Finite Group Databasebeta

← C139×#8717 #48003313

Subgroups — C139×#8717 #48003313

Order 35584.

588 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#2285×C139C211yesmaximal, characteristic
2#1817×C139C211yesmaximal, characteristic
3#1434×C139C211yesmaximal, characteristic
4#1294×C139C214yesmaximal
5C2×#117×C139—21no—
6C22×C42×C139C2211yescharacteristic
7C2×C22⋊C8×C139C2212yes—
8#384×C139C411yescharacteristic, complemented
9#384×C139C411yescharacteristic, complemented
10#382×C139—21no—
11#380×C139—21no—
12#380×C139C2212yes—
13C4×C4⋊C4×C139—21no—
14C4×C4⋊C4×C139C412yescomplemented
15C2×#95×C139—21no—
16C2×#95×C139—21no—
17C2×#95×C139C2212yes—
18#336×C139—21no—
19#336×C139—21no—
20C23×C4×C139—22no—
21C23×C4×C139D411yescharacteristic
22C23×C4×C139D411yescharacteristic
23C23×C4×C139C2311yescharacteristic
24C22×C8×C139—22no—
25#117×C139—44no—
26C2×C4⋊C4×C139—21no—
27C2×C4⋊C4×C139—21no—
28C2×C4⋊C4×C139—21no—
29C2×C4⋊C4×C139—21no—
30C2×C4⋊C4×C139C2×C412yes—
31C2×C4⋊C4×C139C2×C412yes—
32C2×C22⋊C4×C139—22no—
33C2×C42×C139—24no—
34C2×C42×C139—22no—
35C2×C42×C139C2×C411yescharacteristic
36C2×C42×C139C2×C411yescharacteristic
37C2×C42×C139D411yescharacteristic
38C2×C42×C139D411yescharacteristic
39C22⋊C8×C139—24no—
40#95×C139—24no—
41#95×C139—22no—
42#95×C139—22no—
43#95×C139—24no—
44#95×C139—42no—
45C24×C139C2×D411yescharacteristic
46C22×C4×C139—22no—
47C22×C4×C139—22no—
48C22×C4×C139—22no—
49C22×C4×C139—22no—
50C22×C4×C139—24no—
51C22×C4×C139—22no—
52C22×C4×C139—22no—
53C22×C4×C139—41no—
54C22×C4×C139—41no—
55C22×C4×C139—41no—
56C22×C4×C139—42no—
57C22×C4×C139—42no—
58C22×C4×C139—42no—
59C22×C4×C139—42no—
60C22×C4×C139—42no—
61C22×C4×C139—42no—
62C22×C4×C139C22⋊C411yescharacteristic
63C22×C4×C139C22⋊C411yescharacteristic
64C22×C4×C139C22⋊C411yescharacteristic
65C22×C4×C139C22⋊C411yescharacteristic
66C22×C4×C139SD1612yes—
67C22×C4×C139Q1612yes—
68C22×C4×C139C22×C411yescharacteristic
69C22×C4×C139C2×D411yescharacteristic
70C22×C4×C139#4114yes—
71C2×C8×C139—42no—
72C2×C8×C139—42no—
73C2×C8×C139—42no—
74C4⋊C4×C139—42no—
75C4⋊C4×C139—42no—
76C4⋊C4×C139—42no—
77C4⋊C4×C139—42no—
78C4⋊C4×C139—42no—
79C4⋊C4×C139—42no—
80C22⋊C4×C139—44no—
81C42×C139—22no—
82C42×C139—22no—
83C42×C139—22no—
84C42×C139—22no—
85C42×C139—44no—
86C23×C139—21no—
87C23×C139—21no—
88C23×C139—21no—
89C23×C139—21no—
90C23×C139C2×C22⋊C411yescharacteristic
91C23×C139#12312yes—
92C23×C139C2×SD1611yescharacteristic
93C23×C139C2×Q1611yescharacteristic
94C23×C139AGL(1,ℤ/8)12yes—
95C2×C4×C139—21no—
96C2×C4×C139—21no—
97C2×C4×C139—21no—
98C2×C4×C139—21no—
99C2×C4×C139—21no—
100C2×C4×C139—21no—
101C2×C4×C139—21no—
102C2×C4×C139—21no—
103C2×C4×C139—21no—
104C2×C4×C139—21no—
105C2×C4×C139—24no—
106C2×C4×C139—24no—
107C2×C4×C139—21no—
108C2×C4×C139—21no—
109C2×C4×C139—21no—
110C2×C4×C139—44no—
111C2×C4×C139—44no—
112C2×C4×C139—44no—
113C2×C4×C139—44no—
114C2×C4×C139—44no—
115C2×C4×C139—42no—
116C2×C4×C139—42no—
117C2×C4×C139—42no—
118C2×C4×C139—42no—
119C2×C4×C139—42no—
120C2×C4×C139—42no—
121C2×C4×C139—82no—
122C2×C4×C139—82no—
123C2×C4×C139—82no—
124C2×C4×C139—82no—
125C2×C4×C139#10312yes—
126C2×C4×C139#10312yes—
127C2×C4×C139#10412yes—
128C2×C4×C139#11712yes—
129C2×C4×C139#12312yes—
130C8×C139—82no—
131C22×C139—22no—
132C22×C139—22no—
133C22×C139—21no—
134C22×C139—21no—
135C22×C139—22no—
136C22×C139—22no—
137C22×C139—21no—
138C22×C139—21no—
139C22×C139#38111yescharacteristic
140C22×C139#41011yescharacteristic
141C22×C139#41011yescharacteristic
142C22×C139C2×#10311yescharacteristic
143C22×C139#41811yescharacteristic
144C22×C139C2×#10411yescharacteristic
145C22×C139#42111yescharacteristic
146C22×C139#48112yes—
147C22×C139#48412yes—
148C4×C139—22no—
149C4×C139—22no—
150C4×C139—22no—
151C4×C139—22no—
152C4×C139—22no—
153C4×C139—41no—
154C4×C139—84no—
155C4×C139—82no—
156C4×C139—82no—
157C2×C139—22no—
158C2×C139—22no—
159C2×C139#150311yescharacteristic
160C2×C139#150511yescharacteristic
161C2×C139#151411yescharacteristic
162C2×C139#151811yescharacteristic
163C2×C139#182011yescharacteristic
164C2×C139#182411yescharacteristic
165C2×C139#182611yescharacteristic
166#8717C13911yesmaximal, characteristic, direct product factor, Sylow
167C139#871711yescharacteristic, direct product factor, Sylow
168#2285C2×C13911yescharacteristic
169#1817C2×C13911yescharacteristic
170#1434C2×C13911yescharacteristic
171#1294C2×C13914yes—
172C2×#117—21no—
173C22×C42C22×C13911yescharacteristic
174C2×C22⋊C8C22×C13912yes—
175#384C4×C13911yescharacteristic, complemented
176#384C4×C13911yescharacteristic, complemented
177#382—21no—
178#380—21no—
179#380C22×C13912yes—
180C4×C4⋊C4—21no—
181C4×C4⋊C4C4×C13912yescomplemented
182C2×#95—21no—
183C2×#95—21no—
184C2×#95C22×C13912yes—
185#336—21no—
186#336—21no—
187C23×C4—22no—
188C23×C4D4×C13911yescharacteristic
189C23×C4D4×C13911yescharacteristic
190C23×C4C23×C13911yescharacteristic
191C22×C8—22no—
192#117—44no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×C4×C13912yes—
198C2×C4⋊C4C2×C4×C13912yes—
199C2×C22⋊C4—22no—
200C2×C42—24no—
201C2×C42—22no—
202C2×C42C2×C4×C13911yescharacteristic
203C2×C42C2×C4×C13911yescharacteristic
204C2×C42D4×C13911yescharacteristic
205C2×C42D4×C13911yescharacteristic
206C22⋊C8—24no—
207#95—24no—
208#95—22no—
209#95—22no—
210#95—24no—
211#95—42no—
212C24C2×D4×C13911yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—24no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4C22⋊C4×C13911yescharacteristic
230C22×C4C22⋊C4×C13911yescharacteristic
231C22×C4C22⋊C4×C13911yescharacteristic
232C22×C4C22⋊C4×C13911yescharacteristic
233C22×C4SD16×C13912yes—
234C22×C4Q16×C13912yes—
235C22×C4C22×C4×C13911yescharacteristic
236C22×C4C2×D4×C13911yescharacteristic
237C22×C4#41×C13914yes—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C22⋊C4—44no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—22no—
252C42—44no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23C2×C22⋊C4×C13911yescharacteristic
258C23#123×C13912yes—
259C23C2×SD16×C13911yescharacteristic
260C23C2×Q16×C13911yescharacteristic
261C23AGL(1,ℤ/8)×C13912yes—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4#103×C13912yes—
293C2×C4#103×C13912yes—
294C2×C4#104×C13912yes—
295C2×C4#117×C13912yes—
296C2×C4#123×C13912yes—
297C8—82no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22—22no—
302C22—21no—
303C22—21no—
304C22—22no—
305C22—22no—
306C22#381×C13911yescharacteristic
307C22#410×C13911yescharacteristic
308C22#410×C13911yescharacteristic
309C22C2×#103×C13911yescharacteristic
310C22#418×C13911yescharacteristic
311C22C2×#104×C13911yescharacteristic
312C22#421×C13911yescharacteristic
313C22#481×C13912yes—
314C22#484×C13912yes—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—84no—
322C4—82no—
323C4—82no—
324C2—22no—
325C2—22no—
326C2#1503×C13911yescharacteristic
327C2#1505×C13911yescharacteristic
328C2#1514×C13911yescharacteristic
329C2#1518×C13911yescharacteristic
330C2#1820×C13911yescharacteristic
331C2#1824×C13911yescharacteristic
332C2#1826×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC24×C139C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
8. #384×C139C4semidirect
9. #384×C139C4semidirect
14. C4×C4⋊C4×C139C4semidirect
166. #8717C139direct (N × H)
167. C139#8717direct (N × H)
175. #384C4×C139semidirect
176. #384C4×C139semidirect
181. C4×C4⋊C4C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2285×C1392
#1817×C1392
#1434×C1392
#1294×C1392
#8717139