Finite Group Databasebeta

← C139×#9051 #48003647

Subgroups — C139×#9051 #48003647

Order 35584.

436 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3108×C139C211yesmaximal, characteristic
2#2992×C139C211yesmaximal, characteristic
3#1985×C139C211yesmaximal, characteristic, complemented
4#1524×C139C211yesmaximal, characteristic
5#1491×C139C211yesmaximal, characteristic, complemented
6#1302×C139C211yesmaximal, characteristic, complemented
7#1283×C139C211yesmaximal, characteristic, complemented
8#529×C139C2211yescharacteristic
9C2×C4×Q8×C139C2211yescharacteristic
10#483×C139C411yescharacteristic
11#480×C139C411yescharacteristic
12#479×C139—21no—
13#464×C139—21no—
14#451×C139C411yescharacteristic
15#448×C139C411yescharacteristic
16#446×C139—21no—
17C4×Q16×C139—21no—
18C4×SD16×C139—21no—
19#435×C139—21no—
20#435×C139—21no—
21C8×D4×C139—21no—
22#433×C139—21no—
23#432×C139C2211yescharacteristic
24#431×C139C2211yescharacteristic
25#424×C139—21no—
26C2×C4⋊C8×C139C2211yescharacteristic
27C4×M16×C139C2211yescharacteristic
28C2×#97×C139C2211yescharacteristic
29#336×C139—21no—
30#336×C139—21no—
31#330×C139—21no—
32#329×C139—21no—
33Q8⋊C8×C139—21no—
34Q8⋊C8×C139—21no—
35C22×Q8×C139C2×C411yescharacteristic
36C2×Q16×C139—21no—
37C2×SD16×C139—21no—
38C2×M16×C139—21no—
39C2×M16×C139—21no—
40C22×C8×C139—21no—
41C22×C8×C139—21no—
42C22×C8×C139D411yescharacteristic
43C22×C8×C139D411yescharacteristic
44#126×C139—21no—
45#125×C139D411yescharacteristic
46#124×C139D411yescharacteristic
47#123×C139—21no—
48C22⋊Q8×C139C2×C411yescharacteristic
49#121×C139C2×C411yescharacteristic
50C4×Q8×C139—21no—
51C4×Q8×C139—21no—
52C4×Q8×C139—21no—
53C4×Q8×C139—21no—
54C4×Q8×C139D411yescharacteristic
55C4×D4×C139—21no—
56C4×D4×C139D411yescharacteristic
57#117×C139—21no—
58C2×C4⋊C4×C139—21no—
59C2×C4⋊C4×C139C2×C411yescharacteristic
60C2×C42×C139—21no—
61C2×C42×C139C2311yescharacteristic
62#107×C139—21no—
63#106×C139—21no—
64C4⋊C8×C139—21no—
65C4⋊C8×C139—21no—
66C4⋊C8×C139—21no—
67C4⋊C8×C139—21no—
68C4⋊C8×C139—21no—
69C4⋊C8×C139D411yescharacteristic
70C4⋊C8×C139D411yescharacteristic
71#103×C139—21no—
72#103×C139—21no—
73#103×C139—21no—
74#102×C139—21no—
75C22⋊C8×C139—21no—
76C22⋊C8×C139—21no—
77C22⋊C8×C139—21no—
78C22⋊C8×C139C2×C411yescharacteristic
79C22⋊C8×C139C2×C411yescharacteristic
80#97×C139—21no—
81#97×C139—21no—
82#97×C139—21no—
83#97×C139—21no—
84#97×C139—21no—
85C4×C8×C139—21no—
86C4×C8×C139—21no—
87C4×C8×C139—21no—
88C2×Q8×C139—21no—
89C2×Q8×C139—21no—
90C2×Q8×C139—42no—
91C2×Q8×C139C22⋊C411yescharacteristic
92C2×D4×C139—21no—
93C2×D4×C139C22⋊C411yescharacteristic
94C22×C4×C139—21no—
95C22×C4×C139—21no—
96C22×C4×C139—21no—
97C22×C4×C139C22×C411yescharacteristic
98C22×C4×C139C2×D411yescharacteristic
99C22×C4×C139#4111yescharacteristic
100Q16×C139—42no—
101SD16×C139—42no—
102M16×C139—22no—
103M16×C139—41no—
104M16×C139—81no—
105C2×C8×C139—22no—
106C2×C8×C139—21no—
107C2×C8×C139—21no—
108C2×C8×C139—21no—
109C2×C8×C139—21no—
110C2×C8×C139—21no—
111C2×C8×C139—21no—
112C2×C8×C139—41no—
113C2×C8×C139—41no—
114C2×C8×C139—41no—
115C2×C8×C139—41no—
116C2×C8×C139—41no—
117C2×C8×C139—81no—
118C4⋊C4×C139—21no—
119C4⋊C4×C139—21no—
120C4⋊C4×C139—21no—
121C4⋊C4×C139—21no—
122C4⋊C4×C139—21no—
123C4⋊C4×C139—21no—
124C4⋊C4×C139—41no—
125C4⋊C4×C139—41no—
126C4⋊C4×C139C22⋊C411yescharacteristic
127C4⋊C4×C139C22⋊C411yescharacteristic
128C22⋊C4×C139—21no—
129C22⋊C4×C139—21no—
130C22⋊C4×C139—21no—
131C22⋊C4×C139—21no—
132C22⋊C4×C139—21no—
133C42×C139—21no—
134C42×C139—41no—
135C42×C139—41no—
136C42×C139C2×D411yescharacteristic
137C42×C139C2×D411yescharacteristic
138C42×C139C2×D411yescharacteristic
139C42×C139#4111yescharacteristic
140C23×C139—21no—
141C23×C139C4×D411yescharacteristic
142Q8×C139—22no—
143Q8×C139—22no—
144Q8×C139—41no—
145Q8×C139—41no—
146Q8×C139—41no—
147D4×C139—41no—
148D4×C139—41no—
149D4×C139—41no—
150C2×C4×C139—21no—
151C2×C4×C139—21no—
152C2×C4×C139—21no—
153C2×C4×C139—21no—
154C2×C4×C139—22no—
155C2×C4×C139—21no—
156C2×C4×C139—21no—
157C2×C4×C139—21no—
158C2×C4×C139—41no—
159C2×C4×C139—41no—
160C2×C4×C139—41no—
161C2×C4×C139—41no—
162C2×C4×C139—41no—
163C2×C4×C139—41no—
164C2×C4×C139—41no—
165C2×C4×C139—41no—
166C2×C4×C139C2×C22⋊C411yescharacteristic
167C2×C4×C139C4×D411yescharacteristic
168C2×C4×C139#12011yescharacteristic
169C2×C4×C139#12111yescharacteristic
170C2×C4×C139#12111yescharacteristic
171C2×C4×C139#12311yescharacteristic
172C8×C139—42no—
173C8×C139—41no—
174C8×C139—41no—
175C8×C139—42no—
176C8×C139—41no—
177C8×C139—41no—
178C8×C139—41no—
179C8×C139—41no—
180C22×C139—21no—
181C22×C139—21no—
182C22×C139—41no—
183C22×C139—41no—
184C22×C139—41no—
185C22×C139#38611yescharacteristic
186C22×C139#44311yescharacteristic
187C22×C139#44411yescharacteristic
188C4×C139—21no—
189C4×C139—21no—
190C4×C139—21no—
191C4×C139—21no—
192C4×C139—21no—
193C4×C139—41no—
194C4×C139—41no—
195C4×C139—42no—
196C4×C139—41no—
197C4×C139—81no—
198C4×C139#45511yescharacteristic
199C4×C139#45611yescharacteristic
200C2×C139—21no—
201C2×C139—21no—
202C2×C139—81no—
203C2×C139#187611yescharacteristic
204C2×C139#188211yescharacteristic
205C2×C139#189111yescharacteristic
206#9051C13911yesmaximal, characteristic, direct product factor, Sylow
207C139#905111yescharacteristic, direct product factor, Sylow
208#3108C2×C13911yescharacteristic
209#2992C2×C13911yescharacteristic
210#1985C2×C13911yescharacteristic, complemented
211#1524C2×C13911yescharacteristic
212#1491C2×C13911yescharacteristic, complemented
213#1302C2×C13911yescharacteristic, complemented
214#1283C2×C13911yescharacteristic, complemented
215#529C22×C13911yescharacteristic
216C2×C4×Q8C22×C13911yescharacteristic
217#483C4×C13911yescharacteristic
218#480C4×C13911yescharacteristic
219#479—21no—
220#464—21no—
221#451C4×C13911yescharacteristic
222#448C4×C13911yescharacteristic
223#446—21no—
224C4×Q16—21no—
225C4×SD16—21no—
226#435—21no—
227#435—21no—
228C8×D4—21no—
229#433—21no—
230#432C22×C13911yescharacteristic
231#431C22×C13911yescharacteristic
232#424—21no—
233C2×C4⋊C8C22×C13911yescharacteristic
234C4×M16C22×C13911yescharacteristic
235C2×#97C22×C13911yescharacteristic
236#336—21no—
237#336—21no—
238#330—21no—
239#329—21no—
240Q8⋊C8—21no—
241Q8⋊C8—21no—
242C22×Q8C2×C4×C13911yescharacteristic
243C2×Q16—21no—
244C2×SD16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8D4×C13911yescharacteristic
250C22×C8D4×C13911yescharacteristic
251#126—21no—
252#125D4×C13911yescharacteristic
253#124D4×C13911yescharacteristic
254#123—21no—
255C22⋊Q8C2×C4×C13911yescharacteristic
256#121C2×C4×C13911yescharacteristic
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8D4×C13911yescharacteristic
262C4×D4—21no—
263C4×D4D4×C13911yescharacteristic
264#117—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C2×C4×C13911yescharacteristic
267C2×C42—21no—
268C2×C42C23×C13911yescharacteristic
269#107—21no—
270#106—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8D4×C13911yescharacteristic
277C4⋊C8D4×C13911yescharacteristic
278#103—21no—
279#103—21no—
280#103—21no—
281#102—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8C2×C4×C13911yescharacteristic
286C22⋊C8C2×C4×C13911yescharacteristic
287#97—21no—
288#97—21no—
289#97—21no—
290#97—21no—
291#97—21no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C2×Q8C22⋊C4×C13911yescharacteristic
299C2×D4—21no—
300C2×D4C22⋊C4×C13911yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4C22×C4×C13911yescharacteristic
305C22×C4C2×D4×C13911yescharacteristic
306C22×C4#41×C13911yescharacteristic
307Q16—42no—
308SD16—42no—
309M16—22no—
310M16—41no—
311M16—81no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—81no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊C4×C13911yescharacteristic
334C4⋊C4C22⋊C4×C13911yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C42—21no—
341C42—41no—
342C42—41no—
343C42C2×D4×C13911yescharacteristic
344C42C2×D4×C13911yescharacteristic
345C42C2×D4×C13911yescharacteristic
346C42#41×C13911yescharacteristic
347C23—21no—
348C23C4×D4×C13911yescharacteristic
349Q8—22no—
350Q8—22no—
351Q8—41no—
352Q8—41no—
353Q8—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4C2×C22⋊C4×C13911yescharacteristic
374C2×C4C4×D4×C13911yescharacteristic
375C2×C4#120×C13911yescharacteristic
376C2×C4#121×C13911yescharacteristic
377C2×C4#121×C13911yescharacteristic
378C2×C4#123×C13911yescharacteristic
379C8—42no—
380C8—41no—
381C8—41no—
382C8—42no—
383C8—41no—
384C8—41no—
385C8—41no—
386C8—41no—
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22#386×C13911yescharacteristic
393C22#443×C13911yescharacteristic
394C22#444×C13911yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—42no—
403C4—41no—
404C4—81no—
405C4#455×C13911yescharacteristic
406C4#456×C13911yescharacteristic
407C2—21no—
408C2—21no—
409C2—81no—
410C2#1876×C13911yescharacteristic
411C2#1882×C13911yescharacteristic
412C2#1891×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139#120
commutatorC22×C4C22×C4×C139
Frattini, cosocleC2×C42C23×C139
socleC22×C139#386
prime radical#121×C139C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1985×C139C2semidirect
5. #1491×C139C2semidirect
6. #1302×C139C2semidirect
7. #1283×C139C2semidirect
206. #9051C139direct (N × H)
207. C139#9051direct (N × H)
210. #1985C2×C139semidirect
212. #1491C2×C139semidirect
213. #1302C2×C139semidirect
214. #1283C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3108×C1392
#2992×C1392
#1985×C1392
#1524×C1392
#1491×C1392
#1302×C1392
#1283×C1392
#9051139