Finite Group Databasebeta

← #22618193

Subgroups — #22618193

Order 9344.

396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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#17988528C212yesmaximal, complemented
2#17988520C212yesmaximal, complemented
3#17988517C212yesmaximal, complemented
4#17988510C212yesmaximal
5#17988507C212yesmaximal, complemented
6#17988499C211yesmaximal, characteristic
7#17988448C211yesmaximal, characteristic
8#17988445C212yesmaximal
9#399×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C23×Dic73C2211yescharacteristic
12C2×C4⋊Dic73C2212yes—
13C2×#11924007C2212yes—
14C2×#11924007C2212yes—
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C22⋊Dic73C2211yescharacteristic
19#14556498C2212yes—
20#14556498C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2211yescharacteristic
24#14556498C2212yes—
25#14556498C2212yes—
26C2×C4⋊C4×C73C2212yes—
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2211yescharacteristic
30#95×C73C2211yescharacteristic
31C2×Dic146—42no—
32C2×Dic146—41no—
33C22×Dic73—41no—
34C22×Dic73—41no—
35C22×Dic73Q814yescomplemented
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C4⋊Dic73—42no—
41#11924007—42no—
42#11924007—42no—
43#11924007—42no—
44#11924007—42no—
45C22⋊Dic73—41no—
46C22⋊Dic73—42no—
47C24×C73C2311yescharacteristic
48C22×C4×C73C2311yescharacteristic
49C22×C4×C73C2312yes—
50C22×C4×C73C2311yescharacteristic
51C22×C4×C73C2312yes—
52C4⋊C4×C73—41no—
53C4⋊C4×C73—42no—
54C22⋊C4×C73—42no—
55C22⋊C4×C73—41no—
56C23×C73—22no—
57C23×C73—21no—
58C23×C73—21no—
59C23×C73—22no—
60C23×C73C2×Q812yes—
61C23×C73C2411yescharacteristic
62C2×C4×C73—22no—
63C2×C4×C73—21no—
64C2×C4×C73—22no—
65C2×C4×C73—21no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×Dic73—22no—
73C2×Dic73—22no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—44no—
84C2×Dic73C2×Q814yes—
85Dic146—44no—
86C22×C73—22no—
87C22×C73—24no—
88C22×C73—41no—
89C22×C73—42no—
90C22×C73—41no—
91C22×C73C22×Q811yescharacteristic
92C22×C73H(5,𝔽2)11yescharacteristic
93C22×C73H(5,𝔽2)12yes—
94C22×C73H(5,𝔽2)11yescharacteristic
95C22×C732−1+412yes—
96C4×C73—41no—
97C4×C73—42no—
98C4×C73—42no—
99C4×C73—41no—
100Dic73—24no—
101Dic73—42no—
102Dic73—42no—
103Dic73—42no—
104C2×C73—42no—
105C2×C73#54311yescharacteristic
106C2×C73#54412yes—
107C2×C73#56011yescharacteristic
108C2×C73#56212yes—
109C2×C73#56311yescharacteristic
110#2841—731nomaximal, Sylow
111C73#284111yescharacteristic, complemented, Sylow
112#400—732no—
113#399D7311yescharacteristic
114#398—732no—
115#398—732no—
116#396—732no—
117#395—732no—
118#393—731no—
119#381—731no—
120#380—732no—
121C22×Q8—731no—
122C23×C4—731no—
123C2×C4⋊C4—732no—
124C2×C4⋊C4—732no—
125C2×C4⋊C4—732no—
126C2×C4⋊C4—732no—
127C2×C4⋊C4—732no—
128C2×C4⋊C4C2×D7312yes—
129C2×C4⋊C4C2×D7311yescharacteristic
130C2×C22⋊C4—732no—
131C2×C22⋊C4—731no—
132C2×C22⋊C4C2×D7312yes—
133C2×C22⋊C4C2×D7311yescharacteristic
134#95—732no—
135#95—732no—
136#95—732no—
137#95—732no—
138#95—731no—
139#95—732no—
140#95—732no—
141#95C2×D7311yescharacteristic
142C24C22×D7311yescharacteristic
143C2×Q8—2921no—
144C2×Q8—2922no—
145C22×C4—2921no—
146C22×C4—2921no—
147C22×C4—734no—
148C22×C4—732no—
149C22×C4—732no—
150C22×C4—732no—
151C22×C4—732no—
152C22×C4C22×D7311yescharacteristic
153C22×C4C22×D7311yescharacteristic
154C22×C4C22×D7312yes—
155C22×C4C22×D7312yes—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C4⋊C4—2922no—
159C4⋊C4—2922no—
160C4⋊C4—2922no—
161C4⋊C4—2922no—
162C4⋊C4—2922no—
163C22⋊C4—42no—
164C22⋊C4—41no—
165C22⋊C4—2922no—
166C22⋊C4—2921no—
167C23—22no—
168C23—21no—
169C23—21no—
170C23—22no—
171C23Q8×D7312yes—
172C23C23×D7311yescharacteristic
173Q8—2924no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—2924no—
185C2×C4—734no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1462no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1462no—
197C22—22no—
198C22—24no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C2×Q8×D7311yescharacteristic
203C22#1455663611yescharacteristic
204C22#1455663612yes—
205C22#1455663711yescharacteristic
206C22#1455663812yes—
207C4—41no—
208C4—42no—
209C4—42no—
210C4—41no—
211C4—2922no—
212C4—2922no—
213C4—2922no—
214C4—1464no—
215C2—42no—
216C2#1798921211yescharacteristic
217C2#1798921612yes—
218C2#1798932411yescharacteristic
219C2#1798933412yes—
220C2#1798934011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2841
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #17988528C2semidirect
2. #17988520C2semidirect
3. #17988517C2semidirect
5. #17988507C2semidirect
35. C22×Dic73Q8semidirect
111. C73#2841semidirect