D411yescharacteristic
89C2×D73—42no—
90C2×D73—42no—
91C2×D73—42no—
92C4×C73—21no—
93C4×C73—21no—
94C4×C73—21no—
95C4×C73—21no—
96C4×C73AGL(1,ℤ/8)12yes—
97C4×C732−1+412yes—
98Dic73—42no—
99Dic73—42no—
100Dic73—42no—
101C2×C73—41no—
102C2×C73#53611yescharacteristic
103C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
104C2×C73#57511yescharacteristic
105D73—82no—
106#3235—731nomaximal, Sylow
107C73#323511yescharacteristic, complemented, Sylow
108#533—731no—
109#532—731no—
110#501—732no—
111#490—732no—
112#482—734no—
113#476—732no—
114#474—732no—
115#432D7311yescharacteristic, complemented
116C2×#41—1461no—
117C4⋊Q8—731no—
118C4⋊Q8—731no—
119C4⋊Q8—731no—
120#127—731no—
121#125—732no—
122#124—1461no—
123C22⋊Q8—1461no—
124C22⋊Q8—1461no—
125#121—732no—
126#121—1461no—
127C4×Q8—1461no—
128C4×Q8—1461no—
129C4×D4—732no—
130C4×D4—1461no—
131#117—732no—
132C2×C42C2×D7311yescharacteristic
133#107—734no—
134#106—734no—
135C4⋊C8C2×D7312yes—
136#102—734no—
137#102—734no—
138C22⋊C8C2×D7312yes—
139#97C2×D7312yes—
140#41—2924no—
141C2×Q8—1461no—
142C2×Q8—1461no—
143C2×Q8—1461no—
144C2×D4—732no—
145C2×D4—1462no—
146C2×D4—1461no—
147C2×D4—1461no—
148C22×C4—1462no—
149C22×C4D29211yescharacteristic
150C22×C4D29211yescharacteristic
151C22×C4C22×D7311yescharacteristic
152C2×C8C22×D7314yes—
153C4⋊C4—732no—
154C4⋊C4—732no—
155C4⋊C4—732no—
156C4⋊C4—1462no—
157C4⋊C4—1462no—
158C4⋊C4—1461no—
159C4⋊C4—1461no—
160C4⋊C4—1461no—
161C22⋊C4—1462no—
162C22⋊C4—1462no—
163C22⋊C4—1462no—
164C42—1462no—
165C42D29211yescharacteristic
166C42D29211yescharacteristic
167C42C22×D7311yescharacteristic
168C42C22×D7311yescharacteristic
169C23—1462no—
170C23C2×D29211yescharacteristic
171Q8—2922no—
172Q8—2922no—
173Q8—2922no—
174D4—2922no—
175D4—2922no—
176D4—2924no—
177D4—1464no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—2924no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4C2×D29211yescharacteristic
186C2×C4C2×D29211yescharacteristic
187C2×C4C2×D29211yescharacteristic
188C2×C4C2×D29211yescharacteristic
189C2×C4C2×D29211yescharacteristic
190C2×C4C23×D7311yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—2922no—
196C22—2922no—
197C22—2922no—
198C22C22×D29211yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—2922no—
204C4—2922no—
205C4—2922no—
206C4#1455661912yes—
207C4#1455663812yes—
208C2—41no—
209C2—5842no—
210C2#1798916311yescharacteristic
211C2C2×#1455661911yescharacteristic
212C2#1798938711yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#432×C73C2
socleC22×C73C22×D4
hypercenter#432D73
hypocenterC73#3235
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
1. #17989144C2semidirect
3. #17988996C2semidirect
4. #17988952C2semidirect
5. #17988912C2semidirect
6. #17988878C2semidirect
7. #17988868C2semidirect
8. #432×C73C2semidirect
107. C73#3235semidirect
115. #432D73semidirect