Finite Group Databasebeta

← #22609129

Subgroups — #22609129

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#17988935C211yesmaximal, characteristic, complemented
3#17988869C211yesmaximal, characteristic, complemented
4#17988330C211yesmaximal, characteristic, complemented
5#17988317C211yesmaximal, characteristic, complemented
6D4⋊#10596831C211yesmaximal, characteristic, complemented
7#461×C73C211yesmaximal, characteristic, complemented
8C2×#11924028—21no—
9#14556588C2211yescharacteristic
10#14556587—21no—
11#14556565—21no—
12#14556564—22no—
13C4×Dic146C2211yescharacteristic
14#14556553—21no—
15#14556522—21no—
16C4⋊#10596831C2211yescharacteristic
17#14556514—21no—
18#14556511—22no—
19C4×#10596831C2211yescharacteristic
20C2×SD16×C73—21no—
21C4⋊Q8×C73C2211yescharacteristic
22C4×D4×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24#103×C73—21no—
25#11924028—42no—
26#11924028—42no—
27C2×Dic146D411yescharacteristic
28C2×D292—21no—
29C2×D292—21no—
30C2×D292D412yes—
31C2×C22⋊D73—22no—
32C2×C22⋊D73—22no—
33C2×C4×D73—22no—
34C2×#10596831—21no—
35C2×#10596831—21no—
36C4⋊Dic73D411yescharacteristic
37#11924007—21no—
38#11924005—22no—
39C4×Dic73—21no—
40C2×Q8×C73—21no—
41C2×D4×C73D411yescharacteristic
42C22×C4×C73—21no—
43SD16×C73—42no—
44C2×C8×C73—21no—
45C4⋊C4×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73D411yescharacteristic
48C22⋊C4×C73—21no—
49C42×C73C2311yescharacteristic
50C23×C73—21no—
51C22×D73—22no—
52Q8×C73—41no—
53Q8×C73—41no—
54D4×C73—21no—
55D4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73—41no—
58C2×C4×C73—41no—
59C2×C4×C73—41no—
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C22⋊D73—44no—
64C22⋊D73—82no—
65C2×Dic73—21no—
66C2×Dic73—21no—
67D292—42no—
68D292—41no—
69D292—41no—
70D292—41no—
71D292—41no—
72C4×D73—44no—
73Dic146—21no—
74Dic146SD1612yescomplemented
75C8×C73—41no—
76#10596831—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×C73—81no—
88C4×C73C2×SD1611yescharacteristic
89C4×C73#13511yescharacteristic
90C4×C73AGL(1,ℤ/8)11yescharacteristic
91C4×C73AGL(1,ℤ/8)11yescharacteristic
92Dic73—22no—
93Dic73—41no—
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#461D7311yescharacteristic, complemented
105#331—731no—
106Q8⋊C8—731no—
107D4⋊C8—731no—
108C2×#41—1461no—
109C2×SD16—21no—
110C4⋊Q8C2×D7311yescharacteristic
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—21no—
122#103—1461no—
123#102—1462no—
124C4×C8—731no—
125#41—2922no—
126#41—2922no—
127C2×Q8—21no—
128C2×Q8—731no—
129C2×D4—732no—
130C2×D4—1462no—
131C2×D4—1462no—
132C2×D4—1461no—
133C2×D4—1461no—
134C2×D4C22⋊D7311yescharacteristic
135C22×C4—21no—
136C22×C4—1462no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—1461no—
140C2×C8—1461no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—731no—
144C4⋊C4—1461no—
145C4⋊C4C22⋊D7311yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—1462no—
148C42—1461no—
149C42C22×D7311yescharacteristic
150C23—21no—
151C23—1462no—
152Q8—41no—
153Q8—41no—
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—41no—
169C2×C4—2924no—
170C2×C4—1461no—
171C2×C4—1461no—
172C2×C4D4×D7311yescharacteristic
173C2×C4D4×D7311yescharacteristic
174C2×C4C2×C22⋊D7311yescharacteristic
175C8—41no—
176C8—2921no—
177C8—2921no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—2922no—
182C22—2922no—
183C22—2922no—
184C22#1455655911yescharacteristic
185C4—21no—
186C4—41no—
187C4—81no—
188C4—2921no—
189C4—1462no—
190C4SD16×D7311yescharacteristic
191C4#1455661111yescharacteristic
192C4#1455661711yescharacteristic
193C4#1455661811yescharacteristic
194C2—81no—
195C2—5842no—
196C2#1798873011yescharacteristic
197C2#1798873611yescharacteristic
198C2#1798876311yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#461×C73C2
socleC22×C73#120
hypercenter#461D73
hypocenterC73#1642
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #17988935C2semidirect
3. #17988869C2semidirect
4. #17988330C2semidirect
5. #17988317C2semidirect
6. D4⋊#10596831C2semidirect
7. #461×C73C2semidirect
74. Dic146SD16semidirect
100. C73#1642semidirect
104. #461D73semidirect