Finite Group Databasebeta

← #22589517

Subgroups — #22589517

Order 9088.

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

normal subgroups only

This group has 278 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#17986625C211yesmaximal, characteristic, complemented
2C2×#14556043C211yesmaximal, characteristic
3C2×#14556043C211yesmaximal, characteristic
4#17985766C211yesmaximal, characteristic, complemented
5#17985765C211yesmaximal, characteristic, complemented
6#17985765C211yesmaximal, characteristic, complemented
7C2×#99×C71C211yesmaximal, characteristic
8#14556107—22no—
9#14556105—22no—
10#14556105—22no—
11C2×C22⋊Dic71C2211yescharacteristic
12C2×C22⋊Dic71C2211yescharacteristic
13C2×C22⋊Dic71C2211yescharacteristic
14C2×C22⋊Dic71C2211yescharacteristic
15#14556043—22no—
16#14556043—22no—
17C22×D4×C71C2211yescharacteristic
18C2×C22⋊C4×C71C2211yescharacteristic
19C2×C22⋊C4×C71C2211yescharacteristic
20#99×C71—22no—
21C2×Dic142—22no—
22C22×Dic71—21no—
23C22×Dic71—21no—
24C22×Dic71—21no—
25C22×Dic71—21no—
26C4⋊Dic71—22no—
27Dic71⋊C4—24no—
28C22⋊Dic71—21no—
29C22⋊Dic71—21no—
30C22⋊Dic71—21no—
31C22⋊Dic71—21no—
32C22⋊Dic71—21no—
33C22⋊Dic71—21no—
34C22⋊Dic71D412yes—
35C22⋊Dic71D412yes—
36C24×C71Q811yescharacteristic, complemented
37C24×C71C2311yescharacteristic
38C2×D4×C71—21no—
39C2×D4×C71—21no—
40C2×D4×C71—21no—
41C2×D4×C71—21no—
42C2×D4×C71—21no—
43C2×D4×C71—21no—
44C22×C4×C71—21no—
45C22×C4×C71—21no—
46C22×C4×C71Q811yescharacteristic, complemented
47C22⋊C4×C71—21no—
48C22⋊C4×C71—21no—
49C22⋊C4×C71—21no—
50C22⋊C4×C71D412yes—
51C23×C71—21no—
52C23×C71—21no—
53C23×C71—21no—
54C23×C71—81no—
55C23×C71—81no—
56C23×C71C2×D411yescharacteristic
57C23×C71C2×D411yescharacteristic
58C23×C71C2×D411yescharacteristic
59C23×C71C2×Q811yescharacteristic
60C23×C71#4111yescharacteristic
61C23×C71#4111yescharacteristic
62C23×C71#4111yescharacteristic
63D4×C71—41no—
64D4×C71—41no—
65D4×C71—41no—
66D4×C71—41no—
67C2×C4×C71—22no—
68C2×C4×C71—21no—
69C2×C4×C71—21no—
70C2×C4×C71—21no—
71C2×C4×C71—41no—
72C2×C4×C71—81no—
73C2×C4×C71—81no—
74C2×Dic71—22no—
75C2×Dic71—22no—
76C2×Dic71—41no—
77C2×Dic71—41no—
78C2×Dic71—81no—
79C2×Dic71—81no—
80C2×Dic71—81no—
81C2×Dic71—81no—
82Dic142—82no—
83C22×C71—41no—
84C22×C71—41no—
85C22×C71—41no—
86C22×C71—41no—
87C22×C71—41no—
88C22×C71—41no—
89C22×C71—41no—
90C22×C71—41no—
91C22×C71—81no—
92C22×C71—81no—
93C22×C71—81no—
94C22×C71#12011yescharacteristic
95C22×C71C22⋊Q811yescharacteristic
96C22×C71C22⋊Q811yescharacteristic
97C22×C71C22⋊Q811yescharacteristic
98C22×C71#12411yescharacteristic
99C22×C71#12411yescharacteristic
100C22×C71#12411yescharacteristic
101C4×C71—42no—
102C4×C71—41no—
103C4×C71—81no—
104Dic71—42no—
105Dic71—42no—
106Dic71—81no—
107Dic71—81no—
108C2×C71—21no—
109C2×C71—21no—
110C2×C71—21no—
111C2×C71—21no—
112C2×C71—21no—
113C2×C71—21no—
114C2×C71—21no—
115C2×C71—81no—
116C2×C71#39311yescharacteristic
117#2032—711nomaximal, Sylow
118C71#203211yescharacteristic, complemented, Sylow
119#543—711no—
120C2×#99—711no—
121C2×#99—711no—
122C2×#99D7111yescharacteristic
123#342—711no—
124#342—711no—
125#342—711no—
126C22×D4C2×D7111yescharacteristic
127C22⋊Q8—1422no—
128C22⋊Q8—1422no—
129C22⋊Q8—1422no—
130C2×C22⋊C4—711no—
131C2×C22⋊C4—711no—
132C2×C22⋊C4—711no—
133C2×C22⋊C4—711no—
134C2×C22⋊C4C2×D7111yescharacteristic
135C2×C22⋊C4C2×D7111yescharacteristic
136#99—22no—
137#99—1422no—
138#99—1422no—
139C24Dic14211yescharacteristic, complemented
140C24C22×D7111yescharacteristic
141C2×Q8—1422no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—1421no—
151C22×C4—1421no—
152C22×C4—1421no—
153C22×C4—1421no—
154C22×C4Dic14211yescharacteristic, complemented
155C4⋊C4—1424no—
156C4⋊C4—1422no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—712no—
161C22⋊C4—712no—
162C22⋊C4—1421no—
163C22⋊C4—1421no—
164C22⋊C4—1421no—
165C22⋊C4—1421no—
166C22⋊C4—1421no—
167C22⋊C4—1421no—
168C22⋊C4C22⋊D7112yes—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—81no—
173C23—81no—
174C23D4×D7111yescharacteristic
175C23D4×D7111yescharacteristic
176C23C2×C22⋊D7111yescharacteristic
177C23C2×Dic14211yescharacteristic
178C23#1176586411yescharacteristic
179C23#1176586411yescharacteristic
180C23#1176586511yescharacteristic
181Q8—5682no—
182D4—41no—
183D4—41no—
184D4—41no—
185D4—41no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—2841no—
194C2×C4—2841no—
195C2×C4—5681no—
196C2×C4—5681no—
197C2×C4—5681no—
198C2×C4—5681no—
199C2×C4—1422no—
200C2×C4—1422no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22#1455609611yescharacteristic
213C22#1455610511yescharacteristic
214C22#1455610511yescharacteristic
215C22#1455610711yescharacteristic
216C22#1455611411yescharacteristic
217C22#1455611411yescharacteristic
218C22#1455611511yescharacteristic
219C4—42no—
220C4—41no—
221C4—81no—
222C4—2842no—
223C4—2842no—
224C4—5681no—
225C4—5681no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—81no—
234C2#1798591111yescharacteristic
subgroupG/H
centerC2#17985911
commutatorC24×C71C23
FrattiniC24C22×D71
FittingC2×#99×C71C2
socleC2×C71#393
hypercenterC2×#99D71
hypocenterC71#2032
LCSG ▷ C24×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. #17986625C2semidirect
4. #17985766C2semidirect
5. #17985765C2semidirect
6. #17985765C2semidirect
36. C24×C71Q8semidirect
46. C22×C4×C71Q8semidirect
118. C71#2032semidirect
139. C24Dic142semidirect
154. C22×C4Dic142semidirect