Finite Group Databasebeta

← #22619970

Subgroups — #22619970

Order 9344.

384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 145 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#17989144C211yesmaximal, characteristic
2#17988922C212yesmaximal
3#17988882C212yesmaximal, complemented
4#17988797C212yesmaximal, complemented
5#17988743C212yesmaximal
6C4×#11924018C214yesmaximal, complemented
7#17988640C211yesmaximal, characteristic
8C2×C4×Q8×C73C211yesmaximal, characteristic
9C2×#11924018C2214yes—
10#14556591C2211yescharacteristic
11#14556591C2211yescharacteristic
12#14556583—21no—
13#14556570—21no—
14#14556570C2212yes—
15C4×Dic146—21no—
16C4×Dic146C2212yes—
17#14556550—21no—
18#14556524C2214yes—
19C4⋊#10596831C2212yes—
20#14556515C2214yes—
21#14556514C2214yes—
22C22⋊#10596831C2212yes—
23C4×#10596831C2212yes—
24C22×Q8×C73C2211yescharacteristic
25C4×Q8×C73—21no—
26C4×Q8×C73—21no—
27C4×Q8×C73C2212yes—
28C4×Q8×C73C2212yes—
29C2×C4⋊C4×C73—21no—
30C2×C4⋊C4×C73C2211yescharacteristic
31C2×C42×C73—21no—
32C2×C42×C73C2211yescharacteristic
33C2×Dic146—21no—
34C2×Dic146C2312yes—
35#11924018—28no—
36C2×#10596831C2314yes—
37C4⋊Dic73—21no—
38C4⋊Dic73—21no—
39C4⋊Dic73—21no—
40C4⋊Dic73C2312yes—
41#11924007—22no—
42#11924007—22no—
43C22⋊Dic73—22no—
44C4×Dic73—22no—
45C2×Q8×C73—24no—
46C2×Q8×C73—21no—
47C2×Q8×C73C2312yes—
48C22×C4×C73—21no—
49C22×C4×C73—21no—
50C22×C4×C73D411yescharacteristic
51C22×C4×C73D411yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C4⋊C4×C73—22no—
54C4⋊C4×C73—22no—
55C4⋊C4×C73—21no—
56C4⋊C4×C73C2312yes—
57C42×C73—22no—
58C42×C73—22no—
59C42×C73D411yescharacteristic
60C42×C73D411yescharacteristic
61C42×C73C2311yescharacteristic
62C42×C73C2311yescharacteristic
63C23×C73C2×D411yescharacteristic
64Q8×C73—24no—
65Q8×C73—22no—
66Q8×C73#4114yes—
67C2×C4×C73—24no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—41no—
72C2×C4×C73—42no—
73C2×C4×C73Q1614yescomplemented
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2411yescharacteristic
80C2×Dic73—22no—
81C2×Dic73—22no—
82Dic146—24no—
83Dic146—42no—
84#10596831—24no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73C2×Q1612yes—
88C22×C73C22×D411yescharacteristic
89C4×C73—24no—
90C4×C73—21no—
91C4×C73—21no—
92C4×C73—21no—
93C4×C73—42no—
94C4×C73C2×Q1612yes—
95C4×C73C2×Q1612yes—
96C4×C73C2×#4112yes—
97Dic73—42no—
98Dic73—42no—
99C2×C73—22no—
100C2×C73#52511yescharacteristic
101C2×C73C22×Q1611yescharacteristic
102C2×C73#57511yescharacteristic
103#3104—731nomaximal, Sylow
104C73#310411yescharacteristic, complemented, Sylow
105#533—731no—
106C2×C4×Q8D7311yescharacteristic
107#484—732no—
108#477—732no—
109#462—732no—
110#451—732no—
111C4×Q16—734no—
112#431—731no—
113C22×Q8C2×D7311yescharacteristic
114C2×Q16—734no—
115C4⋊Q8—731no—
116C4⋊Q8—731no—
117#125—1461no—
118C22⋊Q8—732no—
119C22⋊Q8—1461no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—732no—
123C4×Q8—1461no—
124C4×Q8C2×D7312yes—
125C4×Q8C2×D7312yes—
126#117—1461no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D7311yescharacteristic
129C2×C42—21no—
130C2×C42C2×D7311yescharacteristic
131#107—734no—
132C4⋊C8—732no—
133#103—734no—
134#103—734no—
135C22⋊C8—732no—
136C4×C8—732no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—732no—
140C2×Q8—1461no—
141C2×Q8C22×D7312yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D7311yescharacteristic
145C22×C4C22⋊D7311yescharacteristic
146C22×C4C22×D7311yescharacteristic
147Q16—1468no—
148C2×C8—734no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—732no—
153C4⋊C4—1462no—
154C4⋊C4—1462no—
155C4⋊C4—1461no—
156C4⋊C4—1461no—
157C4⋊C4—1461no—
158C4⋊C4C22×D7312yes—
159C22⋊C4—1462no—
160C42—22no—
161C42—22no—
162C42—1462no—
163C42C22⋊D7311yescharacteristic
164C42C22⋊D7311yescharacteristic
165C42C22×D7311yescharacteristic
166C42C22×D7311yescharacteristic
167C23C2×C22⋊D7311yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—2922no—
171Q8—1464no—
172Q8#1192402814yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—42no—
179C2×C4—1462no—
180C2×C4—1462no—
181C2×C4#1192401814yescomplemented
182C2×C4C2×C22⋊D7311yescharacteristic
183C2×C4C2×C22⋊D7311yescharacteristic
184C2×C4C2×C22⋊D7311yescharacteristic
185C2×C4C2×C22⋊D7311yescharacteristic
186C2×C4C2×C22⋊D7311yescharacteristic
187C2×C4C23×D7311yescharacteristic
188C8—1464no—
189C22—21no—
190C22—21no—
191C22C2×#1192401812yes—
192C22C22×C22⋊D7311yescharacteristic
193C4—21no—
194C4—21no—
195C4—24no—
196C4—21no—
197C4—42no—
198C4—2922no—
199C4—2922no—
200C4C2×#1192401812yes—
201C4C2×#1192401812yes—
202C4C2×#1192402812yes—
203C2—22no—
204C2#1798909811yescharacteristic
205C2C22×#1192401811yescharacteristic
206C2#1798938511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×C4×Q8×C73C2
socleC22×C73C22×D4
hypercenterC2×C4×Q8D73
hypocenterC73#3104
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #17988882C2semidirect
4. #17988797C2semidirect
6. C4×#11924018C2semidirect
73. C2×C4×C73Q16semidirect
104. C73#3104semidirect
181. C2×C4#11924018semidirect