Finite Group Databasebeta

← #22625381

Subgroups — #22625381

Order 9344.

234 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C4×#11924038C211yesmaximal, characteristic, complemented
2#17989546C211yesmaximal, characteristic, complemented
3#17989444C212yesmaximal, complemented
4#17989442C212yesmaximal, complemented
5#17989119C211yesmaximal, characteristic
6C2×#11924038—21no—
7C2×#11924036—21no—
8#14556646—21no—
9#14556646C2212yes—
10#14556646C2212yes—
11C4×#10596833—21no—
12#14556584—21no—
13#14556582C2211yescharacteristic
14#14556578C2211yescharacteristic
15#14556573—21no—
16#14556571C411yescharacteristic
17#14556562C411yescharacteristic
18C4×Dic146C411yescharacteristic
19C4×C22⋊D73—21no—
20#14556550—21no—
21C42×D73C2211yescharacteristic
22C4×D4×C73C411yescharacteristic
23#11924038—24no—
24#11924036—24no—
25C2×#10596833—22no—
26C2×#10596833—22no—
27C2×Dic146C2×C411yescharacteristic
28C2×C22⋊D73—21no—
29C2×C4×D73C2×C411yescharacteristic
30C2×C4×D73D411yescharacteristic
31C2×C4×D73D411yescharacteristic
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73C2×C411yescharacteristic
35#11924007—21no—
36#11924007—21no—
37C22⋊Dic73—21no—
38C22⋊Dic73—21no—
39C22⋊Dic73—21no—
40#11924005—21no—
41C4×Dic73—21no—
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73C2311yescharacteristic
45C2×D4×C73C2×C411yescharacteristic
46C22×C4×C73—21no—
47C4⋊C4×C73C2×C411yescharacteristic
48C22⋊C4×C73—21no—
49C42×C73C2×C411yescharacteristic
50C23×C73—21no—
51C22×D73C22⋊C411yescharacteristic
52D4×C73—41no—
53C2×C4×C73—21no—
54C2×C4×C73—42no—
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22⋊C411yescharacteristic
57C2×C4×C73C22×C411yescharacteristic
58C22⋊D73—42no—
59C2×Dic73—21no—
60C2×Dic73—21no—
61C2×Dic73C22⋊C411yescharacteristic
62C2×Dic73C2×D411yescharacteristic
63C2×Dic73C2×D411yescharacteristic
64C4×D73—22no—
65C4×D73—22no—
66C4×D73—41no—
67Dic146—41no—
68#10596833—24no—
69#10596833—24no—
70C22×C73—41no—
71C22×C73—41no—
72C22×C73—41no—
73C22×C73C2×C22⋊C411yescharacteristic
74C2×D73—21no—
75C2×D73—21no—
76C2×D73#10412yes—
77C4×C73—21no—
78C4×C73—21no—
79C4×C73—41no—
80C4×C73#10412yes—
81Dic73—21no—
82Dic73—21no—
83Dic73—21no—
84Dic73—41no—
85Dic73—41no—
86C2×C73—81no—
87C2×C73#41311yescharacteristic
88C2×C73C2×#10411yescharacteristic
89C2×C73C2×#10411yescharacteristic
90D73—22no—
91#1524—731nomaximal, Sylow
92C73#152411yescharacteristic, complemented, Sylow
93#529—731no—
94C4×M16—731no—
95C2×#97—731no—
96#330—732no—
97#329—732no—
98C2×M16—1461no—
99C22×C8—1461no—
100#126—1461no—
101#125—731no—
102#124—731no—
103#123—1461no—
104C22⋊Q8—731no—
105#121—731no—
106C4×Q8—731no—
107C4×D4—1461no—
108C4×D4#6440811yescharacteristic
109#117—1461no—
110C2×C42—731no—
111#97—732no—
112#97—732no—
113#97—1461no—
114C4×C8—1461no—
115C2×Q8—731no—
116C2×D4—1461no—
117C2×D4C2×#6440811yescharacteristic
118C22×C4—21no—
119C22×C4—731no—
120C22×C4—731no—
121C22×C4—731no—
122M16—1464no—
123C2×C8—1462no—
124C2×C8—1462no—
125C2×C8—1464no—
126C4⋊C4—731no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4C2×#6440811yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—1461no—
134C22⋊C4—1461no—
135C22⋊C4—1461no—
136C22⋊C4—1461no—
137C42—731no—
138C42—731no—
139C42—731no—
140C42—1461no—
141C42C2×#6440811yescharacteristic
142C23—21no—
143C23—731no—
144Q8—2921no—
145D4—41no—
146D4—2922no—
147C2×C4—21no—
148C2×C4—42no—
149C2×C4—2921no—
150C2×C4—731no—
151C2×C4—731no—
152C2×C4—731no—
153C2×C4—1462no—
154C2×C4—1461no—
155C2×C4—1461no—
156C2×C4—1462no—
157C2×C4C22⋊#6440811yescharacteristic
158C2×C4C22⋊#6440811yescharacteristic
159C2×C4C22×#6440811yescharacteristic
160C8—1464no—
161C8—1464no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22—732no—
166C22—1461no—
167C22—1461no—
168C22C2×C22⋊#6440811yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—2921no—
173C4—2921no—
174C4—1461no—
175C4—1461no—
176C4—1461no—
177C4#1455665512yes—
178C2—81no—
179C2—1462no—
180C2#1798957311yescharacteristic
181C2C2×#1455665511yescharacteristic
182C2D73⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1524
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#11924038C2semidirect
2. #17989546C2semidirect
3. #17989444C2semidirect
4. #17989442C2semidirect
92. C73#1524semidirect