Finite Group Databasebeta

← C139×#7671 #48002267

Subgroups — C139×#7671 #48002267

Order 35584.

468 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2851×C139C211yesmaximal, characteristic
2#1817×C139C211yesmaximal, characteristic
3C4×C22⋊C8×C139C211yesmaximal, characteristic
4#1271×C139C212yesmaximal, complemented
5#1271×C139C212yesmaximal, complemented
6C2×#125×C139C411yescharacteristic
7C22×C42×C139C2211yescharacteristic
8C2×C22⋊C8×C139—21no—
9C2×C22⋊C8×C139—21no—
10C2×C4×C8×C139—21no—
11#389×C139C2211yescharacteristic
12#389×C139C2211yescharacteristic
13#387×C139—21no—
14#387×C139—21no—
15#385×C139—21no—
16#385×C139—21no—
17#382×C139C411yescharacteristic
18#380×C139C411yescharacteristic
19#380×C139C411yescharacteristic
20#336×C139—21no—
21#336×C139C2212yes—
22#336×C139C2212yes—
23C23×C4×C139C2×C411yescharacteristic
24C23×C4×C139D411yescharacteristic
25C23×C4×C139D411yescharacteristic
26C22×C8×C139—22no—
27C22×C8×C139—22no—
28#125×C139—42no—
29C2×C4⋊C4×C139—21no—
30C2×C4⋊C4×C139—21no—
31C2×C4⋊C4×C139—21no—
32C2×C4⋊C4×C139—21no—
33C2×C4⋊C4×C139C2×C411yescharacteristic
34C2×C4⋊C4×C139C2×C411yescharacteristic
35C2×C4⋊C4×C139C2×C411yescharacteristic
36C2×C4⋊C4×C139C2×C411yescharacteristic
37C2×C22⋊C4×C139—21no—
38C2×C22⋊C4×C139—21no—
39C2×C42×C139—42no—
40C2×C42×C139C2×C411yescharacteristic
41C2×C42×C139D411yescharacteristic
42C2×C42×C139D411yescharacteristic
43C2×C42×C139C2311yescharacteristic
44C22⋊C8×C139—24no—
45C22⋊C8×C139—42no—
46C4×C8×C139—42no—
47#95×C139—21no—
48#95×C139—21no—
49#95×C139—21no—
50#95×C139—21no—
51#95×C139—21no—
52#95×C139—21no—
53C24×C139C22⋊C411yescharacteristic
54C22×C4×C139—22no—
55C22×C4×C139—22no—
56C22×C4×C139—22no—
57C22×C4×C139—22no—
58C22×C4×C139—22no—
59C22×C4×C139—22no—
60C22×C4×C139—21no—
61C22×C4×C139—21no—
62C22×C4×C139—21no—
63C22×C4×C139—21no—
64C22×C4×C139—41no—
65C22×C4×C139—41no—
66C22×C4×C139—41no—
67C22×C4×C139C22⋊C411yescharacteristic
68C22×C4×C139C22⋊C411yescharacteristic
69C22×C4×C139C22⋊C411yescharacteristic
70C22×C4×C139C22×C411yescharacteristic
71C22×C4×C139C2×D411yescharacteristic
72C22×C4×C139C2×D411yescharacteristic
73C2×C8×C139—24no—
74C2×C8×C139—42no—
75C2×C8×C139—42no—
76C2×C8×C139—42no—
77C2×C8×C139—42no—
78C2×C8×C139—42no—
79C4⋊C4×C139—22no—
80C4⋊C4×C139—22no—
81C4⋊C4×C139—41no—
82C4⋊C4×C139—41no—
83C4⋊C4×C139—42no—
84C4⋊C4×C139—42no—
85C4⋊C4×C139—42no—
86C4⋊C4×C139—42no—
87C22⋊C4×C139—42no—
88C22⋊C4×C139—42no—
89C42×C139—22no—
90C42×C139—22no—
91C42×C139—41no—
92C42×C139—41no—
93C23×C139—21no—
94C23×C139—21no—
95C23×C139—21no—
96C23×C139—21no—
97C23×C139—21no—
98C23×C139—21no—
99C23×C139#10412yes—
100C23×C139C2×C22⋊C411yescharacteristic
101C2×C4×C139—21no—
102C2×C4×C139—21no—
103C2×C4×C139—21no—
104C2×C4×C139—21no—
105C2×C4×C139—21no—
106C2×C4×C139—21no—
107C2×C4×C139—21no—
108C2×C4×C139—21no—
109C2×C4×C139—21no—
110C2×C4×C139—21no—
111C2×C4×C139—21no—
112C2×C4×C139—21no—
113C2×C4×C139—21no—
114C2×C4×C139—44no—
115C2×C4×C139—44no—
116C2×C4×C139—44no—
117C2×C4×C139—41no—
118C2×C4×C139—41no—
119C2×C4×C139—41no—
120C2×C4×C139—41no—
121C2×C4×C139—41no—
122C2×C4×C139—41no—
123C2×C4×C139—41no—
124C2×C4×C139—41no—
125C2×C4×C139—41no—
126C2×C4×C139—41no—
127C2×C4×C139—41no—
128C2×C4×C139—41no—
129C2×C4×C139#9912yes—
130C2×C4×C139#10112yes—
131C2×C4×C139#13112yes—
132C2×C4×C139#13512yes—
133C2×C4×C139#13512yes—
134C8×C139—44no—
135C8×C139—82no—
136C22×C139—22no—
137C22×C139—22no—
138C22×C139—22no—
139C22×C139—41no—
140C22×C139—41no—
141C22×C139—41no—
142C22×C139—41no—
143C22×C139#40811yescharacteristic
144C22×C139C2×#9911yescharacteristic
145C22×C139C2×#10111yescharacteristic
146C22×C139#41611yescharacteristic
147C22×C139#41611yescharacteristic
148C22×C139C2×#10411yescharacteristic
149C22×C139#42111yescharacteristic
150C4×C139—22no—
151C4×C139—22no—
152C4×C139—22no—
153C4×C139—22no—
154C4×C139—22no—
155C4×C139—41no—
156C4×C139—81no—
157C4×C139—81no—
158C4×C139—81no—
159C4×C139—81no—
160C2×C139—42no—
161C2×C139#147211yescharacteristic
162C2×C139#148211yescharacteristic
163C2×C139#149411yescharacteristic
164C2×C139#150111yescharacteristic
165C2×C139#151611yescharacteristic
166C2×C139#152811yescharacteristic
167C2×C139#154411yescharacteristic
168#7671C13911yesmaximal, characteristic, direct product factor, Sylow
169C139#767111yescharacteristic, direct product factor, Sylow
170#2851C2×C13911yescharacteristic
171#1817C2×C13911yescharacteristic
172C4×C22⋊C8C2×C13911yescharacteristic
173#1271C2×C13912yescomplemented
174#1271C2×C13912yescomplemented
175C2×#125C4×C13911yescharacteristic
176C22×C42C22×C13911yescharacteristic
177C2×C22⋊C8—21no—
178C2×C22⋊C8—21no—
179C2×C4×C8—21no—
180#389C22×C13911yescharacteristic
181#389C22×C13911yescharacteristic
182#387—21no—
183#387—21no—
184#385—21no—
185#385—21no—
186#382C4×C13911yescharacteristic
187#380C4×C13911yescharacteristic
188#380C4×C13911yescharacteristic
189#336—21no—
190#336C22×C13912yes—
191#336C22×C13912yes—
192C23×C4C2×C4×C13911yescharacteristic
193C23×C4D4×C13911yescharacteristic
194C23×C4D4×C13911yescharacteristic
195C22×C8—22no—
196C22×C8—22no—
197#125—42no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4C2×C4×C13911yescharacteristic
203C2×C4⋊C4C2×C4×C13911yescharacteristic
204C2×C4⋊C4C2×C4×C13911yescharacteristic
205C2×C4⋊C4C2×C4×C13911yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42—42no—
209C2×C42C2×C4×C13911yescharacteristic
210C2×C42D4×C13911yescharacteristic
211C2×C42D4×C13911yescharacteristic
212C2×C42C23×C13911yescharacteristic
213C22⋊C8—24no—
214C22⋊C8—42no—
215C4×C8—42no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222C24C22⋊C4×C13911yescharacteristic
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4C22⋊C4×C13911yescharacteristic
237C22×C4C22⋊C4×C13911yescharacteristic
238C22×C4C22⋊C4×C13911yescharacteristic
239C22×C4C22×C4×C13911yescharacteristic
240C22×C4C2×D4×C13911yescharacteristic
241C22×C4C2×D4×C13911yescharacteristic
242C2×C8—24no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C42—22no—
259C42—22no—
260C42—41no—
261C42—41no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#104×C13912yes—
269C23C2×C22⋊C4×C13911yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4#99×C13912yes—
299C2×C4#101×C13912yes—
300C2×C4#131×C13912yes—
301C2×C4#135×C13912yes—
302C2×C4#135×C13912yes—
303C8—44no—
304C8—82no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22#408×C13911yescharacteristic
313C22C2×#99×C13911yescharacteristic
314C22C2×#101×C13911yescharacteristic
315C22#416×C13911yescharacteristic
316C22#416×C13911yescharacteristic
317C22C2×#104×C13911yescharacteristic
318C22#421×C13911yescharacteristic
319C4—22no—
320C4—22no—
321C4—22no—
322C4—22no—
323C4—22no—
324C4—41no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—81no—
329C2—42no—
330C2#1472×C13911yescharacteristic
331C2#1482×C13911yescharacteristic
332C2#1494×C13911yescharacteristic
333C2#1501×C13911yescharacteristic
334C2#1516×C13911yescharacteristic
335C2#1528×C13911yescharacteristic
336C2#1544×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC22×C4C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC24×C139C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1271×C139C2semidirect
5. #1271×C139C2semidirect
168. #7671C139direct (N × H)
169. C139#7671direct (N × H)
173. #1271C2×C139semidirect
174. #1271C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2851×C1392
#1817×C1392
C4×C22⋊C8×C1392
#1271×C1392
#7671139