Finite Group Databasebeta

← #22589991

Subgroups — #22589991

Order 9088.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#17986563C211yesmaximal, characteristic
2#17985973C211yesmaximal, characteristic, complemented
3#17985787C214yesmaximal, complemented
4#413×C71C211yesmaximal, characteristic, complemented
5C22×D284C411yescharacteristic, complemented
6#14556124—21no—
7#14556117—21no—
8#14556102—21no—
9#14556102—21no—
10#14556096C412yescomplemented
11#14556096C2212yes—
12#14556087—21no—
13#14556087C411yescharacteristic, complemented
14#14556043—21no—
15#14556043C2212yes—
16C2×#41×C71C2211yescharacteristic
17C2×M16×C71—21no—
18#101×C71—21no—
19#100×C71C2212yes—
20C23×D71C2×C412yes—
21C2×D284—21no—
22C2×D284—21no—
23C2×D284—41no—
24C2×D284—41no—
25C2×C22⋊D71—22no—
26C2×C22⋊D71—22no—
27C4⋊Dic71—21no—
28C4⋊Dic71—41no—
29C22⋊Dic71—22no—
30C22⋊Dic71C2×C412yes—
31(C2×D71)⋊C4—22no—
32(C2×D71)⋊C4—22no—
33C4×Dic71—21no—
34C4×Dic71—41no—
35#41×C71—41no—
36#41×C71—41no—
37C2×Q8×C71D411yescharacteristic
38C2×D4×C71C2×C411yescharacteristic
39C2×D4×C71D411yescharacteristic
40C2×D4×C71C2311yescharacteristic
41C22×C4×C71C2×C411yescharacteristic
42C22×C4×C71D411yescharacteristic
43C22×C4×C71D411yescharacteristic
44M16×C71—22no—
45M16×C71—41no—
46C2×C8×C71—41no—
47C23×C71C22⋊C411yescharacteristic
48C23×C71C22×C411yescharacteristic
49C23×C71C2×D411yescharacteristic
50C22×D71—22no—
51C22×D71—42no—
52C22×D71—82no—
53Q8×C71—41no—
54D4×C71—41no—
55D4×C71—41no—
56D4×C71—41no—
57C2×C4×C71—21no—
58C2×C4×C71—21no—
59C2×C4×C71—21no—
60C2×C4×C71—21no—
61C2×C4×C71—21no—
62C2×C4×C71—21no—
63C2×C4×C71C22⋊C411yescharacteristic
64C2×C4×C71C22⋊C411yescharacteristic
65C2×C4×C71C22⋊C411yescharacteristic
66C2×C4×C71C2×D411yescharacteristic
67C22⋊D71—82no—
68C22⋊D71—82no—
69C2×Dic71—22no—
70C2×Dic71—42no—
71D284—42no—
72D284—41no—
73D284—41no—
74C8×C71—42no—
75C22×C71—21no—
76C22×C71—21no—
77C22×C71—21no—
78C22×C71—41no—
79C22×C71—41no—
80C22×C71—41no—
81C22×C71C2×C22⋊C411yescharacteristic
82C2×D71—42no—
83C2×D71—42no—
84C2×D71—42no—
85C2×D71—84no—
86C4×C71—21no—
87C4×C71—21no—
88C4×C71—21no—
89C4×C71#9911yescharacteristic
90C4×C71#9911yescharacteristic
91Dic71—42no—
92Dic71—82no—
93C2×C71—21no—
94C2×C71—41no—
95C2×C71—41no—
96C2×C71—41no—
97C2×C71C2×#9911yescharacteristic
98D71—82no—
99#2122—711nomaximal, Sylow
100C71#212211yescharacteristic, complemented, Sylow
101#535—711no—
102#413D7111yescharacteristic, complemented
103#410—711no—
104AΣL(1,𝔽16)—714no—
105C2×#41C2×D7111yescharacteristic
106C22×D4—711no—
107C2×M16—21no—
108#127—1421no—
109#124—1421no—
110#121—1421no—
111#121—1421no—
112#120—712no—
113#120—712no—
114#117—711no—
115#117—1421no—
116#101—21no—
117#100C2×D7112yes—
118#99—712no—
119#99—1421no—
120C24—712no—
121#41—41no—
122#41—41no—
123C2×Q8C22⋊D7111yescharacteristic
124C2×D4—2841no—
125C2×D4—2841no—
126C2×D4—1422no—
127C2×D4—1422no—
128C2×D4—1421no—
129C2×D4—1421no—
130C2×D4C4×D7111yescharacteristic
131C2×D4D28411yescharacteristic
132C2×D4C22×D7111yescharacteristic
133C22×C4C4×D7111yescharacteristic
134C22×C4D28411yescharacteristic
135C22×C4C22⋊D7111yescharacteristic
136M16—22no—
137M16—41no—
138C2×C8—41no—
139C4⋊C4—2841no—
140C4⋊C4—1421no—
141C22⋊C4—712no—
142C22⋊C4—1422no—
143C22⋊C4—1422no—
144C22⋊C4—1422no—
145C42—2841no—
146C42—1421no—
147C23—2842no—
148C23—5682no—
149C23—1422no—
150C23(C2×D71)⋊C411yescharacteristic
151C23C2×C4×D7111yescharacteristic
152C23C2×D28411yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—2842no—
158D4—2841no—
159D4—2841no—
160D4—5682no—
161D4—5682no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—2842no—
169C2×C4—1422no—
170C2×C4(C2×D71)⋊C411yescharacteristic
171C2×C4(C2×D71)⋊C411yescharacteristic
172C2×C4(C2×D71)⋊C411yescharacteristic
173C2×C4C2×C22⋊D7111yescharacteristic
174C8—42no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—2842no—
182C22—2842no—
183C22—2842no—
184C22—5684no—
185C22C2×(C2×D71)⋊C411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—2842no—
190C4—5682no—
191C4#1455604211yescharacteristic
192C4#1455604211yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—5682no—
198C2C2×#1455604211yescharacteristic
subgroupG/H
centerC2C2×#14556042
commutatorC23×C71C22×C4
FrattiniC2×D4C22×D71
Fitting#413×C71C2
socleC2×C71C2×#99
hypercenter#413D71
hypocenterC71#2122
LCSG ▷ C23×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #17985973C2semidirect
3. #17985787C2semidirect
4. #413×C71C2semidirect
5. C22×D284C4semidirect
10. #14556096C4semidirect
13. #14556087C4semidirect
100. C71#2122semidirect
102. #413D71semidirect