Finite Group Databasebeta

← C139×#36018 #48030614

Subgroups — C139×#36018 #48030614

Order 35584.

3030 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C139C211yesmaximal, characteristic, complemented
2C2×#548×C139C212yesmaximal, complemented
3C2×#519×C139C211yesmaximal, characteristic, complemented
4#2619×C139C213yesmaximal, complemented
5#2548×C139C213yesmaximal, complemented
6#2536×C139C213yesmaximal, complemented
7#2426×C139C216yesmaximal, complemented
8#2414×C139C216yesmaximal, complemented
9#2392×C139C213yesmaximal, complemented
10#2351×C139C211yesmaximal, characteristic, complemented
11#2341×C139C212yesmaximal, complemented
12C22×#41×C139C2212yes—
13C23×Q8×C139C2211yescharacteristic
14#550×C139—28no—
15#548×C139—216no—
16C2×#127×C139C2213yes—
17C2×#124×C139C2216yes—
18C2×C22⋊Q8×C139C2216yes—
19C2×#121×C139C2216yes—
20C2×#121×C139C2216yes—
21#519×C139—28no—
22C2×C4×Q8×C139C2213yes—
23C2×C4×Q8×C139C2211yescharacteristic
24C2×C4×Q8×C139C2212yes—
25C2×C4×Q8×C139C2213yes—
26C2×C4×Q8×C139C2211yescharacteristic
27C2×C4×D4×C139C2213yes—
28C2×C4×D4×C139C2216yes—
29C2×#117×C139C2213yes—
30C2×#117×C139C2213yes—
31#398×C139C2213yes—
32#397×C139C2211yescharacteristic
33#396×C139C2216yes—
34#394×C139C2216yes—
35#394×C139C2213yes—
36#394×C139C2216yes—
37#394×C139C2216yes—
38#392×C139C2213yes—
39#392×C139C2216yes—
40#390×C139C2216yes—
41#390×C139C22112yes—
42#390×C139C2216yes—
43#389×C139C2216yes—
44#388×C139C22112yes—
45#382×C139C2213yes—
46#380×C139C2216yes—
47C4×C4⋊C4×C139C2213yes—
48C4×C22⋊C4×C139C2216yes—
49C2×#41×C139—28no—
50C2×#41×C139—28no—
51C2×#41×C139—28no—
52C22×Q8×C139—24no—
53C22×Q8×C139—24no—
54C22×Q8×C139D418yescomplemented
55C22×Q8×C139C2313yes—
56C22×Q8×C139C2311yescharacteristic
57C22×D4×C139C2316yes—
58C22×D4×C139C2316yes—
59C22×D4×C139C2313yes—
60C22×D4×C139C2316yes—
61C23×C4×C139C2316yes—
62C23×C4×C139C2313yes—
63#127×C139—212no—
64#124×C139—224no—
65C22⋊Q8×C139—224no—
66#121×C139—224no—
67#121×C139—224no—
68C4×Q8×C139—24no—
69C4×Q8×C139—28no—
70C4×Q8×C139—212no—
71C4×Q8×C139—212no—
72C4×Q8×C139D418yescomplemented
73C4×D4×C139—224no—
74C4×D4×C139—212no—
75#117×C139—212no—
76#117×C139—212no—
77C2×C4⋊C4×C139C2313yes—
78C2×C4⋊C4×C139C2316yes—
79C2×C4⋊C4×C139C2311yescharacteristic
80C2×C4⋊C4×C139C2313yes—
81C2×C4⋊C4×C139C2313yes—
82C2×C4⋊C4×C139C2316yes—
83C2×C4⋊C4×C139C2316yes—
84C2×C4⋊C4×C139C2313yes—
85C2×C22⋊C4×C139C2316yes—
86C2×C22⋊C4×C139C2316yes—
87C2×C22⋊C4×C139C2311yescharacteristic
88C2×C22⋊C4×C139C2312yes—
89C2×C22⋊C4×C139C2313yes—
90C2×C22⋊C4×C139C23112yes—
91C2×C22⋊C4×C139C2316yes—
92C2×C22⋊C4×C139C2316yes—
93C2×C22⋊C4×C139C23112yes—
94C2×C42×C139C2313yes—
95C2×C42×C139C2316yes—
96C2×C42×C139C2316yes—
97C2×C42×C139C2313yes—
98#95×C139C2312yes—
99#95×C139C2311yescharacteristic
100#95×C139C2316yes—
101#95×C139C2313yes—
102#95×C139C2316yes—
103C24×C139C2416yes—
104C24×C139C2411yescharacteristic
105#41×C139—432no—
106C2×Q8×C139—232no—
107C2×Q8×C139—26no—
108C2×Q8×C139—26no—
109C2×Q8×C139C2×D4112yes—
110C2×Q8×C139C2×D414yes—
111C2×Q8×C139C2×D414yes—
112C2×Q8×C139#4114yes—
113C2×D4×C139—212no—
114C2×D4×C139—26no—
115C2×D4×C139—212no—
116C2×D4×C139—212no—
117C2×D4×C139—212no—
118C2×D4×C139—212no—
119C2×D4×C139—46no—
120C2×D4×C139—46no—
121C2×D4×C139—46no—
122C2×D4×C139—412no—
123C22×C4×C139—26no—
124C22×C4×C139—26no—
125C22×C4×C139—212no—
126C22×C4×C139—212no—
127C22×C4×C139—212no—
128C22×C4×C139C2×D4112yes—
129C22×C4×C139C2416yes—
130C22×C4×C139C2412yes—
131C22×C4×C139C2412yes—
132C22×C4×C139C2411yescharacteristic
133C22×C4×C139C2413yes—
134C22×C4×C139C2411yescharacteristic
135C22×C4×C139C2413yes—
136C22×C4×C139C2413yes—
137C22×C4×C139C2413yes—
138C4⋊C4×C139—26no—
139C4⋊C4×C139—26no—
140C4⋊C4×C139—26no—
141C4⋊C4×C139—22no—
142C4⋊C4×C139—212no—
143C4⋊C4×C139—212no—
144C4⋊C4×C139—46no—
145C4⋊C4×C139C2×D4112yes—
146C22⋊C4×C139—24no—
147C22⋊C4×C139—26no—
148C22⋊C4×C139—22no—
149C22⋊C4×C139—212no—
150C22⋊C4×C139—212no—
151C22⋊C4×C139—224no—
152C22⋊C4×C139—46no—
153C22⋊C4×C139—412no—
154C22⋊C4×C139—46no—
155C42×C139—212no—
156C42×C139—26no—
157C42×C139—212no—
158C42×C139C2×D4112yes—
159C23×C139—21no—
160C23×C139—21no—
161C23×C139—22no—
162C23×C139—22no—
163C23×C139—26no—
164C23×C139—26no—
165C23×C139—26no—
166C23×C139—26no—
167C23×C139—26no—
168C23×C139—26no—
169C23×C139—26no—
170C23×C139C22×D412yes—
171C23×C139C2511yescharacteristic
172Q8×C139—224no—
173Q8×C139#121116yes—
174D4×C139—412no—
175D4×C139—424no—
176D4×C139—424no—
177D4×C139—812no—
178C2×C4×C139—23no—
179C2×C4×C139—23no—
180C2×C4×C139—26no—
181C2×C4×C139—22no—
182C2×C4×C139—224no—
183C2×C4×C139—22no—
184C2×C4×C139—23no—
185C2×C4×C139—21no—
186C2×C4×C139—26no—
187C2×C4×C139—22no—
188C2×C4×C139—22no—
189C2×C4×C139—22no—
190C2×C4×C139—26no—
191C2×C4×C139—22no—
192C2×C4×C139—22no—
193C2×C4×C139—26no—
194C2×C4×C139—26no—
195C2×C4×C139—22no—
196C2×C4×C139—424no—
197C2×C4×C139C22×D416yes—
198C2×C4×C139C22×D412yes—
199C2×C4×C139C22×D416yes—
200C2×C4×C139C22×D416yes—
201C2×C4×C139C22×D416yes—
202C2×C4×C139C2×#4116yes—
203C22×C139—22no—
204C22×C139—24no—
205C22×C139—41no—
206C22×C139—41no—
207C22×C139—42no—
208C22×C139—46no—
209C22×C139—46no—
210C22×C139—46no—
211C22×C139—46no—
212C22×C139—46no—
213C22×C139—46no—
214C22×C139—46no—
215C22×C139C23×D411yescharacteristic
216C22×C139C23×D411yescharacteristic
217C22×C139C22×#4111yescharacteristic
218C22×C139#58512yes—
219C22×C139#58512yes—
220C4×C139—26no—
221C4×C139—22no—
222C4×C139—26no—
223C4×C139—42no—
224C4×C139—43no—
225C4×C139—42no—
226C4×C139—46no—
227C4×C139—41no—
228C4×C139C2×#121112yes—
229C2×C139—42no—
230C2×C139—86no—
231C2×C139C22×#12111yescharacteristic
232C2×C139#348711yescharacteristic
233C2×C139#348712yes—
234C2×C139#350011yescharacteristic
235C2×C139#352412yes—
236#36018C13911yesmaximal, characteristic, direct product factor, Sylow
237C139#3601811yescharacteristic, direct product factor, Sylow
238C2×#550C2×C13911yescharacteristic, complemented
239C2×#548C2×C13912yescomplemented
240C2×#519C2×C13911yescharacteristic, complemented
241#2619C2×C13913yescomplemented
242#2548C2×C13913yescomplemented
243#2536C2×C13913yescomplemented
244#2426C2×C13916yescomplemented
245#2414C2×C13916yescomplemented
246#2392C2×C13913yescomplemented
247#2351C2×C13911yescharacteristic, complemented
248#2341C2×C13912yescomplemented
249C22×#41C22×C13912yes—
250C23×Q8C22×C13911yescharacteristic
251#550—28no—
252#548—216no—
253C2×#127C22×C13913yes—
254C2×#124C22×C13916yes—
255C2×C22⋊Q8C22×C13916yes—
256C2×#121C22×C13916yes—
257C2×#121C22×C13916yes—
258#519—28no—
259C2×C4×Q8C22×C13911yescharacteristic
260C2×C4×Q8C22×C13912yes—
261C2×C4×Q8C22×C13913yes—
262C2×C4×Q8C22×C13913yes—
263C2×C4×Q8C22×C13911yescharacteristic
264C2×C4×D4C22×C13916yes—
265C2×C4×D4C22×C13913yes—
266C2×#117C22×C13913yes—
267C2×#117C22×C13913yes—
268#398C22×C13913yes—
269#397C22×C13911yescharacteristic
270#396C22×C13916yes—
271#394C22×C13916yes—
272#394C22×C13916yes—
273#394C22×C13916yes—
274#394C22×C13913yes—
275#392C22×C13913yes—
276#392C22×C13916yes—
277#390C22×C13916yes—
278#390C22×C13916yes—
279#390C22×C139112yes—
280#389C22×C13916yes—
281#388C22×C139112yes—
282#382C22×C13913yes—
283#380C22×C13916yes—
284C4×C4⋊C4C22×C13913yes—
285C4×C22⋊C4C22×C13916yes—
286C2×#41—28no—
287C2×#41—28no—
288C2×#41—28no—
289C22×Q8—24no—
290C22×Q8—24no—
291C22×Q8D4×C13918yescomplemented
292C22×Q8C23×C13913yes—
293C22×Q8C23×C13911yescharacteristic
294C22×D4C23×C13916yes—
295C22×D4C23×C13916yes—
296C22×D4C23×C13913yes—
297C22×D4C23×C13916yes—
298C23×C4C23×C13916yes—
299C23×C4C23×C13913yes—
300#127—212no—
301#124—224no—
302C22⋊Q8—224no—
303#121—224no—
304#121—224no—
305C4×Q8—24no—
306C4×Q8—28no—
307C4×Q8—212no—
308C4×Q8—212no—
309C4×Q8D4×C13918yescomplemented
310C4×D4—224no—
311C4×D4—212no—
312#117—212no—
313#117—212no—
314C2×C4⋊C4C23×C13913yes—
315C2×C4⋊C4C23×C13913yes—
316C2×C4⋊C4C23×C13913yes—
317C2×C4⋊C4C23×C13911yescharacteristic
318C2×C4⋊C4C23×C13916yes—
319C2×C4⋊C4C23×C13916yes—
320C2×C4⋊C4C23×C13916yes—
321C2×C4⋊C4C23×C13913yes—
322C2×C22⋊C4C23×C13911yescharacteristic
323C2×C22⋊C4C23×C13913yes—
324C2×C22⋊C4C23×C13912yes—
325C2×C22⋊C4C23×C13916yes—
326C2×C22⋊C4C23×C13916yes—
327C2×C22⋊C4C23×C139112yes—
328C2×C22⋊C4C23×C13916yes—
329C2×C22⋊C4C23×C13916yes—
330C2×C22⋊C4C23×C139112yes—
331C2×C42C23×C13913yes—
332C2×C42C23×C13916yes—
333C2×C42C23×C13916yes—
334C2×C42C23×C13913yes—
335#95C23×C13912yes—
336#95C23×C13916yes—
337#95C23×C13911yescharacteristic
338#95C23×C13913yes—
339#95C23×C13916yes—
340C24C24×C13916yes—
341C24C24×C13911yescharacteristic
342#41—432no—
343C2×Q8—232no—
344C2×Q8—26no—
345C2×Q8—26no—
346C2×Q8C2×D4×C139112yes—
347C2×Q8C2×D4×C13914yes—
348C2×Q8C2×D4×C13914yes—
349C2×Q8#41×C13914yes—
350C2×D4—212no—
351C2×D4—26no—
352C2×D4—212no—
353C2×D4—212no—
354C2×D4—212no—
355C2×D4—212no—
356C2×D4—46no—
357C2×D4—46no—
358C2×D4—46no—
359C2×D4—412no—
360C22×C4—26no—
361C22×C4—26no—
362C22×C4—212no—
363C22×C4—212no—
364C22×C4—212no—
365C22×C4C2×D4×C139112yes—
366C22×C4C24×C13916yes—
367C22×C4C24×C13912yes—
368C22×C4C24×C13912yes—
369C22×C4C24×C13911yescharacteristic
370C22×C4C24×C13913yes—
371C22×C4C24×C13911yescharacteristic
372C22×C4C24×C13913yes—
373C22×C4C24×C13913yes—
374C22×C4C24×C13913yes—
375C4⋊C4—26no—
376C4⋊C4—26no—
377C4⋊C4—26no—
378C4⋊C4—22no—
379C4⋊C4—212no—
380C4⋊C4—212no—
381C4⋊C4—46no—
382C4⋊C4C2×D4×C139112yes—
383C22⋊C4—24no—
384C22⋊C4—26no—
385C22⋊C4—22no—
386C22⋊C4—212no—
387C22⋊C4—212no—
388C22⋊C4—224no—
389C22⋊C4—46no—
390C22⋊C4—412no—
391C22⋊C4—46no—
392C42—212no—
393C42—26no—
394C42—212no—
395C42C2×D4×C139112yes—
396C23—21no—
397C23—21no—
398C23—22no—
399C23—22no—
400C23—26no—
401C23—26no—
402C23—26no—
403C23—26no—
404C23—26no—
405C23—26no—
406C23—26no—
407C23C22×D4×C13912yes—
408C23C25×C13911yescharacteristic
409Q8—224no—
410Q8#121×C139116yes—
411D4—412no—
412D4—424no—
413D4—424no—
414D4—812no—
415C2×C4—23no—
416C2×C4—23no—
417C2×C4—26no—
418C2×C4—22no—
419C2×C4—224no—
420C2×C4—22no—
421C2×C4—23no—
422C2×C4—21no—
423C2×C4—26no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—26no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—26no—
431C2×C4—26no—
432C2×C4—22no—
433C2×C4—424no—
434C2×C4C22×D4×C13916yes—
435C2×C4C22×D4×C13912yes—
436C2×C4C22×D4×C13916yes—
437C2×C4C22×D4×C13916yes—
438C2×C4C22×D4×C13916yes—
439C2×C4C2×#41×C13916yes—
440C22—22no—
441C22—24no—
442C22—41no—
443C22—41no—
444C22—42no—
445C22—46no—
446C22—46no—
447C22—46no—
448C22—46no—
449C22—46no—
450C22—46no—
451C22—46no—
452C22C23×D4×C13911yescharacteristic
453C22C23×D4×C13911yescharacteristic
454C22C22×#41×C13911yescharacteristic
455C22#585×C13912yes—
456C22#585×C13912yes—
457C4—26no—
458C4—22no—
459C4—26no—
460C4—42no—
461C4—46no—
462C4—43no—
463C4—42no—
464C4—41no—
465C4C2×#121×C139112yes—
466C2—42no—
467C2—86no—
468C2C22×#121×C13911yescharacteristic
469C2#3487×C13911yescharacteristic
470C2#3487×C13912yes—
471C2#3500×C13911yescharacteristic
472C2#3524×C13912yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#550×C139C2semidirect
2. C2×#548×C139C2semidirect
3. C2×#519×C139C2semidirect
4. #2619×C139C2semidirect
5. #2548×C139C2semidirect
6. #2536×C139C2semidirect
7. #2426×C139C2semidirect
8. #2414×C139C2semidirect
9. #2392×C139C2semidirect
10. #2351×C139C2semidirect
11. #2341×C139C2semidirect
54. C22×Q8×C139D4semidirect
72. C4×Q8×C139D4semidirect
236. #36018C139direct (N × H)
237. C139#36018direct (N × H)
238. C2×#550C2×C139semidirect
239. C2×#548C2×C139semidirect
240. C2×#519C2×C139semidirect
241. #2619C2×C139semidirect
242. #2548C2×C139semidirect
243. #2536C2×C139semidirect
244. #2426C2×C139semidirect
245. #2414C2×C139semidirect
246. #2392C2×C139semidirect
247. #2351C2×C139semidirect
248. #2341C2×C139semidirect
291. C22×Q8D4×C139semidirect
309. C4×Q8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1392
C2×#548×C1392
C2×#519×C1392
#2619×C1392
#2548×C1392
#2536×C1392
#2426×C1392
#2414×C1392
#2392×C1392
#2351×C1392
#2341×C1392
#36018139