Finite Group Databasebeta

← #22615608

Subgroups — #22615608

Order 9344.

540 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#14556548C212yesmaximal, complemented
2#17988517C211yesmaximal, characteristic, complemented
3#17988509C212yesmaximal, complemented
4#17988504C211yesmaximal, characteristic
5#17988479C212yesmaximal, complemented
6#17988472C212yesmaximal, complemented
7#17988465C212yesmaximal
8#17988461C212yesmaximal, complemented
9#382×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11C22×C4×D73C2212yes—
12#14556548—28no—
13C2×C4⋊Dic73C2212yes—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×C4×Dic73C2212yes—
23#14556498C2211yescharacteristic
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26#14556498C2212yes—
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C4⋊C4×C73C2211yescharacteristic
29C2×C42×C73C2211yescharacteristic
30#95×C73C2212yes—
31#95×C73C2212yes—
32C23×D73C2312yes—
33C2×D292—24no—
34C2×D292—41no—
35C22×Dic73C2312yes—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C2×C4×D73—24no—
39C2×C4×D73—24no—
40C2×C4×D73—24no—
41C4⋊Dic73—24no—
42C4⋊Dic73—41no—
43#11924007—24no—
44#11924007—24no—
45#11924005—24no—
46#11924005—24no—
47#11924005—24no—
48#11924005—24no—
49#11924005—42no—
50C4×Dic73—24no—
51C22×C4×C73C2311yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2312yes—
54C22×C4×C73C2312yes—
55C22×C4×C73C2311yescharacteristic
56C4⋊C4×C73—41no—
57C4⋊C4×C73—41no—
58C42×C73D414yescomplemented
59C23×C73C2411yescharacteristic
60C22×D73—22no—
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—22no—
64C22×D73—22no—
65C22×D73—22no—
66C22×D73#4114yes—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73C2×D414yes—
79C2×C4×C73C2×D412yes—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73#4114yes—
89D292—44no—
90C4×D73—216no—
91C22×C73C22×D411yescharacteristic
92C22×C73C2×#4112yes—
93C22×C73C2×#4112yes—
94C22×C73H(5,𝔽2)11yescharacteristic
95C22×C732−1+411yescharacteristic
96C2×D73—24no—
97C2×D73—24no—
98C2×D73—24no—
99C2×D73—42no—
100C2×D73—42no—
101C2×D73—42no—
102C2×D73—42no—
103C4×C73—24no—
104C4×C73—22no—
105C4×C73—41no—
106C4×C73—41no—
107C4×C73—42no—
108Dic73—24no—
109Dic73—42no—
110Dic73—42no—
111C2×C73#52512yes—
112C2×C73#53711yescharacteristic
113C2×C73#55111yescharacteristic
114C2×C73#55212yes—
115C2×C73#55511yescharacteristic
116D73—44no—
117#2609—731nomaximal, Sylow
118C73#260911yescharacteristic, complemented, Sylow
119C2×#117—732no—
120#398—731no—
121#396—732no—
122#394—731no—
123#388—732no—
124#387—732no—
125#386—732no—
126#385—732no—
127#382D7311yescharacteristic, complemented
128C22×D4—731no—
129C23×C4—732no—
130#117—1468no—
131C2×C4⋊C4—731no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4—732no—
135C2×C4⋊C4C2×D7311yescharacteristic
136C2×C4⋊C4C2×D7311yescharacteristic
137C2×C22⋊C4—732no—
138C2×C22⋊C4—732no—
139C2×C22⋊C4—732no—
140C2×C22⋊C4—732no—
141C2×C22⋊C4—732no—
142C2×C42—732no—
143C2×C42C2×D7311yescharacteristic
144#95—731no—
145#95—732no—
146#95—731no—
147#95—732no—
148#95C2×D7312yes—
149#95C2×D7312yes—
150C24—732no—
151C2×D4—2921no—
152C2×D4—1464no—
153C22×C4—732no—
154C22×C4—732no—
155C22×C4—732no—
156C22×C4—1464no—
157C22×C4—1464no—
158C22×C4—1464no—
159C22×C4C22×D7311yescharacteristic
160C22×C4C22×D7311yescharacteristic
161C22×C4C22×D7312yes—
162C22×C4C22×D7312yes—
163C22×C4C22×D7311yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—2921no—
167C4⋊C4—1464no—
168C4⋊C4—1464no—
169C4⋊C4—1464no—
170C22⋊C4—2922no—
171C22⋊C4—1464no—
172C22⋊C4—1464no—
173C22⋊C4—1464no—
174C22⋊C4—1464no—
175C42—1464no—
176C42D29214yescomplemented
177C23—734no—
178C23—1462no—
179C23—1462no—
180C23—1462no—
181C23—1462no—
182C23—1462no—
183C23—1462no—
184C23C23×D7311yescharacteristic
185D4—2924no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—734no—
198C2×C4—14616no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4—1462no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4—1462no—
207C2×C4C2×D29214yes—
208C2×C4C2×D29212yes—
209C22—2922no—
210C22—2922no—
211C22—2922no—
212C22—2922no—
213C22—1464no—
214C22—1464no—
215C22—1464no—
216C22C22×D29211yescharacteristic
217C22#41×D7312yes—
218C22#41×D7312yes—
219C22#1455663611yescharacteristic
220C22#1455663911yescharacteristic
221C4—22no—
222C4—24no—
223C4—41no—
224C4—41no—
225C4—42no—
226C4—2922no—
227C4—2922no—
228C4—1464no—
229C2—2924no—
230C2#1798909912yes—
231C2#1798916811yescharacteristic
232C2#1798926711yescharacteristic
233C2#1798926912yes—
234C2#1798929911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#382×C73C2
hypercenter#382D73
hypocenterC73#2609
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#14556548C2semidirect
2. #17988517C2semidirect
3. #17988509C2semidirect
5. #17988479C2semidirect
6. #17988472C2semidirect
8. #17988461C2semidirect
9. #382×C73C2semidirect
58. C42×C73D4semidirect
118. C73#2609semidirect
127. #382D73semidirect
176. C42D292semidirect