Finite Group Databasebeta

← C139×#20779 #48015375

Subgroups — C139×#20779 #48015375

Order 35584.

802 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#376×C139C211yesmaximal, characteristic
2#1840×C139C212yesmaximal, complemented
3#1832×C139C212yesmaximal, complemented
4#1817×C139C212yesmaximal
5#1797×C139C212yesmaximal
6#1768×C139C212yesmaximal, complemented
7#1749×C139C211yesmaximal, characteristic
8C4×C22⋊C8×C139C211yesmaximal, characteristic
9#1746×C139C212yesmaximal, complemented
10C22×C42×C139C2211yescharacteristic
11C22×C42×C139C2211yescharacteristic
12C22×C42×C139C2211yescharacteristic
13C2×C4⋊C8×C139C2214yes—
14C2×C22⋊C8×C139C2212yes—
15C2×C22⋊C8×C139C2212yes—
16C2×#97×C139C2212yes—
17C2×C4×C8×C139C2212yes—
18#376×C139C412yes—
19#376×C139C412yes—
20#376×C139C2211yescharacteristic
21#376×C139C2211yescharacteristic
22#376×C139C2211yescharacteristic
23#376×C139C2211yescharacteristic
24C2×#95×C139C412yes—
25C2×#95×C139C412yes—
26#336×C139C2214yes—
27#336×C139C2214yes—
28#336×C139C2212yes—
29#336×C139C2212yes—
30#336×C139C2214yes—
31C23×C4×C139C2×C411yescharacteristic
32C23×C4×C139C2×C412yes—
33C23×C4×C139C2×C412yes—
34C23×C4×C139C2×C411yescharacteristic
35C23×C4×C139C2311yescharacteristic
36C22×C8×C139C2314yes—
37C22×C8×C139C2314yes—
38C2×C42×C139—24no—
39C2×C42×C139—24no—
40C2×C42×C139—24no—
41C2×C42×C139C2×C411yescharacteristic
42C2×C42×C139C2×C411yescharacteristic
43C2×C42×C139C2×C412yes—
44C2×C42×C139C2×C412yes—
45C2×C42×C139C2311yescharacteristic
46C2×C42×C139C2311yescharacteristic
47C2×C42×C139C2311yescharacteristic
48C2×C42×C139C2311yescharacteristic
49C2×C42×C139C2311yescharacteristic
50C2×C42×C139C2311yescharacteristic
51C4⋊C8×C139—28no—
52C22⋊C8×C139—24no—
53C22⋊C8×C139—24no—
54#97×C139—24no—
55C4×C8×C139—24no—
56#95×C139C2×C412yes—
57#95×C139C2×C412yes—
58#95×C139C2×C412yes—
59#95×C139C2×C412yes—
60#95×C139C2×C412yes—
61#95×C139C2×C412yes—
62#95×C139C2×C412yes—
63#95×C139C2×C412yes—
64C24×C139C22×C411yescharacteristic
65C22×C4×C139—22no—
66C22×C4×C139—22no—
67C22×C4×C139—22no—
68C22×C4×C139—22no—
69C22×C4×C139—24no—
70C22×C4×C139—24no—
71C22×C4×C139—24no—
72C22×C4×C139—24no—
73C22×C4×C139—24no—
74C22×C4×C139—42no—
75C22×C4×C139—42no—
76C22×C4×C139—42no—
77C22×C4×C139C22×C411yescharacteristic
78C22×C4×C139C22×C411yescharacteristic
79C22×C4×C139C22×C412yes—
80C22×C4×C139C22×C412yes—
81C22×C4×C139C22×C411yescharacteristic
82C22×C4×C139C22×C411yescharacteristic
83C22×C4×C139C22×C412yes—
84C22×C4×C139C22×C412yes—
85C22×C4×C139C22×C411yescharacteristic
86C22×C4×C139#4114yes—
87C22×C4×C139C2411yescharacteristic
88C2×C8×C139—24no—
89C2×C8×C139—24no—
90C2×C8×C139—24no—
91C2×C8×C139—24no—
92C2×C8×C139—24no—
93C2×C8×C139—24no—
94C42×C139—24no—
95C42×C139—24no—
96C42×C139—22no—
97C42×C139—22no—
98C42×C139—22no—
99C42×C139—22no—
100C42×C139—22no—
101C42×C139—22no—
102C42×C139#4114yes—
103C42×C139#4114yes—
104C23×C139—21no—
105C23×C139—21no—
106C23×C139—22no—
107C23×C139#11712yes—
108C23×C139#13114yes—
109C23×C139C23×C411yescharacteristic
110C2×C4×C139—21no—
111C2×C4×C139—21no—
112C2×C4×C139—22no—
113C2×C4×C139—22no—
114C2×C4×C139—22no—
115C2×C4×C139—22no—
116C2×C4×C139—28no—
117C2×C4×C139—21no—
118C2×C4×C139—21no—
119C2×C4×C139—21no—
120C2×C4×C139—21no—
121C2×C4×C139—22no—
122C2×C4×C139—22no—
123C2×C4×C139—22no—
124C2×C4×C139—22no—
125C2×C4×C139—22no—
126C2×C4×C139—22no—
127C2×C4×C139—22no—
128C2×C4×C139—22no—
129C2×C4×C139—22no—
130C2×C4×C139—22no—
131C2×C4×C139—48no—
132C2×C4×C139—48no—
133C2×C4×C139—44no—
134C2×C4×C139—44no—
135C2×C4×C139#11712yes—
136C2×C4×C139#11714yes—
137C2×C4×C139#11714yes—
138C2×C4×C139C2×#4112yes—
139C2×C4×C139C2×#4112yes—
140C2×C4×C139C2×#4112yes—
141C8×C139—44no—
142C8×C139—44no—
143C22×C139—22no—
144C22×C139—24no—
145C22×C139—24no—
146C22×C139—22no—
147C22×C139#43314yes—
148C22×C139C2×#11711yescharacteristic
149C22×C139C2×#11711yescharacteristic
150C22×C139C2×#11711yescharacteristic
151C22×C139C2×#13112yes—
152C22×C139#56812yes—
153C4×C139—24no—
154C4×C139—24no—
155C4×C139—22no—
156C4×C139—41no—
157C4×C139—41no—
158C4×C139—41no—
159C4×C139—41no—
160C4×C139—42no—
161C4×C139—42no—
162C4×C139#52914yes—
163C2×C139—24no—
164C2×C139#228311yescharacteristic
165C2×C139C2×#43311yescharacteristic
166C2×C139#292111yescharacteristic
167C2×C139#292412yes—
168C2×C139#292412yes—
169#20779C13911yesmaximal, characteristic, direct product factor, Sylow
170C139#2077911yescharacteristic, direct product factor, Sylow
171C2×#376C2×C13911yescharacteristic
172#1840C2×C13912yescomplemented
173#1832C2×C13912yescomplemented
174#1817C2×C13912yes—
175#1797C2×C13912yes—
176#1768C2×C13912yescomplemented
177#1749C2×C13911yescharacteristic
178C4×C22⋊C8C2×C13911yescharacteristic
179#1746C2×C13912yescomplemented
180C22×C42C22×C13911yescharacteristic
181C22×C42C22×C13911yescharacteristic
182C22×C42C22×C13911yescharacteristic
183C2×C4⋊C8C22×C13914yes—
184C2×C22⋊C8C22×C13912yes—
185C2×C22⋊C8C22×C13912yes—
186C2×#97C22×C13912yes—
187C2×C4×C8C22×C13912yes—
188#376C4×C13912yes—
189#376C4×C13912yes—
190#376C22×C13911yescharacteristic
191#376C22×C13911yescharacteristic
192#376C22×C13911yescharacteristic
193#376C22×C13911yescharacteristic
194C2×#95C4×C13912yes—
195C2×#95C4×C13912yes—
196#336C22×C13914yes—
197#336C22×C13914yes—
198#336C22×C13914yes—
199#336C22×C13912yes—
200#336C22×C13912yes—
201C23×C4C2×C4×C13911yescharacteristic
202C23×C4C2×C4×C13912yes—
203C23×C4C2×C4×C13912yes—
204C23×C4C2×C4×C13911yescharacteristic
205C23×C4C23×C13911yescharacteristic
206C22×C8C23×C13914yes—
207C22×C8C23×C13914yes—
208C2×C42—24no—
209C2×C42—24no—
210C2×C42—24no—
211C2×C42C2×C4×C13911yescharacteristic
212C2×C42C2×C4×C13911yescharacteristic
213C2×C42C2×C4×C13912yes—
214C2×C42C2×C4×C13912yes—
215C2×C42C23×C13911yescharacteristic
216C2×C42C23×C13911yescharacteristic
217C2×C42C23×C13911yescharacteristic
218C2×C42C23×C13911yescharacteristic
219C2×C42C23×C13911yescharacteristic
220C2×C42C23×C13911yescharacteristic
221C4⋊C8—28no—
222C22⋊C8—24no—
223C22⋊C8—24no—
224#97—24no—
225C4×C8—24no—
226#95C2×C4×C13912yes—
227#95C2×C4×C13912yes—
228#95C2×C4×C13912yes—
229#95C2×C4×C13912yes—
230#95C2×C4×C13912yes—
231#95C2×C4×C13912yes—
232#95C2×C4×C13912yes—
233#95C2×C4×C13912yes—
234C24C22×C4×C13911yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4C22×C4×C13911yescharacteristic
248C22×C4C22×C4×C13911yescharacteristic
249C22×C4C22×C4×C13912yes—
250C22×C4C22×C4×C13912yes—
251C22×C4C22×C4×C13911yescharacteristic
252C22×C4C22×C4×C13911yescharacteristic
253C22×C4C22×C4×C13912yes—
254C22×C4C22×C4×C13912yes—
255C22×C4C22×C4×C13911yescharacteristic
256C22×C4#41×C13914yes—
257C22×C4C24×C13911yescharacteristic
258C2×C8—24no—
259C2×C8—24no—
260C2×C8—24no—
261C2×C8—24no—
262C2×C8—24no—
263C2×C8—24no—
264C42—24no—
265C42—24no—
266C42—22no—
267C42—22no—
268C42—22no—
269C42—22no—
270C42—22no—
271C42—22no—
272C42#41×C13914yes—
273C42#41×C13914yes—
274C23—21no—
275C23—21no—
276C23—22no—
277C23#117×C13912yes—
278C23#131×C13914yes—
279C23C23×C4×C13911yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—28no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—48no—
302C2×C4—48no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4#117×C13912yes—
306C2×C4#117×C13914yes—
307C2×C4#117×C13914yes—
308C2×C4C2×#41×C13912yes—
309C2×C4C2×#41×C13912yes—
310C2×C4C2×#41×C13912yes—
311C8—44no—
312C8—44no—
313C22—22no—
314C22—22no—
315C22—24no—
316C22—24no—
317C22#433×C13914yes—
318C22C2×#117×C13911yescharacteristic
319C22C2×#117×C13911yescharacteristic
320C22C2×#117×C13911yescharacteristic
321C22C2×#131×C13912yes—
322C22#568×C13912yes—
323C4—22no—
324C4—24no—
325C4—24no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—42no—
331C4—42no—
332C4#529×C13914yes—
333C2—24no—
334C2#2283×C13911yescharacteristic
335C2C2×#433×C13911yescharacteristic
336C2#2921×C13911yescharacteristic
337C2#2924×C13912yes—
338C2#2924×C13912yes—
subgroupG/H
centerC22×C4×C139C24
commutatorC23C23×C4×C139
Frattini, cosocleC22×C4C24×C139
socleC23×C139C23×C4
prime radicalC24×C139C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1840×C139C2semidirect
3. #1832×C139C2semidirect
6. #1768×C139C2semidirect
9. #1746×C139C2semidirect
169. #20779C139direct (N × H)
170. C139#20779direct (N × H)
172. #1840C2×C139semidirect
173. #1832C2×C139semidirect
176. #1768C2×C139semidirect
179. #1746C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#376×C1392
#1840×C1392
#1832×C1392
#1817×C1392
#1797×C1392
#1768×C1392
#1749×C1392
C4×C22⋊C8×C1392
#1746×C1392
#20779139