Finite Group Databasebeta

← #29604090

Subgroups — #29604090

Order 15616.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519733C211yesmaximal, characteristic, complemented
2C2×#16839665C211yesmaximal, characteristic
3C2×#16839656C211yesmaximal, characteristic, complemented
4C2×#16839650C211yesmaximal, characteristic, complemented
5C2×#16839642C211yesmaximal, characteristic
6#21444083C211yesmaximal, characteristic, complemented
7#21444062C211yesmaximal, characteristic, complemented
8#21444062C211yesmaximal, characteristic, complemented
9#21444056C211yesmaximal, characteristic, complemented
10#21444056C211yesmaximal, characteristic, complemented
11#21444053C211yesmaximal, characteristic, complemented
12#21444050C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C61×#1438C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C2×#14519733—24no—
18C2×#14519733—24no—
19C2×#14519733—24no—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839665—24no—
36#16839656—24no—
37#16839650—24no—
38#16839642C418yescomplemented
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C23×D4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—22no—
61C23×Dic61—22no—
62C23×Dic61—22no—
63C23×Dic61—22no—
64C23×Dic61C2×C414yes—
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73#14519733—232no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—41no—
77C2×#11758196—22no—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196—41no—
84C2×#11758196—41no—
85C2×#11758196D414yescomplemented
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—22no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—41no—
100C2×C22⋊Dic61—41no—
101C2×C22⋊Dic61—41no—
102C2×C22⋊Dic61—41no—
103C2×C22⋊Dic61C2×C414yes—
104C2×C22⋊Dic61C2×C414yes—
105C2×C22⋊Dic61C2×C414yes—
106C2×C22⋊Dic61D414yes—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—22no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—41no—
117C2×C4×Dic61—41no—
118C2×C4×Dic61D414yescomplemented
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129#14519684C2×C414yes—
130#14519684C2×C414yes—
131C25×C61C2311yescharacteristic
132C25×C61C2311yescharacteristic
133C22×D4×C61—22no—
134C22×D4×C61—22no—
135C22×D4×C61—22no—
136C22×D4×C61—22no—
137C22×D4×C61—41no—
138C22×D4×C61—41no—
139C22×D4×C61C2×C414yes—
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61—22no—
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61—41no—
154C2×C22⋊C4×C61—41no—
155C2×C22⋊C4×C61—41no—
156C2×C22⋊C4×C61—41no—
157#95×C61—22no—
158#95×C61—22no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
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×C61—21no—
185C24×C61C22×C412yes—
186C24×C61C22×C412yes—
187C24×C61C2×D412yes—
188C24×C61#4112yes—
189C24×C61C2411yescharacteristic
190C2×D4×C61—28no—
191C2×D4×C61—28no—
192C2×D4×C61—44no—
193C2×D4×C61—44no—
194C2×D4×C61—44no—
195C2×D4×C61—44no—
196C2×D4×C61—44no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
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×C61C22×C412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D412yes—
229C22×C4×C61#4112yes—
230C22×C4×C61#4112yes—
231C22×C4×C61#4112yes—
232C22×Dic61—28no—
233C22×Dic61—28no—
234C22×Dic61—28no—
235C22×Dic61—28no—
236C22×Dic61—28no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—28no—
250C22×Dic61—28no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
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×Dic61C22×C412yes—
283C22×Dic61C22×C412yes—
284C22×Dic61C22×C412yes—
285C22×Dic61C22×C412yes—
286C22×Dic61C2×D412yes—
287C22×Dic61C2×D412yes—
288C22×Dic61C2×D412yes—
289C22×Dic61C2×D412yes—
290C22×Dic61C2×D412yes—
291C22×Dic61C2×D412yes—
292C22×Dic61#4112yes—
293C22×Dic61#4112yes—
294C22×Dic61#4112yes—
295C22⋊C4×C61—28no—
296C22⋊C4×C61—44no—
297C22⋊C4×C61—44no—
298C22⋊C4×C61—44no—
299C22⋊Dic61—28no—
300C22⋊Dic61—28no—
301C22⋊Dic61—28no—
302C22⋊Dic61—44no—
303C22⋊Dic61—44no—
304C22⋊Dic61—44no—
305C22⋊Dic61—44no—
306C4⋊Dic61—44no—
307#11758196—28no—
308#11758196—28no—
309#11758196—44no—
310C4×Dic61—28no—
311C4×Dic61—28no—
312C4×Dic61—44no—
313C4×Dic61—44no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
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×C61—41no—
383C23×C61C4×D414yes—
384C23×C61C23×C411yescharacteristic
385C23×C61C22×D411yescharacteristic
386C23×C61C22×D411yescharacteristic
387C23×C61C22×D411yescharacteristic
388C23×C61C2×#4111yescharacteristic
389C23×C61C2×#4111yescharacteristic
390C23×C61C2×#4111yescharacteristic
391C23×C61C2×#4111yescharacteristic
392C23×C61C2×#4111yescharacteristic
393C23×C61C2×#4111yescharacteristic
394C23×C61C2×#4111yescharacteristic
395C23×C61H(5,𝔽2)11yescharacteristic
396C23×C61H(5,𝔽2)11yescharacteristic
397C23×C61H(5,𝔽2)11yescharacteristic
398C23×C612−1+411yescharacteristic
399D4×C61—416no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61#11714yescomplemented
435C2×Dic61—232no—
436C2×Dic61—22no—
437C2×Dic61—22no—
438C2×Dic61—22no—
439C2×Dic61—22no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61C4×D414yes—
490C2×Dic61C4×D414yes—
491C2×Dic61#12014yes—
492#14071—611nomaximal, Sylow
493C22×C61—24no—
494C22×C61—24no—
495C22×C61—24no—
496C22×C61—42no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—42no—
500C22×C61—42no—
501C22×C61—42no—
502C22×C61—42no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—42no—
506C22×C61—42no—
507C22×C61—42no—
508C22×C61—42no—
509C22×C61—42no—
510C22×C61—42no—
511C22×C61—42no—
512C22×C61—42no—
513C22×C61—42no—
514C22×C61—42no—
515C22×C61—81no—
516C22×C61—81no—
517C22×C61—81no—
518C22×C61—81no—
519C22×C61—81no—
520C22×C61—81no—
521C22×C61—81no—
522C22×C61—81no—
523C22×C61C2×#11711yescharacteristic
524C22×C61C2×C4×D411yescharacteristic
525C22×C61C2×C4×D411yescharacteristic
526C22×C61C2×C4×D411yescharacteristic
527C22×C61C4×#4111yescharacteristic
528C22×C61#51811yescharacteristic
529C22×C61#52011yescharacteristic
530C22×C61C2×#12011yescharacteristic
531C22×C61#52511yescharacteristic
532C22×C61#52511yescharacteristic
533C22×C61#52511yescharacteristic
534C22×C61#52911yescharacteristic
535C22×C61#52911yescharacteristic
536C22×C61#53211yescharacteristic
537C22×C61#53211yescharacteristic
538C22×C61#53511yescharacteristic
539C22×C61#53711yescharacteristic
540C22×C61#54011yescharacteristic
541C22×C61#54211yescharacteristic
542C22×C61#54611yescharacteristic
543C22×C61#54611yescharacteristic
544C22×C61#54611yescharacteristic
545C22×C61#54611yescharacteristic
546C22×C61#54711yescharacteristic
547C22×C61#54711yescharacteristic
548C22×C61#55011yescharacteristic
549C22×C61#55011yescharacteristic
550C22×C61#55111yescharacteristic
551C22×C61#55111yescharacteristic
552C22×C61#55111yescharacteristic
553C22×C61#55211yescharacteristic
554C22×C61#55311yescharacteristic
555C22×C61#55511yescharacteristic
556C22×C61#55511yescharacteristic
557C22×C61#55611yescharacteristic
558C4×C61—24no—
559C4×C61—42no—
560C4×C61—42no—
561C4×C61—42no—
562C4×C61—81no—
563Dic61—24no—
564Dic61—24no—
565Dic61—24no—
566Dic61—42no—
567Dic61—42no—
568Dic61—42no—
569Dic61—42no—
570Dic61—81no—
571C22×#117—611no—
572C2×#390—611no—
573C2×#388—611no—
574C2×#388—611no—
575C2×#386—611no—
576#1444—611no—
577#1439—611no—
578#1439—611no—
579#1438D6111yescharacteristic
580#1437—611no—
581#1437—611no—
582#1436—611no—
583#1436—611no—
584C22⋊#95—611no—
585C4×#95—611no—
586C2×C61—44no—
587C2×C61—82no—
588C2×C61#229311yescharacteristic
589C2×C61C4×#12011yescharacteristic
590C2×C61#232411yescharacteristic
591C2×C61#234211yescharacteristic
592C2×C61#235411yescharacteristic
593C2×C61#235911yescharacteristic
594C2×C61#236311yescharacteristic
595C2×C61#243011yescharacteristic
596C2×C61#243111yescharacteristic
597C2×C61#247111yescharacteristic
598C2×C61#247411yescharacteristic
599C2×C61#247611yescharacteristic
600C2×C61#247911yescharacteristic
601C2×C61#260111yescharacteristic
602C2×C61#261011yescharacteristic
603C23×D4C2×D6111yescharacteristic
604C24×C4—611no—
605C2×#117—1224no—
606C2×#117—1224no—
607C2×#117—1224no—
608C22×C4⋊C4—611no—
609C22×C4⋊C4—611no—
610C22×C4⋊C4—611no—
611C22×C4⋊C4—611no—
612C22×C22⋊C4—611no—
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4C2×D6111yescharacteristic
620C22×C22⋊C4C2×D6111yescharacteristic
621C22×C22⋊C4C2×D6111yescharacteristic
622C22×C22⋊C4C2×D6111yescharacteristic
623C22×C42—611no—
624C22×C42—611no—
625C22×C42—611no—
626C22×C42—611no—
627#390—1224no—
628#388—1224no—
629#388—1224no—
630#386—618no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95C2×D6111yescharacteristic
644C2×#95C2×D6111yescharacteristic
645C61#1407111yescharacteristic, complemented, Sylow
646C25C22×D6111yescharacteristic
647C25C22×D6111yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C4×D6114yes—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—614no—
659C23×C4—611no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—1222no—
665C23×C4—1222no—
666C23×C4—1222no—
667C23×C4—1222no—
668C23×C4—1222no—
669C23×C4—1222no—
670C23×C4C22×D6111yescharacteristic
671C23×C4C22×D6111yescharacteristic
672C23×C4C22×D6111yescharacteristic
673C23×C4C22×D6111yescharacteristic
674C23×C4C22×D6111yescharacteristic
675#117—12232no—
676C2×C4⋊C4—614no—
677C2×C4⋊C4—1222no—
678C2×C4⋊C4—1222no—
679C2×C4⋊C4—1222no—
680C2×C4⋊C4—1222no—
681C2×C4⋊C4—1222no—
682C2×C4⋊C4—1222no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—1222no—
685C2×C4⋊C4—2441no—
686C2×C4⋊C4—2441no—
687C2×C4⋊C4—2441no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—614no—
701C2×C22⋊C4—614no—
702C2×C22⋊C4—614no—
703C2×C22⋊C4—614no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—2441no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C42—614no—
722C2×C42—1222no—
723C2×C42—1222no—
724C2×C42—1222no—
725C2×C42—1222no—
726C2×C42—1222no—
727C2×C42—1222no—
728C2×C42—1222no—
729C2×C42—1222no—
730C2×C42—1222no—
731C2×C42—2441no—
732C2×C42—2441no—
733#95—22no—
734#95—22no—
735#95—614no—
736#95—614no—
737#95—1222no—
738#95—1222no—
739#95—1222no—
740#95—1222no—
741#95—1222no—
742#95—1222no—
743#95—1222no—
744#95—2441no—
745#95—2441no—
746#95—2441no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
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—
773C24C2×C4×D6112yes—
774C24C2×C4×D6112yes—
775C24D4×D6112yes—
776C24#1175822412yes—
777C24C23×D6111yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
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—612no—
815C22×C4—612no—
816C22×C4—612no—
817C22×C4—612no—
818C22×C4—612no—
819C22×C4—612no—
820C22×C4—612no—
821C22×C4—612no—
822C22×C4—612no—
823C22×C4—612no—
824C22×C4—612no—
825C22×C4—612no—
826C22×C4—612no—
827C22×C4—1228no—
828C22×C4—1228no—
829C22×C4—1228no—
830C22×C4—1228no—
831C22×C4—1228no—
832C22×C4—1228no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1228no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4C2×C4×D6112yes—
878C22×C4D4×D6112yes—
879C22×C4D4×D6112yes—
880C22×C4#1175822412yes—
881C22×C4#1175822412yes—
882C22×C4#1175822412yes—
883C4⋊C4—1228no—
884C4⋊C4—1228no—
885C4⋊C4—2444no—
886C4⋊C4—2444no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—1228no—
892C22⋊C4—1228no—
893C22⋊C4—1228no—
894C22⋊C4—2444no—
895C22⋊C4—2444no—
896C22⋊C4—2444no—
897C22⋊C4—2444no—
898C42—1228no—
899C42—1228no—
900C42—2444no—
901C42—2444no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
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—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—41no—
946C23—41no—
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#1451973714yes—
972C23C22×C4×D6111yescharacteristic
973C23C2×D4×D6111yescharacteristic
974C23C2×D4×D6111yescharacteristic
975C23C2×D4×D6111yescharacteristic
976C23#41×D6111yescharacteristic
977C23#41×D6111yescharacteristic
978C23#41×D6111yescharacteristic
979C23C2×#1175822411yescharacteristic
980C23C2×#1175822411yescharacteristic
981C23C2×#1175822411yescharacteristic
982C23C2×#1175822411yescharacteristic
983C23#1451982211yescharacteristic
984C23#1451982211yescharacteristic
985C23#1451982211yescharacteristic
986C23#1451982411yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
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—614no—
1023C2×C4—614no—
1024C2×C4—614no—
1025C2×C4—12232no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4#1451973314yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C2×#1451973311yescharacteristic
1111C22C4×D4×D6111yescharacteristic
1112C22C4×D4×D6111yescharacteristic
1113C22C2×#1451973711yescharacteristic
1114C22C4×#1175822411yescharacteristic
1115C22#1684023511yescharacteristic
1116C22#1684024111yescharacteristic
1117C22#120×D6111yescharacteristic
1118C22#1684027011yescharacteristic
1119C22#1684027211yescharacteristic
1120C22#1684027211yescharacteristic
1121C22#1684029111yescharacteristic
1122C22#1684029311yescharacteristic
1123C22#1684030711yescharacteristic
1124C22#1684031011yescharacteristic
1125C22#1684032711yescharacteristic
1126C22#1684034111yescharacteristic
1127C22#1684036211yescharacteristic
1128C22#1684038011yescharacteristic
1129C22#1684039911yescharacteristic
1130C22#1684039911yescharacteristic
1131C22#1684039911yescharacteristic
1132C22#1684040111yescharacteristic
1133C22#1684041211yescharacteristic
1134C22#1684041211yescharacteristic
1135C22#1684043011yescharacteristic
1136C22#1684043211yescharacteristic
1137C22#1684044311yescharacteristic
1138C22#1684044311yescharacteristic
1139C22#1684044311yescharacteristic
1140C22#1684044911yescharacteristic
1141C22#1684045711yescharacteristic
1142C22#1684047611yescharacteristic
1143C22#1684047611yescharacteristic
1144C22#1684048111yescharacteristic
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—1224no—
1151C4—1224no—
1152C4—1224no—
1153C4—4881no—
1154C4—2442no—
1155C4—2442no—
1156C4—2442no—
1157C4—2442no—
1158C2—44no—
1159C2—82no—
1160C2#2144828111yescharacteristic
1161C2#2144832411yescharacteristic
1162C2#2144850911yescharacteristic
1163C2#2144867011yescharacteristic
1164C2#2144876711yescharacteristic
1165C2#2144881711yescharacteristic
1166C2#2144886011yescharacteristic
1167C2#2144942211yescharacteristic
1168C2#2144943311yescharacteristic
1169C2#2144993111yescharacteristic
1170C2#2144997011yescharacteristic
1171C2#2145000011yescharacteristic
1172C2#2145005111yescharacteristic
1173C2#2145140911yescharacteristic
1174C2#2145149911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1438C2
socle, cosocleC24×C61C24
prime radicalC23×D4×C61C22
hypercenter#1438D61
hypocenterC61#14071
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×#14519733C2semidirect
3. C2×#16839656C2semidirect
4. C2×#16839650C2semidirect
6. #21444083C2semidirect
7. #21444062C2semidirect
8. #21444062C2semidirect
9. #21444056C2semidirect
10. #21444056C2semidirect
11. #21444053C2semidirect
12. #21444050C2semidirect
13. #21444041C2semidirect
14. #95×Dic61C2semidirect
38. #16839642C4semidirect
85. C2×#11758196D4semidirect
118. C2×C4×Dic61D4semidirect
434. C2×C4×C61#117semidirect
645. C61#14071semidirect
1079. C2×C4#14519733semidirect

Maximal subgroups

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

subgroupindex
C22×#145197332
C2×#168396652
C2×#168396562
C2×#168396502
C2×#168396422
#214440832
#214440622
#214440562
#214440532
#214440502
#214440412
#95×Dic612
C61×#14382
#1407161