Finite Group Databasebeta

← #22586881

Subgroups — #22586881

Order 9088.

286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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#17986510C211yesmaximal, characteristic
2#17985963C211yesmaximal, characteristic, complemented
3#17985735C212yesmaximal, complemented
4#17985732C212yesmaximal, complemented
5#380×C71C211yesmaximal, characteristic, complemented
6C2×#11765865C411yescharacteristic, complemented
7C2×#11765849—21no—
8#14556111—21no—
9#14556107C411yescharacteristic, complemented
10#14556107C2211yescharacteristic
11#14556102C411yescharacteristic, complemented
12#14556102C2211yescharacteristic
13#14556097—21no—
14C4×C22⋊D71—21no—
15C4×C22⋊D71—21no—
16#14556087C411yescharacteristic, complemented
17C22⋊(C71⋊C8)—21no—
18C22⋊(C71⋊C8)C2212yes—
19C23×C4×C71C2211yescharacteristic
20C2×C4⋊C4×C71—21no—
21C2×C22⋊C4×C71—21no—
22#95×C71C2212yes—
23#11765865—42no—
24C2×Dic142C2×C411yescharacteristic
25C2×D284C2×C411yescharacteristic
26C2×C22⋊D71—21no—
27C2×C22⋊D71—21no—
28C2×C22⋊D71—21no—
29C2×C4×D71—21no—
30#11765849—42no—
31C2×C71⋊C8—22no—
32C4⋊Dic71C2×C411yescharacteristic
33C4⋊Dic71C2×C411yescharacteristic
34Dic71⋊C4—21no—
35Dic71⋊C4—21no—
36C22⋊Dic71—21no—
37C22⋊Dic71—21no—
38C22⋊Dic71—21no—
39(C2×D71)⋊C4—21no—
40(C2×D71)⋊C4—21no—
41C4×Dic71—21no—
42C24×C71D411yescharacteristic
43C22×C4×C71—22no—
44C22×C4×C71—42no—
45C22×C4×C71C2×C411yescharacteristic
46C22×C4×C71C2×C411yescharacteristic
47C22×C4×C71D411yescharacteristic
48C22×C4×C71D411yescharacteristic
49C22×C4×C71D411yescharacteristic
50C22×C4×C71C2311yescharacteristic
51C4⋊C4×C71—42no—
52C22⋊C4×C71—42no—
53C23×C71—21no—
54C23×C71—21no—
55C23×C71—41no—
56C23×C71—41no—
57C23×C71C22⋊C411yescharacteristic
58C23×C71C22⋊C411yescharacteristic
59C23×C71C2×D411yescharacteristic
60C22×D71—21no—
61C2×C4×C71—22no—
62C2×C4×C71—22no—
63C2×C4×C71—22no—
64C2×C4×C71—41no—
65C2×C4×C71—41no—
66C2×C4×C71—41no—
67C2×C4×C71—42no—
68C2×C4×C71—42no—
69C2×C4×C71—42no—
70C2×C4×C71C22⋊C411yescharacteristic
71C2×C4×C71C22⋊C411yescharacteristic
72C2×C4×C71C22×C411yescharacteristic
73C2×C4×C71C2×D411yescharacteristic
74C22⋊D71—42no—
75C22⋊D71—42no—
76C22⋊D71—41no—
77C22⋊D71—41no—
78C2×Dic71—21no—
79C2×Dic71—21no—
80C2×Dic71—21no—
81D284—41no—
82C4×D71—42no—
83Dic142—41no—
84C71⋊C8—42no—
85C22×C71—21no—
86C22×C71—21no—
87C22×C71—21no—
88C22×C71—21no—
89C22×C71—21no—
90C22×C71—21no—
91C22×C71—21no—
92C22×C71—21no—
93C22×C71—42no—
94C22×C71—42no—
95C22×C71C2×C22⋊C411yescharacteristic
96C22×C71AGL(1,ℤ/8)11yescharacteristic
97C22×C71#13711yescharacteristic
98C2×D71—41no—
99C2×D71—41no—
100C2×D71—41no—
101C4×C71—21no—
102C4×C71—21no—
103C4×C71—21no—
104C4×C71—82no—
105C4×C71#9912yes—
106Dic71—41no—
107Dic71—41no—
108Dic71—41no—
109C2×C71—21no—
110C2×C71—21no—
111C2×C71—41no—
112C2×C71—41no—
113C2×C71C2×#9911yescharacteristic
114C2×C71#41711yescharacteristic
115C2×C71#42111yescharacteristic
116D71—81no—
117#1513—711nomaximal, Sylow
118C71#151311yescharacteristic, complemented, Sylow
119#525—711no—
120#407—711no—
121#380D7111yescharacteristic, complemented
122#328—712no—
123#327—712no—
124C2×#41—711no—
125C23×C4C2×D7111yescharacteristic
126C2×M16—1421no—
127#123—1421no—
128C22⋊Q8—711no—
129C22⋊Q8—711no—
130#121—711no—
131#121—711no—
132#120—1421no—
133C4×D4—1421no—
134C4×D4—1421no—
135#117—711no—
136C2×C4⋊C4—21no—
137C2×C22⋊C4—21no—
138C22⋊C8—712no—
139C22⋊C8—1421no—
140#95C2×D7112yes—
141C24C22⋊D7111yescharacteristic
142#41—2842no—
143C2×Q8—711no—
144C2×D4—711no—
145C2×D4—1421no—
146C2×D4—1421no—
147C2×D4—1421no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—1421no—
151C22×C4C4×D7111yescharacteristic
152C22×C4C4×D7111yescharacteristic
153C22×C4D28411yescharacteristic
154C22×C4D28411yescharacteristic
155C22×C4C22⋊D7111yescharacteristic
156C22×C4C22×D7111yescharacteristic
157M16—2842no—
158C2×C8—1422no—
159C4⋊C4—42no—
160C4⋊C4—711no—
161C4⋊C4—711no—
162C4⋊C4—1421no—
163C4⋊C4—1421no—
164C22⋊C4—42no—
165C22⋊C4—1421no—
166C22⋊C4—1421no—
167C22⋊C4—1421no—
168C22⋊C4—1421no—
169C22⋊C4—1421no—
170C42—1421no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23—1421no—
176C23(C2×D71)⋊C411yescharacteristic
177C23(C2×D71)⋊C411yescharacteristic
178C23C2×C22⋊D7111yescharacteristic
179Q8—2841no—
180D4—2841no—
181D4—2842no—
182D4—2842no—
183D4—2841no—
184D4—2841no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—2842no—
195C2×C4—1421no—
196C2×C4—1421no—
197C2×C4—1421no—
198C2×C4(C2×D71)⋊C411yescharacteristic
199C2×C4(C2×D71)⋊C411yescharacteristic
200C2×C4C2×C4×D7111yescharacteristic
201C2×C4C2×D28411yescharacteristic
202C8—2842no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—2841no—
214C22—2841no—
215C22—2841no—
216C22C2×(C2×D71)⋊C411yescharacteristic
217C22#1455615411yescharacteristic
218C22#1455615911yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—82no—
223C4—2841no—
224C4—2841no—
225C4—2841no—
226C4#1455604212yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—5681no—
232C2C2×#1455604211yescharacteristic
233C2#1798599811yescharacteristic
234C2#1798601711yescharacteristic
subgroupG/H
centerC22C2×(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#380×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#380D71
hypocenterC71#1513
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #17985963C2semidirect
3. #17985735C2semidirect
4. #17985732C2semidirect
5. #380×C71C2semidirect
6. C2×#11765865C4semidirect
9. #14556107C4semidirect
11. #14556102C4semidirect
16. #14556087C4semidirect
118. C71#1513semidirect
121. #380D71semidirect