Finite Group Databasebeta

← #29603818

Subgroups — #29603818

Order 15616.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic
2C2×#16839667C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic61C211yesmaximal, characteristic
4C22×#14519684C211yesmaximal, characteristic
5#21444089C211yesmaximal, characteristic, complemented
6#21444086C211yesmaximal, characteristic, complemented
7#21444069C211yesmaximal, characteristic, complemented
8#21444069C211yesmaximal, characteristic, complemented
9#21444054C211yesmaximal, characteristic, complemented
10#21444054C211yesmaximal, characteristic, complemented
11#21444048C211yesmaximal, characteristic, complemented
12#21444042C211yesmaximal, characteristic
13#21444041C211yesmaximal, characteristic
14#21444041C211yesmaximal, characteristic
15C2×C61×#385C211yesmaximal, characteristic
16C23×Dic122C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C2×#14519754—24no—
20C2×#14519754—24no—
21C2×#14519754C418yescomplemented
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29#16839667—24no—
30C22⋊C4×Dic61—24no—
31C2×#14519684—24no—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C24×C4×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C61×#385—24no—
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C22×Dic122—22no—
59C22×Dic122—22no—
60C22×Dic122—22no—
61C22×Dic122—22no—
62C22×Dic122—41no—
63C22×Dic122—41no—
64C22×Dic122C2×C414yescomplemented
65C23×Dic61—22no—
66C23×Dic61—22no—
67C23×Dic61—22no—
68C23×Dic61—22no—
69C23×Dic61—22no—
70C23×Dic61—22no—
71C23×Dic61—22no—
72C23×Dic61—22no—
73C23×Dic61—41no—
74C23×Dic61—41no—
75C23×Dic61—41no—
76C23×Dic61—41no—
77C23×Dic61C2×C414yes—
78C23×Dic61Q814yescomplemented
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87#14519754—232no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61C2×C414yescomplemented
91C2×#11758196—22no—
92C2×#11758196—22no—
93C2×#11758196—22no—
94C2×#11758196—22no—
95C2×#11758196C2×C414yescomplemented
96C2×#11758196C2×C414yescomplemented
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61C2×C414yes—
102C2×C22⋊Dic61Q814yescomplemented
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—41no—
108C2×C4×Dic61—41no—
109#14519684—22no—
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117#14519684—22no—
118#14519684—22no—
119#14519684—22no—
120#14519684—41no—
121#14519684—41no—
122#14519684—41no—
123#14519684—41no—
124#14519684—41no—
125#14519684—41no—
126#14519684D414yes—
127C25×C61C2311yescharacteristic
128C23×C4×C61—22no—
129C23×C4×C61—22no—
130C23×C4×C61—22no—
131C23×C4×C61—22no—
132C23×C4×C61—22no—
133C23×C4×C61—41no—
134C23×C4×C61—41no—
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61—22no—
143C2×C4⋊C4×C61—22no—
144C2×C4⋊C4×C61—22no—
145C2×C4⋊C4×C61—41no—
146C2×C4⋊C4×C61—41no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61C2×C414yes—
151C2×C22⋊C4×C61D414yes—
152C2×C22⋊C4×C61D414yes—
153#95×C61—22no—
154#95×C61—22no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61C22×C412yes—
164C24×C61C2×D412yes—
165C24×C61C2×D412yes—
166C24×C61C2×Q812yes—
167C24×C61C2×Q812yes—
168C24×C61#4112yes—
169C24×C61#4112yes—
170C24×C61C2411yescharacteristic
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—28no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
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—44no—
207C22×C4×C61—44no—
208C22×C4×C61—44no—
209C22×C4×C61—44no—
210C22×C4×C61—44no—
211C22×C4×C61—44no—
212C22×C4×C61C22×C412yes—
213C22×C4×C61C22×C412yes—
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2×D412yes—
218C22×C4×C61C2×D412yes—
219C22×C4×C61#4112yes—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—28no—
229C22×Dic61—28no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
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—21no—
250C22×Dic61—21no—
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—28no—
267C22×Dic61—28no—
268C22×Dic61—44no—
269C22×Dic61—44no—
270C22×Dic61—44no—
271C22×Dic61—44no—
272C22×Dic61—44no—
273C22×Dic61—44no—
274C22×Dic61—44no—
275C22×Dic61—44no—
276C22×Dic61—44no—
277C22×Dic61—44no—
278C22×Dic61C22×C412yes—
279C22×Dic61C22×C412yes—
280C22×Dic61C22×C412yes—
281C22×Dic61C22×C412yes—
282C22×Dic61C2×D412yes—
283C22×Dic61C2×D412yes—
284C22×Dic61C2×Q812yes—
285C22×Dic61C2×Q812yes—
286C22×Dic61C2×Q812yes—
287C22×Dic61C2×Q812yes—
288C22×Dic61#4112yes—
289C22×Dic61#4112yes—
290C2×Dic122—28no—
291C2×Dic122—28no—
292C2×Dic122—44no—
293C2×Dic122—44no—
294C2×Dic122—44no—
295C2×Dic122—44no—
296C2×Dic122—44no—
297C4⋊C4×C61—44no—
298C4⋊C4×C61—44no—
299C22⋊C4×C61—44no—
300C22⋊C4×C61C22⋊C4116yes—
301C22⋊Dic61—28no—
302C22⋊Dic61—28no—
303C4⋊Dic61—28no—
304#11758196—28no—
305#11758196—28no—
306C4×Dic61—44no—
307C4×Dic61—44no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
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×C61C2×C22⋊C414yes—
337C23×C61C4×Q814yes—
338C23×C61C4×Q814yes—
339C23×C61C22⋊Q814yes—
340C23×C61C22⋊Q814yes—
341C23×C61#12414yes—
342C23×C61C4⋊Q814yes—
343C23×C61C23×C411yescharacteristic
344C23×C61C22×D411yescharacteristic
345C23×C61C22×D411yescharacteristic
346C23×C61C22×D411yescharacteristic
347C23×C61C22×Q811yescharacteristic
348C23×C61C22×Q811yescharacteristic
349C23×C61C2×#4111yescharacteristic
350C23×C61C2×#4111yescharacteristic
351C23×C61C2×#4111yescharacteristic
352C23×C61C2×#4111yescharacteristic
353C23×C61C2×#4111yescharacteristic
354C23×C61H(5,𝔽2)11yescharacteristic
355C23×C61H(5,𝔽2)11yescharacteristic
356C23×C61H(5,𝔽2)11yescharacteristic
357C23×C612−1+411yescharacteristic
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—416no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61C2×C22⋊C414yes—
400C2×C4×C61C2×C22⋊C414yes—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—22no—
409C2×Dic61—22no—
410C2×Dic61—22no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61—22no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—22no—
423C2×Dic61—22no—
424C2×Dic61—22no—
425C2×Dic61—22no—
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—416no—
432C2×Dic61—416no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61—41no—
439C2×Dic61—41no—
440C2×Dic61—41no—
441C2×Dic61—41no—
442C2×Dic61—41no—
443C2×Dic61—41no—
444C2×Dic61—41no—
445C2×Dic61—41no—
446C2×Dic61—41no—
447C2×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61—41no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61—41no—
454C2×Dic61—41no—
455C2×Dic61—41no—
456C2×Dic61—41no—
457C2×Dic61C4×D414yes—
458C2×Dic61C22⋊Q814yescomplemented
459Dic122—416no—
460#14052—611nomaximal, Sylow
461C22×C61—24no—
462C22×C61—24no—
463C22×C61—24no—
464C22×C61—24no—
465C22×C61—24no—
466C22×C61—24no—
467C22×C61—24no—
468C22×C61—24no—
469C22×C61—24no—
470C22×C61—24no—
471C22×C61—24no—
472C22×C61—24no—
473C22×C61—24no—
474C22×C61—24no—
475C22×C61#39118yescomplemented
476C22×C61C22×C22⋊C411yescharacteristic
477C22×C61C2×C4×D411yescharacteristic
478C22×C61C2×C4×Q811yescharacteristic
479C22×C61C2×C4×Q811yescharacteristic
480C22×C61C4×#4111yescharacteristic
481C22×C61#51811yescharacteristic
482C22×C61#52011yescharacteristic
483C22×C61C2×C22⋊Q811yescharacteristic
484C22×C61C2×C22⋊Q811yescharacteristic
485C22×C61C2×C22⋊Q811yescharacteristic
486C22×C61#52511yescharacteristic
487C22×C61C2×#12411yescharacteristic
488C22×C61#52911yescharacteristic
489C22×C61C2×C4⋊Q811yescharacteristic
490C22×C61#53311yescharacteristic
491C22×C61#53811yescharacteristic
492C22×C61#53911yescharacteristic
493C22×C61#54311yescharacteristic
494C22×C61#54411yescharacteristic
495C22×C61D4211yescharacteristic
496C22×C61D4211yescharacteristic
497C22×C61#54611yescharacteristic
498C22×C61#54611yescharacteristic
499C22×C61#54611yescharacteristic
500C22×C61#54611yescharacteristic
501C22×C61#54611yescharacteristic
502C22×C61#54711yescharacteristic
503C22×C61#54711yescharacteristic
504C22×C61D4×Q811yescharacteristic
505C22×C61#55111yescharacteristic
506C22×C61#55111yescharacteristic
507C22×C61#55211yescharacteristic
508C22×C61#55411yescharacteristic
509C22×C61#55411yescharacteristic
510C22×C61#55411yescharacteristic
511C4×C61—24no—
512C4×C61—24no—
513C4×C61—42no—
514C4×C61—42no—
515C4×C61—81no—
516C4×C61—81no—
517Dic61—24no—
518Dic61—24no—
519Dic61—42no—
520Dic61—42no—
521Dic61—42no—
522Dic61—42no—
523Dic61—42no—
524Dic61—42no—
525C22×C22⋊Q8—611no—
526C2×#391—611no—
527C2×#385D6111yescharacteristic
528C2×C4×C22⋊C4—611no—
529C22×#95—611no—
530#1446—611no—
531#1445—611no—
532#1441—611no—
533#1441—611no—
534#1436—611no—
535#1436—611no—
536C4⋊#95—611no—
537C22⋊#95—611no—
538C22⋊#95—611no—
539C22⋊#95—611no—
540C2×C61—28no—
541C2×C61C2×#39111yescharacteristic
542C2×C61C4×C22⋊Q811yescharacteristic
543C2×C61#232911yescharacteristic
544C2×C61D4×C22⋊C411yescharacteristic
545C2×C61#233911yescharacteristic
546C2×C61#236011yescharacteristic
547C2×C61#236811yescharacteristic
548C2×C61#243711yescharacteristic
549C2×C61#243811yescharacteristic
550C2×C61#244011yescharacteristic
551C2×C61#244911yescharacteristic
552C2×C61#245011yescharacteristic
553C2×C61#247211yescharacteristic
554C2×C61#248811yescharacteristic
555C2×C61#254911yescharacteristic
556C23×Q8—611no—
557C24×C4—611no—
558C24×C4—611no—
559C24×C4C2×D6111yescharacteristic
560C2×C22⋊Q8—618no—
561C2×C22⋊Q8—1224no—
562C2×C22⋊Q8—1224no—
563C22×C4⋊C4—611no—
564C22×C4⋊C4—611no—
565C22×C4⋊C4—611no—
566C22×C4⋊C4C2×D6111yescharacteristic
567C22×C4⋊C4C2×D6111yescharacteristic
568C22×C22⋊C4—611no—
569C22×C22⋊C4—611no—
570C22×C22⋊C4C2×D6111yescharacteristic
571C22×C22⋊C4C2×D6111yescharacteristic
572C22×C42—611no—
573C22×C42—611no—
574#391—1224no—
575#385—24no—
576C4×C22⋊C4—1224no—
577C2×#95—611no—
578C2×#95—611no—
579C2×#95—611no—
580C2×#95—611no—
581C2×#95—611no—
582C2×#95—611no—
583C2×#95—611no—
584C2×#95—611no—
585C2×#95—611no—
586C2×#95—611no—
587C2×#95—611no—
588C2×#95—611no—
589C2×#95—611no—
590C2×#95—611no—
591C2×#95—611no—
592C2×#95—611no—
593C2×#95—611no—
594C2×#95—611no—
595C2×#95—1224no—
596C2×#95C2×D6111yescharacteristic
597C2×#95C2×D6111yescharacteristic
598C61#1405211yescharacteristic, complemented, Sylow
599C25C22×D6111yescharacteristic
600C22×Q8—614no—
601C22×Q8—1222no—
602C22×Q8—1222no—
603C22×Q8—1222no—
604C22×Q8—1222no—
605C22×Q8—2441no—
606C22×Q8—2441no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—22no—
612C23×C4—41no—
613C23×C4—41no—
614C23×C4—611no—
615C23×C4—611no—
616C23×C4—611no—
617C23×C4—611no—
618C23×C4—611no—
619C23×C4—611no—
620C23×C4—611no—
621C23×C4—611no—
622C23×C4—614no—
623C23×C4—614no—
624C23×C4—1222no—
625C23×C4—1222no—
626C23×C4—1222no—
627C23×C4—1222no—
628C23×C4—1222no—
629C23×C4—1222no—
630C23×C4—1222no—
631C23×C4—1222no—
632C23×C4—2441no—
633C23×C4—2441no—
634C23×C4—2441no—
635C23×C4—2441no—
636C23×C4C22×D6111yescharacteristic
637C23×C4C22×D6111yescharacteristic
638C23×C4C22×D6111yescharacteristic
639C23×C4C22×D6111yescharacteristic
640C23×C4C22×D6111yescharacteristic
641C23×C4C22×D6111yescharacteristic
642C22⋊Q8—12232no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—614no—
650C2×C4⋊C4—614no—
651C2×C4⋊C4—614no—
652C2×C4⋊C4—1222no—
653C2×C4⋊C4—1222no—
654C2×C4⋊C4—1222no—
655C2×C4⋊C4—1222no—
656C2×C4⋊C4—1222no—
657C2×C4⋊C4—1222no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—614no—
662C2×C22⋊C4—614no—
663C2×C22⋊C4—1222no—
664C2×C22⋊C4—1222no—
665C2×C22⋊C4—1222no—
666C2×C22⋊C4—1222no—
667C2×C22⋊C4C4×D6114yes—
668C2×C22⋊C4D24414yes—
669C2×C22⋊C4C22⋊D6114yes—
670C2×C42—1222no—
671C2×C42—1222no—
672C2×C42—1222no—
673C2×C42—1222no—
674C2×C42—2441no—
675C2×C42—2441no—
676#95—22no—
677#95—22no—
678#95—614no—
679#95—1222no—
680#95—1222no—
681#95—1222no—
682#95—1222no—
683#95—1222no—
684#95—1222no—
685#95—1222no—
686#95—1222no—
687#95—1222no—
688#95—1222no—
689#95—1222no—
690#95—2441no—
691#95—2441no—
692#95—2441no—
693#95—2441no—
694#95—2441no—
695#95—2441no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24C2×C4×D6112yes—
705C24C2×D24412yes—
706C24#1175822412yes—
707C24#1175822412yes—
708C24Q8×D6112yes—
709C24Q8×D6112yes—
710C24C2×C22⋊D6112yes—
711C24C23×D6111yescharacteristic
712C2×Q8—1228no—
713C2×Q8—1228no—
714C2×Q8—2444no—
715C2×Q8—2444no—
716C2×Q8—2444no—
717C2×Q8—2444no—
718C2×Q8—2444no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—28no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—612no—
761C22×C4—612no—
762C22×C4—612no—
763C22×C4—612no—
764C22×C4—612no—
765C22×C4—612no—
766C22×C4—612no—
767C22×C4—612no—
768C22×C4—612no—
769C22×C4—612no—
770C22×C4—612no—
771C22×C4—612no—
772C22×C4—1228no—
773C22×C4—1228no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1228no—
819C22×C4—1228no—
820C22×C4—2444no—
821C22×C4—2444no—
822C22×C4—2444no—
823C22×C4—2444no—
824C22×C4—2444no—
825C22×C4—2444no—
826C22×C4—2444no—
827C22×C4—2444no—
828C22×C4—2444no—
829C22×C4—2444no—
830C22×C4C2×C4×D6112yes—
831C22×C4C2×C4×D6112yes—
832C22×C4C2×D24412yes—
833C22×C4C2×D24412yes—
834C22×C4D4×D6112yes—
835C22×C4#1175822412yes—
836C22×C4C2×C22⋊D6112yes—
837C22×C4C2×C22⋊D6112yes—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—1228no—
841C4⋊C4—1228no—
842C4⋊C4—1228no—
843C22⋊C4—44no—
844C22⋊C4—1228no—
845C22⋊C4—1228no—
846C22⋊C4#11758198116yes—
847C42—2444no—
848C42—2444no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23C2×#1175819814yes—
878C23#1451974214yes—
879C23#1451974214yes—
880C23#1451975714yes—
881C23#1451975714yes—
882C23#1451976414yes—
883C23#1451977514yes—
884C23C22×C4×D6111yescharacteristic
885C23C2×D4×D6111yescharacteristic
886C23C22×C22⋊D6111yescharacteristic
887C23C22×D24411yescharacteristic
888C23C2×Q8×D6111yescharacteristic
889C23C2×Q8×D6111yescharacteristic
890C23#41×D6111yescharacteristic
891C23#41×D6111yescharacteristic
892C23C2×#1175822411yescharacteristic
893C23C2×#1175822411yescharacteristic
894C23C2×#1175822411yescharacteristic
895C23#1451982211yescharacteristic
896C23#1451982211yescharacteristic
897C23#1451982311yescharacteristic
898C23#1451982411yescharacteristic
899Q8—24416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—416no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—614no—
942C2×C4—614no—
943C2×C4—1222no—
944C2×C4—1222no—
945C2×C4—1222no—
946C2×C4—1222no—
947C2×C4—1222no—
948C2×C4—1222no—
949C2×C4—1222no—
950C2×C4—1222no—
951C2×C4—1222no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1222no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—1222no—
959C2×C4—1222no—
960C2×C4—1222no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—1222no—
967C2×C4—1222no—
968C2×C4—1222no—
969C2×C4—1222no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—24416no—
974C2×C4—24416no—
975C2×C4—2441no—
976C2×C4—2441no—
977C2×C4—2441no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4C2×#1175819814yes—
1000C2×C4C2×#1175819814yes—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22#1683966718yescomplemented
1016C22C22×#1175819811yescharacteristic
1017C22C4×D4×D6111yescharacteristic
1018C22C2×#1451974211yescharacteristic
1019C22C2×#1451974211yescharacteristic
1020C22C4×#1175822411yescharacteristic
1021C22#1684023411yescharacteristic
1022C22#1684024111yescharacteristic
1023C22C22⋊Q8×D6111yescharacteristic
1024C22C2×#1451975711yescharacteristic
1025C22C2×#1451975711yescharacteristic
1026C22#1684026811yescharacteristic
1027C22C2×#1451976411yescharacteristic
1028C22#1684028911yescharacteristic
1029C22C2×#1451977511yescharacteristic
1030C22#1684031411yescharacteristic
1031C22#1684034711yescharacteristic
1032C22#1684035611yescharacteristic
1033C22#1684038711yescharacteristic
1034C22#1684039111yescharacteristic
1035C22D4×C22⋊D6111yescharacteristic
1036C22D4×D24411yescharacteristic
1037C22#1684039911yescharacteristic
1038C22#1684040011yescharacteristic
1039C22#1684040611yescharacteristic
1040C22#1684040711yescharacteristic
1041C22#1684040711yescharacteristic
1042C22#1684041111yescharacteristic
1043C22#1684041611yescharacteristic
1044C22#1684042511yescharacteristic
1045C22#1684043511yescharacteristic
1046C22#1684044311yescharacteristic
1047C22#1684044911yescharacteristic
1048C22#1684046611yescharacteristic
1049C22#1684046611yescharacteristic
1050C22#1684047011yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—42no—
1054C4—42no—
1055C4—81no—
1056C4—81no—
1057C4—1224no—
1058C4—1224no—
1059C4—2442no—
1060C4—2442no—
1061C4—2442no—
1062C4—2442no—
1063C4—2442no—
1064C4—2442no—
1065C2—28no—
1066C2C2×#1683966711yescharacteristic
1067C2#2144835111yescharacteristic
1068C2#2144855011yescharacteristic
1069C2D4×#1175819811yescharacteristic
1070C2#2144864411yescharacteristic
1071C2#2144881911yescharacteristic
1072C2#2144890011yescharacteristic
1073C2#2144948311yescharacteristic
1074C2#2144949311yescharacteristic
1075C2#2144951811yescharacteristic
1076C2#2144962611yescharacteristic
1077C2#2144964111yescharacteristic
1078C2#2144994411yescharacteristic
1079C2#2145014911yescharacteristic
1080C2#2145082711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#385D61
hypocenterC61#14052
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#16839667C2semidirect
5. #21444089C2semidirect
6. #21444086C2semidirect
7. #21444069C2semidirect
8. #21444069C2semidirect
9. #21444054C2semidirect
10. #21444054C2semidirect
11. #21444048C2semidirect
21. C2×#14519754C4semidirect
64. C22×Dic122C2×C4semidirect
78. C23×Dic61Q8semidirect
90. C2×C4⋊Dic61C2×C4semidirect
95. C2×#11758196C2×C4semidirect
96. C2×#11758196C2×C4semidirect
102. C2×C22⋊Dic61Q8semidirect
458. C2×Dic61C22⋊Q8semidirect
475. C22×C61#391semidirect
598. C61#14052semidirect
1015. C22#16839667semidirect

Maximal subgroups

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

subgroupindex
C22×#145197542
C2×#168396672
C2×C22⋊C4×Dic612
C22×#145196842
#214440892
#214440862
#214440692
#214440542
#214440482
#214440422
#214440412
C2×C61×#3852
#1405261