Finite Group Databasebeta

← C139×#10013 #48004609

Subgroups — C139×#10013 #48004609

Order 35584.

598 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3103×C139C211yesmaximal, characteristic, complemented
2#3100×C139C211yesmaximal, characteristic
3#2398×C139C211yesmaximal, characteristic, complemented
4#1963×C139C211yesmaximal, characteristic, complemented
5#1487×C139C211yesmaximal, characteristic, complemented
6#1486×C139C211yesmaximal, characteristic, complemented
7#1274×C139C211yesmaximal, characteristic, complemented
8#532×C139C2211yescharacteristic
9C2×C4×Q8×C139C2211yescharacteristic
10C2×C4×D4×C139C2211yescharacteristic
11#481×C139—21no—
12#480×C139—21no—
13#475×C139—21no—
14#474×C139—21no—
15#460×C139—21no—
16#459×C139—21no—
17#448×C139—21no—
18#447×C139—21no—
19C4×SD16×C139—22no—
20C4×D8×C139—22no—
21#431×C139C2211yescharacteristic
22#431×C139C2211yescharacteristic
23#423×C139C2211yescharacteristic
24C2×#104×C139—22no—
25#400×C139—21no—
26#397×C139—21no—
27#394×C139—21no—
28#393×C139—21no—
29C4×C22⋊C4×C139—22no—
30#376×C139C2211yescharacteristic
31Q8⋊C8×C139—22no—
32D4⋊C8×C139—22no—
33C2×#41×C139—21no—
34C22×Q8×C139D411yescharacteristic
35C22×D4×C139D411yescharacteristic
36C23×C4×C139—21no—
37C2×SD16×C139—22no—
38C2×D8×C139—22no—
39C2×M16×C139—21no—
40C4⋊Q8×C139D411yescharacteristic
41#127×C139D411yescharacteristic
42#124×C139—21no—
43#121×C139—21no—
44#121×C139—21no—
45C4×Q8×C139—21no—
46C4×Q8×C139—21no—
47C4×Q8×C139—21no—
48C4×Q8×C139—21no—
49C4×D4×C139—21no—
50C4×D4×C139—21no—
51C4×D4×C139—21no—
52C4×D4×C139—21no—
53C4×D4×C139—21no—
54C4×D4×C139—21no—
55C2×C4⋊C4×C139—21no—
56C2×C4⋊C4×C139D411yescharacteristic
57C2×C4⋊C4×C139D411yescharacteristic
58C2×C22⋊C4×C139—22no—
59C2×C22⋊C4×C139—22no—
60C2×C22⋊C4×C139—21no—
61C2×C42×C139—21no—
62C2×C42×C139D412yes—
63C2×C42×C139C2311yescharacteristic
64#107×C139—22no—
65#106×C139—22no—
66C4⋊C8×C139—21no—
67C4⋊C8×C139—21no—
68C4⋊C8×C139—21no—
69C4⋊C8×C139—21no—
70#104×C139—44no—
71#103×C139—22no—
72#102×C139—22no—
73#102×C139—22no—
74#102×C139—22no—
75C22⋊C8×C139—21no—
76C22⋊C8×C139—21no—
77C4×C8×C139D412yes—
78C4×C8×C139D412yes—
79#95×C139—22no—
80#95×C139—22no—
81#95×C139—21no—
82#95×C139—21no—
83C24×C139—21no—
84#41×C139—42no—
85#41×C139—42no—
86C2×Q8×C139—21no—
87C2×Q8×C139—21no—
88C2×Q8×C139—21no—
89C2×Q8×C139—42no—
90C2×D4×C139—21no—
91C2×D4×C139—21no—
92C2×D4×C139—21no—
93C2×D4×C139—21no—
94C2×D4×C139—21no—
95C2×D4×C139—42no—
96C2×D4×C139—41no—
97C22×C4×C139—21no—
98C22×C4×C139—22no—
99C22×C4×C139—21no—
100C22×C4×C139—21no—
101C22×C4×C139—41no—
102C22×C4×C139—41no—
103C22×C4×C139—41no—
104C22×C4×C139—42no—
105C22×C4×C139—42no—
106C22×C4×C139C2×D411yescharacteristic
107C22×C4×C139C2×D411yescharacteristic
108C22×C4×C139C2×D411yescharacteristic
109SD16×C139—44no—
110D8×C139—44no—
111M16×C139—42no—
112C2×C8×C139—22no—
113C2×C8×C139—22no—
114C2×C8×C139—41no—
115C4⋊C4×C139—21no—
116C4⋊C4×C139—21no—
117C4⋊C4×C139—21no—
118C4⋊C4×C139—21no—
119C4⋊C4×C139—21no—
120C4⋊C4×C139—21no—
121C4⋊C4×C139—41no—
122C4⋊C4×C139—41no—
123C22⋊C4×C139—44no—
124C22⋊C4×C139—44no—
125C22⋊C4×C139—41no—
126C22⋊C4×C139—41no—
127C22⋊C4×C139—41no—
128C22⋊C4×C139—41no—
129C42×C139—22no—
130C42×C139—22no—
131C42×C139—41no—
132C42×C139—41no—
133C42×C139C2×D411yescharacteristic
134C42×C139C2×D411yescharacteristic
135C42×C139C2×D411yescharacteristic
136C42×C139#4111yescharacteristic
137C23×C139—22no—
138C23×C139—42no—
139C23×C139—41no—
140C23×C139—41no—
141C23×C139—42no—
142C23×C139—41no—
143C23×C139#12011yescharacteristic
144Q8×C139—22no—
145Q8×C139—22no—
146Q8×C139—41no—
147Q8×C139—41no—
148Q8×C139—42no—
149D4×C139—22no—
150D4×C139—22no—
151D4×C139—41no—
152D4×C139—41no—
153D4×C139—42no—
154D4×C139—42no—
155D4×C139—42no—
156D4×C139—82no—
157C2×C4×C139—22no—
158C2×C4×C139—41no—
159C2×C4×C139—41no—
160C2×C4×C139—41no—
161C2×C4×C139—41no—
162C2×C4×C139—42no—
163C2×C4×C139—42no—
164C2×C4×C139—42no—
165C2×C4×C139—41no—
166C2×C4×C139—41no—
167C2×C4×C139—41no—
168C2×C4×C139—42no—
169C2×C4×C139—42no—
170C2×C4×C139—82no—
171C2×C4×C139—81no—
172C2×C4×C139—81no—
173C2×C4×C139—81no—
174C2×C4×C139—81no—
175C2×C4×C139#12011yescharacteristic
176C2×C4×C139#12011yescharacteristic
177C2×C4×C139#12111yescharacteristic
178C2×C4×C139#12111yescharacteristic
179C2×C4×C139#12111yescharacteristic
180C2×C4×C139#12711yescharacteristic
181C2×C4×C139#13512yes—
182C2×C4×C139AGL(1,ℤ/8)12yes—
183C8×C139—42no—
184C8×C139—42no—
185C8×C139—81no—
186C22×C139—21no—
187C22×C139—21no—
188C22×C139—44no—
189C22×C139—42no—
190C22×C139—82no—
191C22×C139—81no—
192C22×C139—81no—
193C22×C139—81no—
194C22×C139—81no—
195C22×C139—81no—
196C22×C139#39211yescharacteristic
197C22×C139#44912yes—
198C4×C139—21no—
199C4×C139—21no—
200C4×C139—21no—
201C4×C139—21no—
202C4×C139—42no—
203C4×C139—82no—
204C4×C139—81no—
205C4×C139—81no—
206C4×C139—81no—
207C4×C139#46312yes—
208C4×C139#49511yescharacteristic
209C4×C139#49611yescharacteristic
210C2×C139—22no—
211C2×C139—82no—
212C2×C139—161no—
213C2×C139#201011yescharacteristic
214C2×C139#201011yescharacteristic
215C2×C139#201211yescharacteristic
216#10013C13911yesmaximal, characteristic, direct product factor, Sylow
217C139#1001311yescharacteristic, direct product factor, Sylow
218#3103C2×C13911yescharacteristic, complemented
219#3100C2×C13911yescharacteristic
220#2398C2×C13911yescharacteristic, complemented
221#1963C2×C13911yescharacteristic, complemented
222#1487C2×C13911yescharacteristic, complemented
223#1486C2×C13911yescharacteristic, complemented
224#1274C2×C13911yescharacteristic, complemented
225#532C22×C13911yescharacteristic
226C2×C4×Q8C22×C13911yescharacteristic
227C2×C4×D4C22×C13911yescharacteristic
228#481—21no—
229#480—21no—
230#475—21no—
231#474—21no—
232#460—21no—
233#459—21no—
234#448—21no—
235#447—21no—
236C4×SD16—22no—
237C4×D8—22no—
238#431C22×C13911yescharacteristic
239#431C22×C13911yescharacteristic
240#423C22×C13911yescharacteristic
241C2×#104—22no—
242#400—21no—
243#397—21no—
244#394—21no—
245#393—21no—
246C4×C22⋊C4—22no—
247#376C22×C13911yescharacteristic
248Q8⋊C8—22no—
249D4⋊C8—22no—
250C2×#41—21no—
251C22×Q8D4×C13911yescharacteristic
252C22×D4D4×C13911yescharacteristic
253C23×C4—21no—
254C2×SD16—22no—
255C2×D8—22no—
256C2×M16—21no—
257C4⋊Q8D4×C13911yescharacteristic
258#127D4×C13911yescharacteristic
259#124—21no—
260#121—21no—
261#121—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4D4×C13911yescharacteristic
274C2×C4⋊C4D4×C13911yescharacteristic
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C42—21no—
279C2×C42D4×C13912yes—
280C2×C42C23×C13911yescharacteristic
281#107—22no—
282#106—22no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287#104—44no—
288#103—22no—
289#102—22no—
290#102—22no—
291#102—22no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C4×C8D4×C13912yes—
295C4×C8D4×C13912yes—
296#95—22no—
297#95—22no—
298#95—21no—
299#95—21no—
300C24—21no—
301#41—42no—
302#41—42no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—42no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—42no—
313C2×D4—41no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4C2×D4×C13911yescharacteristic
324C22×C4C2×D4×C13911yescharacteristic
325C22×C4C2×D4×C13911yescharacteristic
326SD16—44no—
327D8—44no—
328M16—42no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—41no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C22⋊C4—44no—
341C22⋊C4—44no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42—22no—
347C42—22no—
348C42—41no—
349C42—41no—
350C42C2×D4×C13911yescharacteristic
351C42C2×D4×C13911yescharacteristic
352C42C2×D4×C13911yescharacteristic
353C42#41×C13911yescharacteristic
354C23—22no—
355C23—42no—
356C23—41no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23#120×C13911yescharacteristic
361Q8—22no—
362Q8—22no—
363Q8—41no—
364Q8—41no—
365Q8—42no—
366D4—22no—
367D4—22no—
368D4—41no—
369D4—41no—
370D4—42no—
371D4—42no—
372D4—42no—
373D4—82no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—82no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4#120×C13911yescharacteristic
393C2×C4#120×C13911yescharacteristic
394C2×C4#121×C13911yescharacteristic
395C2×C4#121×C13911yescharacteristic
396C2×C4#121×C13911yescharacteristic
397C2×C4#127×C13911yescharacteristic
398C2×C4#135×C13912yes—
399C2×C4AGL(1,ℤ/8)×C13912yes—
400C8—42no—
401C8—42no—
402C8—81no—
403C22—21no—
404C22—21no—
405C22—44no—
406C22—42no—
407C22—82no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22#392×C13911yescharacteristic
414C22#449×C13912yes—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—82no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4#463×C13912yes—
425C4#495×C13911yescharacteristic
426C4#496×C13911yescharacteristic
427C2—22no—
428C2—82no—
429C2—161no—
430C2#2010×C13911yescharacteristic
431C2#2010×C13911yescharacteristic
432C2#2012×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139#127
commutator, Frattini, cosocleC2×C42C23×C139
socleC22×C139#392
prime radical#3100×C139C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3103×C139C2semidirect
3. #2398×C139C2semidirect
4. #1963×C139C2semidirect
5. #1487×C139C2semidirect
6. #1486×C139C2semidirect
7. #1274×C139C2semidirect
216. #10013C139direct (N × H)
217. C139#10013direct (N × H)
218. #3103C2×C139semidirect
220. #2398C2×C139semidirect
221. #1963C2×C139semidirect
222. #1487C2×C139semidirect
223. #1486C2×C139semidirect
224. #1274C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3103×C1392
#3100×C1392
#2398×C1392
#1963×C1392
#1487×C1392
#1486×C1392
#1274×C1392
#10013139