Finite Group Databasebeta

← #22589743

Subgroups — #22589743

Order 9088.

274 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#14556049C212yesmaximal
2#17985869C211yesmaximal, characteristic, complemented
3#17985761C212yesmaximal, complemented
4#17985754C211yesmaximal, characteristic, complemented
5#390×C71C211yesmaximal, characteristic
6C22×C71⋊C8C2212yes—
7C2×C4⋊Dic71—21no—
8C2×C4⋊Dic71—21no—
9C2×C4⋊Dic71C2212yes—
10#14556049—24no—
11C22×D4×C71C2211yescharacteristic
12C2×C4⋊C4×C71C2211yescharacteristic
13C2×C22⋊C4×C71—21no—
14C2×C22⋊C4×C71—21no—
15C2×C42×C71C2211yescharacteristic
16C22×Dic71—22no—
17C2×C71⋊C8—22no—
18C2×C71⋊C8—22no—
19C2×C71⋊C8—22no—
20C4⋊Dic71—22no—
21C4⋊Dic71—22no—
22C4⋊Dic71—42no—
23C4⋊Dic71—42no—
24C24×C71—21no—
25C2×D4×C71—22no—
26C2×D4×C71—22no—
27C2×D4×C71—21no—
28C2×D4×C71D412yes—
29C22×C4×C71—21no—
30C22×C4×C71D411yescharacteristic
31C22×C4×C71D411yescharacteristic
32C22×C4×C71C2311yescharacteristic
33C4⋊C4×C71—22no—
34C22⋊C4×C71—42no—
35C22⋊C4×C71—42no—
36C42×C71—22no—
37C23×C71—22no—
38C23×C71—41no—
39C23×C71—41no—
40C23×C71—41no—
41C23×C71—41no—
42C23×C71—41no—
43C23×C71—41no—
44C23×C71C2×D411yescharacteristic
45D4×C71—24no—
46D4×C71—42no—
47C2×C4×C71—21no—
48C2×C4×C71—21no—
49C2×C4×C71—21no—
50C2×C4×C71—21no—
51C2×C4×C71—41no—
52C2×C4×C71—41no—
53C2×C4×C71—41no—
54C2×C4×C71D812yes—
55C2×C4×C71SD1612yes—
56C2×C4×C71C2×D411yescharacteristic
57C2×C4×C71#4112yes—
58C2×C4×C71#4112yes—
59C2×C4×C71#4111yescharacteristic
60C2×Dic71—42no—
61C2×Dic71—42no—
62C2×Dic71—42no—
63C71⋊C8—42no—
64C22×C71—42no—
65C22×C71—42no—
66C22×C71—42no—
67C22×C71—81no—
68C22×C71—81no—
69C22×C71—81no—
70C22×C71—81no—
71C22×C71#12111yescharacteristic
72C22×C71#12311yescharacteristic
73C22×C71#12411yescharacteristic
74C22×C71C2×D811yescharacteristic
75C22×C71C2×SD1611yescharacteristic
76C22×C71AGL(1,ℤ/8)11yescharacteristic
77C22×C71#13711yescharacteristic
78C4×C71—22no—
79C4×C71—22no—
80C4×C71—81no—
81C4×C71#12312yes—
82C4×C71#12612yes—
83Dic71—82no—
84C2×C71—82no—
85C2×C71#39711yescharacteristic
86C2×C71#45911yescharacteristic
87C2×C71#46111yescharacteristic
88C2×C71#48011yescharacteristic
89C2×C71#48111yescharacteristic
90C2×C71#48611yescharacteristic
91C2×C71#48911yescharacteristic
92#2071—711nomaximal, Sylow
93C71#207111yescharacteristic, complemented, Sylow
94C2×#102—712no—
95#390D7111yescharacteristic
96#384—711no—
97#340—712no—
98#336—711no—
99C22×D4C2×D7111yescharacteristic
100C22×C8—712no—
101C2×C4⋊C4—712no—
102C2×C4⋊C4—1421no—
103C2×C4⋊C4—1421no—
104C2×C4⋊C4C2×D7111yescharacteristic
105C2×C22⋊C4—21no—
106C2×C22⋊C4—21no—
107C2×C42C2×D7111yescharacteristic
108#102—1424no—
109C24—21no—
110C2×D4—22no—
111C2×D4—22no—
112C2×D4—21no—
113C2×D4D28412yes—
114C22×C4—21no—
115C22×C4—1422no—
116C22×C4C22⋊D7111yescharacteristic
117C22×C4C22⋊D7111yescharacteristic
118C22×C4C22×D7111yescharacteristic
119C2×C8—1422no—
120C2×C8—1422no—
121C2×C8—1422no—
122C4⋊C4—22no—
123C4⋊C4—2842no—
124C4⋊C4—2842no—
125C4⋊C4—1422no—
126C4⋊C4—1422no—
127C22⋊C4—42no—
128C22⋊C4—42no—
129C42—22no—
130C23—22no—
131C23—41no—
132C23—41no—
133C23—41no—
134C23—41no—
135C23—41no—
136C23—41no—
137C23C2×C22⋊D7111yescharacteristic
138D4—24no—
139D4—42no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—2842no—
148C2×C4—2842no—
149C2×C4—2842no—
150C2×C4#1176585012yes—
151C2×C4#1176585312yes—
152C2×C4C2×D28411yescharacteristic
153C2×C4#1176586412yes—
154C2×C4#1176586412yes—
155C2×C4#1176586511yescharacteristic
156C8—2842no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22—81no—
161C22—81no—
162C22—81no—
163C22—81no—
164C22#1455610211yescharacteristic
165C22#1455610911yescharacteristic
166C22#1455611511yescharacteristic
167C22C2×#1176585011yescharacteristic
168C22C2×#1176585311yescharacteristic
169C22#1455615311yescharacteristic
170C22#1455615811yescharacteristic
171C4—22no—
172C4—22no—
173C4—81no—
174C4—5682no—
175C4#1455611212yes—
176C4#1455612112yes—
177C2—82no—
178C2#1798592411yescharacteristic
179C2#1798619411yescharacteristic
180C2#1798620411yescharacteristic
181C2#1798631011yescharacteristic
182C2#1798631511yescharacteristic
183C2#1798634511yescharacteristic
184C2#1798635811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D71
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#390×C71C2
socleC23×C71C2×D4
hypercenter#390D71
hypocenterC71#2071
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #17985869C2semidirect
3. #17985761C2semidirect
4. #17985754C2semidirect
93. C71#2071semidirect