Finite Group Databasebeta

← #22589117

Subgroups — #22589117

Order 9088.

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

normal subgroups only

This group has 196 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×#14556063C211yesmaximal, characteristic
2#17986042C211yesmaximal, characteristic
3C2×#14556059C211yesmaximal, characteristic
4#17985955C211yesmaximal, characteristic
5#17985768C211yesmaximal, characteristic
6#17985767C211yesmaximal, characteristic
7#428×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10C22×C71⋊C8C2211yescharacteristic
11C2×C4⋊Dic71C2211yescharacteristic
12#14556063C414yescomplemented
13#14556061—21no—
14#14556059—21no—
15#14556059—21no—
16#14556059—21no—
17#14556039—21no—
18C4×C71⋊C8—21no—
19C2×M16×C71C2211yescharacteristic
20#117×C71C2211yescharacteristic
21C2×C4⋊C4×C71C2211yescharacteristic
22#107×C71—21no—
23#106×C71—21no—
24C22×Dic71—21no—
25#11765849—21no—
26#11765849—21no—
27#11765849C2×C412yes—
28#11765849Q812yes—
29C2×C71⋊C8—21no—
30C2×C71⋊C8—21no—
31C2×C71⋊C8C2×C412yes—
32C2×C71⋊C8D411yescharacteristic
33C2×C71⋊C8D411yescharacteristic
34C2×C71⋊C8Q812yes—
35C4⋊Dic71—21no—
36C4⋊Dic71—21no—
37C22×C4×C71—21no—
38C22×C4×C71C2311yescharacteristic
39M16×C71—21no—
40M16×C71C2×C412yes—
41C2×C8×C71—21no—
42C4⋊C4×C71—21no—
43C4⋊C4×C71—21no—
44C4⋊C4×C71D411yescharacteristic
45C4⋊C4×C71D411yescharacteristic
46C22⋊C4×C71—21no—
47C42×C71—21no—
48C23×C71#4111yescharacteristic
49C2×C4×C71—21no—
50C2×C4×C71—21no—
51C2×C4×C71—41no—
52C2×C4×C71—81no—
53C2×C4×C71C22×C411yescharacteristic
54C2×C4×C71C2×D411yescharacteristic
55C2×C4×C71C2×D411yescharacteristic
56C2×C4×C71C2×Q811yescharacteristic
57C2×C4×C71C2×Q811yescharacteristic
58C2×C4×C71#4111yescharacteristic
59C2×Dic71—41no—
60C2×Dic71—81no—
61C8×C71—22no—
62C71⋊C8—22no—
63C71⋊C8—22no—
64C71⋊C8C4⋊C412yes—
65C71⋊C8C4⋊C412yes—
66C22×C71—21no—
67C22×C71—21no—
68C22×C71C4×Q811yescharacteristic
69C22×C71#12111yescharacteristic
70C22×C71#12511yescharacteristic
71C4×C71—41no—
72C4×C71—41no—
73C4×C71—81no—
74C4×C71C2×C4⋊C411yescharacteristic
75C4×C71C4×D411yescharacteristic
76C4×C71C22⋊Q811yescharacteristic
77C4×C71C4⋊Q811yescharacteristic
78Dic71—81no—
79C2×C71—21no—
80C2×C71—21no—
81C2×C71#38911yescharacteristic
82C2×C71#47111yescharacteristic
83C2×C71#47111yescharacteristic
84#1951—711nomaximal, Sylow
85C71#195111yescharacteristic, complemented, Sylow
86C2×#108—711no—
87#428—711no—
88#428D7111yescharacteristic
89C2×#106—711no—
90#405—711no—
91#343—711no—
92#343—711no—
93C2×M16—711no—
94C2×M16—711no—
95C2×M16C2×D7111yescharacteristic
96C22×C8—711no—
97#117C2×D7111yescharacteristic
98C2×C4⋊C4—711no—
99C2×C4⋊C4C2×D7111yescharacteristic
100#108—714no—
101#107—21no—
102#107—1421no—
103#106—21no—
104#106—1421no—
105#106—1421no—
106#106—1421no—
107#97—1421no—
108C4×C8—1421no—
109C22×C4—21no—
110C22×C4—1421no—
111C22×C4C22×D7111yescharacteristic
112M16—21no—
113M16—712no—
114M16—712no—
115M16—1421no—
116M16—1421no—
117M16C4×D7112yes—
118C2×C8—21no—
119C2×C8—712no—
120C2×C8—711no—
121C2×C8—711no—
122C2×C8—712no—
123C2×C8—1421no—
124C2×C8—1421no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1421no—
128C4⋊C4—1421no—
129C4⋊C4C22⋊D7111yescharacteristic
130C4⋊C4C22⋊D7111yescharacteristic
131C22⋊C4—21no—
132C42—21no—
133C23#1176586411yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—2841no—
139C2×C4—5681no—
140C2×C4C2×C4×D7111yescharacteristic
141C2×C4D4×D7111yescharacteristic
142C2×C4C2×C22⋊D7111yescharacteristic
143C2×C4Q8×D7111yescharacteristic
144C2×C4Q8×D7111yescharacteristic
145C2×C4#1176586511yescharacteristic
146C8—22no—
147C8—712no—
148C8—712no—
149C8—1422no—
150C8—1422no—
151C22—21no—
152C22—21no—
153C22#1455609311yescharacteristic
154C22#1455610011yescharacteristic
155C22#1455611811yescharacteristic
156C4—41no—
157C4—41no—
158C4—81no—
159C4—5681no—
160C4C4⋊C4×D7111yescharacteristic
161C4C4×C22⋊D7111yescharacteristic
162C4#1455610611yescharacteristic
163C4#1455612611yescharacteristic
164C2—21no—
165C2—21no—
166C2#1798589411yescharacteristic
167C2#1798626011yescharacteristic
168C2#1798626411yescharacteristic
subgroupG/H
centerC22#14556100
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#428×C71C2
socleC22×C71#121
hypercenter#428D71
hypocenterC71#1951
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
12. #14556063C4semidirect
85. C71#1951semidirect