Finite Group Databasebeta

← #31814697

Subgroups — #31814697

Order 17792.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C4×D139C211yesmaximal, characteristic, complemented
2C2×#17984826C211yesmaximal, characteristic, complemented
3C2×#17984825C211yesmaximal, characteristic, complemented
4C2×#17984812C211yesmaximal, characteristic
5#22580831C214yesmaximal, complemented
6#22580827C214yesmaximal, complemented
7#22580814C211yesmaximal, characteristic, complemented
8#22580808C211yesmaximal, characteristic, complemented
9#381×C139C211yesmaximal, characteristic, complemented
10C24×D139C2211yescharacteristic
11C22×D556C2212yes—
12C22×C22⋊D139C2211yescharacteristic
13C23×Dic139C2211yescharacteristic
14C22×C4×D139—24no—
15C22×C4×D139—24no—
16C22×C4×D139—24no—
17C22×C4×D139C2214yes—
18#17984826—24no—
19#17984825—24no—
20#17984812—24no—
21C2×C4⋊Dic139C2212yescomplemented
22C2×Dic139⋊C4C2212yescomplemented
23C2×C22⋊Dic139C2211yescharacteristic
24C2×(C2×D139)⋊C4C2214yes—
25C2×(C2×D139)⋊C4C2212yes—
26C2×(C2×D139)⋊C4C2212yescomplemented
27C2×(C2×D139)⋊C4C2212yescomplemented
28C139⋊#95C2214yescomplemented
29C23×C4×C139C2211yescharacteristic
30C2×C22⋊C4×C139C2211yescharacteristic
31C2×C22⋊C4×C139C2211yescharacteristic
32#95×C139C2214yescomplemented
33C23×D139—28no—
34C23×D139—22no—
35C23×D139—22no—
36C23×D139D414yes—
37C23×D139C2311yescharacteristic
38C23×D139C2312yes—
39C2×D556—24no—
40C2×D556—28no—
41C2×C22⋊D139—22no—
42C2×C22⋊D139—22no—
43C2×C22⋊D139—22no—
44C22×Dic139—22no—
45C22×Dic139—22no—
46C22×Dic139D414yescomplemented
47C22×Dic139C2312yes—
48C22×Dic139C2311yescharacteristic
49C22×Dic139C2312yes—
50C2×C4×D139—232no—
51C2×C4×D139—28no—
52C2×C4×D139—28no—
53C2×C4×D139—28no—
54C4⋊Dic139—24no—
55Dic139⋊C4—24no—
56C22⋊Dic139—22no—
57(C2×D139)⋊C4—24no—
58(C2×D139)⋊C4—28no—
59(C2×D139)⋊C4—24no—
60(C2×D139)⋊C4—24no—
61C24×C139C2311yescharacteristic
62C22×C4×C139—22no—
63C22×C4×C139—22no—
64C22×C4×C139D414yescomplemented
65C22×C4×C139C2312yes—
66C22×C4×C139C2312yes—
67C22×C4×C139C2312yes—
68C22⋊C4×C139—22no—
69C22⋊C4×C139—22no—
70C22×D139—216no—
71C22×D139—216no—
72C22×D139—28no—
73C22×D139—22no—
74C22×D139—22no—
75C22×D139—24no—
76C22×D139—216no—
77C22×D139—21no—
78C22×D139—21no—
79C22×D139—21no—
80C22×D139—24no—
81C22×D139C2×D414yes—
82C22×D139#4118yes—
83D556—48no—
84C22⋊D139—44no—
85C2×Dic139—28no—
86C2×Dic139—22no—
87C2×Dic139—22no—
88C2×Dic139—21no—
89C2×Dic139—22no—
90C2×Dic139—21no—
91C2×Dic139—21no—
92C2×Dic139—24no—
93C2×Dic139C2×D414yes—
94C4×D139—232no—
95C23×C139—24no—
96C23×C139C2×D412yes—
97C23×C139C2×D412yes—
98C23×C139C2×D412yes—
99C23×C139C2411yescharacteristic
100C2×C4×C139—28no—
101C2×C4×C139—22no—
102C2×C4×C139—22no—
103C2×C4×C139—22no—
104C2×C4×C139—22no—
105C2×C4×C139—24no—
106C2×C4×C139—24no—
107C2×C4×C139C2×D414yes—
108C22×C139—24no—
109C22×C139—24no—
110C22×C139—24no—
111C22×C139#12014yes—
112C22×C139C22×D411yescharacteristic
113C22×C139C22×D411yescharacteristic
114C22×C139C22×D411yescharacteristic
115C22×C139C2×#4114yes—
116C2×D139—232no—
117C2×D139—24no—
118C2×D139—24no—
119C2×D139—28no—
120C2×D139—28no—
121C2×D139—41no—
122C2×D139—42no—
123C2×D139—42no—
124C2×D139—42no—
125C2×D139#12318yescomplemented
126C4×C139—24no—
127C4×C139—42no—
128C4×C139—42no—
129Dic139—24no—
130Dic139—41no—
131Dic139—42no—
132C2×C139—24no—
133C2×C139C2×#12011yescharacteristic
134C2×C139C2×#12312yes—
135C2×C139#52512yes—
136C2×C139#52512yes—
137D139—28no—
138D139—81no—
139C139#284911yescharacteristic, complemented, Sylow
140#2849—1391nomaximal, Sylow
141C24×C4—1391no—
142C2×#123—1391no—
143C2×#123—1391no—
144C2×#120—1391no—
145#386—1394no—
146#385—1394no—
147#381—1391no—
148#381D13911yescharacteristic, complemented
149#379—1391no—
150C25—1391no—
151C22×D4—1391no—
152C22×D4—1392no—
153C23×C4—2784no—
154C23×C4—2784no—
155C23×C4—2784no—
156C23×C4—1394no—
157C23×C4—1391no—
158C23×C4C2×D13911yescharacteristic
159#123—2784no—
160#123—2784no—
161#120—2784no—
162C2×C4⋊C4—1392no—
163C2×C4⋊C4—1392no—
164C2×C22⋊C4—1391no—
165C2×C22⋊C4—1392no—
166C2×C22⋊C4—1392no—
167C2×C22⋊C4—1392no—
168C2×C22⋊C4—1394no—
169C2×C22⋊C4C2×D13911yescharacteristic
170C2×C22⋊C4C2×D13911yescharacteristic
171#95—1394no—
172#95C2×D13914yescomplemented
173C24—2788no—
174C24—2782no—
175C24—2782no—
176C24—1391no—
177C24—1394no—
178C24—1392no—
179C24C22×D13911yescharacteristic
180C2×D4—2784no—
181C2×D4—2788no—
182C2×D4—2782no—
183C2×D4—2782no—
184C2×D4—2782no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—27832no—
188C22×C4—2788no—
189C22×C4—2788no—
190C22×C4—2782no—
191C22×C4—2782no—
192C22×C4—2788no—
193C22×C4—1392no—
194C22×C4—1391no—
195C22×C4—1394no—
196C22×C4—1392no—
197C22×C4D55614yescomplemented
198C22×C4C22×D13912yes—
199C22×C4C22×D13912yes—
200C22×C4C22×D13912yes—
201C4⋊C4—2784no—
202C4⋊C4—2784no—
203C22⋊C4—22no—
204C22⋊C4—22no—
205C22⋊C4—2788no—
206C22⋊C4—2784no—
207C22⋊C4—2784no—
208C22⋊C4—2782no—
209C22⋊C4—2784no—
210C23—24no—
211C23—27816no—
212C23—27816no—
213C23—27816no—
214C23—2788no—
215C23—2782no—
216C23—2782no—
217C23—2784no—
218C23—2781no—
219C23—2781no—
220C23—2781no—
221C23—2784no—
222C23—1394no—
223C23—1398no—
224C23D4×D13912yes—
225C23D4×D13912yes—
226C23C2×D55612yes—
227C23C23×D13911yescharacteristic
228D4—5568no—
229D4—5564no—
230C2×C4—28no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—27832no—
238C2×C4—2788no—
239C2×C4—2782no—
240C2×C4—2782no—
241C2×C4—2781no—
242C2×C4—2781no—
243C2×C4—2782no—
244C2×C4—2781no—
245C2×C4—2784no—
246C2×C4—1394no—
247C2×C4C2×D55614yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—27832no—
252C22—2784no—
253C22—2784no—
254C22—2788no—
255C22—2788no—
256C22—5561no—
257C22—5562no—
258C22—5562no—
259C22—5562no—
260C22—1398no—
261C22#1798481214yes—
262C22C2×D4×D13911yescharacteristic
263C22C2×D4×D13911yescharacteristic
264C22C22×D55611yescharacteristic
265C22#41×D13914yes—
266C4—24no—
267C4—42no—
268C4—42no—
269C4—2784no—
270C4—5561no—
271C4—5562no—
272C2—24no—
273C2—2788no—
274C2—11121no—
275C2C2×#1798481211yescharacteristic
276C2#123×D13912yes—
277C2#2258146112yes—
278C2#2258146512yes—
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, cosocleC23×C139C24
Fitting#381×C139C2
prime radicalC2×#17984812C2
hypercenter#381D139
hypocenterC139#2849
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C23×C4×D139C2semidirect
2. C2×#17984826C2semidirect
3. C2×#17984825C2semidirect
5. #22580831C2semidirect
6. #22580827C2semidirect
7. #22580814C2semidirect
8. #22580808C2semidirect
9. #381×C139C2semidirect
21. C2×C4⋊Dic139C22semidirect
22. C2×Dic139⋊C4C22semidirect
26. C2×(C2×D139)⋊C4C22semidirect
27. C2×(C2×D139)⋊C4C22semidirect
28. C139⋊#95C22semidirect
32. #95×C139C22semidirect
46. C22×Dic139D4semidirect
64. C22×C4×C139D4semidirect
125. C2×D139#123semidirect
139. C139#2849semidirect
148. #381D139semidirect
172. #95C2×D139semidirect
197. C22×C4D556semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1392
C2×#179848262
C2×#179848252
C2×#179848122
#225808312
#225808272
#225808142
#225808082
#381×C1392
#2849139