Finite Group Databasebeta

← C139×#35924 #48030520

Subgroups — C139×#35924 #48030520

Order 35584.

2300 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2665×C139C213yesmaximal, complemented
2#2572×C139C216yesmaximal, complemented
3#2534×C139C213yesmaximal, complemented
4#2457×C139C216yesmaximal, complemented
5#2404×C139C213yesmaximal, complemented
6#2388×C139C213yesmaximal, complemented
7#2353×C139C213yesmaximal, complemented
8#2339×C139C213yesmaximal, complemented
9#2273×C139C211yesmaximal, characteristic, complemented
10C22×#41×C139C2213yes—
11C2×#123×C139C2213yes—
12C2×#120×C139C2213yes—
13C2×C4×D4×C139C2213yes—
14C2×C4×D4×C139C2216yescomplemented
15C22×C22⋊C4×C139C2213yes—
16#400×C139C2216yescomplemented
17#396×C139C2216yes—
18#395×C139C2213yescomplemented
19#394×C139C2216yes—
20#394×C139C2213yescomplemented
21#393×C139C2216yes—
22#393×C139C2213yescomplemented
23#392×C139C2216yes—
24#392×C139C2211yescharacteristic, complemented
25#391×C139C2216yescomplemented
26#388×C139C2216yes—
27#388×C139C2216yescomplemented
28#387×C139C2216yescomplemented
29#386×C139C2216yes—
30#386×C139C2216yes—
31#386×C139C2216yes—
32#386×C139C2216yes—
33#383×C139C2212yescomplemented
34#383×C139C2213yescomplemented
35#381×C139C2213yes—
36#381×C139C2213yes—
37#381×C139C2216yescomplemented
38#380×C139C2213yes—
39#380×C139C2213yescomplemented
40#379×C139C2211yescharacteristic
41C4×C22⋊C4×C139C2216yes—
42C4×C22⋊C4×C139C2213yes—
43C4×C22⋊C4×C139C2213yes—
44C4×C22⋊C4×C139C2216yescomplemented
45#376×C139C2211yescharacteristic, complemented
46C2×#95×C139C2213yescomplemented
47C25×C139C2311yescharacteristic
48C2×#41×C139—212no—
49C2×#41×C139—412no—
50C22×Q8×C139C2313yes—
51C22×D4×C139C2313yes—
52C22×D4×C139C2313yes—
53C22×D4×C139C2316yes—
54C23×C4×C139C2316yes—
55C23×C4×C139C2313yes—
56C23×C4×C139C2313yes—
57C23×C4×C139C2313yes—
58#123×C139—46no—
59#120×C139—46no—
60C4×D4×C139—212no—
61C4×D4×C139—412no—
62C2×C4⋊C4×C139C2313yes—
63C2×C4⋊C4×C139C2316yes—
64C2×C4⋊C4×C139C2316yes—
65C2×C22⋊C4×C139—212no—
66C2×C22⋊C4×C139C2316yes—
67C2×C22⋊C4×C139C2316yes—
68C2×C22⋊C4×C139C2313yes—
69C2×C22⋊C4×C139C2313yes—
70C2×C22⋊C4×C139C2316yes—
71C2×C22⋊C4×C139C2313yes—
72C2×C22⋊C4×C139C2316yes—
73C2×C22⋊C4×C139C2316yes—
74C2×C22⋊C4×C139C2313yes—
75C2×C22⋊C4×C139C2316yes—
76C2×C42×C139C2313yes—
77C2×C42×C139C2316yes—
78C2×C42×C139C2312yes—
79#95×C139C2311yescharacteristic
80#95×C139C2316yes—
81#95×C139C2316yes—
82#95×C139C2313yes—
83#95×C139C2316yes—
84#95×C139C2316yes—
85#95×C139C2311yescharacteristic
86#95×C139C2316yes—
87#95×C139C2313yes—
88#95×C139C2313yes—
89#95×C139C2313yes—
90#95×C139C2316yes—
91C24×C139—26no—
92C24×C139—43no—
93C24×C139—41no—
94C24×C139C2413yes—
95C24×C139C2413yes—
96#41×C139—448no—
97C2×Q8×C139—26no—
98C2×Q8×C139—46no—
99C2×D4×C139—212no—
100C2×D4×C139—26no—
101C2×D4×C139—212no—
102C2×D4×C139—26no—
103C2×D4×C139—212no—
104C2×D4×C139—26no—
105C2×D4×C139—43no—
106C2×D4×C139—46no—
107C22×C4×C139—212no—
108C22×C4×C139—26no—
109C22×C4×C139—212no—
110C22×C4×C139—26no—
111C22×C4×C139—46no—
112C22×C4×C139—46no—
113C22×C4×C139—46no—
114C22×C4×C139—43no—
115C22×C4×C139—43no—
116C22×C4×C139#41112yescomplemented
117C22×C4×C139C2416yes—
118C22×C4×C139C2411yescharacteristic
119C22×C4×C139C2416yes—
120C22×C4×C139C2413yes—
121C22×C4×C139C2413yes—
122C22×C4×C139C2413yes—
123C22×C4×C139C2413yes—
124C4⋊C4×C139—26no—
125C4⋊C4×C139—46no—
126C4⋊C4×C139—46no—
127C22⋊C4×C139—26no—
128C22⋊C4×C139—212no—
129C22⋊C4×C139—212no—
130C22⋊C4×C139—212no—
131C22⋊C4×C139—26no—
132C22⋊C4×C139—46no—
133C22⋊C4×C139—46no—
134C22⋊C4×C139—46no—
135C22⋊C4×C139—43no—
136C22⋊C4×C139—43no—
137C42×C139—26no—
138C42×C139—42no—
139C42×C139—46no—
140C23×C139—28no—
141C23×C139—26no—
142C23×C139—23no—
143C23×C139—26no—
144C23×C139—23no—
145C23×C139—26no—
146C23×C139—26no—
147C23×C139—23no—
148C23×C139—23no—
149C23×C139—86no—
150C23×C139—86no—
151C23×C139C2×#4116yes—
152C23×C139H(5,𝔽2)16yes—
153C23×C139C2511yescharacteristic
154Q8×C139—412no—
155D4×C139—224no—
156D4×C139—412no—
157D4×C139—424no—
158C2×C4×C139—26no—
159C2×C4×C139—26no—
160C2×C4×C139—23no—
161C2×C4×C139—23no—
162C2×C4×C139—26no—
163C2×C4×C139—23no—
164C2×C4×C139—26no—
165C2×C4×C139—26no—
166C2×C4×C139—26no—
167C2×C4×C139—23no—
168C2×C4×C139—26no—
169C2×C4×C139—26no—
170C2×C4×C139—26no—
171C2×C4×C139—23no—
172C2×C4×C139—412no—
173C2×C4×C139—424no—
174C2×C4×C139—86no—
175C2×C4×C139—86no—
176C2×C4×C139C2×#4116yes—
177C2×C4×C139C2×#4116yes—
178C22×C139—26no—
179C22×C139—212no—
180C22×C139—26no—
181C22×C139—26no—
182C22×C139—26no—
183C22×C139—43no—
184C22×C139—43no—
185C22×C139—46no—
186C22×C139—46no—
187C22×C139—46no—
188C22×C139—88no—
189C22×C139C22×#4113yes—
190C22×C139C2×H(5,𝔽2)13yes—
191C22×C139#58511yescharacteristic
192C4×C139—26no—
193C4×C139—26no—
194C4×C139—41no—
195C4×C139—46no—
196C4×C139—43no—
197C4×C139—46no—
198C4×C139—43no—
199C2×C139—46no—
200C2×C139—46no—
201C2×C139#344411yescharacteristic
202C2×C139#349013yes—
203C2×C139#349413yes—
204#35924C13911yesmaximal, characteristic, direct product factor, Sylow
205C139#3592411yescharacteristic, direct product factor, Sylow
206#2665C2×C13913yescomplemented
207#2572C2×C13916yescomplemented
208#2534C2×C13913yescomplemented
209#2457C2×C13916yescomplemented
210#2404C2×C13913yescomplemented
211#2388C2×C13913yescomplemented
212#2353C2×C13913yescomplemented
213#2339C2×C13913yescomplemented
214#2273C2×C13911yescharacteristic, complemented
215C22×#41C22×C13913yes—
216C2×#123C22×C13913yes—
217C2×#120C22×C13913yes—
218C2×C4×D4C22×C13913yes—
219C2×C4×D4C22×C13916yescomplemented
220C22×C22⋊C4C22×C13913yes—
221#400C22×C13916yescomplemented
222#396C22×C13916yes—
223#395C22×C13913yescomplemented
224#394C22×C13916yes—
225#394C22×C13913yescomplemented
226#393C22×C13916yes—
227#393C22×C13913yescomplemented
228#392C22×C13916yes—
229#392C22×C13911yescharacteristic, complemented
230#391C22×C13916yescomplemented
231#388C22×C13916yes—
232#388C22×C13916yescomplemented
233#387C22×C13916yescomplemented
234#386C22×C13916yes—
235#386C22×C13916yes—
236#386C22×C13916yes—
237#386C22×C13916yes—
238#383C22×C13912yescomplemented
239#383C22×C13913yescomplemented
240#381C22×C13913yes—
241#381C22×C13913yes—
242#381C22×C13916yescomplemented
243#380C22×C13913yes—
244#380C22×C13913yescomplemented
245#379C22×C13911yescharacteristic
246C4×C22⋊C4C22×C13916yes—
247C4×C22⋊C4C22×C13913yes—
248C4×C22⋊C4C22×C13913yes—
249C4×C22⋊C4C22×C13916yescomplemented
250#376C22×C13911yescharacteristic, complemented
251C2×#95C22×C13913yescomplemented
252C25C23×C13911yescharacteristic
253C2×#41—212no—
254C2×#41—412no—
255C22×Q8C23×C13913yes—
256C22×D4C23×C13913yes—
257C22×D4C23×C13913yes—
258C22×D4C23×C13916yes—
259C23×C4C23×C13916yes—
260C23×C4C23×C13913yes—
261C23×C4C23×C13913yes—
262C23×C4C23×C13913yes—
263#123—46no—
264#120—46no—
265C4×D4—212no—
266C4×D4—412no—
267C2×C4⋊C4C23×C13913yes—
268C2×C4⋊C4C23×C13916yes—
269C2×C4⋊C4C23×C13916yes—
270C2×C22⋊C4—212no—
271C2×C22⋊C4C23×C13916yes—
272C2×C22⋊C4C23×C13916yes—
273C2×C22⋊C4C23×C13913yes—
274C2×C22⋊C4C23×C13913yes—
275C2×C22⋊C4C23×C13916yes—
276C2×C22⋊C4C23×C13916yes—
277C2×C22⋊C4C23×C13913yes—
278C2×C22⋊C4C23×C13916yes—
279C2×C22⋊C4C23×C13913yes—
280C2×C22⋊C4C23×C13916yes—
281C2×C42C23×C13913yes—
282C2×C42C23×C13916yes—
283C2×C42C23×C13912yes—
284#95C23×C13911yescharacteristic
285#95C23×C13916yes—
286#95C23×C13913yes—
287#95C23×C13913yes—
288#95C23×C13913yes—
289#95C23×C13911yescharacteristic
290#95C23×C13913yes—
291#95C23×C13916yes—
292#95C23×C13916yes—
293#95C23×C13916yes—
294#95C23×C13916yes—
295#95C23×C13916yes—
296C24—26no—
297C24—43no—
298C24—41no—
299C24C24×C13913yes—
300C24C24×C13913yes—
301#41—448no—
302C2×Q8—26no—
303C2×Q8—46no—
304C2×D4—212no—
305C2×D4—26no—
306C2×D4—212no—
307C2×D4—26no—
308C2×D4—212no—
309C2×D4—26no—
310C2×D4—43no—
311C2×D4—46no—
312C22×C4—212no—
313C22×C4—26no—
314C22×C4—212no—
315C22×C4—26no—
316C22×C4—46no—
317C22×C4—46no—
318C22×C4—46no—
319C22×C4—43no—
320C22×C4—43no—
321C22×C4#41×C139112yescomplemented
322C22×C4C24×C13916yes—
323C22×C4C24×C13911yescharacteristic
324C22×C4C24×C13916yes—
325C22×C4C24×C13913yes—
326C22×C4C24×C13913yes—
327C22×C4C24×C13913yes—
328C22×C4C24×C13913yes—
329C4⋊C4—26no—
330C4⋊C4—46no—
331C4⋊C4—46no—
332C22⋊C4—26no—
333C22⋊C4—212no—
334C22⋊C4—212no—
335C22⋊C4—212no—
336C22⋊C4—26no—
337C22⋊C4—46no—
338C22⋊C4—46no—
339C22⋊C4—46no—
340C22⋊C4—43no—
341C22⋊C4—43no—
342C42—26no—
343C42—42no—
344C42—46no—
345C23—28no—
346C23—26no—
347C23—23no—
348C23—26no—
349C23—23no—
350C23—26no—
351C23—26no—
352C23—23no—
353C23—23no—
354C23—86no—
355C23—86no—
356C23C2×#41×C13916yes—
357C23H(5,𝔽2)×C13916yes—
358C23C25×C13911yescharacteristic
359Q8—412no—
360D4—224no—
361D4—424no—
362D4—412no—
363C2×C4—26no—
364C2×C4—26no—
365C2×C4—23no—
366C2×C4—23no—
367C2×C4—26no—
368C2×C4—23no—
369C2×C4—26no—
370C2×C4—26no—
371C2×C4—26no—
372C2×C4—23no—
373C2×C4—26no—
374C2×C4—26no—
375C2×C4—26no—
376C2×C4—23no—
377C2×C4—412no—
378C2×C4—424no—
379C2×C4—86no—
380C2×C4—86no—
381C2×C4C2×#41×C13916yes—
382C2×C4C2×#41×C13916yes—
383C22—26no—
384C22—212no—
385C22—26no—
386C22—26no—
387C22—26no—
388C22—43no—
389C22—43no—
390C22—46no—
391C22—46no—
392C22—46no—
393C22—88no—
394C22C22×#41×C13913yes—
395C22C2×H(5,𝔽2)×C13913yes—
396C22#585×C13911yescharacteristic
397C4—26no—
398C4—26no—
399C4—41no—
400C4—46no—
401C4—43no—
402C4—46no—
403C4—43no—
404C2—46no—
405C2—46no—
406C2#3444×C13911yescharacteristic
407C2#3490×C13913yes—
408C2#3494×C13913yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2665×C139C2semidirect
2. #2572×C139C2semidirect
3. #2534×C139C2semidirect
4. #2457×C139C2semidirect
5. #2404×C139C2semidirect
6. #2388×C139C2semidirect
7. #2353×C139C2semidirect
8. #2339×C139C2semidirect
9. #2273×C139C2semidirect
14. C2×C4×D4×C139C22semidirect
16. #400×C139C22semidirect
18. #395×C139C22semidirect
20. #394×C139C22semidirect
22. #393×C139C22semidirect
24. #392×C139C22semidirect
25. #391×C139C22semidirect
27. #388×C139C22semidirect
28. #387×C139C22semidirect
33. #383×C139C22semidirect
34. #383×C139C22semidirect
37. #381×C139C22semidirect
39. #380×C139C22semidirect
44. C4×C22⋊C4×C139C22semidirect
45. #376×C139C22semidirect
46. C2×#95×C139C22semidirect
116. C22×C4×C139#41semidirect
204. #35924C139direct (N × H)
205. C139#35924direct (N × H)
206. #2665C2×C139semidirect
207. #2572C2×C139semidirect
208. #2534C2×C139semidirect
209. #2457C2×C139semidirect
210. #2404C2×C139semidirect
211. #2388C2×C139semidirect
212. #2353C2×C139semidirect
213. #2339C2×C139semidirect
214. #2273C2×C139semidirect
219. C2×C4×D4C22×C139semidirect
221. #400C22×C139semidirect
223. #395C22×C139semidirect
225. #394C22×C139semidirect
227. #393C22×C139semidirect
229. #392C22×C139semidirect
230. #391C22×C139semidirect
232. #388C22×C139semidirect
233. #387C22×C139semidirect
238. #383C22×C139semidirect
239. #383C22×C139semidirect
242. #381C22×C139semidirect
244. #380C22×C139semidirect
249. C4×C22⋊C4C22×C139semidirect
250. #376C22×C139semidirect
251. C2×#95C22×C139semidirect
321. C22×C4#41×C139semidirect

Maximal subgroups

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

subgroupindex
#2665×C1392
#2572×C1392
#2534×C1392
#2457×C1392
#2404×C1392
#2388×C1392
#2353×C1392
#2339×C1392
#2273×C1392
#35924139