Finite Group Databasebeta

← #22589783

Subgroups — #22589783

Order 9088.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14556061C211yesmaximal, characteristic, complemented
2#17986000C211yesmaximal, characteristic
3#17985966C211yesmaximal, characteristic
4#17985768C211yesmaximal, characteristic, complemented
5#17985767C211yesmaximal, characteristic, complemented
6#17985763C211yesmaximal, characteristic, complemented
7#417×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10C22×C71⋊C8C2211yescharacteristic
11C2×C4⋊Dic71C2211yescharacteristic
12#14556061—22no—
13#14556052—21no—
14#14556049—21no—
15C22⋊(C71⋊C8)—22no—
16C2×#41×C71C2211yescharacteristic
17C2×M16×C71C2211yescharacteristic
18C2×C4⋊C4×C71C2211yescharacteristic
19#103×C71—21no—
20#102×C71—21no—
21C22×Dic71—21no—
22#11765849—21no—
23#11765849—21no—
24#11765849—21no—
25#11765849—21no—
26C2×C71⋊C8—21no—
27C2×C71⋊C8—21no—
28C2×C71⋊C8—21no—
29C2×C71⋊C8—21no—
30C2×C71⋊C8D412yes—
31C4⋊Dic71—21no—
32C4⋊Dic71—21no—
33#41×C71—21no—
34#41×C71—21no—
35#41×C71—21no—
36#41×C71—21no—
37C2×Q8×C71D411yescharacteristic
38C2×D4×C71—21no—
39C2×D4×C71D411yescharacteristic
40C22×C4×C71—21no—
41C22×C4×C71—21no—
42C22×C4×C71C2311yescharacteristic
43M16×C71—21no—
44M16×C71—21no—
45C2×C8×C71—21no—
46C4⋊C4×C71—21no—
47C4⋊C4×C71—21no—
48C23×C71—21no—
49C23×C71#4111yescharacteristic
50Q8×C71—21no—
51Q8×C71—21no—
52D4×C71—21no—
53D4×C71—21no—
54D4×C71—41no—
55D4×C71—41no—
56C2×C4×C71—21no—
57C2×C4×C71—41no—
58C2×C4×C71—41no—
59C2×C4×C71—41no—
60C2×C4×C71—81no—
61C2×C4×C71C2×D411yescharacteristic
62C2×C4×C71C2×D411yescharacteristic
63C2×C4×C71#4111yescharacteristic
64C2×C4×C71#4111yescharacteristic
65C2×C4×C71#4111yescharacteristic
66C2×C4×C71#4111yescharacteristic
67C2×Dic71—41no—
68C2×Dic71—81no—
69C8×C71—41no—
70C71⋊C8—22no—
71C71⋊C8—41no—
72C71⋊C8—41no—
73C22×C71—21no—
74C22×C71—21no—
75C22×C71—41no—
76C22×C71—41no—
77C22×C71—41no—
78C22×C71#12111yescharacteristic
79C22×C71#12611yescharacteristic
80C22×C71#12611yescharacteristic
81C4×C71—41no—
82C4×C71—81no—
83C4×C71#12311yescharacteristic
84C4×C71#12311yescharacteristic
85C4×C71#12311yescharacteristic
86C4×C71#12411yescharacteristic
87Dic71—81no—
88C2×C71—21no—
89C2×C71—21no—
90C2×C71—81no—
91C2×C71#39711yescharacteristic
92C2×C71#47211yescharacteristic
93C2×C71#47311yescharacteristic
94#2078—711nomaximal, Sylow
95C71#207811yescharacteristic, complemented, Sylow
96C2×#107—711no—
97#417—711no—
98#417D7111yescharacteristic
99#408—711no—
100#343—711no—
101#343—711no—
102#341—711no—
103C2×#41C2×D7111yescharacteristic
104C2×M16—711no—
105C2×M16—711no—
106C2×M16C2×D7111yescharacteristic
107C22×C8—711no—
108C2×C4⋊C4—711no—
109C2×C4⋊C4C2×D7111yescharacteristic
110#107—1422no—
111#103—21no—
112#103—1421no—
113#102—21no—
114#102—1421no—
115C22⋊C8—1422no—
116#41—21no—
117#41—21no—
118#41—21no—
119#41—21no—
120C2×Q8C22⋊D7111yescharacteristic
121C2×D4—21no—
122C2×D4C22⋊D7111yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—1421no—
126C22×C4C22×D7111yescharacteristic
127M16—21no—
128M16—21no—
129M16—1421no—
130M16—1421no—
131M16—1421no—
132M16—1421no—
133C2×C8—21no—
134C2×C8—712no—
135C2×C8—1421no—
136C2×C8—1421no—
137C2×C8—1421no—
138C2×C8—1421no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—1421no—
142C4⋊C4—1421no—
143C23—21no—
144C23#1176586411yescharacteristic
145Q8—21no—
146Q8—21no—
147D4—21no—
148D4—21no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4—2841no—
157C2×C4—5681no—
158C2×C4D4×D7111yescharacteristic
159C2×C4C2×C22⋊D7111yescharacteristic
160C2×C4#1176586411yescharacteristic
161C2×C4#1176586411yescharacteristic
162C2×C4#1176586511yescharacteristic
163C2×C4#1176586511yescharacteristic
164C8—41no—
165C8—2841no—
166C8—2841no—
167C8—1422no—
168C22—21no—
169C22—21no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22#1455610011yescharacteristic
174C22#1455612111yescharacteristic
175C22#1455612111yescharacteristic
176C4—41no—
177C4—81no—
178C4—5681no—
179C4#1455610911yescharacteristic
180C4#1455611011yescharacteristic
181C4#1455611111yescharacteristic
182C4#1455611411yescharacteristic
183C2—21no—
184C2—21no—
185C2—81no—
186C2#1798592711yescharacteristic
187C2#1798626711yescharacteristic
188C2#1798627211yescharacteristic
subgroupG/H
centerC22#14556100
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#417×C71C2
socleC22×C71#121
hypercenter#417D71
hypocenterC71#2078
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#14556061C2semidirect
4. #17985768C2semidirect
5. #17985767C2semidirect
6. #17985763C2semidirect
95. C71#2078semidirect