Finite Group Databasebeta

← C139×#9379 #48003975

Subgroups — C139×#9379 #48003975

Order 35584.

492 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
1#3215×C139C211yesmaximal, characteristic
2#2337×C139C211yesmaximal, characteristic
3#1986×C139C211yesmaximal, characteristic, complemented
4#1527×C139C211yesmaximal, characteristic
5#1515×C139C211yesmaximal, characteristic, complemented
6#1288×C139C211yesmaximal, characteristic, complemented
7#1285×C139C211yesmaximal, characteristic, complemented
8#533×C139C2211yescharacteristic
9C2×#124×C139C2211yescharacteristic
10#497×C139C412yescomplemented
11#489×C139C412yescomplemented
12#464×C139—22no—
13#451×C139—21no—
14#450×C139—21no—
15#432×C139C2211yescharacteristic
16#432×C139C2211yescharacteristic
17C4×M16×C139C2211yescharacteristic
18#391×C139—21no—
19#388×C139—21no—
20#388×C139—21no—
21#386×C139—21no—
22#385×C139—21no—
23#383×C139C2211yescharacteristic
24C4×C4⋊C4×C139C2211yescharacteristic
25C4×C22⋊C4×C139—21no—
26#339×C139—21no—
27#339×C139—21no—
28#329×C139—22no—
29#328×C139—21no—
30#328×C139—21no—
31C22×Q8×C139D411yescharacteristic
32C22×D4×C139D411yescharacteristic
33C23×C4×C139—21no—
34C2×Q16×C139—22no—
35C2×SD16×C139—22no—
36C2×M16×C139—21no—
37C4⋊Q8×C139C2×C411yescharacteristic, complemented
38C4⋊Q8×C139C2×C411yescharacteristic, complemented
39#125×C139—21no—
40#124×C139—21no—
41#124×C139—21no—
42#124×C139C2×C412yes—
43#124×C139D412yes—
44C22⋊Q8×C139—21no—
45C22⋊Q8×C139—21no—
46C4×Q8×C139—21no—
47C4×Q8×C139—21no—
48#117×C139—21no—
49C2×C4⋊C4×C139—21no—
50C2×C4⋊C4×C139—21no—
51C2×C22⋊C4×C139—21no—
52C2×C22⋊C4×C139—21no—
53C2×C22⋊C4×C139—21no—
54C2×C22⋊C4×C139—21no—
55C2×C22⋊C4×C139—21no—
56C2×C42×C139—21no—
57C2×C42×C139D411yescharacteristic
58C2×C42×C139D411yescharacteristic
59C2×C42×C139C2311yescharacteristic
60C4⋊C8×C139—21no—
61C4⋊C8×C139—21no—
62#103×C139—22no—
63#102×C139—22no—
64C22⋊C8×C139—21no—
65C22⋊C8×C139—21no—
66#97×C139—21no—
67#97×C139—21no—
68#97×C139C2×C412yescomplemented
69C4×C8×C139—21no—
70#95×C139—21no—
71#95×C139—21no—
72#95×C139—21no—
73#95×C139—21no—
74#95×C139—21no—
75#95×C139D411yescharacteristic
76#95×C139D411yescharacteristic
77C24×C139—21no—
78C2×Q8×C139—21no—
79C2×Q8×C139—21no—
80C2×Q8×C139—21no—
81C2×Q8×C139—81no—
82C2×Q8×C139C22⋊C412yes—
83C2×D4×C139—21no—
84C2×D4×C139—81no—
85C2×D4×C139C22⋊C412yes—
86C22×C4×C139—21no—
87C22×C4×C139—21no—
88C22×C4×C139—21no—
89C22×C4×C139—21no—
90C22×C4×C139—21no—
91C22×C4×C139—42no—
92C22×C4×C139—81no—
93C22×C4×C139—81no—
94C22×C4×C139C2×D411yescharacteristic
95C22×C4×C139C2×D411yescharacteristic
96C22×C4×C139C2×D411yescharacteristic
97Q16×C139—82no—
98SD16×C139—82no—
99M16×C139—22no—
100M16×C139—41no—
101C2×C8×C139—22no—
102C2×C8×C139—41no—
103C2×C8×C139—41no—
104C4⋊C4×C139—21no—
105C4⋊C4×C139—21no—
106C4⋊C4×C139—21no—
107C4⋊C4×C139—21no—
108C4⋊C4×C139—42no—
109C4⋊C4×C139—41no—
110C4⋊C4×C139—41no—
111C4⋊C4×C139—81no—
112C22⋊C4×C139—22no—
113C22⋊C4×C139—22no—
114C22⋊C4×C139—22no—
115C22⋊C4×C139—22no—
116C22⋊C4×C139—42no—
117C22⋊C4×C139—41no—
118C22⋊C4×C139—81no—
119C22⋊C4×C139—81no—
120C42×C139—41no—
121C42×C139—41no—
122C42×C139—41no—
123C42×C139—81no—
124C42×C139C22×C411yescharacteristic
125C42×C139C2×D411yescharacteristic
126C42×C139#4111yescharacteristic
127C42×C139#4111yescharacteristic
128C23×C139—22no—
129C23×C139—41no—
130C23×C139—41no—
131C23×C139—41no—
132C23×C139—41no—
133C23×C139—41no—
134C23×C139—41no—
135C23×C139#12011yescharacteristic
136Q8×C139—42no—
137Q8×C139—42no—
138Q8×C139—81no—
139Q8×C139—81no—
140D4×C139—42no—
141D4×C139—81no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—22no—
145C2×C4×C139—22no—
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—41no—
156C2×C4×C139—41no—
157C2×C4×C139—41no—
158C2×C4×C139—41no—
159C2×C4×C139—41no—
160C2×C4×C139—41no—
161C2×C4×C139—41no—
162C2×C4×C139—41no—
163C2×C4×C139—84no—
164C2×C4×C139C2×C22⋊C411yescharacteristic
165C2×C4×C139C4×D411yescharacteristic
166C2×C4×C139C4×D411yescharacteristic
167C2×C4×C139#12111yescharacteristic
168C2×C4×C139#12111yescharacteristic
169C2×C4×C139#12311yescharacteristic
170C8×C139—42no—
171C8×C139—42no—
172C8×C139—81no—
173C22×C139—21no—
174C22×C139—21no—
175C22×C139—42no—
176C22×C139—42no—
177C22×C139—42no—
178C22×C139—81no—
179C22×C139—81no—
180C22×C139—81no—
181C22×C139—81no—
182C22×C139#38611yescharacteristic
183C22×C139#45511yescharacteristic
184C22×C139#45611yescharacteristic
185C4×C139—21no—
186C4×C139—21no—
187C4×C139—21no—
188C4×C139—21no—
189C4×C139—21no—
190C4×C139—21no—
191C4×C139—42no—
192C4×C139—42no—
193C4×C139—81no—
194C4×C139—81no—
195C4×C139—81no—
196C4×C139—81no—
197C4×C139—81no—
198C2×C139—21no—
199C2×C139—21no—
200C2×C139—82no—
201C2×C139#188211yescharacteristic
202C2×C139#190611yescharacteristic
203C2×C139#191111yescharacteristic
204#9379C13911yesmaximal, characteristic, direct product factor, Sylow
205C139#937911yescharacteristic, direct product factor, Sylow
206#3215C2×C13911yescharacteristic
207#2337C2×C13911yescharacteristic
208#1986C2×C13911yescharacteristic, complemented
209#1527C2×C13911yescharacteristic
210#1515C2×C13911yescharacteristic, complemented
211#1288C2×C13911yescharacteristic, complemented
212#1285C2×C13911yescharacteristic, complemented
213#533C22×C13911yescharacteristic
214C2×#124C22×C13911yescharacteristic
215#497C4×C13912yescomplemented
216#489C4×C13912yescomplemented
217#464—22no—
218#451—21no—
219#450—21no—
220#432C22×C13911yescharacteristic
221#432C22×C13911yescharacteristic
222C4×M16C22×C13911yescharacteristic
223#391—21no—
224#388—21no—
225#388—21no—
226#386—21no—
227#385—21no—
228#383C22×C13911yescharacteristic
229C4×C4⋊C4C22×C13911yescharacteristic
230C4×C22⋊C4—21no—
231#339—21no—
232#339—21no—
233#329—22no—
234#328—21no—
235#328—21no—
236C22×Q8D4×C13911yescharacteristic
237C22×D4D4×C13911yescharacteristic
238C23×C4—21no—
239C2×Q16—22no—
240C2×SD16—22no—
241C2×M16—21no—
242C4⋊Q8C2×C4×C13911yescharacteristic, complemented
243C4⋊Q8C2×C4×C13911yescharacteristic, complemented
244#125—21no—
245#124—21no—
246#124—21no—
247#124C2×C4×C13912yes—
248#124D4×C13912yes—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253#117—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C42—21no—
262C2×C42D4×C13911yescharacteristic
263C2×C42D4×C13911yescharacteristic
264C2×C42C23×C13911yescharacteristic
265C4⋊C8—21no—
266C4⋊C8—21no—
267#103—22no—
268#102—22no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271#97—21no—
272#97—21no—
273#97C2×C4×C13912yescomplemented
274C4×C8—21no—
275#95—21no—
276#95—21no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95D4×C13911yescharacteristic
281#95D4×C13911yescharacteristic
282C24—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—81no—
287C2×Q8C22⋊C4×C13912yes—
288C2×D4—21no—
289C2×D4—81no—
290C2×D4C22⋊C4×C13912yes—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4C2×D4×C13911yescharacteristic
300C22×C4C2×D4×C13911yescharacteristic
301C22×C4C2×D4×C13911yescharacteristic
302Q16—82no—
303SD16—82no—
304M16—22no—
305M16—41no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—81no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—42no—
322C22⋊C4—41no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C42—41no—
326C42—41no—
327C42—41no—
328C42—81no—
329C42C22×C4×C13911yescharacteristic
330C42C2×D4×C13911yescharacteristic
331C42#41×C13911yescharacteristic
332C42#41×C13911yescharacteristic
333C23—22no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23#120×C13911yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—81no—
344Q8—81no—
345D4—42no—
346D4—81no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
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—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—84no—
369C2×C4C2×C22⋊C4×C13911yescharacteristic
370C2×C4C4×D4×C13911yescharacteristic
371C2×C4C4×D4×C13911yescharacteristic
372C2×C4#121×C13911yescharacteristic
373C2×C4#121×C13911yescharacteristic
374C2×C4#123×C13911yescharacteristic
375C8—42no—
376C8—42no—
377C8—81no—
378C22—21no—
379C22—21no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22#386×C13911yescharacteristic
388C22#455×C13911yescharacteristic
389C22#456×C13911yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—42no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C2—21no—
404C2—21no—
405C2—82no—
406C2#1882×C13911yescharacteristic
407C2#1906×C13911yescharacteristic
408C2#1911×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. #1986×C139C2semidirect
5. #1515×C139C2semidirect
6. #1288×C139C2semidirect
7. #1285×C139C2semidirect
10. #497×C139C4semidirect
11. #489×C139C4semidirect
37. C4⋊Q8×C139C2×C4semidirect
38. C4⋊Q8×C139C2×C4semidirect
68. #97×C139C2×C4semidirect
204. #9379C139direct (N × H)
205. C139#9379direct (N × H)
208. #1986C2×C139semidirect
210. #1515C2×C139semidirect
211. #1288C2×C139semidirect
212. #1285C2×C139semidirect
215. #497C4×C139semidirect
216. #489C4×C139semidirect
242. C4⋊Q8C2×C4×C139semidirect
243. C4⋊Q8C2×C4×C139semidirect
273. #97C2×C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3215×C1392
#2337×C1392
#1986×C1392
#1527×C1392
#1515×C1392
#1288×C1392
#1285×C1392
#9379139