Finite Group Databasebeta

← C139×#8537 #48003133

Subgroups — C139×#8537 #48003133

Order 35584.

794 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C139C211yesmaximal, characteristic
2#1901×C139C212yesmaximal, complemented
3#1870×C139C211yesmaximal, characteristic
4#1472×C139C212yesmaximal, complemented
5#1465×C139C211yesmaximal, characteristic
6C22×M16×C139C2211yescharacteristic
7#554×C139—24no—
8#554×C139—22no—
9D4×Q8×C139—22no—
10#544×C139—21no—
11#543×C139—21no—
12#543×C139C412yes—
13#533×C139—21no—
14C2×C22⋊Q8×C139—21no—
15C2×C22⋊Q8×C139C2212yes—
16#518×C139C412yes—
17C2×C4×D4×C139C2211yescharacteristic
18C2×#101×C139—22no—
19#407×C139C2212yes—
20C2×C22⋊C8×C139—21no—
21C2×C22⋊C8×C139C2211yescharacteristic
22#343×C139—22no—
23#336×C139—21no—
24#324×C139—21no—
25#324×C139—24no—
26#323×C139—21no—
27C22×Q8×C139—21no—
28C22×Q8×C139D412yes—
29C22×D4×C139C2×C411yescharacteristic
30C23×C4×C139D411yescharacteristic
31C23×C4×C139C2311yescharacteristic
32C2×M16×C139—22no—
33C2×M16×C139—22no—
34C2×M16×C139—42no—
35C22×C8×C139—21no—
36C22×C8×C139—21no—
37C4⋊Q8×C139—21no—
38C4⋊Q8×C139—21no—
39C4⋊Q8×C139—24no—
40#125×C139—22no—
41#125×C139—24no—
42C22⋊Q8×C139—22no—
43C22⋊Q8×C139—22no—
44C22⋊Q8×C139—24no—
45C22⋊Q8×C139—24no—
46C22⋊Q8×C139—22no—
47C22⋊Q8×C139—22no—
48C22⋊Q8×C139—24no—
49C22⋊Q8×C139—24no—
50C22⋊Q8×C139—22no—
51C22⋊Q8×C139—22no—
52C22⋊Q8×C139—22no—
53C22⋊Q8×C139—22no—
54C4×Q8×C139—22no—
55C4×Q8×C139—22no—
56C4×D4×C139—24no—
57C4×D4×C139—24no—
58C4×D4×C139—22no—
59C4×D4×C139—22no—
60#117×C139—22no—
61C2×C4⋊C4×C139—21no—
62C2×C4⋊C4×C139—22no—
63C2×C4⋊C4×C139D411yescharacteristic
64C2×C4⋊C4×C139D414yes—
65C2×C4⋊C4×C139D412yes—
66C2×C22⋊C4×C139—22no—
67C2×C22⋊C4×C139C2×C411yescharacteristic
68C2×C22⋊C4×C139C2×C414yes—
69C2×C22⋊C4×C139D411yescharacteristic
70C2×C42×C139D411yescharacteristic
71#101×C139—44no—
72C22⋊C8×C139—22no—
73C22⋊C8×C139—22no—
74C22⋊C8×C139—22no—
75C22⋊C8×C139—42no—
76C24×C139C22⋊C411yescharacteristic
77C24×C139C22×C411yescharacteristic
78C2×Q8×C139—22no—
79C2×Q8×C139—22no—
80C2×Q8×C139—22no—
81C2×Q8×C139—22no—
82C2×Q8×C139—42no—
83C2×Q8×C139—42no—
84C2×Q8×C139—81no—
85C2×Q8×C139—81no—
86C2×D4×C139—22no—
87C2×D4×C139—22no—
88C2×D4×C139—22no—
89C22×C4×C139—22no—
90C22×C4×C139—22no—
91C22×C4×C139—21no—
92C22×C4×C139—21no—
93C22×C4×C139—41no—
94C22×C4×C139—41no—
95C22×C4×C139—41no—
96C22×C4×C139—41no—
97C22×C4×C139C22⋊C411yescharacteristic
98C22×C4×C139C22⋊C411yescharacteristic
99C22×C4×C139C22⋊C414yes—
100C22×C4×C139C22⋊C414yes—
101C22×C4×C139C22⋊C411yescharacteristic
102C22×C4×C139C2×D411yescharacteristic
103C22×C4×C139C2×D412yes—
104C22×C4×C139C2×D411yescharacteristic
105C22×C4×C139C2×D412yes—
106M16×C139—24no—
107M16×C139—42no—
108M16×C139—42no—
109M16×C139—42no—
110C2×C8×C139—22no—
111C2×C8×C139—41no—
112C2×C8×C139—41no—
113C2×C8×C139—41no—
114C2×C8×C139—41no—
115C2×C8×C139—41no—
116C2×C8×C139—42no—
117C4⋊C4×C139—22no—
118C4⋊C4×C139—24no—
119C4⋊C4×C139—22no—
120C4⋊C4×C139—22no—
121C4⋊C4×C139—24no—
122C4⋊C4×C139—22no—
123C4⋊C4×C139—24no—
124C4⋊C4×C139—22no—
125C4⋊C4×C139—22no—
126C4⋊C4×C139—22no—
127C4⋊C4×C139—24no—
128C22⋊C4×C139—24no—
129C22⋊C4×C139—24no—
130C22⋊C4×C139—22no—
131C22⋊C4×C139—24no—
132C22⋊C4×C139—22no—
133C42×C139—24no—
134C42×C139—21no—
135C42×C139—21no—
136C23×C139—21no—
137C23×C139—21no—
138C23×C139—21no—
139C23×C139—21no—
140C23×C139—41no—
141C23×C139—41no—
142C23×C139—41no—
143C23×C139—41no—
144C23×C139#10112yescomplemented
145C23×C139C2×C22⋊C412yes—
146C23×C139C2×C22⋊C411yescharacteristic
147Q8×C139—42no—
148Q8×C139—42no—
149Q8×C139—82no—
150Q8×C139—82no—
151Q8×C139—82no—
152D4×C139—28no—
153C2×C4×C139—21no—
154C2×C4×C139—21no—
155C2×C4×C139—21no—
156C2×C4×C139—22no—
157C2×C4×C139—21no—
158C2×C4×C139—22no—
159C2×C4×C139—21no—
160C2×C4×C139—24no—
161C2×C4×C139—24no—
162C2×C4×C139—21no—
163C2×C4×C139—42no—
164C2×C4×C139—41no—
165C2×C4×C139—41no—
166C2×C4×C139—41no—
167C2×C4×C139—41no—
168C2×C4×C139—44no—
169C2×C4×C139—41no—
170C2×C4×C139—44no—
171C2×C4×C139—81no—
172C2×C4×C139—82no—
173C2×C4×C139—82no—
174C2×C4×C139#10112yescomplemented
175C2×C4×C139#12011yescharacteristic
176C2×C4×C139#12012yes—
177C2×C4×C139#12011yescharacteristic
178C8×C139—42no—
179C8×C139—81no—
180C8×C139—82no—
181C22×C139—21no—
182C22×C139—21no—
183C22×C139—22no—
184C22×C139—22no—
185C22×C139—22no—
186C22×C139—22no—
187C22×C139—42no—
188C22×C139—41no—
189C22×C139—41no—
190C22×C139—81no—
191C22×C139—81no—
192C22×C139—81no—
193C22×C139#37911yescharacteristic
194C22×C139C2×#10111yescharacteristic
195C22×C139C2×#10111yescharacteristic
196C4×C139—22no—
197C4×C139—21no—
198C4×C139—22no—
199C4×C139—41no—
200C4×C139—44no—
201C4×C139—44no—
202C4×C139—41no—
203C4×C139B(4,𝔽2)11yescharacteristic
204C4×C139#45811yescharacteristic
205C2×C139—21no—
206C2×C139—21no—
207C2×C139—42no—
208C2×C139—42no—
209C2×C139#178411yescharacteristic
210C2×C139#179011yescharacteristic
211C2×C139#179111yescharacteristic
212#8537C13911yesmaximal, characteristic, direct product factor, Sylow
213C139#853711yescharacteristic, direct product factor, Sylow
214#3501C2×C13911yescharacteristic
215#1901C2×C13912yescomplemented
216#1870C2×C13911yescharacteristic
217#1472C2×C13912yescomplemented
218#1465C2×C13911yescharacteristic
219C22×M16C22×C13911yescharacteristic
220#554—24no—
221#554—22no—
222D4×Q8—22no—
223#544—21no—
224#543—21no—
225#543C4×C13912yes—
226#533—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C22×C13912yes—
229#518C4×C13912yes—
230C2×C4×D4C22×C13911yescharacteristic
231C2×#101—22no—
232#407C22×C13912yes—
233C2×C22⋊C8—21no—
234C2×C22⋊C8C22×C13911yescharacteristic
235#343—22no—
236#336—21no—
237#324—21no—
238#324—24no—
239#323—21no—
240C22×Q8—21no—
241C22×Q8D4×C13912yes—
242C22×D4C2×C4×C13911yescharacteristic
243C23×C4D4×C13911yescharacteristic
244C23×C4C23×C13911yescharacteristic
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—42no—
248C22×C8—21no—
249C22×C8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—24no—
253#125—22no—
254#125—24no—
255C22⋊Q8—22no—
256C22⋊Q8—22no—
257C22⋊Q8—24no—
258C22⋊Q8—24no—
259C22⋊Q8—22no—
260C22⋊Q8—22no—
261C22⋊Q8—24no—
262C22⋊Q8—24no—
263C22⋊Q8—22no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266C22⋊Q8—22no—
267C4×Q8—22no—
268C4×Q8—22no—
269C4×D4—24no—
270C4×D4—24no—
271C4×D4—22no—
272C4×D4—22no—
273#117—22no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4D4×C13911yescharacteristic
277C2×C4⋊C4D4×C13914yes—
278C2×C4⋊C4D4×C13912yes—
279C2×C22⋊C4—22no—
280C2×C22⋊C4C2×C4×C13911yescharacteristic
281C2×C22⋊C4C2×C4×C13914yes—
282C2×C22⋊C4D4×C13911yescharacteristic
283C2×C42D4×C13911yescharacteristic
284#101—44no—
285C22⋊C8—22no—
286C22⋊C8—22no—
287C22⋊C8—22no—
288C22⋊C8—42no—
289C24C22⋊C4×C13911yescharacteristic
290C24C22×C4×C13911yescharacteristic
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—42no—
296C2×Q8—42no—
297C2×Q8—81no—
298C2×Q8—81no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4C22⋊C4×C13911yescharacteristic
311C22×C4C22⋊C4×C13911yescharacteristic
312C22×C4C22⋊C4×C13914yes—
313C22×C4C22⋊C4×C13914yes—
314C22×C4C22⋊C4×C13911yescharacteristic
315C22×C4C2×D4×C13911yescharacteristic
316C22×C4C2×D4×C13912yes—
317C22×C4C2×D4×C13911yescharacteristic
318C22×C4C2×D4×C13912yes—
319M16—24no—
320M16—42no—
321M16—42no—
322M16—42no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—42no—
330C4⋊C4—22no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—22no—
336C4⋊C4—24no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—22no—
344C22⋊C4—24no—
345C22⋊C4—22no—
346C42—24no—
347C42—21no—
348C42—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23#101×C13912yescomplemented
358C23C2×C22⋊C4×C13912yes—
359C23C2×C22⋊C4×C13911yescharacteristic
360Q8—42no—
361Q8—42no—
362Q8—82no—
363Q8—82no—
364Q8—82no—
365D4—28no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4#101×C13912yescomplemented
388C2×C4#120×C13911yescharacteristic
389C2×C4#120×C13912yes—
390C2×C4#120×C13911yescharacteristic
391C8—42no—
392C8—81no—
393C8—82no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—42no—
401C22—41no—
402C22—41no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22#379×C13911yescharacteristic
407C22C2×#101×C13911yescharacteristic
408C22C2×#101×C13911yescharacteristic
409C4—22no—
410C4—21no—
411C4—22no—
412C4—41no—
413C4—44no—
414C4—44no—
415C4—41no—
416C4B(4,𝔽2)×C13911yescharacteristic
417C4#458×C13911yescharacteristic
418C2—21no—
419C2—21no—
420C2—42no—
421C2—42no—
422C2#1784×C13911yescharacteristic
423C2#1790×C13911yescharacteristic
424C2#1791×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#379
commutatorC24C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC22×D4×C139C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1901×C139C2semidirect
4. #1472×C139C2semidirect
144. C23×C139#101semidirect
174. C2×C4×C139#101semidirect
212. #8537C139direct (N × H)
213. C139#8537direct (N × H)
215. #1901C2×C139semidirect
217. #1472C2×C139semidirect
357. C23#101×C139semidirect
387. C2×C4#101×C139semidirect

Maximal subgroups

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

subgroupindex
#3501×C1392
#1901×C1392
#1870×C1392
#1472×C1392
#1465×C1392
#8537139