Finite Group Databasebeta

← #22621112

Subgroups — #22621112

Order 9344.

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

normal subgroups only

This group has 332 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#17989144C211yesmaximal, characteristic, complemented
2#17989121C211yesmaximal, characteristic
3#17988989C212yesmaximal, complemented
4#17988942C212yesmaximal, complemented
5#17988929C212yesmaximal, complemented
6#17988912C212yesmaximal
7#17988883C211yesmaximal, characteristic, complemented
8#17988878C211yesmaximal, characteristic, complemented
9#17988873C211yesmaximal, characteristic, complemented
10#17988868C211yesmaximal, characteristic, complemented
11#431×C73C211yesmaximal, characteristic, complemented
12#14556591C2211yescharacteristic
13#14556591C2211yescharacteristic
14#14556585—21no—
15#14556583C2211yescharacteristic
16#14556583C2212yes—
17#14556579C2211yescharacteristic
18#14556574—21no—
19#14556570—21no—
20#14556570—21no—
21#14556570C2211yescharacteristic
22#14556565C2211yescharacteristic
23C4×Dic146—21no—
24C4×Dic146—21no—
25C4×Dic146C2211yescharacteristic
26C4×D292C2211yescharacteristic
27C4×C22⋊D73—21no—
28#14556550C2212yes—
29#14556548—21no—
30#14556525C2212yes—
31#14556525C2212yes—
32#14556523C2212yes—
33#14556523C2212yes—
34#14556516C2212yes—
35#14556516C2212yes—
36#14556513C2212yes—
37#14556513C2212yes—
38C2×C42×C73C2211yescharacteristic
39C4⋊C8×C73C2211yescharacteristic
40C4⋊C8×C73C2211yescharacteristic
41C22⋊C8×C73C2212yes—
42C4×C8×C73C2212yes—
43C2×Dic146—21no—
44C2×Dic146—21no—
45C2×Dic146C2311yescharacteristic
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C2×C4×D73—21no—
49C4⋊Dic73—21no—
50C4⋊Dic73—21no—
51C4⋊Dic73C2312yes—
52C4⋊Dic73C2312yes—
53C4⋊Dic73C2311yescharacteristic
54C4⋊Dic73C2311yescharacteristic
55#11924007—21no—
56#11924007—21no—
57#11924007—21no—
58#11924007—22no—
59#11924007—22no—
60#11924007—21no—
61C22⋊Dic73—22no—
62C22⋊Dic73—21no—
63#11924005—21no—
64#11924005—21no—
65#11924005—21no—
66#11924005—21no—
67C4×Dic73—21no—
68C4×Dic73—22no—
69C22×C4×C73D411yescharacteristic
70C22×C4×C73D411yescharacteristic
71C22×C4×C73C2311yescharacteristic
72C2×C8×C73C2312yes—
73C2×C8×C73C2312yes—
74C42×C73D411yescharacteristic
75C42×C73D411yescharacteristic
76C42×C73C2311yescharacteristic
77C42×C73C2311yescharacteristic
78C23×C73C2×D411yescharacteristic
79C22×D73—21no—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—41no—
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2411yescharacteristic
90C22⋊D73—42no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—21no—
96D292—21no—
97D292—21no—
98C4×D73—42no—
99Dic146—21no—
100Dic146—21no—
101Dic146—42no—
102Dic146—42no—
103C8×C73—22no—
104C8×C73—22no—
105C22×C73—21no—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73C22×D411yescharacteristic
109C2×D73—41no—
110C2×D73—41no—
111C2×D73—41no—
112C4×C73—21no—
113C4×C73—21no—
114C4×C73—21no—
115C4×C73—21no—
116C4×C73#13512yes—
117C4×C732−1+411yescharacteristic
118C4×C732−1+411yescharacteristic
119Dic73—41no—
120Dic73—42no—
121Dic73—41no—
122Dic73—42no—
123Dic73—41no—
124C2×C73—41no—
125C2×C73#53611yescharacteristic
126C2×C73C2×#13511yescharacteristic
127C2×C73#57511yescharacteristic
128D73—81no—
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#474—731no—
141#431D7311yescharacteristic, complemented
142C4⋊Q8—731no—
143C4⋊Q8—731no—
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—731no—
157C4×D4—1461no—
158#117—732no—
159#117—1461no—
160C2×C42C2×D7311yescharacteristic
161#107—732no—
162#107—732no—
163#106—732no—
164#106—732no—
165C4⋊C8C2×D7311yescharacteristic
166C4⋊C8C2×D7311yescharacteristic
167#103—732no—
168#103—732no—
169#102—732no—
170#102—732no—
171C22⋊C8C2×D7312yes—
172C4×C8C2×D7312yes—
173C2×Q8—731no—
174C2×Q8—1461no—
175C2×Q8—1461no—
176C2×D4—731no—
177C2×D4—1461no—
178C22×C4—1461no—
179C22×C4D29211yescharacteristic
180C22×C4D29211yescharacteristic
181C22×C4C22×D7311yescharacteristic
182C2×C8C22×D7312yes—
183C2×C8C22×D7312yes—
184C4⋊C4—732no—
185C4⋊C4—732no—
186C4⋊C4—731no—
187C4⋊C4—731no—
188C4⋊C4—1461no—
189C4⋊C4—1461no—
190C4⋊C4—1461no—
191C4⋊C4—1461no—
192C4⋊C4—1462no—
193C4⋊C4—1462no—
194C4⋊C4—1461no—
195C4⋊C4—1461no—
196C22⋊C4—1462no—
197C22⋊C4—1461no—
198C22⋊C4—1461no—
199C22⋊C4—1461no—
200C22⋊C4—1461no—
201C22⋊C4—1461no—
202C42—1462no—
203C42—1461no—
204C42D29211yescharacteristic
205C42D29211yescharacteristic
206C42C22×D7311yescharacteristic
207C42C22×D7311yescharacteristic
208C23—1461no—
209C23C2×D29211yescharacteristic
210Q8—2922no—
211Q8—2922no—
212Q8—1461no—
213Q8—1461no—
214D4—2922no—
215D4—1461no—
216D4—1461no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—2922no—
222C2×C4—1461no—
223C2×C4—1461no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1461no—
227C2×C4C2×D29211yescharacteristic
228C2×C4C2×D29211yescharacteristic
229C2×C4C2×D29211yescharacteristic
230C2×C4C2×D29211yescharacteristic
231C2×C4C2×D29211yescharacteristic
232C2×C4C23×D7311yescharacteristic
233C8—22no—
234C8—22no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—2921no—
239C22—2921no—
240C22—2921no—
241C22C22×D29211yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—2921no—
247C4—2922no—
248C4—2921no—
249C4—2921no—
250C4—2922no—
251C4#1455661312yes—
252C4#1455663811yescharacteristic
253C4#1455663811yescharacteristic
254C2—41no—
255C2—5841no—
256C2#1798916311yescharacteristic
257C2C2×#1455661311yescharacteristic
258C2#1798938711yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#431×C73C2
socleC22×C73C22×D4
hypercenter#431D73
hypocenterC73#3233
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #17989144C2semidirect
3. #17988989C2semidirect
4. #17988942C2semidirect
5. #17988929C2semidirect
7. #17988883C2semidirect
8. #17988878C2semidirect
9. #17988873C2semidirect
10. #17988868C2semidirect
11. #431×C73C2semidirect
130. C73#3233semidirect
141. #431D73semidirect