Finite Group Databasebeta

← C139×#9213 #48003809

Subgroups — C139×#9213 #48003809

Order 35584.

450 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3106×C139C211yesmaximal, characteristic
2#2922×C139C211yesmaximal, characteristic, complemented
3#1525×C139C211yesmaximal, characteristic, complemented
4#1492×C139C211yesmaximal, characteristic, complemented
5#1489×C139C211yesmaximal, characteristic, complemented
6#1299×C139C211yesmaximal, characteristic, complemented
7#1278×C139C211yesmaximal, characteristic, complemented
8#532×C139C2211yescharacteristic
9C4×#41×C139C2211yescharacteristic
10#482×C139—21no—
11#477×C139C411yescharacteristic
12#476×C139C411yescharacteristic
13#460×C139C411yescharacteristic
14#459×C139C411yescharacteristic
15#449×C139—21no—
16C4×SD16×C139—21no—
17C4×D8×C139—21no—
18#433×C139—22no—
19#431×C139—22no—
20#431×C139C2211yescharacteristic
21#424×C139—21no—
22#423×C139C2211yescharacteristic
23#408×C139—21no—
24C4×M16×C139C2211yescharacteristic
25C4×M16×C139C2211yescharacteristic
26C2×C4×C8×C139C2211yescharacteristic
27#329×C139—22no—
28Q8⋊C8×C139—21no—
29D4⋊C8×C139—21no—
30D4⋊C8×C139—22no—
31C2×#41×C139—21no—
32C2×#41×C139D411yescharacteristic
33C2×SD16×C139—21no—
34C2×D8×C139—21no—
35C2×M16×C139—21no—
36C2×M16×C139—21no—
37C2×M16×C139—21no—
38C22×C8×C139—21no—
39C4⋊Q8×C139C2×C411yescharacteristic
40#127×C139C2×C411yescharacteristic
41#124×C139—21no—
42#121×C139—21no—
43#121×C139—21no—
44C4×Q8×C139C2×C411yescharacteristic
45C4×Q8×C139D411yescharacteristic
46C4×D4×C139—21no—
47C4×D4×C139—21no—
48C4×D4×C139—21no—
49C4×D4×C139—21no—
50C4×D4×C139C2×C411yescharacteristic
51C4×D4×C139D411yescharacteristic
52#117×C139—21no—
53#117×C139D411yescharacteristic
54C2×C42×C139—21no—
55C2×C42×C139C2311yescharacteristic
56#107×C139—21no—
57#106×C139—21no—
58C4⋊C8×C139—24no—
59C4⋊C8×C139—21no—
60C4⋊C8×C139—21no—
61C4⋊C8×C139C2×C411yescharacteristic
62C4⋊C8×C139C2×C411yescharacteristic
63#103×C139—21no—
64#102×C139—21no—
65#102×C139—21no—
66#102×C139—21no—
67C22⋊C8×C139—24no—
68C22⋊C8×C139—21no—
69#97×C139—21no—
70#97×C139D412yes—
71C4×C8×C139—21no—
72C4×C8×C139—21no—
73C4×C8×C139—21no—
74C4×C8×C139—21no—
75C4×C8×C139D412yes—
76#41×C139—41no—
77#41×C139—41no—
78#41×C139—81no—
79#41×C139—81no—
80C2×Q8×C139—21no—
81C2×Q8×C139C22⋊C411yescharacteristic
82C2×D4×C139—21no—
83C2×D4×C139—21no—
84C2×D4×C139—21no—
85C2×D4×C139—21no—
86C2×D4×C139—41no—
87C2×D4×C139C22⋊C411yescharacteristic
88C22×C4×C139—21no—
89C22×C4×C139—21no—
90C22×C4×C139—21no—
91C22×C4×C139—41no—
92C22×C4×C139C2×D411yescharacteristic
93C22×C4×C139#4111yescharacteristic
94C22×C4×C139#4111yescharacteristic
95SD16×C139—42no—
96D8×C139—42no—
97M16×C139—22no—
98M16×C139—41no—
99M16×C139—41no—
100M16×C139—41no—
101M16×C139—81no—
102C2×C8×C139—21no—
103C2×C8×C139—21no—
104C2×C8×C139—22no—
105C2×C8×C139—22no—
106C2×C8×C139—41no—
107C2×C8×C139—41no—
108C2×C8×C139—41no—
109C2×C8×C139—41no—
110C4⋊C4×C139—21no—
111C4⋊C4×C139—21no—
112C4⋊C4×C139—21no—
113C4⋊C4×C139—21no—
114C4⋊C4×C139C22⋊C411yescharacteristic
115C4⋊C4×C139C22⋊C411yescharacteristic
116C22⋊C4×C139—21no—
117C22⋊C4×C139—21no—
118C22⋊C4×C139—21no—
119C22⋊C4×C139—41no—
120C22⋊C4×C139—41no—
121C42×C139—21no—
122C42×C139—21no—
123C42×C139—21no—
124C42×C139C22×C411yescharacteristic
125C42×C139C2×D411yescharacteristic
126C42×C139C2×D411yescharacteristic
127C42×C139C2×D411yescharacteristic
128C23×C139—21no—
129C23×C139—41no—
130C23×C139#12311yescharacteristic
131Q8×C139—21no—
132Q8×C139—21no—
133Q8×C139—81no—
134D4×C139—21no—
135D4×C139—21no—
136D4×C139—42no—
137D4×C139—41no—
138D4×C139—41no—
139D4×C139—41no—
140D4×C139—41no—
141D4×C139—81no—
142D4×C139—82no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139—21no—
150C2×C4×C139—21no—
151C2×C4×C139—21no—
152C2×C4×C139—42no—
153C2×C4×C139—41no—
154C2×C4×C139—41no—
155C2×C4×C139—41no—
156C2×C4×C139—41no—
157C2×C4×C139—41no—
158C2×C4×C139—81no—
159C2×C4×C139—81no—
160C2×C4×C139C2×C22⋊C411yescharacteristic
161C2×C4×C139C4×D411yescharacteristic
162C2×C4×C139C4×D411yescharacteristic
163C2×C4×C139#12011yescharacteristic
164C2×C4×C139#12111yescharacteristic
165C2×C4×C139#12111yescharacteristic
166C8×C139—42no—
167C8×C139—42no—
168C8×C139—42no—
169C8×C139—41no—
170C8×C139—41no—
171C8×C139—81no—
172C22×C139—21no—
173C22×C139—21no—
174C22×C139—21no—
175C22×C139—41no—
176C22×C139—41no—
177C22×C139—41no—
178C22×C139—81no—
179C22×C139—81no—
180C22×C139—81no—
181C22×C139#38611yescharacteristic
182C4×C139—21no—
183C4×C139—21no—
184C4×C139—21no—
185C4×C139—41no—
186C4×C139—41no—
187C4×C139—41no—
188C4×C139—81no—
189C4×C139#42111yescharacteristic
190C4×C139#42111yescharacteristic
191C4×C139#44311yescharacteristic
192C4×C139#44411yescharacteristic
193C4×C139#47111yescharacteristic
194C4×C139#47211yescharacteristic
195C2×C139—41no—
196C2×C139—81no—
197C2×C139—161no—
198C2×C139#187611yescharacteristic
199C2×C139#189711yescharacteristic
200C2×C139#190711yescharacteristic
201#9213C13911yesmaximal, characteristic, direct product factor, Sylow
202C139#921311yescharacteristic, direct product factor, Sylow
203#3106C2×C13911yescharacteristic
204#2922C2×C13911yescharacteristic, complemented
205#1525C2×C13911yescharacteristic, complemented
206#1492C2×C13911yescharacteristic, complemented
207#1489C2×C13911yescharacteristic, complemented
208#1299C2×C13911yescharacteristic, complemented
209#1278C2×C13911yescharacteristic, complemented
210#532C22×C13911yescharacteristic
211C4×#41C22×C13911yescharacteristic
212#482—21no—
213#477C4×C13911yescharacteristic
214#476C4×C13911yescharacteristic
215#460C4×C13911yescharacteristic
216#459C4×C13911yescharacteristic
217#449—21no—
218C4×SD16—21no—
219C4×D8—21no—
220#433—22no—
221#431—22no—
222#431C22×C13911yescharacteristic
223#424—21no—
224#423C22×C13911yescharacteristic
225#408—21no—
226C4×M16C22×C13911yescharacteristic
227C4×M16C22×C13911yescharacteristic
228C2×C4×C8C22×C13911yescharacteristic
229#329—22no—
230Q8⋊C8—21no—
231D4⋊C8—21no—
232D4⋊C8—22no—
233C2×#41—21no—
234C2×#41D4×C13911yescharacteristic
235C2×SD16—21no—
236C2×D8—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C22×C8—21no—
241C4⋊Q8C2×C4×C13911yescharacteristic
242#127C2×C4×C13911yescharacteristic
243#124—21no—
244#121—21no—
245#121—21no—
246C4×Q8C2×C4×C13911yescharacteristic
247C4×Q8D4×C13911yescharacteristic
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4C2×C4×C13911yescharacteristic
253C4×D4D4×C13911yescharacteristic
254#117—21no—
255#117D4×C13911yescharacteristic
256C2×C42—21no—
257C2×C42C23×C13911yescharacteristic
258#107—21no—
259#106—21no—
260C4⋊C8—24no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8C2×C4×C13911yescharacteristic
264C4⋊C8C2×C4×C13911yescharacteristic
265#103—21no—
266#102—21no—
267#102—21no—
268#102—21no—
269C22⋊C8—24no—
270C22⋊C8—21no—
271#97—21no—
272#97D4×C13912yes—
273C4×C8—21no—
274C4×C8—21no—
275C4×C8—21no—
276C4×C8—21no—
277C4×C8D4×C13912yes—
278#41—41no—
279#41—41no—
280#41—81no—
281#41—81no—
282C2×Q8—21no—
283C2×Q8C22⋊C4×C13911yescharacteristic
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4C22⋊C4×C13911yescharacteristic
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C13911yescharacteristic
295C22×C4#41×C13911yescharacteristic
296C22×C4#41×C13911yescharacteristic
297SD16—42no—
298D8—42no—
299M16—22no—
300M16—41no—
301M16—41no—
302M16—41no—
303M16—81no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4C22⋊C4×C13911yescharacteristic
317C4⋊C4C22⋊C4×C13911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42C22×C4×C13911yescharacteristic
327C42C2×D4×C13911yescharacteristic
328C42C2×D4×C13911yescharacteristic
329C42C2×D4×C13911yescharacteristic
330C23—21no—
331C23—41no—
332C23#123×C13911yescharacteristic
333Q8—21no—
334Q8—21no—
335Q8—81no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—41no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—81no—
344D4—82no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C2×C22⋊C4×C13911yescharacteristic
363C2×C4C4×D4×C13911yescharacteristic
364C2×C4C4×D4×C13911yescharacteristic
365C2×C4#120×C13911yescharacteristic
366C2×C4#121×C13911yescharacteristic
367C2×C4#121×C13911yescharacteristic
368C8—42no—
369C8—42no—
370C8—42no—
371C8—41no—
372C8—41no—
373C8—81no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22#386×C13911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4#421×C13911yescharacteristic
392C4#421×C13911yescharacteristic
393C4#443×C13911yescharacteristic
394C4#444×C13911yescharacteristic
395C4#471×C13911yescharacteristic
396C4#472×C13911yescharacteristic
397C2—41no—
398C2—81no—
399C2—161no—
400C2#1876×C13911yescharacteristic
401C2#1897×C13911yescharacteristic
402C2#1907×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139#121
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
socleC22×C139#386
prime radical#3106×C139C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2922×C139C2semidirect
3. #1525×C139C2semidirect
4. #1492×C139C2semidirect
5. #1489×C139C2semidirect
6. #1299×C139C2semidirect
7. #1278×C139C2semidirect
201. #9213C139direct (N × H)
202. C139#9213direct (N × H)
204. #2922C2×C139semidirect
205. #1525C2×C139semidirect
206. #1492C2×C139semidirect
207. #1489C2×C139semidirect
208. #1299C2×C139semidirect
209. #1278C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3106×C1392
#2922×C1392
#1525×C1392
#1492×C1392
#1489×C1392
#1299×C1392
#1278×C1392
#9213139