Finite Group Databasebeta

← #22609082

Subgroups — #22609082

Order 9344.

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

normal subgroups only

This group has 234 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#17988939C211yesmaximal, characteristic, complemented
2#17988877C211yesmaximal, characteristic, complemented
3#17988877C211yesmaximal, characteristic, complemented
4#17988333C211yesmaximal, characteristic, complemented
5D4⋊#10596831C211yesmaximal, characteristic, complemented
6D4⋊#10596831C211yesmaximal, characteristic, complemented
7#547×C73C211yesmaximal, characteristic
8#14556591C2211yescharacteristic
9#14556522—21no—
10#14556522—21no—
11C4⋊#10596831C2211yescharacteristic
12C4⋊#10596831C2211yescharacteristic
13#14556514—22no—
14#14556512—21no—
15#14556512—21no—
16C4×#10596831C2211yescharacteristic
17C2×#41×C73—21no—
18C4⋊Q8×C73C2211yescharacteristic
19#123×C73—22no—
20C22⋊Q8×C73—21no—
21#121×C73—21no—
22C4×D4×C73C2211yescharacteristic
23C4×D4×C73C2211yescharacteristic
24C2×C4⋊C4×C73—21no—
25C2×Dic146—21no—
26C2×#10596831—21no—
27C2×#10596831—21no—
28C2×#10596831—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31#41×C73—42no—
32#41×C73—42no—
33C2×Q8×C73—21no—
34C2×D4×C73—22no—
35C2×D4×C73D411yescharacteristic
36C2×D4×C73D411yescharacteristic
37C22×C4×C73—22no—
38C22×C4×C73—21no—
39C22×C4×C73—21no—
40C4⋊C4×C73—22no—
41C4⋊C4×C73—21no—
42C4⋊C4×C73D411yescharacteristic
43C4⋊C4×C73D411yescharacteristic
44C4⋊C4×C73D412yes—
45C22⋊C4×C73—22no—
46C22⋊C4×C73—21no—
47C22⋊C4×C73—21no—
48C42×C73C2311yescharacteristic
49C23×C73—21no—
50C23×C73—21no—
51Q8×C73—41no—
52Q8×C73—41no—
53D4×C73—21no—
54D4×C73—21no—
55D4×C73—21no—
56D4×C73—44no—
57D4×C73SD1612yes—
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73—22no—
61C2×C4×C73—44no—
62C2×C4×C73—41no—
63C2×C4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×Dic73—41no—
70Dic146—42no—
71#10596831—41no—
72#10596831—41no—
73#10596831—41no—
74C22×C73—22no—
75C22×C73—41no—
76C22×C73—41no—
77C22×C73—41no—
78C22×C73—41no—
79C22×C73—41no—
80C22×C73#12011yescharacteristic
81C4×C73—21no—
82C4×C73—41no—
83C4×C73—42no—
84C4×C73—41no—
85C4×C73C2×SD1611yescharacteristic
86C4×C73#13511yescharacteristic
87C4×C73AGL(1,ℤ/8)11yescharacteristic
88C4×C73#13711yescharacteristic
89Dic73—81no—
90C2×C73—42no—
91C2×C73—81no—
92C2×C73#45011yescharacteristic
93C2×C73#45211yescharacteristic
94C2×C73#45411yescharacteristic
95#1635—731nomaximal, Sylow
96C73#163511yescharacteristic, complemented, Sylow
97#547D7311yescharacteristic
98#487—731no—
99#476—731no—
100#476—731no—
101#332—731no—
102D4⋊C8—731no—
103D4⋊C8—731no—
104C2×#41—21no—
105C4⋊Q8—731no—
106C4⋊Q8C2×D7311yescharacteristic
107#123—22no—
108C22⋊Q8—21no—
109#121—21no—
110C4×D4C2×D7311yescharacteristic
111C4×D4C2×D7311yescharacteristic
112C2×C4⋊C4—21no—
113#106—1461no—
114#106—1461no—
115C4⋊C8—731no—
116C4⋊C8—731no—
117#103—1462no—
118#102—1461no—
119#102—1461no—
120C4×C8—731no—
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×Q8—1461no—
125C2×D4—22no—
126C2×D4C22⋊D7311yescharacteristic
127C2×D4C22⋊D7311yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C2×C8—1461no—
132C2×C8—1461no—
133C2×C8—1461no—
134C4⋊C4—22no—
135C4⋊C4—21no—
136C4⋊C4—1461no—
137C4⋊C4—1461no—
138C4⋊C4C22⋊D7312yes—
139C4⋊C4C22⋊D7311yescharacteristic
140C4⋊C4C22⋊D7311yescharacteristic
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C42C22×D7311yescharacteristic
145C23—21no—
146C23—21no—
147Q8—41no—
148Q8—41no—
149Q8—2922no—
150D4—21no—
151D4—21no—
152D4—21no—
153D4—44no—
154D4#1192401612yes—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—44no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—2921no—
164C2×C4C2×C22⋊D7311yescharacteristic
165C2×C4C2×C22⋊D7311yescharacteristic
166C2×C4C2×C22⋊D7311yescharacteristic
167C8—2921no—
168C8—2921no—
169C8—2921no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22#1455656011yescharacteristic
177C4—21no—
178C4—41no—
179C4—42no—
180C4—41no—
181C4—5841no—
182C4C2×#1192401611yescharacteristic
183C4#1455661111yescharacteristic
184C4#1455661711yescharacteristic
185C4#1455662111yescharacteristic
186C2—42no—
187C2—81no—
188C2#1798873811yescharacteristic
189C2#1798874911yescharacteristic
190C2#1798876011yescharacteristic
subgroupG/H
centerC22#14556560
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#547×C73C2
socleC22×C73#120
hypercenter#547D73
hypocenterC73#1635
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #17988939C2semidirect
2. #17988877C2semidirect
3. #17988877C2semidirect
4. #17988333C2semidirect
5. D4⋊#10596831C2semidirect
6. D4⋊#10596831C2semidirect
96. C73#1635semidirect