Finite Group Databasebeta

← C131×#24471 #45710355

Subgroups — C131×#24471 #45710355

Order 33536.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C131C211yesmaximal, characteristic
2#3056×C131C211yesmaximal, characteristic, complemented
3C2×#455×C131C211yesmaximal, characteristic, complemented
4#3007×C131C211yesmaximal, characteristic, complemented
5C2×#421×C131C211yesmaximal, characteristic, complemented
6#2620×C131C211yesmaximal, characteristic, complemented
7#2039×C131C211yesmaximal, characteristic, complemented
8#2037×C131C211yesmaximal, characteristic, complemented
9#2007×C131C211yesmaximal, characteristic, complemented
10#2004×C131C211yesmaximal, characteristic, complemented
11#1900×C131C211yesmaximal, characteristic, complemented
12#1897×C131C211yesmaximal, characteristic, complemented
13#1882×C131C211yesmaximal, characteristic, complemented
14#1859×C131C211yesmaximal, characteristic, complemented
15#1792×C131C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C131C2211yescharacteristic
17C22×#41×C131C2211yescharacteristic
18C2×#137×C131C2211yescharacteristic
19C2×#137×C131C2211yescharacteristic, complemented
20C2×#137×C131C2211yescharacteristic, complemented
21C22×M16×C131C2211yescharacteristic, complemented
22#550×C131—21no—
23#548×C131—21no—
24#546×C131—21no—
25#546×C131—22no—
26D42×C131—22no—
27D42×C131—21no—
28#537×C131—21no—
29#537×C131C2211yescharacteristic
30#535×C131—21no—
31#535×C131C2211yescharacteristic
32C2×#124×C131C2211yescharacteristic, complemented
33#525×C131—21no—
34#525×C131C2211yescharacteristic
35C2×C22⋊Q8×C131C2211yescharacteristic, complemented
36C2×#121×C131—21no—
37C2×#121×C131C2211yescharacteristic
38#520×C131C2211yescharacteristic
39C2×#117×C131C2211yescharacteristic, complemented
40#470×C131—21no—
41#468×C131—21no—
42#467×C131—21no—
43#465×C131—21no—
44#455×C131—24no—
45#452×C131—21no—
46#452×C131—21no—
47#451×C131—21no—
48#450×C131—21no—
49#428×C131C2211yescharacteristic, complemented
50#421×C131—24no—
51C2×#104×C131C2211yescharacteristic
52C2×#104×C131C2211yescharacteristic
53C2×#104×C131C2211yescharacteristic, complemented
54C2×#104×C131C2211yescharacteristic, complemented
55C2×#104×C131C2211yescharacteristic, complemented
56C2×#104×C131C2211yescharacteristic, complemented
57#419×C131C2211yescharacteristic, complemented
58#417×C131C2211yescharacteristic
59#417×C131C2211yescharacteristic, complemented
60#417×C131C2211yescharacteristic, complemented
61C2×#100×C131C2211yescharacteristic, complemented
62C2×#100×C131C2211yescharacteristic, complemented
63#407×C131C2211yescharacteristic, complemented
64#396×C131—22no—
65#394×C131—22no—
66#391×C131C2211yescharacteristic, complemented
67#390×C131C2211yescharacteristic, complemented
68#384×C131C2211yescharacteristic, complemented
69#343×C131C2211yescharacteristic, complemented
70#343×C131C2211yescharacteristic, complemented
71#339×C131C2211yescharacteristic, complemented
72#339×C131C2211yescharacteristic, complemented
73H(5,𝔽2)×C131—22no—
74H(5,𝔽2)×C131—22no—
75H(5,𝔽2)×C131—41no—
76H(5,𝔽2)×C131—41no—
77C2×#41×C131—21no—
78C2×#41×C131—21no—
79C2×#41×C131—21no—
80C2×#41×C131—21no—
81C2×#41×C131—22no—
82C2×#41×C131—22no—
83C2×#41×C131—41no—
84C2×#41×C131—41no—
85C2×#41×C131D411yescharacteristic
86C2×#41×C131D411yescharacteristic
87C2×#41×C131C2311yescharacteristic
88C2×#41×C131C2311yescharacteristic
89C2×#41×C131C2311yescharacteristic
90C22×Q8×C131D411yescharacteristic
91C22×Q8×C131C2311yescharacteristic
92C22×D4×C131—21no—
93C22×D4×C131—22no—
94C22×D4×C131—22no—
95C22×D4×C131—21no—
96C22×D4×C131—21no—
97C22×D4×C131D411yescharacteristic
98C22×D4×C131D412yes—
99C22×D4×C131C2311yescharacteristic
100C23×C4×C131—21no—
101C23×C4×C131C2311yescharacteristic
102#137×C131—22no—
103#137×C131—22no—
104#137×C131—22no—
105#137×C131—41no—
106#137×C131—41no—
107#137×C131—41no—
108C2×Q16×C131—21no—
109C2×Q16×C131—21no—
110C2×Q16×C131—21no—
111C2×SD16×C131—21no—
112C2×SD16×C131—21no—
113C2×SD16×C131—21no—
114C2×M16×C131—21no—
115C2×M16×C131—22no—
116C2×M16×C131—41no—
117C2×M16×C131C2311yescharacteristic
118C2×M16×C131C2311yescharacteristic
119C2×M16×C131C2311yescharacteristic
120C2×M16×C131C2311yescharacteristic
121C22×C8×C131—21no—
122#127×C131—22no—
123#127×C131—21no—
124#124×C131—22no—
125#124×C131—21no—
126#124×C131—22no—
127#124×C131—41no—
128#123×C131—22no—
129#123×C131—21no—
130C22⋊Q8×C131—22no—
131C22⋊Q8×C131—21no—
132C22⋊Q8×C131—21no—
133C22⋊Q8×C131—21no—
134C22⋊Q8×C131—21no—
135C22⋊Q8×C131—21no—
136C22⋊Q8×C131—21no—
137C22⋊Q8×C131D411yescharacteristic
138C22⋊Q8×C131D411yescharacteristic
139#121×C131—22no—
140#121×C131—22no—
141#121×C131—22no—
142#121×C131—22no—
143#121×C131—22no—
144#121×C131—21no—
145#121×C131—21no—
146#121×C131—21no—
147#121×C131—21no—
148#121×C131—21no—
149#121×C131—21no—
150#121×C131—22no—
151#121×C131—21no—
152#121×C131—21no—
153#121×C131D411yescharacteristic
154#121×C131D411yescharacteristic
155#120×C131—22no—
156#120×C131—22no—
157#120×C131—22no—
158#120×C131—21no—
159#120×C131—22no—
160C4×Q8×C131—21no—
161C4×D4×C131—22no—
162C4×D4×C131—22no—
163C4×D4×C131—21no—
164C4×D4×C131—22no—
165C4×D4×C131—21no—
166C4×D4×C131—21no—
167#117×C131—21no—
168#117×C131—22no—
169#117×C131—41no—
170#117×C131C2311yescharacteristic
171C2×C4⋊C4×C131—21no—
172C2×C4⋊C4×C131—21no—
173C2×C4⋊C4×C131—21no—
174C2×C4⋊C4×C131—22no—
175C2×C4⋊C4×C131C2311yescharacteristic
176C2×C4⋊C4×C131C2311yescharacteristic
177C2×C22⋊C4×C131—22no—
178C2×C22⋊C4×C131—21no—
179C2×C22⋊C4×C131—21no—
180C2×C22⋊C4×C131—22no—
181C2×C22⋊C4×C131—22no—
182C2×C22⋊C4×C131D412yes—
183C2×C42×C131C2311yescharacteristic
184C2×C42×C131C2311yescharacteristic
185#107×C131—21no—
186#106×C131—21no—
187#104×C131—22no—
188#104×C131—22no—
189#104×C131—22no—
190#104×C131—22no—
191#104×C131—41no—
192#104×C131D414yescomplemented
193#103×C131—21no—
194#103×C131—21no—
195#103×C131—21no—
196#103×C131—21no—
197#103×C131—21no—
198#102×C131—21no—
199#102×C131—21no—
200#102×C131—21no—
201#100×C131—22no—
202#100×C131—41no—
203C22⋊C8×C131—21no—
204C22⋊C8×C131—21no—
205#95×C131—22no—
206C24×C131—22no—
207C24×C131—21no—
208C24×C131C2×D412yes—
209C24×C131C2×D411yescharacteristic
210#41×C131—21no—
211#41×C131—21no—
212#41×C131—22no—
213#41×C131—22no—
214#41×C131—21no—
215#41×C131—21no—
216#41×C131—21no—
217#41×C131—21no—
218#41×C131—21no—
219#41×C131—21no—
220#41×C131—21no—
221#41×C131—21no—
222#41×C131—42no—
223#41×C131—42no—
224#41×C131—41no—
225#41×C131—41no—
226#41×C131—42no—
227#41×C131—42no—
228#41×C131—42no—
229#41×C131—42no—
230#41×C131—42no—
231#41×C131—42no—
232#41×C131C2×D412yes—
233#41×C131#4112yes—
234C2×Q8×C131—21no—
235C2×Q8×C131—22no—
236C2×Q8×C131—21no—
237C2×Q8×C131—21no—
238C2×Q8×C131—21no—
239C2×Q8×C131—21no—
240C2×Q8×C131—21no—
241C2×Q8×C131—21no—
242C2×Q8×C131—41no—
243C2×Q8×C131C2×D411yescharacteristic
244C2×Q8×C131C2×D411yescharacteristic
245C2×Q8×C131C2×D411yescharacteristic
246C2×D4×C131—21no—
247C2×D4×C131—22no—
248C2×D4×C131—22no—
249C2×D4×C131—22no—
250C2×D4×C131—22no—
251C2×D4×C131—21no—
252C2×D4×C131—21no—
253C2×D4×C131—21no—
254C2×D4×C131—21no—
255C2×D4×C131—21no—
256C2×D4×C131—22no—
257C2×D4×C131—22no—
258C2×D4×C131—22no—
259C2×D4×C131—21no—
260C2×D4×C131—22no—
261C2×D4×C131—21no—
262C2×D4×C131—21no—
263C2×D4×C131—21no—
264C2×D4×C131—21no—
265C2×D4×C131—21no—
266C2×D4×C131—21no—
267C2×D4×C131—21no—
268C2×D4×C131—41no—
269C2×D4×C131—42no—
270C2×D4×C131—42no—
271C2×D4×C131—42no—
272C2×D4×C131—42no—
273C2×D4×C131—44no—
274C2×D4×C131—44no—
275C2×D4×C131—42no—
276C2×D4×C131—42no—
277C2×D4×C131—82no—
278C2×D4×C131—84no—
279C2×D4×C131C2×D411yescharacteristic
280C2×D4×C131C2×D411yescharacteristic
281C2×D4×C131C2×D411yescharacteristic
282C22×C4×C131—21no—
283C22×C4×C131—21no—
284C22×C4×C131—21no—
285C22×C4×C131—21no—
286C22×C4×C131—21no—
287C22×C4×C131—22no—
288C22×C4×C131—21no—
289C22×C4×C131—21no—
290C22×C4×C131—22no—
291C22×C4×C131—21no—
292C22×C4×C131—21no—
293C22×C4×C131—21no—
294C22×C4×C131—21no—
295C22×C4×C131—21no—
296C22×C4×C131—21no—
297C22×C4×C131—21no—
298C22×C4×C131—42no—
299C22×C4×C131—42no—
300C22×C4×C131C2×D411yescharacteristic
301C22×C4×C131C2×D411yescharacteristic
302C22×C4×C131C2×D411yescharacteristic
303C22×C4×C131C2×D411yescharacteristic
304C22×C4×C131C2×D411yescharacteristic
305C22×C4×C131C2×D412yes—
306C22×C4×C131C2411yescharacteristic
307Q16×C131—42no—
308Q16×C131—42no—
309Q16×C131—42no—
310SD16×C131—42no—
311SD16×C131—42no—
312SD16×C131—42no—
313M16×C131—21no—
314M16×C131—21no—
315M16×C131—21no—
316M16×C131—21no—
317M16×C131—21no—
318M16×C131—21no—
319M16×C131—21no—
320M16×C131—42no—
321M16×C131C2×D412yescomplemented
322C2×C8×C131—21no—
323C2×C8×C131—21no—
324C2×C8×C131—21no—
325C2×C8×C131—21no—
326C2×C8×C131—42no—
327C4⋊C4×C131—22no—
328C4⋊C4×C131—22no—
329C4⋊C4×C131—21no—
330C4⋊C4×C131—21no—
331C4⋊C4×C131—21no—
332C4⋊C4×C131—21no—
333C4⋊C4×C131—21no—
334C4⋊C4×C131—21no—
335C4⋊C4×C131—42no—
336C4⋊C4×C131—41no—
337C4⋊C4×C131—41no—
338C4⋊C4×C131—82no—
339C4⋊C4×C131C2×D411yescharacteristic
340C4⋊C4×C131C2×D411yescharacteristic
341C22⋊C4×C131—22no—
342C22⋊C4×C131—22no—
343C22⋊C4×C131—22no—
344C22⋊C4×C131—22no—
345C22⋊C4×C131—22no—
346C22⋊C4×C131—21no—
347C22⋊C4×C131—21no—
348C22⋊C4×C131—21no—
349C22⋊C4×C131—21no—
350C22⋊C4×C131—22no—
351C22⋊C4×C131—22no—
352C22⋊C4×C131—21no—
353C22⋊C4×C131—42no—
354C22⋊C4×C131—44no—
355C22⋊C4×C131—41no—
356C22⋊C4×C131—41no—
357C22⋊C4×C131—82no—
358C42×C131—22no—
359C42×C131—21no—
360C42×C131—21no—
361C42×C131—21no—
362C42×C131—21no—
363C42×C131C2×D412yescomplemented
364C23×C131—21no—
365C23×C131—21no—
366C23×C131—21no—
367C23×C131—22no—
368C23×C131—21no—
369C23×C131—21no—
370C23×C131—22no—
371C23×C131—22no—
372C23×C131—41no—
373C23×C131—41no—
374C23×C131—42no—
375C23×C131—42no—
376C23×C131—44no—
377C23×C131—42no—
378C23×C131—42no—
379C23×C131—81no—
380C23×C131—82no—
381C23×C131—82no—
382C23×C131#12011yescharacteristic
383C23×C131#12011yescharacteristic
384C23×C131C22×D411yescharacteristic
385Q8×C131—21no—
386Q8×C131—21no—
387Q8×C131—21no—
388Q8×C131—21no—
389Q8×C131—21no—
390Q8×C131—42no—
391Q8×C131—41no—
392Q8×C131—41no—
393Q8×C131—41no—
394Q8×C131—41no—
395Q8×C131#12112yes—
396D4×C131—22no—
397D4×C131—22no—
398D4×C131—21no—
399D4×C131—21no—
400D4×C131—21no—
401D4×C131—21no—
402D4×C131—21no—
403D4×C131—42no—
404D4×C131—42no—
405D4×C131—44no—
406D4×C131—42no—
407D4×C131—44no—
408D4×C131—44no—
409D4×C131—42no—
410D4×C131—41no—
411D4×C131—41no—
412D4×C131—41no—
413D4×C131—41no—
414D4×C131—41no—
415D4×C131—41no—
416D4×C131—41no—
417D4×C131—41no—
418D4×C131—81no—
419D4×C131—82no—
420D4×C131—82no—
421D4×C131—82no—
422D4×C131—82no—
423D4×C131#12112yes—
424C2×C4×C131—21no—
425C2×C4×C131—21no—
426C2×C4×C131—21no—
427C2×C4×C131—21no—
428C2×C4×C131—21no—
429C2×C4×C131—21no—
430C2×C4×C131—21no—
431C2×C4×C131—21no—
432C2×C4×C131—21no—
433C2×C4×C131—22no—
434C2×C4×C131—21no—
435C2×C4×C131—21no—
436C2×C4×C131—22no—
437C2×C4×C131—21no—
438C2×C4×C131—22no—
439C2×C4×C131—21no—
440C2×C4×C131—21no—
441C2×C4×C131—21no—
442C2×C4×C131—22no—
443C2×C4×C131—42no—
444C2×C4×C131—42no—
445C2×C4×C131—42no—
446C2×C4×C131—44no—
447C2×C4×C131—41no—
448C2×C4×C131—41no—
449C2×C4×C131—41no—
450C2×C4×C131—41no—
451C2×C4×C131—41no—
452C2×C4×C131—41no—
453C2×C4×C131—42no—
454C2×C4×C131—41no—
455C2×C4×C131—42no—
456C2×C4×C131—41no—
457C2×C4×C131—41no—
458C2×C4×C131—41no—
459C2×C4×C131—41no—
460C2×C4×C131—41no—
461C2×C4×C131—41no—
462C2×C4×C131—82no—
463C2×C4×C131#12011yescharacteristic
464C2×C4×C131#12011yescharacteristic
465C2×C4×C131C22×D411yescharacteristic
466C2×C4×C131C22×D411yescharacteristic
467C2×C4×C131C22×D411yescharacteristic
468C2×C4×C131C2×#4111yescharacteristic
469C2×C4×C131H(5,𝔽2)11yescharacteristic
470C2×C4×C131H(5,𝔽2)11yescharacteristic
471C8×C131—22no—
472C8×C131—41no—
473C8×C131—41no—
474C8×C131—41no—
475C22×C131—21no—
476C22×C131—21no—
477C22×C131—21no—
478C22×C131—21no—
479C22×C131—22no—
480C22×C131—21no—
481C22×C131—21no—
482C22×C131—21no—
483C22×C131—21no—
484C22×C131—41no—
485C22×C131—41no—
486C22×C131—41no—
487C22×C131—41no—
488C22×C131—42no—
489C22×C131—42no—
490C22×C131—41no—
491C22×C131—41no—
492C22×C131—41no—
493C22×C131—42no—
494C22×C131—41no—
495C22×C131—81no—
496C22×C131—81no—
497C22×C131—82no—
498C22×C131—82no—
499C22×C131—84no—
500C22×C131—164no—
501C22×C131C2×#12011yescharacteristic
502C22×C131D4211yescharacteristic
503C22×C131#54611yescharacteristic
504C4×C131—21no—
505C4×C131—21no—
506C4×C131—22no—
507C4×C131—42no—
508C4×C131—41no—
509C4×C131—41no—
510C4×C131—42no—
511C4×C131—41no—
512C4×C131—41no—
513C4×C131—81no—
514C4×C131—81no—
515C4×C131—81no—
516C4×C131C2×#12111yescharacteristic
517C4×C131#53411yescharacteristic
518C4×C131D4211yescharacteristic
519C4×C131#54611yescharacteristic
520C2×C131—21no—
521C2×C131—21no—
522C2×C131—41no—
523C2×C131—41no—
524C2×C131—42no—
525C2×C131—81no—
526C2×C131—82no—
527C2×C131—81no—
528C2×C131#241011yescharacteristic
529C2×C131#301911yescharacteristic
530C2×C131#302211yescharacteristic
531#24471C13111yesmaximal, characteristic, direct product factor, Sylow
532C131#2447111yescharacteristic, direct product factor, Sylow
533#3488C2×C13111yescharacteristic
534#3056C2×C13111yescharacteristic, complemented
535C2×#455C2×C13111yescharacteristic, complemented
536#3007C2×C13111yescharacteristic, complemented
537C2×#421C2×C13111yescharacteristic, complemented
538#2620C2×C13111yescharacteristic, complemented
539#2039C2×C13111yescharacteristic, complemented
540#2037C2×C13111yescharacteristic, complemented
541#2007C2×C13111yescharacteristic, complemented
542#2004C2×C13111yescharacteristic, complemented
543#1900C2×C13111yescharacteristic, complemented
544#1897C2×C13111yescharacteristic, complemented
545#1882C2×C13111yescharacteristic, complemented
546#1859C2×C13111yescharacteristic, complemented
547#1792C2×C13111yescharacteristic, complemented
548C2×H(5,𝔽2)C22×C13111yescharacteristic
549C22×#41C22×C13111yescharacteristic
550C2×#137C22×C13111yescharacteristic
551C2×#137C22×C13111yescharacteristic, complemented
552C2×#137C22×C13111yescharacteristic, complemented
553C22×M16C22×C13111yescharacteristic, complemented
554#550—21no—
555#548—21no—
556#546—21no—
557#546—22no—
558D42—22no—
559D42—21no—
560#537—21no—
561#537C22×C13111yescharacteristic
562#535—21no—
563#535C22×C13111yescharacteristic
564C2×#124C22×C13111yescharacteristic, complemented
565#525—21no—
566#525C22×C13111yescharacteristic
567C2×C22⋊Q8C22×C13111yescharacteristic, complemented
568C2×#121—21no—
569C2×#121C22×C13111yescharacteristic
570#520C22×C13111yescharacteristic
571C2×#117C22×C13111yescharacteristic, complemented
572#470—21no—
573#468—21no—
574#467—21no—
575#465—21no—
576#455—24no—
577#452—21no—
578#452—21no—
579#451—21no—
580#450—21no—
581#428C22×C13111yescharacteristic, complemented
582#421—24no—
583C2×#104C22×C13111yescharacteristic
584C2×#104C22×C13111yescharacteristic
585C2×#104C22×C13111yescharacteristic, complemented
586C2×#104C22×C13111yescharacteristic, complemented
587C2×#104C22×C13111yescharacteristic, complemented
588C2×#104C22×C13111yescharacteristic, complemented
589#419C22×C13111yescharacteristic, complemented
590#417C22×C13111yescharacteristic
591#417C22×C13111yescharacteristic, complemented
592#417C22×C13111yescharacteristic, complemented
593C2×#100C22×C13111yescharacteristic, complemented
594C2×#100C22×C13111yescharacteristic, complemented
595#407C22×C13111yescharacteristic, complemented
596#396—22no—
597#394—22no—
598#391C22×C13111yescharacteristic, complemented
599#390C22×C13111yescharacteristic, complemented
600#384C22×C13111yescharacteristic, complemented
601#343C22×C13111yescharacteristic, complemented
602#343C22×C13111yescharacteristic, complemented
603#339C22×C13111yescharacteristic, complemented
604#339C22×C13111yescharacteristic, complemented
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C13111yescharacteristic
618C2×#41D4×C13111yescharacteristic
619C2×#41C23×C13111yescharacteristic
620C2×#41C23×C13111yescharacteristic
621C2×#41C23×C13111yescharacteristic
622C22×Q8D4×C13111yescharacteristic
623C22×Q8C23×C13111yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C13111yescharacteristic
630C22×D4D4×C13112yes—
631C22×D4C23×C13111yescharacteristic
632C23×C4—21no—
633C23×C4C23×C13111yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C13111yescharacteristic
650C2×M16C23×C13111yescharacteristic
651C2×M16C23×C13111yescharacteristic
652C2×M16C23×C13111yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C13111yescharacteristic
670C22⋊Q8D4×C13111yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C13111yescharacteristic
686#121D4×C13111yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C13111yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C13111yescharacteristic
708C2×C4⋊C4C23×C13111yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C13112yes—
715C2×C42C23×C13111yescharacteristic
716C2×C42C23×C13111yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C13114yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C13112yes—
741C24C2×D4×C13111yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C13112yes—
765#41#41×C13112yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C13111yescharacteristic
776C2×Q8C2×D4×C13111yescharacteristic
777C2×Q8C2×D4×C13111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C13111yescharacteristic
812C2×D4C2×D4×C13111yescharacteristic
813C2×D4C2×D4×C13111yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C13111yescharacteristic
833C22×C4C2×D4×C13111yescharacteristic
834C22×C4C2×D4×C13111yescharacteristic
835C22×C4C2×D4×C13111yescharacteristic
836C22×C4C2×D4×C13111yescharacteristic
837C22×C4C2×D4×C13112yes—
838C22×C4C24×C13111yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C13112yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C13111yescharacteristic
872C4⋊C4C2×D4×C13111yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C13112yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C13111yescharacteristic
915C23#120×C13111yescharacteristic
916C23C22×D4×C13111yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C13112yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C13112yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C13111yescharacteristic
996C2×C4#120×C13111yescharacteristic
997C2×C4C22×D4×C13111yescharacteristic
998C2×C4C22×D4×C13111yescharacteristic
999C2×C4C22×D4×C13111yescharacteristic
1000C2×C4C2×#41×C13111yescharacteristic
1001C2×C4H(5,𝔽2)×C13111yescharacteristic
1002C2×C4H(5,𝔽2)×C13111yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—22no—
1016C22—41no—
1017C22—41no—
1018C22—42no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C13111yescharacteristic
1034C22D42×C13111yescharacteristic
1035C22#546×C13111yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C13111yescharacteristic
1049C4#534×C13111yescharacteristic
1050C4D42×C13111yescharacteristic
1051C4#546×C13111yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2#2410×C13111yescharacteristic
1061C2#3019×C13111yescharacteristic
1062C2#3022×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#3488×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3056×C131C2semidirect
3. C2×#455×C131C2semidirect
4. #3007×C131C2semidirect
5. C2×#421×C131C2semidirect
6. #2620×C131C2semidirect
7. #2039×C131C2semidirect
8. #2037×C131C2semidirect
9. #2007×C131C2semidirect
10. #2004×C131C2semidirect
11. #1900×C131C2semidirect
12. #1897×C131C2semidirect
13. #1882×C131C2semidirect
14. #1859×C131C2semidirect
15. #1792×C131C2semidirect
19. C2×#137×C131C22semidirect
20. C2×#137×C131C22semidirect
21. C22×M16×C131C22semidirect
32. C2×#124×C131C22semidirect
35. C2×C22⋊Q8×C131C22semidirect
39. C2×#117×C131C22semidirect
49. #428×C131C22semidirect
53. C2×#104×C131C22semidirect
54. C2×#104×C131C22semidirect
55. C2×#104×C131C22semidirect
56. C2×#104×C131C22semidirect
57. #419×C131C22semidirect
59. #417×C131C22semidirect
60. #417×C131C22semidirect
61. C2×#100×C131C22semidirect
62. C2×#100×C131C22semidirect
63. #407×C131C22semidirect
66. #391×C131C22semidirect
67. #390×C131C22semidirect
68. #384×C131C22semidirect
69. #343×C131C22semidirect
70. #343×C131C22semidirect
71. #339×C131C22semidirect
72. #339×C131C22semidirect
192. #104×C131D4semidirect
321. M16×C131C2×D4semidirect
363. C42×C131C2×D4semidirect
531. #24471C131direct (N × H)
532. C131#24471direct (N × H)
534. #3056C2×C131semidirect
535. C2×#455C2×C131semidirect
536. #3007C2×C131semidirect
537. C2×#421C2×C131semidirect
538. #2620C2×C131semidirect
539. #2039C2×C131semidirect
540. #2037C2×C131semidirect
541. #2007C2×C131semidirect
542. #2004C2×C131semidirect
543. #1900C2×C131semidirect
544. #1897C2×C131semidirect
545. #1882C2×C131semidirect
546. #1859C2×C131semidirect
547. #1792C2×C131semidirect
551. C2×#137C22×C131semidirect
552. C2×#137C22×C131semidirect
553. C22×M16C22×C131semidirect
564. C2×#124C22×C131semidirect
567. C2×C22⋊Q8C22×C131semidirect
571. C2×#117C22×C131semidirect
581. #428C22×C131semidirect
585. C2×#104C22×C131semidirect
586. C2×#104C22×C131semidirect
587. C2×#104C22×C131semidirect
588. C2×#104C22×C131semidirect
589. #419C22×C131semidirect
591. #417C22×C131semidirect
592. #417C22×C131semidirect
593. C2×#100C22×C131semidirect
594. C2×#100C22×C131semidirect
595. #407C22×C131semidirect
598. #391C22×C131semidirect
599. #390C22×C131semidirect
600. #384C22×C131semidirect
601. #343C22×C131semidirect
602. #343C22×C131semidirect
603. #339C22×C131semidirect
604. #339C22×C131semidirect
724. #104D4×C131semidirect
853. M16C2×D4×C131semidirect
895. C42C2×D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3488×C1312
#3056×C1312
C2×#455×C1312
#3007×C1312
C2×#421×C1312
#2620×C1312
#2039×C1312
#2037×C1312
#2007×C1312
#2004×C1312
#1900×C1312
#1897×C1312
#1882×C1312
#1859×C1312
#1792×C1312
#24471131