Finite Group Databasebeta

← C139×#7580 #48002176

Subgroups — C139×#7580 #48002176

Order 35584.

500 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2293×C139C211yesmaximal, characteristic
2#1839×C139C211yesmaximal, characteristic, complemented
3#1744×C139C211yesmaximal, characteristic, complemented
4#1271×C139C212yesmaximal, complemented
5#1270×C139C212yesmaximal
6C2×C4×D4×C139C411yescharacteristic
7C2×#117×C139—21no—
8C2×C4×C8×C139—21no—
9#390×C139C411yescharacteristic
10#390×C139C2211yescharacteristic
11#389×C139C411yescharacteristic
12#389×C139C2211yescharacteristic
13#388×C139—21no—
14#388×C139—21no—
15C4×C4⋊C4×C139C411yescharacteristic
16C4×C22⋊C4×C139—21no—
17C43×C139C2211yescharacteristic
18#336×C139—21no—
19#336×C139—21no—
20#336×C139—21no—
21#336×C139C2212yes—
22#336×C139C2212yes—
23C22×D4×C139C2×C411yescharacteristic
24C23×C4×C139—21no—
25C22×C8×C139—22no—
26C22×C8×C139—22no—
27C4×D4×C139—22no—
28C4×D4×C139C814yescomplemented
29#117×C139—44no—
30C2×C4⋊C4×C139—21no—
31C2×C4⋊C4×C139—21no—
32C2×C4⋊C4×C139C2×C411yescharacteristic
33C2×C4⋊C4×C139C2×C411yescharacteristic
34C2×C4⋊C4×C139C2×C411yescharacteristic
35C2×C22⋊C4×C139—21no—
36C2×C22⋊C4×C139—21no—
37C2×C22⋊C4×C139—21no—
38C2×C22⋊C4×C139—21no—
39C2×C22⋊C4×C139—21no—
40C2×C42×C139—21no—
41C2×C42×C139C2×C411yescharacteristic
42C2×C42×C139C2×C411yescharacteristic
43C2×C42×C139D411yescharacteristic
44C2×C42×C139D411yescharacteristic
45C2×C42×C139D411yescharacteristic
46C2×C42×C139D411yescharacteristic
47C2×C42×C139C2311yescharacteristic
48C4×C8×C139—24no—
49#95×C139—21no—
50#95×C139—21no—
51#95×C139—21no—
52C24×C139—21no—
53C2×D4×C139—21no—
54C2×D4×C139—41no—
55C2×D4×C139—41no—
56C2×D4×C139C2×C812yes—
57C22×C4×C139—21no—
58C22×C4×C139—24no—
59C22×C4×C139—21no—
60C22×C4×C139—21no—
61C22×C4×C139—42no—
62C22×C4×C139—42no—
63C22×C4×C139C22⋊C411yescharacteristic
64C22×C4×C139C22⋊C411yescharacteristic
65C22×C4×C139C22⋊C411yescharacteristic
66C22×C4×C139C22⋊C411yescharacteristic
67C22×C4×C139C22×C411yescharacteristic
68C22×C4×C139C2×D411yescharacteristic
69C22×C4×C139C2×D411yescharacteristic
70C2×C8×C139—24no—
71C2×C8×C139—42no—
72C2×C8×C139—42no—
73C2×C8×C139—42no—
74C2×C8×C139—42no—
75C2×C8×C139—42no—
76C4⋊C4×C139—21no—
77C4⋊C4×C139—41no—
78C4⋊C4×C139—41no—
79C4⋊C4×C139—42no—
80C4⋊C4×C139—42no—
81C4⋊C4×C139C2×C812yes—
82C22⋊C4×C139—24no—
83C22⋊C4×C139—42no—
84C22⋊C4×C139—42no—
85C22⋊C4×C139—42no—
86C22⋊C4×C139—42no—
87C42×C139—22no—
88C42×C139—22no—
89C42×C139—22no—
90C42×C139—41no—
91C42×C139—41no—
92C42×C139—41no—
93C42×C139—42no—
94C42×C139C2×C812yes—
95C42×C139M1612yes—
96C23×C139—22no—
97C23×C139—41no—
98C23×C139—41no—
99C23×C139—41no—
100C23×C139—41no—
101C23×C139—41no—
102C23×C139—41no—
103C23×C139C2×C22⋊C411yescharacteristic
104D4×C139—42no—
105D4×C139—42no—
106C2×C4×C139—21no—
107C2×C4×C139—21no—
108C2×C4×C139—21no—
109C2×C4×C139—21no—
110C2×C4×C139—21no—
111C2×C4×C139—21no—
112C2×C4×C139—21no—
113C2×C4×C139—21no—
114C2×C4×C139—21no—
115C2×C4×C139—21no—
116C2×C4×C139—21no—
117C2×C4×C139—21no—
118C2×C4×C139—22no—
119C2×C4×C139—21no—
120C2×C4×C139—21no—
121C2×C4×C139—21no—
122C2×C4×C139—48no—
123C2×C4×C139—41no—
124C2×C4×C139—41no—
125C2×C4×C139—41no—
126C2×C4×C139—41no—
127C2×C4×C139—41no—
128C2×C4×C139—41no—
129C2×C4×C139—41no—
130C2×C4×C139—41no—
131C2×C4×C139C22⋊C812yes—
132C2×C4×C139C22⋊C812yes—
133C2×C4×C139#10412yes—
134C2×C4×C139C22×C811yescharacteristic
135C2×C4×C139C2×M1611yescharacteristic
136C2×C4×C139#13512yes—
137C2×C4×C139AGL(1,ℤ/8)12yes—
138C8×C139—44no—
139C8×C139—82no—
140C22×C139—42no—
141C22×C139—42no—
142C22×C139—42no—
143C22×C139—81no—
144C22×C139—81no—
145C22×C139—81no—
146C22×C139—81no—
147C22×C139C2×C22⋊C811yescharacteristic
148C22×C139#41011yescharacteristic
149C22×C139#41311yescharacteristic
150C22×C139#41611yescharacteristic
151C22×C139#41811yescharacteristic
152C22×C139C2×#10411yescharacteristic
153C22×C139#42111yescharacteristic
154C4×C139—21no—
155C4×C139—21no—
156C4×C139—22no—
157C4×C139—22no—
158C4×C139—22no—
159C4×C139—22no—
160C4×C139—22no—
161C4×C139—41no—
162C4×C139—42no—
163C4×C139—81no—
164C4×C139—81no—
165C2×C139—82no—
166C2×C139#145811yescharacteristic
167C2×C139#147611yescharacteristic
168C2×C139#147811yescharacteristic
169C2×C139#150511yescharacteristic
170C2×C139#152111yescharacteristic
171C2×C139#153211yescharacteristic
172C2×C139#155311yescharacteristic
173#7580C13911yesmaximal, characteristic, direct product factor, Sylow
174C139#758011yescharacteristic, direct product factor, Sylow
175#2293C2×C13911yescharacteristic
176#1839C2×C13911yescharacteristic, complemented
177#1744C2×C13911yescharacteristic, complemented
178#1271C2×C13912yescomplemented
179#1270C2×C13912yes—
180C2×C4×D4C4×C13911yescharacteristic
181C2×#117—21no—
182C2×C4×C8—21no—
183#390C4×C13911yescharacteristic
184#390C22×C13911yescharacteristic
185#389C4×C13911yescharacteristic
186#389C22×C13911yescharacteristic
187#388—21no—
188#388—21no—
189C4×C4⋊C4C4×C13911yescharacteristic
190C4×C22⋊C4—21no—
191C43C22×C13911yescharacteristic
192#336—21no—
193#336—21no—
194#336—21no—
195#336C22×C13912yes—
196#336C22×C13912yes—
197C22×D4C2×C4×C13911yescharacteristic
198C23×C4—21no—
199C22×C8—22no—
200C22×C8—22no—
201C4×D4—22no—
202C4×D4C8×C13914yescomplemented
203#117—44no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C2×C4×C13911yescharacteristic
207C2×C4⋊C4C2×C4×C13911yescharacteristic
208C2×C4⋊C4C2×C4×C13911yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42—21no—
215C2×C42C2×C4×C13911yescharacteristic
216C2×C42C2×C4×C13911yescharacteristic
217C2×C42D4×C13911yescharacteristic
218C2×C42D4×C13911yescharacteristic
219C2×C42D4×C13911yescharacteristic
220C2×C42D4×C13911yescharacteristic
221C2×C42C23×C13911yescharacteristic
222C4×C8—24no—
223#95—21no—
224#95—21no—
225#95—21no—
226C24—21no—
227C2×D4—21no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4C2×C8×C13912yes—
231C22×C4—21no—
232C22×C4—24no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4C22⋊C4×C13911yescharacteristic
238C22×C4C22⋊C4×C13911yescharacteristic
239C22×C4C22⋊C4×C13911yescharacteristic
240C22×C4C22⋊C4×C13911yescharacteristic
241C22×C4C22×C4×C13911yescharacteristic
242C22×C4C2×D4×C13911yescharacteristic
243C22×C4C2×D4×C13911yescharacteristic
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4C2×C8×C13912yes—
256C22⋊C4—24no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C42—22no—
262C42—22no—
263C42—22no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—42no—
268C42C2×C8×C13912yes—
269C42M16×C13912yes—
270C23—22no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×C22⋊C4×C13911yescharacteristic
278D4—42no—
279D4—42no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—48no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4C22⋊C8×C13912yes—
306C2×C4C22⋊C8×C13912yes—
307C2×C4#104×C13912yes—
308C2×C4C22×C8×C13911yescharacteristic
309C2×C4C2×M16×C13911yescharacteristic
310C2×C4#135×C13912yes—
311C2×C4AGL(1,ℤ/8)×C13912yes—
312C8—44no—
313C8—82no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C2×C22⋊C8×C13911yescharacteristic
322C22#410×C13911yescharacteristic
323C22#413×C13911yescharacteristic
324C22#416×C13911yescharacteristic
325C22#418×C13911yescharacteristic
326C22C2×#104×C13911yescharacteristic
327C22#421×C13911yescharacteristic
328C4—22no—
329C4—22no—
330C4—22no—
331C4—21no—
332C4—21no—
333C4—22no—
334C4—22no—
335C4—41no—
336C4—42no—
337C4—81no—
338C4—81no—
339C2—82no—
340C2#1458×C13911yescharacteristic
341C2#1476×C13911yescharacteristic
342C2#1478×C13911yescharacteristic
343C2#1505×C13911yescharacteristic
344C2#1521×C13911yescharacteristic
345C2#1532×C13911yescharacteristic
346C2#1553×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC2×C4C22×C8×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC22×D4×C139C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C43×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1839×C139C2semidirect
3. #1744×C139C2semidirect
4. #1271×C139C2semidirect
28. C4×D4×C139C8semidirect
173. #7580C139direct (N × H)
174. C139#7580direct (N × H)
176. #1839C2×C139semidirect
177. #1744C2×C139semidirect
178. #1271C2×C139semidirect
202. C4×D4C8×C139semidirect

Maximal subgroups

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

subgroupindex
#2293×C1392
#1839×C1392
#1744×C1392
#1271×C1392
#1270×C1392
#7580139