Finite Group Databasebeta

← #22620314

Subgroups — #22620314

Order 9344.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#17989143C211yesmaximal, characteristic, complemented
2#124×D73C211yesmaximal, characteristic
3#17988948C212yesmaximal, complemented
4#17988945C212yesmaximal, complemented
5#17988944C211yesmaximal, characteristic, complemented
6#17988942C211yesmaximal, characteristic, complemented
7#17988941C211yesmaximal, characteristic, complemented
8#17988594C212yesmaximal, complemented
9#17988590C212yesmaximal
10C4×#11924011C211yesmaximal, characteristic, complemented
11#488×C73C211yesmaximal, characteristic, complemented
12C2×Q8×D73C2211yescharacteristic
13C2×D4×D73C2211yescharacteristic
14C2×#11924011C2212yes—
15#14556590C2212yescomplemented
16#14556583C2211yescharacteristic, complemented
17#14556580C2211yescharacteristic
18#14556579C2211yescharacteristic
19#14556578C2211yescharacteristic
20#14556577—22no—
21#14556569—22no—
22#14556556—22no—
23#14556549C2212yes—
24C22⋊C4×D73—22no—
25C42×D73C2211yescharacteristic
26#14556516C2212yescomplemented
27#14556515C2212yescomplemented
28#14556514C2212yescomplemented
29#14556513C2212yes—
30#14556512C2212yes—
31#14556511C2212yes—
32#14556501C2212yescomplemented
33C4×#10596831C2211yescharacteristic, complemented
34#125×C73C2211yescharacteristic, complemented
35#124×C73C2211yescharacteristic
36#103×C73C2212yescomplemented
37#102×C73C2212yes—
38C4×C8×C73C2211yescharacteristic, complemented
39C23×D73—21no—
40C2×Dic146—22no—
41C2×Dic146—21no—
42C2×Dic146C2311yescharacteristic
43Q8×D73—24no—
44C2×D292C2311yescharacteristic
45C2×C22⋊D73—21no—
46D4×D73—24no—
47C2×C4×D73—21no—
48C2×C4×D73D412yes—
49C2×C4×D73C2311yescharacteristic
50#11924011—24no—
51C2×#10596831C2312yes—
52C4⋊Dic73C2312yes—
53#11924007—22no—
54#11924007—22no—
55C22⋊Dic73—22no—
56#11924005—22no—
57#11924005—22no—
58#11924005—22no—
59C4×Dic73—22no—
60C4×Dic73D412yes—
61C4×Dic73C2311yescharacteristic
62C2×Q8×C73C2311yescharacteristic
63C2×D4×C73C2311yescharacteristic
64C2×C8×C73C2312yes—
65C4⋊C4×C73—22no—
66C4⋊C4×C73C2312yes—
67C22⋊C4×C73—22no—
68C42×C73C2311yescharacteristic
69C23×C73—21no—
70C22×D73—21no—
71C22×D73—44no—
72C22×D73—42no—
73C22×D73C2×D411yescharacteristic
74Q8×C73—22no—
75D4×C73—22no—
76C2×C4×C73—21no—
77C2×C4×C73—22no—
78C2×C4×C73C2×D412yes—
79C2×C4×C73C2411yescharacteristic
80C22⋊D73—42no—
81C2×Dic73—22no—
82C2×Dic73—21no—
83C2×Dic73C2×D412yes—
84C2×Dic73C2×D411yescharacteristic
85D292—22no—
86C4×D73—42no—
87C4×D73—42no—
88C4×D73#4114yes—
89Dic146—22no—
90Dic146—44no—
91Dic146—42no—
92C8×C73—22no—
93#10596831—22no—
94C22×C73—41no—
95C22×C73—42no—
96C22×C73C22×D411yescharacteristic
97C2×D73—22no—
98C2×D73—41no—
99C2×D73—42no—
100C2×D73—84no—
101C2×D73#12412yes—
102C4×C73—22no—
103C4×C73—41no—
104C4×C73—42no—
105C4×C73C2×#4112yes—
106Dic73—22no—
107Dic73—41no—
108Dic73—42no—
109Dic73#12412yes—
110C2×C73—81no—
111C2×C73C2×#12411yescharacteristic
112C2×C73#57512yes—
113D73—22no—
114D73—81no—
115#3140—731nomaximal, Sylow
116C73#314011yescharacteristic, complemented, Sylow
117#533—731no—
118C2×#124—731no—
119#489—732no—
120#489—732no—
121#488—731no—
122#488—731no—
123#488—731no—
124#488D7311yescharacteristic, complemented
125#419—732no—
126#418—732no—
127C4×M16—731no—
128C22×Q8—731no—
129C22×D4—731no—
130C2×M16—732no—
131C4⋊Q8—732no—
132#125—731no—
133#125C2×D7311yescharacteristic, complemented
134#124—731no—
135#124—731no—
136#124—731no—
137#124—1462no—
138#124C2×D7311yescharacteristic
139C22⋊Q8—1462no—
140C4×Q8—1462no—
141#117—732no—
142C2×C22⋊C4—1462no—
143C2×C42—731no—
144#103—732no—
145#103—732no—
146#103—732no—
147#103C2×D7312yescomplemented
148#102—732no—
149#102—732no—
150#102—732no—
151#102C2×D7312yes—
152#97—732no—
153C4×C8—731no—
154C4×C8C2×D7311yescharacteristic, complemented
155C24—1461no—
156C2×Q8—731no—
157C2×Q8—1462no—
158C2×Q8—1461no—
159C2×Q8—1464no—
160C2×Q8C22×D7311yescharacteristic
161C2×D4—731no—
162C2×D4—1464no—
163C2×D4—1461no—
164C2×D4C22×D7311yescharacteristic
165C22×C4—732no—
166C22×C4—731no—
167C22×C4—1461no—
168M16—1464no—
169C2×C8—732no—
170C2×C8C22×D7312yes—
171C4⋊C4—22no—
172C4⋊C4—732no—
173C4⋊C4—1462no—
174C4⋊C4—1462no—
175C4⋊C4C22×D7312yes—
176C22⋊C4—22no—
177C22⋊C4—1462no—
178C22⋊C4—1462no—
179C22⋊C4—1462no—
180C22⋊C4—1462no—
181C42—732no—
182C42—731no—
183C42—1462no—
184C42C22×D7311yescharacteristic
185C23—21no—
186C23—2922no—
187C23—2924no—
188C23—731no—
189C23—1461no—
190Q8—22no—
191Q8—2922no—
192Q8—2924no—
193Q8—1462no—
194D4—22no—
195D4—2922no—
196D4—1462no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—2922no—
200C2×C4—2922no—
201C2×C4—731no—
202C2×C4—734no—
203C2×C4—732no—
204C2×C4—1462no—
205C2×C4—1461no—
206C2×C4D4×D7312yes—
207C2×C4C23×D7311yescharacteristic
208C8—22no—
209C8—1462no—
210C22—42no—
211C22—41no—
212C22—2922no—
213C22—2921no—
214C22—5844no—
215C22—732no—
216C22—1462no—
217C22C2×D4×D7311yescharacteristic
218C4—22no—
219C4—42no—
220C4—41no—
221C4—2922no—
222C4—2921no—
223C4—732no—
224C4—1462no—
225C4#41×D7312yes—
226C2—81no—
227C2—5841no—
228C2—1462no—
229C2#124×D7311yescharacteristic
230C2#1798938412yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#488×C73C2
socleC22×C73C22×D4
hypercenter#488D73
hypocenterC73#3140
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #17989143C2semidirect
3. #17988948C2semidirect
4. #17988945C2semidirect
5. #17988944C2semidirect
6. #17988942C2semidirect
7. #17988941C2semidirect
8. #17988594C2semidirect
10. C4×#11924011C2semidirect
11. #488×C73C2semidirect
15. #14556590C22semidirect
16. #14556583C22semidirect
26. #14556516C22semidirect
27. #14556515C22semidirect
28. #14556514C22semidirect
32. #14556501C22semidirect
33. C4×#10596831C22semidirect
34. #125×C73C22semidirect
36. #103×C73C22semidirect
38. C4×C8×C73C22semidirect
116. C73#3140semidirect
124. #488D73semidirect
133. #125C2×D73semidirect
147. #103C2×D73semidirect
154. C4×C8C2×D73semidirect