Finite Group Databasebeta

← #22620486

Subgroups — #22620486

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#17989144C211yesmaximal, characteristic, complemented
2#17988983C211yesmaximal, characteristic, complemented
3#17988959C211yesmaximal, characteristic, complemented
4#17988939C211yesmaximal, characteristic, complemented
5#17988933C211yesmaximal, characteristic, complemented
6#17988814C214yesmaximal, complemented
7C4×#11924016C214yesmaximal, complemented
8C2×C4×#10596831C211yesmaximal, characteristic, complemented
9#532×C73C211yesmaximal, characteristic
10C2×#11924016C2214yes—
11C22×#10596831C2212yes—
12#14556591C2211yescharacteristic
13#14556591C2211yescharacteristic
14#14556583—21no—
15#14556570—21no—
16#14556570C2212yes—
17C4×Dic146—21no—
18C4×Dic146C2212yes—
19#14556550—21no—
20#14556522C2214yes—
21#14556514C2214yes—
22#14556512C2214yes—
23C4×#10596831C2212yes—
24C4×#10596831C2211yescharacteristic
25C4×#10596831C2211yescharacteristic
26C2×#41×C73—21no—
27C4⋊Q8×C73C2211yescharacteristic
28#127×C73C2211yescharacteristic
29#124×C73—21no—
30#121×C73—21no—
31#121×C73C2212yes—
32C4×D4×C73—21no—
33C4×D4×C73C2212yes—
34C2×C42×C73C2211yescharacteristic
35C2×Dic146—21no—
36C2×Dic146C2312yes—
37#11924016—28no—
38C2×#10596831—24no—
39C2×#10596831C2312yes—
40C2×#10596831C2312yes—
41C4⋊Dic73—21no—
42C4⋊Dic73—21no—
43C4⋊Dic73—21no—
44C4⋊Dic73C2312yes—
45#11924007—22no—
46#11924007—22no—
47C22⋊Dic73—22no—
48C4×Dic73—22no—
49#41×C73—44no—
50C2×Q8×C73—21no—
51C2×D4×C73—22no—
52C2×D4×C73—21no—
53C2×D4×C73—21no—
54C2×D4×C73C2312yes—
55C22×C4×C73—22no—
56C22×C4×C73D411yescharacteristic
57C22×C4×C73D411yescharacteristic
58C22×C4×C73C2311yescharacteristic
59C4⋊C4×C73—21no—
60C4⋊C4×C73C2312yes—
61C22⋊C4×C73—22no—
62C22⋊C4×C73—22no—
63C42×C73D411yescharacteristic
64C42×C73D411yescharacteristic
65C42×C73C2311yescharacteristic
66C42×C73C2311yescharacteristic
67C23×C73—22no—
68C23×C73C2×D411yescharacteristic
69Q8×C73—42no—
70D4×C73—24no—
71D4×C73—44no—
72D4×C73—42no—
73D4×C73—42no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—44no—
78C2×C4×C73SD1614yescomplemented
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2411yescharacteristic
85C2×Dic73—22no—
86C2×Dic73—22no—
87Dic146—24no—
88Dic146—42no—
89#10596831—22no—
90#10596831#4114yescomplemented
91C22×C73—21no—
92C22×C73—21no—
93C22×C73—42no—
94C22×C73—42no—
95C22×C73—42no—
96C22×C73C2×SD1612yes—
97C22×C73C22×D411yescharacteristic
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—42no—
101C4×C73C2×SD1612yes—
102C4×C73C2×SD1612yes—
103C4×C73#13512yes—
104C4×C73C2×#4112yes—
105Dic73—42no—
106Dic73—42no—
107C2×C73—22no—
108C2×C73—82no—
109C2×C73#53211yescharacteristic
110C2×C73C22×SD1611yescharacteristic
111C2×C73C2×#13511yescharacteristic
112#3167—731nomaximal, Sylow
113C73#316711yescharacteristic, complemented, Sylow
114#533—731no—
115#532D7311yescharacteristic
116#498—731no—
117#492—731no—
118#487—731no—
119#486—731no—
120#465—734no—
121C4×SD16—734no—
122C2×C4×C8—731no—
123C2×#41—21no—
124C2×SD16—734no—
125C22×C8—732no—
126C4⋊Q8—731no—
127C4⋊Q8—731no—
128C4⋊Q8C2×D7311yescharacteristic
129#127C2×D7311yescharacteristic
130#125—1461no—
131#124—21no—
132C22⋊Q8—732no—
133C22⋊Q8—1461no—
134#121—21no—
135#121C2×D7312yes—
136C4×Q8—732no—
137C4×Q8—1461no—
138C4×D4—21no—
139C4×D4C2×D7312yes—
140#117—1461no—
141C2×C42C2×D7311yescharacteristic
142#106—734no—
143#103—734no—
144#102—734no—
145C4×C8—732no—
146C4×C8—731no—
147C4×C8—731no—
148#41—44no—
149C2×Q8—21no—
150C2×Q8—732no—
151C2×Q8—1461no—
152C2×D4—22no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4C22×D7312yes—
156C22×C4—22no—
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—732no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4—1461no—
169C4⋊C4—1461no—
170C4⋊C4—1461no—
171C4⋊C4C22×D7312yes—
172C22⋊C4—22no—
173C22⋊C4—22no—
174C22⋊C4—1462no—
175C42—1462no—
176C42C22⋊D7311yescharacteristic
177C42C22⋊D7311yescharacteristic
178C42C22×D7311yescharacteristic
179C42C22×D7311yescharacteristic
180C23—22no—
181C23C2×C22⋊D7311yescharacteristic
182Q8—42no—
183Q8—2922no—
184Q8—1464no—
185D4—24no—
186D4—44no—
187D4—42no—
188D4—42no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—44no—
193C2×C4—1462no—
194C2×C4—1462no—
195C2×C4#1192401614yescomplemented
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—42no—
207C22—42no—
208C22—42no—
209C22C2×#1192401612yes—
210C22C22×C22⋊D7311yescharacteristic
211C4—21no—
212C4—21no—
213C4—42no—
214C4—2922no—
215C4—2922no—
216C4C2×#1192401612yes—
217C4C2×#1192401612yes—
218C4#1455661112yes—
219C4#41×D7312yes—
220C2—22no—
221C2—82no—
222C2#1798913311yescharacteristic
223C2C22×#1192401611yescharacteristic
224C2C2×#1455661111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#532×C73C2
socleC22×C73C22×D4
hypercenter#532D73
hypocenterC73#3167
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #17989144C2semidirect
2. #17988983C2semidirect
3. #17988959C2semidirect
4. #17988939C2semidirect
5. #17988933C2semidirect
6. #17988814C2semidirect
7. C4×#11924016C2semidirect
8. C2×C4×#10596831C2semidirect
78. C2×C4×C73SD16semidirect
90. #10596831#41semidirect
113. C73#3167semidirect
195. C2×C4#11924016semidirect