Finite Group Databasebeta

← C139×#10443 #48005039

Subgroups — C139×#10443 #48005039

Order 35584.

460 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C139C211yesmaximal, characteristic
2#1801×C139C211yesmaximal, characteristic, complemented
3#1570×C139C211yesmaximal, characteristic, complemented
4#1545×C139C211yesmaximal, characteristic
5#1545×C139C211yesmaximal, characteristic
6#1479×C139C211yesmaximal, characteristic, complemented
7#1301×C139C211yesmaximal, characteristic, complemented
8C22×SD16×C139—21no—
9C2×#127×C139C2211yescharacteristic
10C2×C4×Q8×C139C2211yescharacteristic
11#460×C139—22no—
12#460×C139—22no—
13#431×C139C2211yescharacteristic
14#431×C139C2211yescharacteristic
15#423×C139C2211yescharacteristic
16#423×C139C2211yescharacteristic
17C2×C4⋊C8×C139C2211yescharacteristic
18C2×#102×C139—21no—
19C2×#101×C139—21no—
20#343×C139—21no—
21#334×C139—22no—
22#331×C139—22no—
23#331×C139—22no—
24Q8⋊C8×C139—22no—
25C22×Q8×C139D411yescharacteristic
26C22×D4×C139—21no—
27C22×D4×C139—21no—
28C22×D4×C139—21no—
29C2×SD16×C139—24no—
30C2×SD16×C139—42no—
31C2×SD16×C139—42no—
32C2×M16×C139—21no—
33C2×M16×C139—21no—
34C22×C8×C139—21no—
35#127×C139—21no—
36#127×C139—21no—
37#127×C139—21no—
38#127×C139D412yes—
39C4×Q8×C139—21no—
40C4×Q8×C139—21no—
41C4×Q8×C139—21no—
42C4×Q8×C139—21no—
43C2×C4⋊C4×C139—21no—
44C2×C4⋊C4×C139D411yescharacteristic
45C2×C42×C139—21no—
46C2×C42×C139C2311yescharacteristic
47C4⋊C8×C139—21no—
48C4⋊C8×C139—21no—
49C4⋊C8×C139—21no—
50C4⋊C8×C139—21no—
51C4⋊C8×C139—21no—
52C4⋊C8×C139—21no—
53C4⋊C8×C139D412yes—
54C4⋊C8×C139D412yes—
55#102×C139—24no—
56#101×C139—42no—
57C22⋊C8×C139—21no—
58C22⋊C8×C139—21no—
59C4×C8×C139—21no—
60C4×C8×C139—21no—
61C24×C139—41no—
62C2×Q8×C139—21no—
63C2×Q8×C139—21no—
64C2×Q8×C139—21no—
65C2×Q8×C139—21no—
66C2×Q8×C139—21no—
67C2×Q8×C139SD1612yes—
68C2×D4×C139—22no—
69C2×D4×C139—22no—
70C2×D4×C139—22no—
71C2×D4×C139—41no—
72C2×D4×C139—41no—
73C2×D4×C139—41no—
74C2×D4×C139—41no—
75C2×D4×C139—41no—
76C2×D4×C139—41no—
77C2×D4×C139—41no—
78C2×D4×C139—82no—
79C2×D4×C139—82no—
80C22×C4×C139—21no—
81C22×C4×C139—21no—
82C22×C4×C139C2×D411yescharacteristic
83C22×C4×C139#4111yescharacteristic
84C22×C4×C139#4111yescharacteristic
85SD16×C139—48no—
86M16×C139—41no—
87M16×C139—41no—
88M16×C139—41no—
89M16×C139—41no—
90C2×C8×C139—22no—
91C2×C8×C139—22no—
92C2×C8×C139—41no—
93C2×C8×C139—41no—
94C2×C8×C139—41no—
95C2×C8×C139—41no—
96C2×C8×C139—41no—
97C4⋊C4×C139—21no—
98C4⋊C4×C139—21no—
99C4⋊C4×C139—41no—
100C4⋊C4×C139—41no—
101C42×C139—41no—
102C42×C139—41no—
103C42×C139C2×D411yescharacteristic
104C42×C139C2×D411yescharacteristic
105C42×C139C2×D411yescharacteristic
106C42×C139#4111yescharacteristic
107C23×C139—42no—
108C23×C139—82no—
109C23×C139—82no—
110C23×C139—81no—
111C23×C139—81no—
112C23×C139#12311yescharacteristic
113Q8×C139—22no—
114Q8×C139—22no—
115Q8×C139—41no—
116Q8×C139—41no—
117D4×C139—42no—
118D4×C139—42no—
119D4×C139—82no—
120D4×C139—82no—
121D4×C139—82no—
122D4×C139—81no—
123D4×C139—81no—
124D4×C139—82no—
125C2×C4×C139—22no—
126C2×C4×C139—22no—
127C2×C4×C139—41no—
128C2×C4×C139—41no—
129C2×C4×C139—41no—
130C2×C4×C139—41no—
131C2×C4×C139—81no—
132C2×C4×C139#12011yescharacteristic
133C2×C4×C139#12111yescharacteristic
134C2×C4×C139#12111yescharacteristic
135C2×C4×C139#12111yescharacteristic
136C2×C4×C139#12311yescharacteristic
137C2×C4×C139#12411yescharacteristic
138C2×C4×C139C2×SD1611yescharacteristic
139C2×C4×C139#13511yescharacteristic
140C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
142C8×C139—42no—
143C8×C139—42no—
144C8×C139—81no—
145C8×C139—81no—
146C8×C139—81no—
147C22×C139—21no—
148C22×C139—21no—
149C22×C139—82no—
150C22×C139—82no—
151C22×C139—82no—
152C22×C139—162no—
153C22×C139—162no—
154C22×C139#39411yescharacteristic
155C22×C139#48111yescharacteristic
156C22×C139#48211yescharacteristic
157C4×C139—21no—
158C4×C139—21no—
159C4×C139—21no—
160C4×C139—42no—
161C4×C139—81no—
162C4×C139#44911yescharacteristic
163C4×C139#45011yescharacteristic
164C4×C139#46511yescharacteristic
165C4×C139#46911yescharacteristic
166C4×C139#47112yes—
167C2×C139—21no—
168C2×C139—21no—
169C2×C139—162no—
170C2×C139#203411yescharacteristic
171C2×C139#204611yescharacteristic
172C2×C139#204811yescharacteristic
173#10443C13911yesmaximal, characteristic, direct product factor, Sylow
174C139#1044311yescharacteristic, direct product factor, Sylow
175C2×#460C2×C13911yescharacteristic
176#1801C2×C13911yescharacteristic, complemented
177#1570C2×C13911yescharacteristic, complemented
178#1545C2×C13911yescharacteristic
179#1545C2×C13911yescharacteristic
180#1479C2×C13911yescharacteristic, complemented
181#1301C2×C13911yescharacteristic, complemented
182C22×SD16—21no—
183C2×#127C22×C13911yescharacteristic
184C2×C4×Q8C22×C13911yescharacteristic
185#460—22no—
186#460—22no—
187#431C22×C13911yescharacteristic
188#431C22×C13911yescharacteristic
189#423C22×C13911yescharacteristic
190#423C22×C13911yescharacteristic
191C2×C4⋊C8C22×C13911yescharacteristic
192C2×#102—21no—
193C2×#101—21no—
194#343—21no—
195#334—22no—
196#331—22no—
197#331—22no—
198Q8⋊C8—22no—
199C22×Q8D4×C13911yescharacteristic
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C2×SD16—24no—
204C2×SD16—42no—
205C2×SD16—42no—
206C2×M16—21no—
207C2×M16—21no—
208C22×C8—21no—
209#127—21no—
210#127—21no—
211#127—21no—
212#127D4×C13912yes—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×Q8—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4D4×C13911yescharacteristic
219C2×C42—21no—
220C2×C42C23×C13911yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8D4×C13912yes—
228C4⋊C8D4×C13912yes—
229#102—24no—
230#101—42no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233C4×C8—21no—
234C4×C8—21no—
235C24—41no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8SD16×C13912yes—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—82no—
253C2×D4—82no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4C2×D4×C13911yescharacteristic
257C22×C4#41×C13911yescharacteristic
258C22×C4#41×C13911yescharacteristic
259SD16—48no—
260M16—41no—
261M16—41no—
262M16—41no—
263M16—41no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C42—41no—
276C42—41no—
277C42C2×D4×C13911yescharacteristic
278C42C2×D4×C13911yescharacteristic
279C42C2×D4×C13911yescharacteristic
280C42#41×C13911yescharacteristic
281C23—42no—
282C23—82no—
283C23—82no—
284C23—81no—
285C23—81no—
286C23#123×C13911yescharacteristic
287Q8—22no—
288Q8—22no—
289Q8—41no—
290Q8—41no—
291D4—42no—
292D4—42no—
293D4—82no—
294D4—82no—
295D4—82no—
296D4—81no—
297D4—81no—
298D4—82no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4#120×C13911yescharacteristic
307C2×C4#121×C13911yescharacteristic
308C2×C4#121×C13911yescharacteristic
309C2×C4#121×C13911yescharacteristic
310C2×C4#123×C13911yescharacteristic
311C2×C4#124×C13911yescharacteristic
312C2×C4C2×SD16×C13911yescharacteristic
313C2×C4#135×C13911yescharacteristic
314C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
315C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
316C8—42no—
317C8—42no—
318C8—81no—
319C8—81no—
320C8—81no—
321C22—21no—
322C22—21no—
323C22—82no—
324C22—82no—
325C22—82no—
326C22—162no—
327C22—162no—
328C22#394×C13911yescharacteristic
329C22#481×C13911yescharacteristic
330C22#482×C13911yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4#449×C13911yescharacteristic
337C4#450×C13911yescharacteristic
338C4#465×C13911yescharacteristic
339C4#469×C13911yescharacteristic
340C4#471×C13912yes—
341C2—21no—
342C2—21no—
343C2—162no—
344C2#2034×C13911yescharacteristic
345C2#2046×C13911yescharacteristic
346C2#2048×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#394
commutator, Frattini, cosocleC2×C42C23×C139
prime radicalC2×#127×C139C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1801×C139C2semidirect
3. #1570×C139C2semidirect
6. #1479×C139C2semidirect
7. #1301×C139C2semidirect
173. #10443C139direct (N × H)
174. C139#10443direct (N × H)
176. #1801C2×C139semidirect
177. #1570C2×C139semidirect
180. #1479C2×C139semidirect
181. #1301C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1392
#1801×C1392
#1570×C1392
#1545×C1392
#1479×C1392
#1301×C1392
#10443139