Finite Group Databasebeta

← #22620175

Subgroups — #22620175

Order 9344.

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

normal subgroups only

This group has 418 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#17989192C211yesmaximal, characteristic, complemented
2#17989061C211yesmaximal, characteristic, complemented
3#17988912C212yesmaximal, complemented
4#17988888C212yesmaximal, complemented
5#17988783C212yesmaximal, complemented
6#17988723C212yesmaximal, complemented
7#17988700C212yesmaximal, complemented
8C4×D584C212yesmaximal, complemented
9#433×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11C2×D584C2212yes—
12C2×D584C2212yes—
13#14556588C2211yescharacteristic, complemented
14#14556583C2211yescharacteristic, complemented
15#14556576—22no—
16#14556565C2212yes—
17#14556564—22no—
18C4×D292C2212yes—
19C4×D292C2212yes—
20C4×D292C2212yescomplemented
21#14556553—22no—
22#14556550C2211yescharacteristic
23C22⋊C4×D73—22no—
24#14556525C2212yescomplemented
25#14556523C2212yescomplemented
26#14556513C2212yes—
27#14556513C2212yes—
28#14556513C2212yescomplemented
29#14556513C2212yescomplemented
30#117×C73C2211yescharacteristic
31C4⋊C8×C73C2212yescomplemented
32C22⋊C8×C73C2212yes—
33#97×C73C2211yescharacteristic, complemented
34C4×C8×C73C2211yescharacteristic, complemented
35C23×D73—21no—
36C2×D292—21no—
37C2×D292—24no—
38C2×D292—22no—
39C2×D292C2312yes—
40C2×D292C2312yes—
41C2×C22⋊D73—22no—
42C2×C4×D73—22no—
43C2×C4×D73—22no—
44C2×C4×D73—22no—
45D584—24no—
46D584—24no—
47C4⋊Dic73C2312yes—
48C4⋊Dic73C2312yes—
49#11924007—22no—
50C22⋊Dic73—21no—
51#11924005—22no—
52#11924005—22no—
53#11924005—22no—
54#11924005—22no—
55C4×Dic73—21no—
56C22×C4×C73C2311yescharacteristic
57C2×C8×C73C2312yes—
58C2×C8×C73C2312yes—
59C4⋊C4×C73D412yes—
60C22⋊C4×C73D412yes—
61C42×C73C2311yescharacteristic
62C42×C73C2311yescharacteristic
63C23×C73C2×D411yescharacteristic
64C22×D73—22no—
65C22×D73—24no—
66C22×D73—22no—
67C22×D73—82no—
68C2×C4×C73—22no—
69C2×C4×C73C2×D412yes—
70C2×C4×C73C2×D412yes—
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2411yescharacteristic
73C22⋊D73—82no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76D292—24no—
77D292—22no—
78D292—22no—
79D292—22no—
80D292—82no—
81D292#4114yes—
82C4×D73—82no—
83C4×D73—82no—
84C4×D73—82no—
85C8×C73—22no—
86C8×C73—22no—
87C22×C73—21no—
88C22×C73—22no—
89C22×C73C22×D411yescharacteristic
90C2×D73—24no—
91C2×D73—42no—
92C2×D73—42no—
93C2×D73—42no—
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—84no—
97C4×C73—21no—
98C4×C73—22no—
99C4×C73—22no—
100C4×C73C2×#4112yes—
101Dic73—42no—
102Dic73—42no—
103C2×C73—41no—
104C2×C73#52511yescharacteristic
105C2×C73#57612yes—
106D73—44no—
107D73—82no—
108#3122—731nomaximal, Sylow
109C73#312211yescharacteristic, complemented, Sylow
110#540—731no—
111#518—731no—
112#482—732no—
113#478—732no—
114#459—732no—
115#447—732no—
116#442—732no—
117C4×D8—732no—
118#433D7311yescharacteristic, complemented
119C22×D4—731no—
120C2×D8—732no—
121C2×D8—732no—
122#127—731no—
123#125—731no—
124#123—1462no—
125#121—732no—
126#121—1462no—
127C4×D4—732no—
128C4×D4—732no—
129C4×D4—732no—
130C4×D4—1462no—
131#117—731no—
132#117C2×D7311yescharacteristic
133C2×C22⋊C4—1462no—
134#107—732no—
135#106—732no—
136C4⋊C8C2×D7312yescomplemented
137#102—732no—
138#102—732no—
139#102—732no—
140#102—732no—
141C22⋊C8C2×D7312yes—
142#97C2×D7311yescharacteristic, complemented
143C4×C8C2×D7311yescharacteristic, complemented
144C24—1461no—
145C2×D4—732no—
146C2×D4—732no—
147C2×D4—1464no—
148C2×D4—1462no—
149C2×D4—1462no—
150C2×D4—1461no—
151C22×C4—1462no—
152C22×C4—1462no—
153C22×C4—1462no—
154C22×C4C22×D7311yescharacteristic
155D8—1464no—
156D8—1464no—
157C2×C8C22×D7312yes—
158C2×C8C22×D7312yes—
159C4⋊C4—732no—
160C4⋊C4—732no—
161C4⋊C4—1462no—
162C4⋊C4D29212yes—
163C22⋊C4—1461no—
164C22⋊C4—1462no—
165C22⋊C4—1462no—
166C22⋊C4—1462no—
167C22⋊C4—1462no—
168C22⋊C4D29212yes—
169C42—1461no—
170C42C22×D7311yescharacteristic
171C42C22×D7311yescharacteristic
172C23—5842no—
173C23—1464no—
174C23—1462no—
175C23—1462no—
176C23C2×D29211yescharacteristic
177D4—5842no—
178D4—5842no—
179D4—734no—
180D4—1464no—
181D4—1462no—
182D4—1462no—
183D4—1462no—
184C2×C4—22no—
185C2×C4—5842no—
186C2×C4—5842no—
187C2×C4—5842no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4C2×D29211yescharacteristic
191C2×C4C2×D29212yes—
192C2×C4C2×D29212yes—
193C2×C4C23×D7311yescharacteristic
194C8—22no—
195C8—22no—
196C22—22no—
197C22—21no—
198C22—2922no—
199C22—2922no—
200C22—2922no—
201C22—2922no—
202C22—2922no—
203C22—5844no—
204C22—1464no—
205C22C22×D29211yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—2922no—
210C4—2922no—
211C4#41×D7312yes—
212C2—41no—
213C2—2924no—
214C2—5842no—
215C2#1798909911yescharacteristic
216C2#1798939212yes—
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#433×C73C2
socleC22×C73C22×D4
hypercenter#433D73
hypocenterC73#3122
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #17989192C2semidirect
2. #17989061C2semidirect
3. #17988912C2semidirect
4. #17988888C2semidirect
5. #17988783C2semidirect
6. #17988723C2semidirect
7. #17988700C2semidirect
8. C4×D584C2semidirect
9. #433×C73C2semidirect
13. #14556588C22semidirect
14. #14556583C22semidirect
20. C4×D292C22semidirect
24. #14556525C22semidirect
25. #14556523C22semidirect
28. #14556513C22semidirect
29. #14556513C22semidirect
31. C4⋊C8×C73C22semidirect
33. #97×C73C22semidirect
34. C4×C8×C73C22semidirect
109. C73#3122semidirect
118. #433D73semidirect
136. C4⋊C8C2×D73semidirect
142. #97C2×D73semidirect
143. C4×C8C2×D73semidirect