Finite Group Databasebeta

← #22618078

Subgroups — #22618078

Order 9344.

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

normal subgroups only

This group has 408 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#17988516C212yesmaximal, complemented
2#17988514C212yesmaximal, complemented
3#17988509C212yesmaximal, complemented
4#17988507C211yesmaximal, characteristic, complemented
5#17988504C212yesmaximal
6#17988500C212yesmaximal, complemented
7#17988488C211yesmaximal, characteristic
8#17988473C212yesmaximal, complemented
9#398×C73C211yesmaximal, characteristic, complemented
10C22×Dic146C2211yescharacteristic
11C22×D292C2211yescharacteristic
12C2×C4⋊Dic73C2212yes—
13C2×#11924007C2212yes—
14C2×#11924005C2212yes—
15C2×#11924005C2212yes—
16C2×#11924005C2212yes—
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×C4×Dic73C2211yescharacteristic
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26C2×C4⋊C4×C73C2212yes—
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C4⋊C4×C73C2211yescharacteristic
29#95×C73C2212yes—
30#95×C73C2211yescharacteristic
31C23×D73C2312yes—
32C2×Dic146—41no—
33C2×Dic146—42no—
34C2×D292—22no—
35C2×D292—41no—
36C2×D292—41no—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C4⋊Dic73—42no—
41#11924007—42no—
42#11924005—42no—
43#11924005—42no—
44#11924005—42no—
45#11924005—42no—
46#11924005—42no—
47#11924005—42no—
48C4×Dic73—41no—
49C22×C4×C73C2312yes—
50C22×C4×C73C2311yescharacteristic
51C22×C4×C73C2312yes—
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2311yescharacteristic
54C4⋊C4×C73—24no—
55C4⋊C4×C73—41no—
56C4⋊C4×C73—41no—
57C23×C73C2411yescharacteristic
58C22×D73—22no—
59C22×D73—22no—
60C22×D73—22no—
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—22no—
64C22×D73—22no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—21no—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73#4112yes—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87D292—44no—
88Dic146—44no—
89C22×C73C2×#4111yescharacteristic
90C22×C73H(5,𝔽2)11yescharacteristic
91C22×C73H(5,𝔽2)11yescharacteristic
92C22×C73H(5,𝔽2)12yes—
93C22×C732−1+412yes—
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—42no—
97C2×D73—42no—
98C2×D73—42no—
99C2×D73—42no—
100C2×D73—42no—
101C4×C73—22no—
102C4×C73—42no—
103C4×C73—42no—
104C4×C73—41no—
105C4×C73—41no—
106Dic73—42no—
107Dic73—42no—
108Dic73—42no—
109C2×C73#53811yescharacteristic
110C2×C73#54212yes—
111C2×C73#56011yescharacteristic
112C2×C73#56212yes—
113C2×C73#56311yescharacteristic
114D73—82no—
115#2830—731nomaximal, Sylow
116C73#283011yescharacteristic, complemented, Sylow
117#398D7311yescharacteristic, complemented
118#397—732no—
119#397—732no—
120#396—732no—
121#395—731no—
122#394—732no—
123#393—732no—
124#390—731no—
125#387—732no—
126C22×Q8—731no—
127C22×D4—731no—
128C2×C4⋊C4—732no—
129C2×C4⋊C4—732no—
130C2×C4⋊C4C2×D7312yes—
131C2×C4⋊C4C2×D7311yescharacteristic
132C2×C4⋊C4C2×D7311yescharacteristic
133C2×C22⋊C4—732no—
134C2×C22⋊C4—732no—
135C2×C22⋊C4—732no—
136C2×C22⋊C4—732no—
137C2×C22⋊C4—732no—
138C2×C22⋊C4—732no—
139C2×C42—731no—
140#95—732no—
141#95—732no—
142#95—732no—
143#95—732no—
144#95—731no—
145#95C2×D7312yes—
146#95C2×D7311yescharacteristic
147C24—732no—
148C2×Q8—2921no—
149C2×Q8—2922no—
150C2×D4—2921no—
151C2×D4—2921no—
152C2×D4—1462no—
153C22×C4—732no—
154C22×C4—732no—
155C22×C4—732no—
156C22×C4C22×D7312yes—
157C22×C4C22×D7311yescharacteristic
158C22×C4C22×D7312yes—
159C22×C4C22×D7311yescharacteristic
160C22×C4C22×D7311yescharacteristic
161C4⋊C4—24no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—2922no—
165C4⋊C4—2922no—
166C22⋊C4—2922no—
167C22⋊C4—2922no—
168C22⋊C4—2922no—
169C22⋊C4—2922no—
170C22⋊C4—2922no—
171C22⋊C4—2922no—
172C42—2921no—
173C23—1462no—
174C23—1462no—
175C23—1462no—
176C23—1462no—
177C23—1462no—
178C23—1462no—
179C23—1462no—
180C23C23×D7311yescharacteristic
181Q8—2924no—
182D4—2924no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
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—1462no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4—1462no—
203C2×C4—1462no—
204C2×C4#1192402712yes—
205C22—2922no—
206C22—2922no—
207C22—2922no—
208C22—2922no—
209C22—2922no—
210C22—2922no—
211C22—2922no—
212C22C2×#1192402711yescharacteristic
213C22#1455663611yescharacteristic
214C22#1455663711yescharacteristic
215C22#1455663712yes—
216C22#1455663912yes—
217C4—22no—
218C4—42no—
219C4—42no—
220C4—41no—
221C4—41no—
222C4—2922no—
223C4—2922no—
224C4—2922no—
225C2—5842no—
226C2#1798917411yescharacteristic
227C2#1798921012yes—
228C2#1798932711yescharacteristic
229C2#1798933512yes—
230C2#1798933611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2830
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #17988516C2semidirect
2. #17988514C2semidirect
3. #17988509C2semidirect
4. #17988507C2semidirect
6. #17988500C2semidirect
8. #17988473C2semidirect
9. #398×C73C2semidirect
116. C73#2830semidirect
117. #398D73semidirect