Finite Group Databasebeta

← C139×#8760 #48003356

Subgroups — C139×#8760 #48003356

Order 35584.

530 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2349×C139C211yesmaximal, characteristic
2#1799×C139C211yesmaximal, characteristic
3#1459×C139C211yesmaximal, characteristic
4#1294×C139C212yesmaximal, complemented
5#1289×C139C212yesmaximal, complemented
6C2×C4×D4×C139—21no—
7C2×C4×D4×C139C2211yescharacteristic
8C2×#99×C139—21no—
9C2×C22⋊C8×C139C2212yes—
10#389×C139—21no—
11#385×C139—21no—
12#385×C139—21no—
13#382×C139C411yescharacteristic, complemented
14#380×C139C411yescharacteristic, complemented
15#380×C139C2212yes—
16#380×C139C2211yescharacteristic
17C4×C4⋊C4×C139C411yescharacteristic, complemented
18C2×#95×C139C411yescharacteristic, complemented
19C2×#95×C139C2211yescharacteristic
20#342×C139—21no—
21#324×C139—21no—
22#323×C139—21no—
23C22×D4×C139D411yescharacteristic
24C23×C4×C139—21no—
25C23×C4×C139—21no—
26C23×C4×C139C2×C411yescharacteristic
27C23×C4×C139C2311yescharacteristic
28C22×C8×C139—22no—
29C4×D4×C139—22no—
30C4×D4×C139—22no—
31C4×D4×C139—42no—
32C4×D4×C139—42no—
33C2×C4⋊C4×C139—21no—
34C2×C4⋊C4×C139—21no—
35C2×C4⋊C4×C139—21no—
36C2×C4⋊C4×C139—21no—
37C2×C4⋊C4×C139—22no—
38C2×C4⋊C4×C139D411yescharacteristic
39C2×C22⋊C4×C139—21no—
40C2×C22⋊C4×C139—21no—
41C2×C22⋊C4×C139—22no—
42C2×C22⋊C4×C139D411yescharacteristic
43C2×C22⋊C4×C139D411yescharacteristic
44C2×C42×C139—21no—
45C2×C42×C139C2×C411yescharacteristic
46#99×C139—42no—
47C22⋊C8×C139—22no—
48C22⋊C8×C139—22no—
49#95×C139—21no—
50#95×C139—21no—
51#95×C139—21no—
52#95×C139—22no—
53#95×C139C2×C411yescharacteristic
54#95×C139C2×C411yescharacteristic
55#95×C139C2×C411yescharacteristic
56#95×C139C2×C411yescharacteristic
57C24×C139C22⋊C411yescharacteristic
58C24×C139C2×D411yescharacteristic
59C2×D4×C139—22no—
60C2×D4×C139—22no—
61C2×D4×C139D812yes—
62C2×D4×C139SD1612yes—
63C22×C4×C139—21no—
64C22×C4×C139—21no—
65C22×C4×C139—21no—
66C22×C4×C139—21no—
67C22×C4×C139—21no—
68C22×C4×C139—21no—
69C22×C4×C139—42no—
70C22×C4×C139—42no—
71C22×C4×C139—42no—
72C22×C4×C139—41no—
73C22×C4×C139—41no—
74C22×C4×C139—42no—
75C22×C4×C139—81no—
76C22×C4×C139—81no—
77C22×C4×C139—81no—
78C22×C4×C139—81no—
79C22×C4×C139C22⋊C411yescharacteristic
80C22×C4×C139C22⋊C411yescharacteristic
81C22×C4×C139C22⋊C411yescharacteristic
82C22×C4×C139C22×C411yescharacteristic
83C22×C4×C139C2×D411yescharacteristic
84C22×C4×C139#4112yes—
85C22×C4×C139#4112yes—
86C2×C8×C139—42no—
87C2×C8×C139—82no—
88C4⋊C4×C139—22no—
89C4⋊C4×C139—42no—
90C4⋊C4×C139—42no—
91C4⋊C4×C139—81no—
92C4⋊C4×C139—81no—
93C4⋊C4×C139—82no—
94C22⋊C4×C139—22no—
95C22⋊C4×C139—22no—
96C22⋊C4×C139—42no—
97C22⋊C4×C139—41no—
98C22⋊C4×C139—41no—
99C22⋊C4×C139—42no—
100C22⋊C4×C139—42no—
101C42×C139—21no—
102C42×C139—21no—
103C42×C139—42no—
104C23×C139—21no—
105C23×C139—21no—
106C23×C139—41no—
107C23×C139—41no—
108C23×C139—41no—
109C23×C139—41no—
110C23×C139#10212yes—
111C23×C139C2×C22⋊C411yescharacteristic
112C23×C139#12312yes—
113C23×C139C2×D811yescharacteristic
114C23×C139C2×SD1611yescharacteristic
115C23×C139#13712yes—
116D4×C139—24no—
117D4×C139—24no—
118C2×C4×C139—21no—
119C2×C4×C139—21no—
120C2×C4×C139—22no—
121C2×C4×C139—21no—
122C2×C4×C139—21no—
123C2×C4×C139—41no—
124C2×C4×C139—42no—
125C2×C4×C139—42no—
126C2×C4×C139—41no—
127C2×C4×C139—41no—
128C2×C4×C139—41no—
129C2×C4×C139—41no—
130C2×C4×C139—41no—
131C2×C4×C139—41no—
132C2×C4×C139—41no—
133C2×C4×C139—41no—
134C2×C4×C139—41no—
135C2×C4×C139—41no—
136C2×C4×C139—41no—
137C2×C4×C139—41no—
138C2×C4×C139—41no—
139C2×C4×C139—41no—
140C2×C4×C139—81no—
141C2×C4×C139—81no—
142C2×C4×C139—82no—
143C2×C4×C139—82no—
144C2×C4×C139—84no—
145C2×C4×C139—82no—
146C2×C4×C139—82no—
147C2×C4×C139—82no—
148C2×C4×C139#10212yes—
149C2×C4×C139#11711yescharacteristic
150C2×C4×C139#11711yescharacteristic
151C2×C4×C139#12312yes—
152C8×C139—82no—
153C22×C139—21no—
154C22×C139—22no—
155C22×C139—21no—
156C22×C139—22no—
157C22×C139—22no—
158C22×C139—41no—
159C22×C139—41no—
160C22×C139—42no—
161C22×C139—42no—
162C22×C139—42no—
163C22×C139—41no—
164C22×C139—41no—
165C22×C139#38111yescharacteristic
166C22×C139C2×#10211yescharacteristic
167C22×C139#41911yescharacteristic
168C22×C139#48012yes—
169C22×C139#48312yes—
170C4×C139—22no—
171C4×C139—22no—
172C4×C139—21no—
173C4×C139—21no—
174C4×C139—42no—
175C4×C139—41no—
176C4×C139—41no—
177C4×C139—81no—
178C4×C139—81no—
179C4×C139—81no—
180C4×C139—162no—
181C2×C139—21no—
182C2×C139—22no—
183C2×C139—21no—
184C2×C139—22no—
185C2×C139—42no—
186C2×C139#182311yescharacteristic
187C2×C139#182711yescharacteristic
188C2×C139#182811yescharacteristic
189#8760C13911yesmaximal, characteristic, direct product factor, Sylow
190C139#876011yescharacteristic, direct product factor, Sylow
191#2349C2×C13911yescharacteristic
192#1799C2×C13911yescharacteristic
193#1459C2×C13911yescharacteristic
194#1294C2×C13912yescomplemented
195#1289C2×C13912yescomplemented
196C2×C4×D4—21no—
197C2×C4×D4C22×C13911yescharacteristic
198C2×#99—21no—
199C2×C22⋊C8C22×C13912yes—
200#389—21no—
201#385—21no—
202#385—21no—
203#382C4×C13911yescharacteristic, complemented
204#380C4×C13911yescharacteristic, complemented
205#380C22×C13912yes—
206#380C22×C13911yescharacteristic
207C4×C4⋊C4C4×C13911yescharacteristic, complemented
208C2×#95C4×C13911yescharacteristic, complemented
209C2×#95C22×C13911yescharacteristic
210#342—21no—
211#324—21no—
212#323—21no—
213C22×D4D4×C13911yescharacteristic
214C23×C4—21no—
215C23×C4—21no—
216C23×C4C2×C4×C13911yescharacteristic
217C23×C4C23×C13911yescharacteristic
218C22×C8—22no—
219C4×D4—22no—
220C4×D4—22no—
221C4×D4—42no—
222C4×D4—42no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4D4×C13911yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4D4×C13911yescharacteristic
233C2×C22⋊C4D4×C13911yescharacteristic
234C2×C42—21no—
235C2×C42C2×C4×C13911yescharacteristic
236#99—42no—
237C22⋊C8—22no—
238C22⋊C8—22no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—22no—
243#95C2×C4×C13911yescharacteristic
244#95C2×C4×C13911yescharacteristic
245#95C2×C4×C13911yescharacteristic
246#95C2×C4×C13911yescharacteristic
247C24C22⋊C4×C13911yescharacteristic
248C24C2×D4×C13911yescharacteristic
249C2×D4—22no—
250C2×D4—22no—
251C2×D4D8×C13912yes—
252C2×D4SD16×C13912yes—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—42no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4—81no—
268C22×C4—81no—
269C22×C4C22⋊C4×C13911yescharacteristic
270C22×C4C22⋊C4×C13911yescharacteristic
271C22×C4C22⋊C4×C13911yescharacteristic
272C22×C4C22×C4×C13911yescharacteristic
273C22×C4C2×D4×C13911yescharacteristic
274C22×C4#41×C13912yes—
275C22×C4#41×C13912yes—
276C2×C8—42no—
277C2×C8—82no—
278C4⋊C4—22no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—81no—
282C4⋊C4—81no—
283C4⋊C4—82no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C42—21no—
292C42—21no—
293C42—42no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23#102×C13912yes—
301C23C2×C22⋊C4×C13911yescharacteristic
302C23#123×C13912yes—
303C23C2×D8×C13911yescharacteristic
304C23C2×SD16×C13911yescharacteristic
305C23#137×C13912yes—
306D4—24no—
307D4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—84no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4#102×C13912yes—
339C2×C4#117×C13911yescharacteristic
340C2×C4#117×C13911yescharacteristic
341C2×C4#123×C13912yes—
342C8—82no—
343C22—21no—
344C22—22no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22#381×C13911yescharacteristic
356C22C2×#102×C13911yescharacteristic
357C22#419×C13911yescharacteristic
358C22#480×C13912yes—
359C22#483×C13912yes—
360C4—22no—
361C4—22no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4—162no—
371C2—21no—
372C2—22no—
373C2—21no—
374C2—22no—
375C2—42no—
376C2#1823×C13911yescharacteristic
377C2#1827×C13911yescharacteristic
378C2#1828×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#381
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC22×D4×C139D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1294×C139C2semidirect
5. #1289×C139C2semidirect
13. #382×C139C4semidirect
14. #380×C139C4semidirect
17. C4×C4⋊C4×C139C4semidirect
18. C2×#95×C139C4semidirect
189. #8760C139direct (N × H)
190. C139#8760direct (N × H)
194. #1294C2×C139semidirect
195. #1289C2×C139semidirect
203. #382C4×C139semidirect
204. #380C4×C139semidirect
207. C4×C4⋊C4C4×C139semidirect
208. C2×#95C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2349×C1392
#1799×C1392
#1459×C1392
#1294×C1392
#1289×C1392
#8760139