Finite Group Databasebeta

← #22608763

Subgroups — #22608763

Order 9344.

182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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×#11924013C211yesmaximal, characteristic
2#17988665C211yesmaximal, characteristic, complemented
3#17988652C211yesmaximal, characteristic, complemented
4#17988339C211yesmaximal, characteristic, complemented
5#17988316C211yesmaximal, characteristic, complemented
6#17988309C211yesmaximal, characteristic, complemented
7D4⋊C8×C73C211yesmaximal, characteristic, complemented
8C2×#11924013C411yescharacteristic
9C2×#11924012—21no—
10C2×C8×D73—21no—
11C4×D292C2211yescharacteristic
12#14556524C411yescharacteristic
13C4⋊#10596831C2211yescharacteristic
14#14556512C411yescharacteristic
15#14556511C411yescharacteristic
16C22⋊#10596831—21no—
17#14556503—21no—
18C4×#10596831C2211yescharacteristic
19C4×#10596831C2211yescharacteristic
20C4×D4×C73C2211yescharacteristic
21C4⋊C8×C73C2211yescharacteristic
22C4×C8×C73C2211yescharacteristic
23C2×D292C2×C411yescharacteristic
24C2×C4×D73—21no—
25#11924013—22no—
26#11924012—42no—
27C2×#10596831—21no—
28C2×#10596831C2×C411yescharacteristic
29C2×#10596831C2×C411yescharacteristic
30C2×#10596831D411yescharacteristic
31C2×#10596831D411yescharacteristic
32C8×D73—42no—
33C4⋊Dic73C2×C411yescharacteristic
34#11924005—21no—
35C2×D4×C73C2×C411yescharacteristic
36C22×C4×C73—21no—
37C2×C8×C73—21no—
38C2×C8×C73—21no—
39C4⋊C4×C73C2×C411yescharacteristic
40C22⋊C4×C73—21no—
41C42×C73C2311yescharacteristic
42C23×C73—21no—
43C22×D73—21no—
44D4×C73—21no—
45D4×C73—21no—
46C2×C4×C73—21no—
47C2×C4×C73—41no—
48C2×C4×C73—41no—
49C2×C4×C73C22×C411yescharacteristic
50C2×C4×C73C2×D411yescharacteristic
51C2×C4×C73#4111yescharacteristic
52C2×Dic73—21no—
53D292—21no—
54D292M1612yescomplemented
55C4×D73—41no—
56C4×D73—41no—
57C8×C73—41no—
58C8×C73—41no—
59#10596831—21no—
60#10596831—21no—
61#10596831—21no—
62#10596831—41no—
63#10596831D812yescomplemented
64C22×C73—41no—
65C22×C73—41no—
66C22×C73—41no—
67C22×C73C4×D411yescharacteristic
68C2×D73—22no—
69C2×D73—41no—
70C2×D73—41no—
71C4×C73—21no—
72C4×C73—41no—
73C4×C73C2×M1611yescharacteristic
74C4×C73#13111yescharacteristic
75C4×C73C2×D811yescharacteristic
76C4×C73#13511yescharacteristic
77Dic73—41no—
78C2×C73—81no—
79C2×C73#43511yescharacteristic
80C2×C73C4×D811yescharacteristic
81C2×C73#44411yescharacteristic
82D73—42no—
83#1581—731nomaximal, Sylow
84C73#158111yescharacteristic, complemented, Sylow
85C4×D8—731no—
86#436—731no—
87C8×D4—731no—
88#335—731no—
89D4⋊C8—731no—
90D4⋊C8D7311yescharacteristic, complemented
91#322—731no—
92C2×D8—731no—
93C2×M16—1461no—
94C22×C8—1461no—
95C4×D4—731no—
96C4×D4C2×D7311yescharacteristic
97#107—731no—
98C4⋊C8—731no—
99C4⋊C8C2×D7311yescharacteristic
100#102—731no—
101#102—731no—
102C22⋊C8—1461no—
103C22⋊C8—1461no—
104C4×C8—731no—
105C4×C8—731no—
106C4×C8C2×D7311yescharacteristic
107C2×D4—731no—
108C2×D4C4×D7311yescharacteristic
109C22×C4—21no—
110C22×C4—1461no—
111D8—1462no—
112M16—2922no—
113C2×C8—21no—
114C2×C8—21no—
115C2×C8—2922no—
116C2×C8—731no—
117C2×C8—731no—
118C2×C8—731no—
119C2×C8—731no—
120C2×C8—1461no—
121C4⋊C4—731no—
122C4⋊C4C4×D7311yescharacteristic
123C22⋊C4—21no—
124C22⋊C4—1461no—
125C42C22×D7311yescharacteristic
126C23—21no—
127C23—1461no—
128D4—21no—
129D4—21no—
130D4—732no—
131D4—1461no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—2921no—
136C2×C4—2921no—
137C2×C4—1461no—
138C2×C4C2×C4×D7311yescharacteristic
139C2×C4D4×D7311yescharacteristic
140C2×C4#1192402711yescharacteristic
141C8—41no—
142C8—41no—
143C8—2921no—
144C8—732no—
145C8—1461no—
146C8—1461no—
147C8—1461no—
148C22—41no—
149C22—41no—
150C22—41no—
151C22—2921no—
152C22—2921no—
153C22—1462no—
154C22#1455655111yescharacteristic
155C4—21no—
156C4—41no—
157C4—2921no—
158C4M16×D7311yescharacteristic
159C4#1455659711yescharacteristic
160C4D8×D7311yescharacteristic
161C4#1455661211yescharacteristic
162C2—81no—
163C2—2922no—
164C2#1798866111yescharacteristic
165C2#1798866711yescharacteristic
166C2#1798870611yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
FittingD4⋊C8×C73C2
socleC22×C73C4×D4
hypercenterD4⋊C8D73
hypocenterC73#1581
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #17988665C2semidirect
3. #17988652C2semidirect
4. #17988339C2semidirect
5. #17988316C2semidirect
6. #17988309C2semidirect
7. D4⋊C8×C73C2semidirect
54. D292M16semidirect
63. #10596831D8semidirect
84. C73#1581semidirect
90. D4⋊C8D73semidirect