Finite Group Databasebeta

← #22621108

Subgroups — #22621108

Order 9344.

332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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#17989142C211yesmaximal, characteristic, complemented
2#17989119C211yesmaximal, characteristic
3#17988988C212yesmaximal, complemented
4#17988940C212yesmaximal, complemented
5#17988930C212yesmaximal, complemented
6#17988909C212yesmaximal
7#17988883C211yesmaximal, characteristic, complemented
8#17988877C211yesmaximal, characteristic, complemented
9#17988869C211yesmaximal, characteristic, complemented
10#17988639C211yesmaximal, characteristic, complemented
11#474×C73C211yesmaximal, characteristic, complemented
12#14556591C2211yescharacteristic
13#14556584—21no—
14#14556582C2212yes—
15#14556582C2211yescharacteristic
16#14556578C2211yescharacteristic
17#14556573—21no—
18#14556571—21no—
19#14556571C2211yescharacteristic
20#14556567—21no—
21#14556562C2211yescharacteristic
22Q8×Dic73—21no—
23C4×Dic146C2211yescharacteristic
24#14556556—21no—
25C4×C22⋊D73—21no—
26#14556550—21no—
27#14556549C2212yes—
28C42×D73C2211yescharacteristic
29#14556525C2212yes—
30#14556522C2212yes—
31#14556522C2212yes—
32C4⋊#10596831C2211yescharacteristic
33#14556516C2212yes—
34#14556514C2212yes—
35#14556512C2212yes—
36#14556503C2212yes—
37C8×Dic73C2212yes—
38C4⋊Q8×C73C2211yescharacteristic
39C4×D4×C73C2211yescharacteristic
40#107×C73C2212yes—
41C4⋊C8×C73C2211yescharacteristic
42#102×C73C2212yes—
43C2×Dic146—21no—
44C2×Dic146C2311yescharacteristic
45C2×C22⋊D73—21no—
46C2×C4×D73D411yescharacteristic
47C2×C4×D73D411yescharacteristic
48C2×C4×D73C2311yescharacteristic
49C2×#10596831C2312yes—
50C4⋊Dic73—21no—
51C4⋊Dic73—21no—
52C4⋊Dic73—21no—
53C4⋊Dic73—22no—
54C4⋊Dic73C2312yes—
55C4⋊Dic73C2311yescharacteristic
56#11924007—21no—
57#11924007—21no—
58#11924007—22no—
59C22⋊Dic73—21no—
60C22⋊Dic73—21no—
61C22⋊Dic73—21no—
62#11924005—22no—
63#11924005—21no—
64C4×Dic73—21no—
65C4×Dic73—22no—
66C4×Dic73D411yescharacteristic
67C4×Dic73D411yescharacteristic
68C4×Dic73C2311yescharacteristic
69C2×Q8×C73—21no—
70C2×D4×C73C2311yescharacteristic
71C22×C4×C73—21no—
72C2×C8×C73C2312yes—
73C4⋊C4×C73—21no—
74C4⋊C4×C73C2312yes—
75C4⋊C4×C73C2311yescharacteristic
76C22⋊C4×C73—21no—
77C42×C73C2311yescharacteristic
78C23×C73—21no—
79C22×D73C2×D411yescharacteristic
80Q8×C73—42no—
81D4×C73—21no—
82D4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—42no—
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2411yescharacteristic
89C22⋊D73—42no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73C2×D411yescharacteristic
94C2×Dic73C2×D411yescharacteristic
95C2×Dic73C2×D411yescharacteristic
96C4×D73—22no—
97C4×D73—21no—
98C4×D73—21no—
99C4×D73—41no—
100Dic146—21no—
101Dic146—21no—
102Dic146—42no—
103C8×C73—22no—
104#10596831—22no—
105C22×C73—41no—
106C22×C73—41no—
107C22×C73—41no—
108C22×C73C22×D411yescharacteristic
109C2×D73—21no—
110C2×D73—21no—
111C2×D73—21no—
112C4×C73—21no—
113C4×C73—41no—
114C4×C73—42no—
115C4×C73#13512yes—
116C4×C732−1+411yescharacteristic
117C4×C732−1+411yescharacteristic
118Dic73—21no—
119Dic73—21no—
120Dic73—21no—
121Dic73—41no—
122Dic73—42no—
123Dic73—41no—
124C2×C73—81no—
125C2×C73#53611yescharacteristic
126C2×C73C2×#13511yescharacteristic
127C2×C73#57511yescharacteristic
128D73—41no—
129#3233—731nomaximal, Sylow
130C73#323311yescharacteristic, complemented, Sylow
131#533—731no—
132#529—731no—
133#499—732no—
134#488—732no—
135#485—732no—
136#482—732no—
137#477—731no—
138#476—731no—
139#475—731no—
140#474D7311yescharacteristic, complemented
141#431—731no—
142C4⋊Q8—731no—
143C4⋊Q8C2×D7311yescharacteristic
144#126—1461no—
145#125—731no—
146#125—732no—
147#124—731no—
148#123—1461no—
149C22⋊Q8—731no—
150C22⋊Q8—1461no—
151C22⋊Q8—1461no—
152#121—731no—
153C4×Q8—731no—
154C4×Q8—1461no—
155C4×Q8—1461no—
156C4×D4—1461no—
157C4×D4C2×D7311yescharacteristic
158#117—732no—
159#117—1461no—
160C2×C42—731no—
161#107—732no—
162#107C2×D7312yes—
163#106—732no—
164#106—732no—
165C4⋊C8—731no—
166C4⋊C8C2×D7311yescharacteristic
167#103—732no—
168#103—732no—
169#102—732no—
170#102C2×D7312yes—
171C22⋊C8—732no—
172C4×C8—732no—
173C2×Q8—21no—
174C2×Q8—731no—
175C2×Q8—1461no—
176C2×D4—1461no—
177C2×D4C22×D7311yescharacteristic
178C22×C4—21no—
179C22×C4—731no—
180C22×C4—731no—
181C22×C4—731no—
182C2×C8—732no—
183C2×C8C22×D7312yes—
184C4⋊C4—21no—
185C4⋊C4—732no—
186C4⋊C4—731no—
187C4⋊C4—1461no—
188C4⋊C4—1462no—
189C4⋊C4—1461no—
190C4⋊C4—1461no—
191C4⋊C4—1462no—
192C4⋊C4—1461no—
193C4⋊C4—1461no—
194C4⋊C4C22×D7312yes—
195C4⋊C4C22×D7311yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—1462no—
198C22⋊C4—1461no—
199C22⋊C4—1461no—
200C22⋊C4—1461no—
201C22⋊C4—1461no—
202C42—731no—
203C42—731no—
204C42—731no—
205C42—1462no—
206C42—1461no—
207C42C22×D7311yescharacteristic
208C23—21no—
209C23—731no—
210Q8—42no—
211Q8—2922no—
212Q8—1461no—
213Q8—1461no—
214D4—21no—
215D4—21no—
216D4—2922no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—2921no—
221C2×C4—731no—
222C2×C4—731no—
223C2×C4—731no—
224C2×C4—1461no—
225C2×C4—1461no—
226C2×C4—1462no—
227C2×C4—1462no—
228C2×C4—1461no—
229C2×C4—1461no—
230C2×C4D4×D7311yescharacteristic
231C2×C4D4×D7311yescharacteristic
232C2×C4C23×D7311yescharacteristic
233C8—22no—
234C8—1462no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—1461no—
239C22—1461no—
240C22—1461no—
241C22C2×D4×D7311yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—2921no—
246C4—2922no—
247C4—2921no—
248C4—1461no—
249C4—1461no—
250C4—1461no—
251C4#1455661012yes—
252C4#1455663811yescharacteristic
253C4#1455663911yescharacteristic
254C2—81no—
255C2—2921no—
256C2#1798916011yescharacteristic
257C2C2×#1455661011yescharacteristic
258C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#474×C73C2
socleC22×C73C22×D4
hypercenter#474D73
hypocenterC73#3233
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #17989142C2semidirect
3. #17988988C2semidirect
4. #17988940C2semidirect
5. #17988930C2semidirect
7. #17988883C2semidirect
8. #17988877C2semidirect
9. #17988869C2semidirect
10. #17988639C2semidirect
11. #474×C73C2semidirect
130. C73#3233semidirect
140. #474D73semidirect