Finite Group Databasebeta

← C139×#13418 #48008014

Subgroups — C139×#13418 #48008014

Order 35584.

422 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3156×C139C211yesmaximal, characteristic
2#2148×C139C211yesmaximal, characteristic
3C2×#362×C139C211yesmaximal, characteristic, complemented
4C2×#362×C139C211yesmaximal, characteristic, complemented
5#2143×C139C211yesmaximal, characteristic
6#1953×C139C211yesmaximal, characteristic, complemented
7#1378×C139C211yesmaximal, characteristic, complemented
8C2×#137×C139—21no—
9C2×#135×C139C2211yescharacteristic
10C22×Q16×C139C2211yescharacteristic
11#536×C139—21no—
12C2×M32×C139C2211yescharacteristic
13C2×M32×C139C2211yescharacteristic
14#497×C139—22no—
15#495×C139—21no—
16#494×C139—21no—
17#430×C139—21no—
18C2×#108×C139C2211yescharacteristic
19C2×#108×C139C2211yescharacteristic
20#405×C139C2211yescharacteristic
21#362×C139—22no—
22#362×C139—21no—
23#362×C139—22no—
24#361×C139—21no—
25#359×C139—22no—
26#344×C139—21no—
27C2×#41×C139—21no—
28C22×Q8×C139—21no—
29#137×C139—42no—
30#137×C139—42no—
31#135×C139—21no—
32#135×C139—21no—
33#135×C139—21no—
34#135×C139—21no—
35C2×Q16×C139—22no—
36C2×Q16×C139—21no—
37C2×Q16×C139—21no—
38C2×Q16×C139—21no—
39C2×Q16×C139—21no—
40C2×Q16×C139—21no—
41C2×Q16×C139D411yescharacteristic
42C2×Q16×C139D412yes—
43C2×SD16×C139—22no—
44C2×SD16×C139—21no—
45C2×D8×C139D411yescharacteristic
46C2×M16×C139—21no—
47C2×M16×C139—21no—
48C2×M16×C139D411yescharacteristic
49C22×C8×C139C2311yescharacteristic
50C4⋊Q8×C139—22no—
51#124×C139—22no—
52#123×C139—42no—
53C22⋊Q8×C139—42no—
54#117×C139D411yescharacteristic
55M32×C139—21no—
56M32×C139—21no—
57M32×C139—21no—
58M32×C139—21no—
59C2×C16×C139—21no—
60C2×C16×C139—21no—
61#108×C139—21no—
62#108×C139—21no—
63#108×C139—21no—
64#108×C139—42no—
65#108×C139D412yes—
66#97×C139—21no—
67C4×C8×C139—21no—
68#41×C139—41no—
69#41×C139—41no—
70#41×C139—41no—
71#41×C139—41no—
72C2×Q8×C139—22no—
73C2×Q8×C139—21no—
74C2×Q8×C139—41no—
75C2×Q8×C139—41no—
76C2×Q8×C139—41no—
77C2×Q8×C139—41no—
78C2×Q8×C139—41no—
79C2×D4×C139—21no—
80C2×D4×C139—41no—
81C22×C4×C139—41no—
82C22×C4×C139—41no—
83C22×C4×C139C2×D411yescharacteristic
84Q16×C139—22no—
85Q16×C139—21no—
86Q16×C139—22no—
87Q16×C139—21no—
88Q16×C139—44no—
89Q16×C139—41no—
90Q16×C139—41no—
91SD16×C139—44no—
92SD16×C139—41no—
93SD16×C139—41no—
94D8×C139—21no—
95D8×C139—21no—
96M16×C139—21no—
97M16×C139—22no—
98M16×C139—41no—
99M16×C139—41no—
100M16×C139—41no—
101M16×C139D812yes—
102C2×C8×C139—21no—
103C2×C8×C139—41no—
104C2×C8×C139—41no—
105C2×C8×C139C2×D411yescharacteristic
106C2×C8×C139C2×D411yescharacteristic
107C2×C8×C139C2×D411yescharacteristic
108C2×C8×C139#4111yescharacteristic
109C2×C8×C139#4111yescharacteristic
110C2×C8×C139#4111yescharacteristic
111C4⋊C4×C139—21no—
112C4⋊C4×C139—44no—
113C22⋊C4×C139—44no—
114C22⋊C4×C139SD1612yes—
115C42×C139—21no—
116C16×C139—41no—
117C16×C139—41no—
118C23×C139—41no—
119C23×C139C2×SD1611yescharacteristic
120Q8×C139—41no—
121Q8×C139—42no—
122Q8×C139—42no—
123Q8×C139—41no—
124Q8×C139—81no—
125Q8×C139—81no—
126D4×C139—41no—
127D4×C139—41no—
128D4×C139—81no—
129D4×C139—81no—
130C2×C4×C139—22no—
131C2×C4×C139—42no—
132C2×C4×C139—41no—
133C2×C4×C139—81no—
134C2×C4×C139—81no—
135C2×C4×C139—81no—
136C2×C4×C139—81no—
137C2×C4×C139#12011yescharacteristic
138C2×C4×C139#12111yescharacteristic
139C2×C4×C139#12411yescharacteristic
140C2×C4×C139C2×D811yescharacteristic
141C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
143C8×C139—22no—
144C8×C139—42no—
145C8×C139—81no—
146C8×C139#12111yescharacteristic
147C8×C139#12111yescharacteristic
148C8×C139#12311yescharacteristic
149C8×C139#12311yescharacteristic
150C22×C139—41no—
151C22×C139—82no—
152C22×C139—81no—
153C22×C139#45011yescharacteristic
154C22×C139#46011yescharacteristic
155C22×C139#48611yescharacteristic
156C4×C139—42no—
157C4×C139—81no—
158C4×C139—82no—
159C4×C139#39411yescharacteristic
160C4×C139#44711yescharacteristic
161C4×C139#45911yescharacteristic
162C4×C139#49011yescharacteristic
163C2×C139—21no—
164C2×C139—21no—
165C2×C139—21no—
166C2×C139—161no—
167C2×C139#204111yescharacteristic
168#13418C13911yesmaximal, characteristic, direct product factor, Sylow
169C139#1341811yescharacteristic, direct product factor, Sylow
170#3156C2×C13911yescharacteristic
171#2148C2×C13911yescharacteristic
172C2×#362C2×C13911yescharacteristic, complemented
173C2×#362C2×C13911yescharacteristic, complemented
174#2143C2×C13911yescharacteristic
175#1953C2×C13911yescharacteristic, complemented
176#1378C2×C13911yescharacteristic, complemented
177C2×#137—21no—
178C2×#135C22×C13911yescharacteristic
179C22×Q16C22×C13911yescharacteristic
180#536—21no—
181C2×M32C22×C13911yescharacteristic
182C2×M32C22×C13911yescharacteristic
183#497—22no—
184#495—21no—
185#494—21no—
186#430—21no—
187C2×#108C22×C13911yescharacteristic
188C2×#108C22×C13911yescharacteristic
189#405C22×C13911yescharacteristic
190#362—22no—
191#362—21no—
192#362—22no—
193#361—21no—
194#359—22no—
195#344—21no—
196C2×#41—21no—
197C22×Q8—21no—
198#137—42no—
199#137—42no—
200#135—21no—
201#135—21no—
202#135—21no—
203#135—21no—
204C2×Q16—22no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16D4×C13912yes—
211C2×Q16D4×C13911yescharacteristic
212C2×SD16—22no—
213C2×SD16—21no—
214C2×D8D4×C13911yescharacteristic
215C2×M16—21no—
216C2×M16—21no—
217C2×M16D4×C13911yescharacteristic
218C22×C8C23×C13911yescharacteristic
219C4⋊Q8—22no—
220#124—22no—
221#123—42no—
222C22⋊Q8—42no—
223#117D4×C13911yescharacteristic
224M32—21no—
225M32—21no—
226M32—21no—
227M32—21no—
228C2×C16—21no—
229C2×C16—21no—
230#108—21no—
231#108—21no—
232#108—21no—
233#108—42no—
234#108D4×C13912yes—
235#97—21no—
236C4×C8—21no—
237#41—41no—
238#41—41no—
239#41—41no—
240#41—41no—
241C2×Q8—22no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×D4—21no—
249C2×D4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4C2×D4×C13911yescharacteristic
253Q16—22no—
254Q16—21no—
255Q16—22no—
256Q16—21no—
257Q16—44no—
258Q16—41no—
259Q16—41no—
260SD16—44no—
261SD16—41no—
262SD16—41no—
263D8—21no—
264D8—21no—
265M16—21no—
266M16—22no—
267M16—41no—
268M16—41no—
269M16—41no—
270M16D8×C13912yes—
271C2×C8—21no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8C2×D4×C13911yescharacteristic
275C2×C8C2×D4×C13911yescharacteristic
276C2×C8C2×D4×C13911yescharacteristic
277C2×C8#41×C13911yescharacteristic
278C2×C8#41×C13911yescharacteristic
279C2×C8#41×C13911yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—44no—
282C22⋊C4—44no—
283C22⋊C4SD16×C13912yes—
284C42—21no—
285C16—41no—
286C16—41no—
287C23—41no—
288C23C2×SD16×C13911yescharacteristic
289Q8—42no—
290Q8—41no—
291Q8—41no—
292Q8—42no—
293Q8—81no—
294Q8—81no—
295D4—41no—
296D4—41no—
297D4—81no—
298D4—81no—
299C2×C4—22no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4#120×C13911yescharacteristic
307C2×C4#121×C13911yescharacteristic
308C2×C4#124×C13911yescharacteristic
309C2×C4C2×D8×C13911yescharacteristic
310C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
311C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
312C8—22no—
313C8—42no—
314C8—81no—
315C8#121×C13911yescharacteristic
316C8#121×C13911yescharacteristic
317C8#123×C13911yescharacteristic
318C8#123×C13911yescharacteristic
319C22—41no—
320C22—82no—
321C22—81no—
322C22#450×C13911yescharacteristic
323C22#460×C13911yescharacteristic
324C22#486×C13911yescharacteristic
325C4—42no—
326C4—81no—
327C4—82no—
328C4#394×C13911yescharacteristic
329C4#447×C13911yescharacteristic
330C4#459×C13911yescharacteristic
331C4#490×C13911yescharacteristic
332C2—21no—
333C2—21no—
334C2—21no—
335C2—161no—
336C2#2041×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2041
commutator, Frattini, cosocleC22×C8C23×C139
prime radicalC2×#135×C139C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C22×C4×C139 ◁ #405×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#362×C139C2semidirect
4. C2×#362×C139C2semidirect
6. #1953×C139C2semidirect
7. #1378×C139C2semidirect
168. #13418C139direct (N × H)
169. C139#13418direct (N × H)
172. C2×#362C2×C139semidirect
173. C2×#362C2×C139semidirect
175. #1953C2×C139semidirect
176. #1378C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3156×C1392
#2148×C1392
C2×#362×C1392
#2143×C1392
#1953×C1392
#1378×C1392
#13418139