Finite Group Databasebeta

← C131×#26988 #45712872

Subgroups — C131×#26988 #45712872

Order 33536.

840 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
1C2×#470×C131C211yesmaximal, characteristic
2C2×#441×C131C211yesmaximal, characteristic, complemented
3#2429×C131C211yesmaximal, characteristic
4#2423×C131C211yesmaximal, characteristic
5#2084×C131C211yesmaximal, characteristic, complemented
6#2035×C131C211yesmaximal, characteristic
7#2016×C131C211yesmaximal, characteristic, complemented
8#2001×C131C211yesmaximal, characteristic
9#1956×C131C211yesmaximal, characteristic, complemented
10#1935×C131C211yesmaximal, characteristic, complemented
11#1933×C131C211yesmaximal, characteristic, complemented
12#1894×C131C211yesmaximal, characteristic
13#1878×C131C211yesmaximal, characteristic, complemented
14#1865×C131C211yesmaximal, characteristic, complemented
15#1753×C131C211yesmaximal, characteristic
16C22×Q16×C131C2211yescharacteristic
17C22×Q16×C131C2211yescharacteristic
18C22×M16×C131C2211yescharacteristic
19C2×C4⋊Q8×C131C2211yescharacteristic
20C2×C22⋊Q8×C131C2211yescharacteristic
21C2×C22⋊Q8×C131C2211yescharacteristic
22C2×C22⋊Q8×C131C2211yescharacteristic
23C2×C4×Q8×C131C2211yescharacteristic
24C2×C4×Q8×C131C2211yescharacteristic
25#470×C131—24no—
26#441×C131—24no—
27C2×#106×C131C2211yescharacteristic
28C2×#106×C131C2211yescharacteristic
29C2×#103×C131C2211yescharacteristic
30C2×#103×C131C2211yescharacteristic
31C2×#103×C131C2211yescharacteristic
32C2×#103×C131C2211yescharacteristic
33C2×#103×C131C2211yescharacteristic
34C2×#103×C131C2211yescharacteristic
35C2×#103×C131C2211yescharacteristic
36C2×#103×C131C2211yescharacteristic
37C2×C22⋊C8×C131C2211yescharacteristic
38C2×#97×C131C2211yescharacteristic
39C2×C4×C8×C131C2211yescharacteristic
40#399×C131—21no—
41#398×C131—21no—
42#398×C131—21no—
43#396×C131—21no—
44#391×C131C2211yescharacteristic
45#391×C131C2211yescharacteristic
46#389×C131—21no—
47#389×C131C2211yescharacteristic
48#389×C131C2211yescharacteristic
49#388×C131—21no—
50#388×C131—21no—
51#387×C131—21no—
52#384×C131C2211yescharacteristic
53#380×C131C2211yescharacteristic
54C4×C22⋊C4×C131C2211yescharacteristic
55#340×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#336×C131C2211yescharacteristic
60#336×C131C2211yescharacteristic
61C22×Q8×C131C2311yescharacteristic
62C22×Q8×C131C2311yescharacteristic
63C22×Q8×C131C2311yescharacteristic
64C23×C4×C131C2311yescharacteristic
65C2×Q16×C131—22no—
66C2×Q16×C131—22no—
67C2×Q16×C131—22no—
68C2×Q16×C131—22no—
69C2×Q16×C131—22no—
70C2×Q16×C131—41no—
71C2×M16×C131—22no—
72C2×M16×C131—22no—
73C2×M16×C131—41no—
74C22×C8×C131C2311yescharacteristic
75C22×C8×C131C2311yescharacteristic
76C22×C8×C131C2311yescharacteristic
77C22×C8×C131C2311yescharacteristic
78C4⋊Q8×C131—22no—
79C4⋊Q8×C131—41no—
80C22⋊Q8×C131—22no—
81C22⋊Q8×C131—22no—
82C22⋊Q8×C131—22no—
83C22⋊Q8×C131—41no—
84C22⋊Q8×C131—41no—
85C22⋊Q8×C131—41no—
86C4×Q8×C131—22no—
87C4×Q8×C131—22no—
88C4×Q8×C131—41no—
89C4×Q8×C131—41no—
90C2×C4⋊C4×C131—21no—
91C2×C4⋊C4×C131—21no—
92C2×C4⋊C4×C131—21no—
93C2×C4⋊C4×C131—21no—
94C2×C4⋊C4×C131—21no—
95C2×C4⋊C4×C131—21no—
96C2×C4⋊C4×C131—21no—
97C2×C4⋊C4×C131—21no—
98C2×C4⋊C4×C131—21no—
99C2×C4⋊C4×C131—21no—
100C2×C4⋊C4×C131—21no—
101C2×C4⋊C4×C131C2311yescharacteristic
102C2×C4⋊C4×C131C2311yescharacteristic
103C2×C4⋊C4×C131C2311yescharacteristic
104C2×C4⋊C4×C131C2311yescharacteristic
105C2×C4⋊C4×C131C2311yescharacteristic
106C2×C22⋊C4×C131—21no—
107C2×C22⋊C4×C131—21no—
108C2×C22⋊C4×C131—21no—
109C2×C22⋊C4×C131—21no—
110C2×C22⋊C4×C131D411yescharacteristic
111C2×C22⋊C4×C131D411yescharacteristic
112C2×C42×C131—21no—
113C2×C42×C131—21no—
114C2×C42×C131C2311yescharacteristic
115C2×C42×C131C2311yescharacteristic
116#106×C131—22no—
117#106×C131—22no—
118#103×C131—22no—
119#103×C131—22no—
120#103×C131—22no—
121#103×C131—22no—
122#103×C131—41no—
123#103×C131—41no—
124#103×C131—41no—
125#103×C131D414yes—
126C22⋊C8×C131—22no—
127#97×C131—22no—
128C4×C8×C131—41no—
129#95×C131—21no—
130#95×C131—21no—
131#95×C131—21no—
132#95×C131—21no—
133#95×C131—21no—
134#95×C131—21no—
135#95×C131—21no—
136#95×C131D411yescharacteristic
137#95×C131D411yescharacteristic
138C24×C131C2×D411yescharacteristic
139C2×Q8×C131—21no—
140C2×Q8×C131—21no—
141C2×Q8×C131—21no—
142C2×Q8×C131—21no—
143C2×Q8×C131—21no—
144C2×Q8×C131—21no—
145C2×Q8×C131—21no—
146C2×Q8×C131—21no—
147C2×Q8×C131—21no—
148C2×Q8×C131—21no—
149C2×Q8×C131—21no—
150C2×Q8×C131—21no—
151C2×Q8×C131—21no—
152C2×Q8×C131—21no—
153C2×Q8×C131—21no—
154C2×Q8×C131—21no—
155C2×Q8×C131C2×D412yes—
156C2×Q8×C131#4112yes—
157C22×C4×C131—21no—
158C22×C4×C131—21no—
159C22×C4×C131—21no—
160C22×C4×C131—21no—
161C22×C4×C131—21no—
162C22×C4×C131—21no—
163C22×C4×C131—21no—
164C22×C4×C131—21no—
165C22×C4×C131—21no—
166C22×C4×C131—21no—
167C22×C4×C131—21no—
168C22×C4×C131—21no—
169C22×C4×C131—21no—
170C22×C4×C131—21no—
171C22×C4×C131C2×D411yescharacteristic
172C22×C4×C131C2×D411yescharacteristic
173C22×C4×C131C2×D411yescharacteristic
174C22×C4×C131C2×D411yescharacteristic
175C22×C4×C131C2×D411yescharacteristic
176C22×C4×C131C2411yescharacteristic
177Q16×C131—28no—
178Q16×C131—44no—
179M16×C131—44no—
180C2×C8×C131—21no—
181C2×C8×C131—21no—
182C2×C8×C131—21no—
183C2×C8×C131—21no—
184C2×C8×C131—21no—
185C2×C8×C131—21no—
186C2×C8×C131—21no—
187C2×C8×C131—21no—
188C2×C8×C131—21no—
189C2×C8×C131C2×D412yes—
190C2×C8×C131#4112yes—
191C2×C8×C131#4112yes—
192C4⋊C4×C131—21no—
193C4⋊C4×C131—21no—
194C4⋊C4×C131—21no—
195C4⋊C4×C131—21no—
196C4⋊C4×C131—21no—
197C4⋊C4×C131—21no—
198C4⋊C4×C131—21no—
199C4⋊C4×C131—21no—
200C4⋊C4×C131—21no—
201C4⋊C4×C131—42no—
202C4⋊C4×C131—42no—
203C4⋊C4×C131—42no—
204C4⋊C4×C131—42no—
205C4⋊C4×C131—42no—
206C4⋊C4×C131—42no—
207C4⋊C4×C131—42no—
208C4⋊C4×C131—42no—
209C4⋊C4×C131—42no—
210C4⋊C4×C131—81no—
211C4⋊C4×C131—81no—
212C4⋊C4×C131C2×D412yes—
213C22⋊C4×C131—22no—
214C22⋊C4×C131—22no—
215C22⋊C4×C131—42no—
216C22⋊C4×C131—42no—
217C22⋊C4×C131—42no—
218C22⋊C4×C131—81no—
219C42×C131—21no—
220C42×C131—21no—
221C42×C131—21no—
222C42×C131—21no—
223C42×C131—42no—
224C42×C131—42no—
225C23×C131—21no—
226C23×C131—21no—
227C23×C131—21no—
228C23×C131—21no—
229C23×C131—21no—
230C23×C131—21no—
231C23×C131—21no—
232C23×C131C22×D411yescharacteristic
233Q8×C131—22no—
234Q8×C131—22no—
235Q8×C131—22no—
236Q8×C131—22no—
237Q8×C131—41no—
238Q8×C131—41no—
239Q8×C131—41no—
240Q8×C131—41no—
241Q8×C131—41no—
242Q8×C131—41no—
243Q8×C131—41no—
244Q8×C131—41no—
245C2×C4×C131—21no—
246C2×C4×C131—21no—
247C2×C4×C131—21no—
248C2×C4×C131—21no—
249C2×C4×C131—21no—
250C2×C4×C131—21no—
251C2×C4×C131—21no—
252C2×C4×C131—22no—
253C2×C4×C131—22no—
254C2×C4×C131—21no—
255C2×C4×C131—22no—
256C2×C4×C131—21no—
257C2×C4×C131—21no—
258C2×C4×C131—21no—
259C2×C4×C131—21no—
260C2×C4×C131—21no—
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—41no—
279C2×C4×C131—41no—
280C2×C4×C131—41no—
281C2×C4×C131—41no—
282C2×C4×C131—41no—
283C2×C4×C131—41no—
284C2×C4×C131—41no—
285C2×C4×C131—41no—
286C2×C4×C131#13712yes—
287C2×C4×C131#13712yes—
288C2×C4×C131C22×D411yescharacteristic
289C2×C4×C131C2×#4111yescharacteristic
290C2×C4×C131C2×#4111yescharacteristic
291C2×C4×C131C2×#4111yescharacteristic
292C2×C4×C131H(5,𝔽2)11yescharacteristic
293C2×C4×C131H(5,𝔽2)11yescharacteristic
294C8×C131—22no—
295C8×C131—22no—
296C8×C131—22no—
297C8×C131—41no—
298C22×C131—41no—
299C22×C131—41no—
300C22×C131—41no—
301C22×C131—41no—
302C22×C131—41no—
303C22×C131—41no—
304C22×C131—41no—
305C22×C131#53211yescharacteristic
306C22×C131D4211yescharacteristic
307C22×C131#54611yescharacteristic
308C22×C131C2×#13711yescharacteristic
309C22×C131C2×#13711yescharacteristic
310C22×C131#57711yescharacteristic
311C22×C131#57811yescharacteristic
312C4×C131—22no—
313C4×C131—22no—
314C4×C131—41no—
315C4×C131—42no—
316C4×C131—42no—
317C4×C131—41no—
318C4×C131—42no—
319C4×C131—41no—
320C4×C131—81no—
321C4×C131—81no—
322C4×C131—81no—
323C4×C131—81no—
324C4×C131—81no—
325C4×C131#52511yescharacteristic
326C4×C131#54011yescharacteristic
327C4×C131#54611yescharacteristic
328C4×C131#55311yescharacteristic
329C2×C131—81no—
330C2×C131#246411yescharacteristic
331C2×C131#317811yescharacteristic
332C2×C131#318511yescharacteristic
333C2×C131#327611yescharacteristic
334C2×C131#327811yescharacteristic
335C2×C131#331211yescharacteristic
336C2×C131#331611yescharacteristic
337#26988C13111yesmaximal, characteristic, direct product factor, Sylow
338C131#2698811yescharacteristic, direct product factor, Sylow
339C2×#470C2×C13111yescharacteristic
340C2×#441C2×C13111yescharacteristic, complemented
341#2429C2×C13111yescharacteristic
342#2423C2×C13111yescharacteristic
343#2084C2×C13111yescharacteristic, complemented
344#2035C2×C13111yescharacteristic
345#2016C2×C13111yescharacteristic, complemented
346#2001C2×C13111yescharacteristic
347#1956C2×C13111yescharacteristic, complemented
348#1935C2×C13111yescharacteristic, complemented
349#1933C2×C13111yescharacteristic, complemented
350#1894C2×C13111yescharacteristic
351#1878C2×C13111yescharacteristic, complemented
352#1865C2×C13111yescharacteristic, complemented
353#1753C2×C13111yescharacteristic
354C22×Q16C22×C13111yescharacteristic
355C22×Q16C22×C13111yescharacteristic
356C22×M16C22×C13111yescharacteristic
357C2×C4⋊Q8C22×C13111yescharacteristic
358C2×C22⋊Q8C22×C13111yescharacteristic
359C2×C22⋊Q8C22×C13111yescharacteristic
360C2×C22⋊Q8C22×C13111yescharacteristic
361C2×C4×Q8C22×C13111yescharacteristic
362C2×C4×Q8C22×C13111yescharacteristic
363#470—24no—
364#441—24no—
365C2×#106C22×C13111yescharacteristic
366C2×#106C22×C13111yescharacteristic
367C2×#103C22×C13111yescharacteristic
368C2×#103C22×C13111yescharacteristic
369C2×#103C22×C13111yescharacteristic
370C2×#103C22×C13111yescharacteristic
371C2×#103C22×C13111yescharacteristic
372C2×#103C22×C13111yescharacteristic
373C2×#103C22×C13111yescharacteristic
374C2×#103C22×C13111yescharacteristic
375C2×C22⋊C8C22×C13111yescharacteristic
376C2×#97C22×C13111yescharacteristic
377C2×C4×C8C22×C13111yescharacteristic
378#399—21no—
379#398—21no—
380#398—21no—
381#396—21no—
382#391C22×C13111yescharacteristic
383#391C22×C13111yescharacteristic
384#389—21no—
385#389C22×C13111yescharacteristic
386#389C22×C13111yescharacteristic
387#388—21no—
388#388—21no—
389#387—21no—
390#384C22×C13111yescharacteristic
391#380C22×C13111yescharacteristic
392C4×C22⋊C4C22×C13111yescharacteristic
393#340C22×C13111yescharacteristic
394#340C22×C13111yescharacteristic
395#340C22×C13111yescharacteristic
396#340C22×C13111yescharacteristic
397#336C22×C13111yescharacteristic
398#336C22×C13111yescharacteristic
399C22×Q8C23×C13111yescharacteristic
400C22×Q8C23×C13111yescharacteristic
401C22×Q8C23×C13111yescharacteristic
402C23×C4C23×C13111yescharacteristic
403C2×Q16—22no—
404C2×Q16—22no—
405C2×Q16—22no—
406C2×Q16—22no—
407C2×Q16—22no—
408C2×Q16—41no—
409C2×M16—22no—
410C2×M16—22no—
411C2×M16—41no—
412C22×C8C23×C13111yescharacteristic
413C22×C8C23×C13111yescharacteristic
414C22×C8C23×C13111yescharacteristic
415C22×C8C23×C13111yescharacteristic
416C4⋊Q8—22no—
417C4⋊Q8—41no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—41no—
422C22⋊Q8—41no—
423C22⋊Q8—41no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—41no—
427C4×Q8—41no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4C23×C13111yescharacteristic
440C2×C4⋊C4C23×C13111yescharacteristic
441C2×C4⋊C4C23×C13111yescharacteristic
442C2×C4⋊C4C23×C13111yescharacteristic
443C2×C4⋊C4C23×C13111yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C13111yescharacteristic
449C2×C22⋊C4D4×C13111yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C23×C13111yescharacteristic
453C2×C42C23×C13111yescharacteristic
454#106—22no—
455#106—22no—
456#103—22no—
457#103—22no—
458#103—22no—
459#103—22no—
460#103—41no—
461#103—41no—
462#103—41no—
463#103D4×C13114yes—
464C22⋊C8—22no—
465#97—22no—
466C4×C8—41no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95D4×C13111yescharacteristic
475#95D4×C13111yescharacteristic
476C24C2×D4×C13111yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8C2×D4×C13112yes—
494C2×Q8#41×C13112yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4C2×D4×C13111yescharacteristic
510C22×C4C2×D4×C13111yescharacteristic
511C22×C4C2×D4×C13111yescharacteristic
512C22×C4C2×D4×C13111yescharacteristic
513C22×C4C2×D4×C13111yescharacteristic
514C22×C4C24×C13111yescharacteristic
515Q16—28no—
516Q16—44no—
517M16—44no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8C2×D4×C13112yes—
528C2×C8#41×C13112yes—
529C2×C8#41×C13112yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4C2×D4×C13112yes—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—42no—
562C42—42no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23C22×D4×C13111yescharacteristic
571Q8—22no—
572Q8—22no—
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
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—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4#137×C13112yes—
625C2×C4#137×C13112yes—
626C2×C4C22×D4×C13111yescharacteristic
627C2×C4C2×#41×C13111yescharacteristic
628C2×C4C2×#41×C13111yescharacteristic
629C2×C4C2×#41×C13111yescharacteristic
630C2×C4H(5,𝔽2)×C13111yescharacteristic
631C2×C4H(5,𝔽2)×C13111yescharacteristic
632C8—22no—
633C8—22no—
634C8—22no—
635C8—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22#532×C13111yescharacteristic
644C22D42×C13111yescharacteristic
645C22#546×C13111yescharacteristic
646C22C2×#137×C13111yescharacteristic
647C22C2×#137×C13111yescharacteristic
648C22#577×C13111yescharacteristic
649C22#578×C13111yescharacteristic
650C4—22no—
651C4—22no—
652C4—41no—
653C4—42no—
654C4—41no—
655C4—41no—
656C4—42no—
657C4—42no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4#525×C13111yescharacteristic
664C4#540×C13111yescharacteristic
665C4#546×C13111yescharacteristic
666C4#553×C13111yescharacteristic
667C2—81no—
668C2#2464×C13111yescharacteristic
669C2#3178×C13111yescharacteristic
670C2#3185×C13111yescharacteristic
671C2#3276×C13111yescharacteristic
672C2#3278×C13111yescharacteristic
673C2#3312×C13111yescharacteristic
674C2#3316×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC24×C131C2×D4
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. C2×#441×C131C2semidirect
5. #2084×C131C2semidirect
7. #2016×C131C2semidirect
9. #1956×C131C2semidirect
10. #1935×C131C2semidirect
11. #1933×C131C2semidirect
13. #1878×C131C2semidirect
14. #1865×C131C2semidirect
337. #26988C131direct (N × H)
338. C131#26988direct (N × H)
340. C2×#441C2×C131semidirect
343. #2084C2×C131semidirect
345. #2016C2×C131semidirect
347. #1956C2×C131semidirect
348. #1935C2×C131semidirect
349. #1933C2×C131semidirect
351. #1878C2×C131semidirect
352. #1865C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#470×C1312
C2×#441×C1312
#2429×C1312
#2423×C1312
#2084×C1312
#2035×C1312
#2016×C1312
#2001×C1312
#1956×C1312
#1935×C1312
#1933×C1312
#1894×C1312
#1878×C1312
#1865×C1312
#1753×C1312
#26988131