Finite Group Databasebeta

← #22620491

Subgroups — #22620491

Order 9344.

412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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#17989137C211yesmaximal, characteristic
2#17988983C211yesmaximal, characteristic, complemented
3#17988961C211yesmaximal, characteristic, complemented
4#17988937C211yesmaximal, characteristic, complemented
5#17988935C211yesmaximal, characteristic, complemented
6#17988818C214yesmaximal, complemented
7C4×#11924015C214yesmaximal, complemented
8C2×C4×#10596831C211yesmaximal, characteristic, complemented
9#533×C73C211yesmaximal, characteristic, complemented
10C2×#11924028—21no—
11C2×#11924015C2214yes—
12C22×#10596831C2212yes—
13#14556591C2211yescharacteristic
14#14556588C2211yescharacteristic
15#14556579—21no—
16#14556565—21no—
17#14556565C2212yes—
18C4×D292—21no—
19C4×D292C2212yes—
20#14556522C2214yes—
21#14556515C2214yes—
22#14556511C2214yes—
23C4×#10596831C2212yes—
24C4×#10596831C2211yescharacteristic
25C4×#10596831C2211yescharacteristic
26C4⋊Q8×C73C2211yescharacteristic
27C4⋊Q8×C73C2211yescharacteristic
28#125×C73—21no—
29C22⋊Q8×C73—21no—
30C22⋊Q8×C73C2212yes—
31C4×Q8×C73—21no—
32C4×Q8×C73C2212yes—
33#117×C73—21no—
34C2×C42×C73C2211yescharacteristic
35#11924028—44no—
36C2×Dic146—21no—
37C2×D292—21no—
38C2×D292—21no—
39C2×D292C2312yes—
40C2×C22⋊D73—22no—
41C2×C4×D73—22no—
42#11924015—28no—
43C2×#10596831—24no—
44C2×#10596831C2312yes—
45C2×#10596831C2312yes—
46C4⋊Dic73—21no—
47C4⋊Dic73C2312yes—
48#11924005—22no—
49#11924005—22no—
50C2×Q8×C73—21no—
51C2×Q8×C73C2312yes—
52C22×C4×C73D411yescharacteristic
53C22×C4×C73D411yescharacteristic
54C22×C4×C73C2311yescharacteristic
55C4⋊C4×C73—21no—
56C4⋊C4×C73—21no—
57C4⋊C4×C73—21no—
58C4⋊C4×C73—22no—
59C4⋊C4×C73—22no—
60C4⋊C4×C73C2312yes—
61C22⋊C4×C73—22no—
62C42×C73—22no—
63C42×C73D411yescharacteristic
64C42×C73D411yescharacteristic
65C42×C73C2311yescharacteristic
66C42×C73C2311yescharacteristic
67C23×C73C2×D411yescharacteristic
68C22×D73—22no—
69Q8×C73—24no—
70Q8×C73—42no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73SD1614yescomplemented
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2411yescharacteristic
82C22⋊D73—44no—
83C2×Dic73—22no—
84D292—24no—
85D292—42no—
86D292—42no—
87C4×D73—44no—
88Dic146—42no—
89#10596831—22no—
90#10596831#4114yescomplemented
91C22×C73—21no—
92C22×C73—21no—
93C22×C73C2×SD1612yes—
94C22×C73C22×D411yescharacteristic
95C2×D73—42no—
96C2×D73—42no—
97C2×D73—42no—
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—42no—
101C4×C73—42no—
102C4×C73C2×SD1612yes—
103C4×C73C2×SD1612yes—
104C4×C73#13512yes—
105C4×C73C2×#4112yes—
106Dic73—42no—
107C2×C73—22no—
108C2×C73#53211yescharacteristic
109C2×C73C22×SD1611yescharacteristic
110C2×C73C2×#13511yescharacteristic
111D73—82no—
112#3167—731nomaximal, Sylow
113C73#316711yescharacteristic, complemented, Sylow
114#533D7311yescharacteristic, complemented
115#532—731no—
116#498—731no—
117#492—731no—
118#487—731no—
119#486—731no—
120#465—734no—
121C4×SD16—734no—
122C2×C4×C8—731no—
123C2×#41—1461no—
124C2×SD16—734no—
125C22×C8—732no—
126C4⋊Q8—731no—
127C4⋊Q8C2×D7311yescharacteristic
128C4⋊Q8C2×D7311yescharacteristic
129#127—731no—
130#125—21no—
131#124—1461no—
132C22⋊Q8—21no—
133C22⋊Q8C2×D7312yes—
134#121—732no—
135#121—1461no—
136C4×Q8—21no—
137C4×Q8C2×D7312yes—
138C4×D4—732no—
139C4×D4—1461no—
140#117—21no—
141C2×C42C2×D7311yescharacteristic
142#106—734no—
143#103—734no—
144#102—734no—
145C4×C8—732no—
146C4×C8—731no—
147C4×C8—731no—
148#41—2924no—
149C2×Q8—21no—
150C2×Q8—1461no—
151C2×Q8C22×D7312yes—
152C2×D4—732no—
153C2×D4—1462no—
154C2×D4—1461no—
155C2×D4—1461no—
156C22×C4—1462no—
157C22×C4C22⋊D7311yescharacteristic
158C22×C4C22⋊D7311yescharacteristic
159C22×C4C22×D7311yescharacteristic
160SD16—1468no—
161C2×C8—732no—
162C2×C8—732no—
163C2×C8—1464no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—732no—
170C4⋊C4—1461no—
171C4⋊C4C22×D7312yes—
172C22⋊C4—22no—
173C22⋊C4—1462no—
174C22⋊C4—1462no—
175C42—22no—
176C42C22⋊D7311yescharacteristic
177C42C22⋊D7311yescharacteristic
178C42C22×D7311yescharacteristic
179C42C22×D7311yescharacteristic
180C23—1462no—
181C23C2×C22⋊D7311yescharacteristic
182Q8—24no—
183Q8—42no—
184Q8—2922no—
185D4—2924no—
186D4—2922no—
187D4—2922no—
188D4—1464no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—2924no—
194C2×C4—1462no—
195C2×C4#1192401514yescomplemented
196C2×C4C2×C22⋊D7311yescharacteristic
197C2×C4C2×C22⋊D7311yescharacteristic
198C2×C4C2×C22⋊D7311yescharacteristic
199C2×C4C2×C22⋊D7311yescharacteristic
200C2×C4C2×C22⋊D7311yescharacteristic
201C2×C4C23×D7311yescharacteristic
202C8—734no—
203C8—1462no—
204C22—21no—
205C22—21no—
206C22—2922no—
207C22—2922no—
208C22—2922no—
209C22C2×#1192401512yes—
210C22C22×C22⋊D7311yescharacteristic
211C4—21no—
212C4—21no—
213C4—42no—
214C4—42no—
215C4—2922no—
216C4C2×#1192401512yes—
217C4C2×#1192401512yes—
218C4#1455661112yes—
219C4#41×D7312yes—
220C2—22no—
221C2—5842no—
222C2#1798913311yescharacteristic
223C2C22×#1192401511yescharacteristic
224C2C2×#1455661111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#533×C73C2
socleC22×C73C22×D4
hypercenter#533D73
hypocenterC73#3167
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #17988983C2semidirect
3. #17988961C2semidirect
4. #17988937C2semidirect
5. #17988935C2semidirect
6. #17988818C2semidirect
7. C4×#11924015C2semidirect
8. C2×C4×#10596831C2semidirect
9. #533×C73C2semidirect
75. C2×C4×C73SD16semidirect
90. #10596831#41semidirect
113. C73#3167semidirect
114. #533D73semidirect
195. C2×C4#11924015semidirect