Finite Group Databasebeta

← C139×#9497 #48004093

Subgroups — C139×#9497 #48004093

Order 35584.

1184 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2403×C139C211yesmaximal, characteristic
2#2309×C139C211yesmaximal, characteristic, complemented
3#1781×C139C211yesmaximal, characteristic, complemented
4#1781×C139C212yesmaximal, complemented
5#1304×C139C212yesmaximal, complemented
6C23×D4×C139C2211yescharacteristic
7C23×D4×C139C2211yescharacteristic
8C2×#120×C139—21no—
9C2×#120×C139C412yescomplemented
10C2×#117×C139—21no—
11C2×#99×C139—22no—
12C2×#99×C139—24no—
13#392×C139—22no—
14#390×C139—24no—
15#386×C139—21no—
16#386×C139C412yescomplemented
17#379×C139—21no—
18#379×C139C2212yes—
19#379×C139C2211yescharacteristic
20#379×C139C2212yes—
21C25×C139C2×C411yescharacteristic
22C25×C139D411yescharacteristic
23C25×C139C2311yescharacteristic
24C22×D4×C139—22no—
25C22×D4×C139—21no—
26C22×D4×C139—22no—
27C22×D4×C139—22no—
28C22×D4×C139—21no—
29C22×D4×C139—22no—
30C22×D4×C139—22no—
31C22×D4×C139—44no—
32C22×D4×C139—44no—
33C22×D4×C139C2×C412yes—
34C22×D4×C139D412yes—
35C23×C4×C139C2×C411yescharacteristic
36C23×C4×C139D411yescharacteristic
37#120×C139—44no—
38#120×C139—44no—
39#117×C139—44no—
40C2×C4⋊C4×C139—22no—
41C2×C22⋊C4×C139—22no—
42C2×C22⋊C4×C139—22no—
43C2×C22⋊C4×C139—21no—
44C2×C22⋊C4×C139—22no—
45C2×C22⋊C4×C139—22no—
46C2×C22⋊C4×C139—22no—
47C2×C22⋊C4×C139—22no—
48C2×C22⋊C4×C139—22no—
49C2×C22⋊C4×C139—22no—
50C2×C22⋊C4×C139—21no—
51C2×C22⋊C4×C139—22no—
52C2×C22⋊C4×C139C2×C412yes—
53C2×C22⋊C4×C139D414yescomplemented
54C2×C42×C139—22no—
55#99×C139—48no—
56#99×C139—44no—
57#95×C139—22no—
58C24×C139—21no—
59C24×C139—21no—
60C24×C139—22no—
61C24×C139—21no—
62C24×C139—42no—
63C24×C139—42no—
64C24×C139—42no—
65C24×C139—42no—
66C24×C139—42no—
67C24×C139—42no—
68C24×C139—81no—
69C24×C139—81no—
70C24×C139—81no—
71C24×C139C22⋊C412yes—
72C24×C139C22×C411yescharacteristic
73C24×C139C2×D411yescharacteristic
74C24×C139C2×D411yescharacteristic
75C24×C139C2×D412yes—
76C24×C139#4112yes—
77C2×D4×C139—28no—
78C2×D4×C139—24no—
79C2×D4×C139—24no—
80C2×D4×C139—24no—
81C2×D4×C139—24no—
82C2×D4×C139—24no—
83C2×D4×C139—42no—
84C2×D4×C139—42no—
85C2×D4×C139—44no—
86C2×D4×C139—44no—
87C2×D4×C139—48no—
88C2×D4×C139—42no—
89C2×D4×C139—44no—
90C2×D4×C139—42no—
91C2×D4×C139—44no—
92C2×D4×C139—42no—
93C2×D4×C139—44no—
94C2×D4×C139—41no—
95C2×D4×C139—42no—
96C2×D4×C139—41no—
97C2×D4×C139—44no—
98C2×D4×C139—44no—
99C2×D4×C139—82no—
100C22×C4×C139—21no—
101C22×C4×C139—21no—
102C22×C4×C139—24no—
103C22×C4×C139—21no—
104C22×C4×C139—22no—
105C22×C4×C139—22no—
106C22×C4×C139—24no—
107C22×C4×C139—42no—
108C22×C4×C139—42no—
109C22×C4×C139C22⋊C412yes—
110C4⋊C4×C139—44no—
111C22⋊C4×C139—44no—
112C22⋊C4×C139—44no—
113C22⋊C4×C139—42no—
114C22⋊C4×C139—44no—
115C22⋊C4×C139—44no—
116C22⋊C4×C139—42no—
117C22⋊C4×C139—44no—
118C22⋊C4×C139—44no—
119C22⋊C4×C139—82no—
120C22⋊C4×C139—82no—
121C22⋊C4×C139—81no—
122C22⋊C4×C139—82no—
123C22⋊C4×C139—82no—
124C42×C139—44no—
125C23×C139—22no—
126C23×C139—22no—
127C23×C139—22no—
128C23×C139—22no—
129C23×C139—24no—
130C23×C139—22no—
131C23×C139—24no—
132C23×C139—22no—
133C23×C139—22no—
134C23×C139—22no—
135C23×C139—41no—
136C23×C139—41no—
137C23×C139—41no—
138C23×C139—42no—
139C23×C139—41no—
140C23×C139—42no—
141C23×C139—41no—
142C23×C139—42no—
143C23×C139—42no—
144C23×C139—42no—
145C23×C139—42no—
146C23×C139—42no—
147C23×C139—42no—
148C23×C139—41no—
149C23×C139—42no—
150C23×C139—42no—
151C23×C139—42no—
152C23×C139—42no—
153C23×C139—41no—
154C23×C139—42no—
155C23×C139—42no—
156C23×C139—81no—
157C23×C139—81no—
158C23×C139—82no—
159C23×C139—82no—
160C23×C139—88no—
161C23×C139—88no—
162C23×C139—88no—
163C23×C139C2×C22⋊C411yescharacteristic
164C23×C139C4×D412yes—
165C23×C139#12011yescharacteristic
166C23×C139#12112yes—
167C23×C139#12311yescharacteristic
168D4×C139—48no—
169D4×C139—48no—
170D4×C139—48no—
171D4×C139—44no—
172D4×C139—44no—
173D4×C139—88no—
174C2×C4×C139—22no—
175C2×C4×C139—22no—
176C2×C4×C139—24no—
177C2×C4×C139—22no—
178C2×C4×C139—22no—
179C2×C4×C139—22no—
180C2×C4×C139—24no—
181C2×C4×C139—41no—
182C2×C4×C139—42no—
183C2×C4×C139—41no—
184C2×C4×C139—44no—
185C2×C4×C139—42no—
186C2×C4×C139—44no—
187C2×C4×C139—42no—
188C2×C4×C139—42no—
189C2×C4×C139—44no—
190C2×C4×C139—82no—
191C2×C4×C139—82no—
192C2×C4×C139—82no—
193C2×C4×C139#9914yescomplemented
194C22×C139—21no—
195C22×C139—21no—
196C22×C139—21no—
197C22×C139—21no—
198C22×C139—22no—
199C22×C139—22no—
200C22×C139—21no—
201C22×C139—21no—
202C22×C139—22no—
203C22×C139—22no—
204C22×C139—22no—
205C22×C139—22no—
206C22×C139—21no—
207C22×C139—44no—
208C22×C139—44no—
209C22×C139—44no—
210C22×C139—44no—
211C22×C139—42no—
212C22×C139—42no—
213C22×C139—42no—
214C22×C139—42no—
215C22×C139—84no—
216C22×C139—82no—
217C22×C139—82no—
218C22×C139—84no—
219C22×C139—82no—
220C22×C139—84no—
221C22×C139—84no—
222C22×C139—84no—
223C22×C139—84no—
224C22×C139—81no—
225C22×C139—81no—
226C22×C139#38611yescharacteristic
227C22×C139C2×#9912yes—
228C22×C139B(4,𝔽2)12yes—
229C4×C139—24no—
230C4×C139—42no—
231C4×C139—84no—
232C4×C139—82no—
233C4×C139—162no—
234C2×C139—22no—
235C2×C139—22no—
236C2×C139—42no—
237C2×C139—42no—
238C2×C139—41no—
239C2×C139—82no—
240C2×C139—82no—
241C2×C139#188911yescharacteristic
242C2×C139#189811yescharacteristic
243C2×C139#191311yescharacteristic
244#9497C13911yesmaximal, characteristic, direct product factor, Sylow
245C139#949711yescharacteristic, direct product factor, Sylow
246#2403C2×C13911yescharacteristic
247#2309C2×C13911yescharacteristic, complemented
248#1781C2×C13912yescomplemented
249#1781C2×C13911yescharacteristic, complemented
250#1304C2×C13912yescomplemented
251C23×D4C22×C13911yescharacteristic
252C23×D4C22×C13911yescharacteristic
253C2×#120—21no—
254C2×#120C4×C13912yescomplemented
255C2×#117—21no—
256C2×#99—22no—
257C2×#99—24no—
258#392—22no—
259#390—24no—
260#386—21no—
261#386C4×C13912yescomplemented
262#379—21no—
263#379C22×C13912yes—
264#379C22×C13911yescharacteristic
265#379C22×C13912yes—
266C25C2×C4×C13911yescharacteristic
267C25D4×C13911yescharacteristic
268C25C23×C13911yescharacteristic
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2×C4×C13912yes—
279C22×D4D4×C13912yes—
280C23×C4C2×C4×C13911yescharacteristic
281C23×C4D4×C13911yescharacteristic
282#120—44no—
283#120—44no—
284#117—44no—
285C2×C4⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4C2×C4×C13912yes—
298C2×C22⋊C4D4×C13914yescomplemented
299C2×C42—22no—
300#99—48no—
301#99—44no—
302#95—22no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24C22⋊C4×C13912yes—
317C24C22×C4×C13911yescharacteristic
318C24C2×D4×C13911yescharacteristic
319C24C2×D4×C13911yescharacteristic
320C24C2×D4×C13912yes—
321C24#41×C13912yes—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—48no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—82no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C22⋊C4×C13912yes—
355C4⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—81no—
367C22⋊C4—82no—
368C22⋊C4—82no—
369C42—44no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—24no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23—82no—
404C23—82no—
405C23—88no—
406C23—88no—
407C23—88no—
408C23C2×C22⋊C4×C13911yescharacteristic
409C23C4×D4×C13912yes—
410C23#120×C13911yescharacteristic
411C23#121×C13912yes—
412C23#123×C13911yescharacteristic
413D4—48no—
414D4—48no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4#99×C13914yescomplemented
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—21no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—84no—
461C22—82no—
462C22—82no—
463C22—84no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22—81no—
471C22#386×C13911yescharacteristic
472C22C2×#99×C13912yes—
473C22B(4,𝔽2)×C13912yes—
474C4—24no—
475C4—42no—
476C4—82no—
477C4—84no—
478C4—162no—
479C2—22no—
480C2—22no—
481C2—42no—
482C2—42no—
483C2—41no—
484C2—82no—
485C2—82no—
486C2#1889×C13911yescharacteristic
487C2#1898×C13911yescharacteristic
488C2#1913×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC24C22×C4×C139
Frattini, cosocleC25C23×C139
prime radical#2403×C139C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C25×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2309×C139C2semidirect
3. #1781×C139C2semidirect
4. #1781×C139C2semidirect
5. #1304×C139C2semidirect
9. C2×#120×C139C4semidirect
16. #386×C139C4semidirect
53. C2×C22⋊C4×C139D4semidirect
193. C2×C4×C139#99semidirect
244. #9497C139direct (N × H)
245. C139#9497direct (N × H)
247. #2309C2×C139semidirect
248. #1781C2×C139semidirect
249. #1781C2×C139semidirect
250. #1304C2×C139semidirect
254. C2×#120C4×C139semidirect
261. #386C4×C139semidirect
298. C2×C22⋊C4D4×C139semidirect
438. C2×C4#99×C139semidirect

Maximal subgroups

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

subgroupindex
#2403×C1392
#2309×C1392
#1781×C1392
#1304×C1392
#9497139