Finite Group Databasebeta

← C139×#9112 #48003708

Subgroups — C139×#9112 #48003708

Order 35584.

632 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
1C2×#431×C139C211yesmaximal, characteristic
2#2855×C139C211yesmaximal, characteristic
3C2×#328×C139C212yesmaximal
4#1434×C139C211yesmaximal, characteristic
5#1294×C139C212yesmaximal
6C2×C22⋊Q8×C139C2211yescharacteristic
7C22×C42×C139C2211yescharacteristic
8#431×C139—24no—
9C2×C4⋊C8×C139—21no—
10C2×C22⋊C8×C139C2212yes—
11C2×C4×C8×C139—21no—
12#391×C139C411yescharacteristic, complemented
13#391×C139C411yescharacteristic, complemented
14#389×C139C411yescharacteristic, complemented
15#389×C139C411yescharacteristic, complemented
16#387×C139—21no—
17#387×C139—21no—
18#385×C139—21no—
19#381×C139—21no—
20#380×C139C2211yescharacteristic
21C2×#95×C139—21no—
22C2×#95×C139—21no—
23C2×#95×C139C2212yes—
24#328×C139—24no—
25C22×Q8×C139C2×C411yescharacteristic
26C23×C4×C139—22no—
27C23×C4×C139D411yescharacteristic
28C23×C4×C139D411yescharacteristic
29C23×C4×C139C2311yescharacteristic
30C22×C8×C139—22no—
31C22⋊Q8×C139—22no—
32C22⋊Q8×C139—22no—
33C2×C4⋊C4×C139—21no—
34C2×C4⋊C4×C139—21no—
35C2×C4⋊C4×C139—21no—
36C2×C4⋊C4×C139C2×C411yescharacteristic
37C2×C4⋊C4×C139C2×C411yescharacteristic
38C2×C4⋊C4×C139C2×C411yescharacteristic
39C2×C22⋊C4×C139—21no—
40C2×C22⋊C4×C139—21no—
41C2×C42×C139—22no—
42C2×C42×C139—22no—
43C2×C42×C139C2×C411yescharacteristic
44C2×C42×C139C2×C411yescharacteristic
45C2×C42×C139D411yescharacteristic
46C2×C42×C139D411yescharacteristic
47C4⋊C8×C139—24no—
48C22⋊C8×C139—22no—
49C22⋊C8×C139D414yes—
50C4×C8×C139—24no—
51#95×C139—24no—
52#95×C139—21no—
53#95×C139—21no—
54#95×C139—21no—
55#95×C139—21no—
56#95×C139—21no—
57#95×C139—21no—
58#95×C139—21no—
59#95×C139—22no—
60#95×C139—22no—
61#95×C139—42no—
62C24×C139C2×D411yescharacteristic
63C2×Q8×C139—22no—
64C2×Q8×C139—41no—
65C2×Q8×C139—41no—
66C22×C4×C139—22no—
67C22×C4×C139—22no—
68C22×C4×C139—22no—
69C22×C4×C139—22no—
70C22×C4×C139—24no—
71C22×C4×C139—21no—
72C22×C4×C139—21no—
73C22×C4×C139—21no—
74C22×C4×C139—21no—
75C22×C4×C139—41no—
76C22×C4×C139—41no—
77C22×C4×C139—41no—
78C22×C4×C139—42no—
79C22×C4×C139—42no—
80C22×C4×C139—42no—
81C22×C4×C139—42no—
82C22×C4×C139—42no—
83C22×C4×C139—42no—
84C22×C4×C139C22⋊C411yescharacteristic
85C22×C4×C139C22⋊C411yescharacteristic
86C22×C4×C139C22⋊C411yescharacteristic
87C22×C4×C139C22⋊C411yescharacteristic
88C22×C4×C139SD1612yes—
89C22×C4×C139Q1612yes—
90C22×C4×C139C22×C411yescharacteristic
91C22×C4×C139C2×D411yescharacteristic
92C22×C4×C139C2×D412yes—
93C22×C4×C139#4112yes—
94C2×C8×C139—24no—
95C2×C8×C139—42no—
96C2×C8×C139—42no—
97C4⋊C4×C139—22no—
98C4⋊C4×C139—41no—
99C4⋊C4×C139—41no—
100C4⋊C4×C139—42no—
101C4⋊C4×C139—42no—
102C4⋊C4×C139—41no—
103C4⋊C4×C139—41no—
104C22⋊C4×C139—42no—
105C22⋊C4×C139—42no—
106C42×C139—22no—
107C42×C139—22no—
108C42×C139—21no—
109C42×C139—21no—
110C42×C139—21no—
111C42×C139—21no—
112C23×C139—21no—
113C23×C139—21no—
114C23×C139—21no—
115C23×C139—21no—
116C23×C139C2×C22⋊C411yescharacteristic
117C23×C139#12112yes—
118C23×C139C2×SD1611yescharacteristic
119C23×C139C2×Q1611yescharacteristic
120C23×C139#13512yes—
121Q8×C139—82no—
122C2×C4×C139—21no—
123C2×C4×C139—21no—
124C2×C4×C139—21no—
125C2×C4×C139—21no—
126C2×C4×C139—21no—
127C2×C4×C139—21no—
128C2×C4×C139—21no—
129C2×C4×C139—21no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—24no—
133C2×C4×C139—24no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—42no—
138C2×C4×C139—42no—
139C2×C4×C139—44no—
140C2×C4×C139—44no—
141C2×C4×C139—44no—
142C2×C4×C139—44no—
143C2×C4×C139—41no—
144C2×C4×C139—41no—
145C2×C4×C139—41no—
146C2×C4×C139—41no—
147C2×C4×C139—41no—
148C2×C4×C139—41no—
149C2×C4×C139—41no—
150C2×C4×C139—41no—
151C2×C4×C139—41no—
152C2×C4×C139—41no—
153C2×C4×C139—41no—
154C2×C4×C139—41no—
155C2×C4×C139—82no—
156C2×C4×C139—82no—
157C2×C4×C139—82no—
158C2×C4×C139—82no—
159C2×C4×C139#10312yes—
160C2×C4×C139#10312yes—
161C2×C4×C139#10412yes—
162C2×C4×C139C4×D412yes—
163C2×C4×C139#12011yescharacteristic
164C2×C4×C139#12311yescharacteristic
165C8×C139—44no—
166C22×C139—22no—
167C22×C139—22no—
168C22×C139—22no—
169C22×C139—21no—
170C22×C139—21no—
171C22×C139—21no—
172C22×C139—21no—
173C22×C139—22no—
174C22×C139#38611yescharacteristic
175C22×C139#41011yescharacteristic
176C22×C139#41011yescharacteristic
177C22×C139C2×#10311yescharacteristic
178C22×C139#41611yescharacteristic
179C22×C139C2×#10411yescharacteristic
180C22×C139#42111yescharacteristic
181C22×C139#46512yes—
182C22×C139#46712yes—
183C4×C139—22no—
184C4×C139—22no—
185C4×C139—22no—
186C4×C139—21no—
187C4×C139—22no—
188C4×C139—21no—
189C4×C139—41no—
190C4×C139—84no—
191C4×C139—81no—
192C4×C139—81no—
193C4×C139—81no—
194C4×C139—81no—
195C2×C139—22no—
196C2×C139—22no—
197C2×C139#150011yescharacteristic
198C2×C139#150311yescharacteristic
199C2×C139#151811yescharacteristic
200C2×C139#152111yescharacteristic
201C2×C139#187111yescharacteristic
202C2×C139#189211yescharacteristic
203C2×C139#189911yescharacteristic
204#9112C13911yesmaximal, characteristic, direct product factor, Sylow
205C139#911211yescharacteristic, direct product factor, Sylow
206C2×#431C2×C13911yescharacteristic
207#2855C2×C13911yescharacteristic
208C2×#328C2×C13912yes—
209#1434C2×C13911yescharacteristic
210#1294C2×C13912yes—
211C2×C22⋊Q8C22×C13911yescharacteristic
212C22×C42C22×C13911yescharacteristic
213#431—24no—
214C2×C4⋊C8—21no—
215C2×C22⋊C8C22×C13912yes—
216C2×C4×C8—21no—
217#391C4×C13911yescharacteristic, complemented
218#391C4×C13911yescharacteristic, complemented
219#389C4×C13911yescharacteristic, complemented
220#389C4×C13911yescharacteristic, complemented
221#387—21no—
222#387—21no—
223#385—21no—
224#381—21no—
225#380C22×C13911yescharacteristic
226C2×#95—21no—
227C2×#95—21no—
228C2×#95C22×C13912yes—
229#328—24no—
230C22×Q8C2×C4×C13911yescharacteristic
231C23×C4—22no—
232C23×C4D4×C13911yescharacteristic
233C23×C4D4×C13911yescharacteristic
234C23×C4C23×C13911yescharacteristic
235C22×C8—22no—
236C22⋊Q8—22no—
237C22⋊Q8—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×C4×C13911yescharacteristic
242C2×C4⋊C4C2×C4×C13911yescharacteristic
243C2×C4⋊C4C2×C4×C13911yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C42—22no—
247C2×C42—22no—
248C2×C42C2×C4×C13911yescharacteristic
249C2×C42C2×C4×C13911yescharacteristic
250C2×C42D4×C13911yescharacteristic
251C2×C42D4×C13911yescharacteristic
252C4⋊C8—24no—
253C22⋊C8—22no—
254C22⋊C8D4×C13914yes—
255C4×C8—24no—
256#95—24no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—22no—
265#95—22no—
266#95—42no—
267C24C2×D4×C13911yescharacteristic
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—41no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C22⋊C4×C13911yescharacteristic
290C22×C4C22⋊C4×C13911yescharacteristic
291C22×C4C22⋊C4×C13911yescharacteristic
292C22×C4C22⋊C4×C13911yescharacteristic
293C22×C4SD16×C13912yes—
294C22×C4Q16×C13912yes—
295C22×C4C22×C4×C13911yescharacteristic
296C22×C4C2×D4×C13911yescharacteristic
297C22×C4C2×D4×C13912yes—
298C22×C4#41×C13912yes—
299C2×C8—24no—
300C2×C8—42no—
301C2×C8—42no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C42—22no—
312C42—22no—
313C42—21no—
314C42—21no—
315C42—21no—
316C42—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C22⋊C4×C13911yescharacteristic
322C23#121×C13912yes—
323C23C2×SD16×C13911yescharacteristic
324C23C2×Q16×C13911yescharacteristic
325C23#135×C13912yes—
326Q8—82no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4#103×C13912yes—
365C2×C4#103×C13912yes—
366C2×C4#104×C13912yes—
367C2×C4C4×D4×C13912yes—
368C2×C4#120×C13911yescharacteristic
369C2×C4#123×C13911yescharacteristic
370C8—44no—
371C22—22no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22#386×C13911yescharacteristic
380C22#410×C13911yescharacteristic
381C22#410×C13911yescharacteristic
382C22C2×#103×C13911yescharacteristic
383C22#416×C13911yescharacteristic
384C22C2×#104×C13911yescharacteristic
385C22#421×C13911yescharacteristic
386C22#465×C13912yes—
387C22#467×C13912yes—
388C4—22no—
389C4—22no—
390C4—22no—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—41no—
395C4—84no—
396C4—81no—
397C4—81no—
398C4—81no—
399C4—81no—
400C2—22no—
401C2—22no—
402C2#1500×C13911yescharacteristic
403C2#1503×C13911yescharacteristic
404C2#1518×C13911yescharacteristic
405C2#1521×C13911yescharacteristic
406C2#1871×C13911yescharacteristic
407C2#1892×C13911yescharacteristic
408C2#1899×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC24×C139C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
12. #391×C139C4semidirect
13. #391×C139C4semidirect
14. #389×C139C4semidirect
15. #389×C139C4semidirect
204. #9112C139direct (N × H)
205. C139#9112direct (N × H)
217. #391C4×C139semidirect
218. #391C4×C139semidirect
219. #389C4×C139semidirect
220. #389C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#431×C1392
#2855×C1392
C2×#328×C1392
#1434×C1392
#1294×C1392
#9112139