Finite Group Databasebeta

← C2×#22581184 #31815966

Subgroups — C2×#22581184 #31815966

Order 17792.

564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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
2C23×C139⋊C8C211yesmaximal, characteristic, complemented
3C2×#17984816C211yesmaximal, characteristic
4#22581184C218yesmaximal, direct product factor
5C2×#17984773C211yesmaximal, characteristic, complemented
6C2×#17984766C211yesmaximal, characteristic, complemented
7C2×#17984762C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C139C211yesmaximal, characteristic, complemented
9C22×D556C2211yescharacteristic
10C22×C22⋊D139—21no—
11C2×#14555772—24no—
12C2×#14555772C2214yescomplemented
13C22×C139⋊C8—24no—
14C22×C139⋊C8C2211yescharacteristic
15C22×C139⋊C8C2211yescharacteristic
16C22×C139⋊C8C2214yescomplemented
17#17984816—22no—
18#17984816C2214yes—
19C2×C4⋊Dic139C2211yescharacteristic
20C2×(C2×D139)⋊C4—21no—
21#17984773C2214yescomplemented
22#17984766C2214yescomplemented
23#17984762C2214yescomplemented
24C22×Q8×C139C2211yescharacteristic
25C23×C4×C139C2211yescharacteristic
26C22⋊Q8×C139—22no—
27C22⋊Q8×C139C2214yescomplemented
28C2×C4⋊C4×C139—21no—
29C2×C4⋊C4×C139C2211yescharacteristic
30C2×C22⋊C4×C139—21no—
31C23×D139—21no—
32C2×D556—22no—
33C2×D556—21no—
34C2×D556—22no—
35C2×D556C2312yes—
36C2×C22⋊D139—24no—
37C2×C22⋊D139—44no—
38C22×Dic139—21no—
39#14555772—28no—
40C2×C139⋊C8—28no—
41C2×C139⋊C8—22no—
42C2×C139⋊C8D414yescomplemented
43C2×C139⋊C8C2312yes—
44C2×C139⋊C8C2312yes—
45C4⋊Dic139—21no—
46C4⋊Dic139C2312yes—
47(C2×D139)⋊C4—24no—
48C24×C139D411yescharacteristic
49C2×Q8×C139—21no—
50C2×Q8×C139—22no—
51C2×Q8×C139—22no—
52C2×Q8×C139C2312yes—
53C22×C4×C139—22no—
54C22×C4×C139—22no—
55C22×C4×C139—21no—
56C22×C4×C139—21no—
57C22×C4×C139D411yescharacteristic
58C22×C4×C139D412yes—
59C22×C4×C139C2312yes—
60C22×C4×C139C2311yescharacteristic
61C4⋊C4×C139—24no—
62C4⋊C4×C139—21no—
63C4⋊C4×C139C2312yes—
64C22⋊C4×C139—24no—
65C22×D139—22no—
66C22×D139—42no—
67C22×D139—42no—
68C22×D139—42no—
69D556—22no—
70D556—22no—
71D556—42no—
72C22⋊D139—48no—
73C2×Dic139—22no—
74C2×Dic139—42no—
75C139⋊C8—22no—
76C139⋊C8C2×D414yescomplemented
77C23×C139—22no—
78C23×C139—22no—
79C23×C139SD1614yescomplemented
80C23×C139C2×D412yes—
81C23×C139C2×D411yescharacteristic
82Q8×C139—22no—
83Q8×C139—22no—
84Q8×C139—42no—
85C2×C4×C139—22no—
86C2×C4×C139—24no—
87C2×C4×C139—22no—
88C2×C4×C139—22no—
89C2×C4×C139—22no—
90C2×C4×C139—22no—
91C2×C4×C139—42no—
92C2×C4×C139—42no—
93C2×C4×C139C2×D412yes—
94C2×C4×C139C2×D412yes—
95C2×C4×C139C2×D411yescharacteristic
96C2×C4×C139#4112yes—
97C2×C4×C139C2411yescharacteristic
98C22×C139—22no—
99C22×C139—22no—
100C22×C139—28no—
101C22×C139#12112yes—
102C22×C139C2×SD1612yes—
103C22×C139C2×SD1614yescomplemented
104C22×C139#13512yes—
105C22×C139C22×D411yescharacteristic
106C2×D139—42no—
107C2×D139—42no—
108C2×D139—42no—
109C2×D139—84no—
110C4×C139—22no—
111C4×C139—42no—
112C4×C139—42no—
113C4×C139#12112yes—
114C4×C139C22×D411yescharacteristic
115C4×C139C2×#4111yescharacteristic
116Dic139—42no—
117C2×C139—24no—
118C2×C139#46514yescomplemented
119C2×C139C2×#12111yescharacteristic
120C2×C139C22×SD1611yescharacteristic
121C2×C139C2×#13511yescharacteristic
122D139—82no—
123C139C2×#46511yescharacteristic, complemented, Sylow
124C2×#465—1391nomaximal, Sylow
125C22×SD16—1391no—
126C23×C8—1391no—
127C2×C22⋊Q8D13911yescharacteristic, complemented
128C2×#121—1391no—
129#465—1398no—
130C2×#106—1391no—
131C2×#103—1391no—
132C2×#102—1391no—
133C22×Q8C2×D13911yescharacteristic
134C22×D4—2781no—
135C22×D4—1391no—
136C23×C4C2×D13911yescharacteristic
137C2×SD16—2784no—
138C2×SD16—1394no—
139C22×C8—2784no—
140C22×C8—1391no—
141C22×C8—1394no—
142C22×C8—1391no—
143C22⋊Q8—22no—
144C22⋊Q8C2×D13914yescomplemented
145#121—2782no—
146#121—1394no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—1391no—
149C2×C4⋊C4C2×D13911yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—2781no—
152#106—1394no—
153#103—1394no—
154#102—1394no—
155C24—2781no—
156C24C22⋊D13911yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D13912yes—
161C2×D4—2784no—
162C2×D4—2782no—
163C2×D4—2781no—
164C2×D4—2782no—
165C2×D4—5564no—
166C2×D4—1392no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—2781no—
172C22×C4C22⋊D13912yes—
173C22×C4C22⋊D13911yescharacteristic
174C22×C4C22×D13912yes—
175C22×C4C22×D13911yescharacteristic
176SD16—2788no—
177C2×C8—2782no—
178C2×C8—2788no—
179C2×C8—1392no—
180C2×C8—1394no—
181C2×C8—1392no—
182C4⋊C4—24no—
183C4⋊C4—21no—
184C4⋊C4—2781no—
185C4⋊C4—1392no—
186C4⋊C4C22×D13912yes—
187C22⋊C4—24no—
188C22⋊C4—2784no—
189C23—22no—
190C23—22no—
191C23—2782no—
192C23—5562no—
193C23—5562no—
194C23—5562no—
195C23#1455577214yescomplemented
196C23C2×C22⋊D13912yes—
197C23C2×C22⋊D13911yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—2782no—
202D4—2782no—
203D4—5568no—
204D4—5562no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—2782no—
214C2×C4—5562no—
215C2×C4D4×D13912yes—
216C2×C4C2×C22⋊D13912yes—
217C2×C4C2×C22⋊D13911yescharacteristic
218C2×C4#1455578412yes—
219C2×C4C23×D13911yescharacteristic
220C8—2782no—
221C8—1394no—
222C22—28no—
223C22—22no—
224C22—22no—
225C22—5562no—
226C22—5562no—
227C22—5562no—
228C22—11124no—
229C22#1798481412yes—
230C22C2×#1455577212yes—
231C22C2×#1455577214yescomplemented
232C22#1798486212yes—
233C22C22×C22⋊D13911yescharacteristic
234C4—22no—
235C4—42no—
236C4—42no—
237C4—5562no—
238C4#1798481412yes—
239C4C2×D4×D13911yescharacteristic
240C4C2×#1455578411yescharacteristic
241C2—24no—
242C2—11122no—
243C2#2258118414yesdirect product factor
244C2C2×#1798481411yescharacteristic
245C2C22×#1455577211yescharacteristic
246C2C2×#1798486211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×C22⋊Q8×C139C2
socleC23×C139C2×D4
prime radicalC2×#17984816C2
hypercenterC2×C22⋊Q8D139
hypocenterC139C2×#465
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14555772C2semidirect
2. C23×C139⋊C8C2semidirect
4. #22581184C2direct (N × H)
5. C2×#17984773C2semidirect
6. C2×#17984766C2semidirect
7. C2×#17984762C2semidirect
8. C2×C22⋊Q8×C139C2semidirect
12. C2×#14555772C22semidirect
16. C22×C139⋊C8C22semidirect
21. #17984773C22semidirect
22. #17984766C22semidirect
23. #17984762C22semidirect
27. C22⋊Q8×C139C22semidirect
42. C2×C139⋊C8D4semidirect
76. C139⋊C8C2×D4semidirect
79. C23×C139SD16semidirect
103. C22×C139C2×SD16semidirect
118. C2×C139#465semidirect
123. C139C2×#465semidirect
127. C2×C22⋊Q8D139semidirect
144. C22⋊Q8C2×D139semidirect
195. C23#14555772semidirect
231. C22C2×#14555772semidirect
243. C2#22581184direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145557722
C23×C139⋊C82
C2×#179848162
#225811842
C2×#179847732
C2×#179847662
C2×#179847622
C2×C22⋊Q8×C1392
C2×#465139