Finite Group Databasebeta

← C139×#36063 #48030659

Subgroups — C139×#36063 #48030659

Order 35584.

1816 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2667×C139C213yesmaximal, complemented
2#2553×C139C216yesmaximal, complemented
3#2534×C139C213yesmaximal
4#2515×C139C216yesmaximal, complemented
5#2482×C139C213yesmaximal, complemented
6#2395×C139C213yesmaximal, complemented
7#2353×C139C213yesmaximal, complemented
8#2346×C139C213yesmaximal, complemented
9#2273×C139C211yesmaximal, characteristic, complemented
10C2×#126×C139C2212yescomplemented
11C2×#123×C139C2213yes—
12C2×#120×C139C2211yescharacteristic
13C2×C4×D4×C139C2213yes—
14C2×#117×C139C2213yes—
15C22×C22⋊C4×C139C2213yes—
16#400×C139C2213yescomplemented
17#399×C139C2216yes—
18#399×C139C2211yescharacteristic, complemented
19#398×C139C2216yescomplemented
20#398×C139C2213yescomplemented
21#397×C139C2216yes—
22#397×C139C2213yescomplemented
23#396×C139C2216yes—
24#394×C139C2216yes—
25#389×C139C2216yescomplemented
26#388×C139C2216yes—
27#388×C139C2216yes—
28#388×C139C2216yes—
29#387×C139C2216yescomplemented
30#387×C139C2216yescomplemented
31#386×C139C2216yes—
32#385×C139C2216yes—
33#383×C139C2213yescomplemented
34#382×C139C2216yescomplemented
35#381×C139C2213yes—
36#381×C139C2213yes—
37#380×C139C2213yes—
38#380×C139C2213yescomplemented
39#379×C139C2213yes—
40C4×C4⋊C4×C139C2216yescomplemented
41C4×C22⋊C4×C139C2216yes—
42C4×C22⋊C4×C139C2213yes—
43C4×C22⋊C4×C139C2213yes—
44C4×C22⋊C4×C139C2216yescomplemented
45#376×C139C2213yescomplemented
46C2×#95×C139C2211yescharacteristic, complemented
47C25×C139C2311yescharacteristic
48C22×D4×C139C2313yes—
49C23×C4×C139C2313yes—
50C23×C4×C139C2313yes—
51C23×C4×C139C2313yes—
52#126×C139—44no—
53#123×C139—46no—
54#120×C139—42no—
55C4×D4×C139—212no—
56#117×C139—212no—
57C2×C4⋊C4×C139C2313yes—
58C2×C4⋊C4×C139C2313yes—
59C2×C4⋊C4×C139C2313yes—
60C2×C4⋊C4×C139C2316yes—
61C2×C4⋊C4×C139C2316yes—
62C2×C4⋊C4×C139C2316yes—
63C2×C4⋊C4×C139C2316yes—
64C2×C22⋊C4×C139—212no—
65C2×C22⋊C4×C139C2316yes—
66C2×C22⋊C4×C139C2313yes—
67C2×C22⋊C4×C139C2316yes—
68C2×C22⋊C4×C139C2313yes—
69C2×C22⋊C4×C139C2316yes—
70C2×C22⋊C4×C139C2316yes—
71C2×C22⋊C4×C139C2313yes—
72C2×C22⋊C4×C139C2316yes—
73C2×C22⋊C4×C139C2313yes—
74C2×C42×C139C2316yes—
75C2×C42×C139C2313yes—
76C2×C42×C139C2312yes—
77C2×C42×C139C2316yes—
78#95×C139C2316yes—
79#95×C139C2316yes—
80#95×C139C2316yes—
81#95×C139C2316yes—
82#95×C139C2313yes—
83#95×C139C2311yescharacteristic
84#95×C139C2316yes—
85#95×C139C2311yescharacteristic
86#95×C139C2313yes—
87#95×C139C2316yes—
88#95×C139C2313yes—
89#95×C139C2313yes—
90C24×C139—26no—
91C24×C139—41no—
92C24×C139—43no—
93C24×C139C2413yes—
94C24×C139C2411yescharacteristic
95C2×D4×C139—26no—
96C2×D4×C139—26no—
97C2×D4×C139—43no—
98C22×C4×C139—26no—
99C22×C4×C139—26no—
100C22×C4×C139—46no—
101C22×C4×C139—43no—
102C22×C4×C139—46no—
103C22×C4×C139—43no—
104C22×C4×C139#41112yes—
105C22×C4×C139C2413yes—
106C22×C4×C139C2413yes—
107C22×C4×C139C2416yes—
108C22×C4×C139C2413yes—
109C22×C4×C139C2416yes—
110C22×C4×C139C2413yes—
111C22×C4×C139C2413yes—
112C4⋊C4×C139—26no—
113C4⋊C4×C139—26no—
114C4⋊C4×C139—26no—
115C4⋊C4×C139—46no—
116C4⋊C4×C139—46no—
117C4⋊C4×C139—46no—
118C4⋊C4×C139—46no—
119C22⋊C4×C139—212no—
120C22⋊C4×C139—26no—
121C22⋊C4×C139—212no—
122C22⋊C4×C139—212no—
123C22⋊C4×C139—212no—
124C22⋊C4×C139—26no—
125C22⋊C4×C139—46no—
126C22⋊C4×C139—43no—
127C22⋊C4×C139—43no—
128C42×C139—212no—
129C42×C139—26no—
130C42×C139—46no—
131C42×C139—42no—
132C23×C139—28no—
133C23×C139—26no—
134C23×C139—23no—
135C23×C139—23no—
136C23×C139—26no—
137C23×C139—23no—
138C23×C139—23no—
139C23×C139—86no—
140C23×C139—86no—
141C23×C139C2×#4116yes—
142C23×C139H(5,𝔽2)12yes—
143C23×C139C2511yescharacteristic
144D4×C139—412no—
145C2×C4×C139—26no—
146C2×C4×C139—26no—
147C2×C4×C139—23no—
148C2×C4×C139—26no—
149C2×C4×C139—26no—
150C2×C4×C139—23no—
151C2×C4×C139—26no—
152C2×C4×C139—23no—
153C2×C4×C139—26no—
154C2×C4×C139—26no—
155C2×C4×C139—23no—
156C2×C4×C139—26no—
157C2×C4×C139—26no—
158C2×C4×C139—26no—
159C2×C4×C139—23no—
160C2×C4×C139—412no—
161C2×C4×C139—86no—
162C2×C4×C139—86no—
163C2×C4×C139C2×#4116yes—
164C2×C4×C139C2×#4116yes—
165C22×C139—26no—
166C22×C139—26no—
167C22×C139—26no—
168C22×C139—26no—
169C22×C139—41no—
170C22×C139—43no—
171C22×C139—46no—
172C22×C139—46no—
173C22×C139—88no—
174C22×C139C22×#4113yes—
175C22×C139C2×H(5,𝔽2)11yescharacteristic
176C22×C139#58513yes—
177C4×C139—26no—
178C4×C139—26no—
179C4×C139—43no—
180C4×C139—43no—
181C4×C139—46no—
182C4×C139—46no—
183C4×C139—43no—
184C2×C139—42no—
185C2×C139—46no—
186C2×C139#344411yescharacteristic
187C2×C139#349113yes—
188C2×C139#349413yes—
189#36063C13911yesmaximal, characteristic, direct product factor, Sylow
190C139#3606311yescharacteristic, direct product factor, Sylow
191#2667C2×C13913yescomplemented
192#2553C2×C13916yescomplemented
193#2534C2×C13913yes—
194#2515C2×C13916yescomplemented
195#2482C2×C13913yescomplemented
196#2395C2×C13913yescomplemented
197#2353C2×C13913yescomplemented
198#2346C2×C13913yescomplemented
199#2273C2×C13911yescharacteristic, complemented
200C2×#126C22×C13912yescomplemented
201C2×#123C22×C13913yes—
202C2×#120C22×C13911yescharacteristic
203C2×C4×D4C22×C13913yes—
204C2×#117C22×C13913yes—
205C22×C22⋊C4C22×C13913yes—
206#400C22×C13913yescomplemented
207#399C22×C13916yes—
208#399C22×C13911yescharacteristic, complemented
209#398C22×C13913yescomplemented
210#398C22×C13916yescomplemented
211#397C22×C13916yes—
212#397C22×C13913yescomplemented
213#396C22×C13916yes—
214#394C22×C13916yes—
215#389C22×C13916yescomplemented
216#388C22×C13916yes—
217#388C22×C13916yes—
218#388C22×C13916yes—
219#387C22×C13916yescomplemented
220#387C22×C13916yescomplemented
221#386C22×C13916yes—
222#385C22×C13916yes—
223#383C22×C13913yescomplemented
224#382C22×C13916yescomplemented
225#381C22×C13913yes—
226#381C22×C13913yes—
227#380C22×C13913yes—
228#380C22×C13913yescomplemented
229#379C22×C13913yes—
230C4×C4⋊C4C22×C13916yescomplemented
231C4×C22⋊C4C22×C13913yes—
232C4×C22⋊C4C22×C13913yes—
233C4×C22⋊C4C22×C13916yes—
234C4×C22⋊C4C22×C13916yescomplemented
235#376C22×C13913yescomplemented
236C2×#95C22×C13911yescharacteristic, complemented
237C25C23×C13911yescharacteristic
238C22×D4C23×C13913yes—
239C23×C4C23×C13913yes—
240C23×C4C23×C13913yes—
241C23×C4C23×C13913yes—
242#126—44no—
243#123—46no—
244#120—42no—
245C4×D4—212no—
246#117—212no—
247C2×C4⋊C4C23×C13913yes—
248C2×C4⋊C4C23×C13913yes—
249C2×C4⋊C4C23×C13913yes—
250C2×C4⋊C4C23×C13916yes—
251C2×C4⋊C4C23×C13916yes—
252C2×C4⋊C4C23×C13916yes—
253C2×C4⋊C4C23×C13916yes—
254C2×C22⋊C4—212no—
255C2×C22⋊C4C23×C13916yes—
256C2×C22⋊C4C23×C13916yes—
257C2×C22⋊C4C23×C13916yes—
258C2×C22⋊C4C23×C13913yes—
259C2×C22⋊C4C23×C13913yes—
260C2×C22⋊C4C23×C13916yes—
261C2×C22⋊C4C23×C13913yes—
262C2×C22⋊C4C23×C13913yes—
263C2×C22⋊C4C23×C13916yes—
264C2×C42C23×C13916yes—
265C2×C42C23×C13913yes—
266C2×C42C23×C13912yes—
267C2×C42C23×C13916yes—
268#95C23×C13911yescharacteristic
269#95C23×C13913yes—
270#95C23×C13916yes—
271#95C23×C13913yes—
272#95C23×C13913yes—
273#95C23×C13913yes—
274#95C23×C13911yescharacteristic
275#95C23×C13916yes—
276#95C23×C13916yes—
277#95C23×C13916yes—
278#95C23×C13916yes—
279#95C23×C13916yes—
280C24—26no—
281C24—41no—
282C24—43no—
283C24C24×C13913yes—
284C24C24×C13911yescharacteristic
285C2×D4—26no—
286C2×D4—26no—
287C2×D4—43no—
288C22×C4—26no—
289C22×C4—26no—
290C22×C4—46no—
291C22×C4—43no—
292C22×C4—46no—
293C22×C4—43no—
294C22×C4#41×C139112yes—
295C22×C4C24×C13913yes—
296C22×C4C24×C13913yes—
297C22×C4C24×C13916yes—
298C22×C4C24×C13913yes—
299C22×C4C24×C13916yes—
300C22×C4C24×C13913yes—
301C22×C4C24×C13913yes—
302C4⋊C4—26no—
303C4⋊C4—26no—
304C4⋊C4—26no—
305C4⋊C4—46no—
306C4⋊C4—46no—
307C4⋊C4—46no—
308C4⋊C4—46no—
309C22⋊C4—212no—
310C22⋊C4—26no—
311C22⋊C4—212no—
312C22⋊C4—212no—
313C22⋊C4—212no—
314C22⋊C4—26no—
315C22⋊C4—46no—
316C22⋊C4—43no—
317C22⋊C4—43no—
318C42—212no—
319C42—26no—
320C42—46no—
321C42—42no—
322C23—28no—
323C23—26no—
324C23—23no—
325C23—23no—
326C23—26no—
327C23—23no—
328C23—23no—
329C23—86no—
330C23—86no—
331C23C2×#41×C13916yes—
332C23H(5,𝔽2)×C13912yes—
333C23C25×C13911yescharacteristic
334D4—412no—
335C2×C4—26no—
336C2×C4—26no—
337C2×C4—23no—
338C2×C4—26no—
339C2×C4—26no—
340C2×C4—23no—
341C2×C4—26no—
342C2×C4—23no—
343C2×C4—26no—
344C2×C4—26no—
345C2×C4—23no—
346C2×C4—26no—
347C2×C4—26no—
348C2×C4—26no—
349C2×C4—23no—
350C2×C4—412no—
351C2×C4—86no—
352C2×C4—86no—
353C2×C4C2×#41×C13916yes—
354C2×C4C2×#41×C13916yes—
355C22—26no—
356C22—26no—
357C22—26no—
358C22—26no—
359C22—41no—
360C22—43no—
361C22—46no—
362C22—46no—
363C22—88no—
364C22C22×#41×C13913yes—
365C22C2×H(5,𝔽2)×C13911yescharacteristic
366C22#585×C13913yes—
367C4—26no—
368C4—26no—
369C4—43no—
370C4—43no—
371C4—46no—
372C4—43no—
373C4—46no—
374C2—46no—
375C2—42no—
376C2#3444×C13911yescharacteristic
377C2#3491×C13913yes—
378C2#3494×C13913yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC2×#120×C139C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2667×C139C2semidirect
2. #2553×C139C2semidirect
4. #2515×C139C2semidirect
5. #2482×C139C2semidirect
6. #2395×C139C2semidirect
7. #2353×C139C2semidirect
8. #2346×C139C2semidirect
9. #2273×C139C2semidirect
10. C2×#126×C139C22semidirect
16. #400×C139C22semidirect
18. #399×C139C22semidirect
19. #398×C139C22semidirect
20. #398×C139C22semidirect
22. #397×C139C22semidirect
25. #389×C139C22semidirect
29. #387×C139C22semidirect
30. #387×C139C22semidirect
33. #383×C139C22semidirect
34. #382×C139C22semidirect
38. #380×C139C22semidirect
40. C4×C4⋊C4×C139C22semidirect
44. C4×C22⋊C4×C139C22semidirect
45. #376×C139C22semidirect
46. C2×#95×C139C22semidirect
189. #36063C139direct (N × H)
190. C139#36063direct (N × H)
191. #2667C2×C139semidirect
192. #2553C2×C139semidirect
194. #2515C2×C139semidirect
195. #2482C2×C139semidirect
196. #2395C2×C139semidirect
197. #2353C2×C139semidirect
198. #2346C2×C139semidirect
199. #2273C2×C139semidirect
200. C2×#126C22×C139semidirect
206. #400C22×C139semidirect
208. #399C22×C139semidirect
209. #398C22×C139semidirect
210. #398C22×C139semidirect
212. #397C22×C139semidirect
215. #389C22×C139semidirect
219. #387C22×C139semidirect
220. #387C22×C139semidirect
223. #383C22×C139semidirect
224. #382C22×C139semidirect
228. #380C22×C139semidirect
230. C4×C4⋊C4C22×C139semidirect
234. C4×C22⋊C4C22×C139semidirect
235. #376C22×C139semidirect
236. C2×#95C22×C139semidirect

Maximal subgroups

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

subgroupindex
#2667×C1392
#2553×C1392
#2534×C1392
#2515×C1392
#2482×C1392
#2395×C1392
#2353×C1392
#2346×C1392
#2273×C1392
#36063139