Finite Group Databasebeta

← #22625382

Subgroups — #22625382

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×#11924037C211yesmaximal, characteristic, complemented
2C2×#14556646C211yesmaximal, characteristic, complemented
3#17989444C212yesmaximal, complemented
4#17989442C212yesmaximal, complemented
5#17989118C211yesmaximal, characteristic
6C2×#11924037—21no—
7C22×#10596833—21no—
8#14556646—21no—
9#14556646C2212yes—
10#14556646C2212yes—
11C4×#10596833—21no—
12#14556584—21no—
13#14556582C2211yescharacteristic
14#14556578C2211yescharacteristic
15#14556572—21no—
16#14556570C411yescharacteristic
17#14556556C411yescharacteristic
18D4×Dic73—21no—
19D4×Dic73C411yescharacteristic
20#14556547—21no—
21C2×C4×Dic73C2211yescharacteristic
22#121×C73C411yescharacteristic
23#11924037—24no—
24C2×#10596833—24no—
25C2×#10596833—22no—
26C2×#10596833—22no—
27C2×Dic146C2×C411yescharacteristic
28C22×Dic73—21no—
29C22×Dic73D411yescharacteristic
30C22×Dic73D411yescharacteristic
31C4⋊Dic73—21no—
32C4⋊Dic73C2×C411yescharacteristic
33#11924007—21no—
34#11924007—21no—
35#11924007—21no—
36C22⋊Dic73—21no—
37C22⋊Dic73—21no—
38C22⋊Dic73—21no—
39C22⋊Dic73—21no—
40C4×Dic73—21no—
41C4×Dic73C2×C411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73C2311yescharacteristic
45C2×D4×C73—21no—
46C2×D4×C73C2×C411yescharacteristic
47C22×C4×C73C2×C411yescharacteristic
48C4⋊C4×C73C2×C411yescharacteristic
49C22⋊C4×C73—21no—
50C23×C73—21no—
51C23×C73C22⋊C411yescharacteristic
52D4×C73—41no—
53D4×C73—42no—
54C2×C4×C73—21no—
55C2×C4×C73—41no—
56C2×C4×C73C22⋊C411yescharacteristic
57C2×C4×C73C22×C411yescharacteristic
58C2×Dic73—22no—
59C2×Dic73—22no—
60C2×Dic73—21no—
61C2×Dic73—21no—
62C2×Dic73—42no—
63C2×Dic73C22⋊C411yescharacteristic
64C2×Dic73C22⋊C411yescharacteristic
65C2×Dic73C2×D411yescharacteristic
66C2×Dic73C2×D411yescharacteristic
67Dic146—41no—
68#10596833—24no—
69#10596833—24no—
70C22×C73—21no—
71C22×C73—21no—
72C22×C73—41no—
73C22×C73—41no—
74C22×C73—41no—
75C22×C73#10412yes—
76C22×C73C2×C22⋊C411yescharacteristic
77C4×C73—21no—
78C4×C73—21no—
79C4×C73—41no—
80Dic73—21no—
81Dic73—21no—
82Dic73—21no—
83Dic73—41no—
84Dic73—41no—
85Dic73#10412yes—
86C2×C73—22no—
87C2×C73—81no—
88C2×C73#41311yescharacteristic
89C2×C73C2×#10411yescharacteristic
90C2×C73C2×#10411yescharacteristic
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#6440811yescharacteristic
106C4×Q8—731no—
107C4×D4—731no—
108C4×D4—1461no—
109#117—1461no—
110C2×C42—731no—
111#97—732no—
112#97—732no—
113#97—1461no—
114C4×C8—1461no—
115C2×Q8—731no—
116C2×D4—21no—
117C2×D4C2×#6440811yescharacteristic
118C22×C4—731no—
119C22×C4—731no—
120C22×C4—1461no—
121C22×C4C2×#6440811yescharacteristic
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—731no—
141C42—1461no—
142C23—21no—
143C23C22⋊#6440811yescharacteristic
144Q8—2921no—
145D4—41no—
146D4—42no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—2922no—
150C2×C4—731no—
151C2×C4—731no—
152C2×C4—731no—
153C2×C4—731no—
154C2×C4—1461no—
155C2×C4—1461no—
156C2×C4—1462no—
157C2×C4—1462no—
158C2×C4C22⋊#6440811yescharacteristic
159C2×C4C22×#6440811yescharacteristic
160C8—1464no—
161C8—1464no—
162C22—21no—
163C22—21no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22#1455665512yes—
168C22C2×C22⋊#6440811yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—2921no—
173C4—2921no—
174C4—732no—
175C4—1461no—
176C4—1461no—
177C4—1461no—
178C2—22no—
179C2—81no—
180C2#1798957411yescharacteristic
181C2C2×#1455665511yescharacteristic
182C2D73⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1524
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C4×#11924037C2semidirect
2. C2×#14556646C2semidirect
3. #17989444C2semidirect
4. #17989442C2semidirect
92. C73#1524semidirect