Finite Group Databasebeta

← C2×#22581339 #31816835

Subgroups — C2×#22581339 #31816835

Order 17792.

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

normal subgroups only

This group has 668 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×#14555772C211yesmaximal, characteristic, complemented
2C22×D1112C211yesmaximal, characteristic, complemented
3C22×#14555770C211yesmaximal, characteristic, complemented
4C2×#17984838C211yesmaximal, characteristic, complemented
5C2×#17984831C211yesmaximal, characteristic, complemented
6#22581339C218yesmaximal, direct product factor
7C2×#17984752C211yesmaximal, characteristic, complemented
8C22×SD16×C139C211yesmaximal, characteristic, complemented
9C22×D556C2211yescharacteristic
10C22×D556C2211yescharacteristic
11C22×C22⋊D139—22no—
12C2×#14555772—24no—
13C2×#14555772C2214yescomplemented
14C2×D1112—24no—
15C2×D1112C2214yescomplemented
16C2×#14555770—24no—
17C2×#14555770C2214yescomplemented
18C22×C139⋊C8C2211yescharacteristic
19#17984838—22no—
20#17984838C2214yescomplemented
21#17984831—22no—
22#17984831C2214yescomplemented
23C2×(C2×D139)⋊C4—22no—
24C2×C4×Dic139C2211yescharacteristic
25#17984752C2214yescomplemented
26C22×Q8×C139C2211yescharacteristic
27C22×D4×C139C2211yescharacteristic
28C2×SD16×C139—24no—
29C2×SD16×C139C2214yescomplemented
30C22×C8×C139C2211yescharacteristic
31C23×D139—21no—
32C23×D139—21no—
33C2×D556—22no—
34C2×D556—22no—
35C2×D556—22no—
36C2×D556—22no—
37C2×D556—21no—
38C2×D556—21no—
39C2×D556C2312yes—
40C2×D556C2312yes—
41C2×C22⋊D139—28no—
42C2×C22⋊D139—48no—
43C22×Dic139D412yes—
44#14555772—28no—
45D1112—28no—
46#14555770—28no—
47C2×C139⋊C8D414yescomplemented
48C2×C139⋊C8C2312yes—
49(C2×D139)⋊C4—28no—
50C4×Dic139D412yes—
51C4×Dic139C2312yes—
52C24×C139—21no—
53C2×Q8×C139—21no—
54C2×Q8×C139—22no—
55C2×Q8×C139—22no—
56C2×Q8×C139C2312yes—
57C2×D4×C139—22no—
58C2×D4×C139—22no—
59C2×D4×C139—21no—
60C2×D4×C139C2312yes—
61C22×C4×C139—21no—
62C22×C4×C139C2311yescharacteristic
63SD16×C139—28no—
64C2×C8×C139D414yescomplemented
65C2×C8×C139C2312yes—
66C22×D139—22no—
67C22×D139—22no—
68C22×D139—42no—
69C22×D139—42no—
70C22×D139—44no—
71C22×D139—44no—
72D556—22no—
73D556—22no—
74D556—22no—
75D556—22no—
76D556—42no—
77D556—42no—
78C22⋊D139—416no—
79C2×Dic139—24no—
80C2×Dic139C2×D414yes—
81C139⋊C8C2×D414yescomplemented
82C23×C139—22no—
83C23×C139—42no—
84C23×C139—44no—
85C23×C139C2×D411yescharacteristic
86Q8×C139—22no—
87Q8×C139—22no—
88Q8×C139—42no—
89D4×C139—22no—
90D4×C139—22no—
91D4×C139—42no—
92C2×C4×C139—22no—
93C2×C4×C139—42no—
94C2×C4×C139C2×D411yescharacteristic
95C2×C4×C139C2×D412yes—
96C2×C4×C139C2×D412yes—
97C2×C4×C139C2411yescharacteristic
98C8×C139C2×D414yescomplemented
99C22×C139—42no—
100C22×C139—44no—
101C22×C139—84no—
102C22×C139#12712yes—
103C22×C139AGL(1,ℤ/8)14yes—
104C22×C139C22×D411yescharacteristic
105C2×D139—42no—
106C2×D139—42no—
107C2×D139—44no—
108C2×D139—44no—
109C2×D139—84no—
110C2×D139—84no—
111C4×C139—42no—
112C4×C139#12712yes—
113C4×C139C22×D411yescharacteristic
114C4×C139C22×D411yescharacteristic
115Dic139—24no—
116C2×C139—82no—
117C2×C139#49614yescomplemented
118C2×C139C2×#12711yescharacteristic
119C2×C139C2×AGL(1,ℤ/8)12yes—
120D139—82no—
121D139—82no—
122C139C2×#49611yescharacteristic, complemented, Sylow
123C2×#496—1391nomaximal, Sylow
124C22×SD16—1391no—
125C22×SD16D13911yescharacteristic, complemented
126C22×D8—1391no—
127C22×D8—1391no—
128C2×#127—1391no—
129C2×#124—1391no—
130#496—1398no—
131C2×#97—1391no—
132C22×Q8C2×D13911yescharacteristic
133C22×D4—2782no—
134C22×D4—1391no—
135C22×D4—1391no—
136C22×D4C2×D13911yescharacteristic
137C2×SD16—24no—
138C2×SD16—2784no—
139C2×SD16—1394no—
140C2×SD16C2×D13914yescomplemented
141C2×D8—2784no—
142C2×D8—2784no—
143C2×D8—1394no—
144C2×D8—1394no—
145C22×C8—1391no—
146C22×C8C2×D13911yescharacteristic
147#127—2782no—
148#127—1394no—
149#124—2782no—
150#124—1394no—
151C2×C22⋊C4—2782no—
152C2×C42—1391no—
153#97—1394no—
154C24—21no—
155C24—2781no—
156C24—2781no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D13912yes—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—2788no—
165C2×D4—2782no—
166C2×D4—2782no—
167C2×D4—2781no—
168C2×D4—2781no—
169C2×D4—2782no—
170C2×D4—2782no—
171C2×D4—5568no—
172C2×D4—1392no—
173C2×D4—1392no—
174C2×D4C22×D13912yes—
175C22×C4—21no—
176C22×C4—1392no—
177C22×C4C22×D13911yescharacteristic
178SD16—28no—
179SD16—2788no—
180D8—2788no—
181D8—2788no—
182C2×C8—1394no—
183C2×C8—1392no—
184C2×C8C22⋊D13914yescomplemented
185C2×C8C22×D13912yes—
186C22⋊C4—2788no—
187C42—1392no—
188C42—1392no—
189C23—22no—
190C23—42no—
191C23—44no—
192C23—2782no—
193C23—2782no—
194C23—5562no—
195C23—5562no—
196C23—5564no—
197C23—5564no—
198C23D4×D13911yescharacteristic
199Q8—22no—
200Q8—22no—
201Q8—42no—
202D4—22no—
203D4—22no—
204D4—42no—
205D4—2782no—
206D4—2782no—
207D4—2782no—
208D4—2782no—
209D4—55616no—
210D4—5562no—
211D4—5562no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—2784no—
215C2×C4—1394no—
216C2×C4D4×D13911yescharacteristic
217C2×C4D4×D13912yes—
218C2×C4C2×C22⋊D13912yes—
219C2×C4C23×D13911yescharacteristic
220C8—1394no—
221C8C2×C22⋊D13914yescomplemented
222C22—44no—
223C22—42no—
224C22—84no—
225C22—5564no—
226C22—5564no—
227C22—5562no—
228C22—5562no—
229C22—11124no—
230C22—11124no—
231C22#1798483812yes—
232C22#1798486914yes—
233C22C2×D4×D13911yescharacteristic
234C4—42no—
235C4—2784no—
236C4#1798483812yes—
237C4C2×D4×D13911yescharacteristic
238C4C22×C22⋊D13911yescharacteristic
239C2—82no—
240C2—11122no—
241C2—11122no—
242C2#2258133914yesdirect product factor
243C2C2×#1798483811yescharacteristic
244C2C2×#1798486912yes—
subgroupG/H
centerC23D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC22×SD16×C139C2
socleC23×C139C2×D4
hypercenterC22×SD16D139
hypocenterC139C2×#496
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#14555772C2semidirect
2. C22×D1112C2semidirect
3. C22×#14555770C2semidirect
4. C2×#17984838C2semidirect
5. C2×#17984831C2semidirect
6. #22581339C2direct (N × H)
7. C2×#17984752C2semidirect
8. C22×SD16×C139C2semidirect
13. C2×#14555772C22semidirect
15. C2×D1112C22semidirect
17. C2×#14555770C22semidirect
20. #17984838C22semidirect
22. #17984831C22semidirect
25. #17984752C22semidirect
29. C2×SD16×C139C22semidirect
47. C2×C139⋊C8D4semidirect
64. C2×C8×C139D4semidirect
81. C139⋊C8C2×D4semidirect
98. C8×C139C2×D4semidirect
117. C2×C139#496semidirect
122. C139C2×#496semidirect
125. C22×SD16D139semidirect
140. C2×SD16C2×D139semidirect
184. C2×C8C22⋊D139semidirect
221. C8C2×C22⋊D139semidirect
242. C2#22581339direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145557722
C22×D11122
C22×#145557702
C2×#179848382
C2×#179848312
#225813392
C2×#179847522
C22×SD16×C1392
C2×#496139