Finite Group Databasebeta

← C2×#27161460 #38753130

Subgroups — C2×#27161460 #38753130

Order 25216.

592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#15691348C211yesmaximal, characteristic, complemented
2C22×#15691347C211yesmaximal, characteristic, complemented
3C22×#15691343C211yesmaximal, characteristic
4C2×#20263315C211yesmaximal, characteristic, complemented
5C2×#20263313C211yesmaximal, characteristic, complemented
6#27161460C218yesmaximal, direct product factor
7C2×C8×Dic197C211yesmaximal, characteristic, complemented
8C22×SD16×C197C211yesmaximal, characteristic, complemented
9C22×Dic394C2211yescharacteristic
10C22×D788C2211yescharacteristic
11C2×#15691348—24no—
12C2×#15691348C2214yescomplemented
13C2×#15691347—24no—
14C2×#15691347C2214yescomplemented
15C2×#15691343—24no—
16C2×#15691343C2214yes—
17C22×#13096802C2211yescharacteristic
18#20263315—22no—
19#20263315C2214yescomplemented
20#20263313—22no—
21#20263313C2214yescomplemented
22C2×C22⋊Dic197—22no—
23C2×#15691335—22no—
24C2×C4×Dic197C2211yescharacteristic
25C8×Dic197C2214yescomplemented
26C22×Q8×C197C2211yescharacteristic
27C22×D4×C197C2211yescharacteristic
28C2×SD16×C197—24no—
29C2×SD16×C197C2214yescomplemented
30C22×C8×C197C2211yescharacteristic
31C23×D197—21no—
32C2×Dic394—21no—
33C2×Dic394—22no—
34C2×Dic394—22no—
35C2×Dic394C2312yes—
36C2×D788—22no—
37C2×D788—22no—
38C2×D788—21no—
39C2×D788C2312yes—
40C22×Dic197—21no—
41C22×Dic197D412yes—
42#15691348—28no—
43#15691347—28no—
44#15691343—28no—
45C2×#13096802D414yes—
46C2×#13096802C2312yes—
47C22⋊Dic197—28no—
48#15691335—28no—
49C4×Dic197D412yes—
50C4×Dic197C2312yes—
51C24×C197—21no—
52C2×Q8×C197—21no—
53C2×Q8×C197—22no—
54C2×Q8×C197—22no—
55C2×Q8×C197C2312yes—
56C2×D4×C197—22no—
57C2×D4×C197—22no—
58C2×D4×C197—21no—
59C2×D4×C197C2312yes—
60C22×C4×C197—21no—
61C22×C4×C197C2311yescharacteristic
62SD16×C197—28no—
63C2×C8×C197D414yes—
64C2×C8×C197C2312yes—
65C22×D197—22no—
66C22×D197—42no—
67C22×D197—44no—
68Dic394—22no—
69Dic394—22no—
70Dic394—42no—
71D788—22no—
72D788—22no—
73D788—42no—
74C2×Dic197—24no—
75C2×Dic197—22no—
76C2×Dic197—42no—
77C2×Dic197C2×D414yes—
78#13096802C2×D414yes—
79C23×C197—22no—
80C23×C197—42no—
81C23×C197—44no—
82C23×C197C2×D411yescharacteristic
83Q8×C197—22no—
84Q8×C197—22no—
85Q8×C197—42no—
86D4×C197—22no—
87D4×C197—22no—
88D4×C197—42no—
89C2×C4×C197—22no—
90C2×C4×C197—42no—
91C2×C4×C197C2×D411yescharacteristic
92C2×C4×C197C2×D412yes—
93C2×C4×C197C2×D412yes—
94C2×C4×C197C2411yescharacteristic
95C8×C197C2×D414yes—
96C22×C197—42no—
97C22×C197—44no—
98C22×C197—84no—
99C22×C197#12712yes—
100C22×C197#13514yes—
101C22×C197C22×D411yescharacteristic
102C2×D197—42no—
103C2×D197—44no—
104C2×D197—84no—
105C4×C197—42no—
106C4×C197#12712yes—
107C4×C197C22×D411yescharacteristic
108C4×C197C22×D411yescharacteristic
109Dic197—24no—
110Dic197—42no—
111C2×C197—82no—
112C2×C197#49514yescomplemented
113C2×C197C2×#12711yescharacteristic
114C2×C197C2×#13512yes—
115D197—82no—
116C197C2×#49511yescharacteristic, complemented, Sylow
117C2×#495—1971nomaximal, Sylow
118C22×Q16—1971no—
119C22×SD16—1971no—
120C22×SD16D19711yescharacteristic, complemented
121C22×D8—1971no—
122C2×#124—1971no—
123C2×#124—1971no—
124#495—1978no—
125C2×C4×C8—1971no—
126C22×Q8—1971no—
127C22×Q8C2×D19711yescharacteristic
128C22×D4—1971no—
129C22×D4C2×D19711yescharacteristic
130C2×Q16—3944no—
131C2×Q16—1974no—
132C2×SD16—24no—
133C2×SD16—3944no—
134C2×SD16—1974no—
135C2×SD16C2×D19714yescomplemented
136C2×D8—3944no—
137C2×D8—1974no—
138C22×C8—1971no—
139C22×C8C2×D19711yescharacteristic
140#124—3942no—
141#124—3942no—
142#124—1974no—
143#124—1974no—
144C2×C22⋊C4—3942no—
145C2×C22⋊C4—3942no—
146C2×C42—1971no—
147C4×C8—1974no—
148C24—21no—
149C24—3941no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—3942no—
154C2×Q8—3942no—
155C2×Q8—3941no—
156C2×Q8—1972no—
157C2×Q8C22×D19712yes—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4—3941no—
162C2×D4—3942no—
163C2×D4—3942no—
164C2×D4—1972no—
165C2×D4C22×D19712yes—
166C22×C4—21no—
167C22×C4—3941no—
168C22×C4—1972no—
169C22×C4C22×D19711yescharacteristic
170Q16—3948no—
171SD16—28no—
172SD16—3948no—
173D8—3948no—
174C2×C8—1974no—
175C2×C8—1972no—
176C2×C8C22⋊D19714yes—
177C2×C8C22×D19712yes—
178C22⋊C4—3948no—
179C22⋊C4—3948no—
180C42—1972no—
181C42—1972no—
182C23—22no—
183C23—42no—
184C23—44no—
185C23—7882no—
186C23—7884no—
187C23—3942no—
188C23D4×D19711yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—7882no—
193Q8—3942no—
194Q8—3942no—
195D4—22no—
196D4—22no—
197D4—42no—
198D4—7882no—
199D4—3942no—
200D4—3942no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—7882no—
204C2×C4—3942no—
205C2×C4—3944no—
206C2×C4—1974no—
207C2×C4D4×D19711yescharacteristic
208C2×C4D4×D19712yes—
209C2×C4C2×C22⋊D19712yes—
210C2×C4C23×D19711yescharacteristic
211C8—1974no—
212C8C2×C22⋊D19714yes—
213C22—44no—
214C22—42no—
215C22—84no—
216C22—7884no—
217C22—7882no—
218C22—15764no—
219C22#2026332212yes—
220C22#2026334714yes—
221C22C2×D4×D19711yescharacteristic
222C4—42no—
223C4—7882no—
224C4—3944no—
225C4#2026332212yes—
226C4C2×D4×D19711yescharacteristic
227C4C22×C22⋊D19711yescharacteristic
228C2—82no—
229C2—15762no—
230C2#2716146014yesdirect product factor
231C2C2×#2026332211yescharacteristic
232C2C2×#2026334712yes—
subgroupG/H
centerC23D4×D197
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
FittingC22×SD16×C197C2
socleC23×C197C2×D4
prime radicalC22×#15691343C2
hypercenterC22×SD16D197
hypocenterC197C2×#495
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#15691348C2semidirect
2. C22×#15691347C2semidirect
4. C2×#20263315C2semidirect
5. C2×#20263313C2semidirect
6. #27161460C2direct (N × H)
7. C2×C8×Dic197C2semidirect
8. C22×SD16×C197C2semidirect
12. C2×#15691348C22semidirect
14. C2×#15691347C22semidirect
19. #20263315C22semidirect
21. #20263313C22semidirect
25. C8×Dic197C22semidirect
29. C2×SD16×C197C22semidirect
112. C2×C197#495semidirect
116. C197C2×#495semidirect
120. C22×SD16D197semidirect
135. C2×SD16C2×D197semidirect
230. C2#27161460direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#156913482
C22×#156913472
C22×#156913432
C2×#202633152
C2×#202633132
#271614602
C2×C8×Dic1972
C22×SD16×C1972
C2×#495197