Finite Group Databasebeta

← #22618111

Subgroups — #22618111

Order 9344.

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

normal subgroups only

This group has 332 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
1C73⋊#401C212yesmaximal
2#17988529C212yesmaximal
3#17988527C212yesmaximal
4#17988526C211yesmaximal, characteristic
5#17988520C212yesmaximal
6#17988507C212yesmaximal
7#17988492C211yesmaximal, characteristic
8#17988473C212yesmaximal
9#398×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C2×C4⋊Dic73C2212yes—
12C2×C4⋊Dic73C2211yescharacteristic
13C2×#11924007C2212yes—
14C2×#11924007C2212yes—
15C2×C4×Dic73C2211yescharacteristic
16#14556498C2212yes—
17#14556498C2212yes—
18#14556498C2212yes—
19#14556498C2212yes—
20#14556498C2212yes—
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
31C2×Dic146—22no—
32C2×Dic146—41no—
33C2×Dic146—41no—
34C22×Dic73C2312yes—
35C22×Dic73C2312yes—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C4⋊Dic73—42no—
39C4⋊Dic73—41no—
40#11924007—42no—
41#11924007—42no—
42C4×Dic73—41no—
43C22×C4×C73C2312yes—
44C22×C4×C73C2311yescharacteristic
45C22×C4×C73C2311yescharacteristic
46C22×C4×C73C2312yes—
47C22×C4×C73C2311yescharacteristic
48C4⋊C4×C73—24no—
49C4⋊C4×C73—41no—
50C4⋊C4×C73—41no—
51C23×C73C2411yescharacteristic
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—22no—
55C2×C4×C73—22no—
56C2×C4×C73—21no—
57C2×C4×C73—22no—
58C2×C4×C73—21no—
59C2×C4×C73—22no—
60C2×C4×C73—22no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—22no—
64C2×C4×C73#4112yes—
65C2×Dic73—22no—
66C2×Dic73—22no—
67C2×Dic73—22no—
68C2×Dic73—22no—
69C2×Dic73—22no—
70C2×Dic73—22no—
71C2×Dic73—22no—
72C2×Dic73—22no—
73C2×Dic73—22no—
74C2×Dic73—24no—
75C2×Dic73—22no—
76Dic146—44no—
77C22×C73C2×#4111yescharacteristic
78C22×C73H(5,𝔽2)11yescharacteristic
79C22×C73H(5,𝔽2)11yescharacteristic
80C22×C732−1+412yes—
81C22×C732−1+412yes—
82C4×C73—22no—
83C4×C73—42no—
84C4×C73—42no—
85C4×C73—41no—
86C4×C73—41no—
87Dic73—42no—
88Dic73—42no—
89Dic73—42no—
90Dic73—42no—
91C2×C73#53811yescharacteristic
92C2×C73#54112yes—
93C2×C73#56311yescharacteristic
94C2×C73#56311yescharacteristic
95C2×C73#56312yes—
96#2833—731nomaximal, Sylow
97C73#283311yescharacteristic, complemented, Sylow
98#401—732no—
99#400—731no—
100#400—732no—
101#400—732no—
102#398—732no—
103#398D7311yescharacteristic
104#395—732no—
105#391—731no—
106#387—732no—
107C22×Q8—731no—
108C2×C4⋊C4—732no—
109C2×C4⋊C4—732no—
110C2×C4⋊C4—732no—
111C2×C4⋊C4—731no—
112C2×C4⋊C4C2×D7312yes—
113C2×C4⋊C4C2×D7311yescharacteristic
114C2×C4⋊C4C2×D7311yescharacteristic
115C2×C42—731no—
116#95—732no—
117#95—732no—
118#95—732no—
119#95—732no—
120#95—732no—
121#95—732no—
122#95—732no—
123#95—732no—
124#95—732no—
125#95—731no—
126#95C2×D7312yes—
127#95C2×D7311yescharacteristic
128C2×Q8—2921no—
129C2×Q8—2921no—
130C2×Q8—1462no—
131C22×C4—732no—
132C22×C4—732no—
133C22×C4—732no—
134C22×C4—732no—
135C22×C4C22×D7312yes—
136C22×C4C22×D7311yescharacteristic
137C22×C4C22×D7311yescharacteristic
138C22×C4C22×D7312yes—
139C22×C4C22×D7311yescharacteristic
140C4⋊C4—24no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—2922no—
144C4⋊C4—2922no—
145C4⋊C4—2921no—
146C4⋊C4—2922no—
147C42—2921no—
148C23C23×D7311yescharacteristic
149Q8—2924no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—1462no—
163C2×C4—1462no—
164C2×C4—1462no—
165C2×C4—1462no—
166C2×C4—1462no—
167C2×C4—1462no—
168C2×C4—1462no—
169C2×C4—1462no—
170C2×C4—1464no—
171C2×C4—1462no—
172C2×C4—1462no—
173C2×C4#1192402712yes—
174C22C2×#1192402711yescharacteristic
175C22#1455663611yescharacteristic
176C22#1455663711yescharacteristic
177C22#1455663812yes—
178C22#1455663912yes—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—41no—
183C4—41no—
184C4—2922no—
185C4—2922no—
186C4—2922no—
187C4—2922no—
188C2#1798917411yescharacteristic
189C2#1798919712yes—
190C2#1798933611yescharacteristic
191C2#1798934011yescharacteristic
192C2#1798934112yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2833
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
97. C73#2833semidirect