Finite Group Databasebeta

← #22609156

Subgroups — #22609156

Order 9344.

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

normal subgroups only

This group has 212 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#17989303C211yesmaximal, characteristic
2#17988864C211yesmaximal, characteristic, complemented
3#17988789C211yesmaximal, characteristic, complemented
4#17988336C211yesmaximal, characteristic, complemented
5#17988316C211yesmaximal, characteristic, complemented
6#17988316C211yesmaximal, characteristic, complemented
7#487×C73C211yesmaximal, characteristic, complemented
8C2×#11924015—21no—
9#14556580—22no—
10#14556566—21no—
11#14556566—21no—
12C4×D292C2211yescharacteristic
13C4×D292C2211yescharacteristic
14#14556549—21no—
15#14556549—21no—
16#14556524—21no—
17C4⋊#10596831C2211yescharacteristic
18C4⋊#10596831C2211yescharacteristic
19#14556515—21no—
20#14556511—21no—
21C4⋊Q8×C73C2211yescharacteristic
22C4⋊Q8×C73C2211yescharacteristic
23#103×C73—22no—
24C4×C8×C73C2211yescharacteristic
25C2×D292—22no—
26C2×D292D411yescharacteristic
27C2×D292D411yescharacteristic
28C2×C4×D73—21no—
29C2×C4×D73—21no—
30#11924015—42no—
31C2×#10596831—21no—
32C2×#10596831—21no—
33C4⋊Dic73D411yescharacteristic
34C4⋊Dic73D411yescharacteristic
35#11924005—22no—
36#11924005—22no—
37#11924005—21no—
38#11924005—21no—
39C4×Dic73—22no—
40C2×Q8×C73—21no—
41C2×Q8×C73D412yes—
42C2×C8×C73—21no—
43C4⋊C4×C73—21no—
44C4⋊C4×C73—21no—
45C4⋊C4×C73—21no—
46C4⋊C4×C73—21no—
47C42×C73C2311yescharacteristic
48C22×D73—21no—
49C22×D73—21no—
50Q8×C73—42no—
51Q8×C73—41no—
52Q8×C73—41no—
53C2×C4×C73—22no—
54C2×C4×C73—41no—
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×D411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×Dic73—21no—
59C2×Dic73—21no—
60D292—21no—
61D292—21no—
62D292—21no—
63D292—21no—
64D292—82no—
65C4×D73—41no—
66C4×D73—41no—
67C4×D73—41no—
68C4×D73—41no—
69C8×C73—41no—
70#10596831—41no—
71#10596831—41no—
72C22×C73#12011yescharacteristic
73C2×D73—41no—
74C2×D73—41no—
75C2×D73—41no—
76C2×D73—41no—
77C2×D73—41no—
78C2×D73—41no—
79C4×C73—21no—
80C4×C73—42no—
81C4×C73—81no—
82C4×C73#13511yescharacteristic
83C4×C73#13511yescharacteristic
84C4×C73AGL(1,ℤ/8)11yescharacteristic
85C4×C73#13711yescharacteristic
86Dic73—41no—
87Dic73—41no—
88C2×C73#44911yescharacteristic
89C2×C73#45211yescharacteristic
90C2×C73#45511yescharacteristic
91D73—81no—
92D73—81no—
93#1646—731nomaximal, Sylow
94C73#164611yescharacteristic, complemented, Sylow
95#555—731no—
96#487D7311yescharacteristic, complemented
97#474—731no—
98#461—731no—
99#333—731no—
100D4⋊C8—731no—
101D4⋊C8—731no—
102C2×SD16—1461no—
103C4⋊Q8C2×D7311yescharacteristic
104C4⋊Q8C2×D7311yescharacteristic
105#124—1462no—
106#121—1461no—
107#121—1461no—
108C4×D4—731no—
109C4×D4—731no—
110#117—1461no—
111#117—1461no—
112#107—1461no—
113C4⋊C8—731no—
114C4⋊C8—731no—
115#103—22no—
116#103—1461no—
117#102—1461no—
118C4×C8C2×D7311yescharacteristic
119C2×Q8—21no—
120C2×Q8C22⋊D7312yes—
121C2×D4—731no—
122C2×D4—731no—
123C2×D4—1462no—
124C22×C4—1461no—
125C22×C4—1461no—
126SD16—2922no—
127C2×C8—21no—
128C2×C8—1461no—
129C2×C8—1461no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—731no—
135C4⋊C4—731no—
136C22⋊C4—1462no—
137C22⋊C4—1462no—
138C22⋊C4—1461no—
139C22⋊C4—1461no—
140C42—1462no—
141C42C22×D7311yescharacteristic
142C23—1461no—
143C23—1461no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—5842no—
148D4—1461no—
149D4—1461no—
150D4—1461no—
151D4—1461no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—2921no—
155C2×C4—2921no—
156C2×C4—2921no—
157C2×C4—2921no—
158C2×C4—1461no—
159C2×C4—1461no—
160C2×C4D4×D7311yescharacteristic
161C2×C4D4×D7311yescharacteristic
162C2×C4C2×C22⋊D7311yescharacteristic
163C8—41no—
164C8—2921no—
165C8—2921no—
166C22—2921no—
167C22—2921no—
168C22—2921no—
169C22—2921no—
170C22—2921no—
171C22—2921no—
172C22#1455655911yescharacteristic
173C4—21no—
174C4—42no—
175C4—81no—
176C4—2921no—
177C4—2921no—
178C4#1455661211yescharacteristic
179C4#1455661411yescharacteristic
180C4#1455661811yescharacteristic
181C4#1455662311yescharacteristic
182C2—5841no—
183C2—5841no—
184C2#1798873111yescharacteristic
185C2#1798874811yescharacteristic
186C2#1798876411yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#487×C73C2
socleC22×C73#120
hypercenter#487D73
hypocenterC73#1646
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #17988864C2semidirect
3. #17988789C2semidirect
4. #17988336C2semidirect
5. #17988316C2semidirect
6. #17988316C2semidirect
7. #487×C73C2semidirect
94. C73#1646semidirect
96. #487D73semidirect