Finite Group Databasebeta

← C139×#7730 #48002326

Subgroups — C139×#7730 #48002326

Order 35584.

520 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2850×C139C211yesmaximal, characteristic
2#1817×C139C211yesmaximal, characteristic, complemented
3#1797×C139C211yesmaximal, characteristic, complemented
4#1272×C139C212yesmaximal, complemented
5#1270×C139C212yesmaximal, complemented
6C2×#124×C139C411yescharacteristic
7C2×C22⋊Q8×C139C411yescharacteristic
8C2×#121×C139C411yescharacteristic
9C22×C42×C139C2211yescharacteristic
10C2×C4⋊C8×C139—21no—
11C2×C22⋊C8×C139—21no—
12C2×C22⋊C8×C139—21no—
13#391×C139C2211yescharacteristic
14#390×C139C2211yescharacteristic
15#388×C139—21no—
16#388×C139—21no—
17#386×C139—21no—
18#386×C139—21no—
19#382×C139C411yescharacteristic
20#336×C139—21no—
21#336×C139C2212yes—
22#336×C139C2212yes—
23C22×Q8×C139C2×C411yescharacteristic
24C22×D4×C139—21no—
25C22×D4×C139C2×C411yescharacteristic
26C23×C4×C139C2×C411yescharacteristic
27C23×C4×C139D411yescharacteristic
28C23×C4×C139D411yescharacteristic
29C22×C8×C139—22no—
30C22×C8×C139—22no—
31#124×C139—42no—
32C22⋊Q8×C139—42no—
33#121×C139—42no—
34C2×C4⋊C4×C139—21no—
35C2×C4⋊C4×C139C2×C411yescharacteristic
36C2×C4⋊C4×C139C2×C411yescharacteristic
37C2×C22⋊C4×C139—21no—
38C2×C22⋊C4×C139—21no—
39C2×C22⋊C4×C139—21no—
40C2×C22⋊C4×C139—21no—
41C2×C22⋊C4×C139—21no—
42C2×C22⋊C4×C139—21no—
43C2×C42×C139—42no—
44C2×C42×C139C2×C411yescharacteristic
45C2×C42×C139D411yescharacteristic
46C2×C42×C139D411yescharacteristic
47C2×C42×C139C2311yescharacteristic
48C4⋊C8×C139—42no—
49C22⋊C8×C139—42no—
50C22⋊C8×C139—42no—
51#95×C139—21no—
52#95×C139—21no—
53#95×C139—21no—
54#95×C139—21no—
55C24×C139—21no—
56C24×C139C22⋊C411yescharacteristic
57C2×Q8×C139—22no—
58C2×Q8×C139—41no—
59C2×Q8×C139—41no—
60C2×D4×C139—22no—
61C2×D4×C139—41no—
62C2×D4×C139—41no—
63C2×D4×C139—42no—
64C2×D4×C139—42no—
65C2×D4×C139—42no—
66C22×C4×C139—22no—
67C22×C4×C139—22no—
68C22×C4×C139—22no—
69C22×C4×C139—22no—
70C22×C4×C139—21no—
71C22×C4×C139—21no—
72C22×C4×C139—21no—
73C22×C4×C139—21no—
74C22×C4×C139—21no—
75C22×C4×C139—41no—
76C22×C4×C139—41no—
77C22×C4×C139—41no—
78C22×C4×C139—41no—
79C22×C4×C139C22⋊C411yescharacteristic
80C22×C4×C139C22⋊C411yescharacteristic
81C22×C4×C139C22⋊C411yescharacteristic
82C22×C4×C139C22×C411yescharacteristic
83C22×C4×C139C2×D411yescharacteristic
84C22×C4×C139C2×D411yescharacteristic
85C2×C8×C139—42no—
86C2×C8×C139—42no—
87C2×C8×C139—42no—
88C2×C8×C139—42no—
89C2×C8×C139—42no—
90C2×C8×C139—42no—
91C4⋊C4×C139—41no—
92C4⋊C4×C139—41no—
93C4⋊C4×C139—42no—
94C22⋊C4×C139—42no—
95C22⋊C4×C139—42no—
96C22⋊C4×C139—42no—
97C22⋊C4×C139—42no—
98C22⋊C4×C139—42no—
99C22⋊C4×C139—41no—
100C22⋊C4×C139—41no—
101C42×C139—22no—
102C42×C139—22no—
103C42×C139—41no—
104C42×C139—41no—
105C23×C139—21no—
106C23×C139—21no—
107C23×C139—21no—
108C23×C139—21no—
109C23×C139—21no—
110C23×C139—21no—
111C23×C139—41no—
112C23×C139—41no—
113C23×C139—41no—
114C23×C139—41no—
115C23×C139—41no—
116C23×C139—41no—
117C23×C139—41no—
118C23×C139#10012yes—
119C23×C139C2×C22⋊C411yescharacteristic
120Q8×C139—82no—
121D4×C139—82no—
122D4×C139—84no—
123C2×C4×C139—21no—
124C2×C4×C139—21no—
125C2×C4×C139—21no—
126C2×C4×C139—21no—
127C2×C4×C139—21no—
128C2×C4×C139—21no—
129C2×C4×C139—21no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—44no—
138C2×C4×C139—44no—
139C2×C4×C139—42no—
140C2×C4×C139—42no—
141C2×C4×C139—41no—
142C2×C4×C139—41no—
143C2×C4×C139—41no—
144C2×C4×C139—41no—
145C2×C4×C139—41no—
146C2×C4×C139—41no—
147C2×C4×C139—41no—
148C2×C4×C139—41no—
149C2×C4×C139—41no—
150C2×C4×C139#9912yes—
151C2×C4×C139#13112yes—
152C2×C4×C139#13512yes—
153C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C139#13711yescharacteristic
155C8×C139—82no—
156C8×C139—82no—
157C22×C139—22no—
158C22×C139—22no—
159C22×C139—22no—
160C22×C139—41no—
161C22×C139—41no—
162C22×C139—41no—
163C22×C139—41no—
164C22×C139—81no—
165C22×C139—81no—
166C22×C139—81no—
167C22×C139—81no—
168C22×C139—81no—
169C22×C139—81no—
170C22×C139—81no—
171C22×C139#40811yescharacteristic
172C22×C139C2×#9911yescharacteristic
173C22×C139C2×#10011yescharacteristic
174C22×C139#41611yescharacteristic
175C22×C139#41711yescharacteristic
176C22×C139#42111yescharacteristic
177C22×C139#42111yescharacteristic
178C4×C139—22no—
179C4×C139—21no—
180C4×C139—21no—
181C4×C139—22no—
182C4×C139—22no—
183C4×C139—41no—
184C4×C139—41no—
185C4×C139—81no—
186C4×C139—81no—
187C4×C139—81no—
188C2×C139—42no—
189C2×C139—161no—
190C2×C139#147111yescharacteristic
191C2×C139#148211yescharacteristic
192C2×C139#149511yescharacteristic
193C2×C139#151311yescharacteristic
194C2×C139#151611yescharacteristic
195C2×C139#153311yescharacteristic
196C2×C139#155111yescharacteristic
197#7730C13911yesmaximal, characteristic, direct product factor, Sylow
198C139#773011yescharacteristic, direct product factor, Sylow
199#2850C2×C13911yescharacteristic
200#1817C2×C13911yescharacteristic, complemented
201#1797C2×C13911yescharacteristic, complemented
202#1272C2×C13912yescomplemented
203#1270C2×C13912yescomplemented
204C2×#124C4×C13911yescharacteristic
205C2×C22⋊Q8C4×C13911yescharacteristic
206C2×#121C4×C13911yescharacteristic
207C22×C42C22×C13911yescharacteristic
208C2×C4⋊C8—21no—
209C2×C22⋊C8—21no—
210C2×C22⋊C8—21no—
211#391C22×C13911yescharacteristic
212#390C22×C13911yescharacteristic
213#388—21no—
214#388—21no—
215#386—21no—
216#386—21no—
217#382C4×C13911yescharacteristic
218#336—21no—
219#336C22×C13912yes—
220#336C22×C13912yes—
221C22×Q8C2×C4×C13911yescharacteristic
222C22×D4—21no—
223C22×D4C2×C4×C13911yescharacteristic
224C23×C4C2×C4×C13911yescharacteristic
225C23×C4D4×C13911yescharacteristic
226C23×C4D4×C13911yescharacteristic
227C22×C8—22no—
228C22×C8—22no—
229#124—42no—
230C22⋊Q8—42no—
231#121—42no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4C2×C4×C13911yescharacteristic
234C2×C4⋊C4C2×C4×C13911yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C42—42no—
242C2×C42C2×C4×C13911yescharacteristic
243C2×C42D4×C13911yescharacteristic
244C2×C42D4×C13911yescharacteristic
245C2×C42C23×C13911yescharacteristic
246C4⋊C8—42no—
247C22⋊C8—42no—
248C22⋊C8—42no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253C24—21no—
254C24C22⋊C4×C13911yescharacteristic
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×D4—22no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—42no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4C22⋊C4×C13911yescharacteristic
278C22×C4C22⋊C4×C13911yescharacteristic
279C22×C4C22⋊C4×C13911yescharacteristic
280C22×C4C22×C4×C13911yescharacteristic
281C22×C4C2×D4×C13911yescharacteristic
282C22×C4C2×D4×C13911yescharacteristic
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C42—22no—
300C42—22no—
301C42—41no—
302C42—41no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23#100×C13912yes—
317C23C2×C22⋊C4×C13911yescharacteristic
318Q8—82no—
319D4—82no—
320D4—84no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4#99×C13912yes—
349C2×C4#131×C13912yes—
350C2×C4#135×C13912yes—
351C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
352C2×C4#137×C13911yescharacteristic
353C8—82no—
354C8—82no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22#408×C13911yescharacteristic
370C22C2×#99×C13911yescharacteristic
371C22C2×#100×C13911yescharacteristic
372C22#416×C13911yescharacteristic
373C22#417×C13911yescharacteristic
374C22#421×C13911yescharacteristic
375C22#421×C13911yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—22no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C4—81no—
386C2—42no—
387C2—161no—
388C2#1471×C13911yescharacteristic
389C2#1482×C13911yescharacteristic
390C2#1495×C13911yescharacteristic
391C2#1513×C13911yescharacteristic
392C2#1516×C13911yescharacteristic
393C2#1533×C13911yescharacteristic
394C2#1551×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC22×C4C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC2×#121×C139C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1817×C139C2semidirect
3. #1797×C139C2semidirect
4. #1272×C139C2semidirect
5. #1270×C139C2semidirect
197. #7730C139direct (N × H)
198. C139#7730direct (N × H)
200. #1817C2×C139semidirect
201. #1797C2×C139semidirect
202. #1272C2×C139semidirect
203. #1270C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2850×C1392
#1817×C1392
#1797×C1392
#1272×C1392
#1270×C1392
#7730139