Finite Group Databasebeta

← C139×#9311 #48003907

Subgroups — C139×#9311 #48003907

Order 35584.

514 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3115×C139C211yesmaximal, characteristic
2#2875×C139C211yesmaximal, characteristic, complemented
3#1530×C139C211yesmaximal, characteristic, complemented
4#1488×C139C211yesmaximal, characteristic, complemented
5#1484×C139C211yesmaximal, characteristic, complemented
6#1302×C139C211yesmaximal, characteristic, complemented
7#1291×C139C211yesmaximal, characteristic, complemented
8C2×#131×C139—21no—
9#532×C139C2211yescharacteristic
10C4×#41×C139C2211yescharacteristic
11#482×C139—21no—
12#475×C139C411yescharacteristic
13#474×C139C411yescharacteristic
14#460×C139C411yescharacteristic
15#459×C139C411yescharacteristic
16#449×C139—21no—
17#442×C139—21no—
18#440×C139—21no—
19#432×C139C2211yescharacteristic
20#432×C139C2211yescharacteristic
21#431×C139C2211yescharacteristic
22#405×C139—21no—
23#405×C139—22no—
24C4×M16×C139—21no—
25C4×M16×C139C2211yescharacteristic
26C2×#97×C139—21no—
27C2×#97×C139C2211yescharacteristic
28#329×C139—21no—
29#329×C139—21no—
30Q8⋊C8×C139—21no—
31D4⋊C8×C139—21no—
32D4⋊C8×C139—22no—
33C2×#41×C139—21no—
34C2×#41×C139D411yescharacteristic
35C2×SD16×C139—21no—
36C2×D8×C139—21no—
37#131×C139—24no—
38#131×C139—24no—
39C2×M16×C139—22no—
40C2×M16×C139—21no—
41C22×C8×C139—22no—
42C22×C8×C139—21no—
43C4⋊Q8×C139C2×C411yescharacteristic
44#127×C139C2×C411yescharacteristic
45#124×C139—21no—
46#121×C139—21no—
47#121×C139—21no—
48C4×Q8×C139C2×C411yescharacteristic
49C4×Q8×C139D411yescharacteristic
50C4×D4×C139—21no—
51C4×D4×C139—21no—
52C4×D4×C139—21no—
53C4×D4×C139—21no—
54C4×D4×C139C2×C411yescharacteristic
55C4×D4×C139D411yescharacteristic
56#117×C139—21no—
57#117×C139D411yescharacteristic
58C2×C42×C139—21no—
59C2×C42×C139C2311yescharacteristic
60#107×C139—21no—
61#106×C139—21no—
62C4⋊C8×C139—21no—
63C4⋊C8×C139—21no—
64C4⋊C8×C139C2×C411yescharacteristic
65C4⋊C8×C139C2×C411yescharacteristic
66#103×C139—21no—
67#102×C139—21no—
68#102×C139—21no—
69#102×C139—21no—
70C22⋊C8×C139—21no—
71C22⋊C8×C139—21no—
72C22⋊C8×C139—21no—
73#97×C139—22no—
74#97×C139—21no—
75#97×C139—21no—
76#97×C139—21no—
77#97×C139—21no—
78#97×C139D411yescharacteristic
79#97×C139D411yescharacteristic
80C4×C8×C139—22no—
81C4×C8×C139—21no—
82C4×C8×C139D412yes—
83#41×C139—22no—
84#41×C139—22no—
85#41×C139—82no—
86C2×Q8×C139—21no—
87C2×Q8×C139C22⋊C411yescharacteristic
88C2×D4×C139—21no—
89C2×D4×C139—21no—
90C2×D4×C139—21no—
91C2×D4×C139—21no—
92C2×D4×C139—41no—
93C2×D4×C139C22⋊C411yescharacteristic
94C22×C4×C139—21no—
95C22×C4×C139—21no—
96C22×C4×C139—21no—
97C22×C4×C139—41no—
98C22×C4×C139C2×D411yescharacteristic
99C22×C4×C139#4111yescharacteristic
100C22×C4×C139#4111yescharacteristic
101SD16×C139—42no—
102D8×C139—42no—
103M16×C139—28no—
104M16×C139—22no—
105M16×C139—22no—
106C2×C8×C139—28no—
107C2×C8×C139—22no—
108C2×C8×C139—22no—
109C2×C8×C139—21no—
110C2×C8×C139—22no—
111C2×C8×C139—21no—
112C2×C8×C139—21no—
113C2×C8×C139—21no—
114C2×C8×C139—41no—
115C2×C8×C139—41no—
116C4⋊C4×C139—21no—
117C4⋊C4×C139—21no—
118C4⋊C4×C139—21no—
119C4⋊C4×C139—21no—
120C4⋊C4×C139C22⋊C411yescharacteristic
121C4⋊C4×C139C22⋊C411yescharacteristic
122C22⋊C4×C139—21no—
123C22⋊C4×C139—21no—
124C22⋊C4×C139—21no—
125C22⋊C4×C139—41no—
126C22⋊C4×C139—41no—
127C42×C139—21no—
128C42×C139—21no—
129C42×C139—21no—
130C42×C139C22×C411yescharacteristic
131C42×C139C2×D411yescharacteristic
132C42×C139C2×D411yescharacteristic
133C42×C139C2×D411yescharacteristic
134C23×C139—21no—
135C23×C139—41no—
136C23×C139#12311yescharacteristic
137Q8×C139—21no—
138Q8×C139—81no—
139Q8×C139#10412yes—
140D4×C139—24no—
141D4×C139—21no—
142D4×C139—42no—
143D4×C139—41no—
144D4×C139—41no—
145D4×C139—81no—
146D4×C139—82no—
147D4×C139#10412yes—
148C2×C4×C139—24no—
149C2×C4×C139—21no—
150C2×C4×C139—21no—
151C2×C4×C139—21no—
152C2×C4×C139—21no—
153C2×C4×C139—21no—
154C2×C4×C139—41no—
155C2×C4×C139—41no—
156C2×C4×C139—41no—
157C2×C4×C139—81no—
158C2×C4×C139—81no—
159C2×C4×C139—82no—
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—22no—
167C8×C139—22no—
168C8×C139—24no—
169C8×C139—41no—
170C8×C139—41no—
171C8×C139—81no—
172C8×C139—81no—
173C22×C139—21no—
174C22×C139—21no—
175C22×C139—22no—
176C22×C139—21no—
177C22×C139—41no—
178C22×C139—41no—
179C22×C139—81no—
180C22×C139—81no—
181C22×C139—81no—
182C22×C139#38611yescharacteristic
183C4×C139—21no—
184C4×C139—21no—
185C4×C139—21no—
186C4×C139—22no—
187C4×C139—21no—
188C4×C139—21no—
189C4×C139—41no—
190C4×C139—41no—
191C4×C139—81no—
192C4×C139C2×#10411yescharacteristic
193C4×C139C2×#10411yescharacteristic
194C2×C139—41no—
195C2×C139—42no—
196C2×C139—161no—
197C2×C139#188111yescharacteristic
198C2×C139#189611yescharacteristic
199C2×C139#190311yescharacteristic
200#9311C13911yesmaximal, characteristic, direct product factor, Sylow
201C139#931111yescharacteristic, direct product factor, Sylow
202#3115C2×C13911yescharacteristic
203#2875C2×C13911yescharacteristic, complemented
204#1530C2×C13911yescharacteristic, complemented
205#1488C2×C13911yescharacteristic, complemented
206#1484C2×C13911yescharacteristic, complemented
207#1302C2×C13911yescharacteristic, complemented
208#1291C2×C13911yescharacteristic, complemented
209C2×#131—21no—
210#532C22×C13911yescharacteristic
211C4×#41C22×C13911yescharacteristic
212#482—21no—
213#475C4×C13911yescharacteristic
214#474C4×C13911yescharacteristic
215#460C4×C13911yescharacteristic
216#459C4×C13911yescharacteristic
217#449—21no—
218#442—21no—
219#440—21no—
220#432C22×C13911yescharacteristic
221#432C22×C13911yescharacteristic
222#431C22×C13911yescharacteristic
223#405—21no—
224#405—22no—
225C4×M16—21no—
226C4×M16C22×C13911yescharacteristic
227C2×#97—21no—
228C2×#97C22×C13911yescharacteristic
229#329—21no—
230#329—21no—
231Q8⋊C8—21no—
232D4⋊C8—21no—
233D4⋊C8—22no—
234C2×#41—21no—
235C2×#41D4×C13911yescharacteristic
236C2×SD16—21no—
237C2×D8—21no—
238#131—24no—
239#131—24no—
240C2×M16—22no—
241C2×M16—21no—
242C22×C8—22no—
243C22×C8—21no—
244C4⋊Q8C2×C4×C13911yescharacteristic
245#127C2×C4×C13911yescharacteristic
246#124—21no—
247#121—21no—
248#121—21no—
249C4×Q8C2×C4×C13911yescharacteristic
250C4×Q8D4×C13911yescharacteristic
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4C2×C4×C13911yescharacteristic
256C4×D4D4×C13911yescharacteristic
257#117—21no—
258#117D4×C13911yescharacteristic
259C2×C42—21no—
260C2×C42C23×C13911yescharacteristic
261#107—21no—
262#106—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8C2×C4×C13911yescharacteristic
266C4⋊C8C2×C4×C13911yescharacteristic
267#103—21no—
268#102—21no—
269#102—21no—
270#102—21no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274#97—22no—
275#97—21no—
276#97—21no—
277#97—21no—
278#97—21no—
279#97D4×C13911yescharacteristic
280#97D4×C13911yescharacteristic
281C4×C8—22no—
282C4×C8—21no—
283C4×C8D4×C13912yes—
284#41—22no—
285#41—22no—
286#41—82no—
287C2×Q8—21no—
288C2×Q8C22⋊C4×C13911yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C2×D4C22⋊C4×C13911yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4C2×D4×C13911yescharacteristic
300C22×C4#41×C13911yescharacteristic
301C22×C4#41×C13911yescharacteristic
302SD16—42no—
303D8—42no—
304M16—28no—
305M16—22no—
306M16—22no—
307C2×C8—28no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—41no—
316C2×C8—41no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4C22⋊C4×C13911yescharacteristic
322C4⋊C4C22⋊C4×C13911yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42C22×C4×C13911yescharacteristic
332C42C2×D4×C13911yescharacteristic
333C42C2×D4×C13911yescharacteristic
334C42C2×D4×C13911yescharacteristic
335C23—21no—
336C23—41no—
337C23#123×C13911yescharacteristic
338Q8—21no—
339Q8—81no—
340Q8#104×C13912yes—
341D4—24no—
342D4—21no—
343D4—42no—
344D4—41no—
345D4—41no—
346D4—81no—
347D4—82no—
348D4#104×C13912yes—
349C2×C4—24no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—82no—
361C2×C4C2×C22⋊C4×C13911yescharacteristic
362C2×C4C4×D4×C13911yescharacteristic
363C2×C4C4×D4×C13911yescharacteristic
364C2×C4#120×C13911yescharacteristic
365C2×C4#121×C13911yescharacteristic
366C2×C4#121×C13911yescharacteristic
367C8—22no—
368C8—22no—
369C8—24no—
370C8—41no—
371C8—41no—
372C8—81no—
373C8—81no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22#386×C13911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—22no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—81no—
393C4C2×#104×C13911yescharacteristic
394C4C2×#104×C13911yescharacteristic
395C2—41no—
396C2—42no—
397C2—161no—
398C2#1881×C13911yescharacteristic
399C2#1896×C13911yescharacteristic
400C2#1903×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radical#3115×C139C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2875×C139C2semidirect
3. #1530×C139C2semidirect
4. #1488×C139C2semidirect
5. #1484×C139C2semidirect
6. #1302×C139C2semidirect
7. #1291×C139C2semidirect
200. #9311C139direct (N × H)
201. C139#9311direct (N × H)
203. #2875C2×C139semidirect
204. #1530C2×C139semidirect
205. #1488C2×C139semidirect
206. #1484C2×C139semidirect
207. #1302C2×C139semidirect
208. #1291C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3115×C1392
#2875×C1392
#1530×C1392
#1488×C1392
#1484×C1392
#1302×C1392
#1291×C1392
#9311139