Finite Group Databasebeta

← C139×#8829 #48003425

Subgroups — C139×#8829 #48003425

Order 35584.

556 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C8×C139C211yesmaximal, characteristic
2#1797×C139C211yesmaximal, characteristic
3C4×C22⋊C8×C139C211yesmaximal, characteristic
4C2×#335×C139C212yesmaximal, complemented
5#1277×C139C212yesmaximal, complemented
6C23×C8×C139—21no—
7C22×C42×C139C2211yescharacteristic
8C2×C4⋊C8×C139—21no—
9C2×C4⋊C8×C139—24no—
10C2×C4⋊C8×C139C2211yescharacteristic
11C2×C4⋊C8×C139C2211yescharacteristic
12C2×C4⋊C8×C139C2212yes—
13C2×C22⋊C8×C139—21no—
14C2×C22⋊C8×C139C411yescharacteristic
15C2×C22⋊C8×C139C411yescharacteristic
16C2×C4×C8×C139C2212yes—
17#336×C139—21no—
18#336×C139C412yes—
19#335×C139—24no—
20C23×C4×C139C2×C411yescharacteristic
21C23×C4×C139D411yescharacteristic
22C23×C4×C139Q811yescharacteristic
23C22×C8×C139—24no—
24C22×C8×C139—22no—
25C22×C8×C139—21no—
26C22×C8×C139—21no—
27C22×C8×C139—42no—
28C22×C8×C139—42no—
29C22×C8×C139C2×C412yes—
30C22×C8×C139C2×C412yes—
31C2×C42×C139—22no—
32C2×C42×C139—22no—
33C2×C42×C139C2×C411yescharacteristic
34C2×C42×C139D411yescharacteristic
35C2×C42×C139Q811yescharacteristic
36C2×C42×C139C2311yescharacteristic
37C4⋊C8×C139—24no—
38C4⋊C8×C139—22no—
39C4⋊C8×C139—22no—
40C4⋊C8×C139—22no—
41C4⋊C8×C139D414yes—
42C22⋊C8×C139—22no—
43C22⋊C8×C139—42no—
44C22⋊C8×C139C814yescomplemented
45C4×C8×C139—22no—
46C4×C8×C139—22no—
47C24×C139C4⋊C411yescharacteristic
48C22×C4×C139—22no—
49C22×C4×C139—21no—
50C22×C4×C139—21no—
51C22×C4×C139—22no—
52C22×C4×C139—21no—
53C22×C4×C139—21no—
54C22×C4×C139—22no—
55C22×C4×C139—22no—
56C22×C4×C139—41no—
57C22×C4×C139C4⋊C411yescharacteristic
58C22×C4×C139C4⋊C411yescharacteristic
59C22×C4×C139C4⋊C411yescharacteristic
60C22×C4×C139C2×C812yes—
61C22×C4×C139M1612yes—
62C22×C4×C139D812yes—
63C22×C4×C139Q1612yes—
64C22×C4×C139C22×C411yescharacteristic
65C22×C4×C139C2×D411yescharacteristic
66C22×C4×C139C2×Q811yescharacteristic
67C2×C8×C139—22no—
68C2×C8×C139—22no—
69C2×C8×C139—22no—
70C2×C8×C139—24no—
71C2×C8×C139—22no—
72C2×C8×C139—22no—
73C2×C8×C139—48no—
74C2×C8×C139—42no—
75C2×C8×C139—42no—
76C2×C8×C139—41no—
77C2×C8×C139—41no—
78C2×C8×C139—41no—
79C2×C8×C139—41no—
80C2×C8×C139—41no—
81C2×C8×C139—41no—
82C2×C8×C139C2×C814yescomplemented
83C42×C139—22no—
84C42×C139—21no—
85C42×C139—22no—
86C42×C139—21no—
87C42×C139C2×D412yes—
88C42×C139#4112yes—
89C23×C139—21no—
90C23×C139—21no—
91C23×C139—21no—
92C23×C139—21no—
93C23×C139C4⋊C812yes—
94C23×C139#10712yes—
95C23×C139#10812yes—
96C23×C139C2×C4⋊C411yescharacteristic
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—24no—
104C2×C4×C139—24no—
105C2×C4×C139—22no—
106C2×C4×C139—22no—
107C2×C4×C139—22no—
108C2×C4×C139—22no—
109C2×C4×C139—21no—
110C2×C4×C139—21no—
111C2×C4×C139—21no—
112C2×C4×C139—44no—
113C2×C4×C139C4⋊C812yes—
114C2×C4×C139#10712yes—
115C2×C4×C139C4×D412yes—
116C2×C4×C139#12011yescharacteristic
117C2×C4×C139C22⋊Q812yes—
118C2×C4×C139#12311yescharacteristic
119C2×C4×C139C22×C811yescharacteristic
120C2×C4×C139C2×M1611yescharacteristic
121C2×C4×C139#13112yes—
122C2×C4×C139C2×D811yescharacteristic
123C2×C4×C139C2×Q1611yescharacteristic
124C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C139#13711yescharacteristic
126C8×C139—24no—
127C8×C139—42no—
128C8×C139—44no—
129C8×C139—81no—
130C8×C139—81no—
131C22×C139—22no—
132C22×C139—22no—
133C22×C139—22no—
134C22×C139—22no—
135C22×C139—22no—
136C22×C139—22no—
137C22×C139#33514yescomplemented
138C22×C139#38511yescharacteristic
139C22×C139C2×C4⋊C811yescharacteristic
140C22×C139#42411yescharacteristic
141C22×C139C2×#10711yescharacteristic
142C22×C139#42811yescharacteristic
143C22×C139C2×#10811yescharacteristic
144C22×C139#43011yescharacteristic
145C4×C139—22no—
146C4×C139—22no—
147C4×C139—22no—
148C4×C139—41no—
149C4×C139C8×D412yes—
150C4×C139#43512yes—
151C4×C139#44711yescharacteristic
152C4×C139#45111yescharacteristic
153C4×C139#48011yescharacteristic
154C4×C139#48411yescharacteristic
155C2×C139—24no—
156C2×C139C2×#33511yescharacteristic
157C2×C139#156511yescharacteristic
158C2×C139#157111yescharacteristic
159C2×C139#157311yescharacteristic
160C2×C139#185011yescharacteristic
161C2×C139#185211yescharacteristic
162C2×C139#185511yescharacteristic
163#8829C13911yesmaximal, characteristic, direct product factor, Sylow
164C139#882911yescharacteristic, direct product factor, Sylow
165C22×C4⋊C8C2×C13911yescharacteristic
166#1797C2×C13911yescharacteristic
167C4×C22⋊C8C2×C13911yescharacteristic
168C2×#335C2×C13912yescomplemented
169#1277C2×C13912yescomplemented
170C23×C8—21no—
171C22×C42C22×C13911yescharacteristic
172C2×C4⋊C8—21no—
173C2×C4⋊C8—24no—
174C2×C4⋊C8C22×C13911yescharacteristic
175C2×C4⋊C8C22×C13911yescharacteristic
176C2×C4⋊C8C22×C13912yes—
177C2×C22⋊C8—21no—
178C2×C22⋊C8C4×C13911yescharacteristic
179C2×C22⋊C8C4×C13911yescharacteristic
180C2×C4×C8C22×C13912yes—
181#336—21no—
182#336C4×C13912yes—
183#335—24no—
184C23×C4C2×C4×C13911yescharacteristic
185C23×C4D4×C13911yescharacteristic
186C23×C4Q8×C13911yescharacteristic
187C22×C8—24no—
188C22×C8—22no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—42no—
192C22×C8—42no—
193C22×C8C2×C4×C13912yes—
194C22×C8C2×C4×C13912yes—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42C2×C4×C13911yescharacteristic
198C2×C42D4×C13911yescharacteristic
199C2×C42Q8×C13911yescharacteristic
200C2×C42C23×C13911yescharacteristic
201C4⋊C8—24no—
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—22no—
205C4⋊C8D4×C13914yes—
206C22⋊C8—22no—
207C22⋊C8—42no—
208C22⋊C8C8×C13914yescomplemented
209C4×C8—22no—
210C4×C8—22no—
211C24C4⋊C4×C13911yescharacteristic
212C22×C4—22no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—41no—
221C22×C4C4⋊C4×C13911yescharacteristic
222C22×C4C4⋊C4×C13911yescharacteristic
223C22×C4C4⋊C4×C13911yescharacteristic
224C22×C4C2×C8×C13912yes—
225C22×C4M16×C13912yes—
226C22×C4D8×C13912yes—
227C22×C4Q16×C13912yes—
228C22×C4C22×C4×C13911yescharacteristic
229C22×C4C2×D4×C13911yescharacteristic
230C22×C4C2×Q8×C13911yescharacteristic
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—24no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—48no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8C2×C8×C13914yescomplemented
247C42—22no—
248C42—21no—
249C42—22no—
250C42—21no—
251C42C2×D4×C13912yes—
252C42#41×C13912yes—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23C4⋊C8×C13912yes—
258C23#107×C13912yes—
259C23#108×C13912yes—
260C23C2×C4⋊C4×C13911yescharacteristic
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—44no—
277C2×C4C4⋊C8×C13912yes—
278C2×C4#107×C13912yes—
279C2×C4C4×D4×C13912yes—
280C2×C4#120×C13911yescharacteristic
281C2×C4C22⋊Q8×C13912yes—
282C2×C4#123×C13911yescharacteristic
283C2×C4C22×C8×C13911yescharacteristic
284C2×C4C2×M16×C13911yescharacteristic
285C2×C4#131×C13912yes—
286C2×C4C2×D8×C13911yescharacteristic
287C2×C4C2×Q16×C13911yescharacteristic
288C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
289C2×C4#137×C13911yescharacteristic
290C8—24no—
291C8—42no—
292C8—44no—
293C8—81no—
294C8—81no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22#335×C13914yescomplemented
302C22#385×C13911yescharacteristic
303C22C2×C4⋊C8×C13911yescharacteristic
304C22#424×C13911yescharacteristic
305C22C2×#107×C13911yescharacteristic
306C22#428×C13911yescharacteristic
307C22C2×#108×C13911yescharacteristic
308C22#430×C13911yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—41no—
313C4C8×D4×C13912yes—
314C4#435×C13912yes—
315C4#447×C13911yescharacteristic
316C4#451×C13911yescharacteristic
317C4#480×C13911yescharacteristic
318C4#484×C13911yescharacteristic
319C2—24no—
320C2C2×#335×C13911yescharacteristic
321C2#1565×C13911yescharacteristic
322C2#1571×C13911yescharacteristic
323C2#1573×C13911yescharacteristic
324C2#1850×C13911yescharacteristic
325C2#1852×C13911yescharacteristic
326C2#1855×C13911yescharacteristic
subgroupG/H
centerC22×C4×C139C2×D4
commutatorC2×C4C22×C8×C139
Frattini, cosocleC2×C42C23×C139
socleC23×C139C2×C4⋊C4
prime radicalC24×C139C4⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C139 ◁ C22×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#335×C139C2semidirect
5. #1277×C139C2semidirect
44. C22⋊C8×C139C8semidirect
82. C2×C8×C139C2×C8semidirect
137. C22×C139#335semidirect
163. #8829C139direct (N × H)
164. C139#8829direct (N × H)
168. C2×#335C2×C139semidirect
169. #1277C2×C139semidirect
208. C22⋊C8C8×C139semidirect
246. C2×C8C2×C8×C139semidirect
301. C22#335×C139semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C8×C1392
#1797×C1392
C4×C22⋊C8×C1392
C2×#335×C1392
#1277×C1392
#8829139