Finite Group Databasebeta

← #22610941

Subgroups — #22610941

Order 9344.

392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×Dic292C211yesmaximal, characteristic, complemented
2C2×#14556570C212yesmaximal
3C2×#14556516C212yesmaximal, complemented
4#17988350C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×C73C211yesmaximal, characteristic
6C22×Dic146C2212yes—
7C2×Dic292—24no—
8C2×Dic292—22no—
9#14556570—24no—
10#14556570—24no—
11C2×C4⋊Dic73C2212yes—
12C2×#11924007—22no—
13C2×C22⋊Dic73—22no—
14#14556516—24no—
15C23×C4×C73C2211yescharacteristic
16C22×C8×C73C2211yescharacteristic
17C22×C8×C73C2211yescharacteristic
18C22⋊C8×C73—22no—
19C2×Dic146—22no—
20C2×Dic146—22no—
21C2×Dic146—22no—
22C2×Dic146—22no—
23C2×Dic146—22no—
24C2×Dic146D414yes—
25C22×Dic73—22no—
26C22×Dic73—22no—
27Dic292—28no—
28C4⋊Dic73—22no—
29C4⋊Dic73D414yes—
30#11924007—28no—
31C22⋊Dic73—28no—
32C24×C73D411yescharacteristic
33C22×C4×C73—21no—
34C22×C4×C73—22no—
35C22×C4×C73—22no—
36C22×C4×C73—21no—
37C22×C4×C73D411yescharacteristic
38C22×C4×C73C2311yescharacteristic
39C2×C8×C73—22no—
40C2×C8×C73—21no—
41C2×C8×C73—22no—
42C2×C8×C73D412yes—
43C23×C73—22no—
44C23×C73—21no—
45C23×C73—21no—
46C23×C73—22no—
47C23×C73Q1612yescomplemented
48C23×C73C2×D411yescharacteristic
49C2×C4×C73—22no—
50C2×C4×C73—21no—
51C2×C4×C73—41no—
52C2×C4×C73—42no—
53C2×C4×C73—41no—
54C2×C4×C73C2×D412yes—
55C2×C4×C73C2×D412yes—
56C2×C4×C73C2×D411yescharacteristic
57C2×C4×C73#4111yescharacteristic
58C2×Dic73—24no—
59C2×Dic73—24no—
60C2×Dic73—42no—
61C2×Dic73—42no—
62C2×Dic73—42no—
63C2×Dic73—42no—
64Dic146—24no—
65Dic146—24no—
66Dic146—42no—
67Dic146—42no—
68C8×C73—22no—
69C8×C73—41no—
70C22×C73—24no—
71C22×C73—22no—
72C22×C73—41no—
73C22×C73—42no—
74C22×C73—41no—
75C22×C73#12012yes—
76C22×C73#12111yescharacteristic
77C22×C73C2×Q1611yescharacteristic
78C22×C73#13511yescharacteristic
79C22×C73#13712yes—
80C4×C73—41no—
81C4×C73#12011yescharacteristic
82C4×C73#12112yes—
83C4×C73#12711yescharacteristic
84Dic73—44no—
85Dic73—44no—
86C2×C73—42no—
87C2×C73#39211yescharacteristic
88C2×C73#45112yes—
89C2×C73#45212yes—
90C2×C73#46711yescharacteristic
91C2×C73#47011yescharacteristic
92#2001—731nomaximal, Sylow
93C73#200111yescharacteristic, complemented, Sylow
94C22×Q16—731no—
95C2×C22⋊Q8—732no—
96C2×#103—732no—
97C2×C22⋊C8D7311yescharacteristic
98#340—731no—
99C22×Q8—732no—
100C23×C4C2×D7311yescharacteristic
101C2×Q16—1464no—
102C2×Q16—1462no—
103C22×C8C2×D7311yescharacteristic
104C22×C8C2×D7311yescharacteristic
105C22⋊Q8—1464no—
106C22⋊Q8—1464no—
107C2×C4⋊C4—732no—
108C2×C4⋊C4—1462no—
109C2×C22⋊C4—1462no—
110#103—1464no—
111C22⋊C8—22no—
112C24D29211yescharacteristic
113C2×Q8—734no—
114C2×Q8—1462no—
115C2×Q8—1462no—
116C2×Q8—1462no—
117C2×Q8—1462no—
118C2×Q8—1462no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—1462no—
124C22×C4—1462no—
125C22×C4D29211yescharacteristic
126C22×C4C22×D7311yescharacteristic
127Q16—1468no—
128C2×C8—22no—
129C2×C8—22no—
130C2×C8—21no—
131C2×C8C22⋊D7312yes—
132C4⋊C4—734no—
133C4⋊C4—1468no—
134C4⋊C4—1462no—
135C22⋊C4—1468no—
136C23—22no—
137C23—21no—
138C23—21no—
139C23—22no—
140C23Dic29212yescomplemented
141C23C2×D29211yescharacteristic
142Q8—2922no—
143Q8—2922no—
144Q8—1464no—
145Q8—1464no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—41no—
151C2×C4—2922no—
152C2×C4—2922no—
153C2×C4—2922no—
154C2×C4—2922no—
155C2×C4—1464no—
156C2×C4—1464no—
157C2×C4D4×D7312yes—
158C2×C4D4×D7312yes—
159C2×C4C2×C22⋊D7311yescharacteristic
160C2×C4#1192402811yescharacteristic
161C8—22no—
162C8—41no—
163C22—24no—
164C22—22no—
165C22—42no—
166C22—41no—
167C22—41no—
168C22#1455656112yes—
169C22#1455656511yescharacteristic
170C22C2×Dic29211yescharacteristic
171C22#1455661311yescharacteristic
172C22#1455662412yes—
173C4—41no—
174C4—2924no—
175C4—2924no—
176C4#1455655911yescharacteristic
177C4#1455656412yes—
178C4#1455658711yescharacteristic
179C2—42no—
180C2#1798849611yescharacteristic
181C2#1798874512yes—
182C2#1798875112yes—
183C2#1798882811yescharacteristic
184C2#1798884511yescharacteristic
subgroupG/H
centerC23C2×D292
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×C22⋊C8×C73C2
socleC23×C73C2×D4
hypercenterC2×C22⋊C8D73
hypocenterC73#2001
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×Dic292C2semidirect
3. C2×#14556516C2semidirect
4. #17988350C2semidirect
47. C23×C73Q16semidirect
93. C73#2001semidirect
140. C23Dic292semidirect