Finite Group Databasebeta

← C139×#18220 #48012816

Subgroups — C139×#18220 #48012816

Order 35584.

958 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3502×C139C211yesmaximal, characteristic, complemented
2#3101×C139C212yesmaximal
3#2536×C139C211yesmaximal, characteristic
4#1611×C139C214yesmaximal, complemented
5#1599×C139C214yesmaximal
6#1518×C139C212yesmaximal, complemented
7#1461×C139C211yesmaximal, characteristic, complemented
8Q82×C139—22no—
9#557×C139—22no—
10#557×C139—24no—
11#544×C139—21no—
12#544×C139C2214yes—
13#533×C139—22no—
14#533×C139C2212yes—
15C2×C22⋊Q8×C139—21no—
16#519×C139—21no—
17C2×C4×Q8×C139C2211yescharacteristic
18C2×C4×D4×C139C2211yescharacteristic
19#483×C139C2214yes—
20#476×C139—22no—
21#461×C139—22no—
22#450×C139C2214yes—
23C4×SD16×C139—24no—
24#431×C139C2212yes—
25#398×C139C2212yes—
26#394×C139C2212yes—
27#388×C139—22no—
28#382×C139C2211yescharacteristic
29#380×C139—21no—
30#328×C139C2218yes—
31#324×C139C2214yes—
32C22×Q8×C139D411yescharacteristic
33C22×D4×C139C2311yescharacteristic
34C23×C4×C139—21no—
35C2×SD16×C139—24no—
36C4⋊Q8×C139—22no—
37C4⋊Q8×C139—22no—
38C4⋊Q8×C139—24no—
39C4⋊Q8×C139—28no—
40C4⋊Q8×C139D412yes—
41C4⋊Q8×C139D412yes—
42#125×C139—24no—
43#125×C139—24no—
44#125×C139—28no—
45#125×C139—22no—
46C22⋊Q8×C139—22no—
47C22⋊Q8×C139—24no—
48C22⋊Q8×C139—44no—
49C22⋊Q8×C139C2314yes—
50C4×Q8×C139—24no—
51C4×Q8×C139—24no—
52C4×Q8×C139—24no—
53C4×Q8×C139—24no—
54C4×Q8×C139—22no—
55C4×Q8×C139—22no—
56C4×Q8×C139—22no—
57C4×Q8×C139D414yes—
58C4×D4×C139—22no—
59C4×D4×C139—22no—
60#117×C139—24no—
61#117×C139—22no—
62C2×C4⋊C4×C139—22no—
63C2×C4⋊C4×C139—21no—
64C2×C4⋊C4×C139D411yescharacteristic
65C2×C4⋊C4×C139C2311yescharacteristic
66C2×C4⋊C4×C139C2312yes—
67C2×C22⋊C4×C139—21no—
68C2×C22⋊C4×C139—22no—
69C2×C22⋊C4×C139—22no—
70C2×C42×C139D412yes—
71C2×C42×C139C2311yescharacteristic
72#106×C139—24no—
73C4⋊C8×C139—22no—
74#103×C139—24no—
75#102×C139—24no—
76C22⋊C8×C139C2314yes—
77C4×C8×C139—22no—
78#95×C139—22no—
79#95×C139—21no—
80#95×C139C2312yes—
81C24×C139—21no—
82C2×Q8×C139—24no—
83C2×Q8×C139—22no—
84C2×Q8×C139—22no—
85C2×Q8×C139—22no—
86C2×Q8×C139SD1614yescomplemented
87C2×Q8×C139C2×D414yes—
88C2×D4×C139—22no—
89C2×D4×C139—42no—
90C22×C4×C139—22no—
91C22×C4×C139—21no—
92C22×C4×C139—42no—
93C22×C4×C139—42no—
94C22×C4×C139—42no—
95C22×C4×C139C2×D412yes—
96C22×C4×C139C2×D412yes—
97C22×C4×C139C2×D411yescharacteristic
98C22×C4×C139C2×D411yescharacteristic
99C22×C4×C139C2411yescharacteristic
100SD16×C139—48no—
101C2×C8×C139—24no—
102C4⋊C4×C139—24no—
103C4⋊C4×C139—24no—
104C4⋊C4×C139—24no—
105C4⋊C4×C139—28no—
106C4⋊C4×C139—22no—
107C4⋊C4×C139—22no—
108C4⋊C4×C139—22no—
109C4⋊C4×C139—22no—
110C4⋊C4×C139—24no—
111C4⋊C4×C139—24no—
112C4⋊C4×C139—24no—
113C4⋊C4×C139—22no—
114C4⋊C4×C139—42no—
115C4⋊C4×C139—44no—
116C4⋊C4×C139C2×D414yes—
117C22⋊C4×C139—24no—
118C22⋊C4×C139—44no—
119C22⋊C4×C139—41no—
120C22⋊C4×C139—41no—
121C22⋊C4×C139—44no—
122C42×C139—28no—
123C42×C139—22no—
124C42×C139—22no—
125C42×C139—24no—
126C42×C139C2×D412yes—
127C42×C139C2×D412yes—
128C23×C139—22no—
129C23×C139—41no—
130C23×C139—41no—
131C23×C139—41no—
132C23×C139—41no—
133C23×C139—41no—
134C23×C139—41no—
135C23×C139C22×D411yescharacteristic
136Q8×C139—28no—
137Q8×C139—44no—
138Q8×C139—44no—
139Q8×C139—84no—
140D4×C139—24no—
141D4×C139—42no—
142C2×C4×C139—22no—
143C2×C4×C139—22no—
144C2×C4×C139—24no—
145C2×C4×C139—24no—
146C2×C4×C139—22no—
147C2×C4×C139—41no—
148C2×C4×C139—41no—
149C2×C4×C139—42no—
150C2×C4×C139—42no—
151C2×C4×C139—42no—
152C2×C4×C139—41no—
153C2×C4×C139—42no—
154C2×C4×C139—41no—
155C2×C4×C139—41no—
156C2×C4×C139—84no—
157C2×C4×C139#12011yescharacteristic
158C2×C4×C139#12011yescharacteristic
159C2×C4×C139#12012yes—
160C2×C4×C139C2×SD1614yes—
161C2×C4×C139C2×SD1612yes—
162C2×C4×C139#13712yes—
163C2×C4×C139C22×D412yes—
164C8×C139—44no—
165C22×C139—21no—
166C22×C139—21no—
167C22×C139—42no—
168C22×C139—42no—
169C22×C139—42no—
170C22×C139—81no—
171C22×C139—81no—
172C22×C139—81no—
173C22×C139—81no—
174C22×C139C2×#12011yescharacteristic
175C22×C139C22×SD1611yescharacteristic
176C22×C139C2×#13711yescharacteristic
177C4×C139—24no—
178C4×C139—21no—
179C4×C139—21no—
180C4×C139—22no—
181C4×C139—44no—
182C4×C139—42no—
183C4×C139—44no—
184C4×C139—82no—
185C4×C139—81no—
186C4×C139#44814yes—
187C2×C139—21no—
188C2×C139—21no—
189C2×C139—82no—
190C2×C139C2×#44811yescharacteristic
191C2×C139#302011yescharacteristic
192C2×C139#302511yescharacteristic
193#18220C13911yesmaximal, characteristic, direct product factor, Sylow
194C139#1822011yescharacteristic, direct product factor, Sylow
195#3502C2×C13911yescharacteristic, complemented
196#3101C2×C13912yes—
197#2536C2×C13911yescharacteristic
198#1611C2×C13914yescomplemented
199#1599C2×C13914yes—
200#1518C2×C13912yescomplemented
201#1461C2×C13911yescharacteristic, complemented
202Q82—22no—
203#557—22no—
204#557—24no—
205#544—21no—
206#544C22×C13914yes—
207#533—22no—
208#533C22×C13912yes—
209C2×C22⋊Q8—21no—
210#519—21no—
211C2×C4×Q8C22×C13911yescharacteristic
212C2×C4×D4C22×C13911yescharacteristic
213#483C22×C13914yes—
214#476—22no—
215#461—22no—
216#450C22×C13914yes—
217C4×SD16—24no—
218#431C22×C13912yes—
219#398C22×C13912yes—
220#394C22×C13912yes—
221#388—22no—
222#382C22×C13911yescharacteristic
223#380—21no—
224#328C22×C13918yes—
225#324C22×C13914yes—
226C22×Q8D4×C13911yescharacteristic
227C22×D4C23×C13911yescharacteristic
228C23×C4—21no—
229C2×SD16—24no—
230C4⋊Q8—22no—
231C4⋊Q8—22no—
232C4⋊Q8—24no—
233C4⋊Q8—28no—
234C4⋊Q8D4×C13912yes—
235C4⋊Q8D4×C13912yes—
236#125—24no—
237#125—24no—
238#125—28no—
239#125—22no—
240C22⋊Q8—22no—
241C22⋊Q8—24no—
242C22⋊Q8—44no—
243C22⋊Q8C23×C13914yes—
244C4×Q8—24no—
245C4×Q8—24no—
246C4×Q8—24no—
247C4×Q8—24no—
248C4×Q8—22no—
249C4×Q8—22no—
250C4×Q8—22no—
251C4×Q8D4×C13914yes—
252C4×D4—22no—
253C4×D4—22no—
254#117—24no—
255#117—22no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4D4×C13911yescharacteristic
259C2×C4⋊C4C23×C13911yescharacteristic
260C2×C4⋊C4C23×C13912yes—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C42D4×C13912yes—
265C2×C42C23×C13911yescharacteristic
266#106—24no—
267C4⋊C8—22no—
268#103—24no—
269#102—24no—
270C22⋊C8C23×C13914yes—
271C4×C8—22no—
272#95—22no—
273#95—21no—
274#95C23×C13912yes—
275C24—21no—
276C2×Q8—24no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8SD16×C13914yescomplemented
281C2×Q8C2×D4×C13914yes—
282C2×D4—22no—
283C2×D4—42no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C2×D4×C13912yes—
290C22×C4C2×D4×C13912yes—
291C22×C4C2×D4×C13911yescharacteristic
292C22×C4C2×D4×C13911yescharacteristic
293C22×C4C24×C13911yescharacteristic
294SD16—48no—
295C2×C8—24no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—28no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4—42no—
309C4⋊C4—44no—
310C4⋊C4C2×D4×C13914yes—
311C22⋊C4—24no—
312C22⋊C4—44no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—44no—
316C42—28no—
317C42—22no—
318C42—22no—
319C42—24no—
320C42C2×D4×C13912yes—
321C42C2×D4×C13912yes—
322C23—22no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23C22×D4×C13911yescharacteristic
330Q8—28no—
331Q8—44no—
332Q8—44no—
333Q8—84no—
334D4—24no—
335D4—42no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—84no—
351C2×C4#120×C13911yescharacteristic
352C2×C4#120×C13911yescharacteristic
353C2×C4#120×C13912yes—
354C2×C4C2×SD16×C13914yes—
355C2×C4C2×SD16×C13912yes—
356C2×C4#137×C13912yes—
357C2×C4C22×D4×C13912yes—
358C8—44no—
359C22—21no—
360C22—21no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22C2×#120×C13911yescharacteristic
369C22C22×SD16×C13911yescharacteristic
370C22C2×#137×C13911yescharacteristic
371C4—22no—
372C4—24no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—44no—
377C4—44no—
378C4—82no—
379C4—81no—
380C4#448×C13914yes—
381C2—21no—
382C2—21no—
383C2—82no—
384C2C2×#448×C13911yescharacteristic
385C2#3020×C13911yescharacteristic
386C2#3025×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC22×D4×C139C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3502×C139C2semidirect
4. #1611×C139C2semidirect
6. #1518×C139C2semidirect
7. #1461×C139C2semidirect
86. C2×Q8×C139SD16semidirect
193. #18220C139direct (N × H)
194. C139#18220direct (N × H)
195. #3502C2×C139semidirect
198. #1611C2×C139semidirect
200. #1518C2×C139semidirect
201. #1461C2×C139semidirect
280. C2×Q8SD16×C139semidirect

Maximal subgroups

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

subgroupindex
#3502×C1392
#3101×C1392
#2536×C1392
#1611×C1392
#1599×C1392
#1518×C1392
#1461×C1392
#18220139