Finite Group Databasebeta

← #22609133

Subgroups — #22609133

Order 9344.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#17989258C211yesmaximal, characteristic
2#17988934C211yesmaximal, characteristic, complemented
3#17988873C211yesmaximal, characteristic, complemented
4#17988792C211yesmaximal, characteristic, complemented
5#17988330C211yesmaximal, characteristic, complemented
6#17988319C211yesmaximal, characteristic, complemented
7D4⋊C8×C73C211yesmaximal, characteristic, complemented
8C2×#11924028—21no—
9C2×#11924016—21no—
10#14556591C2211yescharacteristic
11#14556588C2211yescharacteristic
12#14556587—21no—
13#14556565—21no—
14#14556564—22no—
15C4×Dic146C2211yescharacteristic
16#14556553—21no—
17#14556523—21no—
18C4⋊#10596831C2211yescharacteristic
19#14556516—21no—
20#14556514—21no—
21#14556513—22no—
22C4×D4×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24C4×C8×C73C2211yescharacteristic
25#11924028—42no—
26#11924028—42no—
27C2×Dic146—21no—
28C2×Dic146D411yescharacteristic
29C2×D292—21no—
30C2×D292—21no—
31C2×D292D412yes—
32C2×C22⋊D73—22no—
33C2×C22⋊D73—22no—
34C2×C4×D73—22no—
35#11924016—42no—
36C2×#10596831—21no—
37C4⋊Dic73—21no—
38C4⋊Dic73—21no—
39C4⋊Dic73D411yescharacteristic
40#11924007—21no—
41#11924005—22no—
42C4×Dic73—21no—
43C2×D4×C73D411yescharacteristic
44C22×C4×C73—21no—
45C2×C8×C73—21no—
46C2×C8×C73—21no—
47C4⋊C4×C73D411yescharacteristic
48C22⋊C4×C73—21no—
49C42×C73C2311yescharacteristic
50C23×C73—21no—
51C22×D73—22no—
52D4×C73—21no—
53D4×C73—21no—
54C2×C4×C73—21no—
55C2×C4×C73—41no—
56C2×C4×C73—41no—
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C22⋊D73—44no—
61C22⋊D73—82no—
62C2×Dic73—21no—
63C2×Dic73—21no—
64C2×Dic73—41no—
65D292—42no—
66D292—41no—
67D292—41no—
68D292—41no—
69D292—41no—
70C4×D73—44no—
71Dic146—21no—
72Dic146—41no—
73Dic146—41no—
74Dic146SD1612yescomplemented
75C8×C73—41no—
76C8×C73—41no—
77#10596831—41no—
78C22×C73—41no—
79C22×C73—41no—
80C22×C73—41no—
81C22×C73#12011yescharacteristic
82C2×D73—42no—
83C2×D73—42no—
84C2×D73—42no—
85C4×C73—21no—
86C4×C73—41no—
87C4×C73C2×SD1611yescharacteristic
88C4×C73#13511yescharacteristic
89C4×C73AGL(1,ℤ/8)11yescharacteristic
90C4×C73AGL(1,ℤ/8)11yescharacteristic
91Dic73—22no—
92Dic73—41no—
93Dic73—81no—
94C2×C73—81no—
95C2×C73#44911yescharacteristic
96C2×C73#45011yescharacteristic
97C2×C73#45511yescharacteristic
98D73—82no—
99#1642—731nomaximal, Sylow
100C73#164211yescharacteristic, complemented, Sylow
101#550—731no—
102#486—731no—
103#475—731no—
104#461—731no—
105#331—731no—
106Q8⋊C8—731no—
107D4⋊C8D7311yescharacteristic, complemented
108C2×#41—1461no—
109C2×SD16—1461no—
110C4⋊Q8—731no—
111#127—731no—
112#127—1461no—
113#121—1462no—
114#121—1461no—
115C4×Q8—731no—
116C4×D4—1461no—
117C4×D4C2×D7311yescharacteristic
118#106—1461no—
119C4⋊C8—731no—
120C4⋊C8C2×D7311yescharacteristic
121#103—1461no—
122#103—1461no—
123#102—1462no—
124C4×C8C2×D7311yescharacteristic
125#41—2922no—
126#41—2922no—
127C2×Q8—731no—
128C2×Q8—1461no—
129C2×D4—732no—
130C2×D4—1462no—
131C2×D4—1462no—
132C2×D4—1461no—
133C2×D4—1461no—
134C2×D4D29211yescharacteristic
135C22×C4—21no—
136C22×C4—1462no—
137SD16—2922no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—1461no—
141C4⋊C4—731no—
142C4⋊C4—1461no—
143C4⋊C4—1461no—
144C4⋊C4—1461no—
145C4⋊C4D29211yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—1462no—
148C42—1461no—
149C42C22×D7311yescharacteristic
150C23—21no—
151C23—1462no—
152Q8—2921no—
153Q8—2921no—
154Q8—732no—
155Q8—1461no—
156D4—21no—
157D4—21no—
158D4—2922no—
159D4—2924no—
160D4—2921no—
161D4—2921no—
162D4—2921no—
163D4—2921no—
164D4—5842no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—2924no—
169C2×C4—2921no—
170C2×C4—1461no—
171C2×C4—1461no—
172C2×C4D4×D7311yescharacteristic
173C2×C4D4×D7311yescharacteristic
174C2×C4C2×D29211yescharacteristic
175C8—41no—
176C8—41no—
177C8—2921no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—2922no—
182C22—2922no—
183C22—2922no—
184C22#1455656111yescharacteristic
185C4—21no—
186C4—41no—
187C4—2921no—
188C4—5841no—
189C4—1462no—
190C4SD16×D7311yescharacteristic
191C4#1455661311yescharacteristic
192C4#1455661511yescharacteristic
193C4#1455661911yescharacteristic
194C2—81no—
195C2—5842no—
196C2#1798873411yescharacteristic
197C2#1798873911yescharacteristic
198C2#1798876611yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
FittingD4⋊C8×C73C2
socleC22×C73#120
hypercenterD4⋊C8D73
hypocenterC73#1642
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #17988934C2semidirect
3. #17988873C2semidirect
4. #17988792C2semidirect
5. #17988330C2semidirect
6. #17988319C2semidirect
7. D4⋊C8×C73C2semidirect
74. Dic146SD16semidirect
100. C73#1642semidirect
107. D4⋊C8D73semidirect