Finite Group Databasebeta

← C139×#10190 #48004786

Subgroups — C139×#10190 #48004786

Order 35584.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3230×C139C211yesmaximal, characteristic, complemented
2#3077×C139C211yesmaximal, characteristic
3C2×#474×C139C211yesmaximal, characteristic
4#1548×C139C211yesmaximal, characteristic, complemented
5#1481×C139C211yesmaximal, characteristic, complemented
6#1460×C139C211yesmaximal, characteristic
7#1301×C139C211yesmaximal, characteristic, complemented
8#533×C139C2211yescharacteristic
9C2×C4⋊Q8×C139C2211yescharacteristic
10C2×C4×D4×C139C2211yescharacteristic
11#500×C139—21no—
12#487×C139—21no—
13#484×C139—22no—
14#478×C139—22no—
15#477×C139—22no—
16#476×C139—21no—
17#474×C139—22no—
18#474×C139—21no—
19#474×C139—22no—
20#431×C139C2211yescharacteristic
21#431×C139C2211yescharacteristic
22#428×C139—21no—
23C2×#107×C139—21no—
24#423×C139C2211yescharacteristic
25C2×C4⋊C8×C139C2211yescharacteristic
26#418×C139—21no—
27C2×#102×C139—21no—
28#333×C139—22no—
29Q8⋊C8×C139—22no—
30#323×C139—22no—
31C22×Q8×C139—21no—
32C22×D4×C139D411yescharacteristic
33C23×C4×C139—21no—
34C2×M16×C139—21no—
35C22×C8×C139—21no—
36C4⋊Q8×C139—21no—
37C4⋊Q8×C139—21no—
38C4⋊Q8×C139—21no—
39C4⋊Q8×C139D412yes—
40C4⋊Q8×C139D411yescharacteristic
41C4⋊Q8×C139D411yescharacteristic
42#125×C139—21no—
43C22⋊Q8×C139—21no—
44C22⋊Q8×C139—21no—
45C4×Q8×C139—21no—
46C4×Q8×C139—21no—
47C4×D4×C139—21no—
48C4×D4×C139—21no—
49C4×D4×C139—21no—
50C4×D4×C139—21no—
51#117×C139—21no—
52C2×C4⋊C4×C139—21no—
53C2×C4⋊C4×C139—21no—
54C2×C4⋊C4×C139D411yescharacteristic
55C2×C22⋊C4×C139—21no—
56C2×C42×C139C2311yescharacteristic
57#107×C139—24no—
58#107×C139—22no—
59#107×C139—24no—
60#106×C139—22no—
61C4⋊C8×C139—21no—
62C4⋊C8×C139—21no—
63C4⋊C8×C139—21no—
64C4⋊C8×C139—21no—
65C4⋊C8×C139D412yes—
66C4⋊C8×C139D412yes—
67#103×C139—24no—
68#102×C139—24no—
69#102×C139—22no—
70#102×C139—22no—
71C22⋊C8×C139—21no—
72C22⋊C8×C139D412yes—
73C4×C8×C139—21no—
74C4×C8×C139—21no—
75C24×C139—21no—
76C2×Q8×C139—21no—
77C2×Q8×C139—21no—
78C2×Q8×C139—22no—
79C2×Q8×C139—41no—
80C2×Q8×C139—82no—
81C2×D4×C139—21no—
82C2×D4×C139—21no—
83C2×D4×C139—21no—
84C2×D4×C139—21no—
85C2×D4×C139—21no—
86C2×D4×C139Q1612yes—
87C22×C4×C139—21no—
88C22×C4×C139—41no—
89C22×C4×C139—41no—
90C22×C4×C139—41no—
91C22×C4×C139—82no—
92C22×C4×C139C2×D411yescharacteristic
93C22×C4×C139C2×D411yescharacteristic
94C22×C4×C139#4111yescharacteristic
95M16×C139—41no—
96M16×C139—41no—
97C2×C8×C139—22no—
98C2×C8×C139—22no—
99C2×C8×C139—22no—
100C2×C8×C139—41no—
101C2×C8×C139—41no—
102C2×C8×C139—41no—
103C4⋊C4×C139—21no—
104C4⋊C4×C139—22no—
105C4⋊C4×C139—21no—
106C4⋊C4×C139—22no—
107C4⋊C4×C139—21no—
108C4⋊C4×C139—21no—
109C4⋊C4×C139—21no—
110C4⋊C4×C139—21no—
111C4⋊C4×C139—41no—
112C4⋊C4×C139—41no—
113C4⋊C4×C139—41no—
114C4⋊C4×C139—41no—
115C22⋊C4×C139—41no—
116C22⋊C4×C139—41no—
117C22⋊C4×C139—41no—
118C42×C139—41no—
119C42×C139C2×D411yescharacteristic
120C42×C139C2×D411yescharacteristic
121C42×C139C2×D411yescharacteristic
122C42×C139C2×D411yescharacteristic
123C23×C139—22no—
124C23×C139—41no—
125C23×C139—41no—
126C23×C139—81no—
127C23×C139—81no—
128C23×C139#12111yescharacteristic
129Q8×C139—42no—
130Q8×C139—42no—
131Q8×C139—82no—
132Q8×C139—82no—
133D4×C139—22no—
134D4×C139—22no—
135D4×C139—41no—
136D4×C139—41no—
137C2×C4×C139—22no—
138C2×C4×C139—41no—
139C2×C4×C139—41no—
140C2×C4×C139—41no—
141C2×C4×C139—41no—
142C2×C4×C139—42no—
143C2×C4×C139—82no—
144C2×C4×C139—82no—
145C2×C4×C139—82no—
146C2×C4×C139—81no—
147C2×C4×C139#12011yescharacteristic
148C2×C4×C139#12011yescharacteristic
149C2×C4×C139#12011yescharacteristic
150C2×C4×C139#12111yescharacteristic
151C2×C4×C139#12111yescharacteristic
152C2×C4×C139#12711yescharacteristic
153C2×C4×C139C2×Q1611yescharacteristic
154C2×C4×C139#13511yescharacteristic
155C2×C4×C139#13711yescharacteristic
156C2×C4×C139#13711yescharacteristic
157C8×C139—42no—
158C8×C139—42no—
159C8×C139—42no—
160C8×C139—81no—
161C22×C139—21no—
162C22×C139—21no—
163C22×C139—42no—
164C22×C139—82no—
165C22×C139—82no—
166C22×C139—81no—
167C22×C139—81no—
168C22×C139#39211yescharacteristic
169C22×C139#46711yescharacteristic
170C22×C139#47011yescharacteristic
171C4×C139—21no—
172C4×C139—21no—
173C4×C139—21no—
174C4×C139—81no—
175C4×C139—81no—
176C4×C139—82no—
177C4×C139—81no—
178C4×C139#45111yescharacteristic
179C4×C139#45111yescharacteristic
180C4×C139#45211yescharacteristic
181C4×C139#45211yescharacteristic
182C4×C139#47212yes—
183C2×C139—21no—
184C2×C139—21no—
185C2×C139—82no—
186C2×C139#200111yescharacteristic
187C2×C139#200911yescharacteristic
188C2×C139#201811yescharacteristic
189#10190C13911yesmaximal, characteristic, direct product factor, Sylow
190C139#1019011yescharacteristic, direct product factor, Sylow
191#3230C2×C13911yescharacteristic, complemented
192#3077C2×C13911yescharacteristic
193C2×#474C2×C13911yescharacteristic
194#1548C2×C13911yescharacteristic, complemented
195#1481C2×C13911yescharacteristic, complemented
196#1460C2×C13911yescharacteristic
197#1301C2×C13911yescharacteristic, complemented
198#533C22×C13911yescharacteristic
199C2×C4⋊Q8C22×C13911yescharacteristic
200C2×C4×D4C22×C13911yescharacteristic
201#500—21no—
202#487—21no—
203#484—22no—
204#478—22no—
205#477—22no—
206#476—21no—
207#474—21no—
208#474—22no—
209#474—22no—
210#431C22×C13911yescharacteristic
211#431C22×C13911yescharacteristic
212#428—21no—
213C2×#107—21no—
214#423C22×C13911yescharacteristic
215C2×C4⋊C8C22×C13911yescharacteristic
216#418—21no—
217C2×#102—21no—
218#333—22no—
219Q8⋊C8—22no—
220#323—22no—
221C22×Q8—21no—
222C22×D4D4×C13911yescharacteristic
223C23×C4—21no—
224C2×M16—21no—
225C22×C8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C13912yes—
230C4⋊Q8D4×C13911yescharacteristic
231C4⋊Q8D4×C13911yescharacteristic
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C4×D4—21no—
241#117—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4D4×C13911yescharacteristic
245C2×C22⋊C4—21no—
246C2×C42C23×C13911yescharacteristic
247#107—24no—
248#107—22no—
249#107—24no—
250#106—22no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8D4×C13912yes—
256C4⋊C8D4×C13912yes—
257#103—24no—
258#102—24no—
259#102—22no—
260#102—22no—
261C22⋊C8—21no—
262C22⋊C8D4×C13912yes—
263C4×C8—21no—
264C4×C8—21no—
265C24—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—82no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4Q16×C13912yes—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—82no—
282C22×C4C2×D4×C13911yescharacteristic
283C22×C4C2×D4×C13911yescharacteristic
284C22×C4#41×C13911yescharacteristic
285M16—41no—
286M16—41no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—41no—
309C42C2×D4×C13911yescharacteristic
310C42C2×D4×C13911yescharacteristic
311C42C2×D4×C13911yescharacteristic
312C42C2×D4×C13911yescharacteristic
313C23—22no—
314C23—41no—
315C23—41no—
316C23—81no—
317C23—81no—
318C23#121×C13911yescharacteristic
319Q8—42no—
320Q8—42no—
321Q8—82no—
322Q8—82no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4#120×C13911yescharacteristic
338C2×C4#120×C13911yescharacteristic
339C2×C4#120×C13911yescharacteristic
340C2×C4#121×C13911yescharacteristic
341C2×C4#121×C13911yescharacteristic
342C2×C4#127×C13911yescharacteristic
343C2×C4C2×Q16×C13911yescharacteristic
344C2×C4#135×C13911yescharacteristic
345C2×C4#137×C13911yescharacteristic
346C2×C4#137×C13911yescharacteristic
347C8—42no—
348C8—42no—
349C8—42no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—82no—
355C22—82no—
356C22—81no—
357C22—81no—
358C22#392×C13911yescharacteristic
359C22#467×C13911yescharacteristic
360C22#470×C13911yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4—82no—
367C4—81no—
368C4#451×C13911yescharacteristic
369C4#451×C13911yescharacteristic
370C4#452×C13911yescharacteristic
371C4#452×C13911yescharacteristic
372C4#472×C13912yes—
373C2—21no—
374C2—21no—
375C2—82no—
376C2#2001×C13911yescharacteristic
377C2#2009×C13911yescharacteristic
378C2#2018×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#392
commutator, Frattini, cosocleC2×C42C23×C139
prime radicalC22×D4×C139D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3230×C139C2semidirect
4. #1548×C139C2semidirect
5. #1481×C139C2semidirect
7. #1301×C139C2semidirect
189. #10190C139direct (N × H)
190. C139#10190direct (N × H)
191. #3230C2×C139semidirect
194. #1548C2×C139semidirect
195. #1481C2×C139semidirect
197. #1301C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3230×C1392
#3077×C1392
C2×#474×C1392
#1548×C1392
#1481×C1392
#1460×C1392
#1301×C1392
#10190139