Finite Group Databasebeta

← C139×#19265 #48013861

Subgroups — C139×#19265 #48013861

Order 35584.

606 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3170×C139C211yesmaximal, characteristic
2#3113×C139C212yesmaximal
3C2×C8×Q8×C139C211yesmaximal, characteristic
4#1680×C139C214yesmaximal, complemented
5#1674×C139C212yesmaximal, complemented
6#1670×C139C212yesmaximal, complemented
7#1568×C139C211yesmaximal, characteristic
8#1552×C139C212yesmaximal
9#533×C139C2212yes—
10C2×C4×Q8×C139C2211yescharacteristic
11#500×C139C2211yescharacteristic
12#494×C139C2211yescharacteristic
13#487×C139C2212yes—
14#483×C139—22no—
15#475×C139C2214yes—
16#467×C139—21no—
17#467×C139—21no—
18#462×C139C2214yes—
19#451×C139—22no—
20C8×Q8×C139—21no—
21C8×Q8×C139—21no—
22C8×Q8×C139C2212yes—
23C8×Q8×C139C2212yes—
24#441×C139—24no—
25C4×Q16×C139—21no—
26C4×Q16×C139—21no—
27#432×C139C2212yes—
28C2×C4⋊C8×C139—21no—
29C2×C4⋊C8×C139C2211yescharacteristic
30C2×C4×C8×C139—21no—
31C2×C4×C8×C139C2211yescharacteristic
32#335×C139C2212yes—
33#334×C139C2212yes—
34#332×C139C2214yes—
35#332×C139C2214yes—
36C22×Q8×C139D411yescharacteristic
37C2×Q16×C139—24no—
38C2×Q16×C139—21no—
39C2×Q16×C139—21no—
40C22×C8×C139—21no—
41C22×C8×C139D411yescharacteristic
42C22×C8×C139D411yescharacteristic
43C4⋊Q8×C139C2312yes—
44C4⋊Q8×C139C2312yes—
45#125×C139—22no—
46C22⋊Q8×C139—22no—
47C22⋊Q8×C139—22no—
48C4×Q8×C139—21no—
49C4×Q8×C139—21no—
50C4×Q8×C139—22no—
51C4×Q8×C139—22no—
52C4×Q8×C139D412yes—
53C4×Q8×C139C2312yes—
54#117×C139—22no—
55C2×C4⋊C4×C139—21no—
56C2×C4⋊C4×C139D411yescharacteristic
57C2×C42×C139—21no—
58C2×C42×C139C2311yescharacteristic
59#107×C139—21no—
60#107×C139—21no—
61#106×C139—24no—
62C4⋊C8×C139—22no—
63C4⋊C8×C139—22no—
64C4⋊C8×C139—21no—
65C4⋊C8×C139C2312yes—
66C4⋊C8×C139C2314yes—
67#103×C139—24no—
68#103×C139—22no—
69#103×C139—22no—
70#103×C139—24no—
71C22⋊C8×C139—22no—
72#97×C139—22no—
73C4×C8×C139—22no—
74C4×C8×C139—22no—
75C4×C8×C139D411yescharacteristic
76C4×C8×C139D411yescharacteristic
77C4×C8×C139C2311yescharacteristic
78C4×C8×C139C2311yescharacteristic
79C2×Q8×C139—24no—
80C2×Q8×C139—21no—
81C2×Q8×C139—22no—
82C2×Q8×C139—22no—
83C2×Q8×C139C2×D412yes—
84C22×C4×C139—21no—
85C22×C4×C139—21no—
86C22×C4×C139C2×D411yescharacteristic
87C22×C4×C139C2×D411yescharacteristic
88C22×C4×C139#4111yescharacteristic
89Q16×C139—42no—
90Q16×C139—48no—
91Q16×C139—42no—
92C2×C8×C139—22no—
93C2×C8×C139—22no—
94C2×C8×C139—24no—
95C2×C8×C139—41no—
96C2×C8×C139—42no—
97C2×C8×C139C2×D411yescharacteristic
98C2×C8×C139C2×D411yescharacteristic
99C2×C8×C139C2×D411yescharacteristic
100C2×C8×C139C2×D411yescharacteristic
101C4⋊C4×C139—22no—
102C4⋊C4×C139—21no—
103C4⋊C4×C139—22no—
104C4⋊C4×C139—22no—
105C4⋊C4×C139—22no—
106C4⋊C4×C139—22no—
107C4⋊C4×C139—22no—
108C4⋊C4×C139—42no—
109C4⋊C4×C139—42no—
110C4⋊C4×C139C2×D412yes—
111C22⋊C4×C139—42no—
112C42×C139—22no—
113C42×C139—22no—
114C42×C139—42no—
115C42×C139C2×D411yescharacteristic
116C42×C139C2×D411yescharacteristic
117C42×C139#4111yescharacteristic
118C42×C139C2411yescharacteristic
119C23×C139#12111yescharacteristic
120Q8×C139—24no—
121Q8×C139—22no—
122Q8×C139—44no—
123Q8×C139—42no—
124Q8×C139—42no—
125Q8×C139#13514yes—
126C2×C4×C139—24no—
127C2×C4×C139—22no—
128C2×C4×C139—22no—
129C2×C4×C139—22no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—22no—
133C2×C4×C139—42no—
134C2×C4×C139—42no—
135C2×C4×C139—42no—
136C2×C4×C139#12111yescharacteristic
137C2×C4×C139#12111yescharacteristic
138C2×C4×C139#12111yescharacteristic
139C2×C4×C139C22×D411yescharacteristic
140C2×C4×C139C22×D411yescharacteristic
141C2×C4×C139C2×#4111yescharacteristic
142C8×C139—21no—
143C8×C139—21no—
144C8×C139—21no—
145C8×C139—44no—
146C8×C139—42no—
147C8×C139#13712yes—
148C22×C139—21no—
149C22×C139—21no—
150C22×C139#47312yes—
151C22×C139C2×#12111yescharacteristic
152C4×C139—21no—
153C4×C139—24no—
154C4×C139—21no—
155C4×C139—21no—
156C4×C139—21no—
157C4×C139—42no—
158C4×C139—82no—
159C4×C139—82no—
160C4×C139C2×#13512yes—
161C4×C139C2×#13711yescharacteristic
162C4×C139#57511yescharacteristic
163C2×C139—22no—
164C2×C139#303711yescharacteristic
165C2×C139#305011yescharacteristic
166C2×C139C2×#47311yescharacteristic
167#19265C13911yesmaximal, characteristic, direct product factor, Sylow
168C139#1926511yescharacteristic, direct product factor, Sylow
169#3170C2×C13911yescharacteristic
170#3113C2×C13912yes—
171C2×C8×Q8C2×C13911yescharacteristic
172#1680C2×C13914yescomplemented
173#1674C2×C13912yescomplemented
174#1670C2×C13912yescomplemented
175#1568C2×C13911yescharacteristic
176#1552C2×C13912yes—
177#533C22×C13912yes—
178C2×C4×Q8C22×C13911yescharacteristic
179#500C22×C13911yescharacteristic
180#494C22×C13911yescharacteristic
181#487C22×C13912yes—
182#483—22no—
183#475C22×C13914yes—
184#467—21no—
185#467—21no—
186#462C22×C13914yes—
187#451—22no—
188C8×Q8—21no—
189C8×Q8—21no—
190C8×Q8C22×C13912yes—
191C8×Q8C22×C13912yes—
192#441—24no—
193C4×Q16—21no—
194C4×Q16—21no—
195#432C22×C13912yes—
196C2×C4⋊C8—21no—
197C2×C4⋊C8C22×C13911yescharacteristic
198C2×C4×C8—21no—
199C2×C4×C8C22×C13911yescharacteristic
200#335C22×C13912yes—
201#334C22×C13912yes—
202#332C22×C13914yes—
203#332C22×C13914yes—
204C22×Q8D4×C13911yescharacteristic
205C2×Q16—24no—
206C2×Q16—21no—
207C2×Q16—21no—
208C22×C8—21no—
209C22×C8D4×C13911yescharacteristic
210C22×C8D4×C13911yescharacteristic
211C4⋊Q8C23×C13912yes—
212C4⋊Q8C23×C13912yes—
213#125—22no—
214C22⋊Q8—22no—
215C22⋊Q8—22no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×Q8D4×C13912yes—
221C4×Q8C23×C13912yes—
222#117—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4D4×C13911yescharacteristic
225C2×C42—21no—
226C2×C42C23×C13911yescharacteristic
227#107—21no—
228#107—21no—
229#106—24no—
230C4⋊C8—22no—
231C4⋊C8—22no—
232C4⋊C8—21no—
233C4⋊C8C23×C13912yes—
234C4⋊C8C23×C13914yes—
235#103—24no—
236#103—22no—
237#103—22no—
238#103—24no—
239C22⋊C8—22no—
240#97—22no—
241C4×C8—22no—
242C4×C8—22no—
243C4×C8D4×C13911yescharacteristic
244C4×C8D4×C13911yescharacteristic
245C4×C8C23×C13911yescharacteristic
246C4×C8C23×C13911yescharacteristic
247C2×Q8—24no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8C2×D4×C13912yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4C2×D4×C13911yescharacteristic
255C22×C4C2×D4×C13911yescharacteristic
256C22×C4#41×C13911yescharacteristic
257Q16—42no—
258Q16—48no—
259Q16—42no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—24no—
263C2×C8—41no—
264C2×C8—42no—
265C2×C8C2×D4×C13911yescharacteristic
266C2×C8C2×D4×C13911yescharacteristic
267C2×C8C2×D4×C13911yescharacteristic
268C2×C8C2×D4×C13911yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4C2×D4×C13912yes—
279C22⋊C4—42no—
280C42—22no—
281C42—22no—
282C42—42no—
283C42C2×D4×C13911yescharacteristic
284C42C2×D4×C13911yescharacteristic
285C42#41×C13911yescharacteristic
286C42C24×C13911yescharacteristic
287C23#121×C13911yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—44no—
291Q8—42no—
292Q8—42no—
293Q8#135×C13914yes—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4#121×C13911yescharacteristic
305C2×C4#121×C13911yescharacteristic
306C2×C4#121×C13911yescharacteristic
307C2×C4C22×D4×C13911yescharacteristic
308C2×C4C22×D4×C13911yescharacteristic
309C2×C4C2×#41×C13911yescharacteristic
310C8—21no—
311C8—21no—
312C8—21no—
313C8—44no—
314C8—42no—
315C8#137×C13912yes—
316C22—21no—
317C22—21no—
318C22#473×C13912yes—
319C22C2×#121×C13911yescharacteristic
320C4—21no—
321C4—24no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—82no—
327C4—82no—
328C4C2×#135×C13912yes—
329C4C2×#137×C13911yescharacteristic
330C4#575×C13911yescharacteristic
331C2—22no—
332C2#3037×C13911yescharacteristic
333C2#3050×C13911yescharacteristic
334C2C2×#473×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#121
commutator, Frattini, cosocleC42C24×C139
prime radicalC23×C139#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1680×C139C2semidirect
5. #1674×C139C2semidirect
6. #1670×C139C2semidirect
167. #19265C139direct (N × H)
168. C139#19265direct (N × H)
172. #1680C2×C139semidirect
173. #1674C2×C139semidirect
174. #1670C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3170×C1392
#3113×C1392
C2×C8×Q8×C1392
#1680×C1392
#1674×C1392
#1670×C1392
#1568×C1392
#1552×C1392
#19265139