Finite Group Databasebeta

← C139×#13047 #48007643

Subgroups — C139×#13047 #48007643

Order 35584.

888 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 888 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C2×#453×C139C211yesmaximal, characteristic
2#2366×C139C211yesmaximal, characteristic, complemented
3C2×#353×C139C211yesmaximal, characteristic, complemented
4#1790×C139C212yesmaximal, complemented
5#1390×C139C212yesmaximal, complemented
6C2×H(5,𝔽2)×C139C2211yescharacteristic
7C2×AGL(1,ℤ/8)×C139—21no—
8C2×#127×C139C2211yescharacteristic
9C2×C4×D4×C139—22no—
10#453×C139—22no—
11#453×C139C414yescomplemented
12C2×#104×C139—21no—
13C2×#100×C139C2211yescharacteristic
14C2×#99×C139—22no—
15C2×#99×C139C2212yes—
16#390×C139—22no—
17#386×C139—21no—
18#386×C139—22no—
19#386×C139C2212yes—
20C4×C4⋊C4×C139—21no—
21#353×C139—22no—
22H(5,𝔽2)×C139—22no—
23H(5,𝔽2)×C139—21no—
24H(5,𝔽2)×C139—42no—
25H(5,𝔽2)×C139C2×C412yescomplemented
26C2×#41×C139—21no—
27C2×#41×C139—41no—
28C22×D4×C139—22no—
29C22×D4×C139—22no—
30C22×D4×C139—41no—
31C22×D4×C139D411yescharacteristic
32C22×D4×C139C2311yescharacteristic
33C23×C4×C139—21no—
34C23×C4×C139D412yes—
35AGL(1,ℤ/8)×C139—24no—
36AGL(1,ℤ/8)×C139—42no—
37C2×SD16×C139—41no—
38C2×D8×C139—41no—
39C2×M16×C139—21no—
40#127×C139—22no—
41#127×C139C2×C412yes—
42#127×C139D412yes—
43C4×D4×C139—48no—
44C2×C4⋊C4×C139—21no—
45C2×C4⋊C4×C139—21no—
46C2×C22⋊C4×C139—22no—
47C2×C22⋊C4×C139—22no—
48C2×C22⋊C4×C139—22no—
49C2×C22⋊C4×C139—21no—
50C2×C22⋊C4×C139—42no—
51C2×C22⋊C4×C139D412yes—
52C2×C42×C139—22no—
53C2×C42×C139D411yescharacteristic
54#104×C139—24no—
55#100×C139—21no—
56#100×C139C2×C412yescomplemented
57#99×C139—22no—
58#99×C139—22no—
59#99×C139—44no—
60#95×C139—22no—
61#95×C139—42no—
62C24×C139—22no—
63C24×C139—21no—
64C24×C139C2×D412yes—
65#41×C139—22no—
66#41×C139—22no—
67#41×C139—42no—
68#41×C139—41no—
69#41×C139—44no—
70#41×C139—42no—
71#41×C139—41no—
72C2×Q8×C139—21no—
73C2×D4×C139—21no—
74C2×D4×C139—24no—
75C2×D4×C139—24no—
76C2×D4×C139—24no—
77C2×D4×C139—24no—
78C2×D4×C139—21no—
79C2×D4×C139—41no—
80C2×D4×C139—41no—
81C2×D4×C139—44no—
82C2×D4×C139—44no—
83C2×D4×C139—41no—
84C2×D4×C139—41no—
85C2×D4×C139—42no—
86C2×D4×C139—42no—
87C2×D4×C139—42no—
88C2×D4×C139—42no—
89C2×D4×C139—44no—
90C2×D4×C139—41no—
91C2×D4×C139—42no—
92C2×D4×C139C22⋊C412yescomplemented
93C2×D4×C139C22×C411yescharacteristic
94C2×D4×C139C2×D411yescharacteristic
95C2×D4×C139#4112yes—
96C22×C4×C139—21no—
97C22×C4×C139—22no—
98C22×C4×C139—22no—
99C22×C4×C139—22no—
100C22×C4×C139—41no—
101C22×C4×C139—44no—
102C22×C4×C139—44no—
103C22×C4×C139—42no—
104C22×C4×C139—42no—
105C22×C4×C139—81no—
106C22×C4×C139C2×D411yescharacteristic
107SD16×C139—44no—
108D8×C139—44no—
109M16×C139—22no—
110M16×C139—41no—
111C2×C8×C139—41no—
112C4⋊C4×C139—24no—
113C4⋊C4×C139—42no—
114C22⋊C4×C139—44no—
115C22⋊C4×C139—44no—
116C22⋊C4×C139—42no—
117C22⋊C4×C139—42no—
118C22⋊C4×C139—42no—
119C22⋊C4×C139—81no—
120C22⋊C4×C139—84no—
121C42×C139—21no—
122C42×C139—44no—
123C42×C139C22⋊C412yescomplemented
124C23×C139—22no—
125C23×C139—22no—
126C23×C139—24no—
127C23×C139—22no—
128C23×C139—42no—
129C23×C139—42no—
130C23×C139—42no—
131C23×C139—42no—
132C23×C139—42no—
133C23×C139—41no—
134C23×C139—41no—
135C23×C139—41no—
136C23×C139—82no—
137C23×C139—82no—
138C23×C139C4×D412yes—
139C23×C139#12011yescharacteristic
140C23×C139#12112yes—
141Q8×C139—22no—
142Q8×C139—41no—
143D4×C139—22no—
144D4×C139—41no—
145D4×C139—41no—
146D4×C139—42no—
147D4×C139—42no—
148D4×C139—48no—
149D4×C139—48no—
150D4×C139—41no—
151D4×C139—44no—
152D4×C139—44no—
153D4×C139—42no—
154D4×C139—42no—
155D4×C139—81no—
156C2×C4×C139—22no—
157C2×C4×C139—22no—
158C2×C4×C139—22no—
159C2×C4×C139—21no—
160C2×C4×C139—21no—
161C2×C4×C139—24no—
162C2×C4×C139—24no—
163C2×C4×C139—42no—
164C2×C4×C139—42no—
165C2×C4×C139—42no—
166C2×C4×C139—42no—
167C2×C4×C139—41no—
168C2×C4×C139—42no—
169C2×C4×C139—44no—
170C2×C4×C139—42no—
171C2×C4×C139—42no—
172C2×C4×C139—42no—
173C2×C4×C139—82no—
174C2×C4×C139—84no—
175C2×C4×C139—82no—
176C2×C4×C139—82no—
177C2×C4×C139—82no—
178C2×C4×C139C2×C22⋊C411yescharacteristic
179C2×C4×C139#12311yescharacteristic
180C8×C139—42no—
181C22×C139—21no—
182C22×C139—21no—
183C22×C139—22no—
184C22×C139—22no—
185C22×C139—42no—
186C22×C139—42no—
187C22×C139—44no—
188C22×C139—42no—
189C22×C139—42no—
190C22×C139—42no—
191C22×C139—42no—
192C22×C139—82no—
193C22×C139—82no—
194C22×C139—84no—
195C22×C139—81no—
196C22×C139—81no—
197C22×C139—81no—
198C22×C139—81no—
199C22×C139—162no—
200C22×C139#38611yescharacteristic
201C22×C139B(4,𝔽2)11yescharacteristic
202C22×C139B(4,𝔽2)11yescharacteristic
203C4×C139—24no—
204C4×C139—21no—
205C4×C139—21no—
206C4×C139—42no—
207C4×C139—44no—
208C4×C139—82no—
209C4×C139—162no—
210C2×C139—21no—
211C2×C139—21no—
212C2×C139—42no—
213C2×C139—42no—
214C2×C139—82no—
215C2×C139—82no—
216C2×C139#188911yescharacteristic
217C2×C139#219611yescharacteristic
218C2×C139#219811yescharacteristic
219#13047C13911yesmaximal, characteristic, direct product factor, Sylow
220C139#1304711yescharacteristic, direct product factor, Sylow
221C2×#453C2×C13911yescharacteristic
222#2366C2×C13911yescharacteristic, complemented
223C2×#353C2×C13911yescharacteristic, complemented
224#1790C2×C13912yescomplemented
225#1390C2×C13912yescomplemented
226C2×H(5,𝔽2)C22×C13911yescharacteristic
227C2×AGL(1,ℤ/8)—21no—
228C2×#127C22×C13911yescharacteristic
229C2×C4×D4—22no—
230#453—22no—
231#453C4×C13914yescomplemented
232C2×#104—21no—
233C2×#100C22×C13911yescharacteristic
234C2×#99—22no—
235C2×#99C22×C13912yes—
236#390—22no—
237#386—21no—
238#386—22no—
239#386C22×C13912yes—
240C4×C4⋊C4—21no—
241#353—22no—
242H(5,𝔽2)—22no—
243H(5,𝔽2)—21no—
244H(5,𝔽2)—42no—
245H(5,𝔽2)C2×C4×C13912yescomplemented
246C2×#41—21no—
247C2×#41—41no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—41no—
251C22×D4D4×C13911yescharacteristic
252C22×D4C23×C13911yescharacteristic
253C23×C4—21no—
254C23×C4D4×C13912yes—
255AGL(1,ℤ/8)—24no—
256AGL(1,ℤ/8)—42no—
257C2×SD16—41no—
258C2×D8—41no—
259C2×M16—21no—
260#127—22no—
261#127C2×C4×C13912yes—
262#127D4×C13912yes—
263C4×D4—48no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—42no—
271C2×C22⋊C4D4×C13912yes—
272C2×C42—22no—
273C2×C42D4×C13911yescharacteristic
274#104—24no—
275#100—21no—
276#100C2×C4×C13912yescomplemented
277#99—22no—
278#99—22no—
279#99—44no—
280#95—22no—
281#95—42no—
282C24—22no—
283C24—21no—
284C24C2×D4×C13912yes—
285#41—22no—
286#41—22no—
287#41—42no—
288#41—41no—
289#41—44no—
290#41—42no—
291#41—41no—
292C2×Q8—21no—
293C2×D4—21no—
294C2×D4—24no—
295C2×D4—24no—
296C2×D4—24no—
297C2×D4—24no—
298C2×D4—21no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—44no—
302C2×D4—44no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—42no—
308C2×D4—42no—
309C2×D4—44no—
310C2×D4—41no—
311C2×D4—42no—
312C2×D4C22⋊C4×C13912yescomplemented
313C2×D4C22×C4×C13911yescharacteristic
314C2×D4C2×D4×C13911yescharacteristic
315C2×D4#41×C13912yes—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—41no—
321C22×C4—44no—
322C22×C4—44no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—81no—
326C22×C4C2×D4×C13911yescharacteristic
327SD16—44no—
328D8—44no—
329M16—22no—
330M16—41no—
331C2×C8—41no—
332C4⋊C4—24no—
333C4⋊C4—42no—
334C22⋊C4—44no—
335C22⋊C4—44no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—81no—
340C22⋊C4—84no—
341C42—21no—
342C42—44no—
343C42C22⋊C4×C13912yescomplemented
344C23—22no—
345C23—22no—
346C23—24no—
347C23—22no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—82no—
357C23—82no—
358C23C4×D4×C13912yes—
359C23#120×C13911yescharacteristic
360C23#121×C13912yes—
361Q8—22no—
362Q8—41no—
363D4—22no—
364D4—41no—
365D4—41no—
366D4—42no—
367D4—42no—
368D4—41no—
369D4—48no—
370D4—48no—
371D4—44no—
372D4—44no—
373D4—42no—
374D4—42no—
375D4—81no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—84no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4C2×C22⋊C4×C13911yescharacteristic
399C2×C4#123×C13911yescharacteristic
400C8—42no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—22no—
405C22—42no—
406C22—42no—
407C22—44no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—82no—
413C22—82no—
414C22—84no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—162no—
420C22#386×C13911yescharacteristic
421C22B(4,𝔽2)×C13911yescharacteristic
422C22B(4,𝔽2)×C13911yescharacteristic
423C4—24no—
424C4—21no—
425C4—21no—
426C4—42no—
427C4—44no—
428C4—82no—
429C4—162no—
430C2—21no—
431C2—21no—
432C2—42no—
433C2—42no—
434C2—82no—
435C2—82no—
436C2#1889×C13911yescharacteristic
437C2#2196×C13911yescharacteristic
438C2#2198×C13911yescharacteristic
subgroupG/H
center, socleC22×C139B(4,𝔽2)
commutatorC2×D4C22×C4×C139
Frattini, cosocleC22×D4C23×C139
prime radicalC2×#453×C139C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C139 ◁ C22×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2366×C139C2semidirect
3. C2×#353×C139C2semidirect
4. #1790×C139C2semidirect
5. #1390×C139C2semidirect
11. #453×C139C4semidirect
25. H(5,𝔽2)×C139C2×C4semidirect
56. #100×C139C2×C4semidirect
92. C2×D4×C139C22⋊C4semidirect
123. C42×C139C22⋊C4semidirect
219. #13047C139direct (N × H)
220. C139#13047direct (N × H)
222. #2366C2×C139semidirect
223. C2×#353C2×C139semidirect
224. #1790C2×C139semidirect
225. #1390C2×C139semidirect
231. #453C4×C139semidirect
245. H(5,𝔽2)C2×C4×C139semidirect
276. #100C2×C4×C139semidirect
312. C2×D4C22⋊C4×C139semidirect
343. C42C22⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#453×C1392
#2366×C1392
C2×#353×C1392
#1790×C1392
#1390×C1392
#13047139