Finite Group Databasebeta

← C131×#24902 #45710786

Subgroups — C131×#24902 #45710786

Order 33536.

932 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#451×C131C211yesmaximal, characteristic
2C2×C4×Q16×C131C211yesmaximal, characteristic, complemented
3#2421×C131C211yesmaximal, characteristic
4Q8×C22⋊C4×C131C211yesmaximal, characteristic
5#2097×C131C211yesmaximal, characteristic, complemented
6#2075×C131C211yesmaximal, characteristic
7#2056×C131C211yesmaximal, characteristic, complemented
8#2035×C131C211yesmaximal, characteristic
9#1933×C131C211yesmaximal, characteristic, complemented
10#1923×C131C211yesmaximal, characteristic
11#1878×C131C211yesmaximal, characteristic, complemented
12#1878×C131C211yesmaximal, characteristic, complemented
13#1865×C131C211yesmaximal, characteristic, complemented
14#1805×C131C211yesmaximal, characteristic, complemented
15#1787×C131C211yesmaximal, characteristic
16C23×Q8×C131C2211yescharacteristic
17C22×Q16×C131C2211yescharacteristic
18C22×Q16×C131C2211yescharacteristic
19C2×C22⋊Q8×C131C2211yescharacteristic
20C2×C4×Q8×C131C2211yescharacteristic
21C2×C4×Q8×C131C2211yescharacteristic
22C2×C4×Q8×C131C2211yescharacteristic
23#451×C131—24no—
24C4×Q16×C131—24no—
25C2×#107×C131C2211yescharacteristic
26C2×#106×C131C2211yescharacteristic
27C2×C4⋊C8×C131C2211yescharacteristic
28C2×#103×C131C2211yescharacteristic
29C2×#103×C131C2211yescharacteristic
30C2×#103×C131C2211yescharacteristic
31C2×#103×C131C2211yescharacteristic
32C2×#103×C131C2211yescharacteristic
33C2×#103×C131C2211yescharacteristic
34C2×#103×C131C2211yescharacteristic
35C2×#103×C131C2211yescharacteristic
36C2×C22⋊C8×C131C2211yescharacteristic
37C2×C22⋊C8×C131C2211yescharacteristic
38C2×C4×C8×C131C2211yescharacteristic
39#400×C131—21no—
40#397×C131—21no—
41#391×C131—21no—
42#391×C131—21no—
43#391×C131C2211yescharacteristic
44#391×C131C2211yescharacteristic
45#391×C131C2211yescharacteristic
46#389×C131C2211yescharacteristic
47#388×C131—21no—
48#387×C131—21no—
49#382×C131C2211yescharacteristic
50#380×C131—21no—
51#380×C131C2211yescharacteristic
52#380×C131C2211yescharacteristic
53C4×C22⋊C4×C131—21no—
54C4×C22⋊C4×C131C2211yescharacteristic
55#340×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#336×C131C2211yescharacteristic
60#336×C131C2211yescharacteristic
61C22×Q8×C131—22no—
62C22×Q8×C131—22no—
63C22×Q8×C131—21no—
64C22×Q8×C131—22no—
65C22×Q8×C131—22no—
66C22×Q8×C131—41no—
67C22×Q8×C131—41no—
68C22×Q8×C131C2311yescharacteristic
69C22×Q8×C131C2311yescharacteristic
70C22×Q8×C131C2311yescharacteristic
71C23×C4×C131—21no—
72C23×C4×C131C2311yescharacteristic
73C2×Q16×C131—22no—
74C2×Q16×C131—22no—
75C2×Q16×C131—22no—
76C2×Q16×C131—22no—
77C2×Q16×C131—41no—
78C2×Q16×C131D414yes—
79C22×C8×C131C2311yescharacteristic
80C22×C8×C131C2311yescharacteristic
81C22×C8×C131C2311yescharacteristic
82C22×C8×C131C2311yescharacteristic
83C22⋊Q8×C131—22no—
84C22⋊Q8×C131—41no—
85C4×Q8×C131—22no—
86C4×Q8×C131—22no—
87C4×Q8×C131—22no—
88C4×Q8×C131—41no—
89C4×Q8×C131—41no—
90C4×Q8×C131—41no—
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×C131C2311yescharacteristic
97C2×C4⋊C4×C131C2311yescharacteristic
98C2×C4⋊C4×C131C2311yescharacteristic
99C2×C4⋊C4×C131C2311yescharacteristic
100C2×C4⋊C4×C131C2311yescharacteristic
101C2×C22⋊C4×C131—21no—
102C2×C22⋊C4×C131—21no—
103C2×C22⋊C4×C131—21no—
104C2×C22⋊C4×C131D411yescharacteristic
105C2×C22⋊C4×C131D411yescharacteristic
106C2×C42×C131—21no—
107C2×C42×C131—21no—
108C2×C42×C131—21no—
109C2×C42×C131C2311yescharacteristic
110C2×C42×C131C2311yescharacteristic
111#107×C131—22no—
112#106×C131—41no—
113C4⋊C8×C131—41no—
114#103×C131—22no—
115#103×C131—22no—
116#103×C131—22no—
117#103×C131—22no—
118#103×C131—22no—
119#103×C131—22no—
120#103×C131—41no—
121#103×C131—41no—
122C22⋊C8×C131—22no—
123C22⋊C8×C131—41no—
124C4×C8×C131—22no—
125#95×C131—21no—
126#95×C131—21no—
127#95×C131—21no—
128#95×C131—21no—
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—24no—
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—42no—
154C2×Q8×C131—42no—
155C2×Q8×C131—44no—
156C2×Q8×C131—44no—
157C2×Q8×C131—44no—
158C2×Q8×C131—44no—
159C2×Q8×C131C2×D412yes—
160C2×Q8×C131C2×D412yes—
161C2×Q8×C131#4112yes—
162C2×Q8×C131#4112yes—
163C2×Q8×C131#4112yes—
164C22×C4×C131—21no—
165C22×C4×C131—24no—
166C22×C4×C131—21no—
167C22×C4×C131—21no—
168C22×C4×C131—21no—
169C22×C4×C131—21no—
170C22×C4×C131—21no—
171C22×C4×C131—21no—
172C22×C4×C131—21no—
173C22×C4×C131—21no—
174C22×C4×C131—21no—
175C22×C4×C131—21no—
176C22×C4×C131—21no—
177C22×C4×C131—21no—
178C22×C4×C131—21no—
179C22×C4×C131—42no—
180C22×C4×C131—42no—
181C22×C4×C131C2×D411yescharacteristic
182C22×C4×C131C2×D411yescharacteristic
183C22×C4×C131C2×D411yescharacteristic
184C22×C4×C131C2×D411yescharacteristic
185C22×C4×C131C2×D411yescharacteristic
186C22×C4×C131C2411yescharacteristic
187Q16×C131—28no—
188Q16×C131—44no—
189C2×C8×C131—21no—
190C2×C8×C131—21no—
191C2×C8×C131—21no—
192C2×C8×C131—21no—
193C2×C8×C131—21no—
194C2×C8×C131—21no—
195C2×C8×C131—21no—
196C2×C8×C131—21no—
197C2×C8×C131—21no—
198C2×C8×C131—21no—
199C2×C8×C131—21no—
200C2×C8×C131C2×D412yes—
201C4⋊C4×C131—21no—
202C4⋊C4×C131—21no—
203C4⋊C4×C131—21no—
204C4⋊C4×C131—21no—
205C4⋊C4×C131—21no—
206C4⋊C4×C131—21no—
207C4⋊C4×C131—21no—
208C4⋊C4×C131—21no—
209C4⋊C4×C131—21no—
210C4⋊C4×C131—21no—
211C4⋊C4×C131—42no—
212C4⋊C4×C131—42no—
213C4⋊C4×C131—42no—
214C4⋊C4×C131—42no—
215C4⋊C4×C131—42no—
216C22⋊C4×C131—22no—
217C22⋊C4×C131—22no—
218C22⋊C4×C131—42no—
219C22⋊C4×C131—42no—
220C22⋊C4×C131—42no—
221C42×C131—21no—
222C42×C131—21no—
223C42×C131—21no—
224C42×C131—21no—
225C42×C131—42no—
226C42×C131—42no—
227C42×C131—42no—
228C23×C131—21no—
229C23×C131—21no—
230C23×C131—21no—
231C23×C131—21no—
232C23×C131—21no—
233C23×C131—21no—
234C23×C131#13512yes—
235C23×C131C22×D411yescharacteristic
236Q8×C131—22no—
237Q8×C131—22no—
238Q8×C131—22no—
239Q8×C131—22no—
240Q8×C131—22no—
241Q8×C131—22no—
242Q8×C131—22no—
243Q8×C131—48no—
244Q8×C131—41no—
245Q8×C131—41no—
246Q8×C131—41no—
247Q8×C131—41no—
248Q8×C131#12314yes—
249C2×C4×C131—22no—
250C2×C4×C131—21no—
251C2×C4×C131—22no—
252C2×C4×C131—22no—
253C2×C4×C131—21no—
254C2×C4×C131—22no—
255C2×C4×C131—21no—
256C2×C4×C131—21no—
257C2×C4×C131—22no—
258C2×C4×C131—21no—
259C2×C4×C131—21no—
260C2×C4×C131—21no—
261C2×C4×C131—21no—
262C2×C4×C131—21no—
263C2×C4×C131—21no—
264C2×C4×C131—21no—
265C2×C4×C131—21no—
266C2×C4×C131—21no—
267C2×C4×C131—21no—
268C2×C4×C131—48no—
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—41no—
287C2×C4×C131—41no—
288C2×C4×C131—41no—
289C2×C4×C131—41no—
290C2×C4×C131—41no—
291C2×C4×C131—41no—
292C2×C4×C131#13712yes—
293C2×C4×C131C22×D411yescharacteristic
294C2×C4×C131C2×#4111yescharacteristic
295C2×C4×C131C2×#4111yescharacteristic
296C2×C4×C131C2×#4111yescharacteristic
297C2×C4×C131H(5,𝔽2)11yescharacteristic
298C2×C4×C131H(5,𝔽2)11yescharacteristic
299C8×C131—22no—
300C8×C131—41no—
301C8×C131—41no—
302C8×C131—41no—
303C22×C131—22no—
304C22×C131—22no—
305C22×C131—22no—
306C22×C131—41no—
307C22×C131—41no—
308C22×C131—41no—
309C22×C131—41no—
310C22×C131#52511yescharacteristic
311C22×C131D4211yescharacteristic
312C22×C131#54611yescharacteristic
313C22×C131C2×#13511yescharacteristic
314C22×C131C2×#13711yescharacteristic
315C22×C131#57811yescharacteristic
316C22×C131#57811yescharacteristic
317C4×C131—24no—
318C4×C131—22no—
319C4×C131—41no—
320C4×C131—41no—
321C4×C131—42no—
322C4×C131—42no—
323C4×C131—41no—
324C4×C131—41no—
325C4×C131—81no—
326C4×C131—81no—
327C4×C131—81no—
328C4×C131—81no—
329C4×C131—81no—
330C4×C131C2×#12311yescharacteristic
331C4×C131#53811yescharacteristic
332C4×C131#54611yescharacteristic
333C4×C131#55111yescharacteristic
334C2×C131—42no—
335C2×C131#241811yescharacteristic
336C2×C131#310811yescharacteristic
337C2×C131#312711yescharacteristic
338C2×C131#327011yescharacteristic
339C2×C131#328511yescharacteristic
340C2×C131#330011yescharacteristic
341C2×C131#332811yescharacteristic
342#24902C13111yesmaximal, characteristic, direct product factor, Sylow
343C131#2490211yescharacteristic, direct product factor, Sylow
344C2×#451C2×C13111yescharacteristic
345C2×C4×Q16C2×C13111yescharacteristic, complemented
346#2421C2×C13111yescharacteristic
347Q8×C22⋊C4C2×C13111yescharacteristic
348#2097C2×C13111yescharacteristic, complemented
349#2075C2×C13111yescharacteristic
350#2056C2×C13111yescharacteristic, complemented
351#2035C2×C13111yescharacteristic
352#1933C2×C13111yescharacteristic, complemented
353#1923C2×C13111yescharacteristic
354#1878C2×C13111yescharacteristic, complemented
355#1878C2×C13111yescharacteristic, complemented
356#1865C2×C13111yescharacteristic, complemented
357#1805C2×C13111yescharacteristic, complemented
358#1787C2×C13111yescharacteristic
359C23×Q8C22×C13111yescharacteristic
360C22×Q16C22×C13111yescharacteristic
361C22×Q16C22×C13111yescharacteristic
362C2×C22⋊Q8C22×C13111yescharacteristic
363C2×C4×Q8C22×C13111yescharacteristic
364C2×C4×Q8C22×C13111yescharacteristic
365C2×C4×Q8C22×C13111yescharacteristic
366#451—24no—
367C4×Q16—24no—
368C2×#107C22×C13111yescharacteristic
369C2×#106C22×C13111yescharacteristic
370C2×C4⋊C8C22×C13111yescharacteristic
371C2×#103C22×C13111yescharacteristic
372C2×#103C22×C13111yescharacteristic
373C2×#103C22×C13111yescharacteristic
374C2×#103C22×C13111yescharacteristic
375C2×#103C22×C13111yescharacteristic
376C2×#103C22×C13111yescharacteristic
377C2×#103C22×C13111yescharacteristic
378C2×#103C22×C13111yescharacteristic
379C2×C22⋊C8C22×C13111yescharacteristic
380C2×C22⋊C8C22×C13111yescharacteristic
381C2×C4×C8C22×C13111yescharacteristic
382#400—21no—
383#397—21no—
384#391—21no—
385#391—21no—
386#391C22×C13111yescharacteristic
387#391C22×C13111yescharacteristic
388#391C22×C13111yescharacteristic
389#389C22×C13111yescharacteristic
390#388—21no—
391#387—21no—
392#382C22×C13111yescharacteristic
393#380—21no—
394#380C22×C13111yescharacteristic
395#380C22×C13111yescharacteristic
396C4×C22⋊C4—21no—
397C4×C22⋊C4C22×C13111yescharacteristic
398#340C22×C13111yescharacteristic
399#340C22×C13111yescharacteristic
400#340C22×C13111yescharacteristic
401#340C22×C13111yescharacteristic
402#336C22×C13111yescharacteristic
403#336C22×C13111yescharacteristic
404C22×Q8—22no—
405C22×Q8—22no—
406C22×Q8—21no—
407C22×Q8—22no—
408C22×Q8—22no—
409C22×Q8—41no—
410C22×Q8—41no—
411C22×Q8C23×C13111yescharacteristic
412C22×Q8C23×C13111yescharacteristic
413C22×Q8C23×C13111yescharacteristic
414C23×C4—21no—
415C23×C4C23×C13111yescharacteristic
416C2×Q16—22no—
417C2×Q16—22no—
418C2×Q16—22no—
419C2×Q16—22no—
420C2×Q16—41no—
421C2×Q16D4×C13114yes—
422C22×C8C23×C13111yescharacteristic
423C22×C8C23×C13111yescharacteristic
424C22×C8C23×C13111yescharacteristic
425C22×C8C23×C13111yescharacteristic
426C22⋊Q8—22no—
427C22⋊Q8—41no—
428C4×Q8—22no—
429C4×Q8—22no—
430C4×Q8—22no—
431C4×Q8—41no—
432C4×Q8—41no—
433C4×Q8—41no—
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⋊C4D4×C13111yescharacteristic
448C2×C22⋊C4D4×C13111yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C23×C13111yescharacteristic
453C2×C42C23×C13111yescharacteristic
454#107—22no—
455#106—41no—
456C4⋊C8—41no—
457#103—22no—
458#103—22no—
459#103—22no—
460#103—22no—
461#103—22no—
462#103—22no—
463#103—41no—
464#103—41no—
465C22⋊C8—22no—
466C22⋊C8—41no—
467C4×C8—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95D4×C13111yescharacteristic
480#95D4×C13111yescharacteristic
481C24C2×D4×C13111yescharacteristic
482C2×Q8—24no—
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×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8C2×D4×C13112yes—
503C2×Q8C2×D4×C13112yes—
504C2×Q8#41×C13112yes—
505C2×Q8#41×C13112yes—
506C2×Q8#41×C13112yes—
507C22×C4—21no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4C2×D4×C13111yescharacteristic
525C22×C4C2×D4×C13111yescharacteristic
526C22×C4C2×D4×C13111yescharacteristic
527C22×C4C2×D4×C13111yescharacteristic
528C22×C4C2×D4×C13111yescharacteristic
529C22×C4C24×C13111yescharacteristic
530Q16—28no—
531Q16—44no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8C2×D4×C13112yes—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—42no—
569C42—42no—
570C42—42no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23#135×C13112yes—
578C23C22×D4×C13111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—48no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8#123×C13114yes—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—48no—
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—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4#137×C13112yes—
636C2×C4C22×D4×C13111yescharacteristic
637C2×C4C2×#41×C13111yescharacteristic
638C2×C4C2×#41×C13111yescharacteristic
639C2×C4C2×#41×C13111yescharacteristic
640C2×C4H(5,𝔽2)×C13111yescharacteristic
641C2×C4H(5,𝔽2)×C13111yescharacteristic
642C8—22no—
643C8—41no—
644C8—41no—
645C8—41no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22#525×C13111yescharacteristic
654C22D42×C13111yescharacteristic
655C22#546×C13111yescharacteristic
656C22C2×#135×C13111yescharacteristic
657C22C2×#137×C13111yescharacteristic
658C22#578×C13111yescharacteristic
659C22#578×C13111yescharacteristic
660C4—22no—
661C4—24no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—42no—
667C4—42no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4C2×#123×C13111yescharacteristic
674C4#538×C13111yescharacteristic
675C4#546×C13111yescharacteristic
676C4#551×C13111yescharacteristic
677C2—42no—
678C2#2418×C13111yescharacteristic
679C2#3108×C13111yescharacteristic
680C2#3127×C13111yescharacteristic
681C2#3270×C13111yescharacteristic
682C2#3285×C13111yescharacteristic
683C2#3300×C13111yescharacteristic
684C2#3328×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×C4×Q16×C131C2semidirect
5. #2097×C131C2semidirect
7. #2056×C131C2semidirect
9. #1933×C131C2semidirect
11. #1878×C131C2semidirect
12. #1878×C131C2semidirect
13. #1865×C131C2semidirect
14. #1805×C131C2semidirect
342. #24902C131direct (N × H)
343. C131#24902direct (N × H)
345. C2×C4×Q16C2×C131semidirect
348. #2097C2×C131semidirect
350. #2056C2×C131semidirect
352. #1933C2×C131semidirect
354. #1878C2×C131semidirect
355. #1878C2×C131semidirect
356. #1865C2×C131semidirect
357. #1805C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#451×C1312
C2×C4×Q16×C1312
#2421×C1312
Q8×C22⋊C4×C1312
#2097×C1312
#2075×C1312
#2056×C1312
#2035×C1312
#1933×C1312
#1923×C1312
#1878×C1312
#1865×C1312
#1805×C1312
#1787×C1312
#24902131