Finite Group Databasebeta

← #22617349

Subgroups — #22617349

Order 9344.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#17988506C212yesmaximal, complemented
3#17988499C211yesmaximal, characteristic
4#17988491C212yesmaximal, complemented
5#17988481C212yesmaximal
6#17988459C212yesmaximal
7#17988459C211yesmaximal, characteristic
8#17988451C212yesmaximal, complemented
9#393×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C23×Dic73C2211yescharacteristic
12C2×#11924007C2212yes—
13C2×#11924007C2212yes—
14C2×#11924007C2212yes—
15C2×#11924007C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2211yescharacteristic
18C2×C4×Dic73C2212yes—
19#14556498C2212yes—
20#14556498C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26C22×Q8×C73C2211yescharacteristic
27C2×C22⋊C4×C73C2212yes—
28C2×C22⋊C4×C73C2211yescharacteristic
29#95×C73C2211yescharacteristic
30#95×C73C2212yes—
31C2×Dic146—24no—
32C2×Dic146—41no—
33C22×Dic73—42no—
34C22×Dic73—41no—
35C22×Dic73C2312yes—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39#11924007—42no—
40#11924007—42no—
41#11924007—42no—
42#11924007—42no—
43C22⋊Dic73—24no—
44C22⋊Dic73Q814yescomplemented
45C4×Dic73—24no—
46C24×C73C2311yescharacteristic
47C2×Q8×C73—42no—
48C2×Q8×C73—41no—
49C22×C4×C73C2311yescharacteristic
50C22×C4×C73C2312yes—
51C22×C4×C73C2311yescharacteristic
52C22×C4×C73C2312yes—
53C22⋊C4×C73—42no—
54C22⋊C4×C73—41no—
55C23×C73—22no—
56C23×C73—21no—
57C23×C73—22no—
58C23×C73—21no—
59C23×C73C2×Q812yes—
60C23×C73C2411yescharacteristic
61Q8×C73—44no—
62C2×C4×C73—22no—
63C2×C4×C73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—21no—
66C2×C4×C73—22no—
67C2×C4×C73—21no—
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—44no—
83C2×Dic73C2×Q814yes—
84C2×Dic73#4114yes—
85Dic146—44no—
86C22×C73—22no—
87C22×C73—24no—
88C22×C73—42no—
89C22×C73—41no—
90C22×C73—41no—
91C22×C73C22×Q811yescharacteristic
92C22×C73C2×#4112yes—
93C22×C73H(5,𝔽2)12yes—
94C22×C73H(5,𝔽2)11yescharacteristic
95C22×C732−1+411yescharacteristic
96C4×C73—42no—
97C4×C73—41no—
98C4×C73—42no—
99C4×C73—41no—
100Dic73—24no—
101Dic73—24no—
102Dic73—42no—
103Dic73—42no—
104C2×C73—42no—
105C2×C73#54212yes—
106C2×C73#54411yescharacteristic
107C2×C73#55111yescharacteristic
108C2×C73#55412yes—
109C2×C73H(3,𝔽4)11yescharacteristic
110#2763—731nomaximal, Sylow
111C73#276311yescharacteristic, complemented, Sylow
112#400—732no—
113#395—732no—
114#393—731no—
115#393D7311yescharacteristic
116#391—732no—
117#388—732no—
118#385—732no—
119#385—731no—
120#382—732no—
121C22×Q8—731no—
122C22×Q8C2×D7311yescharacteristic
123C23×C4—731no—
124C2×C4⋊C4—732no—
125C2×C4⋊C4—732no—
126C2×C4⋊C4—732no—
127C2×C4⋊C4—732no—
128C2×C22⋊C4—731no—
129C2×C22⋊C4—732no—
130C2×C22⋊C4C2×D7312yes—
131C2×C22⋊C4C2×D7311yescharacteristic
132C2×C42—732no—
133#95—732no—
134#95—732no—
135#95—732no—
136#95—732no—
137#95—732no—
138#95—732no—
139#95—731no—
140#95C2×D7311yescharacteristic
141#95C2×D7312yes—
142C24C22×D7311yescharacteristic
143C2×Q8—42no—
144C2×Q8—41no—
145C2×Q8—2921no—
146C2×Q8—1464no—
147C22×C4—2922no—
148C22×C4—2921no—
149C22×C4—732no—
150C22×C4—732no—
151C22×C4—732no—
152C22×C4—732no—
153C22×C4C22×D7311yescharacteristic
154C22×C4C22×D7312yes—
155C22×C4C22×D7311yescharacteristic
156C22×C4C22×D7312yes—
157C4⋊C4—2922no—
158C4⋊C4—2922no—
159C4⋊C4—2922no—
160C4⋊C4—2922no—
161C22⋊C4—42no—
162C22⋊C4—41no—
163C22⋊C4—734no—
164C22⋊C4—1464no—
165C42—1464no—
166C23—22no—
167C23—21no—
168C23—22no—
169C23—21no—
170C23Q8×D7312yes—
171C23C23×D7311yescharacteristic
172Q8—44no—
173Q8—2924no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—2924no—
185C2×C4—734no—
186C2×C4—734no—
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—42no—
200C22—41no—
201C22—41no—
202C22C2×Q8×D7311yescharacteristic
203C22#41×D7312yes—
204C22#1455663612yes—
205C22#1455663611yescharacteristic
206C22#1455663811yescharacteristic
207C4—42no—
208C4—41no—
209C4—42no—
210C4—41no—
211C4—2922no—
212C4—2922no—
213C4—1464no—
214C4—1464no—
215C2—42no—
216C2#1798920112yes—
217C2#1798921611yescharacteristic
218C2#1798926711yescharacteristic
219C2#1798929112yes—
220C2#1798933011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#393×C73C2
hypercenter#393D73
hypocenterC73#2763
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #17988528C2semidirect
2. #17988506C2semidirect
4. #17988491C2semidirect
8. #17988451C2semidirect
44. C22⋊Dic73Q8semidirect
111. C73#2763semidirect