Finite Group Databasebeta

← #31814729

Subgroups — #31814729

Order 17792.

582 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C2×#17984826C211yesmaximal, characteristic
2C22×C4×Dic139C211yesmaximal, characteristic, complemented
3#22580843C212yesmaximal, complemented
4#22580842C212yesmaximal, complemented
5#22580840C212yesmaximal, complemented
6#22580839C212yesmaximal, complemented
7#22580832C211yesmaximal, characteristic
8#22580830C211yesmaximal, characteristic
9#22580825C211yesmaximal, characteristic, complemented
10#22580814C211yesmaximal, characteristic, complemented
11#385×C139C211yesmaximal, characteristic, complemented
12C22×C22⋊D139C2211yescharacteristic
13C23×Dic139C2211yescharacteristic
14C23×Dic139C2211yescharacteristic
15#17984826—24no—
16C2×C4⋊Dic139C2211yescharacteristic
17C2×C4⋊Dic139C2211yescharacteristic
18C2×Dic139⋊C4C2212yes—
19C2×C22⋊Dic139C2211yescharacteristic
20C2×(C2×D139)⋊C4C2212yes—
21C2×(C2×D139)⋊C4C2212yes—
22C2×(C2×D139)⋊C4C2211yescharacteristic
23C2×(C2×D139)⋊C4C2211yescharacteristic
24C2×C4×Dic139—24no—
25C2×C4×Dic139C2212yes—
26C2×C4×Dic139C2212yes—
27C139⋊#95C2212yes—
28C139⋊#95C2212yes—
29C139⋊#95C2212yes—
30C139⋊#95C2212yes—
31C139⋊#95C2212yes—
32C23×C4×C139C2211yescharacteristic
33C2×C4⋊C4×C139C2212yes—
34C2×C22⋊C4×C139C2211yescharacteristic
35C2×C22⋊C4×C139C2211yescharacteristic
36#95×C139C2212yes—
37C23×D139C2311yescharacteristic
38C2×C22⋊D139—22no—
39C2×C22⋊D139—22no—
40C2×C22⋊D139—22no—
41C22×Dic139—24no—
42C22×Dic139—22no—
43C22×Dic139—22no—
44C22×Dic139—22no—
45C22×Dic139D414yes—
46C22×Dic139C2312yes—
47C22×Dic139C2311yescharacteristic
48C22×Dic139C2311yescharacteristic
49C22×Dic139C2311yescharacteristic
50C22×Dic139C2312yes—
51C4⋊Dic139—22no—
52C4⋊Dic139—22no—
53Dic139⋊C4—24no—
54C22⋊Dic139—22no—
55(C2×D139)⋊C4—22no—
56(C2×D139)⋊C4—22no—
57(C2×D139)⋊C4—24no—
58(C2×D139)⋊C4—24no—
59C4×Dic139—24no—
60C4×Dic139—24no—
61C24×C139C2311yescharacteristic
62C22×C4×C139—22no—
63C22×C4×C139—24no—
64C22×C4×C139C2311yescharacteristic
65C22×C4×C139C2311yescharacteristic
66C22×C4×C139C2312yes—
67C22×C4×C139C2312yes—
68C4⋊C4×C139—24no—
69C22⋊C4×C139—22no—
70C22⋊C4×C139—22no—
71C22×D139—21no—
72C22×D139—22no—
73C22×D139—22no—
74C22×D139—21no—
75C22×D139—21no—
76C22⋊D139—44no—
77C2×Dic139—28no—
78C2×Dic139—28no—
79C2×Dic139—22no—
80C2×Dic139—22no—
81C2×Dic139—21no—
82C2×Dic139—21no—
83C2×Dic139—21no—
84C2×Dic139—21no—
85C2×Dic139—21no—
86C2×Dic139—22no—
87C2×Dic139—22no—
88C2×Dic139—22no—
89C2×Dic139—21no—
90C2×Dic139—21no—
91C2×Dic139C2×D412yes—
92C2×Dic139C2×D412yes—
93C2×Dic139#4114yes—
94C23×C139—22no—
95C23×C139—22no—
96C23×C139C2×D412yes—
97C23×C139#4112yes—
98C23×C139#4112yes—
99C23×C139C2411yescharacteristic
100C2×C4×C139—28no—
101C2×C4×C139—22no—
102C2×C4×C139—22no—
103C2×C4×C139—21no—
104C2×C4×C139—21no—
105C2×C4×C139—22no—
106C2×C4×C139—22no—
107C2×C4×C139—22no—
108C2×C4×C139—22no—
109C2×C4×C139—22no—
110C2×C4×C139#4114yes—
111C22×C139—22no—
112C22×C139—22no—
113C22×C139—24no—
114C22×C139—24no—
115C22×C139#12314yes—
116C22×C139C22×D411yescharacteristic
117C22×C139C2×#4112yes—
118C22×C139C2×#4112yes—
119C22×C139C2×#4111yescharacteristic
120C22×C139C2×#4111yescharacteristic
121C2×D139—41no—
122C2×D139—41no—
123C2×D139—41no—
124C2×D139—42no—
125C2×D139—42no—
126C4×C139—24no—
127C4×C139—41no—
128C4×C139—41no—
129C4×C139—42no—
130Dic139—22no—
131Dic139—22no—
132Dic139—24no—
133Dic139—41no—
134Dic139—42no—
135C2×C139—24no—
136C2×C139C2×#12311yescharacteristic
137C2×C139#52511yescharacteristic
138C2×C139#52511yescharacteristic
139C2×C139#52912yes—
140C2×C139#52912yes—
141D139—81no—
142C139#285311yescharacteristic, complemented, Sylow
143#2853—1391nomaximal, Sylow
144C2×#123—1391no—
145C22×C42—1391no—
146#388—1392no—
147#388—1392no—
148#387—1392no—
149#387—1392no—
150#386—1391no—
151#386—1391no—
152#385—1391no—
153#385D13911yescharacteristic, complemented
154#381—1391no—
155C22×D4—1391no—
156C23×C4—1391no—
157C23×C4—1391no—
158C23×C4C2×D13911yescharacteristic
159#123—2784no—
160C2×C4⋊C4—1391no—
161C2×C4⋊C4—1391no—
162C2×C4⋊C4—1392no—
163C2×C4⋊C4C2×D13912yes—
164C2×C22⋊C4—1391no—
165C2×C22⋊C4—1391no—
166C2×C22⋊C4—1391no—
167C2×C22⋊C4—1392no—
168C2×C22⋊C4—1392no—
169C2×C22⋊C4C2×D13911yescharacteristic
170C2×C22⋊C4C2×D13911yescharacteristic
171C2×C42—2784no—
172C2×C42—1392no—
173C2×C42—1392no—
174#95—1392no—
175#95—1392no—
176#95—1392no—
177#95—1392no—
178#95—1392no—
179#95C2×D13912yes—
180C24—1391no—
181C24C22×D13911yescharacteristic
182C2×D4—2782no—
183C2×D4—2782no—
184C2×D4—2782no—
185C22×C4—22no—
186C22×C4—24no—
187C22×C4—2782no—
188C22×C4—2782no—
189C22×C4—2782no—
190C22×C4—2784no—
191C22×C4—1392no—
192C22×C4—1391no—
193C22×C4—1394no—
194C22×C4—1392no—
195C22×C4—1391no—
196C22×C4—1391no—
197C22×C4C22×D13912yes—
198C22×C4C22×D13911yescharacteristic
199C22×C4C22×D13911yescharacteristic
200C22×C4C22×D13912yes—
201C4⋊C4—24no—
202C4⋊C4—2784no—
203C4⋊C4—2782no—
204C4⋊C4—2782no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—2784no—
208C22⋊C4—2782no—
209C22⋊C4—2782no—
210C22⋊C4—2782no—
211C22⋊C4—2784no—
212C42—2784no—
213C42—2784no—
214C23—22no—
215C23—22no—
216C23—2781no—
217C23—2782no—
218C23—2782no—
219C23—2781no—
220C23—2781no—
221C23D4×D13912yes—
222C23#1455578512yes—
223C23#1455578612yes—
224C23C23×D13911yescharacteristic
225D4—5564no—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—2788no—
237C2×C4—2788no—
238C2×C4—2782no—
239C2×C4—2782no—
240C2×C4—2781no—
241C2×C4—2781no—
242C2×C4—2781no—
243C2×C4—2781no—
244C2×C4—2781no—
245C2×C4—2782no—
246C2×C4—2782no—
247C2×C4—2781no—
248C2×C4—2782no—
249C2×C4—2781no—
250C2×C4—1392no—
251C2×C4—1392no—
252C2×C4—1394no—
253C2×C4#1455578414yes—
254C22—22no—
255C22—22no—
256C22—24no—
257C22—24no—
258C22—5561no—
259C22—5561no—
260C22—5561no—
261C22—5562no—
262C22—5562no—
263C22#1798482714yes—
264C22C2×D4×D13911yescharacteristic
265C22#41×D13912yes—
266C22C2×#1455578412yes—
267C22C2×#1455578511yescharacteristic
268C22C2×#1455578611yescharacteristic
269C4—24no—
270C4—41no—
271C4—41no—
272C4—42no—
273C4—2782no—
274C4—2782no—
275C4—2784no—
276C4—5561no—
277C4—5562no—
278C2—24no—
279C2—11121no—
280C2C2×#1798482711yescharacteristic
281C2#2258145911yescharacteristic
282C2#2258146111yescharacteristic
283C2#2258148312yes—
284C2#2258148912yes—
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, cosocleC23×C139C24
Fitting#385×C139C2
prime radicalC22×C22⋊D139C22
hypercenter#385D139
hypocenterC139#2853
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic139C2semidirect
3. #22580843C2semidirect
4. #22580842C2semidirect
5. #22580840C2semidirect
6. #22580839C2semidirect
9. #22580825C2semidirect
10. #22580814C2semidirect
11. #385×C139C2semidirect
142. C139#2853semidirect
153. #385D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848262
C22×C4×Dic1392
#225808432
#225808422
#225808402
#225808392
#225808322
#225808302
#225808252
#225808142
#385×C1392
#2853139