Finite Group Databasebeta

← C139×#7714 #48002310

Subgroups — C139×#7714 #48002310

Order 35584.

526 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854×C139C211yesmaximal, characteristic
2#1797×C139C211yesmaximal, characteristic, complemented
3#1797×C139C211yesmaximal, characteristic, complemented
4#1271×C139C212yesmaximal, complemented
5#1270×C139C212yesmaximal, complemented
6C2×#123×C139—21no—
7C2×#121×C139C411yescharacteristic
8C22×C42×C139C2211yescharacteristic
9C2×C4⋊C8×C139—21no—
10C2×C4⋊C8×C139—21no—
11C2×C22⋊C8×C139—21no—
12C2×C22⋊C8×C139—21no—
13#390×C139C411yescharacteristic
14#390×C139C2211yescharacteristic
15#389×C139C411yescharacteristic
16#389×C139C2211yescharacteristic
17#388×C139—21no—
18#388×C139—21no—
19#386×C139—21no—
20#380×C139C411yescharacteristic
21#336×C139C2212yes—
22#336×C139C2212yes—
23C22×D4×C139—21no—
24C22×D4×C139C2×C411yescharacteristic
25C23×C4×C139C2×C411yescharacteristic
26C23×C4×C139D411yescharacteristic
27C23×C4×C139D411yescharacteristic
28C22×C8×C139—22no—
29C22×C8×C139—22no—
30#123×C139—42no—
31#123×C139—42no—
32#121×C139—42no—
33C2×C4⋊C4×C139—21no—
34C2×C4⋊C4×C139—21no—
35C2×C4⋊C4×C139C2×C411yescharacteristic
36C2×C4⋊C4×C139C2×C411yescharacteristic
37C2×C4⋊C4×C139C2×C411yescharacteristic
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×C22⋊C4×C139—21no—
44C2×C42×C139—42no—
45C2×C42×C139C2×C411yescharacteristic
46C2×C42×C139D411yescharacteristic
47C2×C42×C139D411yescharacteristic
48C2×C42×C139C2311yescharacteristic
49C4⋊C8×C139—42no—
50C4⋊C8×C139—42no—
51C22⋊C8×C139—42no—
52C22⋊C8×C139—42no—
53#95×C139—21no—
54#95×C139—21no—
55#95×C139—21no—
56C24×C139—21no—
57C24×C139C22⋊C411yescharacteristic
58C2×D4×C139—22no—
59C2×D4×C139—41no—
60C2×D4×C139—41no—
61C2×D4×C139—42no—
62C2×D4×C139—42no—
63C2×D4×C139—42no—
64C22×C4×C139—22no—
65C22×C4×C139—22no—
66C22×C4×C139—21no—
67C22×C4×C139—21no—
68C22×C4×C139—21no—
69C22×C4×C139—21no—
70C22×C4×C139—21no—
71C22×C4×C139—41no—
72C22×C4×C139—41no—
73C22×C4×C139—41no—
74C22×C4×C139—41no—
75C22×C4×C139—41no—
76C22×C4×C139C22⋊C411yescharacteristic
77C22×C4×C139C22⋊C411yescharacteristic
78C22×C4×C139C22⋊C411yescharacteristic
79C22×C4×C139D812yes—
80C22×C4×C139SD1612yes—
81C22×C4×C139C22×C411yescharacteristic
82C22×C4×C139C2×D411yescharacteristic
83C22×C4×C139C2×D411yescharacteristic
84C2×C8×C139—42no—
85C2×C8×C139—42no—
86C2×C8×C139—42no—
87C2×C8×C139—42no—
88C2×C8×C139—42no—
89C2×C8×C139—42no—
90C4⋊C4×C139—22no—
91C4⋊C4×C139—41no—
92C4⋊C4×C139—41no—
93C4⋊C4×C139—42no—
94C4⋊C4×C139—41no—
95C4⋊C4×C139—41no—
96C22⋊C4×C139—42no—
97C22⋊C4×C139—42no—
98C22⋊C4×C139—42no—
99C22⋊C4×C139—42no—
100C22⋊C4×C139—41no—
101C22⋊C4×C139—41no—
102C22⋊C4×C139—41no—
103C22⋊C4×C139—41no—
104C42×C139—22no—
105C42×C139—22no—
106C42×C139—41no—
107C42×C139—41no—
108C23×C139—21no—
109C23×C139—21no—
110C23×C139—21no—
111C23×C139—21no—
112C23×C139—21no—
113C23×C139—21no—
114C23×C139—41no—
115C23×C139—41no—
116C23×C139—41no—
117C23×C139—41no—
118C23×C139—41no—
119C23×C139—41no—
120C23×C139—41no—
121C23×C139#10212yes—
122C23×C139C2×C22⋊C411yescharacteristic
123D4×C139—82no—
124D4×C139—84no—
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—21no—
138C2×C4×C139—42no—
139C2×C4×C139—42no—
140C2×C4×C139—44no—
141C2×C4×C139—42no—
142C2×C4×C139—42no—
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—41no—
151C2×C4×C139—41no—
152C2×C4×C139#9912yes—
153C2×C4×C139#10212yes—
154C2×C4×C139#13112yes—
155C2×C4×C139C2×D811yescharacteristic
156C2×C4×C139C2×SD1611yescharacteristic
157C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C139#13711yescharacteristic
159C8×C139—82no—
160C8×C139—82no—
161C22×C139—22no—
162C22×C139—22no—
163C22×C139—22no—
164C22×C139—41no—
165C22×C139—41no—
166C22×C139—41no—
167C22×C139—41no—
168C22×C139—81no—
169C22×C139—81no—
170C22×C139—81no—
171C22×C139—81no—
172C22×C139—81no—
173C22×C139—81no—
174C22×C139—81no—
175C22×C139#40811yescharacteristic
176C22×C139C2×#9911yescharacteristic
177C22×C139#41311yescharacteristic
178C22×C139C2×#10211yescharacteristic
179C22×C139#41711yescharacteristic
180C22×C139#42111yescharacteristic
181C22×C139#42111yescharacteristic
182C4×C139—22no—
183C4×C139—22no—
184C4×C139—21no—
185C4×C139—21no—
186C4×C139—21no—
187C4×C139—22no—
188C4×C139—21no—
189C4×C139—41no—
190C4×C139—81no—
191C4×C139—81no—
192C4×C139—81no—
193C2×C139—42no—
194C2×C139—161no—
195C2×C139#146811yescharacteristic
196C2×C139#148011yescharacteristic
197C2×C139#149511yescharacteristic
198C2×C139#151311yescharacteristic
199C2×C139#151911yescharacteristic
200C2×C139#153511yescharacteristic
201C2×C139#154711yescharacteristic
202#7714C13911yesmaximal, characteristic, direct product factor, Sylow
203C139#771411yescharacteristic, direct product factor, Sylow
204#2854C2×C13911yescharacteristic
205#1797C2×C13911yescharacteristic, complemented
206#1797C2×C13911yescharacteristic, complemented
207#1271C2×C13912yescomplemented
208#1270C2×C13912yescomplemented
209C2×#123—21no—
210C2×#121C4×C13911yescharacteristic
211C22×C42C22×C13911yescharacteristic
212C2×C4⋊C8—21no—
213C2×C4⋊C8—21no—
214C2×C22⋊C8—21no—
215C2×C22⋊C8—21no—
216#390C4×C13911yescharacteristic
217#390C22×C13911yescharacteristic
218#389C4×C13911yescharacteristic
219#389C22×C13911yescharacteristic
220#388—21no—
221#388—21no—
222#386—21no—
223#380C4×C13911yescharacteristic
224#336C22×C13912yes—
225#336C22×C13912yes—
226C22×D4—21no—
227C22×D4C2×C4×C13911yescharacteristic
228C23×C4C2×C4×C13911yescharacteristic
229C23×C4D4×C13911yescharacteristic
230C23×C4D4×C13911yescharacteristic
231C22×C8—22no—
232C22×C8—22no—
233#123—42no—
234#123—42no—
235#121—42no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C2×C4×C13911yescharacteristic
239C2×C4⋊C4C2×C4×C13911yescharacteristic
240C2×C4⋊C4C2×C4×C13911yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C42—42no—
248C2×C42C2×C4×C13911yescharacteristic
249C2×C42D4×C13911yescharacteristic
250C2×C42D4×C13911yescharacteristic
251C2×C42C23×C13911yescharacteristic
252C4⋊C8—42no—
253C4⋊C8—42no—
254C22⋊C8—42no—
255C22⋊C8—42no—
256#95—21no—
257#95—21no—
258#95—21no—
259C24—21no—
260C24C22⋊C4×C13911yescharacteristic
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4C22⋊C4×C13911yescharacteristic
280C22×C4C22⋊C4×C13911yescharacteristic
281C22×C4C22⋊C4×C13911yescharacteristic
282C22×C4D8×C13912yes—
283C22×C4SD16×C13912yes—
284C22×C4C22×C4×C13911yescharacteristic
285C22×C4C2×D4×C13911yescharacteristic
286C22×C4C2×D4×C13911yescharacteristic
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—22no—
308C42—22no—
309C42—41no—
310C42—41no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23#102×C13912yes—
325C23C2×C22⋊C4×C13911yescharacteristic
326D4—82no—
327D4—84no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4#99×C13912yes—
356C2×C4#102×C13912yes—
357C2×C4#131×C13912yes—
358C2×C4C2×D8×C13911yescharacteristic
359C2×C4C2×SD16×C13911yescharacteristic
360C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
361C2×C4#137×C13911yescharacteristic
362C8—82no—
363C8—82no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#408×C13911yescharacteristic
379C22C2×#99×C13911yescharacteristic
380C22#413×C13911yescharacteristic
381C22C2×#102×C13911yescharacteristic
382C22#417×C13911yescharacteristic
383C22#421×C13911yescharacteristic
384C22#421×C13911yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—21no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—81no—
394C4—81no—
395C4—81no—
396C2—42no—
397C2—161no—
398C2#1468×C13911yescharacteristic
399C2#1480×C13911yescharacteristic
400C2#1495×C13911yescharacteristic
401C2#1513×C13911yescharacteristic
402C2#1519×C13911yescharacteristic
403C2#1535×C13911yescharacteristic
404C2#1547×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. #1797×C139C2semidirect
3. #1797×C139C2semidirect
4. #1271×C139C2semidirect
5. #1270×C139C2semidirect
202. #7714C139direct (N × H)
203. C139#7714direct (N × H)
205. #1797C2×C139semidirect
206. #1797C2×C139semidirect
207. #1271C2×C139semidirect
208. #1270C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2854×C1392
#1797×C1392
#1271×C1392
#1270×C1392
#7714139