Finite Group Databasebeta

← C139×#33920 #48028516

Subgroups — C139×#33920 #48028516

Order 35584.

502 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3342×C139C211yesmaximal, characteristic, complemented
2#3334×C139C211yesmaximal, characteristic
3#2252×C139C211yesmaximal, characteristic, complemented
4#2236×C139C212yesmaximal, complemented
5#2234×C139C212yesmaximal, complemented
6#2225×C139C211yesmaximal, characteristic, complemented
7#2224×C139C211yesmaximal, characteristic, complemented
8#2220×C139C212yesmaximal, complemented
9C4×SD32×C139C211yesmaximal, characteristic, complemented
10#2169×C139C211yesmaximal, characteristic, complemented
11#2159×C139C212yesmaximal, complemented
12#556×C139—21no—
13#547×C139—21no—
14C2×SD32×C139C2211yescharacteristic
15C2×M32×C139C2212yes—
16#500×C139C2211yescharacteristic
17#500×C139C2211yescharacteristic
18#485×C139—22no—
19#480×C139—22no—
20#475×C139—21no—
21#474×C139—21no—
22#467×C139C2212yes—
23#466×C139C2212yes—
24C4×Q16×C139C2211yescharacteristic
25C4×D8×C139C2211yescharacteristic
26C8×D4×C139C2211yescharacteristic
27#427×C139C2212yes—
28C2×#107×C139C2212yes—
29#367×C139C2211yescharacteristic
30#367×C139C2212yes—
31#366×C139C2212yes—
32#366×C139C2212yes—
33#366×C139C2212yes—
34C4⋊C16×C139C2211yescharacteristic
35#358×C139C2211yescharacteristic
36#358×C139C2212yes—
37#357×C139C2211yescharacteristic
38#357×C139C2212yes—
39C22⋊C16×C139C2212yes—
40C4×C16×C139C2211yescharacteristic
41C2×#41×C139—41no—
42C2×Q16×C139C2311yescharacteristic
43C2×D8×C139C2311yescharacteristic
44C22×C8×C139C2312yes—
45C4⋊Q8×C139—21no—
46C4⋊Q8×C139—21no—
47#126×C139—42no—
48#124×C139—41no—
49#123×C139—42no—
50C22⋊Q8×C139—22no—
51C22⋊Q8×C139—41no—
52#121×C139—22no—
53C4×Q8×C139—21no—
54C4×Q8×C139—41no—
55C4×D4×C139—21no—
56C4×D4×C139D411yescharacteristic
57#117×C139—22no—
58C2×C4⋊C4×C139—22no—
59SD32×C139—22no—
60M32×C139—24no—
61C2×C16×C139C2312yes—
62C2×C16×C139C2311yescharacteristic
63C2×C16×C139C2311yescharacteristic
64#107×C139—22no—
65#107×C139—21no—
66#107×C139—21no—
67#107×C139C2311yescharacteristic
68#107×C139C2312yes—
69#107×C139C2311yescharacteristic
70#107×C139C2312yes—
71#106×C139—22no—
72C4⋊C8×C139D411yescharacteristic
73#103×C139—21no—
74#103×C139—22no—
75#102×C139—21no—
76#102×C139—22no—
77C22⋊C8×C139D412yes—
78C4×C8×C139C2311yescharacteristic
79#41×C139—84no—
80C2×Q8×C139—21no—
81C2×Q8×C139—41no—
82C2×Q8×C139—41no—
83C2×D4×C139—21no—
84C2×D4×C139—42no—
85C2×D4×C139D811yescharacteristic
86C22×C4×C139—42no—
87C22×C4×C139—41no—
88C22×C4×C139C2×D412yes—
89Q16×C139—21no—
90Q16×C139—21no—
91D8×C139—21no—
92D8×C139—21no—
93C2×C8×C139—22no—
94C2×C8×C139—22no—
95C2×C8×C139C2×D411yescharacteristic
96C2×C8×C139C2×D412yes—
97C2×C8×C139C2411yescharacteristic
98C4⋊C4×C139—21no—
99C4⋊C4×C139—22no—
100C4⋊C4×C139—21no—
101C4⋊C4×C139—22no—
102C4⋊C4×C139—42no—
103C4⋊C4×C139—41no—
104C4⋊C4×C139—42no—
105C4⋊C4×C139—41no—
106C4⋊C4×C139—41no—
107C4⋊C4×C139D811yescharacteristic
108C22⋊C4×C139—42no—
109C22⋊C4×C139—42no—
110C22⋊C4×C139—41no—
111C22⋊C4×C139—42no—
112C22⋊C4×C139D812yes—
113C42×C139—42no—
114C42×C139—41no—
115C42×C139C2×D411yescharacteristic
116C16×C139—22no—
117C16×C139—21no—
118C16×C139#4112yescomplemented
119C23×C139—41no—
120C23×C139C2×D812yes—
121Q8×C139—41no—
122Q8×C139—41no—
123Q8×C139—82no—
124Q8×C139—82no—
125D4×C139—22no—
126D4×C139—41no—
127D4×C139—41no—
128D4×C139—84no—
129C2×C4×C139—22no—
130C2×C4×C139—22no—
131C2×C4×C139—41no—
132C2×C4×C139—42no—
133C2×C4×C139—41no—
134C2×C4×C139—41no—
135C2×C4×C139—42no—
136C2×C4×C139—84no—
137C2×C4×C139—82no—
138C2×C4×C139C2×D812yes—
139C2×C4×C139C2×D811yescharacteristic
140C2×C4×C139C2×D811yescharacteristic
141C2×C4×C139C22×D411yescharacteristic
142C8×C139—22no—
143C8×C139—21no—
144C8×C139C2×#4111yescharacteristic
145C8×C1392−1+411yescharacteristic
146C22×C139—22no—
147C22×C139—22no—
148C22×C139—22no—
149C22×C139—81no—
150C22×C139—81no—
151C22×C139—81no—
152C22×C139C22×D811yescharacteristic
153C4×C139—22no—
154C4×C139—21no—
155C4×C139—81no—
156C4×C139—81no—
157C4×C139—82no—
158C4×C139—82no—
159C4×C139—81no—
160C4×C139#50912yes—
161C4×C139#54711yescharacteristic
162C4×C139#57811yescharacteristic
163C2×C139—42no—
164C2×C139—161no—
165C2×C139#333411yescharacteristic
166C2×C139C2×#50911yescharacteristic
167C2×C139#341711yescharacteristic
168#33920C13911yesmaximal, characteristic, direct product factor, Sylow
169C139#3392011yescharacteristic, direct product factor, Sylow
170#3342C2×C13911yescharacteristic, complemented
171#3334C2×C13911yescharacteristic
172#2252C2×C13911yescharacteristic, complemented
173#2236C2×C13912yescomplemented
174#2234C2×C13912yescomplemented
175#2225C2×C13911yescharacteristic, complemented
176#2224C2×C13911yescharacteristic, complemented
177#2220C2×C13912yescomplemented
178C4×SD32C2×C13911yescharacteristic, complemented
179#2169C2×C13911yescharacteristic, complemented
180#2159C2×C13912yescomplemented
181#556—21no—
182#547—21no—
183C2×SD32C22×C13911yescharacteristic
184C2×M32C22×C13912yes—
185#500C22×C13911yescharacteristic
186#500C22×C13911yescharacteristic
187#485—22no—
188#480—22no—
189#475—21no—
190#474—21no—
191#467C22×C13912yes—
192#466C22×C13912yes—
193C4×Q16C22×C13911yescharacteristic
194C4×D8C22×C13911yescharacteristic
195C8×D4C22×C13911yescharacteristic
196#427C22×C13912yes—
197C2×#107C22×C13912yes—
198#367C22×C13911yescharacteristic
199#367C22×C13912yes—
200#366C22×C13912yes—
201#366C22×C13912yes—
202#366C22×C13912yes—
203C4⋊C16C22×C13911yescharacteristic
204#358C22×C13911yescharacteristic
205#358C22×C13912yes—
206#357C22×C13911yescharacteristic
207#357C22×C13912yes—
208C22⋊C16C22×C13912yes—
209C4×C16C22×C13911yescharacteristic
210C2×#41—41no—
211C2×Q16C23×C13911yescharacteristic
212C2×D8C23×C13911yescharacteristic
213C22×C8C23×C13912yes—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216#126—42no—
217#124—41no—
218#123—42no—
219C22⋊Q8—22no—
220C22⋊Q8—41no—
221#121—22no—
222C4×Q8—21no—
223C4×Q8—41no—
224C4×D4—21no—
225C4×D4D4×C13911yescharacteristic
226#117—22no—
227C2×C4⋊C4—22no—
228SD32—22no—
229M32—24no—
230C2×C16C23×C13911yescharacteristic
231C2×C16C23×C13912yes—
232C2×C16C23×C13911yescharacteristic
233#107—22no—
234#107—21no—
235#107—21no—
236#107C23×C13912yes—
237#107C23×C13911yescharacteristic
238#107C23×C13911yescharacteristic
239#107C23×C13912yes—
240#106—22no—
241C4⋊C8D4×C13911yescharacteristic
242#103—21no—
243#103—22no—
244#102—21no—
245#102—22no—
246C22⋊C8D4×C13912yes—
247C4×C8C23×C13911yescharacteristic
248#41—84no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×D4—21no—
253C2×D4—42no—
254C2×D4D8×C13911yescharacteristic
255C22×C4—42no—
256C22×C4—41no—
257C22×C4C2×D4×C13912yes—
258Q16—21no—
259Q16—21no—
260D8—21no—
261D8—21no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8C2×D4×C13911yescharacteristic
265C2×C8C2×D4×C13912yes—
266C2×C8C24×C13911yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4D8×C13911yescharacteristic
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4D8×C13912yes—
282C42—42no—
283C42—41no—
284C42C2×D4×C13911yescharacteristic
285C16—22no—
286C16—21no—
287C16#41×C13912yescomplemented
288C23—41no—
289C23C2×D8×C13912yes—
290Q8—41no—
291Q8—41no—
292Q8—82no—
293Q8—82no—
294D4—22no—
295D4—41no—
296D4—41no—
297D4—84no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—84no—
306C2×C4—82no—
307C2×C4C2×D8×C13912yes—
308C2×C4C2×D8×C13911yescharacteristic
309C2×C4C2×D8×C13911yescharacteristic
310C2×C4C22×D4×C13911yescharacteristic
311C8—22no—
312C8—21no—
313C8C2×#41×C13911yescharacteristic
314C82−1+4×C13911yescharacteristic
315C22—22no—
316C22—22no—
317C22—22no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C22×D8×C13911yescharacteristic
322C4—22no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—82no—
327C4—82no—
328C4—81no—
329C4#509×C13912yes—
330C4#547×C13911yescharacteristic
331C4#578×C13911yescharacteristic
332C2—42no—
333C2—161no—
334C2#3334×C13911yescharacteristic
335C2C2×#509×C13911yescharacteristic
336C2#3417×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C22×D8
commutator, Frattini, cosocleC2×C8C24×C139
prime radical#3334×C139C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C4×D4×C139 ◁ C8×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3342×C139C2semidirect
3. #2252×C139C2semidirect
4. #2236×C139C2semidirect
5. #2234×C139C2semidirect
6. #2225×C139C2semidirect
7. #2224×C139C2semidirect
8. #2220×C139C2semidirect
9. C4×SD32×C139C2semidirect
10. #2169×C139C2semidirect
11. #2159×C139C2semidirect
118. C16×C139#41semidirect
168. #33920C139direct (N × H)
169. C139#33920direct (N × H)
170. #3342C2×C139semidirect
172. #2252C2×C139semidirect
173. #2236C2×C139semidirect
174. #2234C2×C139semidirect
175. #2225C2×C139semidirect
176. #2224C2×C139semidirect
177. #2220C2×C139semidirect
178. C4×SD32C2×C139semidirect
179. #2169C2×C139semidirect
180. #2159C2×C139semidirect
287. C16#41×C139semidirect

Maximal subgroups

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

subgroupindex
#3342×C1392
#3334×C1392
#2252×C1392
#2236×C1392
#2234×C1392
#2225×C1392
#2224×C1392
#2220×C1392
C4×SD32×C1392
#2169×C1392
#2159×C1392
#33920139