Finite Group Databasebeta

← #22609038

Subgroups — #22609038

Order 9344.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#17989311C211yesmaximal, characteristic, complemented
2#17988784C211yesmaximal, characteristic, complemented
3#17988779C211yesmaximal, characteristic
4#17988333C211yesmaximal, characteristic, complemented
5#17988319C211yesmaximal, characteristic, complemented
6#17988316C211yesmaximal, characteristic, complemented
7#486×C73C211yesmaximal, characteristic, complemented
8C2×#11924016—21no—
9C2×#11924013—21no—
10#14556586—22no—
11#14556580—21no—
12#14556571—21no—
13Q8×Dic73—21no—
14C4×Dic146C2211yescharacteristic
15C4×D292C2211yescharacteristic
16#14556549—21no—
17C4⋊#10596831C2211yescharacteristic
18C4⋊#10596831C2211yescharacteristic
19#14556512—21no—
20#14556512—21no—
21C4⋊Q8×C73C2211yescharacteristic
22#127×C73C2211yescharacteristic
23#102×C73—22no—
24C4×C8×C73C2211yescharacteristic
25C2×Dic146D411yescharacteristic
26C2×D292D411yescharacteristic
27C2×C4×D73—21no—
28#11924016—42no—
29#11924013—42no—
30C2×#10596831—21no—
31C2×#10596831—21no—
32C4⋊Dic73—22no—
33C4⋊Dic73D411yescharacteristic
34C4⋊Dic73D411yescharacteristic
35#11924007—21no—
36#11924005—22no—
37#11924005—22no—
38#11924005—21no—
39C4×Dic73—22no—
40C4×Dic73—21no—
41C2×Q8×C73—21no—
42C2×D4×C73—21no—
43C2×D4×C73—21no—
44C2×D4×C73—21no—
45C2×C8×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73D412yes—
48C42×C73C2311yescharacteristic
49C23×C73—41no—
50C22×D73—21no—
51Q8×C73—41no—
52Q8×C73—41no—
53D4×C73—42no—
54D4×C73—41no—
55D4×C73—41no—
56D4×C73—41no—
57D4×C73—41no—
58C2×C4×C73—22no—
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C2×Dic73—21no—
63C2×Dic73—21no—
64C2×Dic73—21no—
65D292—21no—
66D292—21no—
67C4×D73—41no—
68C4×D73—41no—
69Dic146—21no—
70Dic146—21no—
71C8×C73—41no—
72#10596831—41no—
73#10596831—41no—
74C22×C73—81no—
75C22×C73—81no—
76C22×C73—81no—
77C22×C73#12011yescharacteristic
78C2×D73—41no—
79C2×D73—41no—
80C2×D73—41no—
81C4×C73—21no—
82C4×C73—42no—
83C4×C73#13511yescharacteristic
84C4×C73#13511yescharacteristic
85C4×C73AGL(1,ℤ/8)11yescharacteristic
86C4×C73AGL(1,ℤ/8)11yescharacteristic
87Dic73—41no—
88Dic73—41no—
89Dic73—41no—
90C2×C73—161no—
91C2×C73#44911yescharacteristic
92C2×C73#44911yescharacteristic
93C2×C73#45411yescharacteristic
94D73—81no—
95#1628—731nomaximal, Sylow
96C73#162811yescharacteristic, complemented, Sylow
97#556—731no—
98#486D7311yescharacteristic, complemented
99#460—731no—
100#459—731no—
101#332—731no—
102Q8⋊C8—731no—
103D4⋊C8—731no—
104C2×SD16—1461no—
105C2×D8—1461no—
106C4⋊Q8C2×D7311yescharacteristic
107#127C2×D7311yescharacteristic
108#126—1462no—
109#124—1461no—
110C22⋊Q8—1461no—
111C4×Q8—731no—
112C4×Q8—1461no—
113C4×D4—731no—
114#117—1461no—
115C4⋊C8—731no—
116C4⋊C8—731no—
117#102—22no—
118#102—1461no—
119#102—1461no—
120C4×C8C2×D7311yescharacteristic
121C2×Q8—21no—
122C2×Q8—731no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—731no—
127C22×C4—1461no—
128SD16—2922no—
129D8—2922no—
130C2×C8—21no—
131C2×C8—1461no—
132C2×C8—1461no—
133C4⋊C4—21no—
134C4⋊C4—731no—
135C4⋊C4—731no—
136C4⋊C4—1462no—
137C4⋊C4—1461no—
138C4⋊C4C22⋊D7312yes—
139C22⋊C4—1462no—
140C22⋊C4—1462no—
141C22⋊C4—1461no—
142C42—1462no—
143C42—1461no—
144C42C22×D7311yescharacteristic
145C23—41no—
146C23—1461no—
147Q8—41no—
148Q8—41no—
149Q8—1461no—
150Q8—1461no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—1461no—
157D4—1461no—
158C2×C4—22no—
159C2×C4—2921no—
160C2×C4—2921no—
161C2×C4—1461no—
162C2×C4—1461no—
163C2×C4—1461no—
164C2×C4D4×D7311yescharacteristic
165C2×C4D4×D7311yescharacteristic
166C2×C4C2×C22⋊D7311yescharacteristic
167C8—41no—
168C8—2921no—
169C8—2921no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—2921no—
174C22—2921no—
175C22—2921no—
176C22#1455655911yescharacteristic
177C4—21no—
178C4—42no—
179C4—2921no—
180C4—2921no—
181C4—2921no—
182C4#1455661011yescharacteristic
183C4#1455661211yescharacteristic
184C4#1455661511yescharacteristic
185C4#1455661811yescharacteristic
186C2—161no—
187C2—5841no—
188C2#1798872911yescharacteristic
189C2#1798873111yescharacteristic
190C2#1798875911yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#486×C73C2
socleC22×C73#120
hypercenter#486D73
hypocenterC73#1628
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #17989311C2semidirect
2. #17988784C2semidirect
4. #17988333C2semidirect
5. #17988319C2semidirect
6. #17988316C2semidirect
7. #486×C73C2semidirect
96. C73#1628semidirect
98. #486D73semidirect