Finite Group Databasebeta

← C139×#12979 #48007575

Subgroups — C139×#12979 #48007575

Order 35584.

456 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3407×C139C211yesmaximal, characteristic, complemented
2#2955×C139C211yesmaximal, characteristic
3#2117×C139C211yesmaximal, characteristic, complemented
4C2×#350×C139C211yesmaximal, characteristic, complemented
5#2113×C139C211yesmaximal, characteristic, complemented
6#1379×C139C211yesmaximal, characteristic, complemented
7#1378×C139C211yesmaximal, characteristic, complemented
8#575×C139C411yescharacteristic
9C2×#131×C139C2211yescharacteristic
10C2×#131×C139C2211yescharacteristic
11#504×C139—22no—
12#504×C139—22no—
13C2×M32×C139—22no—
14C2×M32×C139C2211yescharacteristic
15C2×M32×C139C2211yescharacteristic
16C2×M32×C139C2211yescharacteristic
17C22×C16×C139C2211yescharacteristic
18#444×C139—22no—
19#443×C139—22no—
20#430×C139C411yescharacteristic
21#421×C139C411yescharacteristic
22#421×C139C411yescharacteristic
23#405×C139C2211yescharacteristic
24#350×C139—22no—
25#350×C139—22no—
26C22⋊C16×C139—22no—
27C2×#41×C139C2×C411yescharacteristic
28C2×#41×C139C2×C411yescharacteristic
29#137×C139—21no—
30#137×C139C812yes—
31AGL(1,ℤ/8)×C139—21no—
32AGL(1,ℤ/8)×C139C812yes—
33#135×C139—22no—
34#131×C139—21no—
35#131×C139—21no—
36#131×C139—21no—
37#131×C139—21no—
38#131×C139—21no—
39#131×C139—21no—
40#131×C139D412yes—
41#131×C139D412yes—
42C2×M16×C139—21no—
43C2×M16×C139—21no—
44C2×M16×C139C2×C411yescharacteristic
45C2×M16×C139C2×C411yescharacteristic
46C2×M16×C139C2×C411yescharacteristic
47C22×C8×C139—21no—
48C22×C8×C139—21no—
49C22×C8×C139C2311yescharacteristic
50#117×C139C2×C411yescharacteristic
51M32×C139—24no—
52M32×C139—21no—
53M32×C139—21no—
54M32×C139—21no—
55M32×C139—21no—
56M32×C139—21no—
57M32×C139D412yes—
58C2×C16×C139—24no—
59C2×C16×C139—21no—
60C2×C16×C139—21no—
61C2×C16×C139—21no—
62C2×C16×C139—21no—
63C2×C16×C139—21no—
64C2×C16×C139D412yes—
65#108×C139—22no—
66#104×C139—22no—
67#104×C139—22no—
68#97×C139—21no—
69C4×C8×C139—21no—
70#41×C139—21no—
71#41×C139—21no—
72#41×C139—21no—
73#41×C139—21no—
74#41×C139—21no—
75#41×C139—21no—
76#41×C139C22⋊C412yes—
77#41×C139C2×C812yes—
78C2×Q8×C139C2×C811yescharacteristic
79C2×Q8×C139M1611yescharacteristic
80C2×D4×C139—21no—
81C2×D4×C139—21no—
82C2×D4×C139C2×C811yescharacteristic
83C2×D4×C139M1611yescharacteristic
84C22×C4×C139—21no—
85C22×C4×C139—21no—
86C22×C4×C139C22×C411yescharacteristic
87Q16×C139—22no—
88SD16×C139—22no—
89SD16×C139—22no—
90D8×C139—22no—
91M16×C139—21no—
92M16×C139—21no—
93M16×C139—22no—
94M16×C139—22no—
95M16×C139—21no—
96M16×C139—21no—
97M16×C139—41no—
98M16×C139—41no—
99M16×C139C22⋊C412yes—
100M16×C139C2×C812yes—
101C2×C8×C139—21no—
102C2×C8×C139—21no—
103C2×C8×C139—22no—
104C2×C8×C139—22no—
105C2×C8×C139—21no—
106C2×C8×C139—41no—
107C2×C8×C139—41no—
108C2×C8×C139C2×D411yescharacteristic
109C2×C8×C139C2×D411yescharacteristic
110C2×C8×C139C2×D411yescharacteristic
111C2×C8×C139C2×D411yescharacteristic
112C2×C8×C139#4111yescharacteristic
113C2×C8×C139#4111yescharacteristic
114C4⋊C4×C139—21no—
115C22⋊C4×C139—21no—
116C42×C139—21no—
117C16×C139—22no—
118C16×C139—22no—
119C16×C139—41no—
120C16×C139—41no—
121C23×C139—21no—
122C23×C139—21no—
123C23×C139#13111yescharacteristic
124Q8×C139—21no—
125Q8×C139—21no—
126Q8×C139—21no—
127Q8×C139C22⋊C812yes—
128D4×C139—22no—
129D4×C139—22no—
130D4×C139—21no—
131D4×C139—21no—
132D4×C139—21no—
133D4×C139—41no—
134D4×C139—41no—
135D4×C139C22⋊C812yes—
136C2×C4×C139—21no—
137C2×C4×C139—22no—
138C2×C4×C139—22no—
139C2×C4×C139—21no—
140C2×C4×C139—41no—
141C2×C4×C139—41no—
142C2×C4×C139—41no—
143C2×C4×C139C2×C22⋊C411yescharacteristic
144C2×C4×C139C4×D411yescharacteristic
145C2×C4×C139C4×D411yescharacteristic
146C2×C4×C139C22×C811yescharacteristic
147C2×C4×C139C2×M1611yescharacteristic
148C2×C4×C139#13111yescharacteristic
149C8×C139—22no—
150C8×C139—22no—
151C8×C139—41no—
152C8×C139#12011yescharacteristic
153C8×C139#12111yescharacteristic
154C8×C139#12111yescharacteristic
155C8×C139#12311yescharacteristic
156C22×C139—22no—
157C22×C139—41no—
158C22×C139—42no—
159C22×C139—41no—
160C22×C139—81no—
161C22×C139#40811yescharacteristic
162C22×C139C8×D411yescharacteristic
163C22×C139#43511yescharacteristic
164C4×C139—22no—
165C4×C139—41no—
166C4×C139—81no—
167C4×C139#38611yescharacteristic
168C4×C139C2×C22⋊C811yescharacteristic
169C4×C139C8×D411yescharacteristic
170C4×C139#43511yescharacteristic
171C2×C139—21no—
172C2×C139—21no—
173C2×C139—21no—
174C2×C139—42no—
175C2×C139—81no—
176C2×C139#186911yescharacteristic
177#12979C13911yesmaximal, characteristic, direct product factor, Sylow
178C139#1297911yescharacteristic, direct product factor, Sylow
179#3407C2×C13911yescharacteristic, complemented
180#2955C2×C13911yescharacteristic
181#2117C2×C13911yescharacteristic, complemented
182C2×#350C2×C13911yescharacteristic, complemented
183#2113C2×C13911yescharacteristic, complemented
184#1379C2×C13911yescharacteristic, complemented
185#1378C2×C13911yescharacteristic, complemented
186#575C4×C13911yescharacteristic
187C2×#131C22×C13911yescharacteristic
188C2×#131C22×C13911yescharacteristic
189#504—22no—
190#504—22no—
191C2×M32—22no—
192C2×M32C22×C13911yescharacteristic
193C2×M32C22×C13911yescharacteristic
194C2×M32C22×C13911yescharacteristic
195C22×C16C22×C13911yescharacteristic
196#444—22no—
197#443—22no—
198#430C4×C13911yescharacteristic
199#421C4×C13911yescharacteristic
200#421C4×C13911yescharacteristic
201#405C22×C13911yescharacteristic
202#350—22no—
203#350—22no—
204C22⋊C16—22no—
205C2×#41C2×C4×C13911yescharacteristic
206C2×#41C2×C4×C13911yescharacteristic
207#137—21no—
208#137C8×C13912yes—
209AGL(1,ℤ/8)—21no—
210AGL(1,ℤ/8)C8×C13912yes—
211#135—22no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—21no—
216#131—21no—
217#131—21no—
218#131D4×C13912yes—
219#131D4×C13912yes—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16C2×C4×C13911yescharacteristic
223C2×M16C2×C4×C13911yescharacteristic
224C2×M16C2×C4×C13911yescharacteristic
225C22×C8—21no—
226C22×C8—21no—
227C22×C8C23×C13911yescharacteristic
228#117C2×C4×C13911yescharacteristic
229M32—24no—
230M32—21no—
231M32—21no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32D4×C13912yes—
236C2×C16—24no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16D4×C13912yes—
243#108—22no—
244#104—22no—
245#104—22no—
246#97—21no—
247C4×C8—21no—
248#41—21no—
249#41—21no—
250#41—21no—
251#41—21no—
252#41—21no—
253#41—21no—
254#41C22⋊C4×C13912yes—
255#41C2×C8×C13912yes—
256C2×Q8C2×C8×C13911yescharacteristic
257C2×Q8M16×C13911yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4C2×C8×C13911yescharacteristic
261C2×D4M16×C13911yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4C22×C4×C13911yescharacteristic
265Q16—22no—
266SD16—22no—
267SD16—22no—
268D8—22no—
269M16—21no—
270M16—21no—
271M16—22no—
272M16—22no—
273M16—21no—
274M16—21no—
275M16—41no—
276M16—41no—
277M16C22⋊C4×C13912yes—
278M16C2×C8×C13912yes—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8C2×D4×C13911yescharacteristic
287C2×C8C2×D4×C13911yescharacteristic
288C2×C8C2×D4×C13911yescharacteristic
289C2×C8C2×D4×C13911yescharacteristic
290C2×C8#41×C13911yescharacteristic
291C2×C8#41×C13911yescharacteristic
292C4⋊C4—21no—
293C22⋊C4—21no—
294C42—21no—
295C16—22no—
296C16—22no—
297C16—41no—
298C16—41no—
299C23—21no—
300C23—21no—
301C23#131×C13911yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8C22⋊C8×C13912yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—41no—
313D4C22⋊C8×C13912yes—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4C2×C22⋊C4×C13911yescharacteristic
322C2×C4C4×D4×C13911yescharacteristic
323C2×C4C4×D4×C13911yescharacteristic
324C2×C4C22×C8×C13911yescharacteristic
325C2×C4C2×M16×C13911yescharacteristic
326C2×C4#131×C13911yescharacteristic
327C8—22no—
328C8—22no—
329C8—41no—
330C8#120×C13911yescharacteristic
331C8#121×C13911yescharacteristic
332C8#121×C13911yescharacteristic
333C8#123×C13911yescharacteristic
334C22—22no—
335C22—41no—
336C22—42no—
337C22—41no—
338C22—81no—
339C22#408×C13911yescharacteristic
340C22C8×D4×C13911yescharacteristic
341C22#435×C13911yescharacteristic
342C4—22no—
343C4—41no—
344C4—81no—
345C4#386×C13911yescharacteristic
346C4C2×C22⋊C8×C13911yescharacteristic
347C4C8×D4×C13911yescharacteristic
348C4#435×C13911yescharacteristic
349C2—21no—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—81no—
354C2#1869×C13911yescharacteristic
subgroupG/H
centerC8×C139#120
commutatorC2×C4C22×C8×C139
Frattini, cosocleC22×C8C23×C139
socleC2×C139#1869
prime radical#575×C139C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C8×C139 ◁ C22×C8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3407×C139C2semidirect
3. #2117×C139C2semidirect
4. C2×#350×C139C2semidirect
5. #2113×C139C2semidirect
6. #1379×C139C2semidirect
7. #1378×C139C2semidirect
177. #12979C139direct (N × H)
178. C139#12979direct (N × H)
179. #3407C2×C139semidirect
181. #2117C2×C139semidirect
182. C2×#350C2×C139semidirect
183. #2113C2×C139semidirect
184. #1379C2×C139semidirect
185. #1378C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3407×C1392
#2955×C1392
#2117×C1392
C2×#350×C1392
#2113×C1392
#1379×C1392
#1378×C1392
#12979139