Finite Group Databasebeta

← #22589639

Subgroups — #22589639

Order 9088.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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×#14556159C211yesmaximal, characteristic
2C2×#14556063C211yesmaximal, characteristic, complemented
3#17986001C211yesmaximal, characteristic
4C2×#14556052C211yesmaximal, characteristic, complemented
5#17985967C211yesmaximal, characteristic
6#17985767C211yesmaximal, characteristic, complemented
7C2×#101×C71C211yesmaximal, characteristic, complemented
8C2×#11765865C2211yescharacteristic
9#14556159—22no—
10#14556159—22no—
11C2×#11765855—21no—
12C2×#11765852—21no—
13C2×#11765849C2211yescharacteristic
14C22×C71⋊C8C2211yescharacteristic
15C2×C4⋊Dic71C2211yescharacteristic
16#14556063—22no—
17#14556053—21no—
18#14556052—22no—
19#14556050—21no—
20(C2×D71)⋊C8—22no—
21C22×Q8×C71C2211yescharacteristic
22C2×M16×C71C2211yescharacteristic
23C2×M16×C71C2211yescharacteristic
24#101×C71—22no—
25#11765865—21no—
26#11765865—21no—
27#11765865—21no—
28#11765865—21no—
29C2×Dic142D411yescharacteristic
30C2×D284D411yescharacteristic
31C2×C22⋊D71—21no—
32C22×Dic71—21no—
33C2×C4×D71—21no—
34#11765855—24no—
35#11765852—24no—
36#11765849—21no—
37#11765849D412yes—
38C2×C71⋊C8—21no—
39C2×C71⋊C8—21no—
40C2×C71⋊C8—21no—
41C2×C71⋊C8D412yes—
42C4⋊Dic71—21no—
43C4⋊Dic71—21no—
44C2×Q8×C71—21no—
45C2×Q8×C71—21no—
46C2×Q8×C71—21no—
47C2×Q8×C71—21no—
48C2×Q8×C71—21no—
49C2×Q8×C71D412yes—
50C22×C4×C71—21no—
51C22×C4×C71C2311yescharacteristic
52M16×C71—21no—
53M16×C71—21no—
54M16×C71—21no—
55M16×C71—21no—
56C2×C8×C71—21no—
57C2×C8×C71—21no—
58C23×C71#4111yescharacteristic
59C22×D71—21no—
60Q8×C71—22no—
61Q8×C71—22no—
62Q8×C71—41no—
63Q8×C71—41no—
64C2×C4×C71—22no—
65C2×C4×C71—41no—
66C2×C4×C71—41no—
67C2×C4×C71C2×D411yescharacteristic
68C2×C4×C71C2×D411yescharacteristic
69C2×C4×C71C2×D411yescharacteristic
70C2×C4×C71C2×D411yescharacteristic
71C2×C4×C71#4111yescharacteristic
72C2×C4×C71#4111yescharacteristic
73C22⋊D71—41no—
74C22⋊D71—41no—
75C2×Dic71—21no—
76C2×Dic71—41no—
77C2×Dic71—81no—
78D284—21no—
79D284—21no—
80C4×D71—41no—
81C4×D71—41no—
82Dic142—21no—
83Dic142—21no—
84C8×C71—41no—
85C8×C71—41no—
86C71⋊C8—22no—
87C71⋊C8—22no—
88C22×C71—21no—
89C22×C71—21no—
90C22×C71#12111yescharacteristic
91C22×C71#12311yescharacteristic
92C22×C71#12411yescharacteristic
93C2×D71—41no—
94C2×D71—41no—
95C2×D71—41no—
96C4×C71—42no—
97C4×C71#12011yescharacteristic
98C4×C71#12111yescharacteristic
99C4×C71#12111yescharacteristic
100C4×C71#12311yescharacteristic
101Dic71—41no—
102Dic71—81no—
103C2×C71—21no—
104C2×C71—21no—
105C2×C71#39411yescharacteristic
106C2×C71#47111yescharacteristic
107C2×C71#47311yescharacteristic
108D71—81no—
109#2052—711nomaximal, Sylow
110C71#205211yescharacteristic, complemented, Sylow
111C2×#137—711no—
112C2×#108—711no—
113#417—711no—
114C2×#103—711no—
115C2×#101D7111yescharacteristic, complemented
116#408—711no—
117#343—711no—
118C2×#41—711no—
119C22×Q8C2×D7111yescharacteristic
120#137—1422no—
121#137—1422no—
122C2×Q16—1421no—
123C2×SD16—1421no—
124C2×M16—711no—
125C2×M16C2×D7111yescharacteristic
126C2×M16C2×D7111yescharacteristic
127C22×C8—711no—
128C2×C4⋊C4—711no—
129#108—1422no—
130#103—1421no—
131#103—1422no—
132#102—1421no—
133#101—22no—
134C22⋊C8—1422no—
135#41—1421no—
136#41—1421no—
137#41—1421no—
138#41—1421no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—711no—
145C2×Q8C22⋊D7112yes—
146C2×D4—711no—
147C2×D4—1421no—
148C22×C4—21no—
149C22×C4—1421no—
150C22×C4—1421no—
151C22×C4C22×D7111yescharacteristic
152Q16—1424no—
153SD16—1424no—
154M16—21no—
155M16—21no—
156M16—21no—
157M16—21no—
158M16—712no—
159M16—1421no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—712no—
163C2×C8—1421no—
164C2×C8—1421no—
165C2×C8—1421no—
166C4⋊C4—1421no—
167C4⋊C4—1421no—
168C23—1421no—
169C23#1176586511yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—41no—
173Q8—41no—
174Q8—1421no—
175Q8—1421no—
176D4—2841no—
177D4—2841no—
178D4—1421no—
179D4—1421no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—2841no—
184C2×C4—2841no—
185C2×C4—2841no—
186C2×C4—5681no—
187C2×C4—1421no—
188C2×C4D4×D7111yescharacteristic
189C2×C4D4×D7111yescharacteristic
190C2×C4D4×D7111yescharacteristic
191C2×C4C2×C22⋊D7111yescharacteristic
192C2×C4#1176586411yescharacteristic
193C2×C4#1176586511yescharacteristic
194C8—41no—
195C8—41no—
196C8—1422no—
197C8—1422no—
198C22—21no—
199C22—21no—
200C22—2841no—
201C22—2841no—
202C22—2841no—
203C22#1455610111yescharacteristic
204C22#1455611111yescharacteristic
205C22#1455611411yescharacteristic
206C4—42no—
207C4—2841no—
208C4—5681no—
209C4#1455609611yescharacteristic
210C4#1455610011yescharacteristic
211C4#1455610111yescharacteristic
212C4#1455611011yescharacteristic
213C2—21no—
214C2—21no—
215C2—5681no—
216C2#1798591411yescharacteristic
217C2#1798626511yescharacteristic
218C2#1798627311yescharacteristic
subgroupG/H
centerC22#14556101
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC2×#101×C71C2
socleC22×C71#121
hypercenterC2×#101D71
hypocenterC71#2052
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#14556063C2semidirect
4. C2×#14556052C2semidirect
6. #17985767C2semidirect
7. C2×#101×C71C2semidirect
110. C71#2052semidirect
115. C2×#101D71semidirect