Finite Group Databasebeta

← C139×#9576 #48004172

Subgroups — C139×#9576 #48004172

Order 35584.

370 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#1990×C139C211yesmaximal, characteristic
2#1987×C139C211yesmaximal, characteristic
3#1947×C139C211yesmaximal, characteristic
4#1770×C139C211yesmaximal, characteristic
5C2×#333×C139C211yesmaximal, characteristic
6#1296×C139C211yesmaximal, characteristic
7#1277×C139C211yesmaximal, characteristic
8C2×C4⋊Q8×C139C2211yescharacteristic
9C2×#107×C139—21no—
10C2×C4⋊C8×C139C2211yescharacteristic
11C2×C4⋊C8×C139C2211yescharacteristic
12C2×C4⋊C8×C139C2211yescharacteristic
13C2×#97×C139—21no—
14C2×C4×C8×C139C2211yescharacteristic
15#384×C139C2211yescharacteristic
16C4×C4⋊C4×C139C2211yescharacteristic
17#340×C139—21no—
18#340×C139—21no—
19#340×C139—21no—
20#340×C139—21no—
21#340×C139—21no—
22#336×C139—21no—
23#333×C139C414yescomplemented
24C22×Q8×C139—21no—
25C22×C8×C139—21no—
26C22×C8×C139—21no—
27C22×C8×C139—21no—
28C22×C8×C139D411yescharacteristic
29C22×C8×C139D411yescharacteristic
30C4⋊Q8×C139—21no—
31C4⋊Q8×C139—21no—
32C4⋊Q8×C139—21no—
33C4⋊Q8×C139C2×C412yes—
34C2×C4⋊C4×C139—21no—
35C2×C4⋊C4×C139—21no—
36C2×C4⋊C4×C139—21no—
37C2×C4⋊C4×C139—21no—
38C2×C4⋊C4×C139—21no—
39C2×C4⋊C4×C139D411yescharacteristic
40C2×C4⋊C4×C139D411yescharacteristic
41C2×C42×C139—21no—
42C2×C42×C139C2311yescharacteristic
43#107×C139—42no—
44C4⋊C8×C139—21no—
45C4⋊C8×C139—21no—
46C4⋊C8×C139—21no—
47C4⋊C8×C139—21no—
48C4⋊C8×C139C2×C412yes—
49C4⋊C8×C139C2×C412yes—
50#97×C139—42no—
51C4×C8×C139—21no—
52C4×C8×C139—21no—
53#95×C139—21no—
54C2×Q8×C139—22no—
55C2×Q8×C139—41no—
56C2×Q8×C139—81no—
57C2×Q8×C139—81no—
58C22×C4×C139—21no—
59C22×C4×C139—21no—
60C22×C4×C139—41no—
61C22×C4×C139—41no—
62C22×C4×C139C2×D411yescharacteristic
63C22×C4×C139C2×D411yescharacteristic
64C22×C4×C139#4111yescharacteristic
65C2×C8×C139—21no—
66C2×C8×C139—21no—
67C2×C8×C139—22no—
68C2×C8×C139—22no—
69C2×C8×C139—21no—
70C2×C8×C139—21no—
71C2×C8×C139—21no—
72C2×C8×C139—41no—
73C2×C8×C139—41no—
74C2×C8×C139—41no—
75C2×C8×C139—41no—
76C2×C8×C139—41no—
77C2×C8×C139—41no—
78C2×C8×C139—41no—
79C2×C8×C139Q1612yes—
80C4⋊C4×C139—22no—
81C4⋊C4×C139—22no—
82C4⋊C4×C139—21no—
83C4⋊C4×C139—21no—
84C4⋊C4×C139—21no—
85C4⋊C4×C139—21no—
86C4⋊C4×C139—41no—
87C4⋊C4×C139—41no—
88C4⋊C4×C139—41no—
89C4⋊C4×C139—41no—
90C4⋊C4×C139—41no—
91C4⋊C4×C139—41no—
92C4⋊C4×C139—81no—
93C42×C139—41no—
94C42×C139—41no—
95C42×C139C22×C411yescharacteristic
96C42×C139#4111yescharacteristic
97C42×C139#4111yescharacteristic
98C42×C139#4111yescharacteristic
99C23×C139#12111yescharacteristic
100Q8×C139—82no—
101Q8×C139—82no—
102C2×C4×C139—21no—
103C2×C4×C139—21no—
104C2×C4×C139—42no—
105C2×C4×C139—41no—
106C2×C4×C139—41no—
107C2×C4×C139—41no—
108C2×C4×C139—41no—
109C2×C4×C139—41no—
110C2×C4×C139—41no—
111C2×C4×C139—81no—
112C2×C4×C139—81no—
113C2×C4×C139—81no—
114C2×C4×C139—81no—
115C2×C4×C139—81no—
116C2×C4×C139#11711yescharacteristic
117C2×C4×C139C4×D411yescharacteristic
118C2×C4×C139C4×D411yescharacteristic
119C2×C4×C139#12311yescharacteristic
120C2×C4×C139#12411yescharacteristic
121C2×C4×C139#12611yescharacteristic
122C2×C4×C139C2×Q1611yescharacteristic
123C2×C4×C139#13511yescharacteristic
124C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C139#13711yescharacteristic
127C2×C4×C139#13711yescharacteristic
128C2×C4×C139#13711yescharacteristic
129C2×C4×C139#13711yescharacteristic
130C8×C139—22no—
131C8×C139—42no—
132C8×C139—42no—
133C8×C139—41no—
134C8×C139—81no—
135C22×C139#38811yescharacteristic
136C22×C139#46211yescharacteristic
137C22×C139#46311yescharacteristic
138C22×C139#46811yescharacteristic
139C22×C139#47011yescharacteristic
140C22×C139#47111yescharacteristic
141C22×C139#47211yescharacteristic
142C4×C139—21no—
143C4×C139—21no—
144C4×C139—82no—
145C4×C139—81no—
146C4×C139—81no—
147C4×C139—161no—
148C4×C139C4×Q1611yescharacteristic
149C4×C139#44011yescharacteristic
150C4×C139#44011yescharacteristic
151C4×C139#44111yescharacteristic
152C4×C139#48411yescharacteristic
153C4×C139#48511yescharacteristic
154C4×C139#48911yescharacteristic
155C4×C139#49111yescharacteristic
156C2×C139#169211yescharacteristic
157C2×C139#169611yescharacteristic
158C2×C139#169711yescharacteristic
159C2×C139#170311yescharacteristic
160C2×C139#192811yescharacteristic
161C2×C139#193111yescharacteristic
162C2×C139#193511yescharacteristic
163#9576C13911yesmaximal, characteristic, direct product factor, Sylow
164C139#957611yescharacteristic, direct product factor, Sylow
165#1990C2×C13911yescharacteristic
166#1987C2×C13911yescharacteristic
167#1947C2×C13911yescharacteristic
168#1770C2×C13911yescharacteristic
169C2×#333C2×C13911yescharacteristic
170#1296C2×C13911yescharacteristic
171#1277C2×C13911yescharacteristic
172C2×C4⋊Q8C22×C13911yescharacteristic
173C2×#107—21no—
174C2×C4⋊C8C22×C13911yescharacteristic
175C2×C4⋊C8C22×C13911yescharacteristic
176C2×C4⋊C8C22×C13911yescharacteristic
177C2×#97—21no—
178C2×C4×C8C22×C13911yescharacteristic
179#384C22×C13911yescharacteristic
180C4×C4⋊C4C22×C13911yescharacteristic
181#340—21no—
182#340—21no—
183#340—21no—
184#340—21no—
185#340—21no—
186#336—21no—
187#333C4×C13914yescomplemented
188C22×Q8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8D4×C13911yescharacteristic
193C22×C8D4×C13911yescharacteristic
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C2×C4×C13912yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4D4×C13911yescharacteristic
204C2×C4⋊C4D4×C13911yescharacteristic
205C2×C42—21no—
206C2×C42C23×C13911yescharacteristic
207#107—42no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8C2×C4×C13912yes—
213C4⋊C8C2×C4×C13912yes—
214#97—42no—
215C4×C8—21no—
216C4×C8—21no—
217#95—21no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4C2×D4×C13911yescharacteristic
227C22×C4C2×D4×C13911yescharacteristic
228C22×C4#41×C13911yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8Q16×C13912yes—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—81no—
257C42—41no—
258C42—41no—
259C42C22×C4×C13911yescharacteristic
260C42#41×C13911yescharacteristic
261C42#41×C13911yescharacteristic
262C42#41×C13911yescharacteristic
263C23#121×C13911yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4#117×C13911yescharacteristic
281C2×C4C4×D4×C13911yescharacteristic
282C2×C4C4×D4×C13911yescharacteristic
283C2×C4#123×C13911yescharacteristic
284C2×C4#124×C13911yescharacteristic
285C2×C4#126×C13911yescharacteristic
286C2×C4C2×Q16×C13911yescharacteristic
287C2×C4#135×C13911yescharacteristic
288C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
289C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
290C2×C4#137×C13911yescharacteristic
291C2×C4#137×C13911yescharacteristic
292C2×C4#137×C13911yescharacteristic
293C2×C4#137×C13911yescharacteristic
294C8—22no—
295C8—42no—
296C8—42no—
297C8—41no—
298C8—81no—
299C22#388×C13911yescharacteristic
300C22#462×C13911yescharacteristic
301C22#463×C13911yescharacteristic
302C22#468×C13911yescharacteristic
303C22#470×C13911yescharacteristic
304C22#471×C13911yescharacteristic
305C22#472×C13911yescharacteristic
306C4—21no—
307C4—21no—
308C4—82no—
309C4—81no—
310C4—81no—
311C4—161no—
312C4C4×Q16×C13911yescharacteristic
313C4#440×C13911yescharacteristic
314C4#440×C13911yescharacteristic
315C4#441×C13911yescharacteristic
316C4#484×C13911yescharacteristic
317C4#485×C13911yescharacteristic
318C4#489×C13911yescharacteristic
319C4#491×C13911yescharacteristic
320C2#1692×C13911yescharacteristic
321C2#1696×C13911yescharacteristic
322C2#1697×C13911yescharacteristic
323C2#1703×C13911yescharacteristic
324C2#1928×C13911yescharacteristic
325C2#1931×C13911yescharacteristic
326C2#1935×C13911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C139#121
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
23. #333×C139C4semidirect
163. #9576C139direct (N × H)
164. C139#9576direct (N × H)
187. #333C4×C139semidirect

Maximal subgroups

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

subgroupindex
#1990×C1392
#1987×C1392
#1947×C1392
#1770×C1392
C2×#333×C1392
#1296×C1392
#1277×C1392
#9576139