Finite Group Databasebeta

← #22609166

Subgroups — #22609166

Order 9344.

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

normal subgroups only

This group has 240 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#17988990C211yesmaximal, characteristic, complemented
2#17988867C211yesmaximal, characteristic, complemented
3#17988792C211yesmaximal, characteristic, complemented
4#17988333C211yesmaximal, characteristic, complemented
5D4⋊#10596831C211yesmaximal, characteristic, complemented
6D4⋊#10596831C211yesmaximal, characteristic, complemented
7#547×C73C211yesmaximal, characteristic
8C2×#11924016—21no—
9#14556591C2211yescharacteristic
10#14556524—21no—
11#14556524—22no—
12C4⋊#10596831C2211yescharacteristic
13C4⋊#10596831C2211yescharacteristic
14#14556514—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—
26#11924016—42no—
27C2×#10596831—21no—
28C2×#10596831—21no—
29C2×#10596831—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32#41×C73—42no—
33#41×C73—42no—
34C2×Q8×C73—21no—
35C2×D4×C73—22no—
36C2×D4×C73D411yescharacteristic
37C2×D4×C73D411yescharacteristic
38C22×C4×C73—22no—
39C22×C4×C73—21no—
40C22×C4×C73—21no—
41C4⋊C4×C73—22no—
42C4⋊C4×C73—21no—
43C4⋊C4×C73D411yescharacteristic
44C4⋊C4×C73D411yescharacteristic
45C4⋊C4×C73D412yes—
46C22⋊C4×C73—22no—
47C22⋊C4×C73—21no—
48C22⋊C4×C73—21no—
49C42×C73C2311yescharacteristic
50C23×C73—21no—
51C23×C73—21no—
52Q8×C73—41no—
53Q8×C73—41no—
54D4×C73—21no—
55D4×C73—21no—
56D4×C73—21no—
57D4×C73—44no—
58D4×C73D812yes—
59C2×C4×C73—21no—
60C2×C4×C73—21no—
61C2×C4×C73—22no—
62C2×C4×C73—44no—
63C2×C4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×Dic73—41no—
71Dic146—41no—
72Dic146—41no—
73#10596831—22no—
74#10596831—41no—
75#10596831—41no—
76C22×C73—22no—
77C22×C73—41no—
78C22×C73—41no—
79C22×C73—41no—
80C22×C73—41no—
81C22×C73—41no—
82C22×C73#12011yescharacteristic
83C4×C73—21no—
84C4×C73—41no—
85C4×C73—42no—
86C4×C73—41no—
87C4×C73C2×D811yescharacteristic
88C4×C73#13511yescharacteristic
89C4×C73AGL(1,ℤ/8)11yescharacteristic
90C4×C73#13711yescharacteristic
91Dic73—81no—
92C2×C73—42no—
93C2×C73—81no—
94C2×C73#44711yescharacteristic
95C2×C73#45211yescharacteristic
96C2×C73#45611yescharacteristic
97#1647—731nomaximal, Sylow
98C73#164711yescharacteristic, complemented, Sylow
99#547D7311yescharacteristic
100#500—731no—
101#474—731no—
102#461—731no—
103#332—731no—
104D4⋊C8—731no—
105D4⋊C8—731no—
106C2×#41—21no—
107C2×SD16—1461no—
108C4⋊Q8—731no—
109C4⋊Q8C2×D7311yescharacteristic
110#123—22no—
111C22⋊Q8—21no—
112#121—21no—
113C4×D4C2×D7311yescharacteristic
114C4×D4C2×D7311yescharacteristic
115C2×C4⋊C4—21no—
116#107—1461no—
117#107—1462no—
118C4⋊C8—731no—
119C4⋊C8—731no—
120#103—1461no—
121#102—1461no—
122C4×C8—731no—
123#41—42no—
124#41—42no—
125C2×Q8—21no—
126C2×Q8—1461no—
127C2×D4—22no—
128C2×D4C22⋊D7311yescharacteristic
129C2×D4C22⋊D7311yescharacteristic
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133SD16—2922no—
134C2×C8—1461no—
135C2×C8—1461no—
136C2×C8—1461no—
137C4⋊C4—22no—
138C4⋊C4—21no—
139C4⋊C4—1461no—
140C4⋊C4—1461no—
141C4⋊C4C22⋊D7311yescharacteristic
142C4⋊C4C22⋊D7311yescharacteristic
143C4⋊C4C22⋊D7312yes—
144C22⋊C4—22no—
145C22⋊C4—21no—
146C22⋊C4—21no—
147C42C22×D7311yescharacteristic
148C23—21no—
149C23—21no—
150Q8—41no—
151Q8—41no—
152Q8—2921no—
153Q8—2921no—
154D4—21no—
155D4—21no—
156D4—21no—
157D4—44no—
158D4#1192401312yes—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—44no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—2921no—
168C2×C4C2×C22⋊D7311yescharacteristic
169C2×C4C2×C22⋊D7311yescharacteristic
170C2×C4C2×C22⋊D7311yescharacteristic
171C8—2921no—
172C8—2921no—
173C8—1462no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22#1455656011yescharacteristic
181C4—21no—
182C4—41no—
183C4—42no—
184C4—41no—
185C4—5841no—
186C4C2×#1192401311yescharacteristic
187C4#1455661111yescharacteristic
188C4#1455661711yescharacteristic
189C4#1455662111yescharacteristic
190C2—42no—
191C2—81no—
192C2#1798872111yescharacteristic
193C2#1798874911yescharacteristic
194C2#1798877011yescharacteristic
subgroupG/H
centerC22#14556560
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#547×C73C2
socleC22×C73#120
hypercenter#547D73
hypocenterC73#1647
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. #17988990C2semidirect
2. #17988867C2semidirect
3. #17988792C2semidirect
4. #17988333C2semidirect
5. D4⋊#10596831C2semidirect
6. D4⋊#10596831C2semidirect
98. C73#1647semidirect