Finite Group Databasebeta

← C131×#14375 #45700259

Subgroups — C131×#14375 #45700259

Order 33536.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#386×C131C211yesmaximal, characteristic
2C2×#386×C131C211yesmaximal, characteristic
3C2×#381×C131C211yesmaximal, characteristic, complemented
4#1443×C131C211yesmaximal, characteristic, complemented
5#1443×C131C211yesmaximal, characteristic, complemented
6#1442×C131C211yesmaximal, characteristic, complemented
7#1439×C131C211yesmaximal, characteristic, complemented
8#1439×C131C211yesmaximal, characteristic, complemented
9#1438×C131C211yesmaximal, characteristic
10#1437×C131C211yesmaximal, characteristic, complemented
11#1437×C131C211yesmaximal, characteristic, complemented
12#1434×C131C211yesmaximal, characteristic, complemented
13C22⋊#95×C131C211yesmaximal, characteristic, complemented
14C22⋊#95×C131C211yesmaximal, characteristic, complemented
15C22⋊#95×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C24×C4×C131C2211yescharacteristic
18C24×C4×C131C2211yescharacteristic
19C22×C4⋊C4×C131C2211yescharacteristic
20C22×C22⋊C4×C131C2211yescharacteristic
21C22×C22⋊C4×C131C2211yescharacteristic
22C22×C22⋊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×C22⋊C4×C131C2211yescharacteristic
30C22×C42×C131C2211yescharacteristic
31#386×C131—24no—
32#386×C131C418yescomplemented
33#381×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
55C25×C131C2311yescharacteristic
56C22×D4×C131—22no—
57C22×D4×C131—22no—
58C22×D4×C131—22no—
59C22×D4×C131—22no—
60C22×D4×C131—41no—
61C22×D4×C131—41no—
62C22×D4×C131C2×C414yes—
63C23×C4×C131—22no—
64C23×C4×C131—22no—
65C23×C4×C131—22no—
66C23×C4×C131—22no—
67C23×C4×C131—22no—
68C23×C4×C131—41no—
69C23×C4×C131—41no—
70C23×C4×C131—41no—
71C23×C4×C131—41no—
72C23×C4×C131—41no—
73C23×C4×C131—41no—
74C23×C4×C131—41no—
75C23×C4×C131—41no—
76C23×C4×C131C2×C414yescomplemented
77C23×C4×C131C2311yescharacteristic
78C23×C4×C131C2311yescharacteristic
79C23×C4×C131C2311yescharacteristic
80C23×C4×C131C2311yescharacteristic
81C23×C4×C131C2311yescharacteristic
82C23×C4×C131C2311yescharacteristic
83C23×C4×C131C2311yescharacteristic
84C23×C4×C131C2311yescharacteristic
85C23×C4×C131C2311yescharacteristic
86C23×C4×C131C2311yescharacteristic
87C23×C4×C131C2311yescharacteristic
88C23×C4×C131C2311yescharacteristic
89C23×C4×C131C2311yescharacteristic
90C2×C4⋊C4×C131—41no—
91C2×C4⋊C4×C131—41no—
92C2×C4⋊C4×C131—41no—
93C2×C22⋊C4×C131—22no—
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—22no—
100C2×C22⋊C4×C131—22no—
101C2×C22⋊C4×C131—22no—
102C2×C22⋊C4×C131—22no—
103C2×C22⋊C4×C131—41no—
104C2×C22⋊C4×C131—41no—
105C2×C22⋊C4×C131—41no—
106C2×C22⋊C4×C131—41no—
107C2×C22⋊C4×C131—41no—
108C2×C22⋊C4×C131—41no—
109C2×C22⋊C4×C131—41no—
110C2×C22⋊C4×C131—41no—
111C2×C22⋊C4×C131—41no—
112C2×C22⋊C4×C131—41no—
113C2×C22⋊C4×C131—41no—
114C2×C22⋊C4×C131—41no—
115C2×C22⋊C4×C131—41no—
116C2×C22⋊C4×C131—41no—
117C2×C22⋊C4×C131—41no—
118C2×C22⋊C4×C131—41no—
119C2×C22⋊C4×C131C2×C414yes—
120C2×C22⋊C4×C131C2×C414yes—
121C2×C22⋊C4×C131C2×C414yescomplemented
122C2×C22⋊C4×C131D414yes—
123C2×C42×C131—22no—
124C2×C42×C131—41no—
125C2×C42×C131—41no—
126#95×C131—22no—
127#95×C131—22no—
128#95×C131—22no—
129#95×C131—22no—
130#95×C131—22no—
131#95×C131—22no—
132#95×C131—22no—
133#95×C131—41no—
134#95×C131—41no—
135#95×C131—41no—
136#95×C131—41no—
137#95×C131—41no—
138#95×C131—41no—
139#95×C131—41no—
140#95×C131—41no—
141#95×C131—41no—
142#95×C131—41no—
143#95×C131—41no—
144#95×C131C2×C414yescomplemented
145#95×C131C2×C414yescomplemented
146C24×C131—21no—
147C24×C131—21no—
148C24×C131—21no—
149C24×C131—21no—
150C24×C131—21no—
151C24×C131—21no—
152C24×C131—21no—
153C24×C131—21no—
154C24×C131—21no—
155C24×C131—21no—
156C24×C131—21no—
157C24×C131—21no—
158C24×C131—21no—
159C24×C131—21no—
160C24×C131—21no—
161C24×C131—21no—
162C24×C131—21no—
163C24×C131—21no—
164C24×C131—21no—
165C24×C131—21no—
166C24×C131—21no—
167C24×C131—21no—
168C24×C131—21no—
169C24×C131—21no—
170C24×C131C22×C412yes—
171C24×C131C22×C412yes—
172C24×C131C2×D412yes—
173C24×C131#4112yes—
174C24×C131#4112yes—
175C24×C131#4112yes—
176C24×C131C2411yescharacteristic
177C2×D4×C131—28no—
178C2×D4×C131—28no—
179C2×D4×C131—44no—
180C2×D4×C131—44no—
181C2×D4×C131—44no—
182C2×D4×C131—44no—
183C2×D4×C131—44no—
184C22×C4×C131—28no—
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—21no—
239C22×C4×C131—21no—
240C22×C4×C131—21no—
241C22×C4×C131—21no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—21no—
245C22×C4×C131—21no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—21no—
249C22×C4×C131—21no—
250C22×C4×C131—21no—
251C22×C4×C131—21no—
252C22×C4×C131—21no—
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—21no—
264C22×C4×C131—21no—
265C22×C4×C131—21no—
266C22×C4×C131—21no—
267C22×C4×C131—44no—
268C22×C4×C131—44no—
269C22×C4×C131—44no—
270C22×C4×C131—44no—
271C22×C4×C131—44no—
272C22×C4×C131—44no—
273C22×C4×C131—44no—
274C22×C4×C131—44no—
275C22×C4×C131—44no—
276C22×C4×C131—44no—
277C22×C4×C131—44no—
278C22×C4×C131—44no—
279C22×C4×C131—44no—
280C22×C4×C131C22×C412yes—
281C22×C4×C131C22×C412yes—
282C22×C4×C131C22×C412yes—
283C22×C4×C131C22×C412yes—
284C22×C4×C131C22×C412yes—
285C22×C4×C131C2×D412yes—
286C22×C4×C131C2×D412yes—
287C22×C4×C131#4112yes—
288C22×C4×C131#4112yes—
289C4⋊C4×C131—44no—
290C22⋊C4×C131—44no—
291C22⋊C4×C131—44no—
292C22⋊C4×C131—44no—
293C22⋊C4×C131—44no—
294C22⋊C4×C131—44no—
295C22⋊C4×C131—44no—
296C22⋊C4×C131—44no—
297C22⋊C4×C131—44no—
298C22⋊C4×C131—44no—
299C22⋊C4×C131—44no—
300C42×C131—44no—
301C23×C131—22no—
302C23×C131—22no—
303C23×C131—22no—
304C23×C131—22no—
305C23×C131—22no—
306C23×C131—22no—
307C23×C131—22no—
308C23×C131—22no—
309C23×C131—22no—
310C23×C131—22no—
311C23×C131—22no—
312C23×C131—22no—
313C23×C131—22no—
314C23×C131—22no—
315C23×C131—22no—
316C23×C131—22no—
317C23×C131—22no—
318C23×C131—22no—
319C23×C131—22no—
320C23×C131—22no—
321C23×C131—22no—
322C23×C131—22no—
323C23×C131—22no—
324C23×C131—22no—
325C23×C131—22no—
326C23×C131—22no—
327C23×C131—22no—
328C23×C131—22no—
329C23×C131—22no—
330C23×C131—22no—
331C23×C131—22no—
332C23×C131—22no—
333C23×C131—22no—
334C23×C131—22no—
335C23×C131—22no—
336C23×C131—22no—
337C23×C131—41no—
338C23×C131—41no—
339C23×C131—41no—
340C23×C131—41no—
341C23×C131—41no—
342C23×C131—41no—
343C23×C131—41no—
344C23×C131—41no—
345C23×C131—41no—
346C23×C131—41no—
347C23×C131—41no—
348C23×C131—41no—
349C23×C131—41no—
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—41no—
360C23×C131—41no—
361C23×C131—41no—
362C23×C131—41no—
363C23×C131—41no—
364C23×C131—41no—
365C23×C131—41no—
366C23×C131—41no—
367C23×C131—41no—
368C23×C131—41no—
369C23×C131#11714yes—
370C23×C131C4×D414yes—
371C23×C131C23×C411yescharacteristic
372C23×C131C22×D411yescharacteristic
373C23×C131C2×#4111yescharacteristic
374C23×C131C2×#4111yescharacteristic
375C23×C131C2×#4111yescharacteristic
376C23×C131C2×#4111yescharacteristic
377C23×C131C2×#4111yescharacteristic
378C23×C131H(5,𝔽2)11yescharacteristic
379C23×C131H(5,𝔽2)11yescharacteristic
380C23×C131H(5,𝔽2)11yescharacteristic
381C23×C131H(5,𝔽2)11yescharacteristic
382C23×C131H(5,𝔽2)11yescharacteristic
383C23×C131H(5,𝔽2)11yescharacteristic
384C23×C131H(5,𝔽2)11yescharacteristic
385C23×C1312−1+411yescharacteristic
386D4×C131—416no—
387C2×C4×C131—22no—
388C2×C4×C131—22no—
389C2×C4×C131—22no—
390C2×C4×C131—22no—
391C2×C4×C131—22no—
392C2×C4×C131—22no—
393C2×C4×C131—22no—
394C2×C4×C131—22no—
395C2×C4×C131—22no—
396C2×C4×C131—22no—
397C2×C4×C131—22no—
398C2×C4×C131—22no—
399C2×C4×C131—22no—
400C2×C4×C131—22no—
401C2×C4×C131—22no—
402C2×C4×C131—22no—
403C2×C4×C131—22no—
404C2×C4×C131—22no—
405C2×C4×C131—22no—
406C2×C4×C131—22no—
407C2×C4×C131—22no—
408C2×C4×C131—22no—
409C2×C4×C131—22no—
410C2×C4×C131—22no—
411C2×C4×C131—22no—
412C2×C4×C131—22no—
413C2×C4×C131—22no—
414C2×C4×C131—416no—
415C2×C4×C131—416no—
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—41no—
427C2×C4×C131—41no—
428C2×C4×C131—41no—
429C2×C4×C131—41no—
430C2×C4×C131—41no—
431C2×C4×C131—41no—
432C2×C4×C131—41no—
433C2×C4×C131—41no—
434C2×C4×C131—41no—
435C2×C4×C131—41no—
436C2×C4×C131—41no—
437C2×C4×C131—41no—
438C2×C4×C131—41no—
439C2×C4×C131—41no—
440C2×C4×C131—41no—
441C2×C4×C131—41no—
442C2×C4×C131—41no—
443C2×C4×C131—41no—
444C2×C4×C131—41no—
445C2×C4×C131—41no—
446C2×C4×C131—41no—
447C2×C4×C131—41no—
448C2×C4×C131—41no—
449C2×C4×C131—41no—
450C2×C4×C131—41no—
451C2×C4×C131—41no—
452C2×C4×C131—41no—
453C2×C4×C131—41no—
454C2×C4×C131—41no—
455C2×C4×C131—41no—
456C2×C4×C131—41no—
457C2×C4×C131—41no—
458C2×C4×C131—41no—
459C2×C4×C131—41no—
460C2×C4×C131—41no—
461C2×C4×C131—41no—
462C2×C4×C131—41no—
463C2×C4×C131—41no—
464C2×C4×C131—41no—
465C2×C4×C131—41no—
466C2×C4×C131—41no—
467C2×C4×C131—41no—
468C2×C4×C131—41no—
469C2×C4×C131—41no—
470C2×C4×C131—41no—
471C2×C4×C131—41no—
472C2×C4×C131—41no—
473C2×C4×C131—41no—
474C2×C4×C131—41no—
475C2×C4×C131—41no—
476C2×C4×C131—41no—
477C2×C4×C131—41no—
478C2×C4×C131—41no—
479C2×C4×C131—41no—
480C22×C131—24no—
481C22×C131—24no—
482C22×C131—24no—
483C22×C131—24no—
484C22×C131—24no—
485C22×C131—24no—
486C22×C131—42no—
487C22×C131—42no—
488C22×C131—42no—
489C22×C131—42no—
490C22×C131—42no—
491C22×C131—42no—
492C22×C131—42no—
493C22×C131—42no—
494C22×C131—42no—
495C22×C131—42no—
496C22×C131—42no—
497C22×C131—42no—
498C22×C131—42no—
499C22×C131—42no—
500C22×C131—42no—
501C22×C131—42no—
502C22×C131—42no—
503C22×C131—42no—
504C22×C131—42no—
505C22×C131—42no—
506C22×C131—42no—
507C22×C131—42no—
508C22×C131—42no—
509C22×C131—42no—
510C22×C131C2×#11711yescharacteristic
511C22×C131C2×C4×D411yescharacteristic
512C22×C131C4×#4111yescharacteristic
513C22×C131#51811yescharacteristic
514C22×C131#51811yescharacteristic
515C22×C131#51811yescharacteristic
516C22×C131#52011yescharacteristic
517C22×C131#53411yescharacteristic
518C22×C131#53511yescharacteristic
519C22×C131#53811yescharacteristic
520C22×C131#53811yescharacteristic
521C22×C131#53811yescharacteristic
522C22×C131#53811yescharacteristic
523C22×C131#53811yescharacteristic
524C22×C131#53811yescharacteristic
525C22×C131#53911yescharacteristic
526C22×C131#53911yescharacteristic
527C22×C131#54011yescharacteristic
528C22×C131#54011yescharacteristic
529C22×C131#54611yescharacteristic
530C22×C131#54611yescharacteristic
531C22×C131#54611yescharacteristic
532C22×C131#54711yescharacteristic
533C22×C131#55111yescharacteristic
534C22×C131#55111yescharacteristic
535C22×C131#55111yescharacteristic
536C22×C131#55111yescharacteristic
537C22×C131#55111yescharacteristic
538C22×C131#55211yescharacteristic
539C22×C131#55311yescharacteristic
540C22×C131#55311yescharacteristic
541C22×C131#56011yescharacteristic
542C22×C131#56011yescharacteristic
543C22×C131#56211yescharacteristic
544C22×C131#56211yescharacteristic
545C4×C131—42no—
546C4×C131—42no—
547C4×C131—42no—
548C4×C131—42no—
549C4×C131—42no—
550C4×C131—42no—
551C4×C131—42no—
552C4×C131—42no—
553C4×C131—42no—
554C4×C131—81no—
555C4×C131—81no—
556C4×C131—81no—
557C4×C131—81no—
558C2×C131—44no—
559C2×C131—44no—
560C2×C131#231811yescharacteristic
561C2×C131#232111yescharacteristic
562C2×C131#233311yescharacteristic
563C2×C131#234211yescharacteristic
564C2×C131#235311yescharacteristic
565C2×C131#235911yescharacteristic
566C2×C131#237711yescharacteristic
567C2×C131#269711yescharacteristic
568C2×C131#270311yescharacteristic
569C2×C131#270611yescharacteristic
570C2×C131#270811yescharacteristic
571C2×C131#274311yescharacteristic
572C2×C131#274911yescharacteristic
573C2×C131#275011yescharacteristic
574C2×C131#276011yescharacteristic
575#14375C13111yesmaximal, characteristic, direct product factor, Sylow
576C131#1437511yescharacteristic, direct product factor, Sylow
577C2×#386C2×C13111yescharacteristic
578C2×#386C2×C13111yescharacteristic
579C2×#381C2×C13111yescharacteristic, complemented
580#1443C2×C13111yescharacteristic, complemented
581#1443C2×C13111yescharacteristic, complemented
582#1442C2×C13111yescharacteristic, complemented
583#1439C2×C13111yescharacteristic, complemented
584#1439C2×C13111yescharacteristic, complemented
585#1438C2×C13111yescharacteristic
586#1437C2×C13111yescharacteristic, complemented
587#1437C2×C13111yescharacteristic, complemented
588#1434C2×C13111yescharacteristic, complemented
589C22⋊#95C2×C13111yescharacteristic, complemented
590C22⋊#95C2×C13111yescharacteristic, complemented
591C22⋊#95C2×C13111yescharacteristic, complemented
592C23×D4C22×C13111yescharacteristic
593C24×C4C22×C13111yescharacteristic
594C24×C4C22×C13111yescharacteristic
595C22×C4⋊C4C22×C13111yescharacteristic
596C22×C22⋊C4C22×C13111yescharacteristic
597C22×C22⋊C4C22×C13111yescharacteristic
598C22×C22⋊C4C22×C13111yescharacteristic
599C22×C22⋊C4C22×C13111yescharacteristic
600C22×C22⋊C4C22×C13111yescharacteristic
601C22×C22⋊C4C22×C13111yescharacteristic
602C22×C22⋊C4C22×C13111yescharacteristic
603C22×C22⋊C4C22×C13111yescharacteristic
604C22×C22⋊C4C22×C13111yescharacteristic
605C22×C22⋊C4C22×C13111yescharacteristic
606C22×C42C22×C13111yescharacteristic
607#386—24no—
608#386C4×C13118yescomplemented
609#381—24no—
610C2×#95C22×C13111yescharacteristic
611C2×#95C22×C13111yescharacteristic
612C2×#95C22×C13111yescharacteristic
613C2×#95C22×C13111yescharacteristic
614C2×#95C22×C13111yescharacteristic
615C2×#95C22×C13111yescharacteristic
616C2×#95C22×C13111yescharacteristic
617C2×#95C22×C13111yescharacteristic
618C2×#95C22×C13111yescharacteristic
619C2×#95C22×C13111yescharacteristic
620C2×#95C22×C13111yescharacteristic
621C2×#95C22×C13111yescharacteristic
622C2×#95C22×C13111yescharacteristic
623C2×#95C22×C13111yescharacteristic
624C2×#95C22×C13111yescharacteristic
625C2×#95C22×C13111yescharacteristic
626C2×#95C22×C13111yescharacteristic
627C2×#95C22×C13111yescharacteristic
628C2×#95C22×C13111yescharacteristic
629C2×#95C22×C13111yescharacteristic
630C25C23×C13111yescharacteristic
631C25C23×C13111yescharacteristic
632C22×D4—22no—
633C22×D4—22no—
634C22×D4—22no—
635C22×D4—22no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4C2×C4×C13114yes—
639C23×C4—22no—
640C23×C4—22no—
641C23×C4—22no—
642C23×C4—22no—
643C23×C4—22no—
644C23×C4—41no—
645C23×C4—41no—
646C23×C4—41no—
647C23×C4—41no—
648C23×C4—41no—
649C23×C4—41no—
650C23×C4—41no—
651C23×C4—41no—
652C23×C4C2×C4×C13114yescomplemented
653C23×C4C23×C13111yescharacteristic
654C23×C4C23×C13111yescharacteristic
655C23×C4C23×C13111yescharacteristic
656C23×C4C23×C13111yescharacteristic
657C23×C4C23×C13111yescharacteristic
658C23×C4C23×C13111yescharacteristic
659C23×C4C23×C13111yescharacteristic
660C23×C4C23×C13111yescharacteristic
661C23×C4C23×C13111yescharacteristic
662C23×C4C23×C13111yescharacteristic
663C23×C4C23×C13111yescharacteristic
664C23×C4C23×C13111yescharacteristic
665C23×C4C23×C13111yescharacteristic
666C2×C4⋊C4—41no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4C2×C4×C13114yes—
696C2×C22⋊C4C2×C4×C13114yes—
697C2×C22⋊C4C2×C4×C13114yescomplemented
698C2×C22⋊C4D4×C13114yes—
699C2×C42—22no—
700C2×C42—41no—
701C2×C42—41no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714#95—41no—
715#95—41no—
716#95—41no—
717#95—41no—
718#95—41no—
719#95—41no—
720#95C2×C4×C13114yescomplemented
721#95C2×C4×C13114yescomplemented
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24C22×C4×C13112yes—
747C24C22×C4×C13112yes—
748C24C2×D4×C13112yes—
749C24#41×C13112yes—
750C24#41×C13112yes—
751C24#41×C13112yes—
752C24C24×C13111yescharacteristic
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C22×C4—28no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
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—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4C22×C4×C13112yes—
857C22×C4C22×C4×C13112yes—
858C22×C4C22×C4×C13112yes—
859C22×C4C22×C4×C13112yes—
860C22×C4C22×C4×C13112yes—
861C22×C4C2×D4×C13112yes—
862C22×C4C2×D4×C13112yes—
863C22×C4#41×C13112yes—
864C22×C4#41×C13112yes—
865C4⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C42—44no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23#117×C13114yes—
946C23C4×D4×C13114yes—
947C23C23×C4×C13111yescharacteristic
948C23C22×D4×C13111yescharacteristic
949C23C2×#41×C13111yescharacteristic
950C23C2×#41×C13111yescharacteristic
951C23C2×#41×C13111yescharacteristic
952C23C2×#41×C13111yescharacteristic
953C23C2×#41×C13111yescharacteristic
954C23H(5,𝔽2)×C13111yescharacteristic
955C23H(5,𝔽2)×C13111yescharacteristic
956C23H(5,𝔽2)×C13111yescharacteristic
957C23H(5,𝔽2)×C13111yescharacteristic
958C23H(5,𝔽2)×C13111yescharacteristic
959C23H(5,𝔽2)×C13111yescharacteristic
960C23H(5,𝔽2)×C13111yescharacteristic
961C232−1+4×C13111yescharacteristic
962D4—416no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—416no—
991C2×C4—416no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C22—24no—
1057C22—24no—
1058C22—24no—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22C2×#117×C13111yescharacteristic
1087C22C2×C4×D4×C13111yescharacteristic
1088C22C4×#41×C13111yescharacteristic
1089C22#518×C13111yescharacteristic
1090C22#518×C13111yescharacteristic
1091C22#518×C13111yescharacteristic
1092C22#520×C13111yescharacteristic
1093C22#534×C13111yescharacteristic
1094C22#535×C13111yescharacteristic
1095C22#538×C13111yescharacteristic
1096C22#538×C13111yescharacteristic
1097C22#538×C13111yescharacteristic
1098C22#538×C13111yescharacteristic
1099C22#538×C13111yescharacteristic
1100C22#538×C13111yescharacteristic
1101C22#539×C13111yescharacteristic
1102C22#539×C13111yescharacteristic
1103C22#540×C13111yescharacteristic
1104C22#540×C13111yescharacteristic
1105C22#546×C13111yescharacteristic
1106C22#546×C13111yescharacteristic
1107C22#546×C13111yescharacteristic
1108C22#547×C13111yescharacteristic
1109C22#551×C13111yescharacteristic
1110C22#551×C13111yescharacteristic
1111C22#551×C13111yescharacteristic
1112C22#551×C13111yescharacteristic
1113C22#551×C13111yescharacteristic
1114C22#552×C13111yescharacteristic
1115C22#553×C13111yescharacteristic
1116C22#553×C13111yescharacteristic
1117C22#560×C13111yescharacteristic
1118C22#560×C13111yescharacteristic
1119C22#562×C13111yescharacteristic
1120C22#562×C13111yescharacteristic
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C2—44no—
1135C2—44no—
1136C2#2318×C13111yescharacteristic
1137C2#2321×C13111yescharacteristic
1138C2#2333×C13111yescharacteristic
1139C2#2342×C13111yescharacteristic
1140C2#2353×C13111yescharacteristic
1141C2#2359×C13111yescharacteristic
1142C2#2377×C13111yescharacteristic
1143C2#2697×C13111yescharacteristic
1144C2#2703×C13111yescharacteristic
1145C2#2706×C13111yescharacteristic
1146C2#2708×C13111yescharacteristic
1147C2#2743×C13111yescharacteristic
1148C2#2749×C13111yescharacteristic
1149C2#2750×C13111yescharacteristic
1150C2#2760×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
prime radicalC23×D4×C131C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#381×C131C2semidirect
4. #1443×C131C2semidirect
5. #1443×C131C2semidirect
6. #1442×C131C2semidirect
7. #1439×C131C2semidirect
8. #1439×C131C2semidirect
10. #1437×C131C2semidirect
11. #1437×C131C2semidirect
12. #1434×C131C2semidirect
13. C22⋊#95×C131C2semidirect
14. C22⋊#95×C131C2semidirect
15. C22⋊#95×C131C2semidirect
32. #386×C131C4semidirect
76. C23×C4×C131C2×C4semidirect
121. C2×C22⋊C4×C131C2×C4semidirect
144. #95×C131C2×C4semidirect
145. #95×C131C2×C4semidirect
575. #14375C131direct (N × H)
576. C131#14375direct (N × H)
579. C2×#381C2×C131semidirect
580. #1443C2×C131semidirect
581. #1443C2×C131semidirect
582. #1442C2×C131semidirect
583. #1439C2×C131semidirect
584. #1439C2×C131semidirect
586. #1437C2×C131semidirect
587. #1437C2×C131semidirect
588. #1434C2×C131semidirect
589. C22⋊#95C2×C131semidirect
590. C22⋊#95C2×C131semidirect
591. C22⋊#95C2×C131semidirect
608. #386C4×C131semidirect
652. C23×C4C2×C4×C131semidirect
697. C2×C22⋊C4C2×C4×C131semidirect
720. #95C2×C4×C131semidirect
721. #95C2×C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#386×C1312
C2×#381×C1312
#1443×C1312
#1442×C1312
#1439×C1312
#1438×C1312
#1437×C1312
#1434×C1312
C22⋊#95×C1312
#14375131