Finite Group Databasebeta

← C131×#18414 #45704298

Subgroups — C131×#18414 #45704298

Order 33536.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3534×C131C211yesmaximal, characteristic, complemented
2#3194×C131C211yesmaximal, characteristic, complemented
3#3186×C131C211yesmaximal, characteristic, complemented
4#2661×C131C211yesmaximal, characteristic, complemented
5#1612×C131C211yesmaximal, characteristic, complemented
6#1610×C131C211yesmaximal, characteristic, complemented
7#1609×C131C211yesmaximal, characteristic, complemented
8#1607×C131C211yesmaximal, characteristic, complemented
9#1600×C131C211yesmaximal, characteristic, complemented
10#1598×C131C211yesmaximal, characteristic, complemented
11#1597×C131C211yesmaximal, characteristic, complemented
12#1595×C131C211yesmaximal, characteristic, complemented
13#1507×C131C211yesmaximal, characteristic, complemented
14#1501×C131C211yesmaximal, characteristic, complemented
15#1468×C131C211yesmaximal, characteristic, complemented
16#562×C131—21no—
17#560×C131—21no—
18#553×C131—21no—
19#551×C131—21no—
20#546×C131—21no—
21#546×C131—21no—
22#546×C131—21no—
23D42×C131—21no—
24#540×C131—21no—
25#539×C131—21no—
26#539×C131C2211yescharacteristic
27#538×C131—21no—
28#538×C131C2211yescharacteristic
29#537×C131C2211yescharacteristic
30#534×C131—21no—
31#534×C131C2211yescharacteristic
32#525×C131C2211yescharacteristic
33C2×#123×C131C2211yescharacteristic
34C2×#121×C131C2211yescharacteristic
35C2×#121×C131C2211yescharacteristic, complemented
36#483×C131C2211yescharacteristic, complemented
37#482×C131—21no—
38#480×C131—21no—
39#480×C131C2211yescharacteristic
40#480×C131C2211yescharacteristic, complemented
41#480×C131C2211yescharacteristic, complemented
42#469×C131—21no—
43#468×C131—21no—
44#466×C131—21no—
45#466×C131—21no—
46#450×C131C2211yescharacteristic, complemented
47#449×C131—21no—
48#447×C131—21no—
49#447×C131C2211yescharacteristic
50#447×C131C2211yescharacteristic, complemented
51#447×C131C2211yescharacteristic, complemented
52#407×C131C2211yescharacteristic, complemented
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54#398×C131C2211yescharacteristic, complemented
55#397×C131C2211yescharacteristic, complemented
56#394×C131—21no—
57#394×C131C2211yescharacteristic, complemented
58#392×C131—21no—
59#392×C131C2211yescharacteristic, complemented
60#390×C131—21no—
61#388×C131—21no—
62C4×C22⋊C4×C131C2211yescharacteristic, complemented
63#328×C131C2211yescharacteristic, complemented
64#328×C131C2211yescharacteristic, complemented
65#327×C131C2211yescharacteristic
66#327×C131C2211yescharacteristic
67#327×C131C2211yescharacteristic, complemented
68#327×C131C2211yescharacteristic, complemented
69#327×C131C2211yescharacteristic, complemented
70#327×C131C2211yescharacteristic, complemented
71#324×C131C2211yescharacteristic, complemented
72#324×C131C2211yescharacteristic, complemented
73#323×C131C2211yescharacteristic, complemented
74#323×C131C2211yescharacteristic, complemented
75C2×#41×C131—21no—
76C2×#41×C131D411yescharacteristic, complemented
77C22×D4×C131—21no—
78C22×D4×C131—21no—
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131—21no—
82C22×D4×C131D411yescharacteristic
83C22×D4×C131D411yescharacteristic, complemented
84C22×D4×C131C2311yescharacteristic
85C23×C4×C131C2311yescharacteristic
86C2×SD16×C131—21no—
87C2×D8×C131—21no—
88C2×D8×C131—21no—
89C2×D8×C131—21no—
90C2×M16×C131—21no—
91C22×C8×C131—21no—
92#127×C131—21no—
93#126×C131—21no—
94#126×C131—21no—
95#126×C131—21no—
96#126×C131—21no—
97#125×C131—21no—
98#125×C131—21no—
99#124×C131—21no—
100#124×C131—21no—
101#124×C131—21no—
102#123×C131—21no—
103#123×C131—21no—
104#123×C131—21no—
105#123×C131—21no—
106#123×C131—21no—
107#123×C131—21no—
108#123×C131—21no—
109#123×C131—21no—
110#123×C131—21no—
111#123×C131—21no—
112#123×C131—21no—
113#123×C131—21no—
114#123×C131—21no—
115#123×C131—21no—
116C22⋊Q8×C131—21no—
117C22⋊Q8×C131—21no—
118C22⋊Q8×C131—21no—
119C22⋊Q8×C131—21no—
120C22⋊Q8×C131—21no—
121C22⋊Q8×C131D411yescharacteristic, complemented
122C22⋊Q8×C131C2311yescharacteristic
123#121×C131—21no—
124#121×C131—21no—
125#121×C131—21no—
126#121×C131—21no—
127#121×C131—21no—
128#121×C131—21no—
129#121×C131—21no—
130#121×C131—21no—
131#121×C131—21no—
132#121×C131—21no—
133#121×C131—21no—
134#121×C131—21no—
135#121×C131—21no—
136#121×C131—21no—
137#121×C131—21no—
138#121×C131—21no—
139#121×C131—21no—
140#121×C131—21no—
141#121×C131—21no—
142#121×C131D411yescharacteristic, complemented
143#121×C131D411yescharacteristic, complemented
144#121×C131D411yescharacteristic, complemented
145#121×C131C2311yescharacteristic
146#121×C131C2311yescharacteristic
147#121×C131C2311yescharacteristic
148#120×C131—21no—
149#120×C131—21no—
150#120×C131—21no—
151#120×C131—21no—
152#120×C131—21no—
153#120×C131—21no—
154#120×C131—21no—
155#120×C131—21no—
156C4×D4×C131—21no—
157C4×D4×C131—21no—
158C4×D4×C131—21no—
159C4×D4×C131—21no—
160C4×D4×C131—21no—
161C4×D4×C131—21no—
162C4×D4×C131—21no—
163C4×D4×C131—21no—
164#117×C131—21no—
165#117×C131D411yescharacteristic, complemented
166C2×C4⋊C4×C131—21no—
167C2×C4⋊C4×C131D411yescharacteristic
168C2×C4⋊C4×C131D411yescharacteristic, complemented
169C2×C4⋊C4×C131C2311yescharacteristic
170C2×C4⋊C4×C131C2311yescharacteristic
171C2×C22⋊C4×C131—21no—
172C2×C22⋊C4×C131—21no—
173C2×C22⋊C4×C131—21no—
174C2×C22⋊C4×C131—21no—
175C2×C22⋊C4×C131—21no—
176C2×C22⋊C4×C131—21no—
177C2×C22⋊C4×C131—21no—
178C2×C22⋊C4×C131—21no—
179C2×C22⋊C4×C131—21no—
180C2×C22⋊C4×C131D411yescharacteristic
181C2×C22⋊C4×C131D411yescharacteristic
182C2×C22⋊C4×C131C2311yescharacteristic
183C2×C42×C131—21no—
184#107×C131—21no—
185#107×C131—21no—
186#107×C131—21no—
187#106×C131—21no—
188#103×C131—21no—
189#102×C131—21no—
190#102×C131—21no—
191#102×C131—21no—
192#102×C131—21no—
193#102×C131—21no—
194#102×C131—21no—
195#102×C131—21no—
196C22⋊C8×C131—21no—
197C22⋊C8×C131—21no—
198C22⋊C8×C131C2311yescharacteristic
199C22⋊C8×C131C2311yescharacteristic
200C22⋊C8×C131C2311yescharacteristic
201C22⋊C8×C131C2311yescharacteristic
202#95×C131—21no—
203#95×C131—21no—
204#95×C131C2311yescharacteristic
205#95×C131C2311yescharacteristic
206C24×C131—21no—
207C24×C131—21no—
208C24×C131—21no—
209C24×C131C2×D411yescharacteristic
210C24×C131C2×D411yescharacteristic
211#41×C131—81no—
212#41×C131—81no—
213#41×C131—81no—
214C2×Q8×C131—21no—
215C2×Q8×C131C2×D411yescharacteristic
216C2×D4×C131—21no—
217C2×D4×C131—21no—
218C2×D4×C131—21no—
219C2×D4×C131—21no—
220C2×D4×C131—21no—
221C2×D4×C131—21no—
222C2×D4×C131—21no—
223C2×D4×C131—21no—
224C2×D4×C131—21no—
225C2×D4×C131—21no—
226C2×D4×C131—21no—
227C2×D4×C131—21no—
228C2×D4×C131—21no—
229C2×D4×C131—21no—
230C2×D4×C131—21no—
231C2×D4×C131—21no—
232C2×D4×C131—21no—
233C2×D4×C131—21no—
234C2×D4×C131—21no—
235C2×D4×C131—42no—
236C2×D4×C131—41no—
237C2×D4×C131—41no—
238C2×D4×C131—81no—
239C2×D4×C131—81no—
240C2×D4×C131—81no—
241C2×D4×C131—81no—
242C2×D4×C131—81no—
243C2×D4×C131—81no—
244C2×D4×C131—81no—
245C2×D4×C131—81no—
246C2×D4×C131—81no—
247C2×D4×C131—81no—
248C2×D4×C131—81no—
249C2×D4×C131—82no—
250C2×D4×C131C2×D411yescharacteristic
251C2×D4×C131C2×D411yescharacteristic
252C2×D4×C131C2×D411yescharacteristic
253C22×C4×C131—21no—
254C22×C4×C131—21no—
255C22×C4×C131—21no—
256C22×C4×C131—21no—
257C22×C4×C131—21no—
258C22×C4×C131—21no—
259C22×C4×C131—21no—
260C22×C4×C131—21no—
261C22×C4×C131—21no—
262C22×C4×C131—21no—
263C22×C4×C131—81no—
264C22×C4×C131C2×D411yescharacteristic
265C22×C4×C131C2×D411yescharacteristic
266C22×C4×C131C2×D411yescharacteristic
267C22×C4×C131C2×D411yescharacteristic
268C22×C4×C131C2×D411yescharacteristic
269C22×C4×C131C2×D411yescharacteristic
270C22×C4×C131C2×D411yescharacteristic
271C22×C4×C131C2×D411yescharacteristic
272C22×C4×C131C2411yescharacteristic
273SD16×C131—81no—
274D8×C131—81no—
275D8×C131—81no—
276D8×C131—81no—
277M16×C131—81no—
278C2×C8×C131—21no—
279C2×C8×C131—21no—
280C2×C8×C131—21no—
281C2×C8×C131—21no—
282C2×C8×C131—81no—
283C4⋊C4×C131—21no—
284C4⋊C4×C131—21no—
285C4⋊C4×C131—21no—
286C4⋊C4×C131—21no—
287C4⋊C4×C131—21no—
288C4⋊C4×C131—21no—
289C4⋊C4×C131—21no—
290C4⋊C4×C131—21no—
291C4⋊C4×C131—21no—
292C4⋊C4×C131—21no—
293C4⋊C4×C131—21no—
294C4⋊C4×C131—21no—
295C4⋊C4×C131—21no—
296C4⋊C4×C131—21no—
297C4⋊C4×C131—21no—
298C4⋊C4×C131—81no—
299C4⋊C4×C131C2×D411yescharacteristic
300C4⋊C4×C131C2×D411yescharacteristic
301C4⋊C4×C131C2×D411yescharacteristic
302C4⋊C4×C131C2×D411yescharacteristic
303C22⋊C4×C131—21no—
304C22⋊C4×C131—21no—
305C22⋊C4×C131—21no—
306C22⋊C4×C131—21no—
307C22⋊C4×C131—21no—
308C22⋊C4×C131—21no—
309C22⋊C4×C131—21no—
310C22⋊C4×C131—21no—
311C22⋊C4×C131—21no—
312C22⋊C4×C131—21no—
313C22⋊C4×C131—21no—
314C22⋊C4×C131—21no—
315C22⋊C4×C131—21no—
316C22⋊C4×C131—21no—
317C22⋊C4×C131—21no—
318C22⋊C4×C131—21no—
319C22⋊C4×C131—21no—
320C22⋊C4×C131—21no—
321C22⋊C4×C131—21no—
322C22⋊C4×C131—21no—
323C22⋊C4×C131—21no—
324C22⋊C4×C131—21no—
325C22⋊C4×C131—21no—
326C22⋊C4×C131—21no—
327C22⋊C4×C131—21no—
328C22⋊C4×C131—42no—
329C22⋊C4×C131—42no—
330C22⋊C4×C131—41no—
331C22⋊C4×C131—41no—
332C22⋊C4×C131—81no—
333C22⋊C4×C131—81no—
334C22⋊C4×C131—81no—
335C42×C131—21no—
336C42×C131—21no—
337C42×C131—21no—
338C42×C131—81no—
339C23×C131—21no—
340C23×C131—21no—
341C23×C131—21no—
342C23×C131—21no—
343C23×C131—21no—
344C23×C131—21no—
345C23×C131—21no—
346C23×C131—21no—
347C23×C131—41no—
348C23×C131—41no—
349C23×C131—42no—
350C23×C131—41no—
351C23×C131—41no—
352C23×C131—41no—
353C23×C131—41no—
354C23×C131—41no—
355C23×C131—41no—
356C23×C131—41no—
357C23×C131—41no—
358C23×C131—41no—
359C23×C131—81no—
360C23×C131—81no—
361C23×C131—81no—
362C23×C131—81no—
363C23×C131—81no—
364C23×C131#12011yescharacteristic
365C23×C131#12011yescharacteristic
366C23×C131C22×D411yescharacteristic
367Q8×C131—41no—
368Q8×C131—81no—
369D4×C131—41no—
370D4×C131—41no—
371D4×C131—41no—
372D4×C131—41no—
373D4×C131—41no—
374D4×C131—41no—
375D4×C131—41no—
376D4×C131—42no—
377D4×C131—42no—
378D4×C131—41no—
379D4×C131—41no—
380D4×C131—41no—
381D4×C131—41no—
382D4×C131—41no—
383D4×C131—41no—
384D4×C131—81no—
385D4×C131—81no—
386D4×C131—81no—
387D4×C131—81no—
388D4×C131—81no—
389D4×C131—81no—
390D4×C131—81no—
391D4×C131—81no—
392D4×C131—81no—
393D4×C131—81no—
394D4×C131—81no—
395D4×C131—81no—
396D4×C131—84no—
397D4×C131—82no—
398D4×C131—82no—
399C2×C4×C131—22no—
400C2×C4×C131—21no—
401C2×C4×C131—21no—
402C2×C4×C131—21no—
403C2×C4×C131—21no—
404C2×C4×C131—21no—
405C2×C4×C131—21no—
406C2×C4×C131—21no—
407C2×C4×C131—21no—
408C2×C4×C131—21no—
409C2×C4×C131—21no—
410C2×C4×C131—41no—
411C2×C4×C131—41no—
412C2×C4×C131—41no—
413C2×C4×C131—41no—
414C2×C4×C131—41no—
415C2×C4×C131—41no—
416C2×C4×C131—41no—
417C2×C4×C131—41no—
418C2×C4×C131—41no—
419C2×C4×C131—41no—
420C2×C4×C131—41no—
421C2×C4×C131—41no—
422C2×C4×C131—41no—
423C2×C4×C131—41no—
424C2×C4×C131—41no—
425C2×C4×C131—41no—
426C2×C4×C131—81no—
427C2×C4×C131—81no—
428C2×C4×C131—81no—
429C2×C4×C131—81no—
430C2×C4×C131—81no—
431C2×C4×C131—81no—
432C2×C4×C131—81no—
433C2×C4×C131#12011yescharacteristic
434C2×C4×C131#12011yescharacteristic
435C2×C4×C131C22×D411yescharacteristic
436C2×C4×C131C22×D411yescharacteristic
437C8×C131—41no—
438C8×C131—41no—
439C8×C131—41no—
440C8×C131—41no—
441C22×C131—21no—
442C22×C131—21no—
443C22×C131—21no—
444C22×C131—21no—
445C22×C131—21no—
446C22×C131—21no—
447C22×C131—21no—
448C22×C131—21no—
449C22×C131—41no—
450C22×C131—41no—
451C22×C131—41no—
452C22×C131—41no—
453C22×C131—41no—
454C22×C131—41no—
455C22×C131—41no—
456C22×C131—41no—
457C22×C131—41no—
458C22×C131—41no—
459C22×C131—41no—
460C22×C131—41no—
461C22×C131—81no—
462C22×C131—81no—
463C22×C131—81no—
464C22×C131—81no—
465C22×C131—81no—
466C22×C131—81no—
467C22×C131—81no—
468C22×C131—81no—
469C22×C131—81no—
470C22×C131—81no—
471C22×C131—81no—
472C22×C131—162no—
473C22×C131—162no—
474C22×C131C2×#12011yescharacteristic
475C22×C131#57611yescharacteristic
476C22×C131#57611yescharacteristic
477C4×C131—21no—
478C4×C131—21no—
479C4×C131—21no—
480C4×C131—21no—
481C4×C131—42no—
482C4×C131—41no—
483C4×C131—41no—
484C4×C131—41no—
485C4×C131—41no—
486C4×C131—41no—
487C4×C131—41no—
488C4×C131—41no—
489C4×C131—41no—
490C4×C131—81no—
491C4×C131—81no—
492C2×C131—21no—
493C2×C131—21no—
494C2×C131—41no—
495C2×C131—41no—
496C2×C131—81no—
497C2×C131—81no—
498C2×C131—81no—
499C2×C131—81no—
500C2×C131—161no—
501C2×C131#300811yescharacteristic
502C2×C131#301811yescharacteristic
503C2×C131#302611yescharacteristic
504#18414C13111yesmaximal, characteristic, direct product factor, Sylow
505C131#1841411yescharacteristic, direct product factor, Sylow
506#3534C2×C13111yescharacteristic, complemented
507#3194C2×C13111yescharacteristic, complemented
508#3186C2×C13111yescharacteristic, complemented
509#2661C2×C13111yescharacteristic, complemented
510#1612C2×C13111yescharacteristic, complemented
511#1610C2×C13111yescharacteristic, complemented
512#1609C2×C13111yescharacteristic, complemented
513#1607C2×C13111yescharacteristic, complemented
514#1600C2×C13111yescharacteristic, complemented
515#1598C2×C13111yescharacteristic, complemented
516#1597C2×C13111yescharacteristic, complemented
517#1595C2×C13111yescharacteristic, complemented
518#1507C2×C13111yescharacteristic, complemented
519#1501C2×C13111yescharacteristic, complemented
520#1468C2×C13111yescharacteristic, complemented
521#562—21no—
522#560—21no—
523#553—21no—
524#551—21no—
525#546—21no—
526#546—21no—
527#546—21no—
528D42—21no—
529#540—21no—
530#539—21no—
531#539C22×C13111yescharacteristic
532#538—21no—
533#538C22×C13111yescharacteristic
534#537C22×C13111yescharacteristic
535#534—21no—
536#534C22×C13111yescharacteristic
537#525C22×C13111yescharacteristic
538C2×#123C22×C13111yescharacteristic
539C2×#121C22×C13111yescharacteristic
540C2×#121C22×C13111yescharacteristic, complemented
541#483C22×C13111yescharacteristic, complemented
542#482—21no—
543#480—21no—
544#480C22×C13111yescharacteristic
545#480C22×C13111yescharacteristic, complemented
546#480C22×C13111yescharacteristic, complemented
547#469—21no—
548#468—21no—
549#466—21no—
550#466—21no—
551#450C22×C13111yescharacteristic, complemented
552#449—21no—
553#447—21no—
554#447C22×C13111yescharacteristic
555#447C22×C13111yescharacteristic, complemented
556#447C22×C13111yescharacteristic, complemented
557#407C22×C13111yescharacteristic, complemented
558C2×C22⋊C8C22×C13111yescharacteristic, complemented
559#398C22×C13111yescharacteristic, complemented
560#397C22×C13111yescharacteristic, complemented
561#394—21no—
562#394C22×C13111yescharacteristic, complemented
563#392—21no—
564#392C22×C13111yescharacteristic, complemented
565#390—21no—
566#388—21no—
567C4×C22⋊C4C22×C13111yescharacteristic, complemented
568#328C22×C13111yescharacteristic, complemented
569#328C22×C13111yescharacteristic, complemented
570#327C22×C13111yescharacteristic
571#327C22×C13111yescharacteristic
572#327C22×C13111yescharacteristic, complemented
573#327C22×C13111yescharacteristic, complemented
574#327C22×C13111yescharacteristic, complemented
575#327C22×C13111yescharacteristic, complemented
576#324C22×C13111yescharacteristic, complemented
577#324C22×C13111yescharacteristic, complemented
578#323C22×C13111yescharacteristic, complemented
579#323C22×C13111yescharacteristic, complemented
580C2×#41—21no—
581C2×#41D4×C13111yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C13111yescharacteristic
588C22×D4D4×C13111yescharacteristic, complemented
589C22×D4C23×C13111yescharacteristic
590C23×C4C23×C13111yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C13111yescharacteristic, complemented
627C22⋊Q8C23×C13111yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C13111yescharacteristic, complemented
648#121D4×C13111yescharacteristic, complemented
649#121D4×C13111yescharacteristic, complemented
650#121C23×C13111yescharacteristic
651#121C23×C13111yescharacteristic
652#121C23×C13111yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C13111yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C13111yescharacteristic
673C2×C4⋊C4D4×C13111yescharacteristic, complemented
674C2×C4⋊C4C23×C13111yescharacteristic
675C2×C4⋊C4C23×C13111yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C13111yescharacteristic
686C2×C22⋊C4D4×C13111yescharacteristic
687C2×C22⋊C4C23×C13111yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C13111yescharacteristic
704C22⋊C8C23×C13111yescharacteristic
705C22⋊C8C23×C13111yescharacteristic
706C22⋊C8C23×C13111yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C13111yescharacteristic
710#95C23×C13111yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C13111yescharacteristic
715C24C2×D4×C13111yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C13111yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C13111yescharacteristic
756C2×D4C2×D4×C13111yescharacteristic
757C2×D4C2×D4×C13111yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C13111yescharacteristic
770C22×C4C2×D4×C13111yescharacteristic
771C22×C4C2×D4×C13111yescharacteristic
772C22×C4C2×D4×C13111yescharacteristic
773C22×C4C2×D4×C13111yescharacteristic
774C22×C4C2×D4×C13111yescharacteristic
775C22×C4C2×D4×C13111yescharacteristic
776C22×C4C2×D4×C13111yescharacteristic
777C22×C4C24×C13111yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C13111yescharacteristic
805C4⋊C4C2×D4×C13111yescharacteristic
806C4⋊C4C2×D4×C13111yescharacteristic
807C4⋊C4C2×D4×C13111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C13111yescharacteristic
870C23#120×C13111yescharacteristic
871C23C22×D4×C13111yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C13111yescharacteristic
939C2×C4#120×C13111yescharacteristic
940C2×C4C22×D4×C13111yescharacteristic
941C2×C4C22×D4×C13111yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C13111yescharacteristic
980C22#576×C13111yescharacteristic
981C22#576×C13111yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2#3008×C13111yescharacteristic
1007C2#3018×C13111yescharacteristic
1008C2#3026×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3534×C131C2semidirect
2. #3194×C131C2semidirect
3. #3186×C131C2semidirect
4. #2661×C131C2semidirect
5. #1612×C131C2semidirect
6. #1610×C131C2semidirect
7. #1609×C131C2semidirect
8. #1607×C131C2semidirect
9. #1600×C131C2semidirect
10. #1598×C131C2semidirect
11. #1597×C131C2semidirect
12. #1595×C131C2semidirect
13. #1507×C131C2semidirect
14. #1501×C131C2semidirect
15. #1468×C131C2semidirect
35. C2×#121×C131C22semidirect
36. #483×C131C22semidirect
40. #480×C131C22semidirect
41. #480×C131C22semidirect
46. #450×C131C22semidirect
50. #447×C131C22semidirect
51. #447×C131C22semidirect
52. #407×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
54. #398×C131C22semidirect
55. #397×C131C22semidirect
57. #394×C131C22semidirect
59. #392×C131C22semidirect
62. C4×C22⋊C4×C131C22semidirect
63. #328×C131C22semidirect
64. #328×C131C22semidirect
67. #327×C131C22semidirect
68. #327×C131C22semidirect
69. #327×C131C22semidirect
70. #327×C131C22semidirect
71. #324×C131C22semidirect
72. #324×C131C22semidirect
73. #323×C131C22semidirect
74. #323×C131C22semidirect
76. C2×#41×C131D4semidirect
83. C22×D4×C131D4semidirect
121. C22⋊Q8×C131D4semidirect
142. #121×C131D4semidirect
143. #121×C131D4semidirect
144. #121×C131D4semidirect
165. #117×C131D4semidirect
168. C2×C4⋊C4×C131D4semidirect
504. #18414C131direct (N × H)
505. C131#18414direct (N × H)
506. #3534C2×C131semidirect
507. #3194C2×C131semidirect
508. #3186C2×C131semidirect
509. #2661C2×C131semidirect
510. #1612C2×C131semidirect
511. #1610C2×C131semidirect
512. #1609C2×C131semidirect
513. #1607C2×C131semidirect
514. #1600C2×C131semidirect
515. #1598C2×C131semidirect
516. #1597C2×C131semidirect
517. #1595C2×C131semidirect
518. #1507C2×C131semidirect
519. #1501C2×C131semidirect
520. #1468C2×C131semidirect
540. C2×#121C22×C131semidirect
541. #483C22×C131semidirect
545. #480C22×C131semidirect
546. #480C22×C131semidirect
551. #450C22×C131semidirect
555. #447C22×C131semidirect
556. #447C22×C131semidirect
557. #407C22×C131semidirect
558. C2×C22⋊C8C22×C131semidirect
559. #398C22×C131semidirect
560. #397C22×C131semidirect
562. #394C22×C131semidirect
564. #392C22×C131semidirect
567. C4×C22⋊C4C22×C131semidirect
568. #328C22×C131semidirect
569. #328C22×C131semidirect
572. #327C22×C131semidirect
573. #327C22×C131semidirect
574. #327C22×C131semidirect
575. #327C22×C131semidirect
576. #324C22×C131semidirect
577. #324C22×C131semidirect
578. #323C22×C131semidirect
579. #323C22×C131semidirect
581. C2×#41D4×C131semidirect
588. C22×D4D4×C131semidirect
626. C22⋊Q8D4×C131semidirect
647. #121D4×C131semidirect
648. #121D4×C131semidirect
649. #121D4×C131semidirect
670. #117D4×C131semidirect
673. C2×C4⋊C4D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3534×C1312
#3194×C1312
#3186×C1312
#2661×C1312
#1612×C1312
#1610×C1312
#1609×C1312
#1607×C1312
#1600×C1312
#1598×C1312
#1597×C1312
#1595×C1312
#1507×C1312
#1501×C1312
#1468×C1312
#18414131