Finite Group Databasebeta

← #22621168

Subgroups — #22621168

Order 9344.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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#17989116C211yesmaximal, characteristic
3#17988996C211yesmaximal, characteristic, complemented
4#17988993C211yesmaximal, characteristic, complemented
5#17988946C211yesmaximal, characteristic, complemented
6#17988927C212yesmaximal, complemented
7#17988910C212yesmaximal
8#17988892C212yesmaximal, complemented
9#17988885C212yesmaximal, complemented
10#17988642C211yesmaximal, characteristic, complemented
11#489×C73C211yesmaximal, characteristic, complemented
12#14556591C2211yescharacteristic
13#14556584—21no—
14#14556583C2211yescharacteristic
15#14556582C2212yes—
16#14556573—21no—
17#14556571—21no—
18#14556567—21no—
19#14556567C2211yescharacteristic
20#14556562C2211yescharacteristic
21Q8×Dic73—21no—
22Q8×Dic73C2211yescharacteristic
23#14556556—21no—
24D4×Dic73C2211yescharacteristic
25#14556551—21no—
26#14556549C2212yes—
27#14556547—21no—
28C42×D73C2211yescharacteristic
29#14556525C2212yes—
30#14556524C2212yes—
31#14556523C2212yes—
32#14556522C2212yes—
33#14556520C2212yes—
34#14556515C2212yes—
35#14556512C2212yes—
36#14556503C2212yes—
37#14556502C2211yescharacteristic
38C4⋊Q8×C73C2211yescharacteristic
39#124×C73C2211yescharacteristic
40#103×C73C2212yes—
41#102×C73C2212yes—
42#97×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×C22⋊D73—21no—
45C22×Dic73—21no—
46C2×C4×D73D411yescharacteristic
47C2×C4×D73D411yescharacteristic
48C2×C4×D73C2311yescharacteristic
49C2×#10596831C2312yes—
50C4⋊Dic73—21no—
51C4⋊Dic73—22no—
52C4⋊Dic73—21no—
53C4⋊Dic73C2312yes—
54C4⋊Dic73C2311yescharacteristic
55C4⋊Dic73C2311yescharacteristic
56#11924007—21no—
57#11924007—21no—
58#11924007—21no—
59#11924007—22no—
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×Q8×C73C2311yescharacteristic
71C2×D4×C73C2311yescharacteristic
72C2×C8×C73C2312yes—
73C4⋊C4×C73—21no—
74C4⋊C4×C73C2312yes—
75C22⋊C4×C73—21no—
76C22⋊C4×C73—21no—
77C42×C73C2311yescharacteristic
78C23×C73—21no—
79C22×D73C2×D411yescharacteristic
80Q8×C73—22no—
81Q8×C73—42no—
82D4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2411yescharacteristic
88C22⋊D73—42no—
89C2×Dic73—22no—
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—42no—
93C2×Dic73C2×D411yescharacteristic
94C2×Dic73C2×D411yescharacteristic
95C2×Dic73C2×D411yescharacteristic
96C4×D73—22no—
97C4×D73—41no—
98C4×D73—41no—
99Dic146—42no—
100C8×C73—22no—
101#10596831—22no—
102C22×C73—41no—
103C22×C73—41no—
104C22×C73—41no—
105C22×C73C22×D411yescharacteristic
106C2×D73—21no—
107C2×D73—21no—
108C2×D73—21no—
109C4×C73—21no—
110C4×C73—21no—
111C4×C73—41no—
112C4×C73—42no—
113C4×C732−1+412yes—
114Dic73—21no—
115Dic73—21no—
116Dic73—21no—
117Dic73—42no—
118Dic73—41no—
119Dic73—41no—
120C2×C73—81no—
121C2×C73#53611yescharacteristic
122C2×C73#57511yescharacteristic
123C2×C73#57511yescharacteristic
124D73—41no—
125#3240—731nomaximal, Sylow
126C73#324011yescharacteristic, complemented, Sylow
127#533—731no—
128#529—731no—
129#501—731no—
130#501—731no—
131#489—731no—
132#489D7311yescharacteristic, complemented
133#485—732no—
134#482—732no—
135#479—732no—
136#478—732no—
137#432—731no—
138C4⋊Q8—731no—
139C4⋊Q8C2×D7311yescharacteristic
140#126—1461no—
141#125—732no—
142#125—731no—
143#124C2×D7311yescharacteristic
144#123—1461no—
145C22⋊Q8—731no—
146C22⋊Q8—1461no—
147C22⋊Q8—1461no—
148#121—731no—
149C4×Q8—731no—
150C4×Q8—1461no—
151C4×Q8—1461no—
152C4×D4—731no—
153C4×D4—1461no—
154#117—732no—
155#117—1461no—
156C2×C42—731no—
157#107—732no—
158#107—732no—
159#106—732no—
160#106—732no—
161C4⋊C8—732no—
162#103—732no—
163#103C2×D7312yes—
164#102—732no—
165#102C2×D7312yes—
166C22⋊C8—732no—
167#97—731no—
168#97C2×D7311yescharacteristic
169C2×Q8—21no—
170C2×Q8—1461no—
171C2×Q8C22×D7311yescharacteristic
172C2×D4—1461no—
173C2×D4C22×D7311yescharacteristic
174C22×C4—731no—
175C22×C4—731no—
176C22×C4—731no—
177C22×C4—1461no—
178C2×C8—732no—
179C2×C8C22×D7312yes—
180C4⋊C4—21no—
181C4⋊C4—732no—
182C4⋊C4—731no—
183C4⋊C4—731no—
184C4⋊C4—1461no—
185C4⋊C4—1462no—
186C4⋊C4—1461no—
187C4⋊C4—1462no—
188C4⋊C4—1461no—
189C4⋊C4—1461no—
190C4⋊C4—1461no—
191C4⋊C4C22×D7312yes—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—1462no—
195C22⋊C4—1461no—
196C22⋊C4—1461no—
197C22⋊C4—1461no—
198C42—731no—
199C42—731no—
200C42—731no—
201C42—1462no—
202C42—1461no—
203C42C22×D7311yescharacteristic
204C23—21no—
205C23—731no—
206Q8—22no—
207Q8—42no—
208Q8—2922no—
209D4—22no—
210D4—2922no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—2921no—
214C2×C4—2921no—
215C2×C4—2922no—
216C2×C4—731no—
217C2×C4—731no—
218C2×C4—731no—
219C2×C4—1461no—
220C2×C4—1462no—
221C2×C4—1461no—
222C2×C4—1462no—
223C2×C4D4×D7311yescharacteristic
224C2×C4D4×D7311yescharacteristic
225C2×C4C23×D7311yescharacteristic
226C8—22no—
227C8—1462no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—1461no—
232C22—1461no—
233C22—1461no—
234C22C2×D4×D7311yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—41no—
239C4—2921no—
240C4—2921no—
241C4—2922no—
242C4—1461no—
243C4—1461no—
244C4—1461no—
245C4#1455663812yes—
246C2—81no—
247C2—2921no—
248C2#1798915711yescharacteristic
249C2#1798938311yescharacteristic
250C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#489×C73C2
socleC22×C73C22×D4
hypercenter#489D73
hypocenterC73#3240
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #17989142C2semidirect
3. #17988996C2semidirect
4. #17988993C2semidirect
5. #17988946C2semidirect
6. #17988927C2semidirect
8. #17988892C2semidirect
9. #17988885C2semidirect
10. #17988642C2semidirect
11. #489×C73C2semidirect
126. C73#3240semidirect
132. #489D73semidirect