Finite Group Databasebeta

← #22621167

Subgroups — #22621167

Order 9344.

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

normal subgroups only

This group has 328 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#17989144C211yesmaximal, characteristic, complemented
2#17988997C211yesmaximal, characteristic, complemented
3#17988997C211yesmaximal, characteristic, complemented
4#17988946C211yesmaximal, characteristic, complemented
5#17988946C211yesmaximal, characteristic, complemented
6#17988925C212yesmaximal, complemented
7#17988908C212yesmaximal
8#17988894C212yesmaximal, complemented
9#17988887C212yesmaximal, complemented
10#17988644C211yesmaximal, characteristic, complemented
11#529×C73C211yesmaximal, characteristic
12#14556591C2211yescharacteristic
13#14556591C2211yescharacteristic
14#14556583C2212yes—
15#14556570—21no—
16#14556570—21no—
17C4×Dic146—21no—
18C4×Dic146—21no—
19#14556550C2212yes—
20#14556524C2212yes—
21#14556524C2212yes—
22#14556522C2212yes—
23#14556522C2212yes—
24C4⋊#10596831C2212yes—
25#14556515C2212yes—
26#14556515C2212yes—
27#14556512C2212yes—
28#14556512C2212yes—
29C22⋊#10596831C2212yes—
30#14556502C2211yescharacteristic
31#14556502C2211yescharacteristic
32#126×C73—21no—
33#125×C73C2211yescharacteristic
34#124×C73C2211yescharacteristic
35#123×C73—21no—
36C22⋊Q8×C73C2211yescharacteristic
37#121×C73C2211yescharacteristic
38C4×Q8×C73C2211yescharacteristic
39C4×D4×C73—21no—
40C4×D4×C73C2211yescharacteristic
41#117×C73—21no—
42C2×C42×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146—21no—
45C2×#10596831C2312yes—
46C2×#10596831C2312yes—
47C4⋊Dic73—21no—
48C4⋊Dic73—21no—
49C4⋊Dic73C2312yes—
50C4⋊Dic73C2312yes—
51#11924007—22no—
52#11924007—22no—
53C22⋊Dic73—22no—
54C4×Dic73—22no—
55C2×Q8×C73C2311yescharacteristic
56C2×D4×C73—21no—
57C2×D4×C73C2311yescharacteristic
58C22×C4×C73—21no—
59C22×C4×C73D411yescharacteristic
60C22×C4×C73D411yescharacteristic
61C22×C4×C73C2311yescharacteristic
62C4⋊C4×C73—21no—
63C4⋊C4×C73—21no—
64C4⋊C4×C73—21no—
65C4⋊C4×C73—21no—
66C4⋊C4×C73C2311yescharacteristic
67C4⋊C4×C73C2311yescharacteristic
68C22⋊C4×C73—21no—
69C22⋊C4×C73—21no—
70C22⋊C4×C73—21no—
71C22⋊C4×C73—21no—
72C22⋊C4×C73—21no—
73C42×C73—21no—
74C42×C73D411yescharacteristic
75C42×C73D411yescharacteristic
76C42×C73C2311yescharacteristic
77C42×C73C2311yescharacteristic
78C23×C73—21no—
79C23×C73C2×D411yescharacteristic
80Q8×C73—22no—
81D4×C73—22no—
82D4×C73—42no—
83C2×C4×C73—22no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—41no—
88C2×C4×C73—41no—
89C2×C4×C73—42no—
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2×D411yescharacteristic
92C2×C4×C73C2×D411yescharacteristic
93C2×C4×C73C2×D411yescharacteristic
94C2×C4×C73C2×D411yescharacteristic
95C2×C4×C73C2411yescharacteristic
96C2×Dic73—22no—
97C2×Dic73—22no—
98Dic146—42no—
99Dic146—42no—
100#10596831—22no—
101#10596831—22no—
102C22×C73—21no—
103C22×C73—21no—
104C22×C73—21no—
105C22×C73—41no—
106C22×C73—41no—
107C22×C73—41no—
108C22×C73C22×D411yescharacteristic
109C4×C73—21no—
110C4×C73—21no—
111C4×C73—21no—
112C4×C73—21no—
113C4×C73—21no—
114C4×C73—41no—
115C4×C73—41no—
116C4×C73—41no—
117C4×C732−1+412yes—
118Dic73—42no—
119Dic73—42no—
120C2×C73—41no—
121C2×C73—81no—
122C2×C73#53611yescharacteristic
123C2×C73#57511yescharacteristic
124C2×C73#57511yescharacteristic
125#3240—731nomaximal, Sylow
126C73#324011yescharacteristic, complemented, Sylow
127#533—731no—
128#529D7311yescharacteristic
129#501—731no—
130#501—731no—
131#489—731no—
132#489—731no—
133#485—732no—
134#482—732no—
135#479—732no—
136#478—732no—
137#432—731no—
138C4⋊Q8—731no—
139C4⋊Q8—731no—
140#126—21no—
141#125—732no—
142#125C2×D7311yescharacteristic
143#124C2×D7311yescharacteristic
144#123—21no—
145C22⋊Q8—1461no—
146C22⋊Q8—1461no—
147C22⋊Q8C2×D7311yescharacteristic
148#121C2×D7311yescharacteristic
149C4×Q8—1461no—
150C4×Q8—1461no—
151C4×Q8C2×D7311yescharacteristic
152C4×D4—21no—
153C4×D4C2×D7311yescharacteristic
154#117—21no—
155#117—732no—
156C2×C42C2×D7311yescharacteristic
157#107—732no—
158#107—732no—
159#106—732no—
160#106—732no—
161C4⋊C8—732no—
162#103—732no—
163#103—732no—
164#102—732no—
165#102—732no—
166C22⋊C8—732no—
167#97—731no—
168#97—731no—
169C2×Q8—1461no—
170C2×Q8—1461no—
171C2×Q8C22×D7311yescharacteristic
172C2×D4—21no—
173C2×D4C22×D7311yescharacteristic
174C22×C4—21no—
175C22×C4C22⋊D7311yescharacteristic
176C22×C4C22⋊D7311yescharacteristic
177C22×C4C22×D7311yescharacteristic
178C2×C8—732no—
179C2×C8—732no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—732no—
185C4⋊C4—732no—
186C4⋊C4—1462no—
187C4⋊C4—1462no—
188C4⋊C4—1461no—
189C4⋊C4—1461no—
190C4⋊C4C22×D7311yescharacteristic
191C4⋊C4C22×D7311yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—1462no—
198C42—21no—
199C42—1462no—
200C42C22⋊D7311yescharacteristic
201C42C22⋊D7311yescharacteristic
202C42C22×D7311yescharacteristic
203C42C22×D7311yescharacteristic
204C23—21no—
205C23C2×C22⋊D7311yescharacteristic
206Q8—22no—
207Q8—2922no—
208Q8—2922no—
209D4—22no—
210D4—42no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4C2×C22⋊D7311yescharacteristic
221C2×C4C2×C22⋊D7311yescharacteristic
222C2×C4C2×C22⋊D7311yescharacteristic
223C2×C4C2×C22⋊D7311yescharacteristic
224C2×C4C2×C22⋊D7311yescharacteristic
225C2×C4C23×D7311yescharacteristic
226C8—1462no—
227C8—1462no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22C22×C22⋊D7311yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—41no—
243C4—2922no—
244C4—2922no—
245C4#1455663812yes—
246C2—41no—
247C2—81no—
248C2#1798915811yescharacteristic
249C2#1798938511yescharacteristic
250C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#529×C73C2
socleC22×C73C22×D4
hypercenter#529D73
hypocenterC73#3240
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #17989144C2semidirect
2. #17988997C2semidirect
3. #17988997C2semidirect
4. #17988946C2semidirect
5. #17988946C2semidirect
6. #17988925C2semidirect
8. #17988894C2semidirect
9. #17988887C2semidirect
10. #17988644C2semidirect
126. C73#3240semidirect