Finite Group Databasebeta

← C139×#9175 #48003771

Subgroups — C139×#9175 #48003771

Order 35584.

566 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3077×C139C211yesmaximal, characteristic
2#2349×C139C211yesmaximal, characteristic
3#1518×C139C211yesmaximal, characteristic, complemented
4#1503×C139C211yesmaximal, characteristic, complemented
5#1478×C139C211yesmaximal, characteristic
6#1303×C139C211yesmaximal, characteristic, complemented
7#1286×C139C211yesmaximal, characteristic, complemented
8#533×C139C2211yescharacteristic
9C2×C4×D4×C139—21no—
10C2×C4×D4×C139C2211yescharacteristic
11#478×C139—22no—
12#476×C139C412yescomplemented
13#474×C139C412yescomplemented
14#431×C139C2211yescharacteristic
15#431×C139C2211yescharacteristic
16#428×C139—21no—
17#423×C139C2211yescharacteristic
18#418×C139—21no—
19#389×C139—21no—
20#385×C139—22no—
21#382×C139C2211yescharacteristic
22#380×C139—21no—
23C4×C4⋊C4×C139C2211yescharacteristic
24C2×#95×C139—21no—
25#328×C139—21no—
26#328×C139—21no—
27#328×C139—22no—
28D4⋊C8×C139—22no—
29C22×D4×C139D411yescharacteristic
30C23×C4×C139—21no—
31C23×C4×C139—22no—
32C2×M16×C139—21no—
33C4⋊Q8×C139C2×C411yescharacteristic, complemented
34C4⋊Q8×C139C2×C411yescharacteristic, complemented
35#125×C139—21no—
36C22⋊Q8×C139—21no—
37C22⋊Q8×C139—21no—
38C4×Q8×C139—21no—
39C4×Q8×C139—21no—
40C4×D4×C139—21no—
41C4×D4×C139—21no—
42C4×D4×C139—42no—
43C4×D4×C139—42no—
44C4×D4×C139C2×C412yes—
45C4×D4×C139D412yes—
46#117×C139—21no—
47C2×C4⋊C4×C139—21no—
48C2×C4⋊C4×C139—21no—
49C2×C4⋊C4×C139—22no—
50C2×C4⋊C4×C139D411yescharacteristic
51C2×C22⋊C4×C139—21no—
52C2×C22⋊C4×C139—22no—
53C2×C42×C139—21no—
54C2×C42×C139C2311yescharacteristic
55#107×C139—22no—
56#106×C139—22no—
57C4⋊C8×C139—21no—
58C4⋊C8×C139—21no—
59C4⋊C8×C139—21no—
60C4⋊C8×C139C2×C412yescomplemented
61#102×C139—22no—
62#102×C139—22no—
63C22⋊C8×C139—21no—
64C22⋊C8×C139—21no—
65C4×C8×C139—21no—
66C4×C8×C139—21no—
67#95×C139—22no—
68#95×C139—21no—
69#95×C139D411yescharacteristic
70#95×C139D411yescharacteristic
71#95×C139D412yes—
72C24×C139—21no—
73C2×Q8×C139—21no—
74C2×Q8×C139—21no—
75C2×D4×C139—21no—
76C2×D4×C139—21no—
77C2×D4×C139—21no—
78C2×D4×C139C22⋊C412yes—
79C2×D4×C139SD1612yes—
80C2×D4×C139Q1612yes—
81C22×C4×C139—21no—
82C22×C4×C139—21no—
83C22×C4×C139—22no—
84C22×C4×C139—22no—
85C22×C4×C139—22no—
86C22×C4×C139—21no—
87C22×C4×C139—44no—
88C22×C4×C139—44no—
89C22×C4×C139—82no—
90C22×C4×C139—82no—
91C22×C4×C139C2×D411yescharacteristic
92C22×C4×C139C2×D411yescharacteristic
93C22×C4×C139C2×D411yescharacteristic
94M16×C139—41no—
95M16×C139—41no—
96C2×C8×C139—22no—
97C2×C8×C139—41no—
98C2×C8×C139—41no—
99C4⋊C4×C139—21no—
100C4⋊C4×C139—21no—
101C4⋊C4×C139—21no—
102C4⋊C4×C139—21no—
103C4⋊C4×C139—21no—
104C4⋊C4×C139—42no—
105C4⋊C4×C139—41no—
106C4⋊C4×C139—41no—
107C4⋊C4×C139—41no—
108C4⋊C4×C139—41no—
109C4⋊C4×C139—82no—
110C4⋊C4×C139C22⋊C412yes—
111C22⋊C4×C139—22no—
112C22⋊C4×C139—22no—
113C22⋊C4×C139—44no—
114C22⋊C4×C139—41no—
115C42×C139—41no—
116C42×C139—41no—
117C42×C139—41no—
118C42×C139C22×C411yescharacteristic
119C42×C139C2×D411yescharacteristic
120C42×C139#4111yescharacteristic
121C42×C139#4111yescharacteristic
122C23×C139—22no—
123C23×C139—22no—
124C23×C139—22no—
125C23×C139—42no—
126C23×C139—42no—
127C23×C139#12011yescharacteristic
128Q8×C139—81no—
129Q8×C139—81no—
130D4×C139—22no—
131D4×C139—22no—
132D4×C139—22no—
133D4×C139#10314yes—
134C2×C4×C139—22no—
135C2×C4×C139—22no—
136C2×C4×C139—41no—
137C2×C4×C139—41no—
138C2×C4×C139—42no—
139C2×C4×C139—41no—
140C2×C4×C139—41no—
141C2×C4×C139—41no—
142C2×C4×C139—41no—
143C2×C4×C139—42no—
144C2×C4×C139—42no—
145C2×C4×C139—41no—
146C2×C4×C139—41no—
147C2×C4×C139—41no—
148C2×C4×C139—42no—
149C2×C4×C139—82no—
150C2×C4×C139—82no—
151C2×C4×C139—88no—
152C2×C4×C139C2×C22⋊C411yescharacteristic
153C2×C4×C139C4×D411yescharacteristic
154C2×C4×C139C4×D411yescharacteristic
155C2×C4×C139#12111yescharacteristic
156C2×C4×C139#12111yescharacteristic
157C2×C4×C139#12311yescharacteristic
158C2×C4×C139C2×SD1611yescharacteristic
159C2×C4×C139C2×Q1611yescharacteristic
160C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C139#13711yescharacteristic
162C8×C139—42no—
163C8×C139—81no—
164C8×C139—81no—
165C22×C139—21no—
166C22×C139—21no—
167C22×C139—24no—
168C22×C139—44no—
169C22×C139—44no—
170C22×C139—42no—
171C22×C139—42no—
172C22×C139#38611yescharacteristic
173C22×C139#45011yescharacteristic
174C22×C139#45111yescharacteristic
175C4×C139—21no—
176C4×C139—21no—
177C4×C139—21no—
178C4×C139—21no—
179C4×C139—42no—
180C4×C139—42no—
181C4×C139—81no—
182C4×C139—82no—
183C4×C139—81no—
184C4×C139—81no—
185C4×C139C2×#10311yescharacteristic
186C4×C139#41711yescharacteristic
187C4×C139#48311yescharacteristic
188C4×C139#48411yescharacteristic
189C2×C139—21no—
190C2×C139—21no—
191C2×C139—44no—
192C2×C139#187211yescharacteristic
193C2×C139#190411yescharacteristic
194C2×C139#190611yescharacteristic
195#9175C13911yesmaximal, characteristic, direct product factor, Sylow
196C139#917511yescharacteristic, direct product factor, Sylow
197#3077C2×C13911yescharacteristic
198#2349C2×C13911yescharacteristic
199#1518C2×C13911yescharacteristic, complemented
200#1503C2×C13911yescharacteristic, complemented
201#1478C2×C13911yescharacteristic
202#1303C2×C13911yescharacteristic, complemented
203#1286C2×C13911yescharacteristic, complemented
204#533C22×C13911yescharacteristic
205C2×C4×D4—21no—
206C2×C4×D4C22×C13911yescharacteristic
207#478—22no—
208#476C4×C13912yescomplemented
209#474C4×C13912yescomplemented
210#431C22×C13911yescharacteristic
211#431C22×C13911yescharacteristic
212#428—21no—
213#423C22×C13911yescharacteristic
214#418—21no—
215#389—21no—
216#385—22no—
217#382C22×C13911yescharacteristic
218#380—21no—
219C4×C4⋊C4C22×C13911yescharacteristic
220C2×#95—21no—
221#328—21no—
222#328—21no—
223#328—22no—
224D4⋊C8—22no—
225C22×D4D4×C13911yescharacteristic
226C23×C4—21no—
227C23×C4—22no—
228C2×M16—21no—
229C4⋊Q8C2×C4×C13911yescharacteristic, complemented
230C4⋊Q8C2×C4×C13911yescharacteristic, complemented
231#125—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—42no—
239C4×D4—42no—
240C4×D4C2×C4×C13912yes—
241C4×D4D4×C13912yes—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4D4×C13911yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—22no—
249C2×C42—21no—
250C2×C42C23×C13911yescharacteristic
251#107—22no—
252#106—22no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8C2×C4×C13912yescomplemented
257#102—22no—
258#102—22no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C4×C8—21no—
262C4×C8—21no—
263#95—22no—
264#95—21no—
265#95D4×C13911yescharacteristic
266#95D4×C13911yescharacteristic
267#95D4×C13912yes—
268C24—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4C22⋊C4×C13912yes—
275C2×D4SD16×C13912yes—
276C2×D4Q16×C13912yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—82no—
286C22×C4—82no—
287C22×C4C2×D4×C13911yescharacteristic
288C22×C4C2×D4×C13911yescharacteristic
289C22×C4C2×D4×C13911yescharacteristic
290M16—41no—
291M16—41no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—41no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—82no—
306C4⋊C4C22⋊C4×C13912yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—44no—
310C22⋊C4—41no—
311C42—41no—
312C42—41no—
313C42—41no—
314C42C22×C4×C13911yescharacteristic
315C42C2×D4×C13911yescharacteristic
316C42#41×C13911yescharacteristic
317C42#41×C13911yescharacteristic
318C23—22no—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23#120×C13911yescharacteristic
324Q8—81no—
325Q8—81no—
326D4—22no—
327D4—22no—
328D4—22no—
329D4#103×C13914yes—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—88no—
348C2×C4C2×C22⋊C4×C13911yescharacteristic
349C2×C4C4×D4×C13911yescharacteristic
350C2×C4C4×D4×C13911yescharacteristic
351C2×C4#121×C13911yescharacteristic
352C2×C4#121×C13911yescharacteristic
353C2×C4#123×C13911yescharacteristic
354C2×C4C2×SD16×C13911yescharacteristic
355C2×C4C2×Q16×C13911yescharacteristic
356C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
357C2×C4#137×C13911yescharacteristic
358C8—42no—
359C8—81no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—44no—
365C22—44no—
366C22—42no—
367C22—42no—
368C22#386×C13911yescharacteristic
369C22#450×C13911yescharacteristic
370C22#451×C13911yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—82no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4C2×#103×C13911yescharacteristic
382C4#417×C13911yescharacteristic
383C4#483×C13911yescharacteristic
384C4#484×C13911yescharacteristic
385C2—21no—
386C2—21no—
387C2—44no—
388C2#1872×C13911yescharacteristic
389C2#1904×C13911yescharacteristic
390C2#1906×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC22×D4×C139D4
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
3. #1518×C139C2semidirect
4. #1503×C139C2semidirect
6. #1303×C139C2semidirect
7. #1286×C139C2semidirect
12. #476×C139C4semidirect
13. #474×C139C4semidirect
33. C4⋊Q8×C139C2×C4semidirect
34. C4⋊Q8×C139C2×C4semidirect
60. C4⋊C8×C139C2×C4semidirect
195. #9175C139direct (N × H)
196. C139#9175direct (N × H)
199. #1518C2×C139semidirect
200. #1503C2×C139semidirect
202. #1303C2×C139semidirect
203. #1286C2×C139semidirect
208. #476C4×C139semidirect
209. #474C4×C139semidirect
229. C4⋊Q8C2×C4×C139semidirect
230. C4⋊Q8C2×C4×C139semidirect
256. C4⋊C8C2×C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3077×C1392
#2349×C1392
#1518×C1392
#1503×C1392
#1478×C1392
#1303×C1392
#1286×C1392
#9175139