Finite Group Databasebeta

← C139×#10626 #48005222

Subgroups — C139×#10626 #48005222

Order 35584.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#1984×C139C211yesmaximal, characteristic
2#1834×C139C211yesmaximal, characteristic
3#1803×C139C211yesmaximal, characteristic
4#1803×C139C211yesmaximal, characteristic
5#1296×C139C211yesmaximal, characteristic
6#1296×C139C211yesmaximal, characteristic
7#1277×C139C211yesmaximal, characteristic
8C2×C4×Q8×C139C2211yescharacteristic
9C2×C4⋊C8×C139C2211yescharacteristic
10C2×C4⋊C8×C139C2211yescharacteristic
11C2×C4⋊C8×C139C2211yescharacteristic
12C2×#103×C139—21no—
13C2×#103×C139—21no—
14C2×C4×C8×C139C2211yescharacteristic
15#384×C139C2211yescharacteristic
16#384×C139C2211yescharacteristic
17#340×C139—21no—
18#340×C139—21no—
19#340×C139—21no—
20#340×C139—21no—
21#336×C139—21no—
22#336×C139—21no—
23C22×Q8×C139D411yescharacteristic
24C22×C8×C139—21no—
25C22×C8×C139—21no—
26C22×C8×C139—21no—
27C22×C8×C139D411yescharacteristic
28C22×C8×C139D411yescharacteristic
29C4×Q8×C139—21no—
30C4×Q8×C139—21no—
31C4×Q8×C139—21no—
32C4×Q8×C139—21no—
33C2×C4⋊C4×C139—21no—
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×C139—21no—
40C2×C4⋊C4×C139D411yescharacteristic
41C2×C42×C139—21no—
42C2×C42×C139C2311yescharacteristic
43C4⋊C8×C139—21no—
44C4⋊C8×C139—21no—
45C4⋊C8×C139—21no—
46C4⋊C8×C139—21no—
47C4⋊C8×C139—21no—
48C4⋊C8×C139—21no—
49#103×C139—42no—
50#103×C139—42no—
51C4×C8×C139—21no—
52C4×C8×C139—21no—
53C2×Q8×C139—21no—
54C2×Q8×C139—21no—
55C2×Q8×C139—21no—
56C2×Q8×C139—21no—
57C2×Q8×C139—21no—
58C2×Q8×C139SD1612yes—
59C22×C4×C139—21no—
60C22×C4×C139—21no—
61C22×C4×C139—41no—
62C22×C4×C139—41no—
63C22×C4×C139C2×D411yescharacteristic
64C22×C4×C139C2×D411yescharacteristic
65C22×C4×C139#4111yescharacteristic
66C2×C8×C139—21no—
67C2×C8×C139—21no—
68C2×C8×C139—21no—
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×C139—41no—
80C2×C8×C139—41no—
81C4⋊C4×C139—21no—
82C4⋊C4×C139—21no—
83C4⋊C4×C139—41no—
84C4⋊C4×C139—41no—
85C4⋊C4×C139—41no—
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—41no—
93C4⋊C4×C139—81no—
94C4⋊C4×C139—81no—
95C42×C139—41no—
96C42×C139—41no—
97C42×C139#4111yescharacteristic
98C42×C139#4111yescharacteristic
99C42×C139#4111yescharacteristic
100C42×C139#4111yescharacteristic
101C23×C139#12111yescharacteristic
102Q8×C139—22no—
103Q8×C139—22no—
104Q8×C139—41no—
105Q8×C139—41no—
106C2×C4×C139—21no—
107C2×C4×C139—21no—
108C2×C4×C139—22no—
109C2×C4×C139—41no—
110C2×C4×C139—41no—
111C2×C4×C139—41no—
112C2×C4×C139—41no—
113C2×C4×C139—41no—
114C2×C4×C139—81no—
115C2×C4×C139—81no—
116C2×C4×C139—81no—
117C2×C4×C139—81no—
118C2×C4×C139—81no—
119C2×C4×C139—81no—
120C2×C4×C139#12311yescharacteristic
121C2×C4×C139#12311yescharacteristic
122C2×C4×C139#12311yescharacteristic
123C2×C4×C139#12411yescharacteristic
124C2×C4×C139#12611yescharacteristic
125C2×C4×C139#12611yescharacteristic
126C2×C4×C139C2×SD1611yescharacteristic
127C2×C4×C139#13511yescharacteristic
128C2×C4×C139#13511yescharacteristic
129C2×C4×C139#13511yescharacteristic
130C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C139#13711yescharacteristic
132C2×C4×C139#13711yescharacteristic
133C2×C4×C139#13711yescharacteristic
134C8×C139—41no—
135C8×C139—41no—
136C8×C139—81no—
137C8×C139—81no—
138C8×C139—81no—
139C22×C139#39711yescharacteristic
140C22×C139#46411yescharacteristic
141C22×C139#46411yescharacteristic
142C22×C139#46511yescharacteristic
143C22×C139#46811yescharacteristic
144C22×C139#47211yescharacteristic
145C22×C139#47311yescharacteristic
146C4×C139—21no—
147C4×C139—21no—
148C4×C139—42no—
149C4×C139—81no—
150C4×C139—161no—
151C4×C139—161no—
152C4×C139#48111yescharacteristic
153C4×C139#48211yescharacteristic
154C4×C139#48311yescharacteristic
155C4×C139#48511yescharacteristic
156C4×C139#48511yescharacteristic
157C4×C139#48511yescharacteristic
158C4×C139#48811yescharacteristic
159C4×C139#49111yescharacteristic
160C2×C139#167811yescharacteristic
161C2×C139#168011yescharacteristic
162C2×C139#169811yescharacteristic
163C2×C139#170011yescharacteristic
164C2×C139#207411yescharacteristic
165C2×C139#207711yescharacteristic
166C2×C139#207811yescharacteristic
167#10626C13911yesmaximal, characteristic, direct product factor, Sylow
168C139#1062611yescharacteristic, direct product factor, Sylow
169#1984C2×C13911yescharacteristic
170#1834C2×C13911yescharacteristic
171#1803C2×C13911yescharacteristic
172#1803C2×C13911yescharacteristic
173#1296C2×C13911yescharacteristic
174#1296C2×C13911yescharacteristic
175#1277C2×C13911yescharacteristic
176C2×C4×Q8C22×C13911yescharacteristic
177C2×C4⋊C8C22×C13911yescharacteristic
178C2×C4⋊C8C22×C13911yescharacteristic
179C2×C4⋊C8C22×C13911yescharacteristic
180C2×#103—21no—
181C2×#103—21no—
182C2×C4×C8C22×C13911yescharacteristic
183#384C22×C13911yescharacteristic
184#384C22×C13911yescharacteristic
185#340—21no—
186#340—21no—
187#340—21no—
188#340—21no—
189#336—21no—
190#336—21no—
191C22×Q8D4×C13911yescharacteristic
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8D4×C13911yescharacteristic
196C22×C8D4×C13911yescharacteristic
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4D4×C13911yescharacteristic
209C2×C42—21no—
210C2×C42C23×C13911yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217#103—42no—
218#103—42no—
219C4×C8—21no—
220C4×C8—21no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8SD16×C13912yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4C2×D4×C13911yescharacteristic
232C22×C4C2×D4×C13911yescharacteristic
233C22×C4#41×C13911yescharacteristic
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C42—41no—
264C42—41no—
265C42#41×C13911yescharacteristic
266C42#41×C13911yescharacteristic
267C42#41×C13911yescharacteristic
268C42#41×C13911yescharacteristic
269C23#121×C13911yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4#123×C13911yescharacteristic
289C2×C4#123×C13911yescharacteristic
290C2×C4#123×C13911yescharacteristic
291C2×C4#124×C13911yescharacteristic
292C2×C4#126×C13911yescharacteristic
293C2×C4#126×C13911yescharacteristic
294C2×C4C2×SD16×C13911yescharacteristic
295C2×C4#135×C13911yescharacteristic
296C2×C4#135×C13911yescharacteristic
297C2×C4#135×C13911yescharacteristic
298C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
299C2×C4#137×C13911yescharacteristic
300C2×C4#137×C13911yescharacteristic
301C2×C4#137×C13911yescharacteristic
302C8—41no—
303C8—41no—
304C8—81no—
305C8—81no—
306C8—81no—
307C22#397×C13911yescharacteristic
308C22#464×C13911yescharacteristic
309C22#464×C13911yescharacteristic
310C22#465×C13911yescharacteristic
311C22#468×C13911yescharacteristic
312C22#472×C13911yescharacteristic
313C22#473×C13911yescharacteristic
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—161no—
319C4—161no—
320C4#481×C13911yescharacteristic
321C4#482×C13911yescharacteristic
322C4#483×C13911yescharacteristic
323C4#485×C13911yescharacteristic
324C4#485×C13911yescharacteristic
325C4#485×C13911yescharacteristic
326C4#488×C13911yescharacteristic
327C4#491×C13911yescharacteristic
328C2#1678×C13911yescharacteristic
329C2#1680×C13911yescharacteristic
330C2#1698×C13911yescharacteristic
331C2#1700×C13911yescharacteristic
332C2#2074×C13911yescharacteristic
333C2#2077×C13911yescharacteristic
334C2#2078×C13911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C139#121
commutator, Frattini, cosocleC2×C42C23×C139
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
167. #10626C139direct (N × H)
168. C139#10626direct (N × H)

Maximal subgroups

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

subgroupindex
#1984×C1392
#1834×C1392
#1803×C1392
#1296×C1392
#1277×C1392
#10626139