Finite Group Databasebeta

← C131×#29696 #45715580

Subgroups — C131×#29696 #45715580

Order 33536.

1012 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#542×C131C211yesmaximal, characteristic
2C2×#477×C131C211yesmaximal, characteristic, complemented
3C2×#474×C131C211yesmaximal, characteristic, complemented
4#2628×C131C211yesmaximal, characteristic, complemented
5#2057×C131C212yesmaximal, complemented
6#2042×C131C212yesmaximal, complemented
7#2036×C131C212yesmaximal, complemented
8#2033×C131C212yesmaximal
9#1805×C131C211yesmaximal, characteristic, complemented
10#1804×C131C211yesmaximal, characteristic, complemented
11#1798×C131C211yesmaximal, characteristic, complemented
12#542×C131—24no—
13#542×C131—24no—
14C2×C4⋊Q8×C131C2211yescharacteristic
15C2×C4⋊Q8×C131C2211yescharacteristic
16C2×#126×C131—21no—
17C2×#124×C131—21no—
18C2×#124×C131C2211yescharacteristic
19C2×#123×C131—21no—
20C2×C22⋊Q8×C131—21no—
21C2×C22⋊Q8×C131C2211yescharacteristic
22C2×#121×C131C2211yescharacteristic
23C2×C4×Q8×C131C2211yescharacteristic
24C2×C4×D4×C131C2211yescharacteristic
25C2×#117×C131C2211yescharacteristic
26#477×C131—24no—
27#474×C131—24no—
28C2×#107×C131C2212yes—
29C2×#107×C131C2212yes—
30C2×C4⋊C8×C131C2211yescharacteristic
31C2×C4⋊C8×C131C2211yescharacteristic
32C2×#103×C131C2212yes—
33C2×#103×C131C2212yes—
34C2×#102×C131C2212yes—
35C2×#102×C131C2212yes—
36C2×C22⋊C8×C131C2212yes—
37#400×C131—21no—
38#399×C131—21no—
39#395×C131—21no—
40#393×C131—21no—
41#389×C131C2212yes—
42#382×C131C2211yescharacteristic
43#380×C131C2212yes—
44#340×C131C2212yes—
45#340×C131C2212yes—
46#336×C131C2212yes—
47C22×Q8×C131—21no—
48C22×Q8×C131—21no—
49C22×Q8×C131C2311yescharacteristic
50C22×D4×C131—21no—
51C22×D4×C131C2311yescharacteristic
52C23×C4×C131—21no—
53C23×C4×C131C2311yescharacteristic
54C22×C8×C131C2312yes—
55C22×C8×C131C2312yes—
56C4⋊Q8×C131—22no—
57C4⋊Q8×C131—22no—
58C4⋊Q8×C131—22no—
59C4⋊Q8×C131—22no—
60#126×C131—28no—
61#124×C131—28no—
62#124×C131—22no—
63#124×C131—22no—
64#123×C131—28no—
65C22⋊Q8×C131—28no—
66C22⋊Q8×C131—22no—
67C22⋊Q8×C131—22no—
68#121×C131—22no—
69#121×C131—22no—
70C4×Q8×C131—22no—
71C4×Q8×C131D414yes—
72C4×D4×C131—22no—
73C4×D4×C131D414yes—
74#117×C131—22no—
75#117×C131—22no—
76C2×C4⋊C4×C131—21no—
77C2×C4⋊C4×C131—21no—
78C2×C4⋊C4×C131—21no—
79C2×C4⋊C4×C131—21no—
80C2×C4⋊C4×C131—22no—
81C2×C4⋊C4×C131D411yescharacteristic
82C2×C4⋊C4×C131D411yescharacteristic
83C2×C4⋊C4×C131C2312yes—
84C2×C4⋊C4×C131C2312yes—
85C2×C4⋊C4×C131C2311yescharacteristic
86C2×C4⋊C4×C131C2311yescharacteristic
87C2×C22⋊C4×C131—21no—
88C2×C22⋊C4×C131—21no—
89C2×C22⋊C4×C131—21no—
90C2×C22⋊C4×C131—21no—
91C2×C22⋊C4×C131—21no—
92C2×C22⋊C4×C131—22no—
93C2×C22⋊C4×C131D411yescharacteristic
94C2×C22⋊C4×C131D411yescharacteristic
95C2×C42×C131—21no—
96C2×C42×C131C2311yescharacteristic
97C2×C42×C131C2311yescharacteristic
98#107×C131—24no—
99#107×C131—24no—
100C4⋊C8×C131—22no—
101C4⋊C8×C131—22no—
102#103×C131—24no—
103#103×C131—42no—
104#102×C131—24no—
105#102×C131—42no—
106C22⋊C8×C131—42no—
107#95×C131—22no—
108#95×C131—21no—
109#95×C131—22no—
110#95×C131—21no—
111C24×C131—21no—
112C24×C131C2×D411yescharacteristic
113C2×Q8×C131—24no—
114C2×Q8×C131—21no—
115C2×Q8×C131—21no—
116C2×Q8×C131—21no—
117C2×Q8×C131—21no—
118C2×Q8×C131—21no—
119C2×Q8×C131—42no—
120C2×Q8×C131—82no—
121C2×Q8×C131—82no—
122C2×Q8×C131C2×D412yes—
123C2×D4×C131—24no—
124C2×D4×C131—21no—
125C2×D4×C131—21no—
126C2×D4×C131—21no—
127C2×D4×C131—21no—
128C2×D4×C131—21no—
129C2×D4×C131—82no—
130C2×D4×C131C2×D412yes—
131C22×C4×C131—21no—
132C22×C4×C131—21no—
133C22×C4×C131—21no—
134C22×C4×C131—21no—
135C22×C4×C131—21no—
136C22×C4×C131—21no—
137C22×C4×C131—21no—
138C22×C4×C131—21no—
139C22×C4×C131—21no—
140C22×C4×C131—24no—
141C22×C4×C131—22no—
142C22×C4×C131—22no—
143C22×C4×C131—82no—
144C22×C4×C131C2×D411yescharacteristic
145C22×C4×C131C2×D411yescharacteristic
146C22×C4×C131C2×D411yescharacteristic
147C22×C4×C131C2×D411yescharacteristic
148C22×C4×C131C2×D411yescharacteristic
149C22×C4×C131C2411yescharacteristic
150C2×C8×C131—22no—
151C2×C8×C131—22no—
152C2×C8×C131—22no—
153C2×C8×C131—22no—
154C2×C8×C131—22no—
155C2×C8×C131—22no—
156C4⋊C4×C131—24no—
157C4⋊C4×C131—24no—
158C4⋊C4×C131—24no—
159C4⋊C4×C131—22no—
160C4⋊C4×C131—22no—
161C4⋊C4×C131—21no—
162C4⋊C4×C131—21no—
163C4⋊C4×C131—22no—
164C4⋊C4×C131—22no—
165C4⋊C4×C131—22no—
166C4⋊C4×C131—22no—
167C4⋊C4×C131—42no—
168C4⋊C4×C131—82no—
169C4⋊C4×C131C2×D412yes—
170C4⋊C4×C131C2×D412yes—
171C22⋊C4×C131—24no—
172C22⋊C4×C131—24no—
173C22⋊C4×C131—24no—
174C22⋊C4×C131—24no—
175C22⋊C4×C131—24no—
176C22⋊C4×C131—22no—
177C22⋊C4×C131—22no—
178C22⋊C4×C131—82no—
179C42×C131—24no—
180C42×C131—21no—
181C42×C131—21no—
182C42×C131C2×D412yes—
183C42×C131C2×D412yes—
184C23×C131—21no—
185C23×C131—22no—
186C23×C131—21no—
187C23×C131—21no—
188C23×C131—22no—
189C23×C131—22no—
190C23×C131—41no—
191C23×C131—41no—
192C23×C131—42no—
193C23×C131—42no—
194C23×C131C22×D411yescharacteristic
195Q8×C131—22no—
196Q8×C131—22no—
197Q8×C131—41no—
198Q8×C131—41no—
199Q8×C131—84no—
200Q8×C131—84no—
201D4×C131—22no—
202D4×C131—22no—
203D4×C131—41no—
204D4×C131—41no—
205D4×C131—84no—
206C2×C4×C131—22no—
207C2×C4×C131—22no—
208C2×C4×C131—21no—
209C2×C4×C131—22no—
210C2×C4×C131—21no—
211C2×C4×C131—22no—
212C2×C4×C131—21no—
213C2×C4×C131—22no—
214C2×C4×C131—21no—
215C2×C4×C131—21no—
216C2×C4×C131—22no—
217C2×C4×C131—22no—
218C2×C4×C131—41no—
219C2×C4×C131—41no—
220C2×C4×C131—42no—
221C2×C4×C131—42no—
222C2×C4×C131—41no—
223C2×C4×C131—41no—
224C2×C4×C131—41no—
225C2×C4×C131—41no—
226C2×C4×C131—42no—
227C2×C4×C131—42no—
228C2×C4×C131—42no—
229C2×C4×C131—42no—
230C2×C4×C131—42no—
231C2×C4×C131—42no—
232C2×C4×C131—84no—
233C2×C4×C131#12012yes—
234C2×C4×C131#12012yes—
235C2×C4×C131C22×D411yescharacteristic
236C2×C4×C131C22×D411yescharacteristic
237C2×C4×C131H(5,𝔽2)11yescharacteristic
238C2×C4×C1312−1+411yescharacteristic
239C2×C4×C1312−1+411yescharacteristic
240C2×C4×C1312−1+411yescharacteristic
241C8×C131—42no—
242C8×C131—42no—
243C22×C131—41no—
244C22×C131—42no—
245C22×C131—42no—
246C22×C131—42no—
247C22×C131—42no—
248C22×C131—41no—
249C22×C131—41no—
250C22×C131—42no—
251C22×C131—82no—
252C22×C131—82no—
253C22×C131C2×#12011yescharacteristic
254C22×C131#53611yescharacteristic
255C22×C131#53711yescharacteristic
256C22×C131#57612yes—
257C22×C131#57812yes—
258C4×C131—22no—
259C4×C131—22no—
260C4×C131—41no—
261C4×C131—42no—
262C4×C131—41no—
263C4×C131—42no—
264C4×C131—42no—
265C4×C131—41no—
266C4×C131—82no—
267C4×C131—82no—
268C4×C131#53611yescharacteristic
269C4×C131#53611yescharacteristic
270C4×C131#53711yescharacteristic
271C4×C131#53711yescharacteristic
272C2×C131—81no—
273C2×C131—82no—
274C2×C131#261611yescharacteristic
275C2×C131#300811yescharacteristic
276C2×C131#301111yescharacteristic
277C2×C131#324312yes—
278C2×C131#326212yes—
279#29696C13111yesmaximal, characteristic, direct product factor, Sylow
280C131#2969611yescharacteristic, direct product factor, Sylow
281C2×#542C2×C13111yescharacteristic
282C2×#477C2×C13111yescharacteristic, complemented
283C2×#474C2×C13111yescharacteristic, complemented
284#2628C2×C13111yescharacteristic, complemented
285#2057C2×C13112yescomplemented
286#2042C2×C13112yescomplemented
287#2036C2×C13112yescomplemented
288#2033C2×C13112yes—
289#1805C2×C13111yescharacteristic, complemented
290#1804C2×C13111yescharacteristic, complemented
291#1798C2×C13111yescharacteristic, complemented
292#542—24no—
293#542—24no—
294C2×C4⋊Q8C22×C13111yescharacteristic
295C2×C4⋊Q8C22×C13111yescharacteristic
296C2×#126—21no—
297C2×#124—21no—
298C2×#124C22×C13111yescharacteristic
299C2×#123—21no—
300C2×C22⋊Q8—21no—
301C2×C22⋊Q8C22×C13111yescharacteristic
302C2×#121C22×C13111yescharacteristic
303C2×C4×Q8C22×C13111yescharacteristic
304C2×C4×D4C22×C13111yescharacteristic
305C2×#117C22×C13111yescharacteristic
306#477—24no—
307#474—24no—
308C2×#107C22×C13112yes—
309C2×#107C22×C13112yes—
310C2×C4⋊C8C22×C13111yescharacteristic
311C2×C4⋊C8C22×C13111yescharacteristic
312C2×#103C22×C13112yes—
313C2×#103C22×C13112yes—
314C2×#102C22×C13112yes—
315C2×#102C22×C13112yes—
316C2×C22⋊C8C22×C13112yes—
317#400—21no—
318#399—21no—
319#395—21no—
320#393—21no—
321#389C22×C13112yes—
322#382C22×C13111yescharacteristic
323#380C22×C13112yes—
324#340C22×C13112yes—
325#340C22×C13112yes—
326#336C22×C13112yes—
327C22×Q8—21no—
328C22×Q8—21no—
329C22×Q8C23×C13111yescharacteristic
330C22×D4—21no—
331C22×D4C23×C13111yescharacteristic
332C23×C4—21no—
333C23×C4C23×C13111yescharacteristic
334C22×C8C23×C13112yes—
335C22×C8C23×C13112yes—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340#126—28no—
341#124—28no—
342#124—22no—
343#124—22no—
344#123—28no—
345C22⋊Q8—28no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348#121—22no—
349#121—22no—
350C4×Q8—22no—
351C4×Q8D4×C13114yes—
352C4×D4—22no—
353C4×D4D4×C13114yes—
354#117—22no—
355#117—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4D4×C13111yescharacteristic
362C2×C4⋊C4D4×C13111yescharacteristic
363C2×C4⋊C4C23×C13112yes—
364C2×C4⋊C4C23×C13112yes—
365C2×C4⋊C4C23×C13111yescharacteristic
366C2×C4⋊C4C23×C13111yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4D4×C13111yescharacteristic
374C2×C22⋊C4D4×C13111yescharacteristic
375C2×C42—21no—
376C2×C42C23×C13111yescharacteristic
377C2×C42C23×C13111yescharacteristic
378#107—24no—
379#107—24no—
380C4⋊C8—22no—
381C4⋊C8—22no—
382#103—24no—
383#103—42no—
384#102—24no—
385#102—42no—
386C22⋊C8—42no—
387#95—22no—
388#95—21no—
389#95—21no—
390#95—22no—
391C24—21no—
392C24C2×D4×C13111yescharacteristic
393C2×Q8—24no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—42no—
400C2×Q8—82no—
401C2×Q8—82no—
402C2×Q8C2×D4×C13112yes—
403C2×D4—24no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—82no—
410C2×D4C2×D4×C13112yes—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—82no—
424C22×C4C2×D4×C13111yescharacteristic
425C22×C4C2×D4×C13111yescharacteristic
426C22×C4C2×D4×C13111yescharacteristic
427C22×C4C2×D4×C13111yescharacteristic
428C22×C4C2×D4×C13111yescharacteristic
429C22×C4C24×C13111yescharacteristic
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—82no—
449C4⋊C4C2×D4×C13112yes—
450C4⋊C4C2×D4×C13112yes—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—82no—
459C42—24no—
460C42—21no—
461C42—21no—
462C42C2×D4×C13112yes—
463C42C2×D4×C13112yes—
464C23—21no—
465C23—22no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—22no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23C22×D4×C13111yescharacteristic
475Q8—22no—
476Q8—22no—
477Q8—41no—
478Q8—41no—
479Q8—84no—
480Q8—84no—
481D4—22no—
482D4—22no—
483D4—41no—
484D4—41no—
485D4—84no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—84no—
513C2×C4#120×C13112yes—
514C2×C4#120×C13112yes—
515C2×C4C22×D4×C13111yescharacteristic
516C2×C4C22×D4×C13111yescharacteristic
517C2×C4H(5,𝔽2)×C13111yescharacteristic
518C2×C42−1+4×C13111yescharacteristic
519C2×C42−1+4×C13111yescharacteristic
520C2×C42−1+4×C13111yescharacteristic
521C8—42no—
522C8—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—41no—
527C22—41no—
528C22—42no—
529C22—41no—
530C22—42no—
531C22—82no—
532C22—82no—
533C22C2×#120×C13111yescharacteristic
534C22#536×C13111yescharacteristic
535C22#537×C13111yescharacteristic
536C22#576×C13112yes—
537C22#578×C13112yes—
538C4—22no—
539C4—22no—
540C4—41no—
541C4—42no—
542C4—42no—
543C4—41no—
544C4—41no—
545C4—42no—
546C4—82no—
547C4—82no—
548C4#536×C13111yescharacteristic
549C4#536×C13111yescharacteristic
550C4#537×C13111yescharacteristic
551C4#537×C13111yescharacteristic
552C2—81no—
553C2—82no—
554C2#2616×C13111yescharacteristic
555C2#3008×C13111yescharacteristic
556C2#3011×C13111yescharacteristic
557C2#3243×C13112yes—
558C2#3262×C13112yes—
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×#117×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#477×C131C2semidirect
3. C2×#474×C131C2semidirect
4. #2628×C131C2semidirect
5. #2057×C131C2semidirect
6. #2042×C131C2semidirect
7. #2036×C131C2semidirect
9. #1805×C131C2semidirect
10. #1804×C131C2semidirect
11. #1798×C131C2semidirect
279. #29696C131direct (N × H)
280. C131#29696direct (N × H)
282. C2×#477C2×C131semidirect
283. C2×#474C2×C131semidirect
284. #2628C2×C131semidirect
285. #2057C2×C131semidirect
286. #2042C2×C131semidirect
287. #2036C2×C131semidirect
289. #1805C2×C131semidirect
290. #1804C2×C131semidirect
291. #1798C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#542×C1312
C2×#477×C1312
C2×#474×C1312
#2628×C1312
#2057×C1312
#2042×C1312
#2036×C1312
#2033×C1312
#1805×C1312
#1804×C1312
#1798×C1312
#29696131