Finite Group Databasebeta

← C139×#11773 #48006369

Subgroups — C139×#11773 #48006369

Order 35584.

482 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 106 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
1#2486×C139C211yesmaximal, characteristic
2C4×#99×C139C211yesmaximal, characteristic
3#1466×C139C211yesmaximal, characteristic
4#1344×C139C214yesmaximal, complemented
5C2×#123×C139—21no—
6C2×C4×D4×C139C2211yescharacteristic
7C22×C4⋊C4×C139C411yescharacteristic, complemented
8#432×C139—21no—
9C2×#99×C139—21no—
10#398×C139C412yescomplemented
11#397×C139C2212yes—
12#389×C139—21no—
13#381×C139—21no—
14#380×C139—21no—
15#380×C139C411yescharacteristic, complemented
16C4×C22⋊C4×C139—21no—
17#342×C139C2212yes—
18#323×C139—21no—
19#323×C139C2212yes—
20C22×D4×C139D411yescharacteristic
21C23×C4×C139—21no—
22C23×C4×C139C2×C411yescharacteristic
23C23×C4×C139D411yescharacteristic
24#123×C139—44no—
25C4×D4×C139—41no—
26C4×D4×C139—41no—
27C2×C4⋊C4×C139—22no—
28C2×C4⋊C4×C139—21no—
29C2×C4⋊C4×C139—21no—
30C2×C4⋊C4×C139—41no—
31C2×C4⋊C4×C139—41no—
32C2×C4⋊C4×C139C2×C412yes—
33C2×C4⋊C4×C139C2×C411yescharacteristic
34C2×C22⋊C4×C139—22no—
35C2×C22⋊C4×C139—21no—
36C2×C22⋊C4×C139—22no—
37C2×C22⋊C4×C139D411yescharacteristic
38C2×C22⋊C4×C139C2311yescharacteristic
39C2×C42×C139—41no—
40C2×C42×C139D411yescharacteristic
41C4⋊C8×C139—41no—
42#99×C139—24no—
43C22⋊C8×C139—22no—
44#97×C139—41no—
45#95×C139—22no—
46#95×C139—22no—
47#95×C139—41no—
48#95×C139C2×C412yes—
49C24×C139C22⋊C411yescharacteristic
50C24×C139C2×D411yescharacteristic
51C2×D4×C139—22no—
52C2×D4×C139—22no—
53C2×D4×C139—41no—
54C22×C4×C139—21no—
55C22×C4×C139—21no—
56C22×C4×C139—21no—
57C22×C4×C139—21no—
58C22×C4×C139—22no—
59C22×C4×C139—22no—
60C22×C4×C139—42no—
61C22×C4×C139—42no—
62C22×C4×C139—42no—
63C22×C4×C139—42no—
64C22×C4×C139—42no—
65C22×C4×C139—42no—
66C22×C4×C139C22⋊C411yescharacteristic
67C22×C4×C139C22⋊C411yescharacteristic
68C22×C4×C139C22⋊C411yescharacteristic
69C22×C4×C139C22×C411yescharacteristic
70C22×C4×C139C2×D411yescharacteristic
71C2×C8×C139—42no—
72C4⋊C4×C139—41no—
73C4⋊C4×C139—42no—
74C4⋊C4×C139—42no—
75C4⋊C4×C139—44no—
76C4⋊C4×C139—41no—
77C4⋊C4×C139—41no—
78C22⋊C4×C139—24no—
79C22⋊C4×C139—41no—
80C22⋊C4×C139—41no—
81C22⋊C4×C139—42no—
82C22⋊C4×C139—42no—
83C22⋊C4×C139—44no—
84C42×C139—21no—
85C42×C139—21no—
86C42×C139—82no—
87C23×C139—21no—
88C23×C139—21no—
89C23×C139—21no—
90C23×C139—21no—
91C23×C139—41no—
92C23×C139—41no—
93C23×C139—41no—
94C23×C139—41no—
95C23×C139#10412yes—
96C23×C139C2×C22⋊C411yescharacteristic
97C23×C139AGL(1,ℤ/8)12yes—
98D4×C139—44no—
99C2×C4×C139—22no—
100C2×C4×C139—21no—
101C2×C4×C139—21no—
102C2×C4×C139—21no—
103C2×C4×C139—21no—
104C2×C4×C139—21no—
105C2×C4×C139—21no—
106C2×C4×C139—42no—
107C2×C4×C139—42no—
108C2×C4×C139—42no—
109C2×C4×C139—41no—
110C2×C4×C139—41no—
111C2×C4×C139—41no—
112C2×C4×C139—44no—
113C2×C4×C139—42no—
114C2×C4×C139—42no—
115C2×C4×C139—42no—
116C2×C4×C139—42no—
117C2×C4×C139—42no—
118C2×C4×C139—42no—
119C2×C4×C139—81no—
120C2×C4×C139—84no—
121C2×C4×C139—82no—
122C2×C4×C139—82no—
123C2×C4×C139#9911yescharacteristic
124C2×C4×C139#9911yescharacteristic
125C8×C139—82no—
126C22×C139—21no—
127C22×C139—21no—
128C22×C139—22no—
129C22×C139—22no—
130C22×C139—42no—
131C22×C139—42no—
132C22×C139—42no—
133C22×C139—41no—
134C22×C139—41no—
135C22×C139—41no—
136C22×C139—41no—
137C22×C139—81no—
138C22×C139C2×#9911yescharacteristic
139C22×C139#41811yescharacteristic
140C22×C139C2×#10411yescharacteristic
141C4×C139—21no—
142C4×C139—41no—
143C4×C139—41no—
144C4×C139—41no—
145C4×C139—41no—
146C4×C139—82no—
147C4×C139—84no—
148C4×C139—82no—
149C4×C139#35212yes—
150C2×C139—21no—
151C2×C139—21no—
152C2×C139—42no—
153C2×C139—42no—
154C2×C139#150711yescharacteristic
155C2×C139C2×#35211yescharacteristic
156C2×C139#212911yescharacteristic
157#11773C13911yesmaximal, characteristic, direct product factor, Sylow
158C139#1177311yescharacteristic, direct product factor, Sylow
159#2486C2×C13911yescharacteristic
160C4×#99C2×C13911yescharacteristic
161#1466C2×C13911yescharacteristic
162#1344C2×C13914yescomplemented
163C2×#123—21no—
164C2×C4×D4C22×C13911yescharacteristic
165C22×C4⋊C4C4×C13911yescharacteristic, complemented
166#432—21no—
167C2×#99—21no—
168#398C4×C13912yescomplemented
169#397C22×C13912yes—
170#389—21no—
171#381—21no—
172#380—21no—
173#380C4×C13911yescharacteristic, complemented
174C4×C22⋊C4—21no—
175#342C22×C13912yes—
176#323—21no—
177#323C22×C13912yes—
178C22×D4D4×C13911yescharacteristic
179C23×C4—21no—
180C23×C4C2×C4×C13911yescharacteristic
181C23×C4D4×C13911yescharacteristic
182#123—44no—
183C4×D4—41no—
184C4×D4—41no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4C2×C4×C13912yes—
191C2×C4⋊C4C2×C4×C13911yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4D4×C13911yescharacteristic
196C2×C22⋊C4C23×C13911yescharacteristic
197C2×C42—41no—
198C2×C42D4×C13911yescharacteristic
199C4⋊C8—41no—
200#99—24no—
201C22⋊C8—22no—
202#97—41no—
203#95—22no—
204#95—22no—
205#95—41no—
206#95C2×C4×C13912yes—
207C24C22⋊C4×C13911yescharacteristic
208C24C2×D4×C13911yescharacteristic
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—41no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4C22⋊C4×C13911yescharacteristic
225C22×C4C22⋊C4×C13911yescharacteristic
226C22×C4C22⋊C4×C13911yescharacteristic
227C22×C4C22×C4×C13911yescharacteristic
228C22×C4C2×D4×C13911yescharacteristic
229C2×C8—42no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—44no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C22⋊C4—24no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—44no—
242C42—21no—
243C42—21no—
244C42—82no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23#104×C13912yes—
254C23C2×C22⋊C4×C13911yescharacteristic
255C23AGL(1,ℤ/8)×C13912yes—
256D4—44no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—44no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—84no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4#99×C13911yescharacteristic
282C2×C4#99×C13911yescharacteristic
283C8—82no—
284C22—21no—
285C22—21no—
286C22—22no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22C2×#99×C13911yescharacteristic
297C22#418×C13911yescharacteristic
298C22C2×#104×C13911yescharacteristic
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—82no—
305C4—84no—
306C4—82no—
307C4#352×C13912yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—42no—
312C2#1507×C13911yescharacteristic
313C2C2×#352×C13911yescharacteristic
314C2#2129×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#99
commutatorC22×C4C22×C4×C139
Frattini, cosocleC2×C22⋊C4C23×C139
prime radicalC22×D4×C139D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C22×C4×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1344×C139C2semidirect
7. C22×C4⋊C4×C139C4semidirect
10. #398×C139C4semidirect
15. #380×C139C4semidirect
157. #11773C139direct (N × H)
158. C139#11773direct (N × H)
162. #1344C2×C139semidirect
165. C22×C4⋊C4C4×C139semidirect
168. #398C4×C139semidirect
173. #380C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2486×C1392
C4×#99×C1392
#1466×C1392
#1344×C1392
#11773139