Finite Group Databasebeta

← C2×#17985791 #22589997

Subgroups — C2×#17985791 #22589997

Order 9088.

368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14556124C211yesmaximal, characteristic
2C2×#14556043C211yesmaximal, characteristic, complemented
3#17985791C214yesmaximal, direct product factor
4C2×#99×C71C211yesmaximal, characteristic, complemented
5C22×D284C411yescharacteristic, complemented
6C22×C22⋊D71—21no—
7C22×C22⋊D71—21no—
8#14556124—21no—
9#14556124—21no—
10#14556124C412yescomplemented
11#14556124C2212yes—
12C2×C22⋊Dic71—21no—
13C2×C4×Dic71C411yescharacteristic, complemented
14#14556043—21no—
15#14556043C2212yescomplemented
16C22×D4×C71C2211yescharacteristic
17C2×C22⋊C4×C71—21no—
18#99×C71—21no—
19#99×C71C2212yescomplemented
20C23×D71—21no—
21C2×D284—21no—
22C2×D284—41no—
23C2×D284—41no—
24C2×D284C2×C412yescomplemented
25C2×C22⋊D71—22no—
26C2×C22⋊D71—22no—
27C2×C22⋊D71—22no—
28C2×C22⋊D71—22no—
29C2×C22⋊D71—44no—
30C2×C22⋊D71—44no—
31C22×Dic71—21no—
32C22×Dic71—41no—
33C22⋊Dic71—22no—
34C22⋊Dic71—41no—
35C4×Dic71—21no—
36C4×Dic71C2×C412yescomplemented
37C24×C71D411yescharacteristic
38C24×C71D411yescharacteristic
39C2×D4×C71—41no—
40C2×D4×C71—41no—
41C2×D4×C71C2×C411yescharacteristic
42C2×D4×C71D411yescharacteristic
43C2×D4×C71D411yescharacteristic
44C2×D4×C71C2311yescharacteristic
45C22×C4×C71—41no—
46C22×C4×C71C2×C411yescharacteristic
47C22⋊C4×C71—22no—
48C22⋊C4×C71—41no—
49C23×C71—21no—
50C23×C71—21no—
51C23×C71—21no—
52C23×C71—21no—
53C23×C71—42no—
54C23×C71—42no—
55C23×C71C22⋊C411yescharacteristic
56C23×C71C22⋊C411yescharacteristic
57C23×C71C22⋊C411yescharacteristic
58C23×C71C2×D411yescharacteristic
59C23×C71C2×D411yescharacteristic
60C22×D71—22no—
61C22×D71—42no—
62C22×D71—42no—
63C22×D71—41no—
64C22×D71—41no—
65D4×C71—41no—
66D4×C71—41no—
67D4×C71—41no—
68D4×C71—41no—
69C2×C4×C71—21no—
70C2×C4×C71—21no—
71C2×C4×C71—42no—
72C2×C4×C71—82no—
73C2×C4×C71C22⋊C411yescharacteristic
74C2×C4×C71C22×C411yescharacteristic
75C22⋊D71—44no—
76C22⋊D71—44no—
77C22⋊D71—44no—
78C22⋊D71—44no—
79C2×Dic71—24no—
80C2×Dic71—22no—
81C2×Dic71—42no—
82C2×Dic71—82no—
83D284—42no—
84D284—42no—
85C22×C71—22no—
86C22×C71—21no—
87C22×C71—21no—
88C22×C71—21no—
89C22×C71—21no—
90C22×C71—41no—
91C22×C71—41no—
92C22×C71—41no—
93C22×C71—41no—
94C22×C71—42no—
95C22×C71—42no—
96C22×C71—81no—
97C22×C71—81no—
98C22×C71#9911yescharacteristic
99C22×C71#9911yescharacteristic
100C22×C71C2×C22⋊C411yescharacteristic
101C2×D71—42no—
102C2×D71—42no—
103C2×D71—42no—
104C2×D71—82no—
105C2×D71—82no—
106C4×C71—21no—
107C4×C71—21no—
108C4×C71—82no—
109Dic71—24no—
110Dic71—82no—
111C2×C71—21no—
112C2×C71—21no—
113C2×C71—41no—
114C2×C71—41no—
115C2×C71—41no—
116C2×C71—41no—
117C2×C71#35312yescomplemented
118C2×C71C2×#9911yescharacteristic
119D71—82no—
120C2×#353—711nomaximal, Sylow
121C71C2×#35311yescharacteristic, complemented, Sylow
122C2×#127—711no—
123C2×#99—711no—
124C2×#99D7111yescharacteristic, complemented
125#353—714no—
126C22×D4—711no—
127C22×D4—1421no—
128C22×D4—1421no—
129C22×D4C2×D7111yescharacteristic
130#127—712no—
131#127—712no—
132#127—1421no—
133#127—1421no—
134C2×C22⋊C4—21no—
135C2×C22⋊C4—1421no—
136C2×C42—711no—
137#99—21no—
138#99—712no—
139#99—1421no—
140#99C2×D7112yescomplemented
141C24—1421no—
142C24D28411yescharacteristic
143C24C22⋊D7111yescharacteristic
144C2×D4—41no—
145C2×D4—41no—
146C2×D4—2841no—
147C2×D4—2841no—
148C2×D4—2844no—
149C2×D4—2844no—
150C2×D4—712no—
151C2×D4—1422no—
152C2×D4—1422no—
153C2×D4—1422no—
154C2×D4—1422no—
155C2×D4—1421no—
156C2×D4C4×D7111yescharacteristic
157C2×D4D28411yescharacteristic
158C2×D4C22⋊D7111yescharacteristic
159C2×D4C22×D7111yescharacteristic
160C22×C4—41no—
161C22×C4—2841no—
162C22×C4—1421no—
163C22×C4C4×D7111yescharacteristic
164C22⋊C4—22no—
165C22⋊C4—41no—
166C22⋊C4—2841no—
167C22⋊C4—1422no—
168C42—712no—
169C42—1421no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—42no—
175C23—42no—
176C23—2842no—
177C23—2842no—
178C23—2841no—
179C23—2841no—
180C23—1422no—
181C23(C2×D71)⋊C411yescharacteristic
182C23(C2×D71)⋊C411yescharacteristic
183C23(C2×D71)⋊C411yescharacteristic
184C23C2×C22⋊D7111yescharacteristic
185C23C2×D28411yescharacteristic
186D4—41no—
187D4—41no—
188D4—41no—
189D4—41no—
190D4—2842no—
191D4—2842no—
192D4—2844no—
193D4—2844no—
194D4—2844no—
195D4—2844no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—82no—
200C2×C4—2842no—
201C2×C4—5682no—
202C2×C4—1424no—
203C2×C4—1422no—
204C2×C4(C2×D71)⋊C411yescharacteristic
205C2×C4C2×C4×D7111yescharacteristic
206C22—22no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22—42no—
216C22—42no—
217C22—81no—
218C22—81no—
219C22—2842no—
220C22—2842no—
221C22—2842no—
222C22—5682no—
223C22—5682no—
224C22#1455604211yescharacteristic
225C22#1455604211yescharacteristic
226C22C2×(C2×D71)⋊C411yescharacteristic
227C4—21no—
228C4—21no—
229C4—82no—
230C4—5682no—
231C4—1424no—
232C2—21no—
233C2—21no—
234C2—41no—
235C2—41no—
236C2—41no—
237C2—41no—
238C2—5682no—
239C2#1798579112yesdirect product factor
240C2C2×#1455604211yescharacteristic
subgroupG/H
centerC22#14556042
commutatorC2×C4×C71C22×C4
FrattiniC2×D4C22×D71
FittingC2×#99×C71C2
socleC22×C71#99
hypercenterC2×#99D71
hypocenterC71C2×#353
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#14556043C2semidirect
3. #17985791C2direct (N × H)
4. C2×#99×C71C2semidirect
5. C22×D284C4semidirect
10. #14556124C4semidirect
13. C2×C4×Dic71C4semidirect
15. #14556043C22semidirect
19. #99×C71C22semidirect
24. C2×D284C2×C4semidirect
36. C4×Dic71C2×C4semidirect
117. C2×C71#353semidirect
121. C71C2×#353semidirect
124. C2×#99D71semidirect
140. #99C2×D71semidirect
239. C2#17985791direct (N × H)