Finite Group Databasebeta

← C139×#13389 #48007985

Subgroups — C139×#13389 #48007985

Order 35584.

402 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C139C211yesmaximal, characteristic
2#2161×C139C211yesmaximal, characteristic, complemented
3C2×#361×C139C211yesmaximal, characteristic, complemented
4C2×#361×C139C211yesmaximal, characteristic, complemented
5#2117×C139C211yesmaximal, characteristic, complemented
6#1813×C139C211yesmaximal, characteristic, complemented
7#1388×C139C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C139—21no—
9C22×D8×C139C2211yescharacteristic
10C2×#131×C139C2211yescharacteristic
11C2×M32×C139C2211yescharacteristic
12C2×M32×C139C2211yescharacteristic
13#472×C139—22no—
14#472×C139—22no—
15C2×#108×C139C2211yescharacteristic
16C2×#108×C139C2211yescharacteristic
17C2×#108×C139C2211yescharacteristic
18#413×C139—21no—
19C2×#100×C139—21no—
20#368×C139—22no—
21#361×C139—22no—
22#361×C139—22no—
23#350×C139—22no—
24#338×C139—21no—
25C2×#41×C139D411yescharacteristic
26C22×D4×C139—21no—
27AGL(1,ℤ/8)×C139—24no—
28AGL(1,ℤ/8)×C139—42no—
29C2×SD16×C139—41no—
30C2×D8×C139—21no—
31C2×D8×C139—21no—
32C2×D8×C139—21no—
33C2×D8×C139—21no—
34C2×D8×C139—21no—
35C2×D8×C139—41no—
36C2×D8×C139D412yes—
37#131×C139—21no—
38#131×C139—21no—
39#131×C139—21no—
40#131×C139—21no—
41C2×M16×C139—21no—
42C2×M16×C139—21no—
43C2×M16×C139—21no—
44C2×M16×C139—21no—
45C2×M16×C139D411yescharacteristic
46C22×C8×C139—21no—
47C22×C8×C139C2311yescharacteristic
48M32×C139—21no—
49M32×C139—21no—
50M32×C139—21no—
51M32×C139D412yes—
52C2×C16×C139—21no—
53C2×C16×C139—21no—
54#108×C139—21no—
55#108×C139—21no—
56#108×C139—21no—
57#108×C139—21no—
58#108×C139—21no—
59#108×C139D412yes—
60#101×C139—41no—
61#100×C139—24no—
62#100×C139—41no—
63C24×C139—41no—
64#41×C139—21no—
65#41×C139—21no—
66#41×C139—21no—
67#41×C139—21no—
68C2×Q8×C139D811yescharacteristic
69C2×D4×C139—21no—
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×C139D811yescharacteristic
77C22×C4×C139—21no—
78C22×C4×C139C2×D411yescharacteristic
79SD16×C139—44no—
80D8×C139—22no—
81D8×C139—22no—
82D8×C139—44no—
83D8×C139—41no—
84D8×C139—41no—
85M16×C139—21no—
86M16×C139—22no—
87M16×C139—21no—
88M16×C139—41no—
89M16×C139—41no—
90M16×C139—41no—
91M16×C139—41no—
92M16×C139—41no—
93M16×C139—41no—
94M16×C139—41no—
95C2×C8×C139—21no—
96C2×C8×C139—41no—
97C2×C8×C139—41no—
98C2×C8×C139—41no—
99C2×C8×C139—41no—
100C2×C8×C139—41no—
101C2×C8×C139C2×D411yescharacteristic
102C2×C8×C139C2×D411yescharacteristic
103C2×C8×C139C2×D411yescharacteristic
104C2×C8×C139#4111yescharacteristic
105C2×C8×C139#4111yescharacteristic
106C2×C8×C139#4111yescharacteristic
107C16×C139—22no—
108C16×C139—41no—
109C23×C139—21no—
110C23×C139—42no—
111C23×C139—81no—
112C23×C139—81no—
113C23×C139—162no—
114C23×C139#13711yescharacteristic
115Q8×C139—21no—
116Q8×C139—21no—
117D4×C139—21no—
118D4×C139—21no—
119D4×C139—41no—
120D4×C139—41no—
121D4×C139—42no—
122D4×C139—42no—
123D4×C139—81no—
124D4×C139—81no—
125C2×C4×C139—21no—
126C2×C4×C139—41no—
127C2×C4×C139—41no—
128C2×C4×C139#12011yescharacteristic
129C2×C4×C139#12111yescharacteristic
130C2×C4×C139#12311yescharacteristic
131C2×C4×C139C2×D811yescharacteristic
132C2×C4×C139#13511yescharacteristic
133C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
134C8×C139—41no—
135C8×C139—42no—
136C8×C139—81no—
137C8×C139—81no—
138C8×C139#12111yescharacteristic
139C8×C139#12111yescharacteristic
140C8×C139#12311yescharacteristic
141C8×C139#12411yescharacteristic
142C22×C139—41no—
143C22×C139—41no—
144C22×C139—81no—
145C22×C139—82no—
146C22×C139—162no—
147C22×C139—162no—
148C22×C139—162no—
149C22×C139#45211yescharacteristic
150C22×C139#46811yescharacteristic
151C22×C139#48011yescharacteristic
152C4×C139—41no—
153C4×C139#39411yescharacteristic
154C4×C139#44711yescharacteristic
155C4×C139#46611yescharacteristic
156C4×C139#48211yescharacteristic
157C2×C139—21no—
158C2×C139—21no—
159C2×C139—21no—
160C2×C139—81no—
161C2×C139—162no—
162C2×C139#203311yescharacteristic
163#13389C13911yesmaximal, characteristic, direct product factor, Sylow
164C139#1338911yescharacteristic, direct product factor, Sylow
165C2×#472C2×C13911yescharacteristic
166#2161C2×C13911yescharacteristic, complemented
167C2×#361C2×C13911yescharacteristic, complemented
168C2×#361C2×C13911yescharacteristic, complemented
169#2117C2×C13911yescharacteristic, complemented
170#1813C2×C13911yescharacteristic, complemented
171#1388C2×C13911yescharacteristic, complemented
172C2×AGL(1,ℤ/8)—21no—
173C22×D8C22×C13911yescharacteristic
174C2×#131C22×C13911yescharacteristic
175C2×M32C22×C13911yescharacteristic
176C2×M32C22×C13911yescharacteristic
177#472—22no—
178#472—22no—
179C2×#108C22×C13911yescharacteristic
180C2×#108C22×C13911yescharacteristic
181C2×#108C22×C13911yescharacteristic
182#413—21no—
183C2×#100—21no—
184#368—22no—
185#361—22no—
186#361—22no—
187#350—22no—
188#338—21no—
189C2×#41D4×C13911yescharacteristic
190C22×D4—21no—
191AGL(1,ℤ/8)—24no—
192AGL(1,ℤ/8)—42no—
193C2×SD16—41no—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8—41no—
200C2×D8D4×C13912yes—
201#131—21no—
202#131—21no—
203#131—21no—
204#131—21no—
205C2×M16—21no—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16—21no—
209C2×M16D4×C13911yescharacteristic
210C22×C8—21no—
211C22×C8C23×C13911yescharacteristic
212M32—21no—
213M32—21no—
214M32—21no—
215M32D4×C13912yes—
216C2×C16—21no—
217C2×C16—21no—
218#108—21no—
219#108—21no—
220#108—21no—
221#108—21no—
222#108—21no—
223#108D4×C13912yes—
224#101—41no—
225#100—24no—
226#100—41no—
227C24—41no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—21no—
232C2×Q8D8×C13911yescharacteristic
233C2×D4—21no—
234C2×D4—22no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4D8×C13911yescharacteristic
241C22×C4—21no—
242C22×C4C2×D4×C13911yescharacteristic
243SD16—44no—
244D8—22no—
245D8—22no—
246D8—44no—
247D8—41no—
248D8—41no—
249M16—21no—
250M16—22no—
251M16—21no—
252M16—41no—
253M16—41no—
254M16—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258M16—41no—
259C2×C8—21no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8C2×D4×C13911yescharacteristic
266C2×C8C2×D4×C13911yescharacteristic
267C2×C8C2×D4×C13911yescharacteristic
268C2×C8#41×C13911yescharacteristic
269C2×C8#41×C13911yescharacteristic
270C2×C8#41×C13911yescharacteristic
271C16—22no—
272C16—41no—
273C23—21no—
274C23—42no—
275C23—81no—
276C23—81no—
277C23—162no—
278C23#137×C13911yescharacteristic
279Q8—21no—
280Q8—21no—
281D4—21no—
282D4—21no—
283D4—41no—
284D4—41no—
285D4—42no—
286D4—42no—
287D4—81no—
288D4—81no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4#120×C13911yescharacteristic
293C2×C4#121×C13911yescharacteristic
294C2×C4#123×C13911yescharacteristic
295C2×C4C2×D8×C13911yescharacteristic
296C2×C4#135×C13911yescharacteristic
297C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
298C8—42no—
299C8—41no—
300C8—81no—
301C8—81no—
302C8#121×C13911yescharacteristic
303C8#121×C13911yescharacteristic
304C8#123×C13911yescharacteristic
305C8#124×C13911yescharacteristic
306C22—41no—
307C22—41no—
308C22—81no—
309C22—82no—
310C22—162no—
311C22—162no—
312C22—162no—
313C22#452×C13911yescharacteristic
314C22#468×C13911yescharacteristic
315C22#480×C13911yescharacteristic
316C4—41no—
317C4#394×C13911yescharacteristic
318C4#447×C13911yescharacteristic
319C4#466×C13911yescharacteristic
320C4#482×C13911yescharacteristic
321C2—21no—
322C2—21no—
323C2—21no—
324C2—81no—
325C2—162no—
326C2#2033×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2033
commutator, Frattini, cosocleC22×C8C23×C139
prime radicalC2×#472×C139C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C22×C4×C139 ◁ C2×#131×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2161×C139C2semidirect
3. C2×#361×C139C2semidirect
4. C2×#361×C139C2semidirect
5. #2117×C139C2semidirect
6. #1813×C139C2semidirect
7. #1388×C139C2semidirect
163. #13389C139direct (N × H)
164. C139#13389direct (N × H)
166. #2161C2×C139semidirect
167. C2×#361C2×C139semidirect
168. C2×#361C2×C139semidirect
169. #2117C2×C139semidirect
170. #1813C2×C139semidirect
171. #1388C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#472×C1392
#2161×C1392
C2×#361×C1392
#2117×C1392
#1813×C1392
#1388×C1392
#13389139