Finite Group Databasebeta

← C139×#9367 #48003963

Subgroups — C139×#9367 #48003963

Order 35584.

542 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3094×C139C211yesmaximal, characteristic
2#2346×C139C211yesmaximal, characteristic, complemented
3#1964×C139C211yesmaximal, characteristic
4#1826×C139C211yesmaximal, characteristic, complemented
5#1507×C139C211yesmaximal, characteristic
6#1305×C139C211yesmaximal, characteristic, complemented
7#1297×C139C211yesmaximal, characteristic, complemented
8C2×#121×C139C2211yescharacteristic
9C2×#117×C139C2211yescharacteristic
10#482×C139—22no—
11#481×C139—21no—
12#480×C139—21no—
13#428×C139C412yescomplemented
14#418×C139C412yescomplemented
15C2×#99×C139—22no—
16#407×C139C2211yescharacteristic
17#407×C139C2211yescharacteristic
18#389×C139—21no—
19#388×C139—22no—
20#382×C139—21no—
21#380×C139C2211yescharacteristic
22C4×C4⋊C4×C139—21no—
23C4×C22⋊C4×C139C2211yescharacteristic
24C4×C22⋊C4×C139C2211yescharacteristic
25#376×C139—21no—
26#339×C139—22no—
27#327×C139—21no—
28#327×C139—21no—
29C22×D4×C139—21no—
30C22×D4×C139C2×C411yescharacteristic
31C23×C4×C139C2311yescharacteristic
32C2×M16×C139—21no—
33C2×M16×C139C2×C412yes—
34#121×C139—21no—
35#121×C139—21no—
36#121×C139—21no—
37#121×C139—21no—
38#117×C139—21no—
39#117×C139—21no—
40#117×C139C2×C412yes—
41#117×C139D412yes—
42C2×C4⋊C4×C139—21no—
43C2×C4⋊C4×C139—22no—
44C2×C4⋊C4×C139C2×C411yescharacteristic
45C2×C4⋊C4×C139D411yescharacteristic
46C2×C4⋊C4×C139D411yescharacteristic
47C2×C22⋊C4×C139—21no—
48C2×C22⋊C4×C139—21no—
49C2×C22⋊C4×C139—21no—
50C2×C22⋊C4×C139—21no—
51C2×C22⋊C4×C139D412yes—
52C2×C42×C139—21no—
53C2×C42×C139—22no—
54C2×C42×C139—21no—
55C2×C42×C139—21no—
56#107×C139—22no—
57#106×C139—22no—
58#102×C139—22no—
59#102×C139—22no—
60#99×C139—44no—
61C22⋊C8×C139—21no—
62C22⋊C8×C139—21no—
63C22⋊C8×C139—21no—
64C22⋊C8×C139—21no—
65#95×C139—22no—
66#95×C139—22no—
67#95×C139—21no—
68#95×C139—21no—
69#95×C139D411yescharacteristic
70#95×C139D411yescharacteristic
71C24×C139—21no—
72C24×C139C2×D411yescharacteristic
73C2×D4×C139—21no—
74C2×D4×C139—21no—
75C2×D4×C139—42no—
76C2×D4×C139—42no—
77C2×D4×C139—42no—
78C2×D4×C139—41no—
79C2×D4×C139—41no—
80C22×C4×C139—21no—
81C22×C4×C139—21no—
82C22×C4×C139—21no—
83C22×C4×C139—21no—
84C22×C4×C139—22no—
85C22×C4×C139—21no—
86C22×C4×C139—42no—
87C22×C4×C139—41no—
88C22×C4×C139C22×C411yescharacteristic
89C22×C4×C139C2×D411yescharacteristic
90C22×C4×C139C2×D411yescharacteristic
91C22×C4×C139C2×D411yescharacteristic
92C22×C4×C139#4111yescharacteristic
93C22×C4×C139#4111yescharacteristic
94M16×C139—42no—
95M16×C139—42no—
96C2×C8×C139—22no—
97C2×C8×C139—41no—
98C4⋊C4×C139—21no—
99C4⋊C4×C139—21no—
100C4⋊C4×C139—21no—
101C4⋊C4×C139—21no—
102C4⋊C4×C139—42no—
103C4⋊C4×C139—82no—
104C4⋊C4×C139C22⋊C412yes—
105C4⋊C4×C139C22⋊C412yes—
106C22⋊C4×C139—22no—
107C22⋊C4×C139—22no—
108C22⋊C4×C139—22no—
109C22⋊C4×C139—42no—
110C22⋊C4×C139—41no—
111C22⋊C4×C139—41no—
112C22⋊C4×C139—41no—
113C22⋊C4×C139—42no—
114C42×C139—22no—
115C42×C139—22no—
116C42×C139—42no—
117C42×C139—44no—
118C42×C139—42no—
119C23×C139—21no—
120C23×C139—21no—
121C23×C139—41no—
122C23×C139—41no—
123C23×C139—42no—
124C23×C139—41no—
125C23×C139—81no—
126C23×C139—81no—
127C23×C139C4×D411yescharacteristic
128C23×C139#12011yescharacteristic
129C23×C139#12111yescharacteristic
130D4×C139—42no—
131D4×C139—81no—
132D4×C139—82no—
133D4×C139—81no—
134D4×C139—81no—
135C2×C4×C139—22no—
136C2×C4×C139—22no—
137C2×C4×C139—22no—
138C2×C4×C139—22no—
139C2×C4×C139—22no—
140C2×C4×C139—22no—
141C2×C4×C139—41no—
142C2×C4×C139—41no—
143C2×C4×C139—41no—
144C2×C4×C139—41no—
145C2×C4×C139—42no—
146C2×C4×C139—41no—
147C2×C4×C139—41no—
148C2×C4×C139—41no—
149C2×C4×C139—41no—
150C2×C4×C139—42no—
151C2×C4×C139—42no—
152C2×C4×C139—41no—
153C2×C4×C139—42no—
154C2×C4×C139—42no—
155C2×C4×C139—41no—
156C2×C4×C139—42no—
157C2×C4×C139—41no—
158C2×C4×C139—81no—
159C2×C4×C139—81no—
160C2×C4×C139C2×C22⋊C411yescharacteristic
161C2×C4×C139C4×D411yescharacteristic
162C2×C4×C139#12111yescharacteristic
163C2×C4×C139#12311yescharacteristic
164C8×C139—42no—
165C8×C139—81no—
166C22×C139—21no—
167C22×C139—21no—
168C22×C139—21no—
169C22×C139—21no—
170C22×C139—21no—
171C22×C139—21no—
172C22×C139—21no—
173C22×C139—21no—
174C22×C139—81no—
175C22×C139—81no—
176C22×C139—81no—
177C22×C139—81no—
178C22×C139—81no—
179C22×C139—162no—
180C22×C139#38611yescharacteristic
181C22×C139#45311yescharacteristic
182C22×C139#45411yescharacteristic
183C4×C139—21no—
184C4×C139—21no—
185C4×C139—21no—
186C4×C139—42no—
187C4×C139—42no—
188C4×C139—42no—
189C4×C139—81no—
190C4×C139—82no—
191C4×C139—82no—
192C4×C139—81no—
193C4×C139#41012yes—
194C2×C139—21no—
195C2×C139—21no—
196C2×C139—41no—
197C2×C139—41no—
198C2×C139—161no—
199C2×C139#188311yescharacteristic
200C2×C139#189911yescharacteristic
201C2×C139#190611yescharacteristic
202#9367C13911yesmaximal, characteristic, direct product factor, Sylow
203C139#936711yescharacteristic, direct product factor, Sylow
204#3094C2×C13911yescharacteristic
205#2346C2×C13911yescharacteristic, complemented
206#1964C2×C13911yescharacteristic
207#1826C2×C13911yescharacteristic, complemented
208#1507C2×C13911yescharacteristic
209#1305C2×C13911yescharacteristic, complemented
210#1297C2×C13911yescharacteristic, complemented
211C2×#121C22×C13911yescharacteristic
212C2×#117C22×C13911yescharacteristic
213#482—22no—
214#481—21no—
215#480—21no—
216#428C4×C13912yescomplemented
217#418C4×C13912yescomplemented
218C2×#99—22no—
219#407C22×C13911yescharacteristic
220#407C22×C13911yescharacteristic
221#389—21no—
222#388—22no—
223#382—21no—
224#380C22×C13911yescharacteristic
225C4×C4⋊C4—21no—
226C4×C22⋊C4C22×C13911yescharacteristic
227C4×C22⋊C4C22×C13911yescharacteristic
228#376—21no—
229#339—22no—
230#327—21no—
231#327—21no—
232C22×D4—21no—
233C22×D4C2×C4×C13911yescharacteristic
234C23×C4C23×C13911yescharacteristic
235C2×M16—21no—
236C2×M16C2×C4×C13912yes—
237#121—21no—
238#121—21no—
239#121—21no—
240#121—21no—
241#117—21no—
242#117—21no—
243#117C2×C4×C13912yes—
244#117D4×C13912yes—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4C2×C4×C13911yescharacteristic
248C2×C4⋊C4D4×C13911yescharacteristic
249C2×C4⋊C4D4×C13911yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4D4×C13912yes—
255C2×C42—21no—
256C2×C42—22no—
257C2×C42—21no—
258C2×C42—21no—
259#107—22no—
260#106—22no—
261#102—22no—
262#102—22no—
263#99—44no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268#95—22no—
269#95—22no—
270#95—21no—
271#95—21no—
272#95D4×C13911yescharacteristic
273#95D4×C13911yescharacteristic
274C24—21no—
275C24C2×D4×C13911yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—41no—
282C2×D4—41no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—42no—
290C22×C4—41no—
291C22×C4C22×C4×C13911yescharacteristic
292C22×C4C2×D4×C13911yescharacteristic
293C22×C4C2×D4×C13911yescharacteristic
294C22×C4C2×D4×C13911yescharacteristic
295C22×C4#41×C13911yescharacteristic
296C22×C4#41×C13911yescharacteristic
297M16—42no—
298M16—42no—
299C2×C8—22no—
300C2×C8—41no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—42no—
306C4⋊C4—82no—
307C4⋊C4C22⋊C4×C13912yes—
308C4⋊C4C22⋊C4×C13912yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—42no—
317C42—22no—
318C42—22no—
319C42—42no—
320C42—44no—
321C42—42no—
322C23—21no—
323C23—21no—
324C23—41no—
325C23—41no—
326C23—42no—
327C23—41no—
328C23—81no—
329C23—81no—
330C23C4×D4×C13911yescharacteristic
331C23#120×C13911yescharacteristic
332C23#121×C13911yescharacteristic
333D4—42no—
334D4—81no—
335D4—82no—
336D4—81no—
337D4—81no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4C2×C22⋊C4×C13911yescharacteristic
364C2×C4C4×D4×C13911yescharacteristic
365C2×C4#121×C13911yescharacteristic
366C2×C4#123×C13911yescharacteristic
367C8—42no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—162no—
383C22#386×C13911yescharacteristic
384C22#453×C13911yescharacteristic
385C22#454×C13911yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—42no—
391C4—42no—
392C4—81no—
393C4—82no—
394C4—82no—
395C4—81no—
396C4#410×C13912yes—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—161no—
402C2#1883×C13911yescharacteristic
403C2#1899×C13911yescharacteristic
404C2#1906×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC2×#121×C139C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2346×C139C2semidirect
4. #1826×C139C2semidirect
6. #1305×C139C2semidirect
7. #1297×C139C2semidirect
13. #428×C139C4semidirect
14. #418×C139C4semidirect
202. #9367C139direct (N × H)
203. C139#9367direct (N × H)
205. #2346C2×C139semidirect
207. #1826C2×C139semidirect
209. #1305C2×C139semidirect
210. #1297C2×C139semidirect
216. #428C4×C139semidirect
217. #418C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3094×C1392
#2346×C1392
#1964×C1392
#1826×C1392
#1507×C1392
#1305×C1392
#1297×C1392
#9367139