Finite Group Databasebeta

← C131×#24467 #45710351

Subgroups — C131×#24467 #45710351

Order 33536.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 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
5C22×#104×C131C211yesmaximal, characteristic, complemented
6#2850×C131C211yesmaximal, characteristic, complemented
7#2040×C131C211yesmaximal, characteristic, complemented
8#2037×C131C211yesmaximal, characteristic, complemented
9#2007×C131C211yesmaximal, characteristic, complemented
10#2004×C131C211yesmaximal, characteristic, complemented
11#1900×C131C211yesmaximal, characteristic, complemented
12#1896×C131C211yesmaximal, characteristic, complemented
13#1882×C131C211yesmaximal, characteristic, complemented
14#1860×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
39C22×C42×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
50C2×#104×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#391×C131C2211yescharacteristic, complemented
65#390×C131C2211yescharacteristic, complemented
66#388×C131—22no—
67#386×C131—22no—
68#382×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×C131—21no—
102C23×C4×C131C2311yescharacteristic
103#137×C131—22no—
104#137×C131—22no—
105#137×C131—22no—
106#137×C131—41no—
107#137×C131—41no—
108#137×C131—41no—
109C2×Q16×C131—21no—
110C2×Q16×C131—21no—
111C2×Q16×C131—21no—
112C2×SD16×C131—21no—
113C2×SD16×C131—21no—
114C2×SD16×C131—21no—
115C2×M16×C131—21no—
116C2×M16×C131—22no—
117C2×M16×C131—41no—
118C2×M16×C131C2311yescharacteristic
119C2×M16×C131C2311yescharacteristic
120C2×M16×C131C2311yescharacteristic
121C2×M16×C131C2311yescharacteristic
122C22×C8×C131—21no—
123#127×C131—22no—
124#127×C131—21no—
125#124×C131—22no—
126#124×C131—21no—
127#124×C131—22no—
128#124×C131—41no—
129#123×C131—22no—
130#123×C131—21no—
131C22⋊Q8×C131—22no—
132C22⋊Q8×C131—21no—
133C22⋊Q8×C131—21no—
134C22⋊Q8×C131—21no—
135C22⋊Q8×C131—21no—
136C22⋊Q8×C131—21no—
137C22⋊Q8×C131—21no—
138C22⋊Q8×C131D411yescharacteristic
139C22⋊Q8×C131D411yescharacteristic
140#121×C131—22no—
141#121×C131—22no—
142#121×C131—22no—
143#121×C131—22no—
144#121×C131—22no—
145#121×C131—21no—
146#121×C131—21no—
147#121×C131—21no—
148#121×C131—21no—
149#121×C131—21no—
150#121×C131—21no—
151#121×C131—22no—
152#121×C131—21no—
153#121×C131—21no—
154#121×C131D411yescharacteristic
155#121×C131D411yescharacteristic
156#120×C131—22no—
157#120×C131—22no—
158#120×C131—22no—
159#120×C131—21no—
160#120×C131—22no—
161C4×Q8×C131—21no—
162C4×D4×C131—22no—
163C4×D4×C131—22no—
164C4×D4×C131—21no—
165C4×D4×C131—22no—
166C4×D4×C131—21no—
167C4×D4×C131—21no—
168#117×C131—21no—
169#117×C131C2311yescharacteristic
170C2×C4⋊C4×C131—21no—
171C2×C4⋊C4×C131—21no—
172C2×C4⋊C4×C131C2311yescharacteristic
173C2×C4⋊C4×C131C2311yescharacteristic
174C2×C22⋊C4×C131—22no—
175C2×C22⋊C4×C131—22no—
176C2×C22⋊C4×C131—22no—
177C2×C22⋊C4×C131—21no—
178C2×C22⋊C4×C131D412yes—
179C2×C42×C131—22no—
180C2×C42×C131—21no—
181C2×C42×C131—41no—
182C2×C42×C131C2311yescharacteristic
183C2×C42×C131C2311yescharacteristic
184#107×C131—21no—
185#106×C131—21no—
186#104×C131—22no—
187#104×C131—22no—
188#104×C131—22no—
189#104×C131—22no—
190#104×C131—41no—
191#104×C131D414yescomplemented
192#103×C131—21no—
193#103×C131—21no—
194#103×C131—21no—
195#103×C131—21no—
196#103×C131—21no—
197#102×C131—21no—
198#102×C131—21no—
199#102×C131—21no—
200#100×C131—22no—
201#100×C131—41no—
202C22⋊C8×C131—21no—
203C22⋊C8×C131—21no—
204#95×C131—22no—
205#95×C131—22no—
206C24×C131—22no—
207C24×C131—21no—
208C24×C131C2×D411yescharacteristic
209C24×C131C2×D412yes—
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—44no—
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—21no—
291C22×C4×C131—22no—
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×C131—42no—
301C22×C4×C131—42no—
302C22×C4×C131—42no—
303C22×C4×C131C2×D411yescharacteristic
304C22×C4×C131C2×D411yescharacteristic
305C22×C4×C131C2×D411yescharacteristic
306C22×C4×C131C2×D411yescharacteristic
307C22×C4×C131C2×D411yescharacteristic
308C22×C4×C131C2×D412yes—
309C22×C4×C131C2411yescharacteristic
310Q16×C131—42no—
311Q16×C131—42no—
312Q16×C131—42no—
313SD16×C131—42no—
314SD16×C131—42no—
315SD16×C131—42no—
316M16×C131—21no—
317M16×C131—21no—
318M16×C131—21no—
319M16×C131—21no—
320M16×C131—21no—
321M16×C131—21no—
322M16×C131—21no—
323M16×C131—42no—
324M16×C131C2×D412yescomplemented
325C2×C8×C131—21no—
326C2×C8×C131—21no—
327C2×C8×C131—21no—
328C2×C8×C131—21no—
329C2×C8×C131—42no—
330C4⋊C4×C131—22no—
331C4⋊C4×C131—22no—
332C4⋊C4×C131—21no—
333C4⋊C4×C131—21no—
334C4⋊C4×C131—21no—
335C4⋊C4×C131—21no—
336C4⋊C4×C131—21no—
337C4⋊C4×C131—21no—
338C4⋊C4×C131—41no—
339C4⋊C4×C131—41no—
340C4⋊C4×C131C2×D411yescharacteristic
341C4⋊C4×C131C2×D411yescharacteristic
342C22⋊C4×C131—22no—
343C22⋊C4×C131—22no—
344C22⋊C4×C131—22no—
345C22⋊C4×C131—22no—
346C22⋊C4×C131—22no—
347C22⋊C4×C131—21no—
348C22⋊C4×C131—21no—
349C22⋊C4×C131—21no—
350C22⋊C4×C131—21no—
351C22⋊C4×C131—22no—
352C22⋊C4×C131—22no—
353C22⋊C4×C131—21no—
354C22⋊C4×C131—44no—
355C22⋊C4×C131—44no—
356C22⋊C4×C131—41no—
357C22⋊C4×C131—41no—
358C42×C131—22no—
359C42×C131—21no—
360C42×C131—21no—
361C42×C131—21no—
362C42×C131—21no—
363C42×C131—42no—
364C42×C131C2×D412yescomplemented
365C23×C131—21no—
366C23×C131—21no—
367C23×C131—21no—
368C23×C131—22no—
369C23×C131—22no—
370C23×C131—21no—
371C23×C131—21no—
372C23×C131—22no—
373C23×C131—22no—
374C23×C131—41no—
375C23×C131—42no—
376C23×C131—44no—
377C23×C131—42no—
378C23×C131—42no—
379C23×C131—42no—
380C23×C131—81no—
381C23×C131—82no—
382C23×C131—82no—
383C23×C131#12011yescharacteristic
384C23×C131#12011yescharacteristic
385C23×C131C22×D411yescharacteristic
386Q8×C131—21no—
387Q8×C131—21no—
388Q8×C131—21no—
389Q8×C131—21no—
390Q8×C131—21no—
391Q8×C131—42no—
392Q8×C131—41no—
393Q8×C131—41no—
394Q8×C131—41no—
395Q8×C131—41no—
396Q8×C131#12112yes—
397D4×C131—22no—
398D4×C131—22no—
399D4×C131—21no—
400D4×C131—21no—
401D4×C131—21no—
402D4×C131—21no—
403D4×C131—21no—
404D4×C131—42no—
405D4×C131—42no—
406D4×C131—44no—
407D4×C131—42no—
408D4×C131—44no—
409D4×C131—41no—
410D4×C131—41no—
411D4×C131—41no—
412D4×C131—41no—
413D4×C131—44no—
414D4×C131—42no—
415D4×C131—41no—
416D4×C131—41no—
417D4×C131—41no—
418D4×C131—41no—
419D4×C131—81no—
420D4×C131—82no—
421D4×C131—82no—
422D4×C131—82no—
423D4×C131—82no—
424D4×C131#12112yes—
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—21no—
434C2×C4×C131—22no—
435C2×C4×C131—21no—
436C2×C4×C131—21no—
437C2×C4×C131—22no—
438C2×C4×C131—22no—
439C2×C4×C131—21no—
440C2×C4×C131—22no—
441C2×C4×C131—21no—
442C2×C4×C131—21no—
443C2×C4×C131—21no—
444C2×C4×C131—22no—
445C2×C4×C131—42no—
446C2×C4×C131—42no—
447C2×C4×C131—42no—
448C2×C4×C131—44no—
449C2×C4×C131—41no—
450C2×C4×C131—41no—
451C2×C4×C131—41no—
452C2×C4×C131—48no—
453C2×C4×C131—41no—
454C2×C4×C131—41no—
455C2×C4×C131—41no—
456C2×C4×C131—41no—
457C2×C4×C131—41no—
458C2×C4×C131—42no—
459C2×C4×C131—42no—
460C2×C4×C131—41no—
461C2×C4×C131—41no—
462C2×C4×C131—41no—
463C2×C4×C131—41no—
464C2×C4×C131—82no—
465C2×C4×C131#12011yescharacteristic
466C2×C4×C131#12011yescharacteristic
467C2×C4×C131C22×D411yescharacteristic
468C2×C4×C131C22×D411yescharacteristic
469C2×C4×C131C22×D411yescharacteristic
470C2×C4×C131C2×#4111yescharacteristic
471C2×C4×C131H(5,𝔽2)11yescharacteristic
472C2×C4×C131H(5,𝔽2)11yescharacteristic
473C8×C131—22no—
474C8×C131—41no—
475C8×C131—41no—
476C8×C131—41no—
477C22×C131—21no—
478C22×C131—21no—
479C22×C131—21no—
480C22×C131—21no—
481C22×C131—21no—
482C22×C131—22no—
483C22×C131—21no—
484C22×C131—21no—
485C22×C131—42no—
486C22×C131—42no—
487C22×C131—41no—
488C22×C131—41no—
489C22×C131—41no—
490C22×C131—41no—
491C22×C131—42no—
492C22×C131—42no—
493C22×C131—41no—
494C22×C131—41no—
495C22×C131—41no—
496C22×C131—42no—
497C22×C131—41no—
498C22×C131—84no—
499C22×C131—82no—
500C22×C131—82no—
501C22×C131—164no—
502C22×C131#45512yescomplemented
503C22×C131C2×#12011yescharacteristic
504C22×C131D4211yescharacteristic
505C22×C131#54611yescharacteristic
506C4×C131—21no—
507C4×C131—21no—
508C4×C131—22no—
509C4×C131—42no—
510C4×C131—42no—
511C4×C131—41no—
512C4×C131—41no—
513C4×C131—42no—
514C4×C131—41no—
515C4×C131—41no—
516C4×C131—81no—
517C4×C131—81no—
518C4×C131C2×#12111yescharacteristic
519C4×C131#53411yescharacteristic
520C4×C131D4211yescharacteristic
521C4×C131#54611yescharacteristic
522C2×C131—21no—
523C2×C131—21no—
524C2×C131—22no—
525C2×C131—41no—
526C2×C131—42no—
527C2×C131—81no—
528C2×C131—82no—
529C2×C131—81no—
530C2×C131#241011yescharacteristic
531C2×C131C2×#45511yescharacteristic
532C2×C131#301811yescharacteristic
533#24467C13111yesmaximal, characteristic, direct product factor, Sylow
534C131#2446711yescharacteristic, direct product factor, Sylow
535#3488C2×C13111yescharacteristic
536#3056C2×C13111yescharacteristic, complemented
537C2×#455C2×C13111yescharacteristic, complemented
538#3007C2×C13111yescharacteristic, complemented
539C22×#104C2×C13111yescharacteristic, complemented
540#2850C2×C13111yescharacteristic, complemented
541#2040C2×C13111yescharacteristic, complemented
542#2037C2×C13111yescharacteristic, complemented
543#2007C2×C13111yescharacteristic, complemented
544#2004C2×C13111yescharacteristic, complemented
545#1900C2×C13111yescharacteristic, complemented
546#1896C2×C13111yescharacteristic, complemented
547#1882C2×C13111yescharacteristic, complemented
548#1860C2×C13111yescharacteristic, complemented
549#1792C2×C13111yescharacteristic, complemented
550C2×H(5,𝔽2)C22×C13111yescharacteristic
551C22×#41C22×C13111yescharacteristic
552C2×#137C22×C13111yescharacteristic
553C2×#137C22×C13111yescharacteristic, complemented
554C2×#137C22×C13111yescharacteristic, complemented
555C22×M16C22×C13111yescharacteristic, complemented
556#550—21no—
557#548—21no—
558#546—21no—
559#546—22no—
560D42—22no—
561D42—21no—
562#537—21no—
563#537C22×C13111yescharacteristic
564#535—21no—
565#535C22×C13111yescharacteristic
566C2×#124C22×C13111yescharacteristic, complemented
567#525—21no—
568#525C22×C13111yescharacteristic
569C2×C22⋊Q8C22×C13111yescharacteristic, complemented
570C2×#121—21no—
571C2×#121C22×C13111yescharacteristic
572#520C22×C13111yescharacteristic
573C22×C42C22×C13111yescharacteristic, complemented
574#470—21no—
575#468—21no—
576#467—21no—
577#465—21no—
578#455—24no—
579#452—21no—
580#452—21no—
581#451—21no—
582#450—21no—
583#428C22×C13111yescharacteristic, complemented
584C2×#104—24no—
585C2×#104C22×C13111yescharacteristic
586C2×#104C22×C13111yescharacteristic
587C2×#104C22×C13111yescharacteristic, complemented
588C2×#104C22×C13111yescharacteristic, complemented
589C2×#104C22×C13111yescharacteristic, complemented
590C2×#104C22×C13111yescharacteristic, complemented
591#419C22×C13111yescharacteristic, complemented
592#417C22×C13111yescharacteristic
593#417C22×C13111yescharacteristic, complemented
594#417C22×C13111yescharacteristic, complemented
595C2×#100C22×C13111yescharacteristic, complemented
596C2×#100C22×C13111yescharacteristic, complemented
597#407C22×C13111yescharacteristic, complemented
598#391C22×C13111yescharacteristic, complemented
599#390C22×C13111yescharacteristic, complemented
600#388—22no—
601#386—22no—
602#382C22×C13111yescharacteristic, complemented
603#343C22×C13111yescharacteristic, complemented
604#343C22×C13111yescharacteristic, complemented
605#339C22×C13111yescharacteristic, complemented
606#339C22×C13111yescharacteristic, complemented
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C13111yescharacteristic
620C2×#41D4×C13111yescharacteristic
621C2×#41C23×C13111yescharacteristic
622C2×#41C23×C13111yescharacteristic
623C2×#41C23×C13111yescharacteristic
624C22×Q8D4×C13111yescharacteristic
625C22×Q8C23×C13111yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C13111yescharacteristic
632C22×D4D4×C13112yes—
633C22×D4C23×C13111yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C13111yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C13111yescharacteristic
653C2×M16C23×C13111yescharacteristic
654C2×M16C23×C13111yescharacteristic
655C2×M16C23×C13111yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C13111yescharacteristic
673C22⋊Q8D4×C13111yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C13111yescharacteristic
689#121D4×C13111yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C13111yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C13111yescharacteristic
707C2×C4⋊C4C23×C13111yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C13112yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C13111yescharacteristic
717C2×C42C23×C13111yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C13114yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C13111yescharacteristic
743C24C2×D4×C13112yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C13112yes—
767#41#41×C13112yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C13111yescharacteristic
778C2×Q8C2×D4×C13111yescharacteristic
779C2×Q8C2×D4×C13111yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C13111yescharacteristic
814C2×D4C2×D4×C13111yescharacteristic
815C2×D4C2×D4×C13111yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C13111yescharacteristic
838C22×C4C2×D4×C13111yescharacteristic
839C22×C4C2×D4×C13111yescharacteristic
840C22×C4C2×D4×C13111yescharacteristic
841C22×C4C2×D4×C13111yescharacteristic
842C22×C4C2×D4×C13112yes—
843C22×C4C24×C13111yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C13112yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C13111yescharacteristic
875C4⋊C4C2×D4×C13111yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C13112yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C13111yescharacteristic
918C23#120×C13111yescharacteristic
919C23C22×D4×C13111yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C13112yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C13112yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C13111yescharacteristic
1000C2×C4#120×C13111yescharacteristic
1001C2×C4C22×D4×C13111yescharacteristic
1002C2×C4C22×D4×C13111yescharacteristic
1003C2×C4C22×D4×C13111yescharacteristic
1004C2×C4C2×#41×C13111yescharacteristic
1005C2×C4H(5,𝔽2)×C13111yescharacteristic
1006C2×C4H(5,𝔽2)×C13111yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—22no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—42no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22#455×C13112yescomplemented
1037C22C2×#120×C13111yescharacteristic
1038C22D42×C13111yescharacteristic
1039C22#546×C13111yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—41no—
1047C4—41no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C13111yescharacteristic
1053C4#534×C13111yescharacteristic
1054C4D42×C13111yescharacteristic
1055C4#546×C13111yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2#2410×C13111yescharacteristic
1065C2C2×#455×C13111yescharacteristic
1066C2#3018×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. C22×#104×C131C2semidirect
6. #2850×C131C2semidirect
7. #2040×C131C2semidirect
8. #2037×C131C2semidirect
9. #2007×C131C2semidirect
10. #2004×C131C2semidirect
11. #1900×C131C2semidirect
12. #1896×C131C2semidirect
13. #1882×C131C2semidirect
14. #1860×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. C22×C42×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
64. #391×C131C22semidirect
65. #390×C131C22semidirect
68. #382×C131C22semidirect
69. #343×C131C22semidirect
70. #343×C131C22semidirect
71. #339×C131C22semidirect
72. #339×C131C22semidirect
191. #104×C131D4semidirect
324. M16×C131C2×D4semidirect
364. C42×C131C2×D4semidirect
502. C22×C131#455semidirect
533. #24467C131direct (N × H)
534. C131#24467direct (N × H)
536. #3056C2×C131semidirect
537. C2×#455C2×C131semidirect
538. #3007C2×C131semidirect
539. C22×#104C2×C131semidirect
540. #2850C2×C131semidirect
541. #2040C2×C131semidirect
542. #2037C2×C131semidirect
543. #2007C2×C131semidirect
544. #2004C2×C131semidirect
545. #1900C2×C131semidirect
546. #1896C2×C131semidirect
547. #1882C2×C131semidirect
548. #1860C2×C131semidirect
549. #1792C2×C131semidirect
553. C2×#137C22×C131semidirect
554. C2×#137C22×C131semidirect
555. C22×M16C22×C131semidirect
566. C2×#124C22×C131semidirect
569. C2×C22⋊Q8C22×C131semidirect
573. C22×C42C22×C131semidirect
583. #428C22×C131semidirect
587. C2×#104C22×C131semidirect
588. C2×#104C22×C131semidirect
589. C2×#104C22×C131semidirect
590. C2×#104C22×C131semidirect
591. #419C22×C131semidirect
593. #417C22×C131semidirect
594. #417C22×C131semidirect
595. C2×#100C22×C131semidirect
596. C2×#100C22×C131semidirect
597. #407C22×C131semidirect
598. #391C22×C131semidirect
599. #390C22×C131semidirect
602. #382C22×C131semidirect
603. #343C22×C131semidirect
604. #343C22×C131semidirect
605. #339C22×C131semidirect
606. #339C22×C131semidirect
725. #104D4×C131semidirect
858. M16C2×D4×C131semidirect
898. C42C2×D4×C131semidirect
1036. C22#455×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
C22×#104×C1312
#2850×C1312
#2040×C1312
#2037×C1312
#2007×C1312
#2004×C1312
#1900×C1312
#1896×C1312
#1882×C1312
#1860×C1312
#1792×C1312
#24467131