Finite Group Databasebeta

← #31808983

Subgroups — #31808983

Order 17792.

1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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×D4×D139C211yesmaximal, characteristic
2C2×#17984800C211yesmaximal, characteristic, complemented
3C2×#17984799C211yesmaximal, characteristic, complemented
4#22580856C211yesmaximal, characteristic, complemented
5#22580855C211yesmaximal, characteristic, complemented
6#22580854C211yesmaximal, characteristic, complemented
7#22580853C214yesmaximal, complemented
8#22580808C214yesmaximal, complemented
9#390×C139C211yesmaximal, characteristic, complemented
10C24×D139C2212yes—
11C22×D556C2211yescharacteristic
12C22×C22⋊D139C2212yes—
13C2×D4×D139—24no—
14C2×D4×D139—24no—
15C2×D4×D139C418yescomplemented
16C22×C4×D139C2211yescharacteristic
17#17984800—24no—
18#17984799—24no—
19C2×C4⋊Dic139C2211yescharacteristic, complemented
20C2×Dic139⋊C4C2212yescomplemented
21C2×C22⋊Dic139C2214yescomplemented
22C2×(C2×D139)⋊C4C2212yes—
23C2×(C2×D139)⋊C4C2212yes—
24C2×(C2×D139)⋊C4C2214yescomplemented
25C2×(C2×D139)⋊C4C2214yescomplemented
26C2×C4×Dic139C2212yescomplemented
27C2×C4×Dic139C2211yescharacteristic, complemented
28C22×D4×C139C2211yescharacteristic
29C2×C4⋊C4×C139C2211yescharacteristic, complemented
30C2×C22⋊C4×C139C2214yescomplemented
31C2×C42×C139C2211yescharacteristic, complemented
32C23×D139—24no—
33C23×D139—24no—
34C23×D139—44no—
35C23×D139—44no—
36C23×D139C2×C418yes—
37C23×D139C2312yes—
38C23×D139C2311yescharacteristic
39C2×D556—22no—
40C2×D556—22no—
41C2×D556C2×C414yes—
42C2×C22⋊D139—24no—
43C2×C22⋊D139—24no—
44C2×C22⋊D139C2×C418yes—
45D4×D139—232no—
46C22×Dic139C2312yes—
47C22×Dic139C2312yes—
48C22×Dic139C2311yescharacteristic
49C2×C4×D139C2×C414yes—
50C2×C4×D139D414yes—
51C2×C4×D139D414yes—
52C4⋊Dic139—22no—
53Dic139⋊C4—24no—
54C22⋊Dic139—44no—
55(C2×D139)⋊C4—24no—
56(C2×D139)⋊C4—24no—
57(C2×D139)⋊C4—44no—
58(C2×D139)⋊C4—44no—
59C4×Dic139—24no—
60C4×Dic139—22no—
61C24×C139C2312yes—
62C2×D4×C139—22no—
63C2×D4×C139—22no—
64C2×D4×C139C2×C414yes—
65C22×C4×C139C2312yes—
66C22×C4×C139C2312yes—
67C22×C4×C139C2311yescharacteristic
68C4⋊C4×C139—22no—
69C22⋊C4×C139—44no—
70C42×C139—22no—
71C22×D139—22no—
72C22×D139—22no—
73C22×D139—22no—
74C22×D139—22no—
75C22×D139—24no—
76C22×D139—24no—
77C22×D139—216no—
78C22×D139—416no—
79C22×D139—48no—
80C22×D139—416no—
81C22×D139—48no—
82C22×D139C22×C414yes—
83C22×D139C22×C412yes—
84C22×D139C2×D412yes—
85C22×D139C2×D412yes—
86D556—28no—
87C22⋊D139—216no—
88C2×Dic139—22no—
89C2×Dic139—22no—
90C2×Dic139—22no—
91C2×Dic139—24no—
92C2×Dic139—22no—
93C2×Dic139C22×C412yes—
94C2×Dic139C2×D412yes—
95C2×Dic139C2×D412yes—
96C4×D139C22⋊C4116yescomplemented
97C23×C139—22no—
98C23×C139—22no—
99C23×C139—24no—
100C23×C139—24no—
101C23×C139C22×C414yes—
102C23×C139C2411yescharacteristic
103D4×C139—28no—
104C2×C4×C139—22no—
105C2×C4×C139—22no—
106C2×C4×C139—22no—
107C2×C4×C139—24no—
108C2×C4×C139—22no—
109C2×C4×C139C22×C412yes—
110C2×C4×C139C2×D412yes—
111C2×C4×C139C2×D412yes—
112C22×C139—24no—
113C22×C139—28no—
114C22×C139—42no—
115C22×C139—44no—
116C22×C139—42no—
117C22×C139C23×C411yescharacteristic
118C22×C139C22×D411yescharacteristic
119C22×C139C22×D411yescharacteristic
120C22×C139H(5,𝔽2)12yes—
121C22×C139H(5,𝔽2)12yes—
122C2×D139—24no—
123C2×D139—22no—
124C2×D139—24no—
125C2×D139—22no—
126C2×D139—24no—
127C2×D139—28no—
128C2×D139—432no—
129C2×D139—42no—
130C2×D139—44no—
131C2×D139—42no—
132C2×D139C2×C22⋊C414yes—
133C4×C139—42no—
134C4×C139—42no—
135C4×C139C2×C22⋊C414yes—
136Dic139—42no—
137Dic139—42no—
138Dic139C2×C22⋊C414yes—
139C2×C139—44no—
140C2×C139C22×C22⋊C411yescharacteristic
141C2×C139#51812yes—
142C2×C139#53511yescharacteristic
143C2×C139#53512yes—
144C2×C139#53511yescharacteristic
145D139—24no—
146D139—44no—
147C139#230911yescharacteristic, complemented, Sylow
148#2309—1391nomaximal, Sylow
149C23×D4—1391no—
150C2×#117—1391no—
151C2×#117—1391no—
152#390—1391no—
153#390—1391no—
154#390—1394no—
155#390—1391no—
156#390D13911yescharacteristic, complemented
157#379—1394no—
158C25—1392no—
159C22×D4—2784no—
160C22×D4—2784no—
161C22×D4—1392no—
162C22×D4—1398no—
163C22×D4—1391no—
164C22×D4C2×D13911yescharacteristic
165C23×C4—1391no—
166#117—2784no—
167#117—2784no—
168C2×C4⋊C4—1392no—
169C2×C4⋊C4—1391no—
170C2×C4⋊C4C2×D13911yescharacteristic, complemented
171C2×C22⋊C4—1392no—
172C2×C22⋊C4—1392no—
173C2×C22⋊C4—1394no—
174C2×C22⋊C4—1394no—
175C2×C22⋊C4—1394no—
176C2×C22⋊C4C2×D13914yescomplemented
177C2×C42—1392no—
178C2×C42—1391no—
179C2×C42C2×D13911yescharacteristic, complemented
180C24—2784no—
181C24—2784no—
182C24—5564no—
183C24—5564no—
184C24—1392no—
185C24—1391no—
186C24—1398no—
187C24C22×D13912yes—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—27832no—
191C2×D4—2784no—
192C2×D4—2784no—
193C2×D4—2782no—
194C2×D4—2782no—
195C2×D4—1398no—
196C2×D4—1394no—
197C2×D4C4×D13914yes—
198C22×C4—1392no—
199C22×C4—1392no—
200C22×C4—1391no—
201C22×C4—1394no—
202C22×C4—1394no—
203C22×C4—1394no—
204C22×C4C22×D13912yes—
205C22×C4C22×D13912yes—
206C22×C4C22×D13911yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—2784no—
209C4⋊C4—2782no—
210C22⋊C4—44no—
211C22⋊C4—2784no—
212C22⋊C4—2784no—
213C22⋊C4—5564no—
214C22⋊C4—5564no—
215C22⋊C4—5564no—
216C42—22no—
217C42—2784no—
218C42—2782no—
219C23—22no—
220C23—22no—
221C23—24no—
222C23—24no—
223C23—27816no—
224C23—2782no—
225C23—2782no—
226C23—2782no—
227C23—2782no—
228C23—2784no—
229C23—2784no—
230C23—55616no—
231C23—5568no—
232C23—55616no—
233C23—5568no—
234C23—1394no—
235C23—1392no—
236C23—1392no—
237C23—1392no—
238C23C2×C4×D13914yes—
239C23C23×D13911yescharacteristic
240D4—28no—
241D4—27816no—
242D4—2788no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—22no—
248C2×C4—2782no—
249C2×C4—2782no—
250C2×C4—2782no—
251C2×C4—2782no—
252C2×C4—2784no—
253C2×C4—1392no—
254C2×C4—1392no—
255C2×C4—1392no—
256C2×C4—13916no—
257C2×C4C2×C4×D13912yes—
258C2×C4D4×D13912yes—
259C2×C4D4×D13912yes—
260C22—24no—
261C22—28no—
262C22—42no—
263C22—44no—
264C22—42no—
265C22—2782no—
266C22—2784no—
267C22—2782no—
268C22—2784no—
269C22—2784no—
270C22—2788no—
271C22—55632no—
272C22—5562no—
273C22—5564no—
274C22—5562no—
275C22—1394no—
276C22C22×C4×D13911yescharacteristic
277C22C2×D4×D13911yescharacteristic
278C22C2×D4×D13911yescharacteristic
279C22#1798488712yes—
280C22#1798488812yes—
281C4—42no—
282C4—42no—
283C4—5562no—
284C4—5562no—
285C4—1394no—
286C4C22⋊C4×D13914yes—
287C2—44no—
288C2—2784no—
289C2—5564no—
290C2C2×C22⋊C4×D13911yescharacteristic
291C2#2258142512yes—
292C2#2258151611yescharacteristic
293C2#2258151912yes—
294C2#2258152111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutatorC22×C139C23×C4
Fitting#390×C139C2
socle, cosocleC23×C139C24
prime radicalC22×D4×D139C2
hypercenter#390D139
hypocenterC139#2309
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#17984800C2semidirect
3. C2×#17984799C2semidirect
4. #22580856C2semidirect
5. #22580855C2semidirect
6. #22580854C2semidirect
7. #22580853C2semidirect
8. #22580808C2semidirect
9. #390×C139C2semidirect
15. C2×D4×D139C4semidirect
19. C2×C4⋊Dic139C22semidirect
20. C2×Dic139⋊C4C22semidirect
21. C2×C22⋊Dic139C22semidirect
24. C2×(C2×D139)⋊C4C22semidirect
25. C2×(C2×D139)⋊C4C22semidirect
26. C2×C4×Dic139C22semidirect
27. C2×C4×Dic139C22semidirect
29. C2×C4⋊C4×C139C22semidirect
30. C2×C22⋊C4×C139C22semidirect
31. C2×C42×C139C22semidirect
96. C4×D139C22⋊C4semidirect
147. C139#2309semidirect
156. #390D139semidirect
170. C2×C4⋊C4C2×D139semidirect
176. C2×C22⋊C4C2×D139semidirect
179. C2×C42C2×D139semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1392
C2×#179848002
C2×#179847992
#225808562
#225808552
#225808542
#225808532
#225808082
#390×C1392
#2309139