Finite Group Databasebeta

← C139×#9148 #48003744

Subgroups — C139×#9148 #48003744

Order 35584.

800 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854×C139C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C139C211yesmaximal, characteristic, complemented
3#1817×C139C211yesmaximal, characteristic, complemented
4C2×#327×C139C212yesmaximal
5#1294×C139C212yesmaximal, complemented
6C2×#123×C139—21no—
7C2×#121×C139C2211yescharacteristic
8C22×C4⋊C4×C139—21no—
9C22×C42×C139—21no—
10C22×C42×C139C2211yescharacteristic
11C2×C22⋊C8×C139C2212yes—
12#390×C139C412yescomplemented
13#389×C139C412yescomplemented
14#388×C139—22no—
15#386×C139—21no—
16#380×C139C2211yescharacteristic
17C4×C4⋊C4×C139—24no—
18C2×#95×C139C2212yes—
19#336×C139—22no—
20#327×C139—24no—
21C22×D4×C139—21no—
22C22×D4×C139C2×C411yescharacteristic
23C23×C4×C139—22no—
24C23×C4×C139D411yescharacteristic
25C23×C4×C139D411yescharacteristic
26C23×C4×C139C2311yescharacteristic
27C22×C8×C139—22no—
28#123×C139—42no—
29#123×C139—42no—
30#121×C139—22no—
31#121×C139—22no—
32C2×C4⋊C4×C139—28no—
33C2×C4⋊C4×C139—24no—
34C2×C4⋊C4×C139—22no—
35C2×C4⋊C4×C139C2×C411yescharacteristic
36C2×C4⋊C4×C139C2×C412yes—
37C2×C22⋊C4×C139—21no—
38C2×C22⋊C4×C139—22no—
39C2×C22⋊C4×C139—22no—
40C2×C22⋊C4×C139—21no—
41C2×C42×C139—22no—
42C2×C42×C139—22no—
43C2×C42×C139—24no—
44C2×C42×C139—42no—
45C2×C42×C139—42no—
46C2×C42×C139C2×C412yes—
47C2×C42×C139D412yes—
48C22⋊C8×C139—22no—
49C22⋊C8×C139—22no—
50#95×C139—22no—
51#95×C139—22no—
52#95×C139—21no—
53#95×C139D414yes—
54C24×C139—21no—
55C24×C139C2×D411yescharacteristic
56C2×D4×C139—22no—
57C2×D4×C139—42no—
58C2×D4×C139—41no—
59C2×D4×C139—41no—
60C2×D4×C139—41no—
61C2×D4×C139—41no—
62C2×D4×C139—41no—
63C2×D4×C139—41no—
64C22×C4×C139—21no—
65C22×C4×C139—21no—
66C22×C4×C139—21no—
67C22×C4×C139—21no—
68C22×C4×C139—21no—
69C22×C4×C139—21no—
70C22×C4×C139—24no—
71C22×C4×C139—28no—
72C22×C4×C139—24no—
73C22×C4×C139—22no—
74C22×C4×C139—21no—
75C22×C4×C139—42no—
76C22×C4×C139—44no—
77C22×C4×C139—42no—
78C22×C4×C139—42no—
79C22×C4×C139C22⋊C412yes—
80C22×C4×C139C22⋊C412yes—
81C22×C4×C139D812yes—
82C22×C4×C139SD1612yes—
83C22×C4×C139C22×C411yescharacteristic
84C22×C4×C139C2×D411yescharacteristic
85C22×C4×C139C2×D412yes—
86C22×C4×C139#4112yes—
87C2×C8×C139—44no—
88C2×C8×C139—42no—
89C4⋊C4×C139—216no—
90C4⋊C4×C139—22no—
91C4⋊C4×C139—42no—
92C4⋊C4×C139—44no—
93C22⋊C4×C139—41no—
94C22⋊C4×C139—41no—
95C22⋊C4×C139—44no—
96C22⋊C4×C139—44no—
97C22⋊C4×C139—42no—
98C42×C139—24no—
99C42×C139—24no—
100C42×C139—48no—
101C23×C139—22no—
102C23×C139—22no—
103C23×C139—41no—
104C23×C139—42no—
105C23×C139—41no—
106C23×C139—41no—
107C23×C139—42no—
108C23×C139C2×C22⋊C411yescharacteristic
109C23×C139#12011yescharacteristic
110C23×C139#12311yescharacteristic
111C23×C139C2×D811yescharacteristic
112C23×C139C2×SD1611yescharacteristic
113C23×C139AGL(1,ℤ/8)11yescharacteristic
114C23×C139#13711yescharacteristic
115D4×C139—82no—
116D4×C139—81no—
117D4×C139—81no—
118D4×C139—81no—
119D4×C139—81no—
120C2×C4×C139—24no—
121C2×C4×C139—24no—
122C2×C4×C139—22no—
123C2×C4×C139—22no—
124C2×C4×C139—22no—
125C2×C4×C139—22no—
126C2×C4×C139—22no—
127C2×C4×C139—22no—
128C2×C4×C139—22no—
129C2×C4×C139—22no—
130C2×C4×C139—22no—
131C2×C4×C139—22no—
132C2×C4×C139—28no—
133C2×C4×C139—42no—
134C2×C4×C139—42no—
135C2×C4×C139—44no—
136C2×C4×C139—48no—
137C2×C4×C139—48no—
138C2×C4×C139—44no—
139C2×C4×C139—41no—
140C2×C4×C139—42no—
141C2×C4×C139—42no—
142C2×C4×C139—41no—
143C2×C4×C139—41no—
144C2×C4×C139—42no—
145C2×C4×C139#10214yes—
146C2×C4×C139#10414yes—
147C2×C4×C139C4×D412yes—
148C2×C4×C139#12112yes—
149C8×C139—82no—
150C22×C139—21no—
151C22×C139—21no—
152C22×C139—21no—
153C22×C139—21no—
154C22×C139—22no—
155C22×C139—22no—
156C22×C139—22no—
157C22×C139—22no—
158C22×C139—81no—
159C22×C139—81no—
160C22×C139—81no—
161C22×C139—82no—
162C22×C139—82no—
163C22×C139#38611yescharacteristic
164C22×C139#41012yes—
165C22×C139C2×#10211yescharacteristic
166C22×C139#41711yescharacteristic
167C22×C139C2×#10412yes—
168C22×C139#44711yescharacteristic
169C22×C139#44811yescharacteristic
170C22×C139#48011yescharacteristic
171C22×C139#48111yescharacteristic
172C4×C139—24no—
173C4×C139—24no—
174C4×C139—22no—
175C4×C139—22no—
176C4×C139—48no—
177C4×C139—81no—
178C4×C139—82no—
179C2×C139—21no—
180C2×C139—21no—
181C2×C139—21no—
182C2×C139—21no—
183C2×C139—161no—
184C2×C139#150212yes—
185C2×C139#150912yes—
186C2×C139#187411yescharacteristic
187C2×C139#189611yescharacteristic
188C2×C139#189911yescharacteristic
189#9148C13911yesmaximal, characteristic, direct product factor, Sylow
190C139#914811yescharacteristic, direct product factor, Sylow
191#2854C2×C13911yescharacteristic
192C2×C4×C4⋊C4C2×C13911yescharacteristic, complemented
193#1817C2×C13911yescharacteristic, complemented
194C2×#327C2×C13912yes—
195#1294C2×C13912yescomplemented
196C2×#123—21no—
197C2×#121C22×C13911yescharacteristic
198C22×C4⋊C4—21no—
199C22×C42—21no—
200C22×C42C22×C13911yescharacteristic
201C2×C22⋊C8C22×C13912yes—
202#390C4×C13912yescomplemented
203#389C4×C13912yescomplemented
204#388—22no—
205#386—21no—
206#380C22×C13911yescharacteristic
207C4×C4⋊C4—24no—
208C2×#95C22×C13912yes—
209#336—22no—
210#327—24no—
211C22×D4—21no—
212C22×D4C2×C4×C13911yescharacteristic
213C23×C4—22no—
214C23×C4D4×C13911yescharacteristic
215C23×C4D4×C13911yescharacteristic
216C23×C4C23×C13911yescharacteristic
217C22×C8—22no—
218#123—42no—
219#123—42no—
220#121—22no—
221#121—22no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—28no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4C2×C4×C13911yescharacteristic
226C2×C4⋊C4C2×C4×C13912yes—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—21no—
231C2×C42—22no—
232C2×C42—22no—
233C2×C42—24no—
234C2×C42—42no—
235C2×C42—42no—
236C2×C42C2×C4×C13912yes—
237C2×C42D4×C13912yes—
238C22⋊C8—22no—
239C22⋊C8—22no—
240#95—22no—
241#95—22no—
242#95—21no—
243#95D4×C13914yes—
244C24—21no—
245C24C2×D4×C13911yescharacteristic
246C2×D4—22no—
247C2×D4—42no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—24no—
261C22×C4—28no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—42no—
266C22×C4—44no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4C22⋊C4×C13912yes—
270C22×C4C22⋊C4×C13912yes—
271C22×C4D8×C13912yes—
272C22×C4SD16×C13912yes—
273C22×C4C22×C4×C13911yescharacteristic
274C22×C4C2×D4×C13911yescharacteristic
275C22×C4C2×D4×C13912yes—
276C22×C4#41×C13912yes—
277C2×C8—44no—
278C2×C8—42no—
279C4⋊C4—216no—
280C4⋊C4—22no—
281C4⋊C4—42no—
282C4⋊C4—44no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—44no—
286C22⋊C4—44no—
287C22⋊C4—42no—
288C42—24no—
289C42—24no—
290C42—48no—
291C23—22no—
292C23—22no—
293C23—42no—
294C23—41no—
295C23—41no—
296C23—42no—
297C23—41no—
298C23C2×C22⋊C4×C13911yescharacteristic
299C23#120×C13911yescharacteristic
300C23#123×C13911yescharacteristic
301C23C2×D8×C13911yescharacteristic
302C23C2×SD16×C13911yescharacteristic
303C23AGL(1,ℤ/8)×C13911yescharacteristic
304C23#137×C13911yescharacteristic
305D4—82no—
306D4—81no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—28no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—48no—
326C2×C4—48no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4#102×C13914yes—
336C2×C4#104×C13914yes—
337C2×C4C4×D4×C13912yes—
338C2×C4#121×C13912yes—
339C8—82no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—82no—
349C22—82no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22#386×C13911yescharacteristic
354C22#410×C13912yes—
355C22C2×#102×C13911yescharacteristic
356C22#417×C13911yescharacteristic
357C22C2×#104×C13912yes—
358C22#447×C13911yescharacteristic
359C22#448×C13911yescharacteristic
360C22#480×C13911yescharacteristic
361C22#481×C13911yescharacteristic
362C4—24no—
363C4—24no—
364C4—22no—
365C4—22no—
366C4—48no—
367C4—82no—
368C4—81no—
369C2—21no—
370C2—21no—
371C2—21no—
372C2—21no—
373C2—161no—
374C2#1502×C13912yes—
375C2#1509×C13912yes—
376C2#1874×C13911yescharacteristic
377C2#1896×C13911yescharacteristic
378C2#1899×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC2×#121×C139C22
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
2. C2×C4×C4⋊C4×C139C2semidirect
3. #1817×C139C2semidirect
5. #1294×C139C2semidirect
12. #390×C139C4semidirect
13. #389×C139C4semidirect
189. #9148C139direct (N × H)
190. C139#9148direct (N × H)
192. C2×C4×C4⋊C4C2×C139semidirect
193. #1817C2×C139semidirect
195. #1294C2×C139semidirect
202. #390C4×C139semidirect
203. #389C4×C139semidirect

Maximal subgroups

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

subgroupindex
#2854×C1392
C2×C4×C4⋊C4×C1392
#1817×C1392
C2×#327×C1392
#1294×C1392
#9148139