Finite Group Databasebeta

← #22589518

Subgroups — #22589518

Order 9088.

278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14556042C211yesmaximal, characteristic
3C2×#14556042C211yesmaximal, characteristic
4C2×#14556042C211yesmaximal, characteristic
5#17985766C211yesmaximal, characteristic, complemented
6#17985765C211yesmaximal, characteristic, complemented
7#342×C71C211yesmaximal, characteristic, complemented
8C22×C22⋊D71C2211yescharacteristic
9#14556107—22no—
10#14556105—22no—
11#14556105—22no—
12C2×C22⋊Dic71C2211yescharacteristic
13C2×C22⋊Dic71C2211yescharacteristic
14C2×C22⋊Dic71C2211yescharacteristic
15#14556042—22no—
16#14556042—22no—
17#14556042—22no—
18C2×C22⋊C4×C71C2211yescharacteristic
19C2×C22⋊C4×C71C2211yescharacteristic
20C2×C22⋊C4×C71C2211yescharacteristic
21C23×D71Q811yescharacteristic, complemented
22C2×Dic142—22no—
23C2×C22⋊D71—21no—
24C2×C22⋊D71—21no—
25C2×C22⋊D71—21no—
26C2×C22⋊D71—21no—
27C2×C22⋊D71—21no—
28C2×C22⋊D71—21no—
29C22×Dic71—21no—
30C22×Dic71—21no—
31C22×Dic71—21no—
32C22×Dic71Q811yescharacteristic, complemented
33C4⋊Dic71—22no—
34Dic71⋊C4—24no—
35C22⋊Dic71—21no—
36C22⋊Dic71—21no—
37C22⋊Dic71—21no—
38C22⋊Dic71—21no—
39C22⋊Dic71D412yes—
40C22⋊Dic71D412yes—
41C24×C71C2311yescharacteristic
42C22×C4×C71—21no—
43C22×C4×C71—21no—
44C22×C4×C71—21no—
45C22⋊C4×C71—21no—
46C22⋊C4×C71—21no—
47C22⋊C4×C71—21no—
48C22⋊C4×C71—21no—
49C22⋊C4×C71—21no—
50C22⋊C4×C71D412yes—
51C23×C71—81no—
52C23×C71C2×D411yescharacteristic
53C23×C71C2×D411yescharacteristic
54C23×C71C2×D411yescharacteristic
55C23×C71C2×Q811yescharacteristic
56C23×C71#4111yescharacteristic
57C23×C71#4111yescharacteristic
58C23×C71#4111yescharacteristic
59C22×D71—21no—
60C22×D71—21no—
61C22×D71—21no—
62C22×D71—81no—
63C2×C4×C71—22no—
64C2×C4×C71—41no—
65C2×C4×C71—41no—
66C2×C4×C71—81no—
67C2×C4×C71—81no—
68C2×C4×C71—81no—
69C22⋊D71—41no—
70C22⋊D71—41no—
71C22⋊D71—41no—
72C22⋊D71—41no—
73C2×Dic71—22no—
74C2×Dic71—22no—
75C2×Dic71—21no—
76C2×Dic71—21no—
77C2×Dic71—21no—
78C2×Dic71—41no—
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#12011yescharacteristic
91C22×C71C22⋊Q811yescharacteristic
92C22×C71C22⋊Q811yescharacteristic
93C22×C71C22⋊Q811yescharacteristic
94C22×C71#12411yescharacteristic
95C22×C71#12411yescharacteristic
96C22×C71#12411yescharacteristic
97C2×D71—41no—
98C2×D71—81no—
99C2×D71—81no—
100C2×D71—81no—
101C4×C71—42no—
102C4×C71—81no—
103C4×C71—81no—
104Dic71—42no—
105Dic71—42no—
106Dic71—41no—
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#39311yescharacteristic
116D71—81no—
117#2032—711nomaximal, Sylow
118C71#203211yescharacteristic, complemented, Sylow
119#543—711no—
120C2×#99—711no—
121C2×#99—711no—
122C2×#99—711no—
123#342—711no—
124#342—711no—
125#342D7111yescharacteristic, complemented
126C22×D4—711no—
127C22⋊Q8—1422no—
128C22⋊Q8—1422no—
129C22⋊Q8—1422no—
130C2×C22⋊C4—711no—
131C2×C22⋊C4—711no—
132C2×C22⋊C4—711no—
133C2×C22⋊C4C2×D7111yescharacteristic
134C2×C22⋊C4C2×D7111yescharacteristic
135C2×C22⋊C4C2×D7111yescharacteristic
136#99—1422no—
137#99—1422no—
138#99—1422no—
139C24—711no—
140C24C22×D7111yescharacteristic
141C2×Q8—1422no—
142C2×D4—1421no—
143C2×D4—1421no—
144C2×D4—1421no—
145C2×D4—1421no—
146C2×D4—1421no—
147C2×D4—1421no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—711no—
152C22×C4—1421no—
153C22×C4—1421no—
154C22×C4—1421no—
155C4⋊C4—1424no—
156C4⋊C4—1422no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—712no—
163C22⋊C4—712no—
164C22⋊C4—1421no—
165C22⋊C4—1421no—
166C22⋊C4—1421no—
167C22⋊C4—1421no—
168C22⋊C4D28412yes—
169C23—81no—
170C23—5681no—
171C23—1421no—
172C23—1421no—
173C23—1421no—
174C23D4×D7111yescharacteristic
175C23D4×D7111yescharacteristic
176C23C2×D28411yescharacteristic
177C23Q8×D7111yescharacteristic
178C23#1176586411yescharacteristic
179C23#1176586511yescharacteristic
180C23#1176586511yescharacteristic
181Q8—5682no—
182D4—2841no—
183D4—2841no—
184D4—2841no—
185D4—2841no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—2841no—
193C2×C4—5681no—
194C2×C4—5681no—
195C2×C4—5681no—
196C2×C4—1422no—
197C2×C4—1422no—
198C2×C4—1421no—
199C2×C4—1421no—
200C2×C4—1421no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—2841no—
209C22—5681no—
210C22—5681no—
211C22—5681no—
212C22#1455609811yescharacteristic
213C22#1455610611yescharacteristic
214C22#1455610611yescharacteristic
215C22#1455610811yescharacteristic
216C22#1455611411yescharacteristic
217C22#1455611411yescharacteristic
218C22#1455611611yescharacteristic
219C4—42no—
220C4—81no—
221C4—81no—
222C4—2842no—
223C4—2842no—
224C4—2841no—
225C4—5681no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—5681no—
234C2#1798591211yescharacteristic
subgroupG/H
centerC2#17985912
commutatorC24×C71C23
FrattiniC24C22×D71
Fitting#342×C71C2
socleC2×C71#393
hypercenter#342D71
hypocenterC71#2032
LCSG ▷ C24×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #17986625C2semidirect
5. #17985766C2semidirect
6. #17985765C2semidirect
7. #342×C71C2semidirect
21. C23×D71Q8semidirect
32. C22×Dic71Q8semidirect
118. C71#2032semidirect
125. #342D71semidirect