Finite Group Databasebeta

← C139×#9109 #48003705

Subgroups — C139×#9109 #48003705

Order 35584.

648 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2973×C139C211yesmaximal, characteristic, complemented
2#2321×C139C211yesmaximal, characteristic
3#1459×C139C211yesmaximal, characteristic, complemented
4C2×#323×C139C212yesmaximal, complemented
5#1282×C139C212yesmaximal, complemented
6C2×#120×C139C411yescharacteristic
7C2×C4×D4×C139C2211yescharacteristic
8C22×C22⋊C4×C139C2211yescharacteristic
9#435×C139—24no—
10#432×C139—21no—
11#407×C139—21no—
12C2×C22⋊C8×C139C2212yes—
13C2×C22⋊C8×C139C2212yes—
14#390×C139—21no—
15#388×C139—21no—
16#388×C139—21no—
17#386×C139—21no—
18#386×C139C411yescharacteristic
19#385×C139C411yescharacteristic
20#379×C139C411yescharacteristic
21C4×C22⋊C4×C139C2211yescharacteristic
22#324×C139—21no—
23#323×C139—21no—
24#323×C139—24no—
25C25×C139C2×C411yescharacteristic
26C22×D4×C139—21no—
27C22×D4×C139C2×C411yescharacteristic
28C23×C4×C139C2×C411yescharacteristic
29C23×C4×C139D411yescharacteristic
30C23×C4×C139C2311yescharacteristic
31C2×M16×C139—22no—
32C22×C8×C139—22no—
33C22×C8×C139—22no—
34#120×C139—22no—
35#120×C139—22no—
36C4×D4×C139—22no—
37C4×D4×C139—22no—
38C2×C4⋊C4×C139—21no—
39C2×C4⋊C4×C139D411yescharacteristic
40C2×C22⋊C4×C139—21no—
41C2×C22⋊C4×C139—22no—
42C2×C22⋊C4×C139—21no—
43C2×C22⋊C4×C139—21no—
44C2×C22⋊C4×C139—22no—
45C2×C22⋊C4×C139—21no—
46C2×C22⋊C4×C139—21no—
47C2×C22⋊C4×C139—21no—
48C2×C22⋊C4×C139C2×C411yescharacteristic
49C2×C22⋊C4×C139C2×C411yescharacteristic
50C2×C22⋊C4×C139C2×C411yescharacteristic
51C2×C22⋊C4×C139D411yescharacteristic
52C2×C42×C139—21no—
53C2×C42×C139D411yescharacteristic
54C4⋊C8×C139—22no—
55C22⋊C8×C139—22no—
56C22⋊C8×C139—22no—
57C22⋊C8×C139—22no—
58C22⋊C8×C139—22no—
59C22⋊C8×C139D414yescomplemented
60#97×C139—22no—
61#95×C139—21no—
62#95×C139—21no—
63#95×C139—21no—
64C24×C139—21no—
65C24×C139—22no—
66C24×C139—21no—
67C24×C139—22no—
68C24×C139—81no—
69C24×C139—81no—
70C24×C139C22⋊C411yescharacteristic
71C24×C139M1612yescomplemented
72C24×C139C22×C411yescharacteristic
73C2×D4×C139—22no—
74C2×D4×C139—21no—
75C2×D4×C139—21no—
76C2×D4×C139—22no—
77C2×D4×C139—24no—
78C2×D4×C139—81no—
79C2×D4×C139—81no—
80C22×C4×C139—21no—
81C22×C4×C139—21no—
82C22×C4×C139—21no—
83C22×C4×C139—21no—
84C22×C4×C139—21no—
85C22×C4×C139—22no—
86C22×C4×C139—81no—
87C22×C4×C139—81no—
88C22×C4×C139—81no—
89C22×C4×C139C22⋊C411yescharacteristic
90C22×C4×C139C22⋊C411yescharacteristic
91C22×C4×C139C22⋊C411yescharacteristic
92C22×C4×C139C2×D412yes—
93C22×C4×C139C2×D411yescharacteristic
94C22×C4×C139C2×D411yescharacteristic
95C22×C4×C139#4112yes—
96M16×C139—82no—
97C2×C8×C139—24no—
98C2×C8×C139—42no—
99C2×C8×C139—82no—
100C2×C8×C139—82no—
101C4⋊C4×C139—22no—
102C4⋊C4×C139—81no—
103C22⋊C4×C139—24no—
104C22⋊C4×C139—22no—
105C22⋊C4×C139—21no—
106C22⋊C4×C139—22no—
107C22⋊C4×C139—22no—
108C22⋊C4×C139—41no—
109C22⋊C4×C139—42no—
110C22⋊C4×C139—41no—
111C22⋊C4×C139—81no—
112C22⋊C4×C139—81no—
113C22⋊C4×C139—81no—
114C22⋊C4×C139M1612yescomplemented
115C42×C139—21no—
116C42×C139—21no—
117C42×C139—81no—
118C23×C139—21no—
119C23×C139—22no—
120C23×C139—21no—
121C23×C139—21no—
122C23×C139—24no—
123C23×C139—41no—
124C23×C139—41no—
125C23×C139—41no—
126C23×C139—41no—
127C23×C139—41no—
128C23×C139—41no—
129C23×C139—41no—
130C23×C139—41no—
131C23×C139—41no—
132C23×C139—41no—
133C23×C139—42no—
134C23×C139—82no—
135C23×C139—82no—
136C23×C139—82no—
137C23×C139—82no—
138C23×C139—84no—
139C23×C139C2×C22⋊C411yescharacteristic
140C23×C139C4×D412yes—
141C23×C139C2×M1611yescharacteristic
142C23×C139C2×M1611yescharacteristic
143C23×C139#13112yes—
144D4×C139—42no—
145D4×C139—42no—
146D4×C139—84no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139—21no—
150C2×C4×C139—21no—
151C2×C4×C139—22no—
152C2×C4×C139—21no—
153C2×C4×C139—41no—
154C2×C4×C139—42no—
155C2×C4×C139—42no—
156C2×C4×C139—41no—
157C2×C4×C139—42no—
158C2×C4×C139—41no—
159C2×C4×C139—41no—
160C2×C4×C139—41no—
161C2×C4×C139—41no—
162C2×C4×C139—41no—
163C2×C4×C139—41no—
164C2×C4×C139—41no—
165C2×C4×C139—41no—
166C2×C4×C139—41no—
167C2×C4×C139—41no—
168C2×C4×C139—81no—
169C2×C4×C139—82no—
170C2×C4×C139#12011yescharacteristic
171C2×C4×C139#12112yes—
172C2×C4×C139#12311yescharacteristic
173C8×C139—44no—
174C8×C139—82no—
175C22×C139—21no—
176C22×C139—22no—
177C22×C139—21no—
178C22×C139—22no—
179C22×C139—41no—
180C22×C139—41no—
181C22×C139—42no—
182C22×C139—42no—
183C22×C139—42no—
184C22×C139—42no—
185C22×C139—41no—
186C22×C139—42no—
187C22×C139—41no—
188C22×C139—41no—
189C22×C139—81no—
190C22×C139—84no—
191C22×C139—81no—
192C22×C139—81no—
193C22×C139—84no—
194C22×C139—81no—
195C22×C139—81no—
196C22×C139#38611yescharacteristic
197C22×C139#40711yescharacteristic
198C22×C139#40811yescharacteristic
199C22×C139#43512yes—
200C22×C139#43612yes—
201C4×C139—21no—
202C4×C139—22no—
203C4×C139—21no—
204C4×C139—42no—
205C4×C139—41no—
206C4×C139—41no—
207C4×C139—41no—
208C4×C139—81no—
209C4×C139—81no—
210C2×C139—21no—
211C2×C139—21no—
212C2×C139—22no—
213C2×C139—22no—
214C2×C139—81no—
215C2×C139—82no—
216C2×C139#187011yescharacteristic
217C2×C139#191311yescharacteristic
218C2×C139#191411yescharacteristic
219#9109C13911yesmaximal, characteristic, direct product factor, Sylow
220C139#910911yescharacteristic, direct product factor, Sylow
221#2973C2×C13911yescharacteristic, complemented
222#2321C2×C13911yescharacteristic
223#1459C2×C13911yescharacteristic, complemented
224C2×#323C2×C13912yescomplemented
225#1282C2×C13912yescomplemented
226C2×#120C4×C13911yescharacteristic
227C2×C4×D4C22×C13911yescharacteristic
228C22×C22⋊C4C22×C13911yescharacteristic
229#435—24no—
230#432—21no—
231#407—21no—
232C2×C22⋊C8C22×C13912yes—
233C2×C22⋊C8C22×C13912yes—
234#390—21no—
235#388—21no—
236#388—21no—
237#386—21no—
238#386C4×C13911yescharacteristic
239#385C4×C13911yescharacteristic
240#379C4×C13911yescharacteristic
241C4×C22⋊C4C22×C13911yescharacteristic
242#324—21no—
243#323—21no—
244#323—24no—
245C25C2×C4×C13911yescharacteristic
246C22×D4—21no—
247C22×D4C2×C4×C13911yescharacteristic
248C23×C4C2×C4×C13911yescharacteristic
249C23×C4D4×C13911yescharacteristic
250C23×C4C23×C13911yescharacteristic
251C2×M16—22no—
252C22×C8—22no—
253C22×C8—22no—
254#120—22no—
255#120—22no—
256C4×D4—22no—
257C4×D4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4D4×C13911yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4C2×C4×C13911yescharacteristic
269C2×C22⋊C4C2×C4×C13911yescharacteristic
270C2×C22⋊C4C2×C4×C13911yescharacteristic
271C2×C22⋊C4D4×C13911yescharacteristic
272C2×C42—21no—
273C2×C42D4×C13911yescharacteristic
274C4⋊C8—22no—
275C22⋊C8—22no—
276C22⋊C8—22no—
277C22⋊C8—22no—
278C22⋊C8—22no—
279C22⋊C8D4×C13914yescomplemented
280#97—22no—
281#95—21no—
282#95—21no—
283#95—21no—
284C24—21no—
285C24—22no—
286C24—21no—
287C24—22no—
288C24—81no—
289C24—81no—
290C24C22⋊C4×C13911yescharacteristic
291C24M16×C13912yescomplemented
292C24C22×C4×C13911yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—22no—
297C2×D4—24no—
298C2×D4—81no—
299C2×D4—81no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—81no—
307C22×C4—81no—
308C22×C4—81no—
309C22×C4C22⋊C4×C13911yescharacteristic
310C22×C4C22⋊C4×C13911yescharacteristic
311C22×C4C22⋊C4×C13911yescharacteristic
312C22×C4C2×D4×C13912yes—
313C22×C4C2×D4×C13911yescharacteristic
314C22×C4C2×D4×C13911yescharacteristic
315C22×C4#41×C13912yes—
316M16—82no—
317C2×C8—24no—
318C2×C8—42no—
319C2×C8—82no—
320C2×C8—82no—
321C4⋊C4—22no—
322C4⋊C4—81no—
323C22⋊C4—24no—
324C22⋊C4—22no—
325C22⋊C4—21no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—41no—
329C22⋊C4—42no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4M16×C13912yescomplemented
335C42—21no—
336C42—21no—
337C42—81no—
338C23—22no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—24no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—42no—
353C23—41no—
354C23—82no—
355C23—82no—
356C23—82no—
357C23—82no—
358C23—84no—
359C23C2×C22⋊C4×C13911yescharacteristic
360C23C4×D4×C13912yes—
361C23C2×M16×C13911yescharacteristic
362C23C2×M16×C13911yescharacteristic
363C23#131×C13912yes—
364D4—42no—
365D4—42no—
366D4—84no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—81no—
389C2×C4—82no—
390C2×C4#120×C13911yescharacteristic
391C2×C4#121×C13912yes—
392C2×C4#123×C13911yescharacteristic
393C8—44no—
394C8—82no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—41no—
406C22—42no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—84no—
411C22—81no—
412C22—81no—
413C22—84no—
414C22—81no—
415C22—81no—
416C22#386×C13911yescharacteristic
417C22#407×C13911yescharacteristic
418C22#408×C13911yescharacteristic
419C22#435×C13912yes—
420C22#436×C13912yes—
421C4—21no—
422C4—22no—
423C4—21no—
424C4—42no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—81no—
429C4—81no—
430C2—21no—
431C2—21no—
432C2—22no—
433C2—22no—
434C2—81no—
435C2—82no—
436C2#1870×C13911yescharacteristic
437C2#1913×C13911yescharacteristic
438C2#1914×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC24C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC2×#120×C139C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2973×C139C2semidirect
3. #1459×C139C2semidirect
4. C2×#323×C139C2semidirect
5. #1282×C139C2semidirect
59. C22⋊C8×C139D4semidirect
71. C24×C139M16semidirect
114. C22⋊C4×C139M16semidirect
219. #9109C139direct (N × H)
220. C139#9109direct (N × H)
221. #2973C2×C139semidirect
223. #1459C2×C139semidirect
224. C2×#323C2×C139semidirect
225. #1282C2×C139semidirect
279. C22⋊C8D4×C139semidirect
291. C24M16×C139semidirect
334. C22⋊C4M16×C139semidirect

Maximal subgroups

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

subgroupindex
#2973×C1392
#2321×C1392
#1459×C1392
C2×#323×C1392
#1282×C1392
#9109139