Finite Group Databasebeta

← #22619971

Subgroups — #22619971

Order 9344.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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
2C2×C4×Dic146C211yesmaximal, characteristic
3#17988923C212yesmaximal
4#17988883C212yesmaximal, complemented
5#17988798C212yesmaximal, complemented
6#17988745C212yesmaximal
7C4×Dic292C214yesmaximal, complemented
8#431×C73C211yesmaximal, characteristic
9C22×Dic146C2211yescharacteristic
10C2×Dic292C2214yes—
11#14556591C2211yescharacteristic
12#14556591C2211yescharacteristic
13#14556583—21no—
14#14556570—21no—
15#14556570C2212yes—
16C4×Dic146—21no—
17C4×Dic146—21no—
18C4×Dic146—21no—
19C4×Dic146C2212yes—
20C4×Dic146C2212yes—
21C4×Dic146C2212yes—
22#14556550—21no—
23C2×C4⋊Dic73C2211yescharacteristic
24C2×#11924007—21no—
25C2×C4×Dic73—21no—
26#14556525C2214yes—
27#14556516C2214yes—
28#14556516C2214yes—
29C2×C42×C73C2211yescharacteristic
30C4⋊C8×C73C2212yes—
31C22⋊C8×C73C2212yes—
32C4×C8×C73C2212yes—
33C2×Dic146—21no—
34C2×Dic146—24no—
35C2×Dic146—21no—
36C2×Dic146C2312yes—
37C2×Dic146C2312yes—
38C22×Dic73—21no—
39C22×Dic73—21no—
40Dic292—28no—
41C4⋊Dic73—21no—
42C4⋊Dic73—21no—
43C4⋊Dic73—21no—
44C4⋊Dic73—21no—
45C4⋊Dic73C2312yes—
46C4⋊Dic73C2312yes—
47#11924007—22no—
48#11924007—22no—
49#11924007—22no—
50#11924007—22no—
51C22⋊Dic73—22no—
52C4×Dic73—22no—
53C4×Dic73—22no—
54C4×Dic73—22no—
55C22×C4×C73D411yescharacteristic
56C22×C4×C73D411yescharacteristic
57C22×C4×C73C2311yescharacteristic
58C2×C8×C73C2314yes—
59C42×C73D411yescharacteristic
60C42×C73D411yescharacteristic
61C42×C73C2311yescharacteristic
62C42×C73C2311yescharacteristic
63C23×C73C2×D411yescharacteristic
64C2×C4×C73—22no—
65C2×C4×C73—41no—
66C2×C4×C73Q1614yescomplemented
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2411yescharacteristic
73C2×Dic73—24no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73—42no—
79Dic146—24no—
80Dic146—22no—
81Dic146—24no—
82Dic146—42no—
83Dic146#4114yes—
84C8×C73—24no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73C2×Q1612yes—
88C22×C73C22×D411yescharacteristic
89C4×C73—21no—
90C4×C73—21no—
91C4×C73—21no—
92C4×C73C2×Q1612yes—
93C4×C73C2×Q1612yes—
94C4×C73C2×#4112yes—
95Dic73—24no—
96Dic73—42no—
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×Q8—731no—
107#484—732no—
108#477—732no—
109#462—732no—
110#451—732no—
111C4×Q16—734no—
112#431D7311yescharacteristic
113C22×Q8—731no—
114C2×Q16—734no—
115C4⋊Q8—731no—
116C4⋊Q8—731no—
117#125—1461no—
118C22⋊Q8—732no—
119C22⋊Q8—1461no—
120C4×Q8—732no—
121C4×Q8—732no—
122C4×Q8—732no—
123C4×Q8—1461no—
124C4×Q8—1461no—
125C4×Q8—1461no—
126#117—1461no—
127C2×C4⋊C4—731no—
128C2×C4⋊C4—1461no—
129C2×C42—1461no—
130C2×C42C2×D7311yescharacteristic
131#107—734no—
132C4⋊C8C2×D7312yes—
133#103—734no—
134#103—734no—
135C22⋊C8C2×D7312yes—
136C4×C8C2×D7312yes—
137C2×Q8—732no—
138C2×Q8—732no—
139C2×Q8—1464no—
140C2×Q8—1461no—
141C2×Q8—1461no—
142C22×C4—1461no—
143C22×C4—1461no—
144C22×C4D29211yescharacteristic
145C22×C4D29211yescharacteristic
146C22×C4C22×D7311yescharacteristic
147Q16—1468no—
148C2×C8C22×D7314yes—
149C4⋊C4—732no—
150C4⋊C4—732no—
151C4⋊C4—1462no—
152C4⋊C4—1462no—
153C4⋊C4—1462no—
154C4⋊C4—1462no—
155C4⋊C4—1461no—
156C4⋊C4—1461no—
157C4⋊C4—1461no—
158C4⋊C4—1461no—
159C22⋊C4—1462no—
160C42—1462no—
161C42—1462no—
162C42—1462no—
163C42D29211yescharacteristic
164C42D29211yescharacteristic
165C42C22×D7311yescharacteristic
166C42C22×D7311yescharacteristic
167C23C2×D29211yescharacteristic
168Q8—2922no—
169Q8—734no—
170Q8—1464no—
171Q8—1464no—
172Q8—1462no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—2922no—
176C2×C4—1462no—
177C2×C4—1462no—
178C2×C4—1462no—
179C2×C4—1464no—
180C2×C4—1462no—
181C2×C4Dic29214yescomplemented
182C2×C4C2×D29211yescharacteristic
183C2×C4C2×D29211yescharacteristic
184C2×C4C2×D29211yescharacteristic
185C2×C4C2×D29211yescharacteristic
186C2×C4C2×D29211yescharacteristic
187C2×C4C23×D7311yescharacteristic
188C8—24no—
189C22—21no—
190C22—21no—
191C22C2×Dic29212yes—
192C22C22×D29211yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—2922no—
197C4—2922no—
198C4—2922no—
199C4—1464no—
200C4C2×Dic29212yes—
201C4C2×Dic29212yes—
202C4#41×D7312yes—
203C2—22no—
204C2#1798909911yescharacteristic
205C2C22×Dic29211yescharacteristic
206C2#1798938711yescharacteristic
subgroupG/H
centerC2×C4C2×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#431×C73C2
socleC22×C73C22×D4
hypercenter#431D73
hypocenterC73#3104
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
4. #17988883C2semidirect
5. #17988798C2semidirect
7. C4×Dic292C2semidirect
66. C2×C4×C73Q16semidirect
104. C73#3104semidirect
181. C2×C4Dic292semidirect