Finite Group Databasebeta

← C139×#7647 #48002243

Subgroups — C139×#7647 #48002243

Order 35584.

584 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C139C211yesmaximal, characteristic
2#1817×C139C211yesmaximal, characteristic, complemented
3#1797×C139C211yesmaximal, characteristic, complemented
4#1271×C139C212yesmaximal, complemented
5#1270×C139C212yesmaximal, complemented
6C2×#121×C139C411yescharacteristic
7C2×C4×D4×C139—21no—
8C2×C4×D4×C139C411yescharacteristic
9C22×C42×C139C2211yescharacteristic
10C2×C4⋊C8×C139—21no—
11C2×C22⋊C8×C139—21no—
12C2×C22⋊C8×C139—21no—
13#390×C139C2211yescharacteristic
14#389×C139C2211yescharacteristic
15#388×C139—21no—
16#386×C139—21no—
17#380×C139C411yescharacteristic
18C4×C4⋊C4×C139C411yescharacteristic
19C4×C22⋊C4×C139—21no—
20#336×C139—21no—
21#336×C139C2212yes—
22#336×C139C2212yes—
23C22×D4×C139—21no—
24C22×D4×C139C2×C411yescharacteristic
25C23×C4×C139—21no—
26C23×C4×C139C2×C411yescharacteristic
27C23×C4×C139D411yescharacteristic
28C23×C4×C139D411yescharacteristic
29C22×C8×C139—22no—
30C22×C8×C139—22no—
31#121×C139—22no—
32#121×C139—22no—
33C4×D4×C139—42no—
34C4×D4×C139—42no—
35C4×D4×C139—42no—
36C2×C4⋊C4×C139—21no—
37C2×C4⋊C4×C139C2×C411yescharacteristic
38C2×C4⋊C4×C139C2×C411yescharacteristic
39C2×C4⋊C4×C139C2×C411yescharacteristic
40C2×C22⋊C4×C139—21no—
41C2×C22⋊C4×C139—21no—
42C2×C22⋊C4×C139—21no—
43C2×C22⋊C4×C139—21no—
44C2×C22⋊C4×C139—21no—
45C2×C42×C139—21no—
46C2×C42×C139—42no—
47C2×C42×C139C2×C411yescharacteristic
48C2×C42×C139D411yescharacteristic
49C2×C42×C139D411yescharacteristic
50C2×C42×C139C2311yescharacteristic
51C4⋊C8×C139—42no—
52C22⋊C8×C139—42no—
53C22⋊C8×C139—42no—
54#95×C139—21no—
55#95×C139—21no—
56#95×C139—21no—
57C24×C139—21no—
58C24×C139C22⋊C411yescharacteristic
59C2×D4×C139—24no—
60C2×D4×C139—21no—
61C2×D4×C139—41no—
62C2×D4×C139—41no—
63C2×D4×C139—42no—
64C2×D4×C139—42no—
65C2×D4×C139M1612yes—
66C22×C4×C139—21no—
67C22×C4×C139—22no—
68C22×C4×C139—21no—
69C22×C4×C139—21no—
70C22×C4×C139—22no—
71C22×C4×C139—21no—
72C22×C4×C139—21no—
73C22×C4×C139—41no—
74C22×C4×C139—41no—
75C22×C4×C139—41no—
76C22×C4×C139—41no—
77C22×C4×C139—41no—
78C22×C4×C139—42no—
79C22×C4×C139—42no—
80C22×C4×C139—42no—
81C22×C4×C139C22⋊C411yescharacteristic
82C22×C4×C139C22⋊C411yescharacteristic
83C22×C4×C139C22⋊C411yescharacteristic
84C22×C4×C139D812yes—
85C22×C4×C139SD1612yes—
86C22×C4×C139C22×C411yescharacteristic
87C22×C4×C139C2×D411yescharacteristic
88C22×C4×C139C2×D411yescharacteristic
89C2×C8×C139—42no—
90C2×C8×C139—42no—
91C2×C8×C139—42no—
92C2×C8×C139—42no—
93C2×C8×C139—42no—
94C2×C8×C139—42no—
95C4⋊C4×C139—21no—
96C4⋊C4×C139—41no—
97C4⋊C4×C139—41no—
98C4⋊C4×C139—41no—
99C4⋊C4×C139—41no—
100C4⋊C4×C139M1612yes—
101C22⋊C4×C139—24no—
102C22⋊C4×C139—42no—
103C22⋊C4×C139—42no—
104C22⋊C4×C139—41no—
105C22⋊C4×C139—41no—
106C22⋊C4×C139—42no—
107C42×C139—22no—
108C42×C139—22no—
109C42×C139—41no—
110C42×C139—41no—
111C42×C139—42no—
112C23×C139—21no—
113C23×C139—21no—
114C23×C139—21no—
115C23×C139—21no—
116C23×C139—21no—
117C23×C139—21no—
118C23×C139—22no—
119C23×C139—41no—
120C23×C139—41no—
121C23×C139—41no—
122C23×C139—41no—
123C23×C139—41no—
124C23×C139—41no—
125C23×C139#10212yes—
126C23×C139C2×C22⋊C411yescharacteristic
127D4×C139—42no—
128D4×C139—42no—
129D4×C139—48no—
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—21no—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—22no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—42no—
145C2×C4×C139—42no—
146C2×C4×C139—44no—
147C2×C4×C139—42no—
148C2×C4×C139—42no—
149C2×C4×C139—41no—
150C2×C4×C139—41no—
151C2×C4×C139—41no—
152C2×C4×C139—41no—
153C2×C4×C139—41no—
154C2×C4×C139—41no—
155C2×C4×C139—41no—
156C2×C4×C139—41no—
157C2×C4×C139—84no—
158C2×C4×C139#9912yes—
159C2×C4×C139#10212yes—
160C2×C4×C139C2×M1611yescharacteristic
161C2×C4×C139C2×M1611yescharacteristic
162C2×C4×C139C2×D811yescharacteristic
163C2×C4×C139C2×SD1611yescharacteristic
164C2×C4×C139#13512yes—
165C8×C139—82no—
166C8×C139—82no—
167C22×C139—22no—
168C22×C139—22no—
169C22×C139—22no—
170C22×C139—41no—
171C22×C139—41no—
172C22×C139—41no—
173C22×C139—41no—
174C22×C139—42no—
175C22×C139—42no—
176C22×C139—42no—
177C22×C139—81no—
178C22×C139—81no—
179C22×C139—81no—
180C22×C139—81no—
181C22×C139#40711yescharacteristic
182C22×C139C2×#9911yescharacteristic
183C22×C139#41311yescharacteristic
184C22×C139C2×#10211yescharacteristic
185C22×C139#41611yescharacteristic
186C22×C139#42111yescharacteristic
187C22×C139#42111yescharacteristic
188C4×C139—21no—
189C4×C139—21no—
190C4×C139—22no—
191C4×C139—22no—
192C4×C139—21no—
193C4×C139—22no—
194C4×C139—21no—
195C4×C139—41no—
196C4×C139—42no—
197C4×C139—81no—
198C4×C139—81no—
199C2×C139—42no—
200C2×C139—82no—
201C2×C139#146511yescharacteristic
202C2×C139#148611yescharacteristic
203C2×C139#148811yescharacteristic
204C2×C139#151611yescharacteristic
205C2×C139#151911yescharacteristic
206C2×C139#153511yescharacteristic
207C2×C139#154011yescharacteristic
208#7647C13911yesmaximal, characteristic, direct product factor, Sylow
209C139#764711yescharacteristic, direct product factor, Sylow
210C4×#121C2×C13911yescharacteristic
211#1817C2×C13911yescharacteristic, complemented
212#1797C2×C13911yescharacteristic, complemented
213#1271C2×C13912yescomplemented
214#1270C2×C13912yescomplemented
215C2×#121C4×C13911yescharacteristic
216C2×C4×D4—21no—
217C2×C4×D4C4×C13911yescharacteristic
218C22×C42C22×C13911yescharacteristic
219C2×C4⋊C8—21no—
220C2×C22⋊C8—21no—
221C2×C22⋊C8—21no—
222#390C22×C13911yescharacteristic
223#389C22×C13911yescharacteristic
224#388—21no—
225#386—21no—
226#380C4×C13911yescharacteristic
227C4×C4⋊C4C4×C13911yescharacteristic
228C4×C22⋊C4—21no—
229#336—21no—
230#336C22×C13912yes—
231#336C22×C13912yes—
232C22×D4—21no—
233C22×D4C2×C4×C13911yescharacteristic
234C23×C4—21no—
235C23×C4C2×C4×C13911yescharacteristic
236C23×C4D4×C13911yescharacteristic
237C23×C4D4×C13911yescharacteristic
238C22×C8—22no—
239C22×C8—22no—
240#121—22no—
241#121—22no—
242C4×D4—42no—
243C4×D4—42no—
244C4×D4—42no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4C2×C4×C13911yescharacteristic
247C2×C4⋊C4C2×C4×C13911yescharacteristic
248C2×C4⋊C4C2×C4×C13911yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C42—21no—
255C2×C42—42no—
256C2×C42C2×C4×C13911yescharacteristic
257C2×C42D4×C13911yescharacteristic
258C2×C42D4×C13911yescharacteristic
259C2×C42C23×C13911yescharacteristic
260C4⋊C8—42no—
261C22⋊C8—42no—
262C22⋊C8—42no—
263#95—21no—
264#95—21no—
265#95—21no—
266C24—21no—
267C24C22⋊C4×C13911yescharacteristic
268C2×D4—24no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4M16×C13912yes—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4C22⋊C4×C13911yescharacteristic
291C22×C4C22⋊C4×C13911yescharacteristic
292C22×C4C22⋊C4×C13911yescharacteristic
293C22×C4D8×C13912yes—
294C22×C4SD16×C13912yes—
295C22×C4C22×C4×C13911yescharacteristic
296C22×C4C2×D4×C13911yescharacteristic
297C22×C4C2×D4×C13911yescharacteristic
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—42no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4M16×C13912yes—
310C22⋊C4—24no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—42no—
316C42—22no—
317C42—22no—
318C42—41no—
319C42—41no—
320C42—42no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—22no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23#102×C13912yes—
335C23C2×C22⋊C4×C13911yescharacteristic
336D4—42no—
337D4—42no—
338D4—48no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—84no—
367C2×C4#99×C13912yes—
368C2×C4#102×C13912yes—
369C2×C4C2×M16×C13911yescharacteristic
370C2×C4C2×M16×C13911yescharacteristic
371C2×C4C2×D8×C13911yescharacteristic
372C2×C4C2×SD16×C13911yescharacteristic
373C2×C4#135×C13912yes—
374C8—82no—
375C8—82no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22#407×C13911yescharacteristic
391C22C2×#99×C13911yescharacteristic
392C22#413×C13911yescharacteristic
393C22C2×#102×C13911yescharacteristic
394C22#416×C13911yescharacteristic
395C22#421×C13911yescharacteristic
396C22#421×C13911yescharacteristic
397C4—22no—
398C4—22no—
399C4—21no—
400C4—22no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—42no—
405C4—41no—
406C4—81no—
407C4—81no—
408C2—42no—
409C2—82no—
410C2#1465×C13911yescharacteristic
411C2#1486×C13911yescharacteristic
412C2#1488×C13911yescharacteristic
413C2#1516×C13911yescharacteristic
414C2#1519×C13911yescharacteristic
415C2#1535×C13911yescharacteristic
416C2#1540×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. #1271×C139C2semidirect
5. #1270×C139C2semidirect
208. #7647C139direct (N × H)
209. C139#7647direct (N × H)
211. #1817C2×C139semidirect
212. #1797C2×C139semidirect
213. #1271C2×C139semidirect
214. #1270C2×C139semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1392
#1817×C1392
#1797×C1392
#1271×C1392
#1270×C1392
#7647139