Finite Group Databasebeta

← #22617354

Subgroups — #22617354

Order 9344.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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#17988521C212yesmaximal, complemented
3#17988512C211yesmaximal, characteristic
4#17988499C211yesmaximal, characteristic
5#17988491C212yesmaximal, complemented
6#17988481C212yesmaximal
7#17988460C212yesmaximal
8#17988454C212yesmaximal, complemented
9#381×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007C2212yes—
13C2×#11924007C2212yes—
14C2×#11924007C2212yes—
15C2×C22⋊Dic73C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C4×Dic73C2212yes—
18#14556498C2211yescharacteristic
19#14556498C2212yes—
20#14556498C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26C23×C4×C73C2211yescharacteristic
27C2×C22⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2211yescharacteristic
29#95×C73C2212yes—
30#95×C73C2212yes—
31C2×Dic146—24no—
32C2×Dic146—41no—
33C22×Dic73C2312yes—
34C22×Dic73C2312yes—
35C22×Dic73C2312yes—
36C22×Dic73C2312yes—
37C4⋊Dic73—41no—
38#11924007—42no—
39#11924007—42no—
40#11924007—42no—
41C22⋊Dic73—24no—
42C22⋊Dic73—24no—
43C4×Dic73—24no—
44C24×C73C2311yescharacteristic
45C22×C4×C73—22no—
46C22×C4×C73—41no—
47C22×C4×C73—41no—
48C22×C4×C73C2311yescharacteristic
49C22×C4×C73C2311yescharacteristic
50C22×C4×C73C2312yes—
51C22×C4×C73C2312yes—
52C22⋊C4×C73—41no—
53C22⋊C4×C73—41no—
54C23×C73—22no—
55C23×C73—21no—
56C23×C73—21no—
57C23×C73—22no—
58C23×C73#4112yes—
59C23×C73C2411yescharacteristic
60C2×C4×C73—22no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—22no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—44no—
71C2×Dic73—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#4114yes—
83Dic146—44no—
84C22×C73—22no—
85C22×C73—24no—
86C22×C73—42no—
87C22×C73—41no—
88C22×C73—41no—
89C22×C73C2×#4112yes—
90C22×C73C2×#4111yescharacteristic
91C22×C73H(5,𝔽2)11yescharacteristic
92C22×C73H(5,𝔽2)11yescharacteristic
93C22×C732−1+412yes—
94C4×C73—42no—
95C4×C73—42no—
96C4×C73—41no—
97C4×C73—41no—
98Dic73—24no—
99Dic73—42no—
100Dic73—42no—
101Dic73—42no—
102C2×C73—42no—
103C2×C73#53811yescharacteristic
104C2×C73#54212yes—
105C2×C73#55111yescharacteristic
106C2×C73#55212yes—
107C2×C73#56311yescharacteristic
108#2764—731nomaximal, Sylow
109C73#276411yescharacteristic, complemented, Sylow
110#400—732no—
111#398—732no—
112#397—731no—
113#393—731no—
114#391—732no—
115#388—732no—
116#385—732no—
117#383—732no—
118#381D7311yescharacteristic
119C22×Q8—731no—
120C23×C4C2×D7311yescharacteristic
121C2×C4⋊C4—732no—
122C2×C4⋊C4—732no—
123C2×C4⋊C4—732no—
124C2×C4⋊C4—731no—
125C2×C22⋊C4—732no—
126C2×C22⋊C4—732no—
127C2×C22⋊C4C2×D7311yescharacteristic
128C2×C22⋊C4C2×D7311yescharacteristic
129C2×C42—732no—
130#95—731no—
131#95—732no—
132#95—732no—
133#95—732no—
134#95—732no—
135#95—732no—
136#95—732no—
137#95—731no—
138#95C2×D7312yes—
139#95C2×D7312yes—
140C24C22×D7311yescharacteristic
141C2×Q8—2921no—
142C2×Q8—1464no—
143C22×C4—22no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4—732no—
147C22×C4—732no—
148C22×C4—732no—
149C22×C4—732no—
150C22×C4C22×D7311yescharacteristic
151C22×C4C22×D7311yescharacteristic
152C22×C4C22×D7312yes—
153C22×C4C22×D7312yes—
154C4⋊C4—2922no—
155C4⋊C4—2922no—
156C4⋊C4—2922no—
157C4⋊C4—2921no—
158C22⋊C4—41no—
159C22⋊C4—41no—
160C22⋊C4—1464no—
161C22⋊C4—1464no—
162C42—1464no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23—22no—
167C23#1192402812yes—
168C23C23×D7311yescharacteristic
169Q8—2924no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—44no—
181C2×C4—734no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4—1462no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4—1462no—
193C22—22no—
194C22—24no—
195C22—42no—
196C22—41no—
197C22—41no—
198C22#41×D7312yes—
199C22C2×#1192402811yescharacteristic
200C22#1455663611yescharacteristic
201C22#1455663611yescharacteristic
202C22#1455663812yes—
203C4—42no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—2922no—
208C4—2922no—
209C4—2922no—
210C4—1464no—
211C2—42no—
212C2#1798917511yescharacteristic
213C2#1798920512yes—
214C2#1798926511yescharacteristic
215C2#1798927012yes—
216C2#1798934011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#381×C73C2
hypercenter#381D73
hypocenterC73#2764
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. #17988528C2semidirect
2. #17988521C2semidirect
5. #17988491C2semidirect
8. #17988454C2semidirect
109. C73#2764semidirect