Finite Group Databasebeta

← C139×#33935 #48028531

Subgroups — C139×#33935 #48028531

Order 35584.

518 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3391×C139C211yesmaximal, characteristic
2#3383×C139C211yesmaximal, characteristic, complemented
3#2244×C139C212yesmaximal, complemented
4#2240×C139C211yesmaximal, characteristic, complemented
5#2228×C139C212yesmaximal, complemented
6#2224×C139C211yesmaximal, characteristic, complemented
7#2207×C139C211yesmaximal, characteristic, complemented
8#2207×C139C212yesmaximal, complemented
9#2183×C139C211yesmaximal, characteristic, complemented
10#2175×C139C212yesmaximal, complemented
11C4×SD32×C139C211yesmaximal, characteristic, complemented
12#557×C139—21no—
13#550×C139—21no—
14C2×SD32×C139C2211yescharacteristic
15C2×SD32×C139C2212yes—
16#500×C139C2211yescharacteristic
17#499×C139C2212yes—
18#493×C139C2211yescharacteristic
19#493×C139C2212yes—
20#479×C139—22no—
21#475×C139—21no—
22#459×C139—21no—
23#459×C139—22no—
24C8×Q8×C139C2211yescharacteristic
25C4×Q16×C139C2211yescharacteristic
26C4×Q16×C139C2212yes—
27C4×D8×C139C2211yescharacteristic
28C4×D8×C139C2212yes—
29#367×C139C2211yescharacteristic
30#366×C139C2212yes—
31C4⋊C16×C139C2211yescharacteristic
32C4⋊C16×C139C2212yes—
33#358×C139C2211yescharacteristic
34#357×C139C2211yescharacteristic
35#357×C139C2212yes—
36#357×C139C2212yes—
37#357×C139C2212yes—
38#357×C139C2212yes—
39#346×C139C2212yes—
40C4×C16×C139C2211yescharacteristic
41C2×#41×C139—41no—
42C2×Q16×C139C2311yescharacteristic
43C2×D8×C139—22no—
44C2×D8×C139—21no—
45C2×D8×C139C2311yescharacteristic
46C2×D8×C139C2312yes—
47C4⋊Q8×C139—21no—
48C4⋊Q8×C139—41no—
49#127×C139—22no—
50#127×C139—21no—
51#125×C139—22no—
52#125×C139—42no—
53#121×C139—41no—
54#121×C139—42no—
55C4×Q8×C139—21no—
56C4×Q8×C139—22no—
57C4×Q8×C139—41no—
58C4×Q8×C139D411yescharacteristic
59C4×D4×C139—22no—
60C4×D4×C139—21no—
61SD32×C139—22no—
62SD32×C139—24no—
63C2×C16×C139C2311yescharacteristic
64C2×C16×C139C2312yes—
65C2×C16×C139C2311yescharacteristic
66#107×C139—21no—
67#107×C139C2311yescharacteristic
68#107×C139C2311yescharacteristic
69#107×C139C2312yes—
70#106×C139—22no—
71C4⋊C8×C139D411yescharacteristic
72C4⋊C8×C139D412yes—
73#103×C139—22no—
74#103×C139—21no—
75#102×C139—22no—
76#102×C139—21no—
77C4×C8×C139C2312yes—
78C4×C8×C139C2311yescharacteristic
79#41×C139—84no—
80C2×Q8×C139—21no—
81C2×Q8×C139—41no—
82C2×Q8×C139D811yescharacteristic
83C2×D4×C139—22no—
84C2×D4×C139—21no—
85C2×D4×C139—42no—
86C2×D4×C139—41no—
87C2×D4×C139—42no—
88C2×D4×C139—41no—
89C22×C4×C139—42no—
90C22×C4×C139—41no—
91Q16×C139—21no—
92Q16×C139#4112yescomplemented
93D8×C139—21no—
94D8×C139—22no—
95D8×C139—21no—
96D8×C139—22no—
97D8×C139—82no—
98D8×C139—81no—
99C2×C8×C139C2×D412yes—
100C2×C8×C139C2×D411yescharacteristic
101C2×C8×C139C2411yescharacteristic
102C4⋊C4×C139—21no—
103C4⋊C4×C139—21no—
104C4⋊C4×C139—22no—
105C4⋊C4×C139—41no—
106C4⋊C4×C139—42no—
107C4⋊C4×C139—42no—
108C4⋊C4×C139—42no—
109C4⋊C4×C139—41no—
110C4⋊C4×C139D811yescharacteristic
111C4⋊C4×C139D812yes—
112C22⋊C4×C139—42no—
113C22⋊C4×C139—41no—
114C42×C139—42no—
115C42×C139—41no—
116C42×C139C2×D412yes—
117C42×C139C2×D411yescharacteristic
118C16×C139—21no—
119C16×C139—22no—
120C16×C139—21no—
121C23×C139—42no—
122C23×C139—41no—
123Q8×C139—22no—
124Q8×C139—22no—
125Q8×C139—41no—
126Q8×C139—82no—
127D4×C139—41no—
128D4×C139—42no—
129D4×C139—41no—
130D4×C139—42no—
131D4×C139—84no—
132D4×C139—82no—
133D4×C139—162no—
134D4×C139—161no—
135C2×C4×C139—41no—
136C2×C4×C139—41no—
137C2×C4×C139—42no—
138C2×C4×C139—41no—
139C2×C4×C139—84no—
140C2×C4×C139—82no—
141C2×C4×C139C2×D812yes—
142C2×C4×C139C2×D811yescharacteristic
143C2×C4×C139C2×D812yes—
144C2×C4×C139C2×D811yescharacteristic
145C2×C4×C139C22×D411yescharacteristic
146C8×C139—22no—
147C8×C139—21no—
148C8×C139C2×#4111yescharacteristic
149C8×C1392−1+411yescharacteristic
150C22×C139—82no—
151C22×C139—81no—
152C22×C139—82no—
153C22×C139—81no—
154C22×C139—82no—
155C22×C139—81no—
156C22×C139C22×D811yescharacteristic
157C4×C139—22no—
158C4×C139—22no—
159C4×C139—21no—
160C4×C139—42no—
161C4×C139—81no—
162C4×C139—82no—
163C4×C139—81no—
164C4×C139#50912yes—
165C4×C139#54811yescharacteristic
166C4×C139#57711yescharacteristic
167C2×C139—162no—
168C2×C139—161no—
169C2×C139#335811yescharacteristic
170C2×C139C2×#50911yescharacteristic
171C2×C139#341611yescharacteristic
172#33935C13911yesmaximal, characteristic, direct product factor, Sylow
173C139#3393511yescharacteristic, direct product factor, Sylow
174#3391C2×C13911yescharacteristic
175#3383C2×C13911yescharacteristic, complemented
176#2244C2×C13912yescomplemented
177#2240C2×C13911yescharacteristic, complemented
178#2228C2×C13912yescomplemented
179#2224C2×C13911yescharacteristic, complemented
180#2207C2×C13912yescomplemented
181#2207C2×C13911yescharacteristic, complemented
182#2183C2×C13911yescharacteristic, complemented
183#2175C2×C13912yescomplemented
184C4×SD32C2×C13911yescharacteristic, complemented
185#557—21no—
186#550—21no—
187C2×SD32C22×C13911yescharacteristic
188C2×SD32C22×C13912yes—
189#500C22×C13911yescharacteristic
190#499C22×C13912yes—
191#493C22×C13911yescharacteristic
192#493C22×C13912yes—
193#479—22no—
194#475—21no—
195#459—21no—
196#459—22no—
197C8×Q8C22×C13911yescharacteristic
198C4×Q16C22×C13911yescharacteristic
199C4×Q16C22×C13912yes—
200C4×D8C22×C13911yescharacteristic
201C4×D8C22×C13912yes—
202#367C22×C13911yescharacteristic
203#366C22×C13912yes—
204C4⋊C16C22×C13911yescharacteristic
205C4⋊C16C22×C13912yes—
206#358C22×C13911yescharacteristic
207#357C22×C13911yescharacteristic
208#357C22×C13912yes—
209#357C22×C13912yes—
210#357C22×C13912yes—
211#357C22×C13912yes—
212#346C22×C13912yes—
213C4×C16C22×C13911yescharacteristic
214C2×#41—41no—
215C2×Q16C23×C13911yescharacteristic
216C2×D8—22no—
217C2×D8—21no—
218C2×D8C23×C13911yescharacteristic
219C2×D8C23×C13912yes—
220C4⋊Q8—21no—
221C4⋊Q8—41no—
222#127—22no—
223#127—21no—
224#125—22no—
225#125—42no—
226#121—41no—
227#121—42no—
228C4×Q8—21no—
229C4×Q8—22no—
230C4×Q8—41no—
231C4×Q8D4×C13911yescharacteristic
232C4×D4—22no—
233C4×D4—21no—
234SD32—22no—
235SD32—24no—
236C2×C16C23×C13911yescharacteristic
237C2×C16C23×C13911yescharacteristic
238C2×C16C23×C13912yes—
239#107—21no—
240#107C23×C13912yes—
241#107C23×C13911yescharacteristic
242#107C23×C13911yescharacteristic
243#106—22no—
244C4⋊C8D4×C13911yescharacteristic
245C4⋊C8D4×C13912yes—
246#103—22no—
247#103—21no—
248#102—22no—
249#102—21no—
250C4×C8C23×C13911yescharacteristic
251C4×C8C23×C13912yes—
252#41—84no—
253C2×Q8—21no—
254C2×Q8—41no—
255C2×Q8D8×C13911yescharacteristic
256C2×D4—22no—
257C2×D4—21no—
258C2×D4—42no—
259C2×D4—41no—
260C2×D4—42no—
261C2×D4—41no—
262C22×C4—42no—
263C22×C4—41no—
264Q16—21no—
265Q16#41×C13912yescomplemented
266D8—21no—
267D8—22no—
268D8—21no—
269D8—22no—
270D8—82no—
271D8—81no—
272C2×C8C2×D4×C13912yes—
273C2×C8C2×D4×C13911yescharacteristic
274C2×C8C24×C13911yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—41no—
283C4⋊C4D8×C13911yescharacteristic
284C4⋊C4D8×C13912yes—
285C22⋊C4—42no—
286C22⋊C4—41no—
287C42—42no—
288C42—41no—
289C42C2×D4×C13912yes—
290C42C2×D4×C13911yescharacteristic
291C16—21no—
292C16—22no—
293C16—21no—
294C23—42no—
295C23—41no—
296Q8—22no—
297Q8—22no—
298Q8—41no—
299Q8—82no—
300D4—41no—
301D4—42no—
302D4—41no—
303D4—42no—
304D4—84no—
305D4—82no—
306D4—162no—
307D4—161no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—84no—
313C2×C4—82no—
314C2×C4C2×D8×C13912yes—
315C2×C4C2×D8×C13911yescharacteristic
316C2×C4C2×D8×C13912yes—
317C2×C4C2×D8×C13911yescharacteristic
318C2×C4C22×D4×C13911yescharacteristic
319C8—22no—
320C8—21no—
321C8C2×#41×C13911yescharacteristic
322C82−1+4×C13911yescharacteristic
323C22—82no—
324C22—81no—
325C22—82no—
326C22—81no—
327C22—82no—
328C22—81no—
329C22C22×D8×C13911yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—42no—
334C4—81no—
335C4—82no—
336C4—81no—
337C4#509×C13912yes—
338C4#548×C13911yescharacteristic
339C4#577×C13911yescharacteristic
340C2—162no—
341C2—161no—
342C2#3358×C13911yescharacteristic
343C2C2×#509×C13911yescharacteristic
344C2#3416×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C22×D8
commutator, Frattini, cosocleC2×C8C24×C139
prime radical#3391×C139C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C4×Q8×C139 ◁ C8×Q8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3383×C139C2semidirect
3. #2244×C139C2semidirect
4. #2240×C139C2semidirect
5. #2228×C139C2semidirect
6. #2224×C139C2semidirect
7. #2207×C139C2semidirect
8. #2207×C139C2semidirect
9. #2183×C139C2semidirect
10. #2175×C139C2semidirect
11. C4×SD32×C139C2semidirect
92. Q16×C139#41semidirect
172. #33935C139direct (N × H)
173. C139#33935direct (N × H)
175. #3383C2×C139semidirect
176. #2244C2×C139semidirect
177. #2240C2×C139semidirect
178. #2228C2×C139semidirect
179. #2224C2×C139semidirect
180. #2207C2×C139semidirect
181. #2207C2×C139semidirect
182. #2183C2×C139semidirect
183. #2175C2×C139semidirect
184. C4×SD32C2×C139semidirect
265. Q16#41×C139semidirect

Maximal subgroups

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

subgroupindex
#3391×C1392
#3383×C1392
#2244×C1392
#2240×C1392
#2228×C1392
#2224×C1392
#2207×C1392
#2183×C1392
#2175×C1392
C4×SD32×C1392
#33935139