Finite Group Databasebeta

← C139×#9048 #48003644

Subgroups — C139×#9048 #48003644

Order 35584.

424 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3104×C139C211yesmaximal, characteristic
2#2961×C139C211yesmaximal, characteristic
3#1985×C139C211yesmaximal, characteristic
4#1542×C139C211yesmaximal, characteristic
5#1487×C139C211yesmaximal, characteristic
6#1301×C139C211yesmaximal, characteristic
7#1281×C139C211yesmaximal, characteristic
8#533×C139C2211yescharacteristic
9C2×C4×Q8×C139C2211yescharacteristic
10#484×C139C412yes—
11#477×C139—21no—
12#462×C139—21no—
13#451×C139C412yes—
14#446×C139—22no—
15#446×C139—22no—
16C4×Q16×C139—22no—
17#431×C139C2211yescharacteristic
18#431×C139C2211yescharacteristic
19#424×C139—21no—
20#423×C139C2211yescharacteristic
21C2×C4⋊C8×C139C2211yescharacteristic
22#405×C139—21no—
23C2×#97×C139C2211yescharacteristic
24#336×C139—21no—
25#336×C139—21no—
26#333×C139—21no—
27#332×C139—21no—
28Q8⋊C8×C139—22no—
29C22×Q8×C139C2×C411yescharacteristic
30C2×Q16×C139—22no—
31C2×M16×C139—21no—
32C22×C8×C139—21no—
33C22×C8×C139D411yescharacteristic
34C22×C8×C139D411yescharacteristic
35C4⋊Q8×C139D411yescharacteristic
36C4⋊Q8×C139D411yescharacteristic
37#125×C139—21no—
38C22⋊Q8×C139—21no—
39C22⋊Q8×C139C2×C412yes—
40C4×Q8×C139—21no—
41C4×Q8×C139—21no—
42C4×Q8×C139—21no—
43C4×Q8×C139—21no—
44C4×Q8×C139—21no—
45C4×Q8×C139D412yes—
46#117×C139—21no—
47C2×C4⋊C4×C139—21no—
48C2×C4⋊C4×C139C2×C411yescharacteristic
49C2×C42×C139—21no—
50C2×C42×C139C2311yescharacteristic
51#107×C139—22no—
52C4⋊C8×C139—24no—
53C4⋊C8×C139—21no—
54C4⋊C8×C139—21no—
55C4⋊C8×C139—21no—
56C4⋊C8×C139—21no—
57C4⋊C8×C139—21no—
58C4⋊C8×C139D412yes—
59#103×C139—22no—
60#103×C139—22no—
61C22⋊C8×C139—21no—
62C22⋊C8×C139C2×C412yes—
63#97×C139—22no—
64#97×C139—21no—
65#97×C139—21no—
66C4×C8×C139—22no—
67C4×C8×C139—21no—
68C4×C8×C139—21no—
69C2×Q8×C139—21no—
70C2×Q8×C139—21no—
71C2×Q8×C139—21no—
72C2×Q8×C139—42no—
73C2×Q8×C139C22⋊C412yes—
74C22×C4×C139—21no—
75C22×C4×C139—21no—
76C22×C4×C139C22×C411yescharacteristic
77C22×C4×C139C2×D411yescharacteristic
78C22×C4×C139#4111yescharacteristic
79Q16×C139—44no—
80M16×C139—41no—
81M16×C139—41no—
82C2×C8×C139—21no—
83C2×C8×C139—21no—
84C2×C8×C139—22no—
85C2×C8×C139—22no—
86C2×C8×C139—21no—
87C2×C8×C139—21no—
88C2×C8×C139—21no—
89C2×C8×C139—41no—
90C2×C8×C139—41no—
91C2×C8×C139—41no—
92C2×C8×C139—41no—
93C2×C8×C139Q1612yescomplemented
94C4⋊C4×C139—22no—
95C4⋊C4×C139—21no—
96C4⋊C4×C139—21no—
97C4⋊C4×C139—21no—
98C4⋊C4×C139—22no—
99C4⋊C4×C139—21no—
100C4⋊C4×C139—21no—
101C4⋊C4×C139—41no—
102C4⋊C4×C139—41no—
103C4⋊C4×C139C22⋊C412yes—
104C22⋊C4×C139—22no—
105C42×C139—22no—
106C42×C139—41no—
107C42×C139—41no—
108C42×C139C2×D411yescharacteristic
109C42×C139C2×D411yescharacteristic
110C42×C139C2×D411yescharacteristic
111C42×C139#4111yescharacteristic
112C23×C139C4×D411yescharacteristic
113Q8×C139—22no—
114Q8×C139—22no—
115Q8×C139—42no—
116Q8×C139—41no—
117Q8×C139—41no—
118Q8×C139—81no—
119C2×C4×C139—22no—
120C2×C4×C139—22no—
121C2×C4×C139—22no—
122C2×C4×C139—41no—
123C2×C4×C139—41no—
124C2×C4×C139—41no—
125C2×C4×C139—41no—
126C2×C4×C139—42no—
127C2×C4×C139—41no—
128C2×C4×C139C2×C22⋊C411yescharacteristic
129C2×C4×C139C4×D411yescharacteristic
130C2×C4×C139#12011yescharacteristic
131C2×C4×C139#12111yescharacteristic
132C2×C4×C139#12111yescharacteristic
133C2×C4×C139#12311yescharacteristic
134C2×C4×C139C2×Q1611yescharacteristic
135C2×C4×C139#13511yescharacteristic
136C2×C4×C139#13711yescharacteristic
137C2×C4×C139#13711yescharacteristic
138C8×C139—22no—
139C8×C139—42no—
140C8×C139—41no—
141C8×C139—42no—
142C8×C139—81no—
143C8×C139—81no—
144C22×C139—21no—
145C22×C139—21no—
146C22×C139#38611yescharacteristic
147C22×C139C4×Q1611yescharacteristic
148C22×C139#44111yescharacteristic
149C4×C139—21no—
150C4×C139—21no—
151C4×C139—21no—
152C4×C139—21no—
153C4×C139—42no—
154C4×C139—42no—
155C4×C139—42no—
156C4×C139—81no—
157C4×C139#45111yescharacteristic
158C4×C139#45211yescharacteristic
159C4×C139#46211yescharacteristic
160C4×C139#46411yescharacteristic
161C2×C139—21no—
162C2×C139—21no—
163C2×C139#187811yescharacteristic
164C2×C139#188111yescharacteristic
165C2×C139#189111yescharacteristic
166#9048C13911yesmaximal, characteristic, direct product factor, Sylow
167C139#904811yescharacteristic, direct product factor, Sylow
168#3104C2×C13911yescharacteristic
169#2961C2×C13911yescharacteristic
170#1985C2×C13911yescharacteristic
171#1542C2×C13911yescharacteristic
172#1487C2×C13911yescharacteristic
173#1301C2×C13911yescharacteristic
174#1281C2×C13911yescharacteristic
175#533C22×C13911yescharacteristic
176C2×C4×Q8C22×C13911yescharacteristic
177#484C4×C13912yes—
178#477—21no—
179#462—21no—
180#451C4×C13912yes—
181#446—22no—
182#446—22no—
183C4×Q16—22no—
184#431C22×C13911yescharacteristic
185#431C22×C13911yescharacteristic
186#424—21no—
187#423C22×C13911yescharacteristic
188C2×C4⋊C8C22×C13911yescharacteristic
189#405—21no—
190C2×#97C22×C13911yescharacteristic
191#336—21no—
192#336—21no—
193#333—21no—
194#332—21no—
195Q8⋊C8—22no—
196C22×Q8C2×C4×C13911yescharacteristic
197C2×Q16—22no—
198C2×M16—21no—
199C22×C8—21no—
200C22×C8D4×C13911yescharacteristic
201C22×C8D4×C13911yescharacteristic
202C4⋊Q8D4×C13911yescharacteristic
203C4⋊Q8D4×C13911yescharacteristic
204#125—21no—
205C22⋊Q8—21no—
206C22⋊Q8C2×C4×C13912yes—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8D4×C13912yes—
213#117—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×C4×C13911yescharacteristic
216C2×C42—21no—
217C2×C42C23×C13911yescharacteristic
218#107—22no—
219C4⋊C8—24no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8D4×C13912yes—
226#103—22no—
227#103—22no—
228C22⋊C8—21no—
229C22⋊C8C2×C4×C13912yes—
230#97—22no—
231#97—21no—
232#97—21no—
233C4×C8—22no—
234C4×C8—21no—
235C4×C8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—42no—
240C2×Q8C22⋊C4×C13912yes—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4C22×C4×C13911yescharacteristic
244C22×C4C2×D4×C13911yescharacteristic
245C22×C4#41×C13911yescharacteristic
246Q16—44no—
247M16—41no—
248M16—41no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8Q16×C13912yescomplemented
261C4⋊C4—22no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4C22⋊C4×C13912yes—
271C22⋊C4—22no—
272C42—22no—
273C42—41no—
274C42—41no—
275C42C2×D4×C13911yescharacteristic
276C42C2×D4×C13911yescharacteristic
277C42C2×D4×C13911yescharacteristic
278C42#41×C13911yescharacteristic
279C23C4×D4×C13911yescharacteristic
280Q8—22no—
281Q8—22no—
282Q8—42no—
283Q8—41no—
284Q8—41no—
285Q8—81no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4C2×C22⋊C4×C13911yescharacteristic
296C2×C4C4×D4×C13911yescharacteristic
297C2×C4#120×C13911yescharacteristic
298C2×C4#121×C13911yescharacteristic
299C2×C4#121×C13911yescharacteristic
300C2×C4#123×C13911yescharacteristic
301C2×C4C2×Q16×C13911yescharacteristic
302C2×C4#135×C13911yescharacteristic
303C2×C4#137×C13911yescharacteristic
304C2×C4#137×C13911yescharacteristic
305C8—22no—
306C8—42no—
307C8—41no—
308C8—42no—
309C8—81no—
310C8—81no—
311C22—21no—
312C22—21no—
313C22#386×C13911yescharacteristic
314C22C4×Q16×C13911yescharacteristic
315C22#441×C13911yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—42no—
321C4—42no—
322C4—42no—
323C4—81no—
324C4#451×C13911yescharacteristic
325C4#452×C13911yescharacteristic
326C4#462×C13911yescharacteristic
327C4#464×C13911yescharacteristic
328C2—21no—
329C2—21no—
330C2#1878×C13911yescharacteristic
331C2#1881×C13911yescharacteristic
332C2#1891×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139#120
commutatorC22×C4C22×C4×C139
Frattini, cosocleC2×C42C23×C139
socleC22×C139#386
prime radicalC23×C139C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
93. C2×C8×C139Q16semidirect
166. #9048C139direct (N × H)
167. C139#9048direct (N × H)
260. C2×C8Q16×C139semidirect

Maximal subgroups

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

subgroupindex
#3104×C1392
#2961×C1392
#1985×C1392
#1542×C1392
#1487×C1392
#1301×C1392
#1281×C1392
#9048139