Finite Group Databasebeta

← #22589858

Subgroups — #22589858

Order 9088.

274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14556059C211yesmaximal, characteristic, complemented
2C2×#14556050C211yesmaximal, characteristic
3C2×#14556048C211yesmaximal, characteristic
4#17985900C211yesmaximal, characteristic
5#17985864C211yesmaximal, characteristic, complemented
6#17985753C211yesmaximal, characteristic, complemented
7C2×#107×C71C211yesmaximal, characteristic, complemented
8C22×D284C2211yescharacteristic
9C22×C71⋊C8C2211yescharacteristic
10C2×C4⋊Dic71C2211yescharacteristic
11C2×(C2×D71)⋊C4—22no—
12C2×C4×Dic71C2211yescharacteristic
13#14556059—22no—
14#14556050—22no—
15#14556048—22no—
16C71⋊#95—22no—
17C22×C8×C71C2211yescharacteristic
18C2×C4⋊C4×C71C2211yescharacteristic
19C2×C4⋊C4×C71C2211yescharacteristic
20#107×C71—22no—
21C23×D71—21no—
22C2×D284—21no—
23C2×D284—21no—
24C2×D284—21no—
25C2×D284—21no—
26C2×D284—21no—
27C2×D284Q812yes—
28C22×Dic71—21no—
29C22×Dic71D412yes—
30C2×C71⋊C8—21no—
31C2×C71⋊C8—21no—
32C2×C71⋊C8D412yes—
33C4⋊Dic71—21no—
34C4⋊Dic71—21no—
35(C2×D71)⋊C4—44no—
36C4×Dic71—21no—
37C4×Dic71—21no—
38C22×C4×C71—21no—
39C22×C4×C71—21no—
40C22×C4×C71C2311yescharacteristic
41C2×C8×C71—21no—
42C2×C8×C71—21no—
43C2×C8×C71D412yes—
44C4⋊C4×C71—21no—
45C4⋊C4×C71—21no—
46C4⋊C4×C71—21no—
47C4⋊C4×C71—21no—
48C23×C71C2×D411yescharacteristic
49C22×D71—22no—
50C22×D71—41no—
51C22×D71—41no—
52C22×D71—42no—
53C22×D71—42no—
54C2×C4×C71—41no—
55C2×C4×C71—41no—
56C2×C4×C71—42no—
57C2×C4×C71—42no—
58C2×C4×C71C2×D411yescharacteristic
59C2×C4×C71C2×D411yescharacteristic
60C2×C4×C71C2×Q811yescharacteristic
61C2×C4×C71#4111yescharacteristic
62C2×C4×C71#4111yescharacteristic
63C2×C4×C71#4111yescharacteristic
64C2×Dic71—22no—
65C2×Dic71—22no—
66C2×Dic71—22no—
67C2×Dic71—41no—
68C2×Dic71—42no—
69D284—22no—
70D284—22no—
71D284—41no—
72D284—41no—
73C8×C71—22no—
74C71⋊C8—22no—
75C22×C71C22⋊Q811yescharacteristic
76C22×C71#12311yescharacteristic
77C22×C71#12711yescharacteristic
78C22×C71#13512yes—
79C22×C71AGL(1,ℤ/8)12yes—
80C2×D71—42no—
81C2×D71—44no—
82C2×D71—82no—
83C2×D71—81no—
84C2×D71—81no—
85C4×C71—81no—
86C4×C71—81no—
87C4×C71C22⋊Q811yescharacteristic
88C4×C71C22⋊Q811yescharacteristic
89C4×C71#12311yescharacteristic
90C4×C71#12311yescharacteristic
91Dic71—42no—
92Dic71—81no—
93C2×C71#39911yescharacteristic
94C2×C71#47812yes—
95C2×C71#48212yes—
96C2×C71#49511yescharacteristic
97C2×C71#49611yescharacteristic
98D71—82no—
99#2092—711nomaximal, Sylow
100C71#209211yescharacteristic, complemented, Sylow
101C2×#107D7111yescharacteristic, complemented
102C2×#106—711no—
103C2×#102—711no—
104C2×#102—711no—
105#390—711no—
106#382—711no—
107#336—711no—
108C22×D4—711no—
109C22×C8—711no—
110C22×C8C2×D7111yescharacteristic
111C2×C4⋊C4—711no—
112C2×C4⋊C4C2×D7111yescharacteristic
113C2×C4⋊C4C2×D7111yescharacteristic
114C2×C22⋊C4—1422no—
115C2×C42—711no—
116#107—22no—
117#106—1422no—
118#102—1422no—
119#102—1422no—
120#95—1422no—
121C24—1421no—
122C2×D4—712no—
123C2×D4—1421no—
124C2×D4—1421no—
125C2×D4—1421no—
126C2×D4—1421no—
127C2×D4—1421no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—712no—
131C22×C4—1421no—
132C22×C4C22×D7111yescharacteristic
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—712no—
136C2×C8—1421no—
137C2×C8—1421no—
138C2×C8C22⋊D7112yes—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—1421no—
144C4⋊C4—1421no—
145C22⋊C4—2844no—
146C42—1421no—
147C42—1421no—
148C23—2841no—
149C23—2841no—
150C23—2842no—
151C23—2842no—
152C23—1422no—
153C23D4×D7111yescharacteristic
154D4—2841no—
155D4—2841no—
156D4—1422no—
157D4—1422no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—2841no—
163C2×C4—2842no—
164C2×C4—1422no—
165C2×C4—1422no—
166C2×C4—1422no—
167C2×C4D4×D7111yescharacteristic
168C2×C4C2×C22⋊D7111yescharacteristic
169C2×C4Q8×D7111yescharacteristic
170C2×C4#1176586511yescharacteristic
171C2×C4#1176586511yescharacteristic
172C2×C4#1176586611yescharacteristic
173C8—22no—
174C8—1422no—
175C22—2842no—
176C22—2844no—
177C22—5682no—
178C22—5681no—
179C22—5681no—
180C22#1455610611yescharacteristic
181C22#1455611311yescharacteristic
182C22#1455612411yescharacteristic
183C22#1455615112yes—
184C22#1455615212yes—
185C4—81no—
186C4—81no—
187C4—2842no—
188C4—5681no—
189C4#1455610411yescharacteristic
190C4#1455610611yescharacteristic
191C4#1455611111yescharacteristic
192C4#1455611311yescharacteristic
193C2—5682no—
194C2#1798593411yescharacteristic
195C2#1798630212yes—
196C2#1798632612yes—
197C2#1798638411yescharacteristic
198C2#1798638711yescharacteristic
subgroupG/H
centerC23D4×D71
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC2×#107×C71C2
socleC23×C71C2×D4
hypercenterC2×#107D71
hypocenterC71#2092
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#14556059C2semidirect
5. #17985864C2semidirect
6. #17985753C2semidirect
7. C2×#107×C71C2semidirect
100. C71#2092semidirect
101. C2×#107D71semidirect