Finite Group Databasebeta

← C131×#14096 #45699980

Subgroups — C131×#14096 #45699980

Order 33536.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C131C211yesmaximal, characteristic
2C2×#388×C131C211yesmaximal, characteristic, complemented
3C2×#386×C131C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C131C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C131C211yesmaximal, characteristic, complemented
6#1445×C131C211yesmaximal, characteristic, complemented
7#1440×C131C211yesmaximal, characteristic, complemented
8#1439×C131C211yesmaximal, characteristic, complemented
9#1438×C131C211yesmaximal, characteristic
10#1437×C131C211yesmaximal, characteristic, complemented
11#1436×C131C211yesmaximal, characteristic, complemented
12#1436×C131C211yesmaximal, characteristic, complemented
13C4⋊#95×C131C211yesmaximal, characteristic, complemented
14C22⋊#95×C131C211yesmaximal, characteristic, complemented
15C22⋊#95×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C24×C4×C131C2211yescharacteristic
18C24×C4×C131C2211yescharacteristic
19C2×#123×C131—24no—
20C2×#123×C131—24no—
21C2×#123×C131C418yescomplemented
22C22×C4⋊C4×C131C2211yescharacteristic
23C22×C4⋊C4×C131C2211yescharacteristic
24C22×C4⋊C4×C131C2211yescharacteristic
25C22×C22⋊C4×C131C2211yescharacteristic
26C22×C22⋊C4×C131C2211yescharacteristic
27C22×C22⋊C4×C131C2211yescharacteristic
28C22×C22⋊C4×C131C2211yescharacteristic
29C22×C22⋊C4×C131C2211yescharacteristic
30C22×C22⋊C4×C131C2211yescharacteristic
31C22×C22⋊C4×C131C2211yescharacteristic
32C22×C22⋊C4×C131C2211yescharacteristic
33C22×C22⋊C4×C131C2211yescharacteristic
34C22×C22⋊C4×C131C2211yescharacteristic
35C22×C42×C131C2211yescharacteristic
36C22×C42×C131C2211yescharacteristic
37C22×C42×C131C2211yescharacteristic
38#388×C131—24no—
39#386×C131—24no—
40C4×C22⋊C4×C131—24no—
41C4×C22⋊C4×C131—24no—
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
54C2×#95×C131C2211yescharacteristic
55C2×#95×C131C2211yescharacteristic
56C2×#95×C131C2211yescharacteristic
57C2×#95×C131C2211yescharacteristic
58C25×C131C2311yescharacteristic
59C25×C131C2311yescharacteristic
60C22×D4×C131—22no—
61C22×D4×C131—22no—
62C22×D4×C131—22no—
63C22×D4×C131—22no—
64C22×D4×C131—41no—
65C22×D4×C131—41no—
66C22×D4×C131C2×C414yes—
67C23×C4×C131—22no—
68C23×C4×C131—22no—
69C23×C4×C131—22no—
70C23×C4×C131—22no—
71C23×C4×C131—22no—
72C23×C4×C131—22no—
73C23×C4×C131—22no—
74C23×C4×C131—22no—
75C23×C4×C131—22no—
76C23×C4×C131—41no—
77C23×C4×C131—41no—
78C23×C4×C131—41no—
79C23×C4×C131—41no—
80C23×C4×C131C2×C414yescomplemented
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
90C23×C4×C131C2311yescharacteristic
91C23×C4×C131C2311yescharacteristic
92C23×C4×C131C2311yescharacteristic
93C23×C4×C131C2311yescharacteristic
94#123×C131—232no—
95C2×C4⋊C4×C131—22no—
96C2×C4⋊C4×C131—22no—
97C2×C4⋊C4×C131—22no—
98C2×C4⋊C4×C131—22no—
99C2×C4⋊C4×C131—22no—
100C2×C4⋊C4×C131—22no—
101C2×C4⋊C4×C131—41no—
102C2×C4⋊C4×C131C2×C414yescomplemented
103C2×C4⋊C4×C131C2×C414yescomplemented
104C2×C22⋊C4×C131—22no—
105C2×C22⋊C4×C131—22no—
106C2×C22⋊C4×C131—22no—
107C2×C22⋊C4×C131—22no—
108C2×C22⋊C4×C131—22no—
109C2×C22⋊C4×C131—22no—
110C2×C22⋊C4×C131—22no—
111C2×C22⋊C4×C131—22no—
112C2×C22⋊C4×C131—22no—
113C2×C22⋊C4×C131—22no—
114C2×C22⋊C4×C131—22no—
115C2×C22⋊C4×C131—22no—
116C2×C22⋊C4×C131—22no—
117C2×C22⋊C4×C131—22no—
118C2×C22⋊C4×C131—22no—
119C2×C22⋊C4×C131—22no—
120C2×C22⋊C4×C131—22no—
121C2×C22⋊C4×C131—22no—
122C2×C22⋊C4×C131—22no—
123C2×C22⋊C4×C131—22no—
124C2×C22⋊C4×C131—41no—
125C2×C22⋊C4×C131—41no—
126C2×C22⋊C4×C131—41no—
127C2×C22⋊C4×C131—41no—
128C2×C22⋊C4×C131C2×C414yes—
129C2×C22⋊C4×C131C2×C414yes—
130C2×C22⋊C4×C131C2×C414yescomplemented
131C2×C22⋊C4×C131D414yes—
132C2×C22⋊C4×C131D414yes—
133C2×C22⋊C4×C131D414yes—
134C2×C42×C131—22no—
135C2×C42×C131—22no—
136C2×C42×C131—22no—
137C2×C42×C131—22no—
138C2×C42×C131—22no—
139C2×C42×C131—22no—
140C2×C42×C131—41no—
141C2×C42×C131—41no—
142C2×C42×C131—41no—
143#95×C131—22no—
144#95×C131—22no—
145#95×C131—22no—
146#95×C131—22no—
147#95×C131—22no—
148#95×C131—22no—
149#95×C131—22no—
150#95×C131—22no—
151#95×C131—22no—
152#95×C131—22no—
153#95×C131—22no—
154#95×C131—22no—
155#95×C131—41no—
156#95×C131—41no—
157#95×C131—41no—
158#95×C131—41no—
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×C131—21no—
171C24×C131—21no—
172C24×C131—21no—
173C24×C131—21no—
174C24×C131—21no—
175C24×C131—21no—
176C24×C131—21no—
177C24×C131—21no—
178C24×C131—21no—
179C24×C131—21no—
180C24×C131—21no—
181C24×C131—21no—
182C24×C131—21no—
183C24×C131C22×C412yes—
184C24×C131C22×C412yes—
185C24×C131C2×D412yes—
186C24×C131C2×D412yes—
187C24×C131C2×D412yes—
188C24×C131#4112yes—
189C24×C131C2411yescharacteristic
190C2×D4×C131—28no—
191C2×D4×C131—28no—
192C2×D4×C131—44no—
193C2×D4×C131—44no—
194C2×D4×C131—44no—
195C2×D4×C131—44no—
196C2×D4×C131—44no—
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—28no—
210C22×C4×C131—28no—
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—28no—
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—21no—
268C22×C4×C131—21no—
269C22×C4×C131—21no—
270C22×C4×C131—21no—
271C22×C4×C131—21no—
272C22×C4×C131—21no—
273C22×C4×C131—21no—
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×C131—44no—
281C22×C4×C131—44no—
282C22×C4×C131—44no—
283C22×C4×C131—44no—
284C22×C4×C131—44no—
285C22×C4×C131C22×C412yes—
286C22×C4×C131C22×C412yes—
287C22×C4×C131C22×C412yes—
288C22×C4×C131C22×C412yes—
289C22×C4×C131C22×C412yes—
290C22×C4×C131C2×D412yes—
291C22×C4×C131C2×D412yes—
292C22×C4×C131C2×D412yes—
293C22×C4×C131C2×D412yes—
294C22×C4×C131C2×D412yes—
295C22×C4×C131C2×D412yes—
296C22×C4×C131#4112yes—
297C22×C4×C131#4112yes—
298C22×C4×C131#4112yes—
299C22×C4×C131#4112yes—
300C22×C4×C131#4112yes—
301C22×C4×C131#4112yes—
302C4⋊C4×C131—28no—
303C4⋊C4×C131—28no—
304C4⋊C4×C131—44no—
305C22⋊C4×C131—28no—
306C22⋊C4×C131—28no—
307C22⋊C4×C131—28no—
308C22⋊C4×C131—28no—
309C22⋊C4×C131—28no—
310C22⋊C4×C131—44no—
311C22⋊C4×C131—44no—
312C22⋊C4×C131—44no—
313C22⋊C4×C131—44no—
314C22⋊C4×C131C22⋊C4116yescomplemented
315C42×C131—44no—
316C42×C131—44no—
317C42×C131—44no—
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—22no—
338C23×C131—22no—
339C23×C131—22no—
340C23×C131—22no—
341C23×C131—22no—
342C23×C131—22no—
343C23×C131—22no—
344C23×C131—22no—
345C23×C131—22no—
346C23×C131—22no—
347C23×C131—22no—
348C23×C131—22no—
349C23×C131—22no—
350C23×C131—22no—
351C23×C131—22no—
352C23×C131—22no—
353C23×C131—22no—
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—41no—
370C23×C131—41no—
371C23×C131—41no—
372C23×C131—41no—
373C23×C131—41no—
374C23×C131—41no—
375C23×C131—41no—
376C23×C131—41no—
377C23×C131—41no—
378C23×C131—41no—
379C23×C131—41no—
380C23×C131—41no—
381C23×C131—41no—
382C23×C131—41no—
383C23×C131—41no—
384C23×C131—41no—
385C23×C131—41no—
386C23×C131C2×C22⋊C414yes—
387C23×C131C4×D414yes—
388C23×C131C23×C411yescharacteristic
389C23×C131C22×D411yescharacteristic
390C23×C131C22×D411yescharacteristic
391C23×C131C22×D411yescharacteristic
392C23×C131C2×#4111yescharacteristic
393C23×C131C2×#4111yescharacteristic
394C23×C131C2×#4111yescharacteristic
395C23×C131C2×#4111yescharacteristic
396C23×C131C2×#4111yescharacteristic
397C23×C131C2×#4111yescharacteristic
398C23×C131C2×#4111yescharacteristic
399C23×C131H(5,𝔽2)11yescharacteristic
400C23×C131H(5,𝔽2)11yescharacteristic
401C23×C131H(5,𝔽2)11yescharacteristic
402C23×C1312−1+411yescharacteristic
403D4×C131—416no—
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—22no—
415C2×C4×C131—22no—
416C2×C4×C131—22no—
417C2×C4×C131—22no—
418C2×C4×C131—22no—
419C2×C4×C131—22no—
420C2×C4×C131—22no—
421C2×C4×C131—22no—
422C2×C4×C131—22no—
423C2×C4×C131—22no—
424C2×C4×C131—22no—
425C2×C4×C131—22no—
426C2×C4×C131—22no—
427C2×C4×C131—22no—
428C2×C4×C131—22no—
429C2×C4×C131—22no—
430C2×C4×C131—22no—
431C2×C4×C131—22no—
432C2×C4×C131—22no—
433C2×C4×C131—22no—
434C2×C4×C131—22no—
435C2×C4×C131—22no—
436C2×C4×C131—22no—
437C2×C4×C131—22no—
438C2×C4×C131—22no—
439C2×C4×C131—22no—
440C2×C4×C131—22no—
441C2×C4×C131—22no—
442C2×C4×C131—22no—
443C2×C4×C131—22no—
444C2×C4×C131—22no—
445C2×C4×C131—22no—
446C2×C4×C131—416no—
447C2×C4×C131—416no—
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—
480C2×C4×C131—41no—
481C2×C4×C131—41no—
482C2×C4×C131—41no—
483C2×C4×C131—41no—
484C2×C4×C131—41no—
485C2×C4×C131—41no—
486C2×C4×C131—41no—
487C2×C4×C131—41no—
488C2×C4×C131—41no—
489C2×C4×C131—41no—
490C2×C4×C131—41no—
491C2×C4×C131—41no—
492C2×C4×C131—41no—
493C2×C4×C131—41no—
494C2×C4×C131C2×C22⋊C414yes—
495C2×C4×C131C2×C22⋊C414yes—
496C2×C4×C131#12314yescomplemented
497C22×C131—24no—
498C22×C131—24no—
499C22×C131—24no—
500C22×C131—24no—
501C22×C131—24no—
502C22×C131—24no—
503C22×C131—42no—
504C22×C131—42no—
505C22×C131—42no—
506C22×C131—42no—
507C22×C131—42no—
508C22×C131—42no—
509C22×C131—42no—
510C22×C131—42no—
511C22×C131—42no—
512C22×C131—42no—
513C22×C131—42no—
514C22×C131—42no—
515C22×C131—42no—
516C22×C131—42no—
517C22×C131—42no—
518C22×C131—42no—
519C22×C131—42no—
520C22×C131—42no—
521C22×C131—42no—
522C22×C131—42no—
523C22×C131—42no—
524C22×C131—42no—
525C22×C131—42no—
526C22×C131—42no—
527C22×C131C22×C22⋊C411yescharacteristic
528C22×C131C2×C4×D411yescharacteristic
529C22×C131C4×#4111yescharacteristic
530C22×C131C4×#4111yescharacteristic
531C22×C131C4×#4111yescharacteristic
532C22×C131#51811yescharacteristic
533C22×C131#52011yescharacteristic
534C22×C131C2×#12311yescharacteristic
535C22×C131#52511yescharacteristic
536C22×C131#52511yescharacteristic
537C22×C131#52511yescharacteristic
538C22×C131#52911yescharacteristic
539C22×C131#52911yescharacteristic
540C22×C131#53211yescharacteristic
541C22×C131#53211yescharacteristic
542C22×C131#53811yescharacteristic
543C22×C131#53911yescharacteristic
544C22×C131#54011yescharacteristic
545C22×C131#54211yescharacteristic
546C22×C131D4211yescharacteristic
547C22×C131D4211yescharacteristic
548C22×C131#54611yescharacteristic
549C22×C131#54611yescharacteristic
550C22×C131#54611yescharacteristic
551C22×C131#54611yescharacteristic
552C22×C131#54611yescharacteristic
553C22×C131#54711yescharacteristic
554C22×C131#54711yescharacteristic
555C22×C131#54711yescharacteristic
556C22×C131#55111yescharacteristic
557C22×C131#55111yescharacteristic
558C22×C131#55211yescharacteristic
559C22×C131#55311yescharacteristic
560C22×C131#55311yescharacteristic
561C22×C131#55911yescharacteristic
562C4×C131—24no—
563C4×C131—24no—
564C4×C131—24no—
565C4×C131—42no—
566C4×C131—42no—
567C4×C131—42no—
568C4×C131—42no—
569C4×C131—42no—
570C4×C131—42no—
571C4×C131—42no—
572C4×C131—42no—
573C4×C131—81no—
574C4×C131—81no—
575C2×C131—44no—
576C2×C131—44no—
577C2×C131#229711yescharacteristic
578C2×C131C4×#12311yescharacteristic
579C2×C131#233511yescharacteristic
580C2×C131D4×C22⋊C411yescharacteristic
581C2×C131#233911yescharacteristic
582C2×C131#235911yescharacteristic
583C2×C131#237411yescharacteristic
584C2×C131#241811yescharacteristic
585C2×C131#242211yescharacteristic
586C2×C131#245511yescharacteristic
587C2×C131#245711yescharacteristic
588C2×C131#246411yescharacteristic
589C2×C131#247011yescharacteristic
590C2×C131#255311yescharacteristic
591C2×C131#255711yescharacteristic
592#14096C13111yesmaximal, characteristic, direct product factor, Sylow
593C131#1409611yescharacteristic, direct product factor, Sylow
594C22×#123C2×C13111yescharacteristic
595C2×#388C2×C13111yescharacteristic, complemented
596C2×#386C2×C13111yescharacteristic
597C2×C4×C22⋊C4C2×C13111yescharacteristic, complemented
598C2×C4×C22⋊C4C2×C13111yescharacteristic, complemented
599#1445C2×C13111yescharacteristic, complemented
600#1440C2×C13111yescharacteristic, complemented
601#1439C2×C13111yescharacteristic, complemented
602#1438C2×C13111yescharacteristic
603#1437C2×C13111yescharacteristic, complemented
604#1436C2×C13111yescharacteristic, complemented
605#1436C2×C13111yescharacteristic, complemented
606C4⋊#95C2×C13111yescharacteristic, complemented
607C22⋊#95C2×C13111yescharacteristic, complemented
608C22⋊#95C2×C13111yescharacteristic, complemented
609C23×D4C22×C13111yescharacteristic
610C24×C4C22×C13111yescharacteristic
611C24×C4C22×C13111yescharacteristic
612C2×#123—24no—
613C2×#123—24no—
614C2×#123C4×C13118yescomplemented
615C22×C4⋊C4C22×C13111yescharacteristic
616C22×C4⋊C4C22×C13111yescharacteristic
617C22×C4⋊C4C22×C13111yescharacteristic
618C22×C22⋊C4C22×C13111yescharacteristic
619C22×C22⋊C4C22×C13111yescharacteristic
620C22×C22⋊C4C22×C13111yescharacteristic
621C22×C22⋊C4C22×C13111yescharacteristic
622C22×C22⋊C4C22×C13111yescharacteristic
623C22×C22⋊C4C22×C13111yescharacteristic
624C22×C22⋊C4C22×C13111yescharacteristic
625C22×C22⋊C4C22×C13111yescharacteristic
626C22×C22⋊C4C22×C13111yescharacteristic
627C22×C22⋊C4C22×C13111yescharacteristic
628C22×C42C22×C13111yescharacteristic
629C22×C42C22×C13111yescharacteristic
630C22×C42C22×C13111yescharacteristic
631#388—24no—
632#386—24no—
633C4×C22⋊C4—24no—
634C4×C22⋊C4—24no—
635C2×#95C22×C13111yescharacteristic
636C2×#95C22×C13111yescharacteristic
637C2×#95C22×C13111yescharacteristic
638C2×#95C22×C13111yescharacteristic
639C2×#95C22×C13111yescharacteristic
640C2×#95C22×C13111yescharacteristic
641C2×#95C22×C13111yescharacteristic
642C2×#95C22×C13111yescharacteristic
643C2×#95C22×C13111yescharacteristic
644C2×#95C22×C13111yescharacteristic
645C2×#95C22×C13111yescharacteristic
646C2×#95C22×C13111yescharacteristic
647C2×#95C22×C13111yescharacteristic
648C2×#95C22×C13111yescharacteristic
649C2×#95C22×C13111yescharacteristic
650C2×#95C22×C13111yescharacteristic
651C25C23×C13111yescharacteristic
652C25C23×C13111yescharacteristic
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—41no—
658C22×D4—41no—
659C22×D4C2×C4×C13114yes—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—41no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4—41no—
673C23×C4C2×C4×C13114yescomplemented
674C23×C4C23×C13111yescharacteristic
675C23×C4C23×C13111yescharacteristic
676C23×C4C23×C13111yescharacteristic
677C23×C4C23×C13111yescharacteristic
678C23×C4C23×C13111yescharacteristic
679C23×C4C23×C13111yescharacteristic
680C23×C4C23×C13111yescharacteristic
681C23×C4C23×C13111yescharacteristic
682C23×C4C23×C13111yescharacteristic
683C23×C4C23×C13111yescharacteristic
684C23×C4C23×C13111yescharacteristic
685C23×C4C23×C13111yescharacteristic
686C23×C4C23×C13111yescharacteristic
687#123—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4C2×C4×C13114yescomplemented
696C2×C4⋊C4C2×C4×C13114yescomplemented
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4C2×C4×C13114yes—
722C2×C22⋊C4C2×C4×C13114yes—
723C2×C22⋊C4C2×C4×C13114yescomplemented
724C2×C22⋊C4D4×C13114yes—
725C2×C22⋊C4D4×C13114yes—
726C2×C22⋊C4D4×C13114yes—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—41no—
734C2×C42—41no—
735C2×C42—41no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—41no—
749#95—41no—
750#95—41no—
751#95—41no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C22×C4×C13112yes—
777C24C22×C4×C13112yes—
778C24C2×D4×C13112yes—
779C24C2×D4×C13112yes—
780C24C2×D4×C13112yes—
781C24#41×C13112yes—
782C24C24×C13111yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
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—28no—
803C22×C4—28no—
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—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—28no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
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—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4C22×C4×C13112yes—
879C22×C4C22×C4×C13112yes—
880C22×C4C22×C4×C13112yes—
881C22×C4C22×C4×C13112yes—
882C22×C4C22×C4×C13112yes—
883C22×C4C2×D4×C13112yes—
884C22×C4C2×D4×C13112yes—
885C22×C4C2×D4×C13112yes—
886C22×C4C2×D4×C13112yes—
887C22×C4C2×D4×C13112yes—
888C22×C4C2×D4×C13112yes—
889C22×C4#41×C13112yes—
890C22×C4#41×C13112yes—
891C22×C4#41×C13112yes—
892C22×C4#41×C13112yes—
893C22×C4#41×C13112yes—
894C22×C4#41×C13112yes—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—44no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4C22⋊C4×C131116yescomplemented
908C42—44no—
909C42—44no—
910C42—44no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C2×C22⋊C4×C13114yes—
980C23C4×D4×C13114yes—
981C23C23×C4×C13111yescharacteristic
982C23C22×D4×C13111yescharacteristic
983C23C22×D4×C13111yescharacteristic
984C23C22×D4×C13111yescharacteristic
985C23C2×#41×C13111yescharacteristic
986C23C2×#41×C13111yescharacteristic
987C23C2×#41×C13111yescharacteristic
988C23C2×#41×C13111yescharacteristic
989C23C2×#41×C13111yescharacteristic
990C23C2×#41×C13111yescharacteristic
991C23C2×#41×C13111yescharacteristic
992C23H(5,𝔽2)×C13111yescharacteristic
993C23H(5,𝔽2)×C13111yescharacteristic
994C23H(5,𝔽2)×C13111yescharacteristic
995C232−1+4×C13111yescharacteristic
996D4—416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—416no—
1040C2×C4—416no—
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—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4C2×C22⋊C4×C13114yes—
1088C2×C4C2×C22⋊C4×C13114yes—
1089C2×C4#123×C13114yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C22×C22⋊C4×C13111yescharacteristic
1121C22C2×C4×D4×C13111yescharacteristic
1122C22C4×#41×C13111yescharacteristic
1123C22C4×#41×C13111yescharacteristic
1124C22C4×#41×C13111yescharacteristic
1125C22#518×C13111yescharacteristic
1126C22#520×C13111yescharacteristic
1127C22C2×#123×C13111yescharacteristic
1128C22#525×C13111yescharacteristic
1129C22#525×C13111yescharacteristic
1130C22#525×C13111yescharacteristic
1131C22#529×C13111yescharacteristic
1132C22#529×C13111yescharacteristic
1133C22#532×C13111yescharacteristic
1134C22#532×C13111yescharacteristic
1135C22#538×C13111yescharacteristic
1136C22#539×C13111yescharacteristic
1137C22#540×C13111yescharacteristic
1138C22#542×C13111yescharacteristic
1139C22D42×C13111yescharacteristic
1140C22D42×C13111yescharacteristic
1141C22#546×C13111yescharacteristic
1142C22#546×C13111yescharacteristic
1143C22#546×C13111yescharacteristic
1144C22#546×C13111yescharacteristic
1145C22#546×C13111yescharacteristic
1146C22#547×C13111yescharacteristic
1147C22#547×C13111yescharacteristic
1148C22#547×C13111yescharacteristic
1149C22#551×C13111yescharacteristic
1150C22#551×C13111yescharacteristic
1151C22#552×C13111yescharacteristic
1152C22#553×C13111yescharacteristic
1153C22#553×C13111yescharacteristic
1154C22#559×C13111yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—44no—
1170C2#2297×C13111yescharacteristic
1171C2C4×#123×C13111yescharacteristic
1172C2#2335×C13111yescharacteristic
1173C2D4×C22⋊C4×C13111yescharacteristic
1174C2#2339×C13111yescharacteristic
1175C2#2359×C13111yescharacteristic
1176C2#2374×C13111yescharacteristic
1177C2#2418×C13111yescharacteristic
1178C2#2422×C13111yescharacteristic
1179C2#2455×C13111yescharacteristic
1180C2#2457×C13111yescharacteristic
1181C2#2464×C13111yescharacteristic
1182C2#2470×C13111yescharacteristic
1183C2#2553×C13111yescharacteristic
1184C2#2557×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
2. C2×#388×C131C2semidirect
4. C2×C4×C22⋊C4×C131C2semidirect
5. C2×C4×C22⋊C4×C131C2semidirect
6. #1445×C131C2semidirect
7. #1440×C131C2semidirect
8. #1439×C131C2semidirect
10. #1437×C131C2semidirect
11. #1436×C131C2semidirect
12. #1436×C131C2semidirect
13. C4⋊#95×C131C2semidirect
14. C22⋊#95×C131C2semidirect
15. C22⋊#95×C131C2semidirect
21. C2×#123×C131C4semidirect
80. C23×C4×C131C2×C4semidirect
102. C2×C4⋊C4×C131C2×C4semidirect
103. C2×C4⋊C4×C131C2×C4semidirect
130. C2×C22⋊C4×C131C2×C4semidirect
314. C22⋊C4×C131C22⋊C4semidirect
496. C2×C4×C131#123semidirect
592. #14096C131direct (N × H)
593. C131#14096direct (N × H)
595. C2×#388C2×C131semidirect
597. C2×C4×C22⋊C4C2×C131semidirect
598. C2×C4×C22⋊C4C2×C131semidirect
599. #1445C2×C131semidirect
600. #1440C2×C131semidirect
601. #1439C2×C131semidirect
603. #1437C2×C131semidirect
604. #1436C2×C131semidirect
605. #1436C2×C131semidirect
606. C4⋊#95C2×C131semidirect
607. C22⋊#95C2×C131semidirect
608. C22⋊#95C2×C131semidirect
614. C2×#123C4×C131semidirect
673. C23×C4C2×C4×C131semidirect
695. C2×C4⋊C4C2×C4×C131semidirect
696. C2×C4⋊C4C2×C4×C131semidirect
723. C2×C22⋊C4C2×C4×C131semidirect
907. C22⋊C4C22⋊C4×C131semidirect
1089. C2×C4#123×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1312
C2×#388×C1312
C2×#386×C1312
C2×C4×C22⋊C4×C1312
#1445×C1312
#1440×C1312
#1439×C1312
#1438×C1312
#1437×C1312
#1436×C1312
C4⋊#95×C1312
C22⋊#95×C1312
#14096131