Finite Group Databasebeta

← C131×#14488 #45700372

Subgroups — C131×#14488 #45700372

Order 33536.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C131C211yesmaximal, characteristic
2C2×#388×C131C211yesmaximal, characteristic
3C2×#385×C131C211yesmaximal, characteristic
4#1444×C131C211yesmaximal, characteristic, complemented
5#1442×C131C211yesmaximal, characteristic, complemented
6#1442×C131C211yesmaximal, characteristic, complemented
7#1441×C131C211yesmaximal, characteristic, complemented
8#1439×C131C211yesmaximal, characteristic
9#1439×C131C211yesmaximal, characteristic
10#1436×C131C211yesmaximal, characteristic, complemented
11C4⋊#95×C131C211yesmaximal, characteristic, complemented
12C4⋊#95×C131C211yesmaximal, characteristic, complemented
13#1434×C131C211yesmaximal, characteristic, complemented
14C22⋊#95×C131C211yesmaximal, characteristic
15C22⋊#95×C131C211yesmaximal, characteristic
16C24×C4×C131C2211yescharacteristic
17C22×C4⋊C4×C131C2211yescharacteristic
18C22×C4⋊C4×C131C2211yescharacteristic
19C22×C4⋊C4×C131C2211yescharacteristic
20C22×C4⋊C4×C131C2211yescharacteristic
21C22×C4⋊C4×C131C2211yescharacteristic
22C22×C4⋊C4×C131C2211yescharacteristic
23C22×C22⋊C4×C131C2211yescharacteristic
24C22×C22⋊C4×C131C2211yescharacteristic
25C22×C22⋊C4×C131C2211yescharacteristic
26C22×C22⋊C4×C131C2211yescharacteristic
27C22×C22⋊C4×C131C2211yescharacteristic
28C22×C22⋊C4×C131C2211yescharacteristic
29C22×C42×C131C2211yescharacteristic
30C22×C42×C131C2211yescharacteristic
31#388×C131—24no—
32#388×C131C418yescomplemented
33#385×C131—24no—
34C2×#95×C131C2211yescharacteristic
35C2×#95×C131C2211yescharacteristic
36C2×#95×C131C2211yescharacteristic
37C2×#95×C131C2211yescharacteristic
38C2×#95×C131C2211yescharacteristic
39C2×#95×C131C2211yescharacteristic
40C2×#95×C131C2211yescharacteristic
41C2×#95×C131C2211yescharacteristic
42C2×#95×C131C2211yescharacteristic
43C2×#95×C131C2211yescharacteristic
44C2×#95×C131C2211yescharacteristic
45C2×#95×C131C2211yescharacteristic
46C2×#95×C131C2211yescharacteristic
47C2×#95×C131C2211yescharacteristic
48C2×#95×C131C2211yescharacteristic
49C2×#95×C131C2211yescharacteristic
50C2×#95×C131C2211yescharacteristic
51C2×#95×C131C2211yescharacteristic
52C2×#95×C131C2211yescharacteristic
53C2×#95×C131C2211yescharacteristic
54C25×C131C2311yescharacteristic
55C23×C4×C131—22no—
56C23×C4×C131—22no—
57C23×C4×C131—22no—
58C23×C4×C131—41no—
59C23×C4×C131—41no—
60C23×C4×C131—41no—
61C23×C4×C131—41no—
62C23×C4×C131C2311yescharacteristic
63C23×C4×C131C2311yescharacteristic
64C23×C4×C131C2311yescharacteristic
65C23×C4×C131C2311yescharacteristic
66C23×C4×C131C2311yescharacteristic
67C23×C4×C131C2311yescharacteristic
68C23×C4×C131C2311yescharacteristic
69C23×C4×C131C2311yescharacteristic
70C23×C4×C131C2311yescharacteristic
71C23×C4×C131C2311yescharacteristic
72C23×C4×C131C2311yescharacteristic
73C23×C4×C131C2311yescharacteristic
74C23×C4×C131C2311yescharacteristic
75C23×C4×C131C2311yescharacteristic
76C2×C4⋊C4×C131—22no—
77C2×C4⋊C4×C131—22no—
78C2×C4⋊C4×C131—22no—
79C2×C4⋊C4×C131—22no—
80C2×C4⋊C4×C131—22no—
81C2×C4⋊C4×C131—22no—
82C2×C4⋊C4×C131—22no—
83C2×C4⋊C4×C131—41no—
84C2×C4⋊C4×C131—41no—
85C2×C4⋊C4×C131—41no—
86C2×C4⋊C4×C131—41no—
87C2×C4⋊C4×C131—41no—
88C2×C4⋊C4×C131—41no—
89C2×C4⋊C4×C131—41no—
90C2×C4⋊C4×C131—41no—
91C2×C4⋊C4×C131—41no—
92C2×C4⋊C4×C131—41no—
93C2×C4⋊C4×C131C2×C414yescomplemented
94C2×C22⋊C4×C131—22no—
95C2×C22⋊C4×C131—22no—
96C2×C22⋊C4×C131—22no—
97C2×C22⋊C4×C131—22no—
98C2×C22⋊C4×C131—22no—
99C2×C22⋊C4×C131—41no—
100C2×C22⋊C4×C131—41no—
101C2×C22⋊C4×C131—41no—
102C2×C22⋊C4×C131—41no—
103C2×C22⋊C4×C131—41no—
104C2×C22⋊C4×C131—41no—
105C2×C22⋊C4×C131—41no—
106C2×C22⋊C4×C131—41no—
107C2×C22⋊C4×C131C2×C414yes—
108C2×C22⋊C4×C131C2×C414yes—
109C2×C22⋊C4×C131C2×C414yes—
110C2×C22⋊C4×C131D414yes—
111C2×C22⋊C4×C131Q814yes—
112C2×C42×C131—22no—
113C2×C42×C131—22no—
114C2×C42×C131—41no—
115C2×C42×C131—41no—
116C2×C42×C131—41no—
117C2×C42×C131C2×C414yescomplemented
118#95×C131—22no—
119#95×C131—22no—
120#95×C131—22no—
121#95×C131—22no—
122#95×C131—22no—
123#95×C131—22no—
124#95×C131—22no—
125#95×C131—41no—
126#95×C131—41no—
127#95×C131—41no—
128#95×C131—41no—
129#95×C131—41no—
130#95×C131—41no—
131#95×C131—41no—
132#95×C131—41no—
133#95×C131—41no—
134#95×C131—41no—
135#95×C131—41no—
136#95×C131C2×C414yescomplemented
137#95×C131C2×C414yescomplemented
138C24×C131—21no—
139C24×C131—21no—
140C24×C131—21no—
141C24×C131—21no—
142C24×C131—21no—
143C24×C131—21no—
144C24×C131—21no—
145C24×C131—21no—
146C24×C131—21no—
147C24×C131—21no—
148C24×C131—21no—
149C24×C131—21no—
150C24×C131C22×C412yes—
151C24×C131C2×D412yes—
152C24×C131C2×Q812yes—
153C24×C131C2411yescharacteristic
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—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×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—21no—
180C22×C4×C131—21no—
181C22×C4×C131—21no—
182C22×C4×C131—21no—
183C22×C4×C131—21no—
184C22×C4×C131—21no—
185C22×C4×C131—21no—
186C22×C4×C131—21no—
187C22×C4×C131—21no—
188C22×C4×C131—21no—
189C22×C4×C131—21no—
190C22×C4×C131—21no—
191C22×C4×C131—21no—
192C22×C4×C131—21no—
193C22×C4×C131—21no—
194C22×C4×C131—21no—
195C22×C4×C131—21no—
196C22×C4×C131—21no—
197C22×C4×C131—21no—
198C22×C4×C131—21no—
199C22×C4×C131—21no—
200C22×C4×C131—21no—
201C22×C4×C131—21no—
202C22×C4×C131—21no—
203C22×C4×C131—21no—
204C22×C4×C131—21no—
205C22×C4×C131—21no—
206C22×C4×C131—21no—
207C22×C4×C131—21no—
208C22×C4×C131—21no—
209C22×C4×C131—21no—
210C22×C4×C131—21no—
211C22×C4×C131—21no—
212C22×C4×C131—21no—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—21no—
220C22×C4×C131—21no—
221C22×C4×C131—21no—
222C22×C4×C131—21no—
223C22×C4×C131—21no—
224C22×C4×C131—21no—
225C22×C4×C131—21no—
226C22×C4×C131—21no—
227C22×C4×C131—21no—
228C22×C4×C131—21no—
229C22×C4×C131—21no—
230C22×C4×C131—21no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—21no—
237C22×C4×C131—21no—
238C22×C4×C131—44no—
239C22×C4×C131—44no—
240C22×C4×C131—44no—
241C22×C4×C131—44no—
242C22×C4×C131—44no—
243C22×C4×C131—44no—
244C22×C4×C131—44no—
245C22×C4×C131C22×C412yes—
246C22×C4×C131C22×C412yes—
247C22×C4×C131C22×C412yes—
248C22×C4×C131C22×C412yes—
249C22×C4×C131C22×C412yes—
250C22×C4×C131C22×C412yes—
251C22×C4×C131C2×D412yes—
252C22×C4×C131C2×D412yes—
253C22×C4×C131C2×Q812yes—
254C22×C4×C131C2×Q812yes—
255C22×C4×C131#4112yes—
256C22×C4×C131#4112yes—
257C22×C4×C131#4112yes—
258C22×C4×C131#4112yes—
259C4⋊C4×C131—44no—
260C4⋊C4×C131—44no—
261C4⋊C4×C131—44no—
262C4⋊C4×C131—44no—
263C4⋊C4×C131—44no—
264C4⋊C4×C131—44no—
265C22⋊C4×C131—44no—
266C22⋊C4×C131—44no—
267C22⋊C4×C131—44no—
268C22⋊C4×C131—44no—
269C22⋊C4×C131—44no—
270C22⋊C4×C131C4⋊C4116yescomplemented
271C42×C131—44no—
272C42×C131—44no—
273C23×C131—22no—
274C23×C131—22no—
275C23×C131—22no—
276C23×C131—22no—
277C23×C131—22no—
278C23×C131—22no—
279C23×C131—22no—
280C23×C131—22no—
281C23×C131—22no—
282C23×C131—22no—
283C23×C131—22no—
284C23×C131—22no—
285C23×C131—22no—
286C23×C131—22no—
287C23×C131—22no—
288C23×C131—22no—
289C23×C131—22no—
290C23×C131—22no—
291C23×C131—41no—
292C23×C131—41no—
293C23×C131—41no—
294C23×C131—41no—
295C23×C131—41no—
296C23×C131—41no—
297C23×C131—41no—
298C23×C131—41no—
299C23×C131—41no—
300C23×C131—41no—
301C23×C131—41no—
302C23×C131—41no—
303C23×C131—41no—
304C23×C131—41no—
305C23×C131—41no—
306C23×C131—41no—
307C23×C131C2×C4⋊C414yes—
308C23×C131C23×C411yescharacteristic
309C23×C131C22×D411yescharacteristic
310C23×C131C22×Q811yescharacteristic
311C23×C131C2×#4111yescharacteristic
312C23×C131C2×#4111yescharacteristic
313C23×C131C2×#4111yescharacteristic
314C23×C131C2×#4111yescharacteristic
315C23×C131H(5,𝔽2)11yescharacteristic
316C23×C131H(5,𝔽2)11yescharacteristic
317C23×C131H(5,𝔽2)11yescharacteristic
318C23×C131H(5,𝔽2)11yescharacteristic
319C23×C131H(5,𝔽2)11yescharacteristic
320C23×C131H(5,𝔽2)11yescharacteristic
321C23×C1312−1+411yescharacteristic
322C23×C1312−1+411yescharacteristic
323C2×C4×C131—22no—
324C2×C4×C131—22no—
325C2×C4×C131—22no—
326C2×C4×C131—22no—
327C2×C4×C131—22no—
328C2×C4×C131—22no—
329C2×C4×C131—22no—
330C2×C4×C131—22no—
331C2×C4×C131—22no—
332C2×C4×C131—22no—
333C2×C4×C131—22no—
334C2×C4×C131—22no—
335C2×C4×C131—22no—
336C2×C4×C131—22no—
337C2×C4×C131—22no—
338C2×C4×C131—22no—
339C2×C4×C131—22no—
340C2×C4×C131—22no—
341C2×C4×C131—22no—
342C2×C4×C131—22no—
343C2×C4×C131—22no—
344C2×C4×C131—22no—
345C2×C4×C131—22no—
346C2×C4×C131—22no—
347C2×C4×C131—22no—
348C2×C4×C131—22no—
349C2×C4×C131—22no—
350C2×C4×C131—22no—
351C2×C4×C131—22no—
352C2×C4×C131—22no—
353C2×C4×C131—22no—
354C2×C4×C131—22no—
355C2×C4×C131—22no—
356C2×C4×C131—22no—
357C2×C4×C131—22no—
358C2×C4×C131—22no—
359C2×C4×C131—416no—
360C2×C4×C131—41no—
361C2×C4×C131—41no—
362C2×C4×C131—41no—
363C2×C4×C131—41no—
364C2×C4×C131—41no—
365C2×C4×C131—41no—
366C2×C4×C131—41no—
367C2×C4×C131—41no—
368C2×C4×C131—41no—
369C2×C4×C131—41no—
370C2×C4×C131—41no—
371C2×C4×C131—41no—
372C2×C4×C131—41no—
373C2×C4×C131—41no—
374C2×C4×C131—41no—
375C2×C4×C131—41no—
376C2×C4×C131—41no—
377C2×C4×C131—41no—
378C2×C4×C131—41no—
379C2×C4×C131—41no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—41no—
383C2×C4×C131—41no—
384C2×C4×C131—41no—
385C2×C4×C131—41no—
386C2×C4×C131—41no—
387C2×C4×C131—41no—
388C2×C4×C131—41no—
389C2×C4×C131—41no—
390C2×C4×C131—41no—
391C2×C4×C131—41no—
392C2×C4×C131—41no—
393C2×C4×C131—41no—
394C2×C4×C131—41no—
395C2×C4×C131—41no—
396C2×C4×C131—41no—
397C2×C4×C131—41no—
398C2×C4×C131—41no—
399C2×C4×C131—41no—
400C2×C4×C131—41no—
401C2×C4×C131—41no—
402C2×C4×C131—41no—
403C2×C4×C131—41no—
404C2×C4×C131—41no—
405C2×C4×C131—41no—
406C2×C4×C131—41no—
407C2×C4×C131—41no—
408C2×C4×C131—41no—
409C2×C4×C131—41no—
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×C131C2×C4⋊C414yes—
421C2×C4×C131C2×C4⋊C414yes—
422C22×C131—24no—
423C22×C131—24no—
424C22×C131—24no—
425C22×C131—42no—
426C22×C131—42no—
427C22×C131—42no—
428C22×C131—42no—
429C22×C131—42no—
430C22×C131—42no—
431C22×C131—42no—
432C22×C131—42no—
433C22×C131—42no—
434C22×C131—42no—
435C22×C131—42no—
436C22×C131—42no—
437C22×C131C22×C4⋊C411yescharacteristic
438C22×C131C4×#4111yescharacteristic
439C22×C131C4×#4111yescharacteristic
440C22×C131#51811yescharacteristic
441C22×C131#51811yescharacteristic
442C22×C131#52011yescharacteristic
443C22×C131#52011yescharacteristic
444C22×C131#53511yescharacteristic
445C22×C131#53611yescharacteristic
446C22×C131#53811yescharacteristic
447C22×C131#53811yescharacteristic
448C22×C131#53811yescharacteristic
449C22×C131#53911yescharacteristic
450C22×C131#54011yescharacteristic
451C22×C131#54211yescharacteristic
452C22×C131#54211yescharacteristic
453C22×C131#54211yescharacteristic
454C22×C131#54411yescharacteristic
455C22×C131#54411yescharacteristic
456C22×C131#54611yescharacteristic
457C22×C131#54611yescharacteristic
458C22×C131#54611yescharacteristic
459C22×C131#54611yescharacteristic
460C22×C131#55111yescharacteristic
461C22×C131#55211yescharacteristic
462C22×C131#55311yescharacteristic
463C22×C131#55411yescharacteristic
464C22×C131#55411yescharacteristic
465C22×C131#55411yescharacteristic
466C22×C131#55411yescharacteristic
467C22×C131#55611yescharacteristic
468C22×C131#56011yescharacteristic
469C22×C131#56011yescharacteristic
470C22×C131#56211yescharacteristic
471C22×C131#56211yescharacteristic
472C4×C131—24no—
473C4×C131—24no—
474C4×C131—42no—
475C4×C131—42no—
476C4×C131—42no—
477C4×C131—42no—
478C4×C131—42no—
479C4×C131—42no—
480C4×C131—42no—
481C4×C131—42no—
482C4×C131—81no—
483C4×C131—81no—
484C4×C131—81no—
485C4×C131—81no—
486C2×C131—44no—
487C2×C131#231711yescharacteristic
488C2×C131#233511yescharacteristic
489C2×C131#233711yescharacteristic
490C2×C131#234911yescharacteristic
491C2×C131#234911yescharacteristic
492C2×C131#237311yescharacteristic
493C2×C131#237711yescharacteristic
494C2×C131#268511yescharacteristic
495C2×C131#268711yescharacteristic
496C2×C131#270011yescharacteristic
497C2×C131#270311yescharacteristic
498C2×C131#274211yescharacteristic
499C2×C131#276811yescharacteristic
500C2×C131#278811yescharacteristic
501C2×C131#279011yescharacteristic
502#14488C13111yesmaximal, characteristic, direct product factor, Sylow
503C131#1448811yescharacteristic, direct product factor, Sylow
504C2×#388C2×C13111yescharacteristic
505C2×#388C2×C13111yescharacteristic
506C2×#385C2×C13111yescharacteristic
507#1444C2×C13111yescharacteristic, complemented
508#1442C2×C13111yescharacteristic, complemented
509#1442C2×C13111yescharacteristic, complemented
510#1441C2×C13111yescharacteristic, complemented
511#1439C2×C13111yescharacteristic
512#1439C2×C13111yescharacteristic
513#1436C2×C13111yescharacteristic, complemented
514C4⋊#95C2×C13111yescharacteristic, complemented
515C4⋊#95C2×C13111yescharacteristic, complemented
516#1434C2×C13111yescharacteristic, complemented
517C22⋊#95C2×C13111yescharacteristic
518C22⋊#95C2×C13111yescharacteristic
519C24×C4C22×C13111yescharacteristic
520C22×C4⋊C4C22×C13111yescharacteristic
521C22×C4⋊C4C22×C13111yescharacteristic
522C22×C4⋊C4C22×C13111yescharacteristic
523C22×C4⋊C4C22×C13111yescharacteristic
524C22×C4⋊C4C22×C13111yescharacteristic
525C22×C4⋊C4C22×C13111yescharacteristic
526C22×C22⋊C4C22×C13111yescharacteristic
527C22×C22⋊C4C22×C13111yescharacteristic
528C22×C22⋊C4C22×C13111yescharacteristic
529C22×C22⋊C4C22×C13111yescharacteristic
530C22×C22⋊C4C22×C13111yescharacteristic
531C22×C22⋊C4C22×C13111yescharacteristic
532C22×C42C22×C13111yescharacteristic
533C22×C42C22×C13111yescharacteristic
534#388—24no—
535#388C4×C13118yescomplemented
536#385—24no—
537C2×#95C22×C13111yescharacteristic
538C2×#95C22×C13111yescharacteristic
539C2×#95C22×C13111yescharacteristic
540C2×#95C22×C13111yescharacteristic
541C2×#95C22×C13111yescharacteristic
542C2×#95C22×C13111yescharacteristic
543C2×#95C22×C13111yescharacteristic
544C2×#95C22×C13111yescharacteristic
545C2×#95C22×C13111yescharacteristic
546C2×#95C22×C13111yescharacteristic
547C2×#95C22×C13111yescharacteristic
548C2×#95C22×C13111yescharacteristic
549C2×#95C22×C13111yescharacteristic
550C2×#95C22×C13111yescharacteristic
551C2×#95C22×C13111yescharacteristic
552C2×#95C22×C13111yescharacteristic
553C2×#95C22×C13111yescharacteristic
554C2×#95C22×C13111yescharacteristic
555C2×#95C22×C13111yescharacteristic
556C2×#95C22×C13111yescharacteristic
557C25C23×C13111yescharacteristic
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4C23×C13111yescharacteristic
566C23×C4C23×C13111yescharacteristic
567C23×C4C23×C13111yescharacteristic
568C23×C4C23×C13111yescharacteristic
569C23×C4C23×C13111yescharacteristic
570C23×C4C23×C13111yescharacteristic
571C23×C4C23×C13111yescharacteristic
572C23×C4C23×C13111yescharacteristic
573C23×C4C23×C13111yescharacteristic
574C23×C4C23×C13111yescharacteristic
575C23×C4C23×C13111yescharacteristic
576C23×C4C23×C13111yescharacteristic
577C23×C4C23×C13111yescharacteristic
578C23×C4C23×C13111yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4C2×C4×C13114yescomplemented
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4C2×C4×C13114yes—
611C2×C22⋊C4C2×C4×C13114yes—
612C2×C22⋊C4C2×C4×C13114yes—
613C2×C22⋊C4D4×C13114yes—
614C2×C22⋊C4Q8×C13114yes—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42C2×C4×C13114yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95C2×C4×C13114yescomplemented
640#95C2×C4×C13114yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C13112yes—
654C24C2×D4×C13112yes—
655C24C2×Q8×C13112yes—
656C24C24×C13111yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4C22×C4×C13112yes—
749C22×C4C22×C4×C13112yes—
750C22×C4C22×C4×C13112yes—
751C22×C4C22×C4×C13112yes—
752C22×C4C22×C4×C13112yes—
753C22×C4C22×C4×C13112yes—
754C22×C4C2×D4×C13112yes—
755C22×C4C2×D4×C13112yes—
756C22×C4C2×Q8×C13112yes—
757C22×C4C2×Q8×C13112yes—
758C22×C4#41×C13112yes—
759C22×C4#41×C13112yes—
760C22×C4#41×C13112yes—
761C22×C4#41×C13112yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4C4⋊C4×C131116yescomplemented
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C13114yes—
811C23C23×C4×C13111yescharacteristic
812C23C22×D4×C13111yescharacteristic
813C23C22×Q8×C13111yescharacteristic
814C23C2×#41×C13111yescharacteristic
815C23C2×#41×C13111yescharacteristic
816C23C2×#41×C13111yescharacteristic
817C23C2×#41×C13111yescharacteristic
818C23H(5,𝔽2)×C13111yescharacteristic
819C23H(5,𝔽2)×C13111yescharacteristic
820C23H(5,𝔽2)×C13111yescharacteristic
821C23H(5,𝔽2)×C13111yescharacteristic
822C23H(5,𝔽2)×C13111yescharacteristic
823C23H(5,𝔽2)×C13111yescharacteristic
824C232−1+4×C13111yescharacteristic
825C232−1+4×C13111yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—416no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
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×C4C2×C4⋊C4×C13114yes—
924C2×C4C2×C4⋊C4×C13114yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C13111yescharacteristic
941C22C4×#41×C13111yescharacteristic
942C22C4×#41×C13111yescharacteristic
943C22#518×C13111yescharacteristic
944C22#518×C13111yescharacteristic
945C22#520×C13111yescharacteristic
946C22#520×C13111yescharacteristic
947C22#535×C13111yescharacteristic
948C22#536×C13111yescharacteristic
949C22#538×C13111yescharacteristic
950C22#538×C13111yescharacteristic
951C22#538×C13111yescharacteristic
952C22#539×C13111yescharacteristic
953C22#540×C13111yescharacteristic
954C22#542×C13111yescharacteristic
955C22#542×C13111yescharacteristic
956C22#542×C13111yescharacteristic
957C22#544×C13111yescharacteristic
958C22#544×C13111yescharacteristic
959C22#546×C13111yescharacteristic
960C22#546×C13111yescharacteristic
961C22#546×C13111yescharacteristic
962C22#546×C13111yescharacteristic
963C22#551×C13111yescharacteristic
964C22#552×C13111yescharacteristic
965C22#553×C13111yescharacteristic
966C22#554×C13111yescharacteristic
967C22#554×C13111yescharacteristic
968C22#554×C13111yescharacteristic
969C22#554×C13111yescharacteristic
970C22#556×C13111yescharacteristic
971C22#560×C13111yescharacteristic
972C22#560×C13111yescharacteristic
973C22#562×C13111yescharacteristic
974C22#562×C13111yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2#2317×C13111yescharacteristic
991C2#2335×C13111yescharacteristic
992C2#2337×C13111yescharacteristic
993C2#2349×C13111yescharacteristic
994C2#2349×C13111yescharacteristic
995C2#2373×C13111yescharacteristic
996C2#2377×C13111yescharacteristic
997C2#2685×C13111yescharacteristic
998C2#2687×C13111yescharacteristic
999C2#2700×C13111yescharacteristic
1000C2#2703×C13111yescharacteristic
1001C2#2742×C13111yescharacteristic
1002C2#2768×C13111yescharacteristic
1003C2#2788×C13111yescharacteristic
1004C2#2790×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
prime radicalC25×C131C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1444×C131C2semidirect
5. #1442×C131C2semidirect
6. #1442×C131C2semidirect
7. #1441×C131C2semidirect
10. #1436×C131C2semidirect
11. C4⋊#95×C131C2semidirect
12. C4⋊#95×C131C2semidirect
13. #1434×C131C2semidirect
32. #388×C131C4semidirect
93. C2×C4⋊C4×C131C2×C4semidirect
117. C2×C42×C131C2×C4semidirect
136. #95×C131C2×C4semidirect
137. #95×C131C2×C4semidirect
270. C22⋊C4×C131C4⋊C4semidirect
502. #14488C131direct (N × H)
503. C131#14488direct (N × H)
507. #1444C2×C131semidirect
508. #1442C2×C131semidirect
509. #1442C2×C131semidirect
510. #1441C2×C131semidirect
513. #1436C2×C131semidirect
514. C4⋊#95C2×C131semidirect
515. C4⋊#95C2×C131semidirect
516. #1434C2×C131semidirect
535. #388C4×C131semidirect
596. C2×C4⋊C4C2×C4×C131semidirect
620. C2×C42C2×C4×C131semidirect
639. #95C2×C4×C131semidirect
640. #95C2×C4×C131semidirect
773. C22⋊C4C4⋊C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1312
C2×#385×C1312
#1444×C1312
#1442×C1312
#1441×C1312
#1439×C1312
#1436×C1312
C4⋊#95×C1312
#1434×C1312
C22⋊#95×C1312
#14488131