Finite Group Databasebeta

← C139×#9027 #48003623

Subgroups — C139×#9027 #48003623

Order 35584.

660 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C139C211yesmaximal, characteristic
2#2316×C139C211yesmaximal, characteristic
3#1823×C139C212yesmaximal
4C2×#324×C139C211yesmaximal, characteristic
5#1294×C139C212yesmaximal
6C2×#117×C139—21no—
7C22×C4⋊C4×C139—21no—
8C22×C4⋊C4×C139C2211yescharacteristic
9C22×C4⋊C4×C139C2211yescharacteristic
10C2×C22⋊C8×C139C2212yes—
11#398×C139—22no—
12#398×C139C414yescomplemented
13#389×C139—24no—
14#380×C139—21no—
15#380×C139C2212yes—
16C2×#95×C139—21no—
17C2×#95×C139C2211yescharacteristic
18#340×C139—24no—
19#324×C139—22no—
20C23×C4×C139—21no—
21C23×C4×C139—21no—
22C23×C4×C139D411yescharacteristic
23C23×C4×C139D411yescharacteristic
24C23×C4×C139C2311yescharacteristic
25C22×C8×C139—22no—
26#117×C139—42no—
27#117×C139—42no—
28C2×C4⋊C4×C139—22no—
29C2×C4⋊C4×C139—22no—
30C2×C4⋊C4×C139—22no—
31C2×C4⋊C4×C139—22no—
32C2×C4⋊C4×C139—22no—
33C2×C4⋊C4×C139—24no—
34C2×C4⋊C4×C139—21no—
35C2×C4⋊C4×C139—22no—
36C2×C4⋊C4×C139—42no—
37C2×C4⋊C4×C139—42no—
38C2×C4⋊C4×C139C2×C412yes—
39C2×C4⋊C4×C139C2×C412yes—
40C2×C4⋊C4×C139D412yes—
41C2×C4⋊C4×C139D414yes—
42C2×C22⋊C4×C139—22no—
43C2×C42×C139—22no—
44C22⋊C8×C139—22no—
45C22⋊C8×C139—22no—
46#95×C139—22no—
47#95×C139—24no—
48#95×C139—21no—
49#95×C139—22no—
50#95×C139C2×C412yes—
51C24×C139C2×D411yescharacteristic
52C22×C4×C139—21no—
53C22×C4×C139—21no—
54C22×C4×C139—21no—
55C22×C4×C139—21no—
56C22×C4×C139—24no—
57C22×C4×C139—22no—
58C22×C4×C139—21no—
59C22×C4×C139—21no—
60C22×C4×C139—22no—
61C22×C4×C139—24no—
62C22×C4×C139—42no—
63C22×C4×C139—42no—
64C22×C4×C139—41no—
65C22×C4×C139—41no—
66C22×C4×C139—42no—
67C22×C4×C139—41no—
68C22×C4×C139—41no—
69C22×C4×C139—41no—
70C22×C4×C139—41no—
71C22×C4×C139—41no—
72C22×C4×C139—41no—
73C22×C4×C139C22⋊C412yes—
74C22×C4×C139C22⋊C412yes—
75C22×C4×C139D812yes—
76C22×C4×C139SD1612yes—
77C22×C4×C139C22×C411yescharacteristic
78C22×C4×C139C2×D412yes—
79C22×C4×C139C2×D411yescharacteristic
80C22×C4×C139#4112yes—
81C2×C8×C139—44no—
82C2×C8×C139—42no—
83C4⋊C4×C139—24no—
84C4⋊C4×C139—24no—
85C4⋊C4×C139—24no—
86C4⋊C4×C139—44no—
87C4⋊C4×C139—44no—
88C4⋊C4×C139—48no—
89C4⋊C4×C139—42no—
90C4⋊C4×C139—82no—
91C22⋊C4×C139—42no—
92C22⋊C4×C139—42no—
93C42×C139—44no—
94C23×C139—22no—
95C23×C139—22no—
96C23×C139C2×C22⋊C411yescharacteristic
97C23×C139#12011yescharacteristic
98C23×C139#12311yescharacteristic
99C23×C139C2×D811yescharacteristic
100C23×C139C2×SD1611yescharacteristic
101C23×C139AGL(1,ℤ/8)11yescharacteristic
102C23×C139#13711yescharacteristic
103C2×C4×C139—22no—
104C2×C4×C139—22no—
105C2×C4×C139—22no—
106C2×C4×C139—22no—
107C2×C4×C139—24no—
108C2×C4×C139—22no—
109C2×C4×C139—22no—
110C2×C4×C139—24no—
111C2×C4×C139—22no—
112C2×C4×C139—41no—
113C2×C4×C139—41no—
114C2×C4×C139—42no—
115C2×C4×C139—44no—
116C2×C4×C139—44no—
117C2×C4×C139—42no—
118C2×C4×C139—42no—
119C2×C4×C139—42no—
120C2×C4×C139—42no—
121C2×C4×C139—42no—
122C2×C4×C139—42no—
123C2×C4×C139—42no—
124C2×C4×C139—44no—
125C2×C4×C139—44no—
126C2×C4×C139—44no—
127C2×C4×C139—81no—
128C2×C4×C139—81no—
129C2×C4×C139—81no—
130C2×C4×C139—81no—
131C2×C4×C139—81no—
132C2×C4×C139#10214yes—
133C2×C4×C139C4×D412yes—
134C2×C4×C139#12112yes—
135C8×C139—82no—
136C22×C139—22no—
137C22×C139—22no—
138C22×C139—22no—
139C22×C139—22no—
140C22×C139—21no—
141C22×C139—21no—
142C22×C139—21no—
143C22×C139—21no—
144C22×C139#38611yescharacteristic
145C22×C139C2×#10211yescharacteristic
146C22×C139#41711yescharacteristic
147C22×C139#44711yescharacteristic
148C22×C139#44811yescharacteristic
149C22×C139#45612yes—
150C22×C139#45812yes—
151C22×C139#48011yescharacteristic
152C22×C139#48111yescharacteristic
153C4×C139—24no—
154C4×C139—22no—
155C4×C139—22no—
156C4×C139—44no—
157C4×C139—42no—
158C4×C139—84no—
159C4×C139—82no—
160C2×C139—21no—
161C2×C139—21no—
162C2×C139—21no—
163C2×C139—21no—
164C2×C139#161012yes—
165C2×C139#161112yes—
166C2×C139#187411yescharacteristic
167C2×C139#188611yescharacteristic
168C2×C139#189011yescharacteristic
169#9027C13911yesmaximal, characteristic, direct product factor, Sylow
170C139#902711yescharacteristic, direct product factor, Sylow
171C2×#398C2×C13911yescharacteristic
172#2316C2×C13911yescharacteristic
173#1823C2×C13912yes—
174C2×#324C2×C13911yescharacteristic
175#1294C2×C13912yes—
176C2×#117—21no—
177C22×C4⋊C4—21no—
178C22×C4⋊C4C22×C13911yescharacteristic
179C22×C4⋊C4C22×C13911yescharacteristic
180C2×C22⋊C8C22×C13912yes—
181#398—22no—
182#398C4×C13914yescomplemented
183#389—24no—
184#380—21no—
185#380C22×C13912yes—
186C2×#95—21no—
187C2×#95C22×C13911yescharacteristic
188#340—24no—
189#324—22no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4D4×C13911yescharacteristic
193C23×C4D4×C13911yescharacteristic
194C23×C4C23×C13911yescharacteristic
195C22×C8—22no—
196#117—42no—
197#117—42no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—24no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—42no—
207C2×C4⋊C4—42no—
208C2×C4⋊C4C2×C4×C13912yes—
209C2×C4⋊C4C2×C4×C13912yes—
210C2×C4⋊C4D4×C13912yes—
211C2×C4⋊C4D4×C13914yes—
212C2×C22⋊C4—22no—
213C2×C42—22no—
214C22⋊C8—22no—
215C22⋊C8—22no—
216#95—22no—
217#95—24no—
218#95—21no—
219#95—22no—
220#95C2×C4×C13912yes—
221C24C2×D4×C13911yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—24no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—42no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C22⋊C4×C13912yes—
244C22×C4C22⋊C4×C13912yes—
245C22×C4D8×C13912yes—
246C22×C4SD16×C13912yes—
247C22×C4C22×C4×C13911yescharacteristic
248C22×C4C2×D4×C13912yes—
249C22×C4C2×D4×C13911yescharacteristic
250C22×C4#41×C13912yes—
251C2×C8—44no—
252C2×C8—42no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—44no—
257C4⋊C4—44no—
258C4⋊C4—48no—
259C4⋊C4—42no—
260C4⋊C4—82no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C42—44no—
264C23—22no—
265C23—22no—
266C23C2×C22⋊C4×C13911yescharacteristic
267C23#120×C13911yescharacteristic
268C23#123×C13911yescharacteristic
269C23C2×D8×C13911yescharacteristic
270C23C2×SD16×C13911yescharacteristic
271C23AGL(1,ℤ/8)×C13911yescharacteristic
272C23#137×C13911yescharacteristic
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—24no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4#102×C13914yes—
303C2×C4C4×D4×C13912yes—
304C2×C4#121×C13912yes—
305C8—82no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22#386×C13911yescharacteristic
315C22C2×#102×C13911yescharacteristic
316C22#417×C13911yescharacteristic
317C22#447×C13911yescharacteristic
318C22#448×C13911yescharacteristic
319C22#456×C13912yes—
320C22#458×C13912yes—
321C22#480×C13911yescharacteristic
322C22#481×C13911yescharacteristic
323C4—24no—
324C4—22no—
325C4—22no—
326C4—44no—
327C4—42no—
328C4—84no—
329C4—82no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2#1610×C13912yes—
335C2#1611×C13912yes—
336C2#1874×C13911yescharacteristic
337C2#1886×C13911yescharacteristic
338C2#1890×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC24×C139C2×D4
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
12. #398×C139C4semidirect
169. #9027C139direct (N × H)
170. C139#9027direct (N × H)
182. #398C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1392
#2316×C1392
#1823×C1392
C2×#324×C1392
#1294×C1392
#9027139