Finite Group Databasebeta

← #29609373

Subgroups — #29609373

Order 15616.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839671C211yesmaximal, characteristic
2C2×#16839664C211yesmaximal, characteristic, complemented
3C2×#16839662C211yesmaximal, characteristic, complemented
4C2×#16839652C211yesmaximal, characteristic, complemented
5C2×#16839640C211yesmaximal, characteristic, complemented
6C2×#16839638C211yesmaximal, characteristic, complemented
7#21444064C211yesmaximal, characteristic, complemented
8#21444063C211yesmaximal, characteristic, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444058C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444052C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839671C418yescomplemented
35#16839664—24no—
36#16839662—24no—
37#16839652—24no—
38#16839640—24no—
39#16839638—24no—
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C22×C4⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C61×#388—24no—
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C24×D61C2311yescharacteristic
60C22×D244—22no—
61C22×D244—22no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—41no—
65C22×D244—41no—
66C22×D244C2×C414yes—
67C22×C22⋊D61—22no—
68C22×C22⋊D61—22no—
69C22×C22⋊D61—22no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—41no—
72C22×C22⋊D61—41no—
73C22×C22⋊D61—41no—
74C22×C22⋊D61—41no—
75C22×C22⋊D61—41no—
76C22×C22⋊D61—41no—
77C22×C22⋊D61—41no—
78C22×C22⋊D61—41no—
79C22×C22⋊D61C2×C414yes—
80C22×C22⋊D61C2×C414yescomplemented
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—41no—
91C22×C4×D61—41no—
92C22×C4×D61—41no—
93C22×C4×D61—41no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61—22no—
96C2×C4⋊Dic61—41no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—41no—
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—22no—
102C2×C22⋊Dic61—41no—
103C2×C22⋊Dic61—41no—
104C2×C22⋊Dic61—41no—
105C2×C22⋊Dic61—41no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—41no—
119C2×#11758198—41no—
120C2×#11758198—41no—
121C2×#11758198—41no—
122C2×#11758198—41no—
123C2×#11758198—41no—
124C2×#11758198—41no—
125C2×#11758198—41no—
126C2×#11758198—41no—
127C2×#11758198—41no—
128C2×#11758198—41no—
129C2×#11758198—41no—
130C2×#11758198C2×C414yes—
131C2×#11758198C2×C414yescomplemented
132C2×#11758198D414yescomplemented
133C2×C4×Dic61—22no—
134C2×C4×Dic61—22no—
135C2×C4×Dic61—41no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684—41no—
140#14519684—41no—
141#14519684—41no—
142#14519684—41no—
143#14519684—41no—
144#14519684C2×C414yescomplemented
145#14519684D414yescomplemented
146C25×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61—22no—
154C2×C4⋊C4×C61—22no—
155C2×C4⋊C4×C61—41no—
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61—22no—
158C2×C22⋊C4×C61—22no—
159C2×C22⋊C4×C61—22no—
160C2×C22⋊C4×C61—22no—
161C2×C22⋊C4×C61—22no—
162C2×C22⋊C4×C61—41no—
163C2×C22⋊C4×C61—41no—
164C2×C22⋊C4×C61C2×C414yescomplemented
165C2×C42×C61—22no—
166C2×C42×C61—22no—
167C2×C42×C61—41no—
168#95×C61—22no—
169#95×C61D414yescomplemented
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61C22×C412yes—
185C24×C61C2411yescharacteristic
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
206C23×D61—21no—
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211C23×D61—21no—
212C23×D61C22×C412yes—
213C23×D61C22×C412yes—
214C23×D61C2×D412yes—
215C23×D61#4112yes—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61C22×C412yes—
251C22×C4×C61C22×C412yes—
252C22×C4×C61C2×D412yes—
253C22×C4×C61C2×D412yes—
254C22×C4×C61C2×D412yes—
255C22×C4×C61C2×D412yes—
256C22×C4×C61C2×D412yes—
257C22×C4×C61#4112yes—
258C2×C22⋊D61—28no—
259C2×C22⋊D61—28no—
260C2×C22⋊D61—44no—
261C2×C22⋊D61—44no—
262C2×C22⋊D61—44no—
263C2×C22⋊D61—44no—
264C2×C22⋊D61—44no—
265C2×C22⋊D61—44no—
266C2×C22⋊D61—44no—
267C2×C22⋊D61—44no—
268C2×C22⋊D61—44no—
269C2×C22⋊D61—44no—
270C2×C22⋊D61—44no—
271C2×C22⋊D61—44no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61—21no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61C22×C412yes—
309C22×Dic61C22×C412yes—
310C22×Dic61C2×D412yes—
311C22×Dic61C2×D412yes—
312C22×Dic61C2×D412yes—
313C22×Dic61#4112yes—
314C2×D244—28no—
315C2×D244—28no—
316C2×D244—44no—
317C2×D244—44no—
318C2×D244—44no—
319C2×D244—44no—
320C2×D244—44no—
321C2×C4×D61—44no—
322C2×C4×D61—44no—
323C2×C4×D61—44no—
324C2×C4×D61—44no—
325C2×C4×D61—44no—
326C2×C4×D61—44no—
327C2×C4×D61—44no—
328C4⋊C4×C61—44no—
329C22⋊C4×C61—28no—
330C22⋊C4×C61—44no—
331C22⋊C4×C61—44no—
332C42×C61—44no—
333C22⋊Dic61—44no—
334C22⋊Dic61—44no—
335#11758198—28no—
336#11758198—44no—
337#11758198—44no—
338#11758198—44no—
339#11758198—44no—
340#11758198—44no—
341#11758198—44no—
342#11758198—44no—
343#11758198—44no—
344C4⋊Dic61—44no—
345#11758196—44no—
346C4×Dic61—44no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61C23×C411yescharacteristic
383C23×C61C22×D411yescharacteristic
384C23×C61C22×D411yescharacteristic
385C23×C61C22×D411yescharacteristic
386C23×C61C2×#4111yescharacteristic
387C23×C61C2×#4111yescharacteristic
388C23×C61C2×#4111yescharacteristic
389C23×C61H(5,𝔽2)11yescharacteristic
390C23×C61H(5,𝔽2)11yescharacteristic
391C23×C61H(5,𝔽2)11yescharacteristic
392C23×C61H(5,𝔽2)11yescharacteristic
393C23×C61H(5,𝔽2)11yescharacteristic
394C23×C61H(5,𝔽2)11yescharacteristic
395C23×C61H(5,𝔽2)11yescharacteristic
396C23×C612−1+411yescharacteristic
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—22no—
401C22×D61—22no—
402C22×D61—22no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—22no—
409C22×D61—22no—
410C22×D61—22no—
411C22×D61—22no—
412C22×D61—22no—
413C22×D61—22no—
414C22×D61—22no—
415C22×D61—22no—
416C22×D61—22no—
417C22×D61—22no—
418C22×D61—22no—
419C22×D61—22no—
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—41no—
423C22×D61—41no—
424C22×D61—41no—
425C22×D61—41no—
426C22×D61—41no—
427C22×D61—41no—
428C22×D61—41no—
429C22×D61—41no—
430C22×D61—41no—
431C22×D61—41no—
432C22×D61—41no—
433C22×D61—41no—
434C22×D61—41no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—41no—
451C22×D61—41no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61—41no—
455C22×D61—41no—
456C22×D61—41no—
457C22×D61—41no—
458C22×D61—41no—
459C22×D61—41no—
460C22×D61—41no—
461C22×D61—41no—
462C22×D61—41no—
463C22×D61—41no—
464C22×D61—41no—
465C22×D61—41no—
466C22×D61C4×D414yes—
467C2×C4×C61—22no—
468C2×C4×C61—22no—
469C2×C4×C61—22no—
470C2×C4×C61—22no—
471C2×C4×C61—22no—
472C2×C4×C61—22no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—22no—
476C2×C4×C61—22no—
477C2×C4×C61—22no—
478C2×C4×C61—22no—
479C2×C4×C61—22no—
480C2×C4×C61—22no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—22no—
484C2×C4×C61—22no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—41no—
489C2×C4×C61—41no—
490C2×C4×C61—41no—
491C2×C4×C61—41no—
492C2×C4×C61—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61—41no—
496C2×C4×C61—41no—
497C2×C4×C61—41no—
498C2×C4×C61—41no—
499C2×C4×C61—41no—
500C2×C4×C61—41no—
501C2×C4×C61—41no—
502C2×C4×C61—41no—
503C2×C4×C61—41no—
504C2×C4×C61—41no—
505C2×C4×C61—41no—
506C2×C4×C61—41no—
507C2×C4×C61—41no—
508C2×C4×C61C4×D414yes—
509C22⋊D61—416no—
510C22⋊D61—416no—
511C2×Dic61—22no—
512C2×Dic61—22no—
513C2×Dic61—22no—
514C2×Dic61—22no—
515C2×Dic61—22no—
516C2×Dic61—22no—
517C2×Dic61—22no—
518C2×Dic61—22no—
519C2×Dic61—22no—
520C2×Dic61—22no—
521C2×Dic61—22no—
522C2×Dic61—22no—
523C2×Dic61—22no—
524C2×Dic61—22no—
525C2×Dic61—22no—
526C2×Dic61—41no—
527C2×Dic61—41no—
528C2×Dic61—41no—
529C2×Dic61—41no—
530C2×Dic61—41no—
531C2×Dic61—41no—
532C2×Dic61—41no—
533C2×Dic61—41no—
534C2×Dic61—41no—
535C2×Dic61—41no—
536C2×Dic61—41no—
537C2×Dic61—41no—
538C2×Dic61—41no—
539C2×Dic61—41no—
540C2×Dic61—41no—
541C2×Dic61—41no—
542C2×Dic61—41no—
543C2×Dic61—41no—
544C2×Dic61—41no—
545C2×Dic61—41no—
546C2×Dic61—41no—
547C2×Dic61—41no—
548C2×Dic61—41no—
549C2×Dic61—41no—
550C2×Dic61—41no—
551C2×Dic61—41no—
552C2×Dic61C4×D414yes—
553D244—416no—
554C4×D61—416no—
555#14521—611nomaximal, Sylow
556C22×C61—42no—
557C22×C61—42no—
558C22×C61—42no—
559C22×C61—42no—
560C22×C61—42no—
561C22×C61—42no—
562C22×C61—42no—
563C22×C61—81no—
564C22×C61—81no—
565C22×C61—81no—
566C22×C61—81no—
567C22×C61—81no—
568C22×C61—81no—
569C22×C61—81no—
570C22×C61—81no—
571C22×C61C2×C4×D411yescharacteristic
572C22×C61C2×C4×D411yescharacteristic
573C22×C61C2×C4×D411yescharacteristic
574C22×C61#51811yescharacteristic
575C22×C61#51811yescharacteristic
576C22×C61#51811yescharacteristic
577C22×C61#52011yescharacteristic
578C22×C61#53411yescharacteristic
579C22×C61#53511yescharacteristic
580C22×C61#53511yescharacteristic
581C22×C61#53711yescharacteristic
582C22×C61#53711yescharacteristic
583C22×C61#53711yescharacteristic
584C22×C61#53811yescharacteristic
585C22×C61#53911yescharacteristic
586C22×C61#54011yescharacteristic
587C22×C61#54011yescharacteristic
588C22×C61#54211yescharacteristic
589C22×C61#54211yescharacteristic
590C22×C61D4211yescharacteristic
591C22×C61D4211yescharacteristic
592C22×C61D4211yescharacteristic
593C22×C61#54611yescharacteristic
594C22×C61#54611yescharacteristic
595C22×C61#54611yescharacteristic
596C22×C61#54611yescharacteristic
597C22×C61#55011yescharacteristic
598C22×C61#55011yescharacteristic
599C22×C61#55111yescharacteristic
600C22×C61#55111yescharacteristic
601C22×C61#55911yescharacteristic
602C22×C61#56011yescharacteristic
603C22×C61#56011yescharacteristic
604C22×C61#56011yescharacteristic
605C22×C61H(3,𝔽4)11yescharacteristic
606C2×D61—24no—
607C2×D61—24no—
608C2×D61—24no—
609C2×D61—42no—
610C2×D61—42no—
611C2×D61—42no—
612C2×D61—42no—
613C2×D61—42no—
614C2×D61—42no—
615C2×D61—42no—
616C2×D61—42no—
617C2×D61—42no—
618C2×D61—42no—
619C2×D61—42no—
620C2×D61—42no—
621C2×D61—42no—
622C2×D61—42no—
623C2×D61—42no—
624C2×D61—42no—
625C2×D61—42no—
626C2×D61—42no—
627C2×D61—42no—
628C2×D61—81no—
629C2×D61—81no—
630C2×D61—81no—
631C2×D61—81no—
632C2×D61—81no—
633C2×D61—81no—
634C2×D61—81no—
635C2×D61—81no—
636C4×C61—24no—
637C4×C61—42no—
638C4×C61—42no—
639C4×C61—42no—
640C4×C61—42no—
641C4×C61—42no—
642Dic61—24no—
643Dic61—42no—
644Dic61—42no—
645Dic61—42no—
646Dic61—81no—
647Dic61—81no—
648C2×#392—611no—
649C2×#390—611no—
650C2×#390—611no—
651C2×#388—611no—
652C2×#388D6111yescharacteristic, complemented
653C2×#386—611no—
654C2×#386—611no—
655#1439—611no—
656#1439—611no—
657#1439—611no—
658#1438—611no—
659#1438—611no—
660#1436—611no—
661#1436—611no—
662C22⋊#95—611no—
663C2×C61—82no—
664C2×C61#232411yescharacteristic
665C2×C61#232411yescharacteristic
666C2×C61#232511yescharacteristic
667C2×C61#235811yescharacteristic
668C2×C61#235811yescharacteristic
669C2×C61#236611yescharacteristic
670C2×C61#237511yescharacteristic
671C2×C61#267011yescharacteristic
672C2×C61#267311yescharacteristic
673C2×C61#267311yescharacteristic
674C2×C61#267511yescharacteristic
675C2×C61#270511yescharacteristic
676C2×C61#270511yescharacteristic
677C2×C61#271211yescharacteristic
678C2×C61#275211yescharacteristic
679D61—44no—
680D61—82no—
681C23×D4—611no—
682C23×D4—611no—
683C23×D4—611no—
684C24×C4—611no—
685C22×C4⋊C4—611no—
686C22×C4⋊C4—611no—
687C22×C4⋊C4C2×D6111yescharacteristic
688C22×C22⋊C4—611no—
689C22×C22⋊C4—611no—
690C22×C22⋊C4—611no—
691C22×C22⋊C4—611no—
692C22×C22⋊C4—611no—
693C22×C22⋊C4—611no—
694C22×C22⋊C4—611no—
695C22×C22⋊C4—611no—
696C22×C22⋊C4—611no—
697C22×C22⋊C4—611no—
698C22×C22⋊C4—611no—
699C22×C22⋊C4C2×D6111yescharacteristic
700C22×C22⋊C4C2×D6111yescharacteristic
701C22×C22⋊C4C2×D6111yescharacteristic
702C22×C42—611no—
703C22×C42C2×D6111yescharacteristic
704#392—618no—
705#390—1224no—
706#390—1224no—
707#388—24no—
708#388—1224no—
709#386—1224no—
710#386—1224no—
711C2×#95—611no—
712C2×#95—611no—
713C2×#95—611no—
714C2×#95—611no—
715C2×#95—611no—
716C2×#95—611no—
717C2×#95—611no—
718C2×#95—611no—
719C2×#95—611no—
720C2×#95—611no—
721C2×#95C2×D6111yescharacteristic
722C2×#95C2×D6111yescharacteristic
723C61#1452111yescharacteristic, complemented, Sylow
724C25—611no—
725C25—611no—
726C25C22×D6111yescharacteristic
727C22×D4—614no—
728C22×D4—614no—
729C22×D4—614no—
730C22×D4—1222no—
731C22×D4—1222no—
732C22×D4—1222no—
733C22×D4—1222no—
734C22×D4—1222no—
735C22×D4—1222no—
736C22×D4—1222no—
737C22×D4—1222no—
738C22×D4—2441no—
739C22×D4—2441no—
740C22×D4—2441no—
741C22×D4—2441no—
742C22×D4—2441no—
743C22×D4—2441no—
744C22×D4—2441no—
745C22×D4—2441no—
746C22×D4—2441no—
747C22×D4—2441no—
748C23×C4—611no—
749C23×C4—611no—
750C23×C4—611no—
751C23×C4—611no—
752C23×C4—611no—
753C23×C4—611no—
754C23×C4—1222no—
755C23×C4—1222no—
756C23×C4—1222no—
757C23×C4—2441no—
758C23×C4—2441no—
759C23×C4—2441no—
760C23×C4—2441no—
761C23×C4C22×D6111yescharacteristic
762C23×C4C22×D6111yescharacteristic
763C23×C4C22×D6111yescharacteristic
764C23×C4C22×D6111yescharacteristic
765C23×C4C22×D6111yescharacteristic
766C23×C4C22×D6111yescharacteristic
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4—1222no—
771C2×C4⋊C4—1222no—
772C2×C4⋊C4—1222no—
773C2×C4⋊C4—1222no—
774C2×C4⋊C4—2441no—
775C2×C4⋊C4—2441no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—614no—
785C2×C22⋊C4—614no—
786C2×C22⋊C4—614no—
787C2×C22⋊C4—1222no—
788C2×C22⋊C4—1222no—
789C2×C22⋊C4—1222no—
790C2×C22⋊C4—1222no—
791C2×C22⋊C4—1222no—
792C2×C22⋊C4—1222no—
793C2×C22⋊C4—1222no—
794C2×C22⋊C4—1222no—
795C2×C22⋊C4—1222no—
796C2×C22⋊C4—1222no—
797C2×C22⋊C4—1222no—
798C2×C22⋊C4—1222no—
799C2×C22⋊C4—1222no—
800C2×C22⋊C4—1222no—
801C2×C22⋊C4—2441no—
802C2×C22⋊C4—2441no—
803C2×C22⋊C4—2441no—
804C2×C22⋊C4—2441no—
805C2×C22⋊C4—2441no—
806C2×C22⋊C4—2441no—
807C2×C22⋊C4—2441no—
808C2×C22⋊C4—2441no—
809C2×C22⋊C4—2441no—
810C2×C22⋊C4—2441no—
811C2×C22⋊C4—2441no—
812C2×C22⋊C4—2441no—
813C2×C22⋊C4—2441no—
814C2×C22⋊C4—2441no—
815C2×C22⋊C4—2441no—
816C2×C22⋊C4—2441no—
817C2×C22⋊C4C4×D6114yescomplemented
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—41no—
821C2×C42—1222no—
822C2×C42—1222no—
823C2×C42—2441no—
824#95—22no—
825#95—614no—
826#95—614no—
827#95—1222no—
828#95—1222no—
829#95—1222no—
830#95—2441no—
831#95—2441no—
832#95—2441no—
833#95—2441no—
834#95—2441no—
835#95C22⋊D6114yescomplemented
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—
850C24—612no—
851C24—612no—
852C24—612no—
853C24—612no—
854C24—1221no—
855C24—1221no—
856C24—1221no—
857C24—1221no—
858C24—1221no—
859C24—1221no—
860C24—1221no—
861C24—1221no—
862C24—1221no—
863C24—1221no—
864C24—1221no—
865C24—1221no—
866C24—1221no—
867C24—1221no—
868C24—1221no—
869C24—1221no—
870C24—1221no—
871C24—1221no—
872C24—1221no—
873C24—1221no—
874C24—1221no—
875C24—1221no—
876C24—1221no—
877C24—1221no—
878C24—1221no—
879C24—1221no—
880C24C2×C4×D6112yes—
881C24C23×D6111yescharacteristic
882C2×D4—1228no—
883C2×D4—1228no—
884C2×D4—1228no—
885C2×D4—1228no—
886C2×D4—2444no—
887C2×D4—2444no—
888C2×D4—2444no—
889C2×D4—2444no—
890C2×D4—2444no—
891C2×D4—2444no—
892C2×D4—2444no—
893C2×D4—2444no—
894C2×D4—2444no—
895C2×D4—2444no—
896C2×D4—2444no—
897C2×D4—2444no—
898C2×D4—2444no—
899C2×D4—2444no—
900C2×D4—2444no—
901C2×D4—2444no—
902C2×D4—2444no—
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—612no—
938C22×C4—612no—
939C22×C4—612no—
940C22×C4—612no—
941C22×C4—612no—
942C22×C4—612no—
943C22×C4—1221no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1221no—
977C22×C4—1221no—
978C22×C4—1221no—
979C22×C4—2444no—
980C22×C4—2444no—
981C22×C4—2444no—
982C22×C4—2444no—
983C22×C4—2444no—
984C22×C4—2444no—
985C22×C4—2444no—
986C22×C4C2×C4×D6112yes—
987C22×C4C2×C4×D6112yes—
988C22×C4#1175822212yes—
989C22×C4D4×D6112yes—
990C22×C4D4×D6112yes—
991C22×C4C2×C22⋊D6112yes—
992C22×C4C2×C22⋊D6112yes—
993C22×C4C2×C22⋊D6112yes—
994C4⋊C4—44no—
995C4⋊C4—2444no—
996C4⋊C4—2444no—
997C22⋊C4—28no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—1228no—
1001C22⋊C4—2444no—
1002C22⋊C4—2444no—
1003C22⋊C4—2444no—
1004C22⋊C4—2444no—
1005C22⋊C4—2444no—
1006C22⋊C4—2444no—
1007C22⋊C4—2444no—
1008C22⋊C4—2444no—
1009C22⋊C4—2444no—
1010C22⋊C4—2444no—
1011C42—44no—
1012C42—2444no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
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—614no—
1049C23—1222no—
1050C23—1222no—
1051C23—1222no—
1052C23—1222no—
1053C23—1222no—
1054C23—1222no—
1055C23—1222no—
1056C23—1222no—
1057C23—1222no—
1058C23—1222no—
1059C23—1222no—
1060C23—1222no—
1061C23—1222no—
1062C23—1222no—
1063C23—1222no—
1064C23—1222no—
1065C23—1222no—
1066C23—1222no—
1067C23—1222no—
1068C23—1222no—
1069C23—1222no—
1070C23—1222no—
1071C23—1222no—
1072C23—1222no—
1073C23—1222no—
1074C23—2441no—
1075C23—2441no—
1076C23—2441no—
1077C23—2441no—
1078C23—2441no—
1079C23—2441no—
1080C23—2441no—
1081C23—2441no—
1082C23—2441no—
1083C23—2441no—
1084C23—2441no—
1085C23—2441no—
1086C23—2441no—
1087C23—2441no—
1088C23—2441no—
1089C23—2441no—
1090C23—2441no—
1091C23—2441no—
1092C23—2441no—
1093C23—2441no—
1094C23—2441no—
1095C23—2441no—
1096C23—2441no—
1097C23—2441no—
1098C23—2441no—
1099C23—2441no—
1100C23—2441no—
1101C23—2441no—
1102C23—2441no—
1103C23—2441no—
1104C23—2441no—
1105C23—2441no—
1106C23—2441no—
1107C23—2441no—
1108C23—2441no—
1109C23—2441no—
1110C23—2441no—
1111C23—2441no—
1112C23—2441no—
1113C23—2441no—
1114C23—2441no—
1115C23—2441no—
1116C23—2441no—
1117C23—2441no—
1118C23C22×C4×D6111yescharacteristic
1119C23C2×D4×D6111yescharacteristic
1120C23C2×D4×D6111yescharacteristic
1121C23C22×C22⋊D6111yescharacteristic
1122C23#41×D6111yescharacteristic
1123C23#41×D6111yescharacteristic
1124C23C2×#1175822211yescharacteristic
1125C23#1451982211yescharacteristic
1126C23#1451982211yescharacteristic
1127C23#1451982311yescharacteristic
1128C23#1451982311yescharacteristic
1129C23#1451982311yescharacteristic
1130C23#1451982311yescharacteristic
1131C23#1451982311yescharacteristic
1132C23#1451982411yescharacteristic
1133D4—24416no—
1134D4—24416no—
1135D4—24416no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
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—614no—
1178C2×C4—1222no—
1179C2×C4—1222no—
1180C2×C4—1222no—
1181C2×C4—1222no—
1182C2×C4—1222no—
1183C2×C4—1222no—
1184C2×C4—1222no—
1185C2×C4—1222no—
1186C2×C4—1222no—
1187C2×C4—1222no—
1188C2×C4—1222no—
1189C2×C4—1222no—
1190C2×C4—1222no—
1191C2×C4—1222no—
1192C2×C4—1222no—
1193C2×C4—24416no—
1194C2×C4—2441no—
1195C2×C4—2441no—
1196C2×C4—2441no—
1197C2×C4—2441no—
1198C2×C4—2441no—
1199C2×C4—2441no—
1200C2×C4—2441no—
1201C2×C4—2441no—
1202C2×C4—2441no—
1203C2×C4—2441no—
1204C2×C4—2441no—
1205C2×C4—2441no—
1206C2×C4—2441no—
1207C2×C4—2441no—
1208C2×C4—2441no—
1209C2×C4—2441no—
1210C2×C4—2441no—
1211C2×C4—2441no—
1212C2×C4—2441no—
1213C2×C4—2441no—
1214C2×C4—2441no—
1215C2×C4—2441no—
1216C2×C4—2441no—
1217C2×C4—2441no—
1218C2×C4—2441no—
1219C2×C4—2441no—
1220C2×C4C4×C22⋊D6114yes—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—1224no—
1237C22—1224no—
1238C22—1224no—
1239C22—4881no—
1240C22—4881no—
1241C22—4881no—
1242C22—4881no—
1243C22—4881no—
1244C22—4881no—
1245C22—4881no—
1246C22—4881no—
1247C22—2442no—
1248C22—2442no—
1249C22—2442no—
1250C22—2442no—
1251C22—2442no—
1252C22—2442no—
1253C22—2442no—
1254C22—2442no—
1255C22—2442no—
1256C22—2442no—
1257C22—2442no—
1258C22—2442no—
1259C22—2442no—
1260C22—2442no—
1261C22—2442no—
1262C22—2442no—
1263C22—2442no—
1264C22—2442no—
1265C22—2442no—
1266C22C4×D4×D6111yescharacteristic
1267C22C4×D4×D6111yescharacteristic
1268C22C2×C4×C22⋊D6111yescharacteristic
1269C22#1684023411yescharacteristic
1270C22#1684023411yescharacteristic
1271C22#1684023611yescharacteristic
1272C22#1684024211yescharacteristic
1273C22#1684032311yescharacteristic
1274C22#1684032611yescharacteristic
1275C22#1684033011yescharacteristic
1276C22#1684033911yescharacteristic
1277C22#1684034011yescharacteristic
1278C22#1684034111yescharacteristic
1279C22#1684034611yescharacteristic
1280C22#1684035311yescharacteristic
1281C22#1684036411yescharacteristic
1282C22#1684036711yescharacteristic
1283C22#1684037811yescharacteristic
1284C22#1684038311yescharacteristic
1285C22D4×C22⋊D6111yescharacteristic
1286C22D4×C22⋊D6111yescharacteristic
1287C22#1684039611yescharacteristic
1288C22#1684040011yescharacteristic
1289C22#1684040411yescharacteristic
1290C22#1684040511yescharacteristic
1291C22#1684040811yescharacteristic
1292C22#1684043111yescharacteristic
1293C22#1684043311yescharacteristic
1294C22#1684043711yescharacteristic
1295C22#1684044111yescharacteristic
1296C22#1684049511yescharacteristic
1297C22#1684050011yescharacteristic
1298C22#1684050211yescharacteristic
1299C22#1684050311yescharacteristic
1300C22#1684050411yescharacteristic
1301C4—24no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—1224no—
1308C4—4881no—
1309C4—4881no—
1310C4—2442no—
1311C4—2442no—
1312C4—2442no—
1313C2—82no—
1314C2—4882no—
1315C2—2444no—
1316C2#2144850711yescharacteristic
1317C2#2144851211yescharacteristic
1318C2#2144852311yescharacteristic
1319C2#2144879611yescharacteristic
1320C2#2144879711yescharacteristic
1321C2#2144888111yescharacteristic
1322C2#2144895911yescharacteristic
1323C2#2145204011yescharacteristic
1324C2#2145208511yescharacteristic
1325C2#2145208611yescharacteristic
1326C2#2145210911yescharacteristic
1327C2#2145248611yescharacteristic
1328C2#2145248911yescharacteristic
1329C2#2145259111yescharacteristic
1330C2#2145308411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC2×#16839671C2
hypercenterC2×#388D61
hypocenterC61#14521
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16839664C2semidirect
3. C2×#16839662C2semidirect
4. C2×#16839652C2semidirect
5. C2×#16839640C2semidirect
6. C2×#16839638C2semidirect
7. #21444064C2semidirect
8. #21444063C2semidirect
9. #21444061C2semidirect
10. #21444058C2semidirect
11. #21444058C2semidirect
12. #21444053C2semidirect
13. #21444052C2semidirect
14. #21444040C2semidirect
15. C2×C61×#388C2semidirect
34. #16839671C4semidirect
80. C22×C22⋊D61C2×C4semidirect
131. C2×#11758198C2×C4semidirect
132. C2×#11758198D4semidirect
144. #14519684C2×C4semidirect
145. #14519684D4semidirect
164. C2×C22⋊C4×C61C2×C4semidirect
169. #95×C61D4semidirect
652. C2×#388D61semidirect
723. C61#14521semidirect
817. C2×C22⋊C4C4×D61semidirect
835. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396712
C2×#168396642
C2×#168396622
C2×#168396522
C2×#168396402
C2×#168396382
#214440642
#214440632
#214440612
#214440582
#214440532
#214440522
#214440402
C2×C61×#3882
#1452161