Finite Group Databasebeta

← C139×#10186 #48004782

Subgroups — C139×#10186 #48004782

Order 35584.

528 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3229×C139C211yesmaximal, characteristic, complemented
2#3077×C139C211yesmaximal, characteristic
3C2×#461×C139C211yesmaximal, characteristic
4#1546×C139C211yesmaximal, characteristic, complemented
5#1481×C139C211yesmaximal, characteristic, complemented
6#1460×C139C211yesmaximal, characteristic
7#1301×C139C211yesmaximal, characteristic, complemented
8C22×SD16×C139—21no—
9#533×C139C2211yescharacteristic
10C2×C4⋊Q8×C139C2211yescharacteristic
11C2×C4×D4×C139C2211yescharacteristic
12#498×C139—21no—
13#487×C139—21no—
14#483×C139—22no—
15#478×C139—22no—
16#476×C139—21no—
17#475×C139—22no—
18#474×C139—21no—
19#461×C139—22no—
20#461×C139—22no—
21#431×C139C2211yescharacteristic
22#431×C139C2211yescharacteristic
23#428×C139—21no—
24#423×C139C2211yescharacteristic
25C2×C4⋊C8×C139C2211yescharacteristic
26#418×C139—21no—
27C2×#103×C139—21no—
28#332×C139—22no—
29Q8⋊C8×C139—22no—
30#323×C139—22no—
31C22×Q8×C139—21no—
32C22×D4×C139D411yescharacteristic
33C23×C4×C139—21no—
34C2×SD16×C139—24no—
35C2×SD16×C139—42no—
36C2×SD16×C139—42no—
37C2×M16×C139—21no—
38C22×C8×C139—21no—
39C4⋊Q8×C139—21no—
40C4⋊Q8×C139—21no—
41C4⋊Q8×C139—21no—
42C4⋊Q8×C139D412yes—
43C4⋊Q8×C139D411yescharacteristic
44C4⋊Q8×C139D411yescharacteristic
45#125×C139—21no—
46C22⋊Q8×C139—21no—
47C22⋊Q8×C139—21no—
48C4×Q8×C139—21no—
49C4×Q8×C139—21no—
50C4×D4×C139—21no—
51C4×D4×C139—21no—
52C4×D4×C139—21no—
53C4×D4×C139—21no—
54#117×C139—21no—
55C2×C4⋊C4×C139—21no—
56C2×C4⋊C4×C139—21no—
57C2×C4⋊C4×C139D411yescharacteristic
58C2×C22⋊C4×C139—21no—
59C2×C42×C139C2311yescharacteristic
60#107×C139—22no—
61#106×C139—22no—
62#106×C139—24no—
63C4⋊C8×C139—21no—
64C4⋊C8×C139—21no—
65C4⋊C8×C139—21no—
66C4⋊C8×C139—21no—
67C4⋊C8×C139D412yes—
68C4⋊C8×C139D412yes—
69#103×C139—24no—
70#103×C139—24no—
71#102×C139—22no—
72#102×C139—22no—
73C22⋊C8×C139—21no—
74C22⋊C8×C139D412yes—
75C4×C8×C139—21no—
76C4×C8×C139—21no—
77C24×C139—21no—
78C2×Q8×C139—21no—
79C2×Q8×C139—22no—
80C2×Q8×C139—21no—
81C2×Q8×C139—41no—
82C2×Q8×C139—41no—
83C2×Q8×C139—41no—
84C2×Q8×C139—41no—
85C2×Q8×C139—41no—
86C2×D4×C139—21no—
87C2×D4×C139—21no—
88C2×D4×C139—21no—
89C2×D4×C139—21no—
90C2×D4×C139—21no—
91C2×D4×C139SD1612yes—
92C22×C4×C139—21no—
93C22×C4×C139—41no—
94C22×C4×C139—41no—
95C22×C4×C139—41no—
96C22×C4×C139—82no—
97C22×C4×C139C2×D411yescharacteristic
98C22×C4×C139C2×D411yescharacteristic
99C22×C4×C139#4111yescharacteristic
100SD16×C139—48no—
101M16×C139—41no—
102M16×C139—41no—
103C2×C8×C139—22no—
104C2×C8×C139—22no—
105C2×C8×C139—22no—
106C2×C8×C139—41no—
107C2×C8×C139—41no—
108C2×C8×C139—41no—
109C4⋊C4×C139—21no—
110C4⋊C4×C139—21no—
111C4⋊C4×C139—21no—
112C4⋊C4×C139—22no—
113C4⋊C4×C139—21no—
114C4⋊C4×C139—21no—
115C4⋊C4×C139—22no—
116C4⋊C4×C139—21no—
117C4⋊C4×C139—41no—
118C4⋊C4×C139—41no—
119C4⋊C4×C139—41no—
120C4⋊C4×C139—41no—
121C22⋊C4×C139—41no—
122C22⋊C4×C139—41no—
123C22⋊C4×C139—41no—
124C42×C139—41no—
125C42×C139C2×D411yescharacteristic
126C42×C139C2×D411yescharacteristic
127C42×C139C2×D411yescharacteristic
128C42×C139C2×D411yescharacteristic
129C23×C139—22no—
130C23×C139—41no—
131C23×C139—41no—
132C23×C139—81no—
133C23×C139—81no—
134C23×C139#12111yescharacteristic
135Q8×C139—42no—
136Q8×C139—42no—
137Q8×C139—42no—
138Q8×C139—42no—
139Q8×C139—81no—
140Q8×C139—81no—
141D4×C139—22no—
142D4×C139—22no—
143D4×C139—41no—
144D4×C139—41no—
145C2×C4×C139—22no—
146C2×C4×C139—41no—
147C2×C4×C139—41no—
148C2×C4×C139—41no—
149C2×C4×C139—41no—
150C2×C4×C139—42no—
151C2×C4×C139—82no—
152C2×C4×C139—81no—
153C2×C4×C139—81no—
154C2×C4×C139—82no—
155C2×C4×C139—81no—
156C2×C4×C139#12011yescharacteristic
157C2×C4×C139#12011yescharacteristic
158C2×C4×C139#12011yescharacteristic
159C2×C4×C139#12111yescharacteristic
160C2×C4×C139#12111yescharacteristic
161C2×C4×C139#12711yescharacteristic
162C2×C4×C139C2×SD1611yescharacteristic
163C2×C4×C139#13511yescharacteristic
164C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C139#13711yescharacteristic
166C8×C139—42no—
167C8×C139—42no—
168C8×C139—42no—
169C8×C139—81no—
170C22×C139—21no—
171C22×C139—21no—
172C22×C139—42no—
173C22×C139—82no—
174C22×C139—82no—
175C22×C139—81no—
176C22×C139—81no—
177C22×C139#39211yescharacteristic
178C22×C139#46511yescharacteristic
179C22×C139#46811yescharacteristic
180C4×C139—21no—
181C4×C139—21no—
182C4×C139—21no—
183C4×C139—82no—
184C4×C139—81no—
185C4×C139—81no—
186C4×C139—81no—
187C4×C139#44811yescharacteristic
188C4×C139#44911yescharacteristic
189C4×C139#45011yescharacteristic
190C4×C139#45211yescharacteristic
191C4×C139#47112yes—
192C2×C139—21no—
193C2×C139—21no—
194C2×C139—82no—
195C2×C139#200011yescharacteristic
196C2×C139#200911yescharacteristic
197C2×C139#201911yescharacteristic
198#10186C13911yesmaximal, characteristic, direct product factor, Sylow
199C139#1018611yescharacteristic, direct product factor, Sylow
200#3229C2×C13911yescharacteristic, complemented
201#3077C2×C13911yescharacteristic
202C2×#461C2×C13911yescharacteristic
203#1546C2×C13911yescharacteristic, complemented
204#1481C2×C13911yescharacteristic, complemented
205#1460C2×C13911yescharacteristic
206#1301C2×C13911yescharacteristic, complemented
207C22×SD16—21no—
208#533C22×C13911yescharacteristic
209C2×C4⋊Q8C22×C13911yescharacteristic
210C2×C4×D4C22×C13911yescharacteristic
211#498—21no—
212#487—21no—
213#483—22no—
214#478—22no—
215#476—21no—
216#475—22no—
217#474—21no—
218#461—22no—
219#461—22no—
220#431C22×C13911yescharacteristic
221#431C22×C13911yescharacteristic
222#428—21no—
223#423C22×C13911yescharacteristic
224C2×C4⋊C8C22×C13911yescharacteristic
225#418—21no—
226C2×#103—21no—
227#332—22no—
228Q8⋊C8—22no—
229#323—22no—
230C22×Q8—21no—
231C22×D4D4×C13911yescharacteristic
232C23×C4—21no—
233C2×SD16—24no—
234C2×SD16—42no—
235C2×SD16—42no—
236C2×M16—21no—
237C22×C8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8D4×C13912yes—
242C4⋊Q8D4×C13911yescharacteristic
243C4⋊Q8D4×C13911yescharacteristic
244#125—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253#117—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C13911yescharacteristic
257C2×C22⋊C4—21no—
258C2×C42C23×C13911yescharacteristic
259#107—22no—
260#106—22no—
261#106—24no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8D4×C13912yes—
267C4⋊C8D4×C13912yes—
268#103—24no—
269#103—24no—
270#102—22no—
271#102—22no—
272C22⋊C8—21no—
273C22⋊C8D4×C13912yes—
274C4×C8—21no—
275C4×C8—21no—
276C24—21no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—21no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4SD16×C13912yes—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—82no—
296C22×C4C2×D4×C13911yescharacteristic
297C22×C4C2×D4×C13911yescharacteristic
298C22×C4#41×C13911yescharacteristic
299SD16—48no—
300M16—41no—
301M16—41no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—41no—
324C42C2×D4×C13911yescharacteristic
325C42C2×D4×C13911yescharacteristic
326C42C2×D4×C13911yescharacteristic
327C42C2×D4×C13911yescharacteristic
328C23—22no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23#121×C13911yescharacteristic
334Q8—42no—
335Q8—42no—
336Q8—42no—
337Q8—42no—
338Q8—81no—
339Q8—81no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4#120×C13911yescharacteristic
356C2×C4#120×C13911yescharacteristic
357C2×C4#120×C13911yescharacteristic
358C2×C4#121×C13911yescharacteristic
359C2×C4#121×C13911yescharacteristic
360C2×C4#127×C13911yescharacteristic
361C2×C4C2×SD16×C13911yescharacteristic
362C2×C4#135×C13911yescharacteristic
363C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
364C2×C4#137×C13911yescharacteristic
365C8—42no—
366C8—42no—
367C8—42no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—82no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22#392×C13911yescharacteristic
377C22#465×C13911yescharacteristic
378C22#468×C13911yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4#448×C13911yescharacteristic
387C4#449×C13911yescharacteristic
388C4#450×C13911yescharacteristic
389C4#452×C13911yescharacteristic
390C4#471×C13912yes—
391C2—21no—
392C2—21no—
393C2—82no—
394C2#2000×C13911yescharacteristic
395C2#2009×C13911yescharacteristic
396C2#2019×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#392
commutator, Frattini, cosocleC2×C42C23×C139
prime radicalC22×D4×C139D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3229×C139C2semidirect
4. #1546×C139C2semidirect
5. #1481×C139C2semidirect
7. #1301×C139C2semidirect
198. #10186C139direct (N × H)
199. C139#10186direct (N × H)
200. #3229C2×C139semidirect
203. #1546C2×C139semidirect
204. #1481C2×C139semidirect
206. #1301C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3229×C1392
#3077×C1392
C2×#461×C1392
#1546×C1392
#1481×C1392
#1460×C1392
#1301×C1392
#10186139