Finite Group Databasebeta

← C139×#9289 #48003885

Subgroups — C139×#9289 #48003885

Order 35584.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3206×C139C211yesmaximal, characteristic
2#2932×C139C211yesmaximal, characteristic
3#1993×C139C211yesmaximal, characteristic, complemented
4#1549×C139C211yesmaximal, characteristic, complemented
5#1517×C139C211yesmaximal, characteristic
6#1286×C139C211yesmaximal, characteristic, complemented
7#1275×C139C211yesmaximal, characteristic, complemented
8C2×#131×C139—21no—
9#532×C139C2211yescharacteristic
10C2×C4⋊Q8×C139C2211yescharacteristic
11#492×C139C412yescomplemented
12#487×C139C412yescomplemented
13#461×C139—22no—
14#448×C139—22no—
15#435×C139—22no—
16#435×C139—22no—
17#431×C139C2211yescharacteristic
18#431×C139C2211yescharacteristic
19#423×C139C2211yescharacteristic
20#408×C139—21no—
21C2×#97×C139C2211yescharacteristic
22#382×C139C2211yescharacteristic
23#340×C139—21no—
24#340×C139—21no—
25#332×C139—22no—
26#327×C139—22no—
27C2×#41×C139—21no—
28C22×Q8×C139—21no—
29C2×SD16×C139—24no—
30#131×C139—42no—
31#131×C139—42no—
32C2×M16×C139—22no—
33C2×M16×C139—21no—
34C22×C8×C139—22no—
35C22×C8×C139D411yescharacteristic
36C22×C8×C139D411yescharacteristic
37C4⋊Q8×C139—21no—
38C4⋊Q8×C139—21no—
39C4⋊Q8×C139—21no—
40C4⋊Q8×C139C2×C412yes—
41C4⋊Q8×C139C2×C411yescharacteristic
42#127×C139C2×C411yescharacteristic
43#124×C139—21no—
44#121×C139—21no—
45#121×C139D412yes—
46C4×D4×C139—21no—
47C4×D4×C139D412yes—
48C2×C4⋊C4×C139—21no—
49C2×C4⋊C4×C139—21no—
50C2×C4⋊C4×C139—21no—
51C2×C42×C139C2311yescharacteristic
52C4⋊C8×C139—21no—
53C4⋊C8×C139—21no—
54C4⋊C8×C139—21no—
55C4⋊C8×C139D412yes—
56#103×C139—24no—
57C22⋊C8×C139—24no—
58C22⋊C8×C139—21no—
59C22⋊C8×C139—21no—
60#97×C139—21no—
61#97×C139—21no—
62C4×C8×C139—21no—
63C4×C8×C139C2×C412yes—
64#95×C139—21no—
65#95×C139—21no—
66#41×C139—41no—
67#41×C139—41no—
68#41×C139—41no—
69#41×C139—41no—
70C2×Q8×C139—21no—
71C2×Q8×C139—22no—
72C2×Q8×C139—41no—
73C2×Q8×C139—82no—
74C2×D4×C139—22no—
75C2×D4×C139—21no—
76C2×D4×C139—21no—
77C2×D4×C139C22⋊C412yes—
78C22×C4×C139—22no—
79C22×C4×C139—41no—
80C22×C4×C139—41no—
81C22×C4×C139C2×D411yescharacteristic
82C22×C4×C139C2×D411yescharacteristic
83C22×C4×C139#4111yescharacteristic
84SD16×C139—84no—
85M16×C139—44no—
86M16×C139—41no—
87M16×C139—41no—
88C2×C8×C139—21no—
89C2×C8×C139—21no—
90C2×C8×C139—22no—
91C2×C8×C139—21no—
92C2×C8×C139—22no—
93C2×C8×C139—21no—
94C2×C8×C139—21no—
95C2×C8×C139—44no—
96C2×C8×C139—41no—
97C2×C8×C139SD1612yescomplemented
98C4⋊C4×C139—21no—
99C4⋊C4×C139—22no—
100C4⋊C4×C139—22no—
101C4⋊C4×C139—41no—
102C4⋊C4×C139—41no—
103C4⋊C4×C139—41no—
104C4⋊C4×C139—41no—
105C4⋊C4×C139C22⋊C412yes—
106C22⋊C4×C139—22no—
107C22⋊C4×C139—22no—
108C42×C139C22×C411yescharacteristic
109C42×C139C2×D411yescharacteristic
110C42×C139C2×D411yescharacteristic
111C42×C139#4111yescharacteristic
112C23×C139—22no—
113C23×C139#12111yescharacteristic
114Q8×C139—44no—
115Q8×C139—41no—
116Q8×C139—41no—
117Q8×C139—82no—
118D4×C139—42no—
119D4×C139—42no—
120D4×C139—42no—
121D4×C139—41no—
122D4×C139—41no—
123D4×C139—81no—
124C2×C4×C139—22no—
125C2×C4×C139—41no—
126C2×C4×C139—41no—
127C2×C4×C139—42no—
128C2×C4×C139—42no—
129C2×C4×C139—42no—
130C2×C4×C139—82no—
131C2×C4×C139—81no—
132C2×C4×C139—81no—
133C2×C4×C139—81no—
134C2×C4×C139C2×C22⋊C411yescharacteristic
135C2×C4×C139C4×D411yescharacteristic
136C2×C4×C139C4×D411yescharacteristic
137C2×C4×C139#12011yescharacteristic
138C2×C4×C139#12111yescharacteristic
139C2×C4×C139#12311yescharacteristic
140C2×C4×C139C2×SD1611yescharacteristic
141C2×C4×C139#13511yescharacteristic
142C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C139#13711yescharacteristic
144C8×C139—22no—
145C8×C139—42no—
146C8×C139—42no—
147C8×C139—41no—
148C8×C139—81no—
149C22×C139—21no—
150C22×C139—21no—
151C22×C139—42no—
152C22×C139—42no—
153C22×C139—42no—
154C22×C139#38611yescharacteristic
155C22×C139#46111yescharacteristic
156C22×C139#46311yescharacteristic
157C4×C139—21no—
158C4×C139—21no—
159C4×C139—21no—
160C4×C139—21no—
161C4×C139—42no—
162C4×C139—82no—
163C4×C139—161no—
164C4×C139C4×SD1611yescharacteristic
165C4×C139#44011yescharacteristic
166C4×C139#45011yescharacteristic
167C4×C139#45211yescharacteristic
168C2×C139—21no—
169C2×C139—21no—
170C2×C139—82no—
171C2×C139#187711yescharacteristic
172C2×C139#190211yescharacteristic
173C2×C139#191011yescharacteristic
174#9289C13911yesmaximal, characteristic, direct product factor, Sylow
175C139#928911yescharacteristic, direct product factor, Sylow
176#3206C2×C13911yescharacteristic
177#2932C2×C13911yescharacteristic
178#1993C2×C13911yescharacteristic, complemented
179#1549C2×C13911yescharacteristic, complemented
180#1517C2×C13911yescharacteristic
181#1286C2×C13911yescharacteristic, complemented
182#1275C2×C13911yescharacteristic, complemented
183C2×#131—21no—
184#532C22×C13911yescharacteristic
185C2×C4⋊Q8C22×C13911yescharacteristic
186#492C4×C13912yescomplemented
187#487C4×C13912yescomplemented
188#461—22no—
189#448—22no—
190#435—22no—
191#435—22no—
192#431C22×C13911yescharacteristic
193#431C22×C13911yescharacteristic
194#423C22×C13911yescharacteristic
195#408—21no—
196C2×#97C22×C13911yescharacteristic
197#382C22×C13911yescharacteristic
198#340—21no—
199#340—21no—
200#332—22no—
201#327—22no—
202C2×#41—21no—
203C22×Q8—21no—
204C2×SD16—24no—
205#131—42no—
206#131—42no—
207C2×M16—22no—
208C2×M16—21no—
209C22×C8—22no—
210C22×C8D4×C13911yescharacteristic
211C22×C8D4×C13911yescharacteristic
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8C2×C4×C13912yes—
216C4⋊Q8C2×C4×C13911yescharacteristic
217#127C2×C4×C13911yescharacteristic
218#124—21no—
219#121—21no—
220#121D4×C13912yes—
221C4×D4—21no—
222C4×D4D4×C13912yes—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C42C23×C13911yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8D4×C13912yes—
231#103—24no—
232C22⋊C8—24no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235#97—21no—
236#97—21no—
237C4×C8—21no—
238C4×C8C2×C4×C13912yes—
239#95—21no—
240#95—21no—
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—82no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4C22⋊C4×C13912yes—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4C2×D4×C13911yescharacteristic
257C22×C4C2×D4×C13911yescharacteristic
258C22×C4#41×C13911yescharacteristic
259SD16—84no—
260M16—44no—
261M16—41no—
262M16—41no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—22no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—44no—
271C2×C8—41no—
272C2×C8SD16×C13912yescomplemented
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4C22⋊C4×C13912yes—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C42C22×C4×C13911yescharacteristic
284C42C2×D4×C13911yescharacteristic
285C42C2×D4×C13911yescharacteristic
286C42#41×C13911yescharacteristic
287C23—22no—
288C23#121×C13911yescharacteristic
289Q8—44no—
290Q8—41no—
291Q8—41no—
292Q8—82no—
293D4—42no—
294D4—42no—
295D4—42no—
296D4—41no—
297D4—41no—
298D4—81no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4C2×C22⋊C4×C13911yescharacteristic
310C2×C4C4×D4×C13911yescharacteristic
311C2×C4C4×D4×C13911yescharacteristic
312C2×C4#120×C13911yescharacteristic
313C2×C4#121×C13911yescharacteristic
314C2×C4#123×C13911yescharacteristic
315C2×C4C2×SD16×C13911yescharacteristic
316C2×C4#135×C13911yescharacteristic
317C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
318C2×C4#137×C13911yescharacteristic
319C8—22no—
320C8—42no—
321C8—42no—
322C8—41no—
323C8—81no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22#386×C13911yescharacteristic
330C22#461×C13911yescharacteristic
331C22#463×C13911yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—42no—
337C4—82no—
338C4—161no—
339C4C4×SD16×C13911yescharacteristic
340C4#440×C13911yescharacteristic
341C4#450×C13911yescharacteristic
342C4#452×C13911yescharacteristic
343C2—21no—
344C2—21no—
345C2—82no—
346C2#1877×C13911yescharacteristic
347C2#1902×C13911yescharacteristic
348C2#1910×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radical#532×C139C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1993×C139C2semidirect
4. #1549×C139C2semidirect
6. #1286×C139C2semidirect
7. #1275×C139C2semidirect
11. #492×C139C4semidirect
12. #487×C139C4semidirect
97. C2×C8×C139SD16semidirect
174. #9289C139direct (N × H)
175. C139#9289direct (N × H)
178. #1993C2×C139semidirect
179. #1549C2×C139semidirect
181. #1286C2×C139semidirect
182. #1275C2×C139semidirect
186. #492C4×C139semidirect
187. #487C4×C139semidirect
272. C2×C8SD16×C139semidirect

Maximal subgroups

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

subgroupindex
#3206×C1392
#2932×C1392
#1993×C1392
#1549×C1392
#1517×C1392
#1286×C1392
#1275×C1392
#9289139