Finite Group Databasebeta

← #22620303

Subgroups — #22620303

Order 9344.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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#17989140C211yesmaximal, characteristic, complemented
2C2×#14556587C211yesmaximal, characteristic
3#17988950C214yesmaximal, complemented
4#17988932C214yesmaximal, complemented
5#17988593C211yesmaximal, characteristic, complemented
6#17988592C211yesmaximal, characteristic, complemented
7#17988591C211yesmaximal, characteristic, complemented
8M16×Dic73C211yesmaximal, characteristic, complemented
9#418×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11C22×C22⋊D73—22no—
12C2×#11924012C2211yescharacteristic
13#14556590C2212yescomplemented
14#14556587—22no—
15#14556587C2212yes—
16#14556587C2212yes—
17#14556582C2212yescomplemented
18#14556568—22no—
19C4×Dic146—22no—
20#14556550C2211yescharacteristic
21C2×C4×Dic73C2211yescharacteristic
22#14556513C2214yescomplemented
23#14556512C2214yescomplemented
24#14556511C2214yescomplemented
25#14556501C2212yescomplemented
26C8×Dic73C2212yescomplemented
27C22×D4×C73C2211yescharacteristic
28C2×M16×C73C2211yescharacteristic
29#117×C73C2211yescharacteristic
30#102×C73C2214yescomplemented
31C23×D73—21no—
32C2×Dic146—22no—
33C2×D292—22no—
34C2×D292—22no—
35C2×D292—21no—
36C2×D292C2312yes—
37C2×C22⋊D73—24no—
38C2×C22⋊D73—24no—
39C2×C22⋊D73—48no—
40C22×Dic73D412yes—
41#11924012—22no—
42C2×#10596831C2312yes—
43C4⋊Dic73—22no—
44C4⋊Dic73C2312yes—
45#11924007—22no—
46#11924007—22no—
47C22⋊Dic73—21no—
48C4×Dic73—21no—
49C4×Dic73D412yes—
50C4×Dic73C2311yescharacteristic
51C4×Dic73C2311yescharacteristic
52C24×C73—21no—
53C2×D4×C73—21no—
54C2×D4×C73—22no—
55C2×D4×C73—22no—
56C2×D4×C73C2312yes—
57C22×C4×C73C2311yescharacteristic
58M16×C73—22no—
59C2×C8×C73C2312yes—
60C4⋊C4×C73C2312yes—
61C22⋊C4×C73—21no—
62C42×C73—21no—
63C23×C73—22no—
64C23×C73—44no—
65C23×C73—42no—
66C23×C73C2×D411yescharacteristic
67C22×D73—22no—
68C22×D73—44no—
69C22×D73—42no—
70D4×C73—22no—
71D4×C73—22no—
72D4×C73—42no—
73C2×C4×C73—22no—
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73#4112yes—
76C2×C4×C73#4112yes—
77C2×C4×C73C2411yescharacteristic
78C22⋊D73—48no—
79C22⋊D73—48no—
80C2×Dic73—24no—
81C2×Dic73—22no—
82C2×Dic73C2×D412yes—
83C2×Dic73C2×D412yes—
84D292—22no—
85D292—22no—
86D292—42no—
87Dic146—44no—
88C8×C73—22no—
89#10596831—22no—
90C22×C73—22no—
91C22×C73—42no—
92C22×C73—44no—
93C22×C73—84no—
94C22×C73#12412yes—
95C22×C73C22×D411yescharacteristic
96C2×D73—42no—
97C2×D73—44no—
98C2×D73—84no—
99C4×C73—42no—
100C4×C73#12412yes—
101C4×C73C2×#4111yescharacteristic
102C4×C73C2×#4111yescharacteristic
103Dic73—22no—
104Dic73—42no—
105Dic73AGL(1,ℤ/8)14yes—
106C2×C73—22no—
107C2×C73—82no—
108C2×C73C2×#12411yescharacteristic
109C2×C73C2×AGL(1,ℤ/8)12yes—
110D73—82no—
111#3138—731nomaximal, Sylow
112C73#313811yescharacteristic, complemented, Sylow
113#533—731no—
114C2×#127—731no—
115#490—734no—
116#486—734no—
117#418—731no—
118#418—731no—
119#418—731no—
120#418D7311yescharacteristic, complemented
121C4×M16—731no—
122C22×D4—731no—
123C22×D4—1462no—
124C22×D4C2×D7311yescharacteristic
125C2×M16—731no—
126C2×M16C2×D7311yescharacteristic
127C4⋊Q8—732no—
128#127—732no—
129#127—732no—
130#127—1462no—
131#125—732no—
132C22⋊Q8—1462no—
133C4×Q8—1462no—
134#117—731no—
135#117C2×D7311yescharacteristic
136C2×C42—731no—
137#102—734no—
138#102—734no—
139#102—734no—
140#102C2×D7314yescomplemented
141#97—732no—
142C4×C8—732no—
143C24—21no—
144C24—1461no—
145C2×Q8—1462no—
146C2×D4—21no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—2928no—
150C2×D4—732no—
151C2×D4—1464no—
152C2×D4—1464no—
153C2×D4—1461no—
154C2×D4—1462no—
155C2×D4—1462no—
156C2×D4C22×D7312yes—
157C22×C4—732no—
158C22×C4C22×D7311yescharacteristic
159M16—22no—
160M16—1462no—
161C2×C8—732no—
162C2×C8C22×D7312yes—
163C4⋊C4—732no—
164C4⋊C4—1462no—
165C4⋊C4—1462no—
166C4⋊C4—1462no—
167C4⋊C4C22×D7312yes—
168C22⋊C4—21no—
169C22⋊C4—1461no—
170C42—21no—
171C42—732no—
172C42—731no—
173C42—731no—
174C42—1461no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—2924no—
179C23—2922no—
180C23—1462no—
181C23D4×D7311yescharacteristic
182Q8—2924no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—2928no—
187D4—2928no—
188D4—2922no—
189D4—1462no—
190D4—1462no—
191C2×C4—22no—
192C2×C4—732no—
193C2×C4—732no—
194C2×C4—1462no—
195C2×C4—1464no—
196C2×C4D4×D7311yescharacteristic
197C2×C4#1192402712yes—
198C2×C4#1192402812yes—
199C2×C4C23×D7311yescharacteristic
200C8—22no—
201C8—1462no—
202C22—22no—
203C22—42no—
204C22—44no—
205C22—84no—
206C22—2922no—
207C22—2924no—
208C22—5844no—
209C22#1455657712yes—
210C22C2×D4×D7311yescharacteristic
211C4—42no—
212C4—2922no—
213C4—734no—
214C4—1462no—
215C4#1455657712yes—
216C4C2×#1192402711yescharacteristic
217C4C2×#1192402811yescharacteristic
218C2—22no—
219C2—82no—
220C2—5842no—
221C2C2×#1455657711yescharacteristic
222C2AGL(1,ℤ/8)×D7312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#418×C73C2
socleC22×C73C22×D4
hypercenter#418D73
hypocenterC73#3138
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #17989140C2semidirect
3. #17988950C2semidirect
4. #17988932C2semidirect
5. #17988593C2semidirect
6. #17988592C2semidirect
7. #17988591C2semidirect
8. M16×Dic73C2semidirect
9. #418×C73C2semidirect
13. #14556590C22semidirect
17. #14556582C22semidirect
22. #14556513C22semidirect
23. #14556512C22semidirect
24. #14556511C22semidirect
25. #14556501C22semidirect
26. C8×Dic73C22semidirect
30. #102×C73C22semidirect
112. C73#3138semidirect
120. #418D73semidirect
140. #102C2×D73semidirect