Finite Group Databasebeta

← #22621146

Subgroups — #22621146

Order 9344.

322 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 111 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
2#17989142C211yesmaximal, characteristic
3#17988993C211yesmaximal, characteristic, complemented
4#17988957C211yesmaximal, characteristic, complemented
5#17988956C211yesmaximal, characteristic, complemented
6#17988931C212yesmaximal
7#17988930C212yesmaximal
8#17988881C212yesmaximal, complemented
9#17988871C212yesmaximal, complemented
10#17988642C211yesmaximal, characteristic
11#501×C73C211yesmaximal, characteristic, complemented
12#14556591C2211yescharacteristic
13#14556590C2211yescharacteristic
14#14556590C2211yescharacteristic
15#14556583C2211yescharacteristic
16#14556582—21no—
17#14556571C2212yes—
18#14556569—21no—
19#14556569—21no—
20#14556567—21no—
21Q8×Dic73—21no—
22#14556556—21no—
23#14556556—21no—
24#14556556C2212yes—
25#14556549—21no—
26#14556549C2211yescharacteristic
27#14556549C2211yescharacteristic
28C42×D73C2211yescharacteristic
29#14556524C2212yes—
30#14556522C2212yes—
31#14556520C2212yes—
32#14556516C2212yes—
33#14556516C2212yes—
34#14556514C2212yes—
35#14556514C2212yes—
36#14556503C2212yes—
37#14556502C2211yescharacteristic
38C4⋊Q8×C73C2211yescharacteristic
39#125×C73C2211yescharacteristic
40#107×C73C2212yes—
41#106×C73C2212yes—
42#97×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146—21no—
45C2×Dic146C2312yes—
46C2×C4×D73D411yescharacteristic
47C2×C4×D73D411yescharacteristic
48C2×C4×D73C2311yescharacteristic
49C2×#10596831C2312yes—
50C4⋊Dic73—21no—
51C4⋊Dic73—21no—
52C4⋊Dic73—22no—
53C4⋊Dic73C2311yescharacteristic
54C4⋊Dic73C2311yescharacteristic
55#11924007—21no—
56#11924007—21no—
57#11924007—21no—
58#11924007—21no—
59#11924007—22no—
60#11924005—22no—
61#11924005—21no—
62#11924005—21no—
63C4×Dic73—22no—
64C4×Dic73—21no—
65C4×Dic73—21no—
66C4×Dic73D411yescharacteristic
67C4×Dic73D411yescharacteristic
68C4×Dic73C2311yescharacteristic
69C2×Q8×C73—21no—
70C2×C8×C73C2312yes—
71C4⋊C4×C73—21no—
72C4⋊C4×C73—21no—
73C4⋊C4×C73—21no—
74C4⋊C4×C73C2311yescharacteristic
75C4⋊C4×C73C2312yes—
76C4⋊C4×C73C2311yescharacteristic
77C42×C73C2311yescharacteristic
78C22×D73C2×D411yescharacteristic
79Q8×C73—42no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2411yescharacteristic
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73C2×D411yescharacteristic
90C2×Dic73C2×D411yescharacteristic
91C2×Dic73C2×D411yescharacteristic
92C4×D73—22no—
93C4×D73—22no—
94C4×D73—41no—
95Dic146—24no—
96Dic146—42no—
97Dic146—42no—
98C8×C73—22no—
99#10596831—22no—
100C22×C73C22×D411yescharacteristic
101C2×D73—21no—
102C2×D73—21no—
103C2×D73—21no—
104C4×C73—21no—
105C4×C73—21no—
106C4×C73—41no—
107C4×C73—41no—
108C4×C73—42no—
109C4×C732−1+412yes—
110Dic73—21no—
111Dic73—21no—
112Dic73—42no—
113Dic73—41no—
114Dic73—41no—
115Dic73#13712yes—
116C2×C73#53611yescharacteristic
117C2×C73C2×#13711yescharacteristic
118C2×C73#57511yescharacteristic
119D73—41no—
120#3237—731nomaximal, Sylow
121C73#323711yescharacteristic, complemented, Sylow
122#533—731no—
123#533—731no—
124#501—731no—
125#501D7311yescharacteristic, complemented
126#491—731no—
127#491—731no—
128#485—732no—
129#485—732no—
130#477—732no—
131#475—732no—
132#432—731no—
133C4⋊Q8—731no—
134C4⋊Q8—731no—
135C4⋊Q8—731no—
136C4⋊Q8C2×D7311yescharacteristic
137#125—731no—
138#125—1461no—
139#125C2×D7311yescharacteristic
140C22⋊Q8—732no—
141C22⋊Q8—1461no—
142C22⋊Q8—1461no—
143C22⋊Q8—1461no—
144C4×Q8—732no—
145C4×Q8—1461no—
146C4×Q8—1461no—
147C4×Q8—1461no—
148#117—731no—
149#117—731no—
150#117—1461no—
151C2×C42—731no—
152#107—732no—
153#107C2×D7312yes—
154#106—732no—
155#106C2×D7312yes—
156C4⋊C8—732no—
157#103—732no—
158#103—732no—
159#103—732no—
160#103—732no—
161C22⋊C8—732no—
162#97—731no—
163#97C2×D7311yescharacteristic
164C2×Q8—21no—
165C2×Q8—732no—
166C2×Q8—1461no—
167C2×Q8—1461no—
168C22×C4—731no—
169C22×C4—731no—
170C22×C4—731no—
171C2×C8—732no—
172C2×C8C22×D7312yes—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—731no—
177C4⋊C4—731no—
178C4⋊C4—1462no—
179C4⋊C4—1461no—
180C4⋊C4—1461no—
181C4⋊C4—1462no—
182C4⋊C4—1461no—
183C4⋊C4—1461no—
184C4⋊C4—1461no—
185C4⋊C4—1461no—
186C4⋊C4C22×D7311yescharacteristic
187C4⋊C4C22×D7311yescharacteristic
188C4⋊C4C22×D7312yes—
189C22⋊C4—1461no—
190C22⋊C4—1461no—
191C22⋊C4—1462no—
192C42—731no—
193C42—731no—
194C42—731no—
195C42—1461no—
196C42—1461no—
197C42—1462no—
198C42C22×D7311yescharacteristic
199C23—731no—
200Q8—42no—
201Q8—2922no—
202Q8—2922no—
203Q8—1464no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—2921no—
208C2×C4—731no—
209C2×C4—731no—
210C2×C4—731no—
211C2×C4—1462no—
212C2×C4—1461no—
213C2×C4—1461no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4D4×D7311yescharacteristic
217C2×C4D4×D7311yescharacteristic
218C2×C4C23×D7311yescharacteristic
219C8—22no—
220C8—1462no—
221C22—1461no—
222C22—1461no—
223C22—1461no—
224C22C2×D4×D7311yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—42no—
229C4—41no—
230C4—2921no—
231C4—2921no—
232C4—2922no—
233C4—732no—
234C4—1461no—
235C4—1461no—
236C4#1455663912yes—
237C2—2921no—
238C2#1798916211yescharacteristic
239C2#137×D7311yescharacteristic
240C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#501×C73C2
socleC22×C73C22×D4
hypercenter#501D73
hypocenterC73#3237
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #17988993C2semidirect
4. #17988957C2semidirect
5. #17988956C2semidirect
8. #17988881C2semidirect
9. #17988871C2semidirect
11. #501×C73C2semidirect
121. C73#3237semidirect
125. #501D73semidirect