Finite Group Databasebeta

← #22607751

Subgroups — #22607751

Order 9344.

202 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 61 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#17988489C211yesmaximal, characteristic
2#17988342C211yesmaximal, characteristic, complemented
3#336×C73C211yesmaximal, characteristic, complemented
4C22×D292C411yescharacteristic
5C22×#10596831—21no—
6C2×C4⋊Dic73C411yescharacteristic
7C2×#11924005—21no—
8C2×#11924005—21no—
9C22×C8×C73—21no—
10C2×C42×C73C2211yescharacteristic
11C23×D73—21no—
12C2×D292—21no—
13C2×D292—41no—
14C2×D292—41no—
15C2×D292C812yescomplemented
16C22×Dic73—21no—
17C2×#10596831—22no—
18C2×#10596831—41no—
19C2×#10596831—41no—
20C4⋊Dic73—41no—
21#11924005—41no—
22#11924005—41no—
23#11924005—41no—
24#11924005—41no—
25C22×C4×C73C2×C411yescharacteristic
26C22×C4×C73D411yescharacteristic
27C22×C4×C73D411yescharacteristic
28C2×C8×C73—22no—
29C2×C8×C73—41no—
30C2×C8×C73—41no—
31C42×C73—41no—
32C23×C73C22⋊C411yescharacteristic
33C22×D73—22no—
34C22×D73—41no—
35C22×D73—41no—
36C22×D73—41no—
37C22×D73—41no—
38C22×D73—41no—
39C22×D73—41no—
40C2×C4×C73—21no—
41C2×C4×C73—21no—
42C2×C4×C73—21no—
43C2×C4×C73—21no—
44C2×C4×C73—21no—
45C2×C4×C73—21no—
46C2×C4×C73C2×C811yescharacteristic
47C2×C4×C73M1611yescharacteristic
48C2×C4×C73D811yescharacteristic
49C2×C4×C73D811yescharacteristic
50C2×C4×C73SD1611yescharacteristic
51C2×C4×C73SD1611yescharacteristic
52C2×Dic73—41no—
53C2×Dic73—41no—
54C2×Dic73—41no—
55D292—42no—
56D292—42no—
57C8×C73—42no—
58#10596831—42no—
59C22×C73C22⋊C811yescharacteristic
60C22×C73#9911yescharacteristic
61C22×C73#10011yescharacteristic
62C22×C73#10211yescharacteristic
63C22×C73#10211yescharacteristic
64C22×C73#10411yescharacteristic
65C22×C73#10411yescharacteristic
66C2×D73—42no—
67C2×D73—42no—
68C2×D73—42no—
69C2×D73—81no—
70C2×D73—81no—
71C2×D73—81no—
72C2×D73—81no—
73C4×C73—21no—
74C4×C73—21no—
75C4×C73—21no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—21no—
79Dic73—81no—
80C2×C73#32311yescharacteristic
81C2×C73D4⋊C811yescharacteristic
82C2×C73D4⋊C811yescharacteristic
83C2×C73#32711yescharacteristic
84C2×C73#32711yescharacteristic
85C2×C73#32911yescharacteristic
86C2×C73#33111yescharacteristic
87D73—82no—
88#1270—731nomaximal, Sylow
89C73#127011yescharacteristic, complemented, Sylow
90#390—731no—
91#336—731no—
92#336D7311yescharacteristic, complemented
93C22×D4—731no—
94C22×C8—21no—
95C22×C8—1461no—
96C2×C4⋊C4—731no—
97C2×C22⋊C4—1461no—
98C2×C22⋊C4—1461no—
99C2×C42C2×D7311yescharacteristic
100C24—1461no—
101C2×D4—2921no—
102C2×D4—2921no—
103C2×D4—732no—
104C2×D4—1461no—
105C22×C4—1461no—
106C22×C4C4×D7311yescharacteristic
107C22×C4D29211yescharacteristic
108C22×C4C22⋊D7311yescharacteristic
109C2×C8—22no—
110C2×C8—41no—
111C2×C8—41no—
112C2×C8—2921no—
113C2×C8—2921no—
114C2×C8—1462no—
115C4⋊C4—2921no—
116C22⋊C4—2921no—
117C22⋊C4—2921no—
118C22⋊C4—2921no—
119C22⋊C4—2921no—
120C42—41no—
121C23—2921no—
122C23—2921no—
123C23—2921no—
124C23—2921no—
125C23—2921no—
126C23—2921no—
127C23—1462no—
128C23#1192400511yescharacteristic
129D4—2922no—
130D4—2922no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—2921no—
138C2×C4—2921no—
139C2×C4—2921no—
140C2×C4C8×D7311yescharacteristic
141C2×C4#1192401111yescharacteristic
142C2×C4#1192401311yescharacteristic
143C2×C4D58411yescharacteristic
144C2×C4#1192401511yescharacteristic
145C2×C4#1192401711yescharacteristic
146C8—42no—
147C8—2922no—
148C22—2922no—
149C22—2922no—
150C22—2922no—
151C22—5841no—
152C22—5841no—
153C22—5841no—
154C22—5841no—
155C22#1455650311yescharacteristic
156C22#1455650511yescharacteristic
157C22#1455650711yescharacteristic
158C22#1455651111yescharacteristic
159C22#1455651311yescharacteristic
160C22#1455651711yescharacteristic
161C22#1455651911yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—21no—
168C4—5841no—
169C2—5842no—
170C2#1798831011yescharacteristic
171C2#1798831411yescharacteristic
172C2#1798831611yescharacteristic
173C2#1798832011yescharacteristic
174C2#1798832211yescharacteristic
175C2#1798832611yescharacteristic
176C2#1798833011yescharacteristic
subgroupG/H
centerC23#11924005
commutatorC2×C4×C73C2×C8
FrattiniC2×C42C2×D73
Fitting#336×C73C2
socleC23×C73C22⋊C4
hypercenter#336D73
hypocenterC73#1270
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
2. #17988342C2semidirect
3. #336×C73C2semidirect
15. C2×D292C8semidirect
89. C73#1270semidirect
92. #336D73semidirect