Finite Group Databasebeta

← #22608577

Subgroups — #22608577

Order 9344.

256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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#17989135C211yesmaximal, characteristic
2#17988639C211yesmaximal, characteristic, complemented
3C4⋊C8×D73C211yesmaximal, characteristic, complemented
4#17988334C211yesmaximal, characteristic, complemented
5#17988332C211yesmaximal, characteristic, complemented
6#17988331C211yesmaximal, characteristic, complemented
7#331×C73C211yesmaximal, characteristic, complemented
8C2×#11924027—21no—
9C2×C8×D73—21no—
10#14556591C2211yescharacteristic
11#14556578—21no—
12#14556562—21no—
13#14556562C412yes—
14D4×Dic73—21no—
15D4×Dic73C412yes—
16C42×D73C2211yescharacteristic
17C4⋊#10596831C2211yescharacteristic
18C4⋊#10596831C2211yescharacteristic
19#14556520—21no—
20#14556503—21no—
21C8×Dic73—21no—
22#127×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24C4⋊C8×C73C2211yescharacteristic
25#11924027—42no—
26#11924027—42no—
27C2×Dic146—21no—
28C2×C22⋊D73—22no—
29C22×Dic73—22no—
30C2×C4×D73C2×C411yescharacteristic
31C2×C4×D73D411yescharacteristic
32C2×C4×D73D411yescharacteristic
33C2×#10596831—21no—
34C2×#10596831—21no—
35C8×D73—42no—
36C4⋊Dic73—21no—
37C4⋊Dic73C2×C412yes—
38C22⋊Dic73—22no—
39C22⋊Dic73—22no—
40C4×Dic73C2×C411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C2×D4×C73—21no—
44C2×D4×C73—21no—
45C2×D4×C73C2×C412yes—
46C2×C8×C73—21no—
47C2×C8×C73—21no—
48C42×C73C2311yescharacteristic
49C23×C73—22no—
50C22×D73C22⋊C411yescharacteristic
51D4×C73—42no—
52D4×C73—41no—
53D4×C73—41no—
54D4×C73—41no—
55D4×C73—41no—
56C2×C4×C73C22×C411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C22⋊D73—44no—
60C2×Dic73—22no—
61C2×Dic73—44no—
62C2×Dic73C22⋊C411yescharacteristic
63C2×Dic73C22⋊C411yescharacteristic
64C2×Dic73C22⋊C411yescharacteristic
65C4×D73—21no—
66C4×D73—21no—
67C4×D73—41no—
68C4×D73D812yes—
69C4×D73SD1612yes—
70Dic146—41no—
71Dic146—41no—
72C8×C73—41no—
73C8×C73—41no—
74#10596831—41no—
75#10596831—41no—
76C22×C73—42no—
77C22×C73—42no—
78C22×C73—42no—
79C22×C73C2×C22⋊C411yescharacteristic
80C2×D73—21no—
81C2×D73—21no—
82C2×D73#10212yes—
83C4×C73—21no—
84C4×C73C2×D811yescharacteristic
85C4×C73C2×SD1611yescharacteristic
86C4×C73#13511yescharacteristic
87C4×C73#13511yescharacteristic
88Dic73—21no—
89Dic73—21no—
90Dic73—42no—
91Dic73#10212yes—
92C2×C73—82no—
93C2×C73#41311yescharacteristic
94C2×C73C2×#10211yescharacteristic
95C2×C73#41611yescharacteristic
96D73—22no—
97#1540—731nomaximal, Sylow
98C73#154011yescharacteristic, complemented, Sylow
99#532—731no—
100#431—731no—
101C2×C4⋊C8—731no—
102#332—731no—
103#332—731no—
104#331—731no—
105#331D7311yescharacteristic, complemented
106C2×#41—1461no—
107C22×C8—1461no—
108C4⋊Q8—731no—
109#127C2×D7311yescharacteristic
110#124—1461no—
111#121—732no—
112#121—1461no—
113C4×D4—732no—
114C4×D4—1461no—
115C2×C42—731no—
116C4⋊C8—731no—
117C4⋊C8—731no—
118C4⋊C8—1461no—
119C4⋊C8C2×D7311yescharacteristic
120C4⋊C8C2×D7311yescharacteristic
121C22⋊C8—1461no—
122C4×C8—1461no—
123#41—2922no—
124#41—2922no—
125C2×Q8—1461no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—1462no—
129C2×D4C4×D7312yes—
130C22×C4—731no—
131C22×C4—731no—
132C22×C4—731no—
133C22×C4—1462no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—2922no—
137C2×C8—1461no—
138C2×C8—1461no—
139C4⋊C4—732no—
140C4⋊C4—1461no—
141C22⋊C4—1462no—
142C22⋊C4—1462no—
143C42—731no—
144C42—731no—
145C42—731no—
146C42C22×D7311yescharacteristic
147C23—22no—
148C23—731no—
149Q8—2921no—
150Q8—2921no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—2924no—
157C2×C4—2921no—
158C2×C4—2924no—
159C2×C4—731no—
160C2×C4—732no—
161C2×C4—732no—
162C2×C4—731no—
163C2×C4—731no—
164C2×C4—1462no—
165C2×C4—1461no—
166C2×C4—1461no—
167C2×C4C2×C4×D7311yescharacteristic
168C2×C4D4×D7311yescharacteristic
169C2×C4D4×D7311yescharacteristic
170C8—41no—
171C8—41no—
172C8—2921no—
173C8—2921no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—732no—
178C22—1461no—
179C22—1461no—
180C22C22⋊C4×D7311yescharacteristic
181C4—21no—
182C4—2922no—
183C4—732no—
184C4—1461no—
185C4—1461no—
186C4D8×D7311yescharacteristic
187C4SD16×D7311yescharacteristic
188C4#1455661011yescharacteristic
189C4#1455661211yescharacteristic
190C2—82no—
191C2—1462no—
192C2#1798856811yescharacteristic
193C2#102×D7311yescharacteristic
194C2#1798858011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#331×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#331D73
hypocenterC73#1540
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #17988639C2semidirect
3. C4⋊C8×D73C2semidirect
4. #17988334C2semidirect
5. #17988332C2semidirect
6. #17988331C2semidirect
7. #331×C73C2semidirect
98. C73#1540semidirect
105. #331D73semidirect