Finite Group Databasebeta

← #22589636

Subgroups — #22589636

Order 9088.

262 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 71 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, complemented
2#17986000C211yesmaximal, characteristic
3C2×#14556052C211yesmaximal, characteristic, complemented
4C2×#14556047C211yesmaximal, characteristic, complemented
5#17985966C211yesmaximal, characteristic
6#17985767C211yesmaximal, characteristic, complemented
7C2×#137×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10C22×C71⋊C8C2211yescharacteristic
11C2×C4⋊Dic71C2211yescharacteristic
12#14556063—22no—
13#14556052—22no—
14#14556052—21no—
15#14556049—21no—
16#14556047—22no—
17C22⋊(C71⋊C8)—22no—
18C2×#41×C71C2211yescharacteristic
19C22×Q8×C71C2211yescharacteristic
20#137×C71—22no—
21#137×C71—22no—
22C2×Q16×C71—21no—
23C2×SD16×C71—21no—
24C2×M16×C71C2211yescharacteristic
25C22×Dic71—21no—
26#11765849—21no—
27#11765849—21no—
28#11765849—21no—
29#11765849—21no—
30C2×C71⋊C8—21no—
31C2×C71⋊C8—21no—
32C2×C71⋊C8—21no—
33C2×C71⋊C8—21no—
34C2×C71⋊C8D412yes—
35C4⋊Dic71—21no—
36C4⋊Dic71—21no—
37#41×C71—21no—
38#41×C71—21no—
39#41×C71—21no—
40#41×C71—21no—
41C2×Q8×C71—21no—
42C2×Q8×C71—21no—
43C2×Q8×C71—21no—
44C2×Q8×C71—21no—
45C2×Q8×C71—21no—
46C2×Q8×C71D411yescharacteristic
47C2×Q8×C71D412yes—
48C2×D4×C71—21no—
49C2×D4×C71D411yescharacteristic
50C22×C4×C71—21no—
51C22×C4×C71—21no—
52C22×C4×C71C2311yescharacteristic
53Q16×C71—24no—
54SD16×C71—24no—
55M16×C71—21no—
56M16×C71D412yes—
57C2×C8×C71—21no—
58C23×C71—21no—
59C23×C71#4111yescharacteristic
60Q8×C71—22no—
61Q8×C71—21no—
62Q8×C71—22no—
63Q8×C71—21no—
64Q8×C71—41no—
65Q8×C71—41no—
66D4×C71—21no—
67D4×C71—21no—
68D4×C71—41no—
69D4×C71—41no—
70C2×C4×C71—21no—
71C2×C4×C71—22no—
72C2×C4×C71—41no—
73C2×C4×C71—41no—
74C2×C4×C71—41no—
75C2×C4×C71—41no—
76C2×C4×C71C2×D411yescharacteristic
77C2×C4×C71C2×D411yescharacteristic
78C2×C4×C71C2×D411yescharacteristic
79C2×C4×C71C2×D411yescharacteristic
80C2×C4×C71#4111yescharacteristic
81C2×C4×C71#4111yescharacteristic
82C2×Dic71—41no—
83C2×Dic71—81no—
84C8×C71—22no—
85C71⋊C8—22no—
86C71⋊C8—41no—
87C71⋊C8—41no—
88C22×C71—21no—
89C22×C71—21no—
90C22×C71—41no—
91C22×C71—41no—
92C22×C71—41no—
93C22×C71#12111yescharacteristic
94C22×C71#12311yescharacteristic
95C22×C71#12411yescharacteristic
96C4×C71—41no—
97C4×C71—42no—
98C4×C71#12011yescharacteristic
99C4×C71#12111yescharacteristic
100C4×C71#12111yescharacteristic
101C4×C71#12311yescharacteristic
102Dic71—81no—
103C2×C71—21no—
104C2×C71—21no—
105C2×C71—81no—
106C2×C71#39411yescharacteristic
107C2×C71#47111yescharacteristic
108C2×C71#47311yescharacteristic
109#2052—711nomaximal, Sylow
110C71#205211yescharacteristic, complemented, Sylow
111C2×#137D7111yescharacteristic
112C2×#108—711no—
113#417—711no—
114C2×#103—711no—
115C2×#101—711no—
116#408—711no—
117#343—711no—
118C2×#41C2×D7111yescharacteristic
119C22×Q8C2×D7111yescharacteristic
120#137—22no—
121#137—22no—
122C2×Q16—21no—
123C2×SD16—21no—
124C2×M16—711no—
125C2×M16—711no—
126C2×M16C2×D7111yescharacteristic
127C22×C8—711no—
128C2×C4⋊C4—711no—
129#108—1422no—
130#103—1422no—
131#103—1421no—
132#102—1421no—
133#101—1422no—
134C22⋊C8—1422no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8C22⋊D7112yes—
145C2×Q8C22⋊D7111yescharacteristic
146C2×D4—21no—
147C2×D4C22⋊D7111yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—1421no—
151C22×C4C22×D7111yescharacteristic
152Q16—24no—
153SD16—24no—
154M16—21no—
155M16—1421no—
156M16—1421no—
157M16—1421no—
158M16—1421no—
159M16C22⋊D7112yes—
160C2×C8—21no—
161C2×C8—712no—
162C2×C8—1421no—
163C2×C8—1421no—
164C2×C8—1421no—
165C2×C8—1421no—
166C4⋊C4—1421no—
167C4⋊C4—1421no—
168C23—21no—
169C23#1176586411yescharacteristic
170Q8—22no—
171Q8—21no—
172Q8—22no—
173Q8—21no—
174Q8—41no—
175Q8—41no—
176D4—21no—
177D4—21no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2841no—
187C2×C4—5681no—
188C2×C4D4×D7111yescharacteristic
189C2×C4C2×C22⋊D7111yescharacteristic
190C2×C4C2×C22⋊D7111yescharacteristic
191C2×C4C2×C22⋊D7111yescharacteristic
192C2×C4#1176586411yescharacteristic
193C2×C4#1176586411yescharacteristic
194C8—22no—
195C8—2841no—
196C8—2841no—
197C8—1422no—
198C22—21no—
199C22—21no—
200C22—41no—
201C22—41no—
202C22—41no—
203C22#1455610011yescharacteristic
204C22#1455610911yescharacteristic
205C22#1455611511yescharacteristic
206C4—41no—
207C4—42no—
208C4—5681no—
209C4#1455609711yescharacteristic
210C4#1455609911yescharacteristic
211C4#1455610011yescharacteristic
212C4#1455610911yescharacteristic
213C2—21no—
214C2—21no—
215C2—81no—
216C2#1798591311yescharacteristic
217C2#1798626411yescharacteristic
218C2#1798627211yescharacteristic
subgroupG/H
centerC22#14556100
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC2×#137×C71C2
socleC22×C71#121
hypercenterC2×#137D71
hypocenterC71#2052
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#14556063C2semidirect
3. C2×#14556052C2semidirect
4. C2×#14556047C2semidirect
6. #17985767C2semidirect
110. C71#2052semidirect