Finite Group Databasebeta

← #22589584

Subgroups — #22589584

Order 9088.

298 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14556126C211yesmaximal, characteristic
2C2×#14556053C211yesmaximal, characteristic
3C2×#14556052C211yesmaximal, characteristic
4C2×#14556051C211yesmaximal, characteristic
5#17985895C211yesmaximal, characteristic
6#17985753C211yesmaximal, characteristic
7C2×#103×C71C211yesmaximal, characteristic
8C22×Dic142C2211yescharacteristic
9C22×C71⋊C8C2211yescharacteristic
10#14556126—22no—
11#14556126—22no—
12C2×C4⋊Dic71C2211yescharacteristic
13C2×Dic71⋊C4—21no—
14C2×Dic71⋊C4—21no—
15C2×Dic71⋊C4—21no—
16C2×C4×Dic71C2211yescharacteristic
17#14556053—22no—
18#14556052—22no—
19#14556051—22no—
20C71⋊#95—21no—
21C22×Q8×C71C2211yescharacteristic
22C22×C8×C71C2211yescharacteristic
23C2×C4⋊C4×C71C2211yescharacteristic
24#103×C71—22no—
25C2×Dic142—21no—
26C2×Dic142—21no—
27C2×Dic142—21no—
28C2×Dic142—21no—
29C2×Dic142—21no—
30C2×Dic142D412yes—
31C22×Dic71—21no—
32C22×Dic71—21no—
33C22×Dic71D411yescharacteristic
34C22×Dic71D411yescharacteristic
35C2×C71⋊C8—21no—
36C2×C71⋊C8—21no—
37C2×C71⋊C8—21no—
38C4⋊Dic71—21no—
39C4⋊Dic71D412yes—
40Dic71⋊C4—24no—
41Dic71⋊C4—24no—
42Dic71⋊C4—42no—
43C4×Dic71—21no—
44C4×Dic71—21no—
45C2×Q8×C71—21no—
46C2×Q8×C71—21no—
47C2×Q8×C71—21no—
48C2×Q8×C71—21no—
49C2×Q8×C71—21no—
50C2×Q8×C71D412yes—
51C22×C4×C71—21no—
52C22×C4×C71—21no—
53C22×C4×C71C2311yescharacteristic
54C2×C8×C71—21no—
55C2×C8×C71—21no—
56C2×C8×C71—21no—
57C4⋊C4×C71—21no—
58C4⋊C4×C71—21no—
59C23×C71C2×D411yescharacteristic
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×C71—41no—
68C2×C4×C71—41no—
69C2×C4×C71—41no—
70C2×C4×C71C2×D411yescharacteristic
71C2×C4×C71C2×D411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71#4111yescharacteristic
74C2×C4×C71#4111yescharacteristic
75C2×C4×C71#4111yescharacteristic
76C2×Dic71—21no—
77C2×Dic71—21no—
78C2×Dic71—21no—
79C2×Dic71—21no—
80C2×Dic71—22no—
81C2×Dic71—22no—
82C2×Dic71—41no—
83C2×Dic71—41no—
84C2×Dic71—41no—
85C2×Dic71—41no—
86C2×Dic71SD1612yes—
87C2×Dic71Q1612yes—
88Dic142—22no—
89Dic142—22no—
90Dic142—41no—
91Dic142—41no—
92C8×C71—41no—
93C71⋊C8—41no—
94C22×C71#12011yescharacteristic
95C22×C71#12111yescharacteristic
96C22×C71#12411yescharacteristic
97C22×C71C2×SD1611yescharacteristic
98C22×C71C2×Q1611yescharacteristic
99C22×C71#13711yescharacteristic
100C22×C71#13711yescharacteristic
101C4×C71—42no—
102C4×C71—81no—
103C4×C71#12111yescharacteristic
104C4×C71#12111yescharacteristic
105C4×C71#12311yescharacteristic
106C4×C71#12311yescharacteristic
107Dic71—22no—
108Dic71—22no—
109Dic71—42no—
110Dic71—42no—
111C2×C71#39411yescharacteristic
112C2×C71#44811yescharacteristic
113C2×C71#45111yescharacteristic
114C2×C71#46111yescharacteristic
115C2×C71#46211yescharacteristic
116C2×C71#48711yescharacteristic
117C2×C71#49111yescharacteristic
118#2043—711nomaximal, Sylow
119C71#204311yescharacteristic, complemented, Sylow
120C2×C4⋊Q8—711no—
121C2×#103—711no—
122C2×#103—711no—
123C2×#103—711no—
124C2×#103D7111yescharacteristic
125#389—711no—
126#336—711no—
127C22×Q8—711no—
128C22×Q8C2×D7111yescharacteristic
129C22×C8—711no—
130C22×C8C2×D7111yescharacteristic
131C4⋊Q8—1422no—
132C4⋊Q8—1422no—
133C2×C4⋊C4—711no—
134C2×C4⋊C4—1421no—
135C2×C4⋊C4—1421no—
136C2×C4⋊C4—1421no—
137C2×C4⋊C4C2×D7111yescharacteristic
138C2×C42—711no—
139#103—22no—
140#103—1422no—
141#103—1422no—
142#103—1422no—
143#95—1421no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—712no—
150C2×Q8—1421no—
151C2×Q8—1421no—
152C2×Q8—1421no—
153C2×Q8—1421no—
154C2×Q8—1421no—
155C2×Q8C22⋊D7112yes—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—711no—
159C22×C4—711no—
160C22×C4—1421no—
161C22×C4—1421no—
162C22×C4C22×D7111yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—1421no—
167C2×C8—1421no—
168C2×C8—1421no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—2842no—
172C4⋊C4—712no—
173C4⋊C4—1424no—
174C4⋊C4—1424no—
175C4⋊C4—1421no—
176C42—1421no—
177C42—1421no—
178C23D4×D7111yescharacteristic
179Q8—22no—
180Q8—22no—
181Q8—41no—
182Q8—41no—
183Q8—2841no—
184Q8—2841no—
185Q8—1422no—
186Q8—1422no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—2841no—
194C2×C4—2841no—
195C2×C4—2841no—
196C2×C4—2841no—
197C2×C4—712no—
198C2×C4—712no—
199C2×C4—1422no—
200C2×C4—1422no—
201C2×C4—1421no—
202C2×C4—1421no—
203C2×C4—1421no—
204C2×C4—1421no—
205C2×C4D4×D7111yescharacteristic
206C2×C4D4×D7111yescharacteristic
207C2×C4C2×C22⋊D7111yescharacteristic
208C2×C4#1176586411yescharacteristic
209C2×C4#1176586511yescharacteristic
210C2×C4#1176586511yescharacteristic
211C8—41no—
212C8—2841no—
213C22#1455609611yescharacteristic
214C22#1455610111yescharacteristic
215C22#1455611411yescharacteristic
216C22SD16×D7111yescharacteristic
217C22Q16×D7111yescharacteristic
218C22#1455615711yescharacteristic
219C22#1455616011yescharacteristic
220C4—42no—
221C4—81no—
222C4—2842no—
223C4—2842no—
224C4—1422no—
225C4—1422no—
226C4#1455610011yescharacteristic
227C4#1455610111yescharacteristic
228C4#1455611011yescharacteristic
229C4#1455611111yescharacteristic
230C2#1798591411yescharacteristic
231C2#1798613611yescharacteristic
232C2#1798615311yescharacteristic
233C2#1798620311yescharacteristic
234C2#1798620811yescharacteristic
235C2#1798634811yescharacteristic
236C2#1798636611yescharacteristic
subgroupG/H
centerC23D4×D71
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC2×#103×C71C2
socleC23×C71C2×D4
hypercenterC2×#103D71
hypocenterC71#2043
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
119. C71#2043semidirect