Finite Group Databasebeta

← C139×#7781 #48002377

Subgroups — C139×#7781 #48002377

Order 35584.

536 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 98 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#2733×C139C211yesmaximal, characteristic
2#2024×C139C211yesmaximal, characteristic, complemented
3#2023×C139C211yesmaximal, characteristic, complemented
4#2013×C139C211yesmaximal, characteristic, complemented
5#1272×C139C211yesmaximal, characteristic, complemented
6#1270×C139C211yesmaximal, characteristic, complemented
7#1270×C139C211yesmaximal, characteristic, complemented
8C22×SD16×C139—21no—
9C2×C4⋊Q8×C139C2211yescharacteristic
10C2×#124×C139—21no—
11C2×#103×C139—21no—
12C2×#103×C139—21no—
13C2×#102×C139—21no—
14#394×C139—21no—
15#392×C139—21no—
16#392×C139—21no—
17#391×C139C2211yescharacteristic
18#390×C139C2211yescharacteristic
19#390×C139C2211yescharacteristic
20#388×C139—21no—
21#388×C139—21no—
22#340×C139—21no—
23#340×C139—21no—
24#336×C139C2211yescharacteristic
25#336×C139C2211yescharacteristic
26#336×C139C2211yescharacteristic
27C22×Q8×C139—21no—
28C22×Q8×C139D411yescharacteristic
29C22×D4×C139—21no—
30C22×D4×C139—21no—
31C22×D4×C139D411yescharacteristic
32C22×D4×C139D411yescharacteristic
33C2×SD16×C139—42no—
34C2×SD16×C139—42no—
35C2×SD16×C139—42no—
36C22×C8×C139—21no—
37C22×C8×C139—21no—
38C22×C8×C139—21no—
39C4⋊Q8×C139—42no—
40#124×C139—42no—
41#124×C139—42no—
42C2×C4⋊C4×C139—21no—
43C2×C4⋊C4×C139—21no—
44C2×C4⋊C4×C139D411yescharacteristic
45C2×C4⋊C4×C139D411yescharacteristic
46C2×C4⋊C4×C139D411yescharacteristic
47C2×C22⋊C4×C139—21no—
48C2×C22⋊C4×C139—21no—
49C2×C22⋊C4×C139—21no—
50C2×C22⋊C4×C139—21no—
51C2×C22⋊C4×C139—21no—
52C2×C22⋊C4×C139—21no—
53C2×C22⋊C4×C139—21no—
54C2×C22⋊C4×C139—21no—
55C2×C42×C139—21no—
56C2×C42×C139C2311yescharacteristic
57#103×C139—42no—
58#103×C139—42no—
59#102×C139—42no—
60#95×C139—21no—
61#95×C139—21no—
62#95×C139—21no—
63C24×C139—21no—
64C24×C139—21no—
65C2×Q8×C139—21no—
66C2×Q8×C139—22no—
67C2×Q8×C139—41no—
68C2×Q8×C139—41no—
69C2×Q8×C139—41no—
70C2×Q8×C139—41no—
71C2×Q8×C139—41no—
72C2×Q8×C139—41no—
73C2×Q8×C139—41no—
74C2×Q8×C139SD1612yescomplemented
75C2×D4×C139—21no—
76C2×D4×C139—21no—
77C2×D4×C139—21no—
78C2×D4×C139—21no—
79C2×D4×C139—41no—
80C2×D4×C139—41no—
81C2×D4×C139—41no—
82C2×D4×C139—41no—
83C2×D4×C139—42no—
84C2×D4×C139—81no—
85C2×D4×C139—81no—
86C2×D4×C139—81no—
87C2×D4×C139—81no—
88C2×D4×C139—81no—
89C22×C4×C139—21no—
90C22×C4×C139—21no—
91C22×C4×C139—21no—
92C22×C4×C139—21no—
93C22×C4×C139—41no—
94C22×C4×C139C2×D411yescharacteristic
95C22×C4×C139C2×D411yescharacteristic
96C22×C4×C139C2×D411yescharacteristic
97SD16×C139—48no—
98C2×C8×C139—22no—
99C2×C8×C139—41no—
100C2×C8×C139—41no—
101C2×C8×C139—41no—
102C2×C8×C139—41no—
103C2×C8×C139—41no—
104C2×C8×C139—41no—
105C2×C8×C139—41no—
106C2×C8×C139—41no—
107C4⋊C4×C139—22no—
108C4⋊C4×C139—22no—
109C4⋊C4×C139—41no—
110C4⋊C4×C139—41no—
111C4⋊C4×C139—41no—
112C4⋊C4×C139—41no—
113C4⋊C4×C139—41no—
114C22⋊C4×C139—42no—
115C22⋊C4×C139—42no—
116C22⋊C4×C139—41no—
117C22⋊C4×C139—41no—
118C22⋊C4×C139—41no—
119C22⋊C4×C139—41no—
120C22⋊C4×C139—41no—
121C22⋊C4×C139—41no—
122C22⋊C4×C139—41no—
123C22⋊C4×C139—41no—
124C22⋊C4×C139—81no—
125C22⋊C4×C139—81no—
126C42×C139—41no—
127C42×C139—42no—
128C23×C139—41no—
129C23×C139—41no—
130C23×C139—41no—
131C23×C139—41no—
132C23×C139—41no—
133C23×C139—41no—
134C23×C139—41no—
135C23×C139—41no—
136C23×C139—41no—
137C23×C139—41no—
138C23×C139—41no—
139C23×C139—41no—
140C23×C139—41no—
141C23×C139—41no—
142C23×C139#12011yescharacteristic
143Q8×C139—42no—
144Q8×C139—42no—
145Q8×C139—42no—
146Q8×C139—81no—
147Q8×C139—81no—
148Q8×C139—81no—
149D4×C139—42no—
150D4×C139—42no—
151D4×C139—81no—
152D4×C139—81no—
153D4×C139—84no—
154D4×C139—84no—
155C2×C4×C139—21no—
156C2×C4×C139—21no—
157C2×C4×C139—21no—
158C2×C4×C139—21no—
159C2×C4×C139—21no—
160C2×C4×C139—21no—
161C2×C4×C139—22no—
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—41no—
169C2×C4×C139—41no—
170C2×C4×C139—41no—
171C2×C4×C139—41no—
172C2×C4×C139—41no—
173C2×C4×C139—42no—
174C2×C4×C139—81no—
175C2×C4×C139—81no—
176C2×C4×C139C2×SD1611yescharacteristic
177C2×C4×C139#13511yescharacteristic
178C2×C4×C139#13511yescharacteristic
179C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C139#13711yescharacteristic
182C8×C139—42no—
183C8×C139—81no—
184C8×C139—81no—
185C22×C139—81no—
186C22×C139—81no—
187C22×C139—81no—
188C22×C139—81no—
189C22×C139—81no—
190C22×C139—81no—
191C22×C139—81no—
192C22×C139—81no—
193C22×C139—81no—
194C22×C139—81no—
195C22×C139—81no—
196C22×C139—81no—
197C22×C139—81no—
198C22×C139—81no—
199C22×C139#44911yescharacteristic
200C22×C139#45011yescharacteristic
201C22×C139#45211yescharacteristic
202C22×C139#45311yescharacteristic
203C22×C139#45511yescharacteristic
204C22×C139#45511yescharacteristic
205C22×C139B(4,𝔽2)11yescharacteristic
206C4×C139—21no—
207C4×C139—21no—
208C4×C139—21no—
209C4×C139—21no—
210C4×C139—21no—
211C4×C139—21no—
212C4×C139—42no—
213C4×C139—82no—
214C4×C139—81no—
215C4×C139—81no—
216C4×C139—81no—
217C2×C139—161no—
218C2×C139—161no—
219C2×C139#160011yescharacteristic
220C2×C139#160111yescharacteristic
221C2×C139#160611yescharacteristic
222C2×C139#163111yescharacteristic
223C2×C139#164211yescharacteristic
224C2×C139#164611yescharacteristic
225C2×C139#165911yescharacteristic
226#7781C13911yesmaximal, characteristic, direct product factor, Sylow
227C139#778111yescharacteristic, direct product factor, Sylow
228#2733C2×C13911yescharacteristic
229#2024C2×C13911yescharacteristic, complemented
230#2023C2×C13911yescharacteristic, complemented
231#2013C2×C13911yescharacteristic, complemented
232#1272C2×C13911yescharacteristic, complemented
233#1270C2×C13911yescharacteristic, complemented
234#1270C2×C13911yescharacteristic, complemented
235C22×SD16—21no—
236C2×C4⋊Q8C22×C13911yescharacteristic
237C2×#124—21no—
238C2×#103—21no—
239C2×#103—21no—
240C2×#102—21no—
241#394—21no—
242#392—21no—
243#392—21no—
244#391C22×C13911yescharacteristic
245#390C22×C13911yescharacteristic
246#390C22×C13911yescharacteristic
247#388—21no—
248#388—21no—
249#340—21no—
250#340—21no—
251#336C22×C13911yescharacteristic
252#336C22×C13911yescharacteristic
253#336C22×C13911yescharacteristic
254C22×Q8—21no—
255C22×Q8D4×C13911yescharacteristic
256C22×D4—21no—
257C22×D4—21no—
258C22×D4D4×C13911yescharacteristic
259C22×D4D4×C13911yescharacteristic
260C2×SD16—42no—
261C2×SD16—42no—
262C2×SD16—42no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C4⋊Q8—42no—
267#124—42no—
268#124—42no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4D4×C13911yescharacteristic
272C2×C4⋊C4D4×C13911yescharacteristic
273C2×C4⋊C4D4×C13911yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C42—21no—
283C2×C42C23×C13911yescharacteristic
284#103—42no—
285#103—42no—
286#102—42no—
287#95—21no—
288#95—21no—
289#95—21no—
290C24—21no—
291C24—21no—
292C2×Q8—21no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8SD16×C13912yescomplemented
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—42no—
311C2×D4—81no—
312C2×D4—81no—
313C2×D4—81no—
314C2×D4—81no—
315C2×D4—81no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4C2×D4×C13911yescharacteristic
322C22×C4C2×D4×C13911yescharacteristic
323C22×C4C2×D4×C13911yescharacteristic
324SD16—48no—
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—81no—
352C22⋊C4—81no—
353C42—41no—
354C42—42no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23#120×C13911yescharacteristic
370Q8—42no—
371Q8—42no—
372Q8—42no—
373Q8—81no—
374Q8—81no—
375Q8—81no—
376D4—42no—
377D4—42no—
378D4—81no—
379D4—81no—
380D4—84no—
381D4—84no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4C2×SD16×C13911yescharacteristic
404C2×C4#135×C13911yescharacteristic
405C2×C4#135×C13911yescharacteristic
406C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
407C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
408C2×C4#137×C13911yescharacteristic
409C8—42no—
410C8—81no—
411C8—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#449×C13911yescharacteristic
427C22#450×C13911yescharacteristic
428C22#452×C13911yescharacteristic
429C22#453×C13911yescharacteristic
430C22#455×C13911yescharacteristic
431C22#455×C13911yescharacteristic
432C22B(4,𝔽2)×C13911yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—82no—
441C4—81no—
442C4—81no—
443C4—81no—
444C2—161no—
445C2—161no—
446C2#1600×C13911yescharacteristic
447C2#1601×C13911yescharacteristic
448C2#1606×C13911yescharacteristic
449C2#1631×C13911yescharacteristic
450C2#1642×C13911yescharacteristic
451C2#1646×C13911yescharacteristic
452C2#1659×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutator, Frattini, cosocleC2×C42C23×C139
prime radical#2733×C139C2
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2024×C139C2semidirect
3. #2023×C139C2semidirect
4. #2013×C139C2semidirect
5. #1272×C139C2semidirect
6. #1270×C139C2semidirect
7. #1270×C139C2semidirect
74. C2×Q8×C139SD16semidirect
226. #7781C139direct (N × H)
227. C139#7781direct (N × H)
229. #2024C2×C139semidirect
230. #2023C2×C139semidirect
231. #2013C2×C139semidirect
232. #1272C2×C139semidirect
233. #1270C2×C139semidirect
234. #1270C2×C139semidirect
301. C2×Q8SD16×C139semidirect

Maximal subgroups

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

subgroupindex
#2733×C1392
#2024×C1392
#2023×C1392
#2013×C1392
#1272×C1392
#1270×C1392
#7781139