Finite Group Databasebeta

← C131×#26724 #45712608

Subgroups — C131×#26724 #45712608

Order 33536.

826 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2491×C131C211yesmaximal, characteristic
2#2360×C131C211yesmaximal, characteristic, complemented
3#2055×C131C211yesmaximal, characteristic, complemented
4#2035×C131C211yesmaximal, characteristic, complemented
5#2024×C131C211yesmaximal, characteristic, complemented
6#2000×C131C211yesmaximal, characteristic
7#1988×C131C211yesmaximal, characteristic, complemented
8#1934×C131C211yesmaximal, characteristic, complemented
9#1926×C131C211yesmaximal, characteristic, complemented
10#1923×C131C211yesmaximal, characteristic, complemented
11#1920×C131C211yesmaximal, characteristic, complemented
12#1880×C131C211yesmaximal, characteristic, complemented
13#1874×C131C211yesmaximal, characteristic
14#1824×C131C211yesmaximal, characteristic, complemented
15C4×#103×C131C211yesmaximal, characteristic, complemented
16C22×SD16×C131C2211yescharacteristic
17C2×C4⋊Q8×C131C2211yescharacteristic
18C2×#124×C131—21no—
19C2×C22⋊Q8×C131C2211yescharacteristic
20C2×#121×C131C2211yescharacteristic
21C2×C4×Q8×C131C2211yescharacteristic
22C22×C4⋊C4×C131C2211yescharacteristic
23C2×#106×C131C2211yescharacteristic
24C2×C4⋊C8×C131C2211yescharacteristic
25C2×#103×C131C2211yescharacteristic
26C2×#103×C131C2211yescharacteristic
27C2×#103×C131C2211yescharacteristic
28C2×#102×C131C2211yescharacteristic
29C2×#102×C131C2211yescharacteristic
30C2×#102×C131C2211yescharacteristic
31C2×C22⋊C8×C131C2211yescharacteristic
32C2×C22⋊C8×C131C2211yescharacteristic
33C2×C4×C8×C131C2211yescharacteristic
34#394×C131—21no—
35#393×C131—21no—
36#391×C131C2211yescharacteristic
37#390×C131C2211yescharacteristic
38#390×C131C2211yescharacteristic
39#389×C131—21no—
40#389×C131C2211yescharacteristic
41#388×C131—21no—
42#387×C131—21no—
43#385×C131—21no—
44#380×C131C2211yescharacteristic
45C4×C4⋊C4×C131C2211yescharacteristic
46C4×C4⋊C4×C131C2211yescharacteristic
47C4×C22⋊C4×C131—21no—
48C4×C22⋊C4×C131C2211yescharacteristic
49#340×C131C2211yescharacteristic
50#340×C131C2211yescharacteristic
51#340×C131C2211yescharacteristic
52#340×C131C2211yescharacteristic
53#340×C131C2211yescharacteristic
54#340×C131C2211yescharacteristic
55#340×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic
57#336×C131C2211yescharacteristic
58#336×C131C2211yescharacteristic
59C22×Q8×C131—21no—
60C22×Q8×C131C2311yescharacteristic
61C22×D4×C131—21no—
62C22×D4×C131C2311yescharacteristic
63C23×C4×C131—21no—
64C23×C4×C131C2311yescharacteristic
65C2×SD16×C131—22no—
66C2×SD16×C131—41no—
67C2×SD16×C131—41no—
68C22×C8×C131C2311yescharacteristic
69C22×C8×C131C2311yescharacteristic
70C22×C8×C131C2311yescharacteristic
71C22×C8×C131C2311yescharacteristic
72C4⋊Q8×C131—22no—
73C4⋊Q8×C131—41no—
74#124×C131—44no—
75C22⋊Q8×C131—22no—
76C22⋊Q8×C131—22no—
77#121×C131—22no—
78#121×C131—41no—
79C4×Q8×C131—22no—
80C4×Q8×C131—41no—
81C2×C4⋊C4×C131—21no—
82C2×C4⋊C4×C131—22no—
83C2×C4⋊C4×C131—21no—
84C2×C4⋊C4×C131—21no—
85C2×C4⋊C4×C131—21no—
86C2×C4⋊C4×C131—21no—
87C2×C4⋊C4×C131—41no—
88C2×C4⋊C4×C131C2311yescharacteristic
89C2×C4⋊C4×C131C2311yescharacteristic
90C2×C4⋊C4×C131C2311yescharacteristic
91C2×C4⋊C4×C131C2311yescharacteristic
92C2×C4⋊C4×C131C2311yescharacteristic
93C2×C4⋊C4×C131C2311yescharacteristic
94C2×C22⋊C4×C131—21no—
95C2×C22⋊C4×C131—21no—
96C2×C22⋊C4×C131—21no—
97C2×C22⋊C4×C131—21no—
98C2×C22⋊C4×C131—21no—
99C2×C22⋊C4×C131—21no—
100C2×C22⋊C4×C131—21no—
101C2×C22⋊C4×C131D411yescharacteristic
102C2×C22⋊C4×C131D411yescharacteristic
103C2×C42×C131—21no—
104C2×C42×C131—21no—
105C2×C42×C131—21no—
106C2×C42×C131C2311yescharacteristic
107C2×C42×C131C2311yescharacteristic
108#106×C131—22no—
109C4⋊C8×C131—41no—
110#103×C131—22no—
111#103×C131—22no—
112#103×C131—41no—
113#102×C131—22no—
114#102×C131—22no—
115#102×C131—41no—
116C22⋊C8×C131—41no—
117C22⋊C8×C131—41no—
118C4×C8×C131—41no—
119#95×C131—21no—
120#95×C131—21no—
121#95×C131—21no—
122#95×C131—21no—
123#95×C131—21no—
124#95×C131—21no—
125#95×C131D411yescharacteristic
126#95×C131D411yescharacteristic
127C24×C131—21no—
128C24×C131C2×D411yescharacteristic
129C2×Q8×C131—21no—
130C2×Q8×C131—21no—
131C2×Q8×C131—21no—
132C2×Q8×C131—21no—
133C2×Q8×C131—21no—
134C2×Q8×C131—42no—
135C2×Q8×C131—42no—
136C2×Q8×C131—81no—
137C2×Q8×C131#4112yes—
138C2×D4×C131—21no—
139C2×D4×C131—21no—
140C2×D4×C131—21no—
141C2×D4×C131—21no—
142C2×D4×C131—21no—
143C2×D4×C131—21no—
144C2×D4×C131—42no—
145C2×D4×C131—42no—
146C2×D4×C131—81no—
147C22×C4×C131—21no—
148C22×C4×C131—21no—
149C22×C4×C131—21no—
150C22×C4×C131—21no—
151C22×C4×C131—21no—
152C22×C4×C131—21no—
153C22×C4×C131—21no—
154C22×C4×C131—21no—
155C22×C4×C131—21no—
156C22×C4×C131—21no—
157C22×C4×C131—21no—
158C22×C4×C131—21no—
159C22×C4×C131—21no—
160C22×C4×C131—42no—
161C22×C4×C131—42no—
162C22×C4×C131—81no—
163C22×C4×C131C2×D411yescharacteristic
164C22×C4×C131C2×D411yescharacteristic
165C22×C4×C131C2×D411yescharacteristic
166C22×C4×C131C2×D411yescharacteristic
167C22×C4×C131C2×D411yescharacteristic
168C22×C4×C131C2411yescharacteristic
169SD16×C131—44no—
170C2×C8×C131—21no—
171C2×C8×C131—21no—
172C2×C8×C131—21no—
173C2×C8×C131—21no—
174C2×C8×C131—21no—
175C2×C8×C131—21no—
176C2×C8×C131—21no—
177C2×C8×C131—21no—
178C2×C8×C131—21no—
179C2×C8×C131—21no—
180C2×C8×C131—21no—
181C2×C8×C131—21no—
182C4⋊C4×C131—24no—
183C4⋊C4×C131—21no—
184C4⋊C4×C131—21no—
185C4⋊C4×C131—21no—
186C4⋊C4×C131—21no—
187C4⋊C4×C131—21no—
188C4⋊C4×C131—21no—
189C4⋊C4×C131—21no—
190C4⋊C4×C131—21no—
191C4⋊C4×C131—21no—
192C4⋊C4×C131—42no—
193C4⋊C4×C131—42no—
194C4⋊C4×C131—42no—
195C4⋊C4×C131—81no—
196C4⋊C4×C131#4112yes—
197C4⋊C4×C131#4112yes—
198C4⋊C4×C131#4112yes—
199C22⋊C4×C131—24no—
200C22⋊C4×C131—41no—
201C22⋊C4×C131—42no—
202C22⋊C4×C131—42no—
203C22⋊C4×C131—42no—
204C22⋊C4×C131—42no—
205C22⋊C4×C131—42no—
206C22⋊C4×C131—81no—
207C22⋊C4×C131SD1614yescomplemented
208C42×C131—21no—
209C42×C131—21no—
210C42×C131—21no—
211C42×C131—21no—
212C42×C131—42no—
213C42×C131—42no—
214C42×C131—81no—
215C23×C131—21no—
216C23×C131—21no—
217C23×C131—21no—
218C23×C131—21no—
219C23×C131—21no—
220C23×C131—21no—
221C23×C131—41no—
222C23×C131—41no—
223C23×C131—41no—
224C23×C131—41no—
225C23×C131—41no—
226C23×C131—41no—
227C23×C131—41no—
228C23×C131C2×SD1612yes—
229C23×C131C22×D411yescharacteristic
230Q8×C131—22no—
231Q8×C131—22no—
232Q8×C131—41no—
233Q8×C131—41no—
234Q8×C131—84no—
235D4×C131—41no—
236D4×C131—41no—
237D4×C131—41no—
238D4×C131—41no—
239D4×C131—84no—
240C2×C4×C131—21no—
241C2×C4×C131—21no—
242C2×C4×C131—21no—
243C2×C4×C131—21no—
244C2×C4×C131—22no—
245C2×C4×C131—22no—
246C2×C4×C131—21no—
247C2×C4×C131—21no—
248C2×C4×C131—21no—
249C2×C4×C131—22no—
250C2×C4×C131—21no—
251C2×C4×C131—22no—
252C2×C4×C131—21no—
253C2×C4×C131—21no—
254C2×C4×C131—21no—
255C2×C4×C131—21no—
256C2×C4×C131—21no—
257C2×C4×C131—41no—
258C2×C4×C131—41no—
259C2×C4×C131—41no—
260C2×C4×C131—41no—
261C2×C4×C131—41no—
262C2×C4×C131—41no—
263C2×C4×C131—41no—
264C2×C4×C131—41no—
265C2×C4×C131—41no—
266C2×C4×C131—41no—
267C2×C4×C131—41no—
268C2×C4×C131—41no—
269C2×C4×C131—41no—
270C2×C4×C131—41no—
271C2×C4×C131—41no—
272C2×C4×C131—41no—
273C2×C4×C131—41no—
274C2×C4×C131—41no—
275C2×C4×C131—41no—
276C2×C4×C131—41no—
277C2×C4×C131—41no—
278C2×C4×C131—84no—
279C2×C4×C131C2×SD1612yes—
280C2×C4×C131C2×SD1612yes—
281C2×C4×C131C2×#4111yescharacteristic
282C2×C4×C131C2×#4111yescharacteristic
283C2×C4×C131C2×#4111yescharacteristic
284C2×C4×C131C2×#4111yescharacteristic
285C2×C4×C131H(5,𝔽2)11yescharacteristic
286C2×C4×C131H(5,𝔽2)11yescharacteristic
287C8×C131—41no—
288C8×C131—41no—
289C8×C131—41no—
290C8×C131—41no—
291C22×C131—22no—
292C22×C131—22no—
293C22×C131—22no—
294C22×C131—41no—
295C22×C131—41no—
296C22×C131—41no—
297C22×C131—41no—
298C22×C131—81no—
299C22×C131—81no—
300C22×C131—81no—
301C22×C131—81no—
302C22×C131—81no—
303C22×C131—81no—
304C22×C131—81no—
305C22×C131#52511yescharacteristic
306C22×C131#54611yescharacteristic
307C22×C131#54611yescharacteristic
308C22×C131C22×SD1611yescharacteristic
309C22×C131#57511yescharacteristic
310C22×C131#57611yescharacteristic
311C22×C131#57811yescharacteristic
312C4×C131—22no—
313C4×C131—22no—
314C4×C131—42no—
315C4×C131—41no—
316C4×C131—42no—
317C4×C131—42no—
318C4×C131—41no—
319C4×C131—42no—
320C4×C131—41no—
321C4×C131—81no—
322C4×C131—81no—
323C4×C131—81no—
324C4×C131#52911yescharacteristic
325C4×C131#53811yescharacteristic
326C4×C131#55511yescharacteristic
327C4×C131#55911yescharacteristic
328C2×C131—42no—
329C2×C131—161no—
330C2×C131#245911yescharacteristic
331C2×C131#310311yescharacteristic
332C2×C131#312411yescharacteristic
333C2×C131#329511yescharacteristic
334C2×C131#329811yescharacteristic
335C2×C131#331911yescharacteristic
336C2×C131#332711yescharacteristic
337#26724C13111yesmaximal, characteristic, direct product factor, Sylow
338C131#2672411yescharacteristic, direct product factor, Sylow
339#2491C2×C13111yescharacteristic
340#2360C2×C13111yescharacteristic, complemented
341#2055C2×C13111yescharacteristic, complemented
342#2035C2×C13111yescharacteristic, complemented
343#2024C2×C13111yescharacteristic, complemented
344#2000C2×C13111yescharacteristic
345#1988C2×C13111yescharacteristic, complemented
346#1934C2×C13111yescharacteristic, complemented
347#1926C2×C13111yescharacteristic, complemented
348#1923C2×C13111yescharacteristic, complemented
349#1920C2×C13111yescharacteristic, complemented
350#1880C2×C13111yescharacteristic, complemented
351#1874C2×C13111yescharacteristic
352#1824C2×C13111yescharacteristic, complemented
353C4×#103C2×C13111yescharacteristic, complemented
354C22×SD16C22×C13111yescharacteristic
355C2×C4⋊Q8C22×C13111yescharacteristic
356C2×#124—21no—
357C2×C22⋊Q8C22×C13111yescharacteristic
358C2×#121C22×C13111yescharacteristic
359C2×C4×Q8C22×C13111yescharacteristic
360C22×C4⋊C4C22×C13111yescharacteristic
361C2×#106C22×C13111yescharacteristic
362C2×C4⋊C8C22×C13111yescharacteristic
363C2×#103C22×C13111yescharacteristic
364C2×#103C22×C13111yescharacteristic
365C2×#103C22×C13111yescharacteristic
366C2×#102C22×C13111yescharacteristic
367C2×#102C22×C13111yescharacteristic
368C2×#102C22×C13111yescharacteristic
369C2×C22⋊C8C22×C13111yescharacteristic
370C2×C22⋊C8C22×C13111yescharacteristic
371C2×C4×C8C22×C13111yescharacteristic
372#394—21no—
373#393—21no—
374#391C22×C13111yescharacteristic
375#390C22×C13111yescharacteristic
376#390C22×C13111yescharacteristic
377#389—21no—
378#389C22×C13111yescharacteristic
379#388—21no—
380#387—21no—
381#385—21no—
382#380C22×C13111yescharacteristic
383C4×C4⋊C4C22×C13111yescharacteristic
384C4×C4⋊C4C22×C13111yescharacteristic
385C4×C22⋊C4—21no—
386C4×C22⋊C4C22×C13111yescharacteristic
387#340C22×C13111yescharacteristic
388#340C22×C13111yescharacteristic
389#340C22×C13111yescharacteristic
390#340C22×C13111yescharacteristic
391#340C22×C13111yescharacteristic
392#340C22×C13111yescharacteristic
393#340C22×C13111yescharacteristic
394#340C22×C13111yescharacteristic
395#336C22×C13111yescharacteristic
396#336C22×C13111yescharacteristic
397C22×Q8—21no—
398C22×Q8C23×C13111yescharacteristic
399C22×D4—21no—
400C22×D4C23×C13111yescharacteristic
401C23×C4—21no—
402C23×C4C23×C13111yescharacteristic
403C2×SD16—22no—
404C2×SD16—41no—
405C2×SD16—41no—
406C22×C8C23×C13111yescharacteristic
407C22×C8C23×C13111yescharacteristic
408C22×C8C23×C13111yescharacteristic
409C22×C8C23×C13111yescharacteristic
410C4⋊Q8—22no—
411C4⋊Q8—41no—
412#124—44no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415#121—22no—
416#121—41no—
417C4×Q8—22no—
418C4×Q8—41no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4C23×C13111yescharacteristic
427C2×C4⋊C4C23×C13111yescharacteristic
428C2×C4⋊C4C23×C13111yescharacteristic
429C2×C4⋊C4C23×C13111yescharacteristic
430C2×C4⋊C4C23×C13111yescharacteristic
431C2×C4⋊C4C23×C13111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4D4×C13111yescharacteristic
440C2×C22⋊C4D4×C13111yescharacteristic
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C23×C13111yescharacteristic
445C2×C42C23×C13111yescharacteristic
446#106—22no—
447C4⋊C8—41no—
448#103—22no—
449#103—22no—
450#103—41no—
451#102—22no—
452#102—22no—
453#102—41no—
454C22⋊C8—41no—
455C22⋊C8—41no—
456C4×C8—41no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95D4×C13111yescharacteristic
464#95D4×C13111yescharacteristic
465C24—21no—
466C24C2×D4×C13111yescharacteristic
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—81no—
475C2×Q8#41×C13112yes—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—81no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4C2×D4×C13111yescharacteristic
502C22×C4C2×D4×C13111yescharacteristic
503C22×C4C2×D4×C13111yescharacteristic
504C22×C4C2×D4×C13111yescharacteristic
505C22×C4C2×D4×C13111yescharacteristic
506C22×C4C24×C13111yescharacteristic
507SD16—44no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C4⋊C4—24no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4#41×C13112yes—
535C4⋊C4#41×C13112yes—
536C4⋊C4#41×C13112yes—
537C22⋊C4—24no—
538C22⋊C4—41no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—81no—
545C22⋊C4SD16×C13114yescomplemented
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—42no—
552C42—81no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23C2×SD16×C13112yes—
567C23C22×D4×C13111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—84no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—84no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—84no—
617C2×C4C2×SD16×C13112yes—
618C2×C4C2×SD16×C13112yes—
619C2×C4C2×#41×C13111yescharacteristic
620C2×C4C2×#41×C13111yescharacteristic
621C2×C4C2×#41×C13111yescharacteristic
622C2×C4C2×#41×C13111yescharacteristic
623C2×C4H(5,𝔽2)×C13111yescharacteristic
624C2×C4H(5,𝔽2)×C13111yescharacteristic
625C8—41no—
626C8—41no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22#525×C13111yescharacteristic
644C22#546×C13111yescharacteristic
645C22#546×C13111yescharacteristic
646C22C22×SD16×C13111yescharacteristic
647C22#575×C13111yescharacteristic
648C22#576×C13111yescharacteristic
649C22#578×C13111yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—42no—
657C4—41no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4#529×C13111yescharacteristic
663C4#538×C13111yescharacteristic
664C4#555×C13111yescharacteristic
665C4#559×C13111yescharacteristic
666C2—42no—
667C2—161no—
668C2#2459×C13111yescharacteristic
669C2#3103×C13111yescharacteristic
670C2#3124×C13111yescharacteristic
671C2#3295×C13111yescharacteristic
672C2#3298×C13111yescharacteristic
673C2#3319×C13111yescharacteristic
674C2#3327×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C4×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2360×C131C2semidirect
3. #2055×C131C2semidirect
4. #2035×C131C2semidirect
5. #2024×C131C2semidirect
7. #1988×C131C2semidirect
8. #1934×C131C2semidirect
9. #1926×C131C2semidirect
10. #1923×C131C2semidirect
11. #1920×C131C2semidirect
12. #1880×C131C2semidirect
14. #1824×C131C2semidirect
15. C4×#103×C131C2semidirect
207. C22⋊C4×C131SD16semidirect
337. #26724C131direct (N × H)
338. C131#26724direct (N × H)
340. #2360C2×C131semidirect
341. #2055C2×C131semidirect
342. #2035C2×C131semidirect
343. #2024C2×C131semidirect
345. #1988C2×C131semidirect
346. #1934C2×C131semidirect
347. #1926C2×C131semidirect
348. #1923C2×C131semidirect
349. #1920C2×C131semidirect
350. #1880C2×C131semidirect
352. #1824C2×C131semidirect
353. C4×#103C2×C131semidirect
545. C22⋊C4SD16×C131semidirect

Maximal subgroups

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

subgroupindex
#2491×C1312
#2360×C1312
#2055×C1312
#2035×C1312
#2024×C1312
#2000×C1312
#1988×C1312
#1934×C1312
#1926×C1312
#1923×C1312
#1920×C1312
#1880×C1312
#1874×C1312
#1824×C1312
C4×#103×C1312
#26724131