Finite Group Databasebeta

← C139×#12967 #48007563

Subgroups — C139×#12967 #48007563

Order 35584.

516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 118 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#2379×C139C211yesmaximal, characteristic
2C2×#354×C139C211yesmaximal, characteristic
3#1885×C139C211yesmaximal, characteristic
4#1867×C139C212yesmaximal
5#1390×C139C212yesmaximal
6C2×#124×C139C2211yescharacteristic
7#518×C139C2211yescharacteristic
8#419×C139—21no—
9C2×#100×C139C2211yescharacteristic
10C2×#99×C139C2212yes—
11#391×C139—21no—
12#388×C139—22no—
13#386×C139C2212yes—
14#385×C139—22no—
15#385×C139—22no—
16#382×C139—21no—
17#354×C139C414yescomplemented
18#342×C139—22no—
19#339×C139—21no—
20C22×Q8×C139D411yescharacteristic
21C22×D4×C139C2311yescharacteristic
22C23×C4×C139D412yes—
23C2×M16×C139—21no—
24#124×C139—22no—
25#124×C139C2×C412yes—
26#124×C139Q812yes—
27C4×D4×C139—41no—
28C4×D4×C139—41no—
29#117×C139—21no—
30C2×C4⋊C4×C139—21no—
31C2×C4⋊C4×C139—21no—
32C2×C4⋊C4×C139—21no—
33C2×C4⋊C4×C139—42no—
34C2×C22⋊C4×C139—22no—
35C2×C22⋊C4×C139—22no—
36C2×C22⋊C4×C139—22no—
37C2×C22⋊C4×C139—22no—
38C2×C22⋊C4×C139D412yes—
39C2×C42×C139—21no—
40C2×C42×C139D411yescharacteristic
41#103×C139—41no—
42#103×C139—41no—
43#100×C139—22no—
44#99×C139—22no—
45#99×C139C2×C414yes—
46#95×C139—22no—
47#95×C139—22no—
48#95×C139—22no—
49#95×C139—42no—
50C24×C139C2×D412yes—
51C2×Q8×C139—21no—
52C2×Q8×C139—41no—
53C2×Q8×C139—41no—
54C2×Q8×C139C4⋊C412yescomplemented
55C2×D4×C139—41no—
56C2×D4×C139—41no—
57C2×D4×C139C22×C411yescharacteristic
58C2×D4×C139C2×Q811yescharacteristic
59C2×D4×C139#4112yes—
60C22×C4×C139—21no—
61C22×C4×C139—21no—
62C22×C4×C139—22no—
63C22×C4×C139—22no—
64C22×C4×C139—22no—
65C22×C4×C139—22no—
66C22×C4×C139—42no—
67C22×C4×C139—42no—
68C22×C4×C139—82no—
69C22×C4×C139C2×D411yescharacteristic
70M16×C139—41no—
71M16×C139—41no—
72C2×C8×C139—41no—
73C4⋊C4×C139—21no—
74C4⋊C4×C139—21no—
75C4⋊C4×C139—81no—
76C4⋊C4×C139—81no—
77C4⋊C4×C139—81no—
78C4⋊C4×C139—84no—
79C22⋊C4×C139—24no—
80C22⋊C4×C139—24no—
81C22⋊C4×C139—24no—
82C22⋊C4×C139—42no—
83C22⋊C4×C139—42no—
84C22⋊C4×C139—41no—
85C22⋊C4×C139—42no—
86C22⋊C4×C139—82no—
87C42×C139—21no—
88C42×C139—41no—
89C42×C139—81no—
90C42×C139C4⋊C412yescomplemented
91C23×C139—22no—
92C23×C139—22no—
93C23×C139—42no—
94C23×C139—42no—
95C23×C139C4×D412yes—
96C23×C139#12011yescharacteristic
97C23×C139C22⋊Q812yes—
98Q8×C139—42no—
99Q8×C139—81no—
100D4×C139—41no—
101D4×C139—41no—
102D4×C139—42no—
103C2×C4×C139—21no—
104C2×C4×C139—21no—
105C2×C4×C139—22no—
106C2×C4×C139—22no—
107C2×C4×C139—41no—
108C2×C4×C139—41no—
109C2×C4×C139—41no—
110C2×C4×C139—41no—
111C2×C4×C139—44no—
112C2×C4×C139—42no—
113C2×C4×C139—42no—
114C2×C4×C139—42no—
115C2×C4×C139—42no—
116C2×C4×C139—44no—
117C2×C4×C139—41no—
118C2×C4×C139—41no—
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—82no—
126C2×C4×C139C2×C4⋊C411yescharacteristic
127C2×C4×C139#12311yescharacteristic
128C8×C139—81no—
129C22×C139—21no—
130C22×C139—21no—
131C22×C139—22no—
132C22×C139—22no—
133C22×C139—42no—
134C22×C139—42no—
135C22×C139—42no—
136C22×C139—42no—
137C22×C139—82no—
138C22×C139#38511yescharacteristic
139C22×C139B(4,𝔽2)11yescharacteristic
140C22×C139#45811yescharacteristic
141C4×C139—21no—
142C4×C139—21no—
143C4×C139—42no—
144C4×C139—42no—
145C4×C139—82no—
146C4×C139—84no—
147C4×C139—82no—
148C4×C139—81no—
149C4×C139—81no—
150C2×C139—21no—
151C2×C139—21no—
152C2×C139—42no—
153C2×C139—42no—
154C2×C139#186711yescharacteristic
155C2×C139#219911yescharacteristic
156C2×C139#220111yescharacteristic
157#12967C13911yesmaximal, characteristic, direct product factor, Sylow
158C139#1296711yescharacteristic, direct product factor, Sylow
159#2379C2×C13911yescharacteristic
160C2×#354C2×C13911yescharacteristic
161#1885C2×C13911yescharacteristic
162#1867C2×C13912yes—
163#1390C2×C13912yes—
164C2×#124C22×C13911yescharacteristic
165#518C22×C13911yescharacteristic
166#419—21no—
167C2×#100C22×C13911yescharacteristic
168C2×#99C22×C13912yes—
169#391—21no—
170#388—22no—
171#386C22×C13912yes—
172#385—22no—
173#385—22no—
174#382—21no—
175#354C4×C13914yescomplemented
176#342—22no—
177#339—21no—
178C22×Q8D4×C13911yescharacteristic
179C22×D4C23×C13911yescharacteristic
180C23×C4D4×C13912yes—
181C2×M16—21no—
182#124—22no—
183#124C2×C4×C13912yes—
184#124Q8×C13912yes—
185C4×D4—41no—
186C4×D4—41no—
187#117—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—42no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4D4×C13912yes—
197C2×C42—21no—
198C2×C42D4×C13911yescharacteristic
199#103—41no—
200#103—41no—
201#100—22no—
202#99—22no—
203#99C2×C4×C13914yes—
204#95—22no—
205#95—22no—
206#95—22no—
207#95—42no—
208C24C2×D4×C13912yes—
209C2×Q8—21no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8C4⋊C4×C13912yescomplemented
213C2×D4—41no—
214C2×D4—41no—
215C2×D4C22×C4×C13911yescharacteristic
216C2×D4C2×Q8×C13911yescharacteristic
217C2×D4#41×C13912yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—82no—
227C22×C4C2×D4×C13911yescharacteristic
228M16—41no—
229M16—41no—
230C2×C8—41no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C4⋊C4—81no—
236C4⋊C4—84no—
237C22⋊C4—24no—
238C22⋊C4—24no—
239C22⋊C4—24no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—41no—
243C22⋊C4—42no—
244C22⋊C4—82no—
245C42—21no—
246C42—41no—
247C42—81no—
248C42C4⋊C4×C13912yescomplemented
249C23—22no—
250C23—22no—
251C23—42no—
252C23—42no—
253C23C4×D4×C13912yes—
254C23#120×C13911yescharacteristic
255C23C22⋊Q8×C13912yes—
256Q8—42no—
257Q8—81no—
258D4—41no—
259D4—41no—
260D4—42no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—44no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—44no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4C2×C4⋊C4×C13911yescharacteristic
285C2×C4#123×C13911yescharacteristic
286C8—81no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—82no—
296C22#385×C13911yescharacteristic
297C22B(4,𝔽2)×C13911yescharacteristic
298C22#458×C13911yescharacteristic
299C4—21no—
300C4—21no—
301C4—42no—
302C4—42no—
303C4—82no—
304C4—84no—
305C4—82no—
306C4—81no—
307C4—81no—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—42no—
312C2#1867×C13911yescharacteristic
313C2#2199×C13911yescharacteristic
314C2#2201×C13911yescharacteristic
subgroupG/H
center, socleC22×C139B(4,𝔽2)
commutatorC2×D4C22×C4×C139
Frattini, cosocleC22×D4C23×C139
prime radicalC22×D4×C139C23
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C139 ◁ C22×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
17. #354×C139C4semidirect
54. C2×Q8×C139C4⋊C4semidirect
90. C42×C139C4⋊C4semidirect
157. #12967C139direct (N × H)
158. C139#12967direct (N × H)
175. #354C4×C139semidirect
212. C2×Q8C4⋊C4×C139semidirect
248. C42C4⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2379×C1392
C2×#354×C1392
#1885×C1392
#1867×C1392
#1390×C1392
#12967139