Finite Group Databasebeta

← C139×#7786 #48002382

Subgroups — C139×#7786 #48002382

Order 35584.

682 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 106 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
1#2679×C139C211yesmaximal, characteristic
2#2093×C139C211yesmaximal, characteristic, complemented
3#2071×C139C212yesmaximal, complemented
4#1270×C139C211yesmaximal, characteristic, complemented
5#1270×C139C212yesmaximal, complemented
6C2×#120×C139—22no—
7C2×#120×C139—21no—
8C2×#107×C139—21no—
9C2×#102×C139—22no—
10C2×#102×C139—21no—
11#394×C139—21no—
12#394×C139—22no—
13#390×C139C2212yes—
14#390×C139C2211yescharacteristic
15#384×C139C2211yescharacteristic, complemented
16#340×C139—22no—
17#336×C139C2212yescomplemented
18#336×C139C2211yescharacteristic, complemented
19C25×C139—21no—
20C22×D4×C139—21no—
21C22×D4×C139—22no—
22C22×D4×C139D412yes—
23C22×D4×C139D411yescharacteristic
24C22×C8×C139—21no—
25C22×C8×C139—22no—
26#120×C139—44no—
27#120×C139—42no—
28#120×C139—44no—
29#120×C139—42no—
30C2×C4⋊C4×C139—21no—
31C2×C4⋊C4×C139—22no—
32C2×C4⋊C4×C139D411yescharacteristic
33C2×C4⋊C4×C139D412yes—
34C2×C22⋊C4×C139—22no—
35C2×C22⋊C4×C139—21no—
36C2×C22⋊C4×C139—22no—
37C2×C22⋊C4×C139—22no—
38C2×C22⋊C4×C139—22no—
39C2×C42×C139C2311yescharacteristic
40#107×C139—42no—
41#102×C139—42no—
42#102×C139—44no—
43#95×C139—21no—
44C24×C139—22no—
45C24×C139—21no—
46C24×C139—44no—
47C24×C139—42no—
48C24×C139—81no—
49C24×C139—82no—
50C24×C139—81no—
51C2×D4×C139—22no—
52C2×D4×C139—21no—
53C2×D4×C139—41no—
54C2×D4×C139—42no—
55C2×D4×C139—42no—
56C2×D4×C139—41no—
57C2×D4×C139—44no—
58C2×D4×C139—44no—
59C2×D4×C139—44no—
60C2×D4×C139—81no—
61C2×D4×C139—82no—
62C2×D4×C139D814yes—
63C2×D4×C139SD1612yes—
64C22×C4×C139—21no—
65C22×C4×C139—22no—
66C22×C4×C139—41no—
67C22×C4×C139C2×D412yes—
68C22×C4×C139C2×D411yescharacteristic
69C2×C8×C139—22no—
70C2×C8×C139—41no—
71C2×C8×C139—41no—
72C2×C8×C139—42no—
73C2×C8×C139—42no—
74C2×C8×C139—42no—
75C4⋊C4×C139—41no—
76C4⋊C4×C139—42no—
77C4⋊C4×C139—41no—
78C4⋊C4×C139—41no—
79C4⋊C4×C139—42no—
80C4⋊C4×C139—42no—
81C22⋊C4×C139—44no—
82C22⋊C4×C139—42no—
83C22⋊C4×C139—42no—
84C22⋊C4×C139—42no—
85C22⋊C4×C139—42no—
86C22⋊C4×C139—42no—
87C22⋊C4×C139—42no—
88C22⋊C4×C139—42no—
89C42×C139—41no—
90C23×C139—24no—
91C23×C139—22no—
92C23×C139—42no—
93C23×C139—42no—
94C23×C139—42no—
95C23×C139—41no—
96C23×C139—42no—
97C23×C139—42no—
98C23×C139—42no—
99C23×C139—42no—
100C23×C139—42no—
101C23×C139—41no—
102C23×C139—84no—
103C23×C139—88no—
104C23×C139—88no—
105C23×C139—84no—
106C23×C139—84no—
107C23×C139#12011yescharacteristic
108D4×C139—44no—
109D4×C139—42no—
110D4×C139—82no—
111D4×C139—81no—
112D4×C139—84no—
113D4×C139—88no—
114C2×C4×C139—21no—
115C2×C4×C139—22no—
116C2×C4×C139—22no—
117C2×C4×C139—21no—
118C2×C4×C139—42no—
119C2×C4×C139—42no—
120C2×C4×C139—42no—
121C2×C4×C139—41no—
122C2×C4×C139—42no—
123C2×C4×C139—82no—
124C2×C4×C139—81no—
125C2×C4×C139C2×D812yes—
126C2×C4×C139C2×SD1611yescharacteristic
127C2×C4×C139AGL(1,ℤ/8)12yes—
128C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
129C8×C139—42no—
130C8×C139—82no—
131C22×C139—44no—
132C22×C139—42no—
133C22×C139—44no—
134C22×C139—44no—
135C22×C139—44no—
136C22×C139—816no—
137C22×C139—82no—
138C22×C139—82no—
139C22×C139—82no—
140C22×C139—81no—
141C22×C139—82no—
142C22×C139—81no—
143C22×C139—82no—
144C22×C139#44712yes—
145C22×C139#45011yescharacteristic
146C22×C139#45311yescharacteristic
147C22×C139#45512yes—
148C22×C139#45811yescharacteristic
149C4×C139—22no—
150C4×C139—22no—
151C4×C139—21no—
152C4×C139—21no—
153C4×C139—81no—
154C4×C139—82no—
155C4×C139—161no—
156C2×C139—84no—
157C2×C139—82no—
158C2×C139#160712yes—
159C2×C139#161311yescharacteristic
160C2×C139#161911yescharacteristic
161C2×C139#163912yes—
162C2×C139#165911yescharacteristic
163#7786C13911yesmaximal, characteristic, direct product factor, Sylow
164C139#778611yescharacteristic, direct product factor, Sylow
165#2679C2×C13911yescharacteristic
166#2093C2×C13911yescharacteristic, complemented
167#2071C2×C13912yescomplemented
168#1270C2×C13911yescharacteristic, complemented
169#1270C2×C13912yescomplemented
170C2×#120—22no—
171C2×#120—21no—
172C2×#107—21no—
173C2×#102—22no—
174C2×#102—21no—
175#394—22no—
176#394—21no—
177#390C22×C13912yes—
178#390C22×C13911yescharacteristic
179#384C22×C13911yescharacteristic, complemented
180#340—22no—
181#336C22×C13912yescomplemented
182#336C22×C13911yescharacteristic, complemented
183C25—21no—
184C22×D4—21no—
185C22×D4—22no—
186C22×D4D4×C13912yes—
187C22×D4D4×C13911yescharacteristic
188C22×C8—21no—
189C22×C8—22no—
190#120—44no—
191#120—42no—
192#120—44no—
193#120—42no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4D4×C13912yes—
197C2×C4⋊C4D4×C13911yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C42C23×C13911yescharacteristic
204#107—42no—
205#102—42no—
206#102—44no—
207#95—21no—
208C24—22no—
209C24—21no—
210C24—44no—
211C24—42no—
212C24—81no—
213C24—82no—
214C24—81no—
215C2×D4—22no—
216C2×D4—21no—
217C2×D4—41no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—41no—
221C2×D4—44no—
222C2×D4—44no—
223C2×D4—44no—
224C2×D4—81no—
225C2×D4—82no—
226C2×D4D8×C13914yes—
227C2×D4SD16×C13912yes—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—41no—
231C22×C4C2×D4×C13912yes—
232C22×C4C2×D4×C13911yescharacteristic
233C2×C8—22no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C22⋊C4—44no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C42—41no—
254C23—24no—
255C23—22no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—41no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—41no—
266C23—84no—
267C23—88no—
268C23—88no—
269C23—84no—
270C23—84no—
271C23#120×C13911yescharacteristic
272D4—44no—
273D4—42no—
274D4—82no—
275D4—81no—
276D4—84no—
277D4—88no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—82no—
288C2×C4—81no—
289C2×C4C2×D8×C13912yes—
290C2×C4C2×SD16×C13911yescharacteristic
291C2×C4AGL(1,ℤ/8)×C13912yes—
292C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
293C8—42no—
294C8—82no—
295C22—44no—
296C22—42no—
297C22—44no—
298C22—44no—
299C22—44no—
300C22—816no—
301C22—82no—
302C22—82no—
303C22—82no—
304C22—81no—
305C22—82no—
306C22—81no—
307C22—82no—
308C22#447×C13912yes—
309C22#450×C13911yescharacteristic
310C22#453×C13911yescharacteristic
311C22#455×C13912yes—
312C22#458×C13911yescharacteristic
313C4—22no—
314C4—22no—
315C4—21no—
316C4—21no—
317C4—81no—
318C4—82no—
319C4—161no—
320C2—84no—
321C2—82no—
322C2#1607×C13912yes—
323C2#1613×C13911yescharacteristic
324C2#1619×C13911yescharacteristic
325C2#1639×C13912yes—
326C2#1659×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutator, Frattini, cosocleC2×C42C23×C139
prime radical#2679×C139C2
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2093×C139C2semidirect
3. #2071×C139C2semidirect
4. #1270×C139C2semidirect
5. #1270×C139C2semidirect
15. #384×C139C22semidirect
17. #336×C139C22semidirect
18. #336×C139C22semidirect
163. #7786C139direct (N × H)
164. C139#7786direct (N × H)
166. #2093C2×C139semidirect
167. #2071C2×C139semidirect
168. #1270C2×C139semidirect
169. #1270C2×C139semidirect
179. #384C22×C139semidirect
181. #336C22×C139semidirect
182. #336C22×C139semidirect

Maximal subgroups

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

subgroupindex
#2679×C1392
#2093×C1392
#2071×C1392
#1270×C1392
#7786139