Finite Group Databasebeta

← C139×#9021 #48003617

Subgroups — C139×#9021 #48003617

Order 35584.

812 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C139C211yesmaximal, characteristic
2#2315×C139C211yesmaximal, characteristic
3#1824×C139C212yesmaximal, complemented
4C2×#323×C139C211yesmaximal, characteristic
5#1294×C139C212yesmaximal, complemented
6C22×C4⋊C4×C139—21no—
7C22×C4⋊C4×C139C2211yescharacteristic
8C22×C22⋊C4×C139—21no—
9C22×C22⋊C4×C139—21no—
10C22×C22⋊C4×C139C2211yescharacteristic
11C2×C22⋊C8×C139C2212yes—
12#399×C139—22no—
13#399×C139C414yescomplemented
14#385×C139—24no—
15#380×C139—21no—
16#380×C139C2212yes—
17C2×#95×C139C2211yescharacteristic
18#340×C139—24no—
19#323×C139—22no—
20C25×C139D411yescharacteristic
21C23×C4×C139—21no—
22C23×C4×C139—21no—
23C23×C4×C139—22no—
24C23×C4×C139D411yescharacteristic
25C23×C4×C139C2311yescharacteristic
26C22×C8×C139—22no—
27C2×C4⋊C4×C139—22no—
28C2×C4⋊C4×C139—22no—
29C2×C4⋊C4×C139—24no—
30C2×C4⋊C4×C139—21no—
31C2×C4⋊C4×C139—22no—
32C2×C4⋊C4×C139—44no—
33C2×C4⋊C4×C139C2×C412yescomplemented
34C2×C4⋊C4×C139D414yes—
35C2×C22⋊C4×C139—22no—
36C2×C22⋊C4×C139—22no—
37C2×C22⋊C4×C139—22no—
38C2×C22⋊C4×C139—24no—
39C2×C22⋊C4×C139—22no—
40C2×C22⋊C4×C139—44no—
41C2×C22⋊C4×C139—42no—
42C2×C22⋊C4×C139—42no—
43C2×C22⋊C4×C139C2×C412yes—
44C2×C22⋊C4×C139D412yes—
45C22⋊C8×C139—22no—
46C22⋊C8×C139—22no—
47#95×C139—22no—
48#95×C139—21no—
49#95×C139—22no—
50#95×C139C2×C412yescomplemented
51C24×C139—21no—
52C24×C139—21no—
53C24×C139—21no—
54C24×C139—21no—
55C24×C139—42no—
56C24×C139—42no—
57C24×C139C22⋊C412yes—
58C24×C139SD1612yes—
59C24×C139Q1612yes—
60C24×C139C2×D411yescharacteristic
61C22×C4×C139—24no—
62C22×C4×C139—22no—
63C22×C4×C139—21no—
64C22×C4×C139—21no—
65C22×C4×C139—22no—
66C22×C4×C139—24no—
67C22×C4×C139—42no—
68C22×C4×C139—42no—
69C22×C4×C139—41no—
70C22×C4×C139—41no—
71C22×C4×C139—42no—
72C22×C4×C139—42no—
73C22×C4×C139—44no—
74C22×C4×C139—42no—
75C22×C4×C139—41no—
76C22×C4×C139—41no—
77C22×C4×C139—82no—
78C22×C4×C139—82no—
79C22×C4×C139C22⋊C412yes—
80C22×C4×C139C22×C411yescharacteristic
81C22×C4×C139C2×D412yes—
82C22×C4×C139C2×D411yescharacteristic
83C22×C4×C139#4112yes—
84C2×C8×C139—44no—
85C2×C8×C139—42no—
86C4⋊C4×C139—24no—
87C4⋊C4×C139—44no—
88C4⋊C4×C139—48no—
89C4⋊C4×C139—42no—
90C4⋊C4×C139—82no—
91C22⋊C4×C139—24no—
92C22⋊C4×C139—24no—
93C22⋊C4×C139—48no—
94C22⋊C4×C139—44no—
95C22⋊C4×C139—42no—
96C22⋊C4×C139—42no—
97C23×C139—22no—
98C23×C139—22no—
99C23×C139—22no—
100C23×C139—22no—
101C23×C139—22no—
102C23×C139—22no—
103C23×C139—22no—
104C23×C139—22no—
105C23×C139—42no—
106C23×C139—42no—
107C23×C139—44no—
108C23×C139—44no—
109C23×C139—42no—
110C23×C139—42no—
111C23×C139—82no—
112C23×C139—82no—
113C23×C139—81no—
114C23×C139—81no—
115C23×C139#10314yes—
116C23×C139C2×C22⋊C411yescharacteristic
117C23×C139#12011yescharacteristic
118C23×C139#12311yescharacteristic
119C23×C139C2×SD1611yescharacteristic
120C23×C139C2×Q1611yescharacteristic
121C23×C139AGL(1,ℤ/8)11yescharacteristic
122C23×C139#13711yescharacteristic
123C2×C4×C139—24no—
124C2×C4×C139—24no—
125C2×C4×C139—22no—
126C2×C4×C139—41no—
127C2×C4×C139—41no—
128C2×C4×C139—42no—
129C2×C4×C139—44no—
130C2×C4×C139—44no—
131C2×C4×C139—42no—
132C2×C4×C139—42no—
133C2×C4×C139—42no—
134C2×C4×C139—42no—
135C2×C4×C139—42no—
136C2×C4×C139—42no—
137C2×C4×C139—42no—
138C2×C4×C139—44no—
139C2×C4×C139—44no—
140C2×C4×C139—44no—
141C2×C4×C139—81no—
142C2×C4×C139—82no—
143C2×C4×C139—88no—
144C2×C4×C139—82no—
145C2×C4×C139C4×D412yes—
146C2×C4×C139#12112yes—
147C8×C139—82no—
148C22×C139—22no—
149C22×C139—22no—
150C22×C139—22no—
151C22×C139—22no—
152C22×C139—21no—
153C22×C139—21no—
154C22×C139—21no—
155C22×C139—21no—
156C22×C139—24no—
157C22×C139—44no—
158C22×C139—44no—
159C22×C139—44no—
160C22×C139—42no—
161C22×C139—42no—
162C22×C139—82no—
163C22×C139—82no—
164C22×C139—82no—
165C22×C139#38611yescharacteristic
166C22×C139C2×#10311yescharacteristic
167C22×C139#41711yescharacteristic
168C22×C139#45011yescharacteristic
169C22×C139#45111yescharacteristic
170C22×C139#45312yes—
171C22×C139#45812yes—
172C22×C139#48311yescharacteristic
173C22×C139#48411yescharacteristic
174C4×C139—22no—
175C4×C139—22no—
176C4×C139—44no—
177C4×C139—42no—
178C4×C139—84no—
179C4×C139—82no—
180C2×C139—21no—
181C2×C139—21no—
182C2×C139—21no—
183C2×C139—21no—
184C2×C139—44no—
185C2×C139#161312yes—
186C2×C139#161412yes—
187C2×C139#187211yescharacteristic
188C2×C139#188711yescharacteristic
189C2×C139#189011yescharacteristic
190#9021C13911yesmaximal, characteristic, direct product factor, Sylow
191C139#902111yescharacteristic, direct product factor, Sylow
192C2×#399C2×C13911yescharacteristic
193#2315C2×C13911yescharacteristic
194#1824C2×C13912yescomplemented
195C2×#323C2×C13911yescharacteristic
196#1294C2×C13912yescomplemented
197C22×C4⋊C4—21no—
198C22×C4⋊C4C22×C13911yescharacteristic
199C22×C22⋊C4—21no—
200C22×C22⋊C4—21no—
201C22×C22⋊C4C22×C13911yescharacteristic
202C2×C22⋊C8C22×C13912yes—
203#399—22no—
204#399C4×C13914yescomplemented
205#385—24no—
206#380—21no—
207#380C22×C13912yes—
208C2×#95C22×C13911yescharacteristic
209#340—24no—
210#323—22no—
211C25D4×C13911yescharacteristic
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—22no—
215C23×C4D4×C13911yescharacteristic
216C23×C4C23×C13911yescharacteristic
217C22×C8—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—44no—
224C2×C4⋊C4C2×C4×C13912yescomplemented
225C2×C4⋊C4D4×C13914yes—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—24no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—44no—
232C2×C22⋊C4—42no—
233C2×C22⋊C4—42no—
234C2×C22⋊C4C2×C4×C13912yes—
235C2×C22⋊C4D4×C13912yes—
236C22⋊C8—22no—
237C22⋊C8—22no—
238#95—22no—
239#95—21no—
240#95—22no—
241#95C2×C4×C13912yescomplemented
242C24—21no—
243C24—21no—
244C24—21no—
245C24—21no—
246C24—42no—
247C24—42no—
248C24C22⋊C4×C13912yes—
249C24SD16×C13912yes—
250C24Q16×C13912yes—
251C24C2×D4×C13911yescharacteristic
252C22×C4—24no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—44no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—82no—
269C22×C4—82no—
270C22×C4C22⋊C4×C13912yes—
271C22×C4C22×C4×C13911yescharacteristic
272C22×C4C2×D4×C13912yes—
273C22×C4C2×D4×C13911yescharacteristic
274C22×C4#41×C13912yes—
275C2×C8—44no—
276C2×C8—42no—
277C4⋊C4—24no—
278C4⋊C4—44no—
279C4⋊C4—48no—
280C4⋊C4—42no—
281C4⋊C4—82no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—48no—
285C22⋊C4—44no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—42no—
297C23—42no—
298C23—44no—
299C23—44no—
300C23—42no—
301C23—42no—
302C23—82no—
303C23—82no—
304C23—81no—
305C23—81no—
306C23#103×C13914yes—
307C23C2×C22⋊C4×C13911yescharacteristic
308C23#120×C13911yescharacteristic
309C23#123×C13911yescharacteristic
310C23C2×SD16×C13911yescharacteristic
311C23C2×Q16×C13911yescharacteristic
312C23AGL(1,ℤ/8)×C13911yescharacteristic
313C23#137×C13911yescharacteristic
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—82no—
334C2×C4—88no—
335C2×C4—82no—
336C2×C4C4×D4×C13912yes—
337C2×C4#121×C13912yes—
338C8—82no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—24no—
348C22—44no—
349C22—44no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22#386×C13911yescharacteristic
357C22C2×#103×C13911yescharacteristic
358C22#417×C13911yescharacteristic
359C22#450×C13911yescharacteristic
360C22#451×C13911yescharacteristic
361C22#453×C13912yes—
362C22#458×C13912yes—
363C22#483×C13911yescharacteristic
364C22#484×C13911yescharacteristic
365C4—22no—
366C4—22no—
367C4—44no—
368C4—42no—
369C4—84no—
370C4—82no—
371C2—21no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—44no—
376C2#1613×C13912yes—
377C2#1614×C13912yes—
378C2#1872×C13911yescharacteristic
379C2#1887×C13911yescharacteristic
380C2#1890×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC25×C139D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1824×C139C2semidirect
5. #1294×C139C2semidirect
13. #399×C139C4semidirect
33. C2×C4⋊C4×C139C2×C4semidirect
50. #95×C139C2×C4semidirect
190. #9021C139direct (N × H)
191. C139#9021direct (N × H)
194. #1824C2×C139semidirect
196. #1294C2×C139semidirect
204. #399C4×C139semidirect
224. C2×C4⋊C4C2×C4×C139semidirect
241. #95C2×C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1392
#2315×C1392
#1824×C1392
C2×#323×C1392
#1294×C1392
#9021139