Finite Group Databasebeta

← #22615411

Subgroups — #22615411

Order 9344.

596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#14556565C211yesmaximal, characteristic
2#17988526C212yesmaximal, complemented
3#17988504C212yesmaximal, complemented
4#17988477C214yesmaximal, complemented
5#17988466C212yesmaximal, complemented
6#17988466C212yesmaximal, complemented
7C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C73C211yesmaximal, characteristic, complemented
9C22×D292C2211yescharacteristic
10C22×C22⋊D73C2212yes—
11#14556565—24no—
12C2×C4⋊Dic73C2211yescharacteristic
13C2×C22⋊Dic73C2212yes—
14C2×#11924005C2214yes—
15C2×#11924005C2212yes—
16C2×#11924005C2214yes—
17C2×C4×Dic73C2212yes—
18#14556498C2212yes—
19#14556498C2214yes—
20#14556498C2214yes—
21C23×C4×C73C2211yescharacteristic
22C23×C4×C73C2211yescharacteristic
23C23×C4×C73C2211yescharacteristic
24C2×C4⋊C4×C73—24no—
25C2×C4⋊C4×C73C2212yes—
26C2×C4⋊C4×C73C2212yes—
27C23×D73C2312yes—
28C2×D292—22no—
29C2×D292—42no—
30C2×C22⋊D73—24no—
31C2×C22⋊D73—28no—
32C22×Dic73C2312yes—
33C22×Dic73C2314yes—
34C4⋊Dic73—22no—
35C22⋊Dic73—24no—
36#11924005—24no—
37#11924005—28no—
38#11924005—44no—
39C4×Dic73—42no—
40C24×C73C2311yescharacteristic
41C22×C4×C73—22no—
42C22×C4×C73—24no—
43C22×C4×C73—22no—
44C22×C4×C73—42no—
45C22×C4×C73—42no—
46C22×C4×C73D414yes—
47C22×C4×C73C2312yes—
48C22×C4×C73C2311yescharacteristic
49C22×C4×C73C2311yescharacteristic
50C22×C4×C73C2312yes—
51C4⋊C4×C73—24no—
52C4⋊C4×C73—24no—
53C23×C73—22no—
54C23×C73—22no—
55C23×C73C2×D412yes—
56C23×C73#4114yes—
57C23×C73C2411yescharacteristic
58C22×D73—22no—
59C22×D73—24no—
60C22×D73—24no—
61C22×D73—24no—
62C2×C4×C73—28no—
63C2×C4×C73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—24no—
69C2×C4×C73—44no—
70C2×C4×C73—44no—
71C2×C4×C73C2×D412yes—
72C2×C4×C73C2×D412yes—
73C2×C4×C73#4114yes—
74C22⋊D73—48no—
75C2×Dic73—22no—
76C2×Dic73—24no—
77C2×Dic73—24no—
78C2×Dic73—24no—
79C2×Dic73—24no—
80D292—44no—
81C22×C73—22no—
82C22×C73—22no—
83C22×C73—28no—
84C22×C73#12414yes—
85C22×C73C22×D411yescharacteristic
86C22×C73C2×#4112yes—
87C22×C73C2×#4112yes—
88C22×C73H(5,𝔽2)12yes—
89C2×D73—42no—
90C2×D73—42no—
91C2×D73—42no—
92C2×D73—48no—
93C4×C73—24no—
94C4×C73—22no—
95C4×C73—22no—
96C4×C73—42no—
97Dic73—42no—
98Dic73—44no—
99C2×C73—24no—
100C2×C73#52511yescharacteristic
101C2×C73C2×#12411yescharacteristic
102C2×C73#53411yescharacteristic
103C2×C73#55314yes—
104D73—82no—
105#2591—731nomaximal, Sylow
106C73#259111yescharacteristic, complemented, Sylow
107C2×#121—731no—
108C22×C4⋊C4D7311yescharacteristic, complemented
109#400—732no—
110#394—732no—
111#388—734no—
112#386—732no—
113#386—732no—
114C4×C22⋊C4—731no—
115C22×D4—732no—
116C22×D4—731no—
117C23×C4C2×D7311yescharacteristic
118C23×C4C2×D7311yescharacteristic
119C23×C4C2×D7311yescharacteristic
120#121—1464no—
121C2×C4⋊C4—24no—
122C2×C4⋊C4—731no—
123C2×C4⋊C4C2×D7312yes—
124C2×C4⋊C4C2×D7312yes—
125C2×C22⋊C4—734no—
126C2×C22⋊C4—732no—
127C2×C22⋊C4—732no—
128C2×C22⋊C4—734no—
129C2×C42—732no—
130#95—732no—
131#95—734no—
132#95—734no—
133C24—732no—
134C24C22×D7311yescharacteristic
135C2×D4—2922no—
136C2×D4—1464no—
137C2×D4—1468no—
138C2×D4—1462no—
139C22×C4—22no—
140C22×C4—24no—
141C22×C4—22no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—732no—
145C22×C4—734no—
146C22×C4C22⋊D7314yes—
147C22×C4C22×D7312yes—
148C22×C4C22×D7311yescharacteristic
149C22×C4C22×D7311yescharacteristic
150C22×C4C22×D7312yes—
151C4⋊C4—24no—
152C4⋊C4—24no—
153C4⋊C4—1462no—
154C22⋊C4—2924no—
155C22⋊C4—1464no—
156C22⋊C4—1464no—
157C22⋊C4—1468no—
158C42—2922no—
159C23—22no—
160C23—22no—
161C23—1462no—
162C23—1464no—
163C23—1464no—
164C23—1464no—
165C23C2×C22⋊D7312yes—
166C23#1192402914yes—
167C23C23×D7311yescharacteristic
168D4—2924no—
169D4—2928no—
170C2×C4—28no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—44no—
179C2×C4—1462no—
180C2×C4—1464no—
181C2×C4—1464no—
182C2×C4—1464no—
183C2×C4—1464no—
184C2×C4C2×C22⋊D7312yes—
185C2×C4C2×C22⋊D7312yes—
186C2×C4#1192402814yes—
187C22—22no—
188C22—28no—
189C22—22no—
190C22—2922no—
191C22—2928no—
192C22—2922no—
193C22—2922no—
194C22#1455658014yes—
195C22C22×C22⋊D7311yescharacteristic
196C22C2×#1192402812yes—
197C22C2×#1192402912yes—
198C22#1455663612yes—
199C4—22no—
200C4—22no—
201C4—24no—
202C4—42no—
203C4—2924no—
204C4—2922no—
205C2—24no—
206C2—5842no—
207C2#1798909811yescharacteristic
208C2C2×#1455658011yescharacteristic
209C2#1798914611yescharacteristic
210C2#1798928514yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC22×C4⋊C4×C73C2
hypercenterC22×C4⋊C4D73
hypocenterC73#2591
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #17988526C2semidirect
3. #17988504C2semidirect
4. #17988477C2semidirect
5. #17988466C2semidirect
6. #17988466C2semidirect
7. C4×C22⋊Dic73C2semidirect
8. C22×C4⋊C4×C73C2semidirect
106. C73#2591semidirect
108. C22×C4⋊C4D73semidirect