Finite Group Databasebeta

← C139×#36979 #48031575

Subgroups — C139×#36979 #48031575

Order 35584.

1398 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2855×C139C212yesmaximal
2#2776×C139C214yesmaximal, complemented
3#2769×C139C214yesmaximal, complemented
4#2762×C139C214yesmaximal, complemented
5#2758×C139C214yesmaximal, complemented
6#2659×C139C211yesmaximal, characteristic
7#2646×C139C211yesmaximal, characteristic
8#2505×C139C214yesmaximal
9#2493×C139C214yesmaximal
10#2329×C139C212yesmaximal
11C2×#383×C139C211yesmaximal, characteristic
12C2×C22⋊Q8×C139C2212yes—
13C22×C42×C139C2211yescharacteristic
14#401×C139C2214yes—
15#400×C139C2214yes—
16#400×C139C2214yes—
17#400×C139C2214yes—
18#400×C139C2214yes—
19#400×C139C2214yes—
20#400×C139C2214yes—
21#400×C139C2214yes—
22#398×C139C2214yes—
23#398×C139C2214yes—
24#398×C139C2214yes—
25#395×C139C2214yes—
26#391×C139C2214yes—
27#391×C139C2212yes—
28#391×C139C2212yes—
29#389×C139C2212yes—
30#389×C139C2214yes—
31#389×C139C2212yes—
32#389×C139C2214yes—
33#387×C139C2214yes—
34#387×C139C2214yes—
35#387×C139C2214yes—
36#387×C139C2214yes—
37#387×C139C2214yes—
38#387×C139C2214yes—
39#387×C139C2214yes—
40#387×C139C2214yes—
41#387×C139C2214yes—
42#385×C139C2214yes—
43#385×C139C2214yes—
44#385×C139C2214yes—
45#383×C139C2214yes—
46#383×C139C2214yes—
47#383×C139C2214yes—
48#382×C139C2214yes—
49#381×C139C2214yes—
50#380×C139C2212yes—
51#380×C139C2214yes—
52C4×C22⋊C4×C139C2214yes—
53C2×#95×C139C2211yescharacteristic
54C2×#95×C139C2211yescharacteristic
55C2×#95×C139C2212yes—
56C2×#95×C139C2212yes—
57C22×Q8×C139C2312yes—
58C23×C4×C139C2311yescharacteristic
59C23×C4×C139C2311yescharacteristic
60C23×C4×C139C2312yes—
61C23×C4×C139C2312yes—
62C23×C4×C139C2311yescharacteristic
63C22⋊Q8×C139—28no—
64C2×C4⋊C4×C139C2314yes—
65C2×C4⋊C4×C139C2312yes—
66C2×C4⋊C4×C139C2314yes—
67C2×C4⋊C4×C139C2314yes—
68C2×C4⋊C4×C139C2314yes—
69C2×C4⋊C4×C139C2312yes—
70C2×C4⋊C4×C139C2314yes—
71C2×C4⋊C4×C139C2314yes—
72C2×C4⋊C4×C139C2314yes—
73C2×C4⋊C4×C139C2314yes—
74C2×C4⋊C4×C139C2312yes—
75C2×C4⋊C4×C139C2314yes—
76C2×C22⋊C4×C139C2314yes—
77C2×C22⋊C4×C139C2314yes—
78C2×C42×C139—24no—
79C2×C42×C139C2312yes—
80C2×C42×C139C2312yes—
81C2×C42×C139C2314yes—
82C2×C42×C139C2314yes—
83#95×C139C2314yes—
84#95×C139C2314yes—
85#95×C139C2314yes—
86#95×C139C2314yes—
87#95×C139C2314yes—
88#95×C139C2314yes—
89#95×C139C2314yes—
90#95×C139C2314yes—
91#95×C139C2314yes—
92#95×C139C2314yes—
93#95×C139C2314yes—
94#95×C139C2314yes—
95#95×C139C2314yes—
96#95×C139C2314yes—
97#95×C139C2314yes—
98#95×C139C2314yes—
99#95×C139C2314yes—
100#95×C139C2314yes—
101#95×C139C2314yes—
102#95×C139C2314yes—
103#95×C139C2314yes—
104C24×C139C2411yescharacteristic
105C2×Q8×C139—24no—
106C2×Q8×C139—42no—
107C2×Q8×C139—42no—
108C22×C4×C139—22no—
109C22×C4×C139—22no—
110C22×C4×C139—24no—
111C22×C4×C139—24no—
112C22×C4×C139—24no—
113C22×C4×C139—42no—
114C22×C4×C139—41no—
115C22×C4×C139—41no—
116C22×C4×C139—42no—
117C22×C4×C139—42no—
118C22×C4×C139—42no—
119C22×C4×C139—42no—
120C22×C4×C139#4114yes—
121C22×C4×C139C2411yescharacteristic
122C22×C4×C139C2411yescharacteristic
123C22×C4×C139C2414yes—
124C22×C4×C139C2414yes—
125C22×C4×C139C2412yes—
126C22×C4×C139C2414yes—
127C22×C4×C139C2414yes—
128C22×C4×C139C2414yes—
129C22×C4×C139C2414yes—
130C22×C4×C139C2412yes—
131C4⋊C4×C139—24no—
132C4⋊C4×C139—28no—
133C4⋊C4×C139—42no—
134C4⋊C4×C139—42no—
135C4⋊C4×C139—44no—
136C4⋊C4×C139—44no—
137C4⋊C4×C139—44no—
138C4⋊C4×C139—44no—
139C4⋊C4×C139—44no—
140C4⋊C4×C139—44no—
141C4⋊C4×C139—44no—
142C4⋊C4×C139—44no—
143C22⋊C4×C139—28no—
144C22⋊C4×C139—28no—
145C42×C139—24no—
146C42×C139—24no—
147C42×C139—44no—
148C42×C139—44no—
149C23×C139—22no—
150C23×C139—21no—
151C23×C139—21no—
152C23×C139C2×#4112yes—
153C23×C1392−1+414yes—
154C23×C139C2511yescharacteristic
155Q8×C139—84no—
156C2×C4×C139—22no—
157C2×C4×C139—22no—
158C2×C4×C139—21no—
159C2×C4×C139—21no—
160C2×C4×C139—22no—
161C2×C4×C139—24no—
162C2×C4×C139—24no—
163C2×C4×C139—24no—
164C2×C4×C139—24no—
165C2×C4×C139—22no—
166C2×C4×C139—22no—
167C2×C4×C139—24no—
168C2×C4×C139—24no—
169C2×C4×C139—24no—
170C2×C4×C139—24no—
171C2×C4×C139—24no—
172C2×C4×C139—24no—
173C2×C4×C139—24no—
174C2×C4×C139—24no—
175C2×C4×C139—24no—
176C2×C4×C139—24no—
177C2×C4×C139—24no—
178C2×C4×C139—22no—
179C2×C4×C139—22no—
180C2×C4×C139—24no—
181C2×C4×C139—24no—
182C2×C4×C139—24no—
183C2×C4×C139—44no—
184C2×C4×C139—44no—
185C2×C4×C139—44no—
186C2×C4×C139—84no—
187C2×C4×C139—84no—
188C2×C4×C139C2×#4114yes—
189C22×C139—22no—
190C22×C139—22no—
191C22×C139—24no—
192C22×C139—24no—
193C22×C139#54114yes—
194C22×C139C22×#4111yescharacteristic
195C22×C139C2×2−1+412yes—
196C22×C139#58512yes—
197C22×C139#58511yescharacteristic
198C22×C139#58511yescharacteristic
199C4×C139—24no—
200C4×C139—41no—
201C4×C139—41no—
202C4×C139—44no—
203C4×C139—44no—
204C4×C139—42no—
205C4×C139—44no—
206C4×C139—44no—
207C4×C139—44no—
208C4×C139—44no—
209C2×C139—24no—
210C2×C139C2×#54111yescharacteristic
211C2×C139#349111yescharacteristic
212C2×C139#349311yescharacteristic
213C2×C139#356412yes—
214C2×C139#356412yes—
215#36979C13911yesmaximal, characteristic, direct product factor, Sylow
216C139#3697911yescharacteristic, direct product factor, Sylow
217#2855C2×C13912yes—
218#2776C2×C13914yescomplemented
219#2769C2×C13914yescomplemented
220#2762C2×C13914yescomplemented
221#2758C2×C13914yescomplemented
222#2659C2×C13911yescharacteristic
223#2646C2×C13911yescharacteristic
224#2505C2×C13914yes—
225#2493C2×C13914yes—
226#2329C2×C13912yes—
227C2×#383C2×C13911yescharacteristic
228C2×C22⋊Q8C22×C13912yes—
229C22×C42C22×C13911yescharacteristic
230#401C22×C13914yes—
231#400C22×C13914yes—
232#400C22×C13914yes—
233#400C22×C13914yes—
234#400C22×C13914yes—
235#400C22×C13914yes—
236#400C22×C13914yes—
237#400C22×C13914yes—
238#398C22×C13914yes—
239#398C22×C13914yes—
240#398C22×C13914yes—
241#395C22×C13914yes—
242#391C22×C13914yes—
243#391C22×C13912yes—
244#391C22×C13912yes—
245#389C22×C13914yes—
246#389C22×C13912yes—
247#389C22×C13912yes—
248#389C22×C13914yes—
249#387C22×C13914yes—
250#387C22×C13914yes—
251#387C22×C13914yes—
252#387C22×C13914yes—
253#387C22×C13914yes—
254#387C22×C13914yes—
255#387C22×C13914yes—
256#387C22×C13914yes—
257#387C22×C13914yes—
258#385C22×C13914yes—
259#385C22×C13914yes—
260#385C22×C13914yes—
261#383C22×C13914yes—
262#383C22×C13914yes—
263#383C22×C13914yes—
264#382C22×C13914yes—
265#381C22×C13914yes—
266#380C22×C13912yes—
267#380C22×C13914yes—
268C4×C22⋊C4C22×C13914yes—
269C2×#95C22×C13911yescharacteristic
270C2×#95C22×C13911yescharacteristic
271C2×#95C22×C13912yes—
272C2×#95C22×C13912yes—
273C22×Q8C23×C13912yes—
274C23×C4C23×C13911yescharacteristic
275C23×C4C23×C13912yes—
276C23×C4C23×C13912yes—
277C23×C4C23×C13911yescharacteristic
278C23×C4C23×C13911yescharacteristic
279C22⋊Q8—28no—
280C2×C4⋊C4C23×C13914yes—
281C2×C4⋊C4C23×C13912yes—
282C2×C4⋊C4C23×C13912yes—
283C2×C4⋊C4C23×C13914yes—
284C2×C4⋊C4C23×C13914yes—
285C2×C4⋊C4C23×C13912yes—
286C2×C4⋊C4C23×C13914yes—
287C2×C4⋊C4C23×C13914yes—
288C2×C4⋊C4C23×C13914yes—
289C2×C4⋊C4C23×C13914yes—
290C2×C4⋊C4C23×C13914yes—
291C2×C4⋊C4C23×C13914yes—
292C2×C22⋊C4C23×C13914yes—
293C2×C22⋊C4C23×C13914yes—
294C2×C42—24no—
295C2×C42C23×C13912yes—
296C2×C42C23×C13912yes—
297C2×C42C23×C13914yes—
298C2×C42C23×C13914yes—
299#95C23×C13914yes—
300#95C23×C13914yes—
301#95C23×C13914yes—
302#95C23×C13914yes—
303#95C23×C13914yes—
304#95C23×C13914yes—
305#95C23×C13914yes—
306#95C23×C13914yes—
307#95C23×C13914yes—
308#95C23×C13914yes—
309#95C23×C13914yes—
310#95C23×C13914yes—
311#95C23×C13914yes—
312#95C23×C13914yes—
313#95C23×C13914yes—
314#95C23×C13914yes—
315#95C23×C13914yes—
316#95C23×C13914yes—
317#95C23×C13914yes—
318#95C23×C13914yes—
319#95C23×C13914yes—
320C24C24×C13911yescharacteristic
321C2×Q8—24no—
322C2×Q8—42no—
323C2×Q8—42no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—42no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4#41×C13914yes—
337C22×C4C24×C13911yescharacteristic
338C22×C4C24×C13911yescharacteristic
339C22×C4C24×C13914yes—
340C22×C4C24×C13914yes—
341C22×C4C24×C13912yes—
342C22×C4C24×C13914yes—
343C22×C4C24×C13914yes—
344C22×C4C24×C13914yes—
345C22×C4C24×C13914yes—
346C22×C4C24×C13912yes—
347C4⋊C4—24no—
348C4⋊C4—28no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—44no—
352C4⋊C4—44no—
353C4⋊C4—44no—
354C4⋊C4—44no—
355C4⋊C4—44no—
356C4⋊C4—44no—
357C4⋊C4—44no—
358C4⋊C4—44no—
359C22⋊C4—28no—
360C22⋊C4—28no—
361C42—24no—
362C42—24no—
363C42—44no—
364C42—44no—
365C23—22no—
366C23—21no—
367C23—21no—
368C23C2×#41×C13912yes—
369C232−1+4×C13914yes—
370C23C25×C13911yescharacteristic
371Q8—84no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—84no—
403C2×C4—84no—
404C2×C4C2×#41×C13914yes—
405C22—24no—
406C22—24no—
407C22—22no—
408C22—22no—
409C22#541×C13914yes—
410C22C22×#41×C13911yescharacteristic
411C22C2×2−1+4×C13912yes—
412C22#585×C13912yes—
413C22#585×C13911yescharacteristic
414C22#585×C13911yescharacteristic
415C4—24no—
416C4—44no—
417C4—44no—
418C4—44no—
419C4—44no—
420C4—41no—
421C4—41no—
422C4—44no—
423C4—42no—
424C4—44no—
425C2—24no—
426C2C2×#541×C13911yescharacteristic
427C2#3491×C13911yescharacteristic
428C2#3493×C13911yescharacteristic
429C2#3564×C13912yes—
430C2#3564×C13912yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC24×C139C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2776×C139C2semidirect
3. #2769×C139C2semidirect
4. #2762×C139C2semidirect
5. #2758×C139C2semidirect
215. #36979C139direct (N × H)
216. C139#36979direct (N × H)
218. #2776C2×C139semidirect
219. #2769C2×C139semidirect
220. #2762C2×C139semidirect
221. #2758C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2855×C1392
#2776×C1392
#2769×C1392
#2762×C1392
#2758×C1392
#2659×C1392
#2646×C1392
#2505×C1392
#2493×C1392
#2329×C1392
C2×#383×C1392
#36979139