Finite Group Databasebeta

← C139×#8507 #48003103

Subgroups — C139×#8507 #48003103

Order 35584.

736 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#563×C139C211yesmaximal, characteristic
2#1992×C139C212yesmaximal, complemented
3#1959×C139C211yesmaximal, characteristic
4C2×#330×C139C212yesmaximal, complemented
5C2×#329×C139C211yesmaximal, characteristic
6#563×C139—24no—
7#563×C139—22no—
8#563×C139C414yescomplemented
9C2×C4⋊Q8×C139—21no—
10C2×#126×C139—22no—
11C2×#125×C139C2212yes—
12C2×#124×C139C2211yescharacteristic
13C2×#123×C139—21no—
14C2×C22⋊Q8×C139—22no—
15C2×#103×C139—21no—
16C2×#102×C139—21no—
17C2×#97×C139C2212yes—
18C2×#97×C139C2211yescharacteristic
19#384×C139C2211yescharacteristic
20#340×C139—22no—
21#340×C139—22no—
22#330×C139—24no—
23#329×C139—22no—
24C22×Q8×C139—21no—
25C22×Q8×C139D411yescharacteristic
26C22×D4×C139D411yescharacteristic
27C23×C4×C139—21no—
28C22×C8×C139—21no—
29C22×C8×C139—22no—
30C4⋊Q8×C139—24no—
31C4⋊Q8×C139—24no—
32#126×C139—28no—
33#126×C139—28no—
34#125×C139—22no—
35#125×C139—22no—
36#125×C139C2×C414yes—
37#125×C139D414yes—
38#124×C139—22no—
39#124×C139C2×C412yes—
40#124×C139D412yes—
41#123×C139—24no—
42#123×C139—24no—
43C22⋊Q8×C139—28no—
44C22⋊Q8×C139—28no—
45C2×C4⋊C4×C139—22no—
46C2×C4⋊C4×C139—22no—
47C2×C4⋊C4×C139—22no—
48C2×C4⋊C4×C139—21no—
49C2×C4⋊C4×C139—22no—
50C2×C4⋊C4×C139D412yes—
51C2×C4⋊C4×C139D412yes—
52C2×C22⋊C4×C139—22no—
53C2×C22⋊C4×C139—21no—
54C2×C22⋊C4×C139—22no—
55C2×C42×C139—21no—
56C2×C42×C139C2311yescharacteristic
57#103×C139—42no—
58#102×C139—42no—
59#97×C139—22no—
60#97×C139—22no—
61#97×C139—22no—
62C24×C139—21no—
63C2×Q8×C139—24no—
64C2×Q8×C139—21no—
65C2×Q8×C139—41no—
66C2×Q8×C139—41no—
67C2×Q8×C139—81no—
68C2×Q8×C139—81no—
69C2×Q8×C139C22⋊C412yes—
70C2×D4×C139—21no—
71C2×D4×C139—41no—
72C2×D4×C139—41no—
73C2×D4×C139C22⋊C412yes—
74C22×C4×C139—22no—
75C22×C4×C139—21no—
76C22×C4×C139—22no—
77C22×C4×C139—24no—
78C22×C4×C139—41no—
79C22×C4×C139—81no—
80C22×C4×C139—81no—
81C22×C4×C139C2×D412yes—
82C22×C4×C139C2×D411yescharacteristic
83C2×C8×C139—22no—
84C2×C8×C139—24no—
85C2×C8×C139—42no—
86C2×C8×C139—41no—
87C2×C8×C139—42no—
88C2×C8×C139—41no—
89C4⋊C4×C139—28no—
90C4⋊C4×C139—24no—
91C4⋊C4×C139—24no—
92C4⋊C4×C139—24no—
93C4⋊C4×C139—24no—
94C4⋊C4×C139—22no—
95C4⋊C4×C139—22no—
96C4⋊C4×C139—41no—
97C4⋊C4×C139—41no—
98C4⋊C4×C139—44no—
99C4⋊C4×C139C22⋊C414yes—
100C4⋊C4×C139C22⋊C414yes—
101C22⋊C4×C139—28no—
102C22⋊C4×C139—24no—
103C22⋊C4×C139—24no—
104C22⋊C4×C139—24no—
105C42×C139—24no—
106C42×C139C22×C411yescharacteristic
107C42×C139C2×D412yes—
108C42×C139C2×D411yescharacteristic
109C23×C139—22no—
110C23×C139—41no—
111C23×C139—42no—
112C23×C139—41no—
113C23×C139—42no—
114C23×C139#12011yescharacteristic
115Q8×C139—42no—
116Q8×C139—81no—
117Q8×C139—84no—
118D4×C139—42no—
119D4×C139—81no—
120C2×C4×C139—21no—
121C2×C4×C139—22no—
122C2×C4×C139—21no—
123C2×C4×C139—22no—
124C2×C4×C139—24no—
125C2×C4×C139—22no—
126C2×C4×C139—24no—
127C2×C4×C139—42no—
128C2×C4×C139—41no—
129C2×C4×C139—42no—
130C2×C4×C139—42no—
131C2×C4×C139—41no—
132C2×C4×C139—42no—
133C2×C4×C139—84no—
134C2×C4×C139—81no—
135C2×C4×C139—82no—
136C2×C4×C139C2×C22⋊C412yes—
137C2×C4×C139C2×C22⋊C411yescharacteristic
138C2×C4×C139#12012yes—
139C2×C4×C139#12011yescharacteristic
140C8×C139—42no—
141C8×C139—44no—
142C22×C139—42no—
143C22×C139—44no—
144C22×C139—81no—
145C22×C139—81no—
146C22×C139—82no—
147C22×C139#37911yescharacteristic
148C22×C139#45311yescharacteristic
149C22×C139#45412yes—
150C22×C139#45511yescharacteristic
151C22×C139#45612yes—
152C4×C139—21no—
153C4×C139—21no—
154C4×C139—22no—
155C4×C139—22no—
156C4×C139—44no—
157C4×C139—42no—
158C4×C139—44no—
159C4×C139—161no—
160C2×C139—82no—
161C2×C139#165711yescharacteristic
162C2×C139#166011yescharacteristic
163C2×C139#166412yes—
164C2×C139#179211yescharacteristic
165C2×C139#179312yes—
166#8507C13911yesmaximal, characteristic, direct product factor, Sylow
167C139#850711yescharacteristic, direct product factor, Sylow
168C2×#563C2×C13911yescharacteristic
169#1992C2×C13912yescomplemented
170#1959C2×C13911yescharacteristic
171C2×#330C2×C13912yescomplemented
172C2×#329C2×C13911yescharacteristic
173#563—24no—
174#563—22no—
175#563C4×C13914yescomplemented
176C2×C4⋊Q8—21no—
177C2×#126—22no—
178C2×#125C22×C13912yes—
179C2×#124C22×C13911yescharacteristic
180C2×#123—21no—
181C2×C22⋊Q8—22no—
182C2×#103—21no—
183C2×#102—21no—
184C2×#97C22×C13911yescharacteristic
185C2×#97C22×C13912yes—
186#384C22×C13911yescharacteristic
187#340—22no—
188#340—22no—
189#330—24no—
190#329—22no—
191C22×Q8—21no—
192C22×Q8D4×C13911yescharacteristic
193C22×D4D4×C13911yescharacteristic
194C23×C4—21no—
195C22×C8—22no—
196C22×C8—21no—
197C4⋊Q8—24no—
198C4⋊Q8—24no—
199#126—28no—
200#126—28no—
201#125—22no—
202#125—22no—
203#125C2×C4×C13914yes—
204#125D4×C13914yes—
205#124—22no—
206#124C2×C4×C13912yes—
207#124D4×C13912yes—
208#123—24no—
209#123—24no—
210C22⋊Q8—28no—
211C22⋊Q8—28no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4D4×C13912yes—
218C2×C4⋊C4D4×C13912yes—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—22no—
222C2×C42—21no—
223C2×C42C23×C13911yescharacteristic
224#103—42no—
225#102—42no—
226#97—22no—
227#97—22no—
228#97—22no—
229C24—21no—
230C2×Q8—24no—
231C2×Q8—21no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—81no—
235C2×Q8—81no—
236C2×Q8C22⋊C4×C13912yes—
237C2×D4—21no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4C22⋊C4×C13912yes—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—24no—
245C22×C4—41no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4C2×D4×C13912yes—
249C22×C4C2×D4×C13911yescharacteristic
250C2×C8—22no—
251C2×C8—24no—
252C2×C8—42no—
253C2×C8—41no—
254C2×C8—42no—
255C2×C8—41no—
256C4⋊C4—28no—
257C4⋊C4—24no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—44no—
266C4⋊C4C22⋊C4×C13914yes—
267C4⋊C4C22⋊C4×C13914yes—
268C22⋊C4—28no—
269C22⋊C4—24no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C42—24no—
273C42C22×C4×C13911yescharacteristic
274C42C2×D4×C13912yes—
275C42C2×D4×C13911yescharacteristic
276C23—22no—
277C23—41no—
278C23—42no—
279C23—41no—
280C23—42no—
281C23#120×C13911yescharacteristic
282Q8—42no—
283Q8—81no—
284Q8—84no—
285D4—42no—
286D4—81no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—22no—
293C2×C4—24no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—84no—
301C2×C4—81no—
302C2×C4—82no—
303C2×C4C2×C22⋊C4×C13912yes—
304C2×C4C2×C22⋊C4×C13911yescharacteristic
305C2×C4#120×C13912yes—
306C2×C4#120×C13911yescharacteristic
307C8—42no—
308C8—44no—
309C22—42no—
310C22—44no—
311C22—81no—
312C22—81no—
313C22—82no—
314C22#379×C13911yescharacteristic
315C22#453×C13911yescharacteristic
316C22#454×C13912yes—
317C22#455×C13911yescharacteristic
318C22#456×C13912yes—
319C4—21no—
320C4—21no—
321C4—22no—
322C4—22no—
323C4—44no—
324C4—42no—
325C4—44no—
326C4—161no—
327C2—82no—
328C2#1657×C13911yescharacteristic
329C2#1660×C13911yescharacteristic
330C2#1664×C13912yes—
331C2#1792×C13911yescharacteristic
332C2#1793×C13912yes—
subgroupG/H
center, socleC23×C139#120
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC22×D4×C139D4
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
2. #1992×C139C2semidirect
4. C2×#330×C139C2semidirect
8. #563×C139C4semidirect
166. #8507C139direct (N × H)
167. C139#8507direct (N × H)
169. #1992C2×C139semidirect
171. C2×#330C2×C139semidirect
175. #563C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#563×C1392
#1992×C1392
#1959×C1392
C2×#330×C1392
C2×#329×C1392
#8507139