Finite Group Databasebeta

← C131×#16270 #45702154

Subgroups — C131×#16270 #45702154

Order 33536.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C131C211yesmaximal, characteristic, complemented
2C2×#392×C131C211yesmaximal, characteristic
3C2×#386×C131C211yesmaximal, characteristic, complemented
4C2×#386×C131C211yesmaximal, characteristic, complemented
5#1443×C131C211yesmaximal, characteristic, complemented
6#1443×C131C211yesmaximal, characteristic, complemented
7#1440×C131C211yesmaximal, characteristic, complemented
8#1440×C131C211yesmaximal, characteristic, complemented
9#1439×C131C211yesmaximal, characteristic, complemented
10#1439×C131C211yesmaximal, characteristic, complemented
11#1438×C131C211yesmaximal, characteristic, complemented
12#1438×C131C211yesmaximal, characteristic, complemented
13#1438×C131C211yesmaximal, characteristic, complemented
14#1438×C131C211yesmaximal, characteristic, complemented
15C22⋊#95×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C23×D4×C131C2211yescharacteristic
19C24×C4×C131C2211yescharacteristic
20C22×C4⋊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×C22⋊C4×C131C2211yescharacteristic
31C22×C22⋊C4×C131C2211yescharacteristic
32C22×C22⋊C4×C131C2211yescharacteristic
33C22×C22⋊C4×C131C2211yescharacteristic
34C22×C22⋊C4×C131C2211yescharacteristic
35#397×C131—24no—
36#392×C131—24no—
37#386×C131—24no—
38#386×C131—24no—
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
54C2×#95×C131C2211yescharacteristic
55C25×C131C2311yescharacteristic
56C25×C131C2311yescharacteristic
57C25×C131C2311yescharacteristic
58C22×D4×C131—22no—
59C22×D4×C131—22no—
60C22×D4×C131—22no—
61C22×D4×C131—22no—
62C22×D4×C131—22no—
63C22×D4×C131—22no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—22no—
67C22×D4×C131—22no—
68C22×D4×C131—41no—
69C22×D4×C131—41no—
70C22×D4×C131—41no—
71C22×D4×C131—41no—
72C22×D4×C131—41no—
73C22×D4×C131—41no—
74C22×D4×C131—41no—
75C22×D4×C131—41no—
76C22×D4×C131—41no—
77C22×D4×C131—41no—
78C22×D4×C131D414yes—
79C23×C4×C131—22no—
80C23×C4×C131—22no—
81C23×C4×C131—22no—
82C23×C4×C131—41no—
83C23×C4×C131—41no—
84C23×C4×C131—41no—
85C23×C4×C131—41no—
86C23×C4×C131C2311yescharacteristic
87C23×C4×C131C2311yescharacteristic
88C23×C4×C131C2311yescharacteristic
89C23×C4×C131C2311yescharacteristic
90C23×C4×C131C2311yescharacteristic
91C23×C4×C131C2311yescharacteristic
92C23×C4×C131C2311yescharacteristic
93C23×C4×C131C2311yescharacteristic
94C23×C4×C131C2311yescharacteristic
95C23×C4×C131C2311yescharacteristic
96C23×C4×C131C2311yescharacteristic
97C23×C4×C131C2311yescharacteristic
98C2×C4⋊C4×C131—22no—
99C2×C4⋊C4×C131—41no—
100C2×C4⋊C4×C131—41no—
101C2×C22⋊C4×C131—22no—
102C2×C22⋊C4×C131—22no—
103C2×C22⋊C4×C131—22no—
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—41no—
120C2×C22⋊C4×C131—41no—
121C2×C22⋊C4×C131—41no—
122C2×C22⋊C4×C131—41no—
123C2×C22⋊C4×C131—41no—
124C2×C22⋊C4×C131—41no—
125C2×C22⋊C4×C131—41no—
126C2×C22⋊C4×C131—41no—
127C2×C22⋊C4×C131—41no—
128C2×C22⋊C4×C131—41no—
129C2×C22⋊C4×C131—41no—
130C2×C22⋊C4×C131—41no—
131C2×C22⋊C4×C131—41no—
132C2×C22⋊C4×C131—41no—
133C2×C22⋊C4×C131—41no—
134C2×C22⋊C4×C131—41no—
135C2×C22⋊C4×C131—41no—
136C2×C22⋊C4×C131—41no—
137C2×C22⋊C4×C131—41no—
138C2×C22⋊C4×C131—41no—
139C2×C22⋊C4×C131—41no—
140C2×C22⋊C4×C131—41no—
141C2×C22⋊C4×C131—41no—
142C2×C22⋊C4×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—41no—
151#95×C131—41no—
152#95×C131—41no—
153#95×C131—41no—
154#95×C131—41no—
155#95×C131—41no—
156#95×C131—41no—
157#95×C131—41no—
158#95×C131D414yescomplemented
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×C131—21no—
184C24×C131—21no—
185C24×C131—21no—
186C24×C131—21no—
187C24×C131—21no—
188C24×C131—21no—
189C24×C131—21no—
190C24×C131—21no—
191C24×C131—21no—
192C24×C131—21no—
193C24×C131—21no—
194C24×C131—21no—
195C24×C131—21no—
196C24×C131—21no—
197C24×C131—21no—
198C24×C131—21no—
199C24×C131C2×D412yes—
200C24×C131C2×D412yes—
201C24×C131#4112yes—
202C24×C131#4112yes—
203C24×C131#4112yes—
204C24×C131C2411yescharacteristic
205C2×D4×C131—28no—
206C2×D4×C131—28no—
207C2×D4×C131—44no—
208C2×D4×C131—44no—
209C2×D4×C131—44no—
210C2×D4×C131—44no—
211C2×D4×C131—44no—
212C2×D4×C131—44no—
213C2×D4×C131—44no—
214C2×D4×C131—44no—
215C2×D4×C131—44no—
216C2×D4×C131—44no—
217C2×D4×C131—44no—
218C2×D4×C131—44no—
219C2×D4×C131—44no—
220C2×D4×C131—44no—
221C2×D4×C131—44no—
222C2×D4×C131—44no—
223C2×D4×C131—44no—
224C2×D4×C131—44no—
225C2×D4×C131—44no—
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—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—21no—
275C22×C4×C131—21no—
276C22×C4×C131—21no—
277C22×C4×C131—21no—
278C22×C4×C131—21no—
279C22×C4×C131—21no—
280C22×C4×C131—21no—
281C22×C4×C131—21no—
282C22×C4×C131—21no—
283C22×C4×C131—21no—
284C22×C4×C131—21no—
285C22×C4×C131—21no—
286C22×C4×C131—21no—
287C22×C4×C131—21no—
288C22×C4×C131—21no—
289C22×C4×C131—21no—
290C22×C4×C131—21no—
291C22×C4×C131—21no—
292C22×C4×C131—21no—
293C22×C4×C131—21no—
294C22×C4×C131—21no—
295C22×C4×C131—21no—
296C22×C4×C131—21no—
297C22×C4×C131—21no—
298C22×C4×C131—21no—
299C22×C4×C131—21no—
300C22×C4×C131—21no—
301C22×C4×C131—21no—
302C22×C4×C131—21no—
303C22×C4×C131—21no—
304C22×C4×C131—44no—
305C22×C4×C131—44no—
306C22×C4×C131—44no—
307C22×C4×C131—44no—
308C22×C4×C131—44no—
309C22×C4×C131—44no—
310C22×C4×C131—44no—
311C22×C4×C131C2×D412yes—
312C22×C4×C131C2×D412yes—
313C22×C4×C131C2×D412yes—
314C22×C4×C131C2×D412yes—
315C22×C4×C131#4112yes—
316C22×C4×C131#4112yes—
317C4⋊C4×C131—44no—
318C22⋊C4×C131—44no—
319C22⋊C4×C131—44no—
320C22⋊C4×C131—44no—
321C22⋊C4×C131—44no—
322C22⋊C4×C131—44no—
323C22⋊C4×C131—44no—
324C22⋊C4×C131—44no—
325C22⋊C4×C131—44no—
326C22⋊C4×C131—44no—
327C22⋊C4×C131—44no—
328C22⋊C4×C131—44no—
329C22⋊C4×C131—44no—
330C22⋊C4×C131—44no—
331C22⋊C4×C131—44no—
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—22no—
355C23×C131—22no—
356C23×C131—22no—
357C23×C131—22no—
358C23×C131—22no—
359C23×C131—22no—
360C23×C131—22no—
361C23×C131—22no—
362C23×C131—22no—
363C23×C131—22no—
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×C131—41no—
387C23×C131—41no—
388C23×C131—41no—
389C23×C131—41no—
390C23×C131—41no—
391C23×C131—41no—
392C23×C131—41no—
393C23×C131—41no—
394C23×C131—41no—
395C23×C131—41no—
396C23×C131—41no—
397C23×C131—41no—
398C23×C131—41no—
399C23×C131—41no—
400C23×C131—41no—
401C23×C131—41no—
402C23×C131—41no—
403C23×C131—41no—
404C23×C131—41no—
405C23×C131—41no—
406C23×C131—41no—
407C23×C131—41no—
408C23×C131—41no—
409C23×C131—41no—
410C23×C131—41no—
411C23×C131—41no—
412C23×C131—41no—
413C23×C131—41no—
414C23×C131—41no—
415C23×C131—41no—
416C23×C131—41no—
417C23×C131—41no—
418C23×C131—41no—
419C23×C131—41no—
420C23×C131—41no—
421C23×C131—41no—
422C23×C131—41no—
423C23×C131—41no—
424C23×C131—41no—
425C23×C131—41no—
426C23×C131—41no—
427C23×C131—41no—
428C23×C131—41no—
429C23×C131—41no—
430C23×C131—41no—
431C23×C131—41no—
432C23×C131—41no—
433C23×C131—41no—
434C23×C131—41no—
435C23×C131—41no—
436C23×C131#12314yes—
437C23×C131C22×D411yescharacteristic
438C23×C131C22×D411yescharacteristic
439C23×C131C2×#4111yescharacteristic
440C23×C131C2×#4111yescharacteristic
441C23×C131C2×#4111yescharacteristic
442C23×C131C2×#4111yescharacteristic
443C23×C131C2×#4111yescharacteristic
444C23×C131H(5,𝔽2)11yescharacteristic
445C23×C131H(5,𝔽2)11yescharacteristic
446C23×C131H(5,𝔽2)11yescharacteristic
447C23×C131H(5,𝔽2)11yescharacteristic
448C23×C131H(5,𝔽2)11yescharacteristic
449C23×C131H(5,𝔽2)11yescharacteristic
450C23×C131H(5,𝔽2)11yescharacteristic
451C23×C131H(5,𝔽2)11yescharacteristic
452D4×C131—416no—
453D4×C131—416no—
454D4×C131—416no—
455C2×C4×C131—22no—
456C2×C4×C131—22no—
457C2×C4×C131—22no—
458C2×C4×C131—22no—
459C2×C4×C131—22no—
460C2×C4×C131—22no—
461C2×C4×C131—22no—
462C2×C4×C131—22no—
463C2×C4×C131—22no—
464C2×C4×C131—22no—
465C2×C4×C131—22no—
466C2×C4×C131—22no—
467C2×C4×C131—22no—
468C2×C4×C131—22no—
469C2×C4×C131—22no—
470C2×C4×C131—22no—
471C2×C4×C131—22no—
472C2×C4×C131—22no—
473C2×C4×C131—416no—
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×C131—41no—
495C2×C4×C131—41no—
496C2×C4×C131—41no—
497C2×C4×C131—41no—
498C2×C4×C131—41no—
499C2×C4×C131—41no—
500C2×C4×C131—41no—
501C2×C4×C131—41no—
502C2×C4×C131—41no—
503C2×C4×C131—41no—
504C2×C4×C131—41no—
505C2×C4×C131—41no—
506C2×C4×C131—41no—
507C2×C4×C131—41no—
508C2×C4×C131—41no—
509C2×C4×C131—41no—
510C2×C4×C131—41no—
511C2×C4×C131—41no—
512C2×C4×C131—41no—
513C2×C4×C131—41no—
514C2×C4×C131—41no—
515C2×C4×C131—41no—
516C2×C4×C131—41no—
517C2×C4×C131—41no—
518C2×C4×C131—41no—
519C2×C4×C131—41no—
520C2×C4×C131—41no—
521C2×C4×C131—41no—
522C2×C4×C131—41no—
523C2×C4×C131—41no—
524C2×C4×C131—41no—
525C2×C4×C131—41no—
526C2×C4×C131—41no—
527C2×C4×C131—41no—
528C2×C4×C131—41no—
529C2×C4×C131—41no—
530C2×C4×C131—41no—
531C2×C4×C131—41no—
532C2×C4×C131—41no—
533C2×C4×C131—41no—
534C2×C4×C131—41no—
535C2×C4×C131—41no—
536C2×C4×C131—41no—
537C2×C4×C131—41no—
538C2×C4×C131—41no—
539C2×C4×C131—41no—
540C22×C131—24no—
541C22×C131—24no—
542C22×C131—24no—
543C22×C131—42no—
544C22×C131—42no—
545C22×C131—42no—
546C22×C131—42no—
547C22×C131—42no—
548C22×C131—42no—
549C22×C131—42no—
550C22×C131—42no—
551C22×C131—42no—
552C22×C131—42no—
553C22×C131—42no—
554C22×C131—42no—
555C22×C131—42no—
556C22×C131—42no—
557C22×C131—42no—
558C22×C131—42no—
559C22×C131—42no—
560C22×C131—42no—
561C22×C131—42no—
562C22×C131—42no—
563C22×C131—42no—
564C22×C131—42no—
565C22×C131—42no—
566C22×C131—42no—
567C22×C131—42no—
568C22×C131—42no—
569C22×C131—81no—
570C22×C131—81no—
571C22×C131—81no—
572C22×C131—81no—
573C22×C131—81no—
574C22×C131—81no—
575C22×C131—81no—
576C22×C131—81no—
577C22×C131—81no—
578C22×C131—81no—
579C22×C131—81no—
580C22×C131—81no—
581C22×C131—81no—
582C22×C131—81no—
583C22×C131—81no—
584C22×C131—81no—
585C22×C131C2×#12311yescharacteristic
586C22×C131#52511yescharacteristic
587C22×C131#52911yescharacteristic
588C22×C131#53411yescharacteristic
589C22×C131#53411yescharacteristic
590C22×C131#53511yescharacteristic
591C22×C131#53511yescharacteristic
592C22×C131#53811yescharacteristic
593C22×C131#53811yescharacteristic
594C22×C131#53811yescharacteristic
595C22×C131#53811yescharacteristic
596C22×C131#53811yescharacteristic
597C22×C131#53811yescharacteristic
598C22×C131#53811yescharacteristic
599C22×C131#53811yescharacteristic
600C22×C131#53811yescharacteristic
601C22×C131#53811yescharacteristic
602C22×C131#54011yescharacteristic
603C22×C131#54011yescharacteristic
604C22×C131D4211yescharacteristic
605C22×C131#54611yescharacteristic
606C22×C131#54611yescharacteristic
607C22×C131#54611yescharacteristic
608C22×C131#54611yescharacteristic
609C22×C131#54611yescharacteristic
610C22×C131#55011yescharacteristic
611C22×C131#55111yescharacteristic
612C22×C131#55111yescharacteristic
613C22×C131#55311yescharacteristic
614C22×C131#55311yescharacteristic
615C22×C131#55311yescharacteristic
616C22×C131#56011yescharacteristic
617C22×C131#56011yescharacteristic
618C22×C131#56011yescharacteristic
619C22×C131#56011yescharacteristic
620C4×C131—42no—
621C4×C131—42no—
622C4×C131—42no—
623C4×C131—42no—
624C4×C131—42no—
625C4×C131—42no—
626C4×C131—81no—
627C4×C131—81no—
628C4×C131—81no—
629C4×C131—81no—
630C4×C131—81no—
631C4×C131—81no—
632C2×C131—44no—
633C2×C131—82no—
634C2×C131—82no—
635C2×C131#241811yescharacteristic
636C2×C131#244411yescharacteristic
637C2×C131#246711yescharacteristic
638C2×C131#262211yescharacteristic
639C2×C131#263111yescharacteristic
640C2×C131#264811yescharacteristic
641C2×C131#267311yescharacteristic
642C2×C131#267811yescharacteristic
643C2×C131#268811yescharacteristic
644C2×C131#269711yescharacteristic
645C2×C131#270311yescharacteristic
646C2×C131#271411yescharacteristic
647C2×C131#274911yescharacteristic
648C2×C131#277811yescharacteristic
649C2×C131#282511yescharacteristic
650#16270C13111yesmaximal, characteristic, direct product factor, Sylow
651C131#1627011yescharacteristic, direct product factor, Sylow
652C2×#397C2×C13111yescharacteristic, complemented
653C2×#392C2×C13111yescharacteristic
654C2×#386C2×C13111yescharacteristic, complemented
655C2×#386C2×C13111yescharacteristic, complemented
656#1443C2×C13111yescharacteristic, complemented
657#1443C2×C13111yescharacteristic, complemented
658#1440C2×C13111yescharacteristic, complemented
659#1440C2×C13111yescharacteristic, complemented
660#1439C2×C13111yescharacteristic, complemented
661#1439C2×C13111yescharacteristic, complemented
662#1438C2×C13111yescharacteristic, complemented
663#1438C2×C13111yescharacteristic, complemented
664#1438C2×C13111yescharacteristic, complemented
665#1438C2×C13111yescharacteristic, complemented
666C22⋊#95C2×C13111yescharacteristic, complemented
667C23×D4C22×C13111yescharacteristic
668C23×D4C22×C13111yescharacteristic
669C23×D4C22×C13111yescharacteristic
670C24×C4C22×C13111yescharacteristic
671C22×C4⋊C4C22×C13111yescharacteristic
672C22×C22⋊C4C22×C13111yescharacteristic
673C22×C22⋊C4C22×C13111yescharacteristic
674C22×C22⋊C4C22×C13111yescharacteristic
675C22×C22⋊C4C22×C13111yescharacteristic
676C22×C22⋊C4C22×C13111yescharacteristic
677C22×C22⋊C4C22×C13111yescharacteristic
678C22×C22⋊C4C22×C13111yescharacteristic
679C22×C22⋊C4C22×C13111yescharacteristic
680C22×C22⋊C4C22×C13111yescharacteristic
681C22×C22⋊C4C22×C13111yescharacteristic
682C22×C22⋊C4C22×C13111yescharacteristic
683C22×C22⋊C4C22×C13111yescharacteristic
684C22×C22⋊C4C22×C13111yescharacteristic
685C22×C22⋊C4C22×C13111yescharacteristic
686#397—24no—
687#392—24no—
688#386—24no—
689#386—24no—
690C2×#95C22×C13111yescharacteristic
691C2×#95C22×C13111yescharacteristic
692C2×#95C22×C13111yescharacteristic
693C2×#95C22×C13111yescharacteristic
694C2×#95C22×C13111yescharacteristic
695C2×#95C22×C13111yescharacteristic
696C2×#95C22×C13111yescharacteristic
697C2×#95C22×C13111yescharacteristic
698C2×#95C22×C13111yescharacteristic
699C2×#95C22×C13111yescharacteristic
700C2×#95C22×C13111yescharacteristic
701C2×#95C22×C13111yescharacteristic
702C2×#95C22×C13111yescharacteristic
703C2×#95C22×C13111yescharacteristic
704C2×#95C22×C13111yescharacteristic
705C2×#95C22×C13111yescharacteristic
706C25C23×C13111yescharacteristic
707C25C23×C13111yescharacteristic
708C25C23×C13111yescharacteristic
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4D4×C13114yes—
730C23×C4—22no—
731C23×C4—22no—
732C23×C4—22no—
733C23×C4—41no—
734C23×C4—41no—
735C23×C4—41no—
736C23×C4—41no—
737C23×C4C23×C13111yescharacteristic
738C23×C4C23×C13111yescharacteristic
739C23×C4C23×C13111yescharacteristic
740C23×C4C23×C13111yescharacteristic
741C23×C4C23×C13111yescharacteristic
742C23×C4C23×C13111yescharacteristic
743C23×C4C23×C13111yescharacteristic
744C23×C4C23×C13111yescharacteristic
745C23×C4C23×C13111yescharacteristic
746C23×C4C23×C13111yescharacteristic
747C23×C4C23×C13111yescharacteristic
748C23×C4C23×C13111yescharacteristic
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C4⋊C4—41no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95—41no—
805#95—41no—
806#95—41no—
807#95—41no—
808#95—41no—
809#95D4×C13114yescomplemented
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24C2×D4×C13112yes—
851C24C2×D4×C13112yes—
852C24#41×C13112yes—
853C24#41×C13112yes—
854C24#41×C13112yes—
855C24C24×C13111yescharacteristic
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4C2×D4×C13112yes—
963C22×C4C2×D4×C13112yes—
964C22×C4C2×D4×C13112yes—
965C22×C4C2×D4×C13112yes—
966C22×C4#41×C13112yes—
967C22×C4#41×C13112yes—
968C4⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23#123×C13114yes—
1088C23C22×D4×C13111yescharacteristic
1089C23C22×D4×C13111yescharacteristic
1090C23C2×#41×C13111yescharacteristic
1091C23C2×#41×C13111yescharacteristic
1092C23C2×#41×C13111yescharacteristic
1093C23C2×#41×C13111yescharacteristic
1094C23C2×#41×C13111yescharacteristic
1095C23H(5,𝔽2)×C13111yescharacteristic
1096C23H(5,𝔽2)×C13111yescharacteristic
1097C23H(5,𝔽2)×C13111yescharacteristic
1098C23H(5,𝔽2)×C13111yescharacteristic
1099C23H(5,𝔽2)×C13111yescharacteristic
1100C23H(5,𝔽2)×C13111yescharacteristic
1101C23H(5,𝔽2)×C13111yescharacteristic
1102C23H(5,𝔽2)×C13111yescharacteristic
1103D4—416no—
1104D4—416no—
1105D4—416no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—416no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22C2×#123×C13111yescharacteristic
1237C22#525×C13111yescharacteristic
1238C22#529×C13111yescharacteristic
1239C22#534×C13111yescharacteristic
1240C22#534×C13111yescharacteristic
1241C22#535×C13111yescharacteristic
1242C22#535×C13111yescharacteristic
1243C22#538×C13111yescharacteristic
1244C22#538×C13111yescharacteristic
1245C22#538×C13111yescharacteristic
1246C22#538×C13111yescharacteristic
1247C22#538×C13111yescharacteristic
1248C22#538×C13111yescharacteristic
1249C22#538×C13111yescharacteristic
1250C22#538×C13111yescharacteristic
1251C22#538×C13111yescharacteristic
1252C22#538×C13111yescharacteristic
1253C22#540×C13111yescharacteristic
1254C22#540×C13111yescharacteristic
1255C22D42×C13111yescharacteristic
1256C22#546×C13111yescharacteristic
1257C22#546×C13111yescharacteristic
1258C22#546×C13111yescharacteristic
1259C22#546×C13111yescharacteristic
1260C22#546×C13111yescharacteristic
1261C22#550×C13111yescharacteristic
1262C22#551×C13111yescharacteristic
1263C22#551×C13111yescharacteristic
1264C22#553×C13111yescharacteristic
1265C22#553×C13111yescharacteristic
1266C22#553×C13111yescharacteristic
1267C22#560×C13111yescharacteristic
1268C22#560×C13111yescharacteristic
1269C22#560×C13111yescharacteristic
1270C22#560×C13111yescharacteristic
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C2—44no—
1284C2—82no—
1285C2—82no—
1286C2#2418×C13111yescharacteristic
1287C2#2444×C13111yescharacteristic
1288C2#2467×C13111yescharacteristic
1289C2#2622×C13111yescharacteristic
1290C2#2631×C13111yescharacteristic
1291C2#2648×C13111yescharacteristic
1292C2#2673×C13111yescharacteristic
1293C2#2678×C13111yescharacteristic
1294C2#2688×C13111yescharacteristic
1295C2#2697×C13111yescharacteristic
1296C2#2703×C13111yescharacteristic
1297C2#2714×C13111yescharacteristic
1298C2#2749×C13111yescharacteristic
1299C2#2778×C13111yescharacteristic
1300C2#2825×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutator, Frattini, cosocleC24C24×C131
prime radicalC2×#392×C131C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#397×C131C2semidirect
3. C2×#386×C131C2semidirect
4. C2×#386×C131C2semidirect
5. #1443×C131C2semidirect
6. #1443×C131C2semidirect
7. #1440×C131C2semidirect
8. #1440×C131C2semidirect
9. #1439×C131C2semidirect
10. #1439×C131C2semidirect
11. #1438×C131C2semidirect
12. #1438×C131C2semidirect
13. #1438×C131C2semidirect
14. #1438×C131C2semidirect
15. C22⋊#95×C131C2semidirect
158. #95×C131D4semidirect
650. #16270C131direct (N × H)
651. C131#16270direct (N × H)
652. C2×#397C2×C131semidirect
654. C2×#386C2×C131semidirect
655. C2×#386C2×C131semidirect
656. #1443C2×C131semidirect
657. #1443C2×C131semidirect
658. #1440C2×C131semidirect
659. #1440C2×C131semidirect
660. #1439C2×C131semidirect
661. #1439C2×C131semidirect
662. #1438C2×C131semidirect
663. #1438C2×C131semidirect
664. #1438C2×C131semidirect
665. #1438C2×C131semidirect
666. C22⋊#95C2×C131semidirect
809. #95D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1312
C2×#392×C1312
C2×#386×C1312
#1443×C1312
#1440×C1312
#1439×C1312
#1438×C1312
C22⋊#95×C1312
#16270131