Finite Group Databasebeta

← #22617751

Subgroups — #22617751

Order 9344.

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

normal subgroups only

This group has 344 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#17988526C211yesmaximal, characteristic
2#17988525C212yesmaximal
3#17988525C212yesmaximal
4#17988517C211yesmaximal, characteristic
5#17988473C212yesmaximal
6#17988473C212yesmaximal
7#17988471C212yesmaximal
8#17988468C212yesmaximal
9#384×C73C211yesmaximal, characteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007C2212yes—
13C2×#11924007C2212yes—
14C2×C4×Dic73C2212yes—
15#14556498C2212yes—
16#14556498C2212yes—
17#14556498C2212yes—
18#14556498C2212yes—
19#14556498C2212yes—
20#14556498C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2211yescharacteristic
25#14556498C2211yescharacteristic
26C2×C4⋊C4×C73C2212yes—
27C2×C4⋊C4×C73C2212yes—
28C2×C4⋊C4×C73C2211yescharacteristic
29C2×C4⋊C4×C73C2211yescharacteristic
30C2×C42×C73C2211yescharacteristic
31C22×Dic73C2312yes—
32C22×Dic73C2312yes—
33C22×Dic73C2312yes—
34C22×Dic73C2312yes—
35C4⋊Dic73—41no—
36C4⋊Dic73—41no—
37#11924007—24no—
38#11924007—24no—
39C4×Dic73—42no—
40C22×C4×C73C2312yes—
41C22×C4×C73C2311yescharacteristic
42C22×C4×C73C2311yescharacteristic
43C22×C4×C73C2312yes—
44C22×C4×C73C2311yescharacteristic
45C4⋊C4×C73—24no—
46C4⋊C4×C73—24no—
47C4⋊C4×C73—41no—
48C4⋊C4×C73—41no—
49C42×C73—22no—
50C23×C73C2411yescharacteristic
51C2×C4×C73—22no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—22no—
55C2×C4×C73—22no—
56C2×C4×C73—22no—
57C2×C4×C73—22no—
58C2×C4×C73—22no—
59C2×C4×C73—22no—
60C2×C4×C73—21no—
61C2×C4×C73—21no—
62C2×C4×C73#4114yes—
63C2×C4×C73#4112yes—
64C2×Dic73—22no—
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—
75C22×C73C2×#4112yes—
76C22×C73C2×#4111yescharacteristic
77C22×C73H(5,𝔽2)11yescharacteristic
78C22×C732−1+411yescharacteristic
79C22×C732−1+412yes—
80C4×C73—22no—
81C4×C73—24no—
82C4×C73—42no—
83C4×C73—41no—
84C4×C73—41no—
85Dic73—42no—
86Dic73—42no—
87Dic73—42no—
88Dic73—42no—
89C2×C73#53911yescharacteristic
90C2×C73#54112yes—
91C2×C73#55212yes—
92C2×C73#55911yescharacteristic
93C2×C73#56311yescharacteristic
94#2794—731nomaximal, Sylow
95C73#279411yescharacteristic, complemented, Sylow
96#400—732no—
97#400—732no—
98#400—731no—
99#398—731no—
100#387—732no—
101#387—732no—
102#387—732no—
103#387—732no—
104#384D7311yescharacteristic
105C2×C4⋊C4—731no—
106C2×C4⋊C4—731no—
107C2×C4⋊C4—732no—
108C2×C4⋊C4—732no—
109C2×C4⋊C4C2×D7312yes—
110C2×C4⋊C4C2×D7312yes—
111C2×C4⋊C4C2×D7311yescharacteristic
112C2×C4⋊C4C2×D7311yescharacteristic
113C2×C42—732no—
114C2×C42C2×D7311yescharacteristic
115#95—732no—
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—731no—
125#95—731no—
126C22×C4—732no—
127C22×C4—732no—
128C22×C4—732no—
129C22×C4—732no—
130C22×C4C22×D7312yes—
131C22×C4C22×D7311yescharacteristic
132C22×C4C22×D7311yescharacteristic
133C22×C4C22×D7312yes—
134C22×C4C22×D7311yescharacteristic
135C4⋊C4—24no—
136C4⋊C4—24no—
137C4⋊C4—41no—
138C4⋊C4—41no—
139C4⋊C4—2921no—
140C4⋊C4—2921no—
141C4⋊C4—1464no—
142C4⋊C4—1464no—
143C42—22no—
144C42—2922no—
145C23C23×D7311yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—1462no—
158C2×C4—1462no—
159C2×C4—1462no—
160C2×C4—1462no—
161C2×C4—1462no—
162C2×C4—1462no—
163C2×C4—1462no—
164C2×C4—1462no—
165C2×C4—1462no—
166C2×C4—1462no—
167C2×C4—1464no—
168C2×C4#1192402714yes—
169C2×C4#1192402812yes—
170C22C2×#1192402712yes—
171C22C2×#1192402811yescharacteristic
172C22#1455663611yescharacteristic
173C22#1455663911yescharacteristic
174C22#1455663912yes—
175C4—22no—
176C4—24no—
177C4—42no—
178C4—41no—
179C4—41no—
180C4—2922no—
181C4—2922no—
182C4—2922no—
183C4—2922no—
184C2#1798918411yescharacteristic
185C2#1798919812yes—
186C2#1798927212yes—
187C2#1798932311yescharacteristic
188C2#1798933611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#384×C73C2
hypercenter#384D73
hypocenterC73#2794
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
95. C73#2794semidirect