Finite Group Databasebeta

← #22620333

Subgroups — #22620333

Order 9344.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#17989138C211yesmaximal, characteristic
2#125×D73C211yesmaximal, characteristic, complemented
3#17988955C211yesmaximal, characteristic, complemented
4#17988953C211yesmaximal, characteristic, complemented
5#17988952C211yesmaximal, characteristic, complemented
6#17988943C214yesmaximal, complemented
7#17988587C214yesmaximal, complemented
8#17988539C211yesmaximal, characteristic, complemented
9#491×C73C211yesmaximal, characteristic, complemented
10C2×#11924029C2212yes—
11C2×#11924011C2212yes—
12#14556588C2211yescharacteristic
13#14556583C2211yescharacteristic
14#14556582C2212yes—
15#14556581—22no—
16#14556580C2212yes—
17#14556566—22no—
18#14556553—22no—
19C4⋊C4×D73—22no—
20C4⋊C4×D73C2212yes—
21C42×D73C2211yescharacteristic
22#14556515C2214yes—
23#14556513C2214yes—
24#14556511C2214yes—
25#14556502C2211yescharacteristic
26C8×Dic73C2212yes—
27C4⋊Q8×C73C2211yescharacteristic
28#125×C73C2211yescharacteristic
29#103×C73C2214yes—
30#97×C73C2211yescharacteristic
31#11924029—28no—
32C2×D292—22no—
33C2×D292—22no—
34C2×D292C2312yes—
35C2×C4×D73—22no—
36C2×C4×D73—22no—
37C2×C4×D73D412yes—
38C2×C4×D73C2311yescharacteristic
39#11924011—24no—
40C2×#10596831C2312yes—
41C4⋊Dic73—22no—
42C4⋊Dic73C2312yes—
43#11924007—22no—
44#11924007—22no—
45#11924007—22no—
46#11924005—24no—
47C4×Dic73D412yes—
48C4×Dic73C2311yescharacteristic
49C2×Q8×C73C2312yes—
50C2×C8×C73C2312yes—
51C4⋊C4×C73—22no—
52C4⋊C4×C73—22no—
53C4⋊C4×C73C2312yes—
54C42×C73C2311yescharacteristic
55C22×D73—22no—
56C22×D73C2×D411yescharacteristic
57Q8×C73—24no—
58C2×C4×C73—22no—
59C2×C4×C73—22no—
60C2×C4×C73C2×D412yes—
61C2×C4×C73C2411yescharacteristic
62C2×Dic73—22no—
63C2×Dic73C2×D412yes—
64C2×Dic73C2×D411yescharacteristic
65D292—24no—
66D292—44no—
67D292—44no—
68C4×D73—42no—
69C4×D73—44no—
70C4×D73—44no—
71C4×D73#4114yes—
72C8×C73—22no—
73#10596831—22no—
74C22×C73C22×D411yescharacteristic
75C2×D73—22no—
76C2×D73—42no—
77C2×D73—44no—
78C2×D73#12412yes—
79C4×C73—22no—
80C4×C73—42no—
81C4×C73—42no—
82C4×C73C2×#4112yes—
83Dic73—22no—
84Dic73—42no—
85Dic73#12412yes—
86C2×C73C2×#12411yescharacteristic
87C2×C73#57512yes—
88D73—22no—
89D73—82no—
90#3142—731nomaximal, Sylow
91C73#314211yescharacteristic, complemented, Sylow
92#532—731no—
93C2×#125—731no—
94#491—731no—
95#491D7311yescharacteristic, complemented
96#490—731no—
97#490—731no—
98#488—734no—
99#417—734no—
100C4×M16—731no—
101C2×#41—732no—
102C2×M16—732no—
103C4⋊Q8C2×D7311yescharacteristic
104#127—731no—
105#125—732no—
106#125—731no—
107#125—1462no—
108#125C2×D7311yescharacteristic
109#124—732no—
110#121—1462no—
111C4×D4—1462no—
112C2×C4⋊C4—732no—
113C2×C4⋊C4—1462no—
114C2×C42—731no—
115#103—734no—
116#103C2×D7314yes—
117#102—734no—
118#102—734no—
119#97—731no—
120#97C2×D7311yescharacteristic
121C4×C8—732no—
122#41—1468no—
123C2×Q8C22×D7312yes—
124C2×D4—732no—
125C2×D4—1462no—
126C2×D4—1462no—
127C22×C4—732no—
128C22×C4—731no—
129C22×C4—1462no—
130C22×C4—1462no—
131M16—1464no—
132C2×C8—732no—
133C2×C8C22×D7312yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—732no—
137C4⋊C4—1462no—
138C4⋊C4—1462no—
139C4⋊C4—1462no—
140C4⋊C4—1462no—
141C4⋊C4C22×D7312yes—
142C22⋊C4—1464no—
143C42—732no—
144C42—731no—
145C42C22×D7311yescharacteristic
146C23—731no—
147C23—1462no—
148Q8—24no—
149D4—2924no—
150D4—2924no—
151D4—1464no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—2922no—
155C2×C4—2924no—
156C2×C4—2924no—
157C2×C4—731no—
158C2×C4—734no—
159C2×C4—732no—
160C2×C4—1462no—
161C2×C4D4×D7312yes—
162C2×C4C23×D7311yescharacteristic
163C8—22no—
164C8—1462no—
165C22—2924no—
166C22—2922no—
167C22—732no—
168C22—1462no—
169C22C2×D4×D7311yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—2922no—
174C4—732no—
175C4—1462no—
176C4#41×D7312yes—
177C2—5842no—
178C2—1462no—
179C2#124×D7311yescharacteristic
180C2#1798938612yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#491×C73C2
socleC22×C73C22×D4
hypercenter#491D73
hypocenterC73#3142
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #125×D73C2semidirect
3. #17988955C2semidirect
4. #17988953C2semidirect
5. #17988952C2semidirect
6. #17988943C2semidirect
7. #17988587C2semidirect
8. #17988539C2semidirect
9. #491×C73C2semidirect
91. C73#3142semidirect
95. #491D73semidirect