Finite Group Databasebeta

← C139×#13374 #48007970

Subgroups — C139×#13374 #48007970

Order 35584.

360 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3163×C139C211yesmaximal, characteristic, complemented
2#2145×C139C211yesmaximal, characteristic
3C2×#360×C139C211yesmaximal, characteristic
4#1976×C139C211yesmaximal, characteristic
5#1386×C139C211yesmaximal, characteristic, complemented
6#1384×C139C211yesmaximal, characteristic, complemented
7#1378×C139C211yesmaximal, characteristic, complemented
8C2×#135×C139C2211yescharacteristic
9#544×C139—21no—
10C2×M32×C139C2211yescharacteristic
11C2×M32×C139C2211yescharacteristic
12#501×C139—22no—
13#499×C139—21no—
14#498×C139—21no—
15#428×C139—21no—
16#427×C139C2211yescharacteristic
17#427×C139C2211yescharacteristic
18C2×#106×C139C2211yescharacteristic
19#421×C139—21no—
20#410×C139—21no—
21#405×C139C2211yescharacteristic
22#360×C139—22no—
23#360×C139—21no—
24#360×C139—21no—
25C2×#41×C139—21no—
26#135×C139—21no—
27#135×C139—21no—
28#135×C139—21no—
29#135×C139—21no—
30C2×Q16×C139Q811yescharacteristic, complemented
31C2×SD16×C139—21no—
32C2×D8×C139Q811yescharacteristic, complemented
33C2×M16×C139D411yescharacteristic
34C22×C8×C139C2311yescharacteristic
35C4⋊Q8×C139—22no—
36C4⋊Q8×C139—41no—
37#125×C139—22no—
38#125×C139—41no—
39C22⋊Q8×C139—42no—
40#117×C139—21no—
41#117×C139—21no—
42#117×C139D411yescharacteristic
43C2×C4⋊C4×C139—21no—
44M32×C139—21no—
45M32×C139—21no—
46M32×C139—21no—
47M32×C139—21no—
48C2×C16×C139—21no—
49C2×C16×C139—21no—
50#107×C139—22no—
51#107×C139—21no—
52#107×C139—21no—
53#106×C139—22no—
54#106×C139—21no—
55#106×C139—21no—
56#106×C139D412yes—
57#106×C139D411yescharacteristic
58#106×C139D411yescharacteristic
59#104×C139—42no—
60#99×C139—42no—
61#97×C139—21no—
62C4×C8×C139—21no—
63#41×C139—41no—
64#41×C139—41no—
65#41×C139—41no—
66#41×C139—41no—
67C2×Q8×C139—21no—
68C2×Q8×C139—42no—
69C2×D4×C139—21no—
70C2×D4×C139—41no—
71C22×C4×C139—41no—
72C22×C4×C139—41no—
73C22×C4×C139C2×D411yescharacteristic
74Q16×C139—21no—
75Q16×C139—21no—
76SD16×C139—41no—
77SD16×C139—41no—
78D8×C139—21no—
79D8×C139—21no—
80M16×C139—21no—
81M16×C139SD1612yes—
82C2×C8×C139—21no—
83C2×C8×C139C2×D411yescharacteristic
84C2×C8×C139C2×D411yescharacteristic
85C2×C8×C139C2×Q811yescharacteristic
86C2×C8×C139#4111yescharacteristic
87C2×C8×C139#4111yescharacteristic
88C2×C8×C139#4111yescharacteristic
89C4⋊C4×C139—21no—
90C4⋊C4×C139—22no—
91C4⋊C4×C139—21no—
92C4⋊C4×C139—21no—
93C4⋊C4×C139—42no—
94C4⋊C4×C139—42no—
95C4⋊C4×C139—42no—
96C4⋊C4×C139—41no—
97C4⋊C4×C139—41no—
98C22⋊C4×C139—41no—
99C22⋊C4×C139—41no—
100C22⋊C4×C139D812yes—
101C42×C139—21no—
102C42×C139—41no—
103C42×C139—41no—
104C16×C139—41no—
105C16×C139—41no—
106C23×C139—41no—
107C23×C139C2×D811yescharacteristic
108Q8×C139—41no—
109Q8×C139—41no—
110Q8×C139—162no—
111D4×C139—41no—
112D4×C139—41no—
113D4×C139—81no—
114D4×C139—81no—
115C2×C4×C139—22no—
116C2×C4×C139—41no—
117C2×C4×C139—41no—
118C2×C4×C139—42no—
119C2×C4×C139—41no—
120C2×C4×C139—81no—
121C2×C4×C139—81no—
122C2×C4×C139—81no—
123C2×C4×C139—161no—
124C2×C4×C139#12011yescharacteristic
125C2×C4×C139C22⋊Q811yescharacteristic
126C2×C4×C139#12411yescharacteristic
127C2×C4×C139C2×SD1611yescharacteristic
128C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C139#13711yescharacteristic
130C8×C139—22no—
131C8×C139C22⋊Q811yescharacteristic
132C8×C139C22⋊Q811yescharacteristic
133C8×C139#12411yescharacteristic
134C8×C139#12411yescharacteristic
135C22×C139—41no—
136C22×C139—81no—
137C22×C139—161no—
138C22×C139#44711yescharacteristic
139C22×C139#47411yescharacteristic
140C22×C139#48611yescharacteristic
141C4×C139—42no—
142C4×C139—81no—
143C4×C139—82no—
144C4×C139—81no—
145C4×C139—81no—
146C4×C139—161no—
147C4×C139#39311yescharacteristic
148C4×C139#44811yescharacteristic
149C4×C139#47611yescharacteristic
150C4×C139#48911yescharacteristic
151C2×C139—21no—
152C2×C139—21no—
153C2×C139—21no—
154C2×C139—161no—
155C2×C139#202311yescharacteristic
156#13374C13911yesmaximal, characteristic, direct product factor, Sylow
157C139#1337411yescharacteristic, direct product factor, Sylow
158#3163C2×C13911yescharacteristic, complemented
159#2145C2×C13911yescharacteristic
160C2×#360C2×C13911yescharacteristic
161#1976C2×C13911yescharacteristic
162#1386C2×C13911yescharacteristic, complemented
163#1384C2×C13911yescharacteristic, complemented
164#1378C2×C13911yescharacteristic, complemented
165C2×#135C22×C13911yescharacteristic
166#544—21no—
167C2×M32C22×C13911yescharacteristic
168C2×M32C22×C13911yescharacteristic
169#501—22no—
170#499—21no—
171#498—21no—
172#428—21no—
173#427C22×C13911yescharacteristic
174#427C22×C13911yescharacteristic
175C2×#106C22×C13911yescharacteristic
176#421—21no—
177#410—21no—
178#405C22×C13911yescharacteristic
179#360—22no—
180#360—21no—
181#360—21no—
182C2×#41—21no—
183#135—21no—
184#135—21no—
185#135—21no—
186#135—21no—
187C2×Q16Q8×C13911yescharacteristic, complemented
188C2×SD16—21no—
189C2×D8Q8×C13911yescharacteristic, complemented
190C2×M16D4×C13911yescharacteristic
191C22×C8C23×C13911yescharacteristic
192C4⋊Q8—22no—
193C4⋊Q8—41no—
194#125—22no—
195#125—41no—
196C22⋊Q8—42no—
197#117—21no—
198#117—21no—
199#117D4×C13911yescharacteristic
200C2×C4⋊C4—21no—
201M32—21no—
202M32—21no—
203M32—21no—
204M32—21no—
205C2×C16—21no—
206C2×C16—21no—
207#107—22no—
208#107—21no—
209#107—21no—
210#106—22no—
211#106—21no—
212#106—21no—
213#106D4×C13912yes—
214#106D4×C13911yescharacteristic
215#106D4×C13911yescharacteristic
216#104—42no—
217#99—42no—
218#97—21no—
219C4×C8—21no—
220#41—41no—
221#41—41no—
222#41—41no—
223#41—41no—
224C2×Q8—21no—
225C2×Q8—42no—
226C2×D4—21no—
227C2×D4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4C2×D4×C13911yescharacteristic
231Q16—21no—
232Q16—21no—
233SD16—41no—
234SD16—41no—
235D8—21no—
236D8—21no—
237M16—21no—
238M16SD16×C13912yes—
239C2×C8—21no—
240C2×C8C2×D4×C13911yescharacteristic
241C2×C8C2×D4×C13911yescharacteristic
242C2×C8C2×Q8×C13911yescharacteristic
243C2×C8#41×C13911yescharacteristic
244C2×C8#41×C13911yescharacteristic
245C2×C8#41×C13911yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—22no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4D8×C13912yes—
258C42—21no—
259C42—41no—
260C42—41no—
261C16—41no—
262C16—41no—
263C23—41no—
264C23C2×D8×C13911yescharacteristic
265Q8—41no—
266Q8—41no—
267Q8—162no—
268D4—41no—
269D4—41no—
270D4—81no—
271D4—81no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—161no—
281C2×C4#120×C13911yescharacteristic
282C2×C4C22⋊Q8×C13911yescharacteristic
283C2×C4#124×C13911yescharacteristic
284C2×C4C2×SD16×C13911yescharacteristic
285C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
286C2×C4#137×C13911yescharacteristic
287C8—22no—
288C8C22⋊Q8×C13911yescharacteristic
289C8C22⋊Q8×C13911yescharacteristic
290C8#124×C13911yescharacteristic
291C8#124×C13911yescharacteristic
292C22—41no—
293C22—81no—
294C22—161no—
295C22#447×C13911yescharacteristic
296C22#474×C13911yescharacteristic
297C22#486×C13911yescharacteristic
298C4—42no—
299C4—82no—
300C4—81no—
301C4—81no—
302C4—81no—
303C4—161no—
304C4#393×C13911yescharacteristic
305C4#448×C13911yescharacteristic
306C4#476×C13911yescharacteristic
307C4#489×C13911yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—161no—
312C2#2023×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2023
commutator, Frattini, cosocleC22×C8C23×C139
prime radicalC2×#135×C139C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C22×C4×C139 ◁ #405×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3163×C139C2semidirect
5. #1386×C139C2semidirect
6. #1384×C139C2semidirect
7. #1378×C139C2semidirect
30. C2×Q16×C139Q8semidirect
32. C2×D8×C139Q8semidirect
156. #13374C139direct (N × H)
157. C139#13374direct (N × H)
158. #3163C2×C139semidirect
162. #1386C2×C139semidirect
163. #1384C2×C139semidirect
164. #1378C2×C139semidirect
187. C2×Q16Q8×C139semidirect
189. C2×D8Q8×C139semidirect

Maximal subgroups

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

subgroupindex
#3163×C1392
#2145×C1392
C2×#360×C1392
#1976×C1392
#1386×C1392
#1384×C1392
#1378×C1392
#13374139