Finite Group Databasebeta

← C139×#9326 #48003922

Subgroups — C139×#9326 #48003922

Order 35584.

574 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3112×C139C211yesmaximal, characteristic
2#2276×C139C211yesmaximal, characteristic, complemented
3#1980×C139C211yesmaximal, characteristic
4#1505×C139C211yesmaximal, characteristic
5#1491×C139C211yesmaximal, characteristic, complemented
6#1300×C139C211yesmaximal, characteristic, complemented
7#1285×C139C211yesmaximal, characteristic, complemented
8#532×C139C2211yescharacteristic
9C2×C4×Q8×C139—21no—
10C2×C4×Q8×C139C2211yescharacteristic
11#480×C139—21no—
12#477×C139C412yescomplemented
13#460×C139C412yescomplemented
14#448×C139—21no—
15#440×C139—22no—
16#432×C139C2211yescharacteristic
17#432×C139C2211yescharacteristic
18C2×#104×C139—22no—
19C4×M16×C139C2211yescharacteristic
20C4×C4⋊C4×C139—21no—
21C4×C4⋊C4×C139—22no—
22C4×C4⋊C4×C139—21no—
23C4×C4⋊C4×C139C2211yescharacteristic
24#376×C139—21no—
25#376×C139C2211yescharacteristic
26#327×C139—21no—
27#327×C139—21no—
28Q8⋊C8×C139—22no—
29C2×#41×C139—21no—
30C22×Q8×C139D411yescharacteristic
31C2×SD16×C139—22no—
32C2×M16×C139—21no—
33C4⋊Q8×C139C2×C411yescharacteristic
34#127×C139C2×C411yescharacteristic
35#124×C139—21no—
36#121×C139—21no—
37#121×C139—21no—
38C4×Q8×C139—28no—
39C4×Q8×C139—21no—
40C4×Q8×C139—21no—
41C4×Q8×C139C2×C412yes—
42C4×Q8×C139D412yes—
43C4×D4×C139—21no—
44C4×D4×C139—21no—
45C2×C4⋊C4×C139—22no—
46C2×C4⋊C4×C139—21no—
47C2×C4⋊C4×C139—21no—
48C2×C4⋊C4×C139D411yescharacteristic
49C2×C42×C139—22no—
50C2×C42×C139—21no—
51C2×C42×C139—21no—
52C2×C42×C139—22no—
53C2×C42×C139D412yes—
54C2×C42×C139C2311yescharacteristic
55#107×C139—22no—
56C4⋊C8×C139—21no—
57C4⋊C8×C139C2×C412yes—
58#104×C139—44no—
59#103×C139—22no—
60#102×C139—22no—
61C22⋊C8×C139—21no—
62C22⋊C8×C139—21no—
63#97×C139—21no—
64#97×C139—21no—
65#97×C139—21no—
66C4×C8×C139—21no—
67#95×C139—22no—
68#95×C139—21no—
69#95×C139—21no—
70#95×C139D411yescharacteristic
71#95×C139D411yescharacteristic
72#41×C139—42no—
73#41×C139—42no—
74C2×Q8×C139—24no—
75C2×Q8×C139—21no—
76C2×Q8×C139—21no—
77C2×Q8×C139C22⋊C412yes—
78C2×D4×C139—21no—
79C2×D4×C139—21no—
80C2×D4×C139—21no—
81C2×D4×C139—41no—
82C22×C4×C139—21no—
83C22×C4×C139—21no—
84C22×C4×C139—21no—
85C22×C4×C139—22no—
86C22×C4×C139—21no—
87C22×C4×C139—41no—
88C22×C4×C139C2×D411yescharacteristic
89C22×C4×C139C2×D411yescharacteristic
90C22×C4×C139C2×D411yescharacteristic
91SD16×C139—44no—
92M16×C139—22no—
93M16×C139—41no—
94C2×C8×C139—22no—
95C2×C8×C139—41no—
96C2×C8×C139—41no—
97C4⋊C4×C139—28no—
98C4⋊C4×C139—24no—
99C4⋊C4×C139—22no—
100C4⋊C4×C139—22no—
101C4⋊C4×C139—21no—
102C4⋊C4×C139—21no—
103C4⋊C4×C139—21no—
104C4⋊C4×C139C22⋊C412yes—
105C22⋊C4×C139—41no—
106C22⋊C4×C139—41no—
107C42×C139—28no—
108C42×C139—24no—
109C42×C139—22no—
110C42×C139—22no—
111C42×C139—42no—
112C42×C139—82no—
113C42×C139C22×C411yescharacteristic
114C42×C139C2×D411yescharacteristic
115C42×C139#4111yescharacteristic
116C42×C139#4111yescharacteristic
117C23×C139—41no—
118C23×C139#12011yescharacteristic
119Q8×C139—24no—
120Q8×C139—22no—
121Q8×C139—42no—
122Q8×C139#10414yescomplemented
123D4×C139—42no—
124D4×C139—42no—
125D4×C139—81no—
126D4×C139—81no—
127D4×C139—81no—
128C2×C4×C139—24no—
129C2×C4×C139—22no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—22no—
133C2×C4×C139—22no—
134C2×C4×C139—24no—
135C2×C4×C139—22no—
136C2×C4×C139—22no—
137C2×C4×C139—41no—
138C2×C4×C139—41no—
139C2×C4×C139—42no—
140C2×C4×C139—41no—
141C2×C4×C139—42no—
142C2×C4×C139—41no—
143C2×C4×C139—41no—
144C2×C4×C139—41no—
145C2×C4×C139—41no—
146C2×C4×C139—41no—
147C2×C4×C139—82no—
148C2×C4×C139C2×C22⋊C411yescharacteristic
149C2×C4×C139C4×D411yescharacteristic
150C2×C4×C139C4×D411yescharacteristic
151C2×C4×C139#12111yescharacteristic
152C2×C4×C139#12111yescharacteristic
153C2×C4×C139#12311yescharacteristic
154C8×C139—42no—
155C8×C139—42no—
156C8×C139—81no—
157C22×C139—21no—
158C22×C139—21no—
159C22×C139—81no—
160C22×C139—81no—
161C22×C139—81no—
162C22×C139#38611yescharacteristic
163C22×C139#45311yescharacteristic
164C22×C139#45411yescharacteristic
165C4×C139—21no—
166C4×C139—21no—
167C4×C139—24no—
168C4×C139—21no—
169C4×C139—21no—
170C4×C139—21no—
171C4×C139—44no—
172C4×C139—42no—
173C4×C139—42no—
174C4×C139—42no—
175C4×C139—81no—
176C4×C139C2×#10412yes—
177C2×C139—21no—
178C2×C139—21no—
179C2×C139—161no—
180C2×C139#188311yescharacteristic
181C2×C139#189611yescharacteristic
182C2×C139#190511yescharacteristic
183#9326C13911yesmaximal, characteristic, direct product factor, Sylow
184C139#932611yescharacteristic, direct product factor, Sylow
185#3112C2×C13911yescharacteristic
186#2276C2×C13911yescharacteristic, complemented
187#1980C2×C13911yescharacteristic
188#1505C2×C13911yescharacteristic
189#1491C2×C13911yescharacteristic, complemented
190#1300C2×C13911yescharacteristic, complemented
191#1285C2×C13911yescharacteristic, complemented
192#532C22×C13911yescharacteristic
193C2×C4×Q8—21no—
194C2×C4×Q8C22×C13911yescharacteristic
195#480—21no—
196#477C4×C13912yescomplemented
197#460C4×C13912yescomplemented
198#448—21no—
199#440—22no—
200#432C22×C13911yescharacteristic
201#432C22×C13911yescharacteristic
202C2×#104—22no—
203C4×M16C22×C13911yescharacteristic
204C4×C4⋊C4—21no—
205C4×C4⋊C4—22no—
206C4×C4⋊C4—21no—
207C4×C4⋊C4C22×C13911yescharacteristic
208#376—21no—
209#376C22×C13911yescharacteristic
210#327—21no—
211#327—21no—
212Q8⋊C8—22no—
213C2×#41—21no—
214C22×Q8D4×C13911yescharacteristic
215C2×SD16—22no—
216C2×M16—21no—
217C4⋊Q8C2×C4×C13911yescharacteristic
218#127C2×C4×C13911yescharacteristic
219#124—21no—
220#121—21no—
221#121—21no—
222C4×Q8—28no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8C2×C4×C13912yes—
226C4×Q8D4×C13912yes—
227C4×D4—21no—
228C4×D4—21no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4D4×C13911yescharacteristic
233C2×C42—22no—
234C2×C42—21no—
235C2×C42—21no—
236C2×C42—22no—
237C2×C42D4×C13912yes—
238C2×C42C23×C13911yescharacteristic
239#107—22no—
240C4⋊C8—21no—
241C4⋊C8C2×C4×C13912yes—
242#104—44no—
243#103—22no—
244#102—22no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247#97—21no—
248#97—21no—
249#97—21no—
250C4×C8—21no—
251#95—22no—
252#95—21no—
253#95—21no—
254#95D4×C13911yescharacteristic
255#95D4×C13911yescharacteristic
256#41—42no—
257#41—42no—
258C2×Q8—24no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8C22⋊C4×C13912yes—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4C2×D4×C13911yescharacteristic
273C22×C4C2×D4×C13911yescharacteristic
274C22×C4C2×D4×C13911yescharacteristic
275SD16—44no—
276M16—22no—
277M16—41no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C4⋊C4—28no—
282C4⋊C4—24no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4C22⋊C4×C13912yes—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42—28no—
292C42—24no—
293C42—22no—
294C42—22no—
295C42—42no—
296C42—82no—
297C42C22×C4×C13911yescharacteristic
298C42C2×D4×C13911yescharacteristic
299C42#41×C13911yescharacteristic
300C42#41×C13911yescharacteristic
301C23—41no—
302C23#120×C13911yescharacteristic
303Q8—24no—
304Q8—22no—
305Q8—42no—
306Q8#104×C13914yescomplemented
307D4—42no—
308D4—42no—
309D4—81no—
310D4—81no—
311D4—81no—
312C2×C4—24no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—82no—
332C2×C4C2×C22⋊C4×C13911yescharacteristic
333C2×C4C4×D4×C13911yescharacteristic
334C2×C4C4×D4×C13911yescharacteristic
335C2×C4#121×C13911yescharacteristic
336C2×C4#121×C13911yescharacteristic
337C2×C4#123×C13911yescharacteristic
338C8—42no—
339C8—42no—
340C8—81no—
341C22—21no—
342C22—21no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#386×C13911yescharacteristic
347C22#453×C13911yescharacteristic
348C22#454×C13911yescharacteristic
349C4—21no—
350C4—21no—
351C4—24no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—44no—
356C4—42no—
357C4—42no—
358C4—42no—
359C4—81no—
360C4C2×#104×C13912yes—
361C2—21no—
362C2—21no—
363C2—161no—
364C2#1883×C13911yescharacteristic
365C2#1896×C13911yescharacteristic
366C2#1905×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radical#532×C139C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2276×C139C2semidirect
5. #1491×C139C2semidirect
6. #1300×C139C2semidirect
7. #1285×C139C2semidirect
12. #477×C139C4semidirect
13. #460×C139C4semidirect
122. Q8×C139#104semidirect
183. #9326C139direct (N × H)
184. C139#9326direct (N × H)
186. #2276C2×C139semidirect
189. #1491C2×C139semidirect
190. #1300C2×C139semidirect
191. #1285C2×C139semidirect
196. #477C4×C139semidirect
197. #460C4×C139semidirect
306. Q8#104×C139semidirect

Maximal subgroups

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

subgroupindex
#3112×C1392
#2276×C1392
#1980×C1392
#1505×C1392
#1491×C1392
#1300×C1392
#1285×C1392
#9326139