Finite Group Databasebeta

← #22609159

Subgroups — #22609159

Order 9344.

212 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 57 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#17988937C211yesmaximal, characteristic, complemented
2#17988867C211yesmaximal, characteristic, complemented
3#17988792C211yesmaximal, characteristic, complemented
4#17988336C211yesmaximal, characteristic, complemented
5D4⋊#10596831C211yesmaximal, characteristic, complemented
6D4⋊#10596831C211yesmaximal, characteristic, complemented
7#555×C73C211yesmaximal, characteristic
8C2×#11924016—21no—
9#14556591C2211yescharacteristic
10#14556524—21no—
11C4⋊#10596831C2211yescharacteristic
12C4⋊#10596831C2211yescharacteristic
13#14556515—22no—
14#14556514—21no—
15#14556512—21no—
16C4×#10596831C2211yescharacteristic
17C4⋊Q8×C73C2211yescharacteristic
18#124×C73—22no—
19#121×C73—21no—
20#121×C73—21no—
21C4×D4×C73C2211yescharacteristic
22C4×D4×C73C2211yescharacteristic
23#117×C73—21no—
24#117×C73—21no—
25C2×Dic146—21no—
26#11924016—42no—
27C2×#10596831—21no—
28C2×#10596831—21no—
29C2×#10596831—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C2×Q8×C73D412yes—
33C2×D4×C73—22no—
34C2×D4×C73D411yescharacteristic
35C2×D4×C73D411yescharacteristic
36C22×C4×C73—21no—
37C22×C4×C73—21no—
38C4⋊C4×C73—21no—
39C4⋊C4×C73—21no—
40C4⋊C4×C73D411yescharacteristic
41C4⋊C4×C73D411yescharacteristic
42C22⋊C4×C73—22no—
43C22⋊C4×C73—22no—
44C22⋊C4×C73—21no—
45C22⋊C4×C73—21no—
46C42×C73—22no—
47C42×C73C2311yescharacteristic
48C23×C73—21no—
49C23×C73—21no—
50Q8×C73—42no—
51D4×C73—21no—
52D4×C73—21no—
53D4×C73—21no—
54D4×C73—21no—
55D4×C73—82no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—22no—
59C2×C4×C73—41no—
60C2×C4×C73—41no—
61C2×C4×C73—41no—
62C2×C4×C73—41no—
63C2×C4×C73C2×D411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C2×Dic73—41no—
67Dic146—41no—
68Dic146—41no—
69#10596831—41no—
70#10596831—41no—
71#10596831—41no—
72C22×C73—41no—
73C22×C73—41no—
74C22×C73—41no—
75C22×C73—41no—
76C22×C73—41no—
77C22×C73—41no—
78C22×C73#12011yescharacteristic
79C4×C73—21no—
80C4×C73—41no—
81C4×C73—41no—
82C4×C73—42no—
83C4×C73#13511yescharacteristic
84C4×C73#13511yescharacteristic
85C4×C73AGL(1,ℤ/8)11yescharacteristic
86C4×C73#13711yescharacteristic
87Dic73—81no—
88C2×C73—81no—
89C2×C73—81no—
90C2×C73#44911yescharacteristic
91C2×C73#45211yescharacteristic
92C2×C73#45511yescharacteristic
93#1646—731nomaximal, Sylow
94C73#164611yescharacteristic, complemented, Sylow
95#555D7311yescharacteristic
96#487—731no—
97#474—731no—
98#461—731no—
99#333—731no—
100D4⋊C8—731no—
101D4⋊C8—731no—
102C2×SD16—1461no—
103C4⋊Q8—731no—
104C4⋊Q8C2×D7311yescharacteristic
105#124—22no—
106#121—21no—
107#121—21no—
108C4×D4C2×D7311yescharacteristic
109C4×D4C2×D7311yescharacteristic
110#117—21no—
111#117—21no—
112#107—1461no—
113C4⋊C8—731no—
114C4⋊C8—731no—
115#103—1462no—
116#103—1461no—
117#102—1461no—
118C4×C8—731no—
119C2×Q8—1461no—
120C2×Q8C22⋊D7312yes—
121C2×D4—22no—
122C2×D4C22⋊D7311yescharacteristic
123C2×D4C22⋊D7311yescharacteristic
124C22×C4—21no—
125C22×C4—21no—
126SD16—2922no—
127C2×C8—1461no—
128C2×C8—1461no—
129C2×C8—1461no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—1461no—
133C4⋊C4—1461no—
134C4⋊C4C22⋊D7311yescharacteristic
135C4⋊C4C22⋊D7311yescharacteristic
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C42—22no—
141C42C22×D7311yescharacteristic
142C23—21no—
143C23—21no—
144Q8—42no—
145Q8—2921no—
146Q8—2921no—
147D4—21no—
148D4—21no—
149D4—21no—
150D4—21no—
151D4—82no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—2921no—
160C2×C4C2×C22⋊D7311yescharacteristic
161C2×C4C2×C22⋊D7311yescharacteristic
162C2×C4C2×C22⋊D7311yescharacteristic
163C8—2921no—
164C8—2921no—
165C8—2921no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#1455656011yescharacteristic
173C4—21no—
174C4—41no—
175C4—41no—
176C4—42no—
177C4—5841no—
178C4#1455661111yescharacteristic
179C4#1455661111yescharacteristic
180C4#1455661611yescharacteristic
181C4#1455662111yescharacteristic
182C2—81no—
183C2—81no—
184C2#1798873211yescharacteristic
185C2#1798874911yescharacteristic
186C2#1798876511yescharacteristic
subgroupG/H
centerC22#14556560
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#555×C73C2
socleC22×C73#120
hypercenter#555D73
hypocenterC73#1646
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #17988937C2semidirect
2. #17988867C2semidirect
3. #17988792C2semidirect
4. #17988336C2semidirect
5. D4⋊#10596831C2semidirect
6. D4⋊#10596831C2semidirect
94. C73#1646semidirect