Finite Group Databasebeta

← #22589909

Subgroups — #22589909

Order 9088.

198 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 79 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#17985897C211yesmaximal, characteristic
2#17985865C211yesmaximal, characteristic
3#17985762C211yesmaximal, characteristic
4#17985762C211yesmaximal, characteristic
5#17985762C211yesmaximal, characteristic
6#17985762C211yesmaximal, characteristic
7#336×C71C211yesmaximal, characteristic
8C2×C4⋊Dic71C2211yescharacteristic
9C2×C4⋊Dic71C2211yescharacteristic
10C2×C4⋊Dic71C2211yescharacteristic
11C2×C4⋊Dic71C2211yescharacteristic
12C2×Dic71⋊C4—21no—
13C71⋊#95—21no—
14C71⋊#95—21no—
15C71⋊#95—21no—
16C22×C8×C71C2211yescharacteristic
17C22×C8×C71C2211yescharacteristic
18C2×C42×C71C2211yescharacteristic
19C22×Dic71—21no—
20C22×Dic71—21no—
21C22×Dic71—21no—
22C22×Dic71—21no—
23C4⋊Dic71—21no—
24C4⋊Dic71—21no—
25C4⋊Dic71—21no—
26C4⋊Dic71—21no—
27C4⋊Dic71—21no—
28C4⋊Dic71—21no—
29C4⋊Dic71—21no—
30C4⋊Dic71Q812yes—
31Dic71⋊C4—42no—
32C22×C4×C71D411yescharacteristic
33C22×C4×C71D411yescharacteristic
34C22×C4×C71C2311yescharacteristic
35C2×C8×C71—21no—
36C2×C8×C71—21no—
37C2×C8×C71—21no—
38C2×C8×C71—21no—
39C2×C8×C71—21no—
40C2×C8×C71—21no—
41C42×C71—21no—
42C42×C71—21no—
43C23×C71C2×D411yescharacteristic
44C2×C4×C71—21no—
45C2×C4×C71—21no—
46C2×C4×C71—21no—
47C2×C4×C71—21no—
48C2×C4×C71—21no—
49C2×C4×C71—21no—
50C2×C4×C71C2×Q811yescharacteristic
51C2×C4×C71#4111yescharacteristic
52C2×C4×C71#4111yescharacteristic
53C2×C4×C71#4111yescharacteristic
54C2×C4×C71#4111yescharacteristic
55C2×C4×C71#4111yescharacteristic
56C2×Dic71—22no—
57C2×Dic71—41no—
58C2×Dic71—41no—
59C2×Dic71—41no—
60C2×Dic71—41no—
61C2×Dic71—41no—
62C2×Dic71—41no—
63C2×Dic71—41no—
64C2×Dic71—41no—
65C2×Dic71—41no—
66C2×Dic71—41no—
67C2×Dic71—41no—
68C8×C71—41no—
69C8×C71—41no—
70C22×C71C22⋊Q811yescharacteristic
71C22×C71#12311yescharacteristic
72C22×C71#12411yescharacteristic
73C22×C71#13511yescharacteristic
74C22×C71#13511yescharacteristic
75C22×C71AGL(1,ℤ/8)11yescharacteristic
76C22×C71#13711yescharacteristic
77C4×C71—41no—
78C4×C71—41no—
79C4×C71#12511yescharacteristic
80C4×C71#12511yescharacteristic
81C4×C71#12611yescharacteristic
82C4×C71#12611yescharacteristic
83Dic71—42no—
84Dic71—81no—
85Dic71—81no—
86Dic71—81no—
87C2×C71#40011yescharacteristic
88C2×C71#47811yescharacteristic
89C2×C71#47911yescharacteristic
90C2×C71#48211yescharacteristic
91C2×C71#48511yescharacteristic
92C2×C71#48811yescharacteristic
93C2×C71#48911yescharacteristic
94#2101—711nomaximal, Sylow
95C71#210111yescharacteristic, complemented, Sylow
96#389—711no—
97#382—711no—
98#340—711no—
99#340—711no—
100#340—711no—
101#340—711no—
102#336D7111yescharacteristic
103C22×C8C2×D7111yescharacteristic
104C22×C8C2×D7111yescharacteristic
105C2×C4⋊C4—711no—
106C2×C4⋊C4—711no—
107C2×C4⋊C4—711no—
108C2×C4⋊C4—711no—
109C2×C4⋊C4—1421no—
110C2×C42C2×D7111yescharacteristic
111#95—1421no—
112#95—1421no—
113#95—1421no—
114C22×C4—1421no—
115C22×C4—1421no—
116C22×C4—1421no—
117C22×C4—1421no—
118C22×C4D28411yescharacteristic
119C22×C4D28411yescharacteristic
120C22×C4C22×D7111yescharacteristic
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—21no—
127C4⋊C4—2842no—
128C4⋊C4—712no—
129C4⋊C4—1421no—
130C4⋊C4—1421no—
131C4⋊C4—1421no—
132C4⋊C4—1421no—
133C4⋊C4—1421no—
134C4⋊C4—1421no—
135C4⋊C4—1421no—
136C42—21no—
137C42—21no—
138C23C2×D28411yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2841no—
146C2×C4—2841no—
147C2×C4—2841no—
148C2×C4—2841no—
149C2×C4—2841no—
150C2×C4—2841no—
151C2×C4—2841no—
152C2×C4—2841no—
153C2×C4—2841no—
154C2×C4—2841no—
155C2×C4—2841no—
156C2×C4—1422no—
157C2×C4Q8×D7111yescharacteristic
158C2×C4#1176586411yescharacteristic
159C2×C4#1176586411yescharacteristic
160C2×C4#1176586411yescharacteristic
161C2×C4#1176586511yescharacteristic
162C2×C4#1176586511yescharacteristic
163C8—41no—
164C8—41no—
165C22#1455610811yescharacteristic
166C22#1455611211yescharacteristic
167C22#1455611611yescharacteristic
168C22#1455615011yescharacteristic
169C22#1455615011yescharacteristic
170C22#1455615611yescharacteristic
171C22#1455616111yescharacteristic
172C4—41no—
173C4—41no—
174C4—2842no—
175C4—5681no—
176C4—5681no—
177C4—5681no—
178C4#1455611811yescharacteristic
179C4#1455611811yescharacteristic
180C4#1455612111yescharacteristic
181C4#1455612111yescharacteristic
182C2#1798593911yescharacteristic
183C2#1798630011yescharacteristic
184C2#1798630711yescharacteristic
185C2#1798632411yescharacteristic
186C2#1798634111yescharacteristic
187C2#1798635411yescharacteristic
188C2#1798635911yescharacteristic
subgroupG/H
centerC23C2×D284
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#336×C71C2
socleC23×C71C2×D4
hypercenter#336D71
hypocenterC71#2101
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
95. C71#2101semidirect