Finite Group Databasebeta

← #29604104

Subgroups — #29604104

Order 15616.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839657C211yesmaximal, characteristic, complemented
2C2×#16839656C211yesmaximal, characteristic
3C2×#16839646C211yesmaximal, characteristic, complemented
4C2×#16839635C211yesmaximal, characteristic
5#21444078C211yesmaximal, characteristic, complemented
6#21444069C211yesmaximal, characteristic, complemented
7#21444066C211yesmaximal, characteristic
8#21444062C211yesmaximal, characteristic
9#21444056C211yesmaximal, characteristic
10#21444052C211yesmaximal, characteristic, complemented
11#21444052C211yesmaximal, characteristic, complemented
12#21444051C211yesmaximal, characteristic, complemented
13#21444042C211yesmaximal, characteristic
14C4×#14519684C211yesmaximal, characteristic, complemented
15C22×#117×C61C211yesmaximal, characteristic
16C22×#11758196C2211yescharacteristic
17C22×#11758196C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26#16839657—24no—
27#16839656—24no—
28#16839646—24no—
29#16839635C418yescomplemented
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
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
48C24×C4×C61C2211yescharacteristic
49C2×#117×C61—24no—
50C2×#117×C61—24no—
51C2×#117×C61—24no—
52C22×C4⋊C4×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic
57C22×C42×C61C2211yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C2×#11758196—22no—
67C2×#11758196—22no—
68C2×#11758196—22no—
69C2×#11758196—22no—
70C2×#11758196—22no—
71C2×#11758196—22no—
72C2×#11758196—22no—
73C2×#11758196—22no—
74C2×#11758196—22no—
75C2×#11758196—41no—
76C2×#11758196C2×C414yes—
77C2×#11758196C2×C414yes—
78C2×C22⋊Dic61—22no—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—22no—
86C2×C22⋊Dic61—41no—
87C2×C22⋊Dic61—41no—
88C2×C22⋊Dic61C2×C414yes—
89C2×C22⋊Dic61C2×C414yes—
90C2×C4×Dic61—22no—
91C2×C4×Dic61—22no—
92C2×C4×Dic61—22no—
93C2×C4×Dic61—22no—
94C2×C4×Dic61—41no—
95C2×C4×Dic61—41no—
96#14519684—22no—
97#14519684—22no—
98#14519684—22no—
99#14519684—22no—
100#14519684—22no—
101#14519684—22no—
102#14519684—22no—
103#14519684—22no—
104#14519684—22no—
105#14519684—22no—
106#14519684—22no—
107#14519684—22no—
108#14519684—22no—
109#14519684—22no—
110#14519684—22no—
111#14519684—41no—
112#14519684C2×C414yes—
113#14519684C2×C414yes—
114C25×C61C2311yescharacteristic
115C23×C4×C61—22no—
116C23×C4×C61—22no—
117C23×C4×C61—22no—
118C23×C4×C61—22no—
119C23×C4×C61—22no—
120C23×C4×C61—22no—
121C23×C4×C61C2×C414yes—
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128#117×C61—232no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61—22no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—22no—
134C2×C4⋊C4×C61D414yes—
135C2×C22⋊C4×C61—22no—
136C2×C22⋊C4×C61—22no—
137C2×C22⋊C4×C61—22no—
138C2×C22⋊C4×C61—22no—
139C2×C22⋊C4×C61—22no—
140C2×C22⋊C4×C61D414yes—
141C2×C42×C61—22no—
142C2×C42×C61—22no—
143C2×C42×C61—22no—
144C2×C42×C61—22no—
145C2×C42×C61—22no—
146C2×C42×C61D414yes—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61C22×C412yes—
160C24×C61C2×D412yes—
161C24×C61#4112yes—
162C24×C61C2411yescharacteristic
163C22×C4×C61—28no—
164C22×C4×C61—28no—
165C22×C4×C61—28no—
166C22×C4×C61—28no—
167C22×C4×C61—28no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
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—21no—
180C22×C4×C61—28no—
181C22×C4×C61—28no—
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×C61C22×C412yes—
201C22×C4×C61C22×C412yes—
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2×D412yes—
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2×D412yes—
210C22×C4×C61#4112yes—
211C22×C4×C61#4112yes—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
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—21no—
229C22×Dic61—21no—
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×Dic61C22×C412yes—
261C22×Dic61C22×C412yes—
262C22×Dic61C22×C412yes—
263C22×Dic61C22×C412yes—
264C22×Dic61#4112yes—
265C22×Dic61#4112yes—
266C22×Dic61#4112yes—
267C22×Dic61#4112yes—
268C4⋊C4×C61—28no—
269C4⋊C4×C61—28no—
270C22⋊C4×C61—28no—
271C22⋊C4×C61—28no—
272C42×C61—28no—
273C42×C61—28no—
274C22⋊Dic61—28no—
275C22⋊Dic61—28no—
276C22⋊Dic61—44no—
277C22⋊Dic61—44no—
278#11758196—28no—
279#11758196—28no—
280#11758196—44no—
281#11758196—44no—
282C4×Dic61—44no—
283C4×Dic61—44no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61C4×D414yes—
319C23×C61C23×C411yescharacteristic
320C23×C61C22×D411yescharacteristic
321C23×C61C22×D411yescharacteristic
322C23×C61C22×D411yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61C2×#4111yescharacteristic
325C23×C61C2×#4111yescharacteristic
326C23×C61C2×#4111yescharacteristic
327C23×C61C2×#4111yescharacteristic
328C23×C61C2×#4111yescharacteristic
329C23×C61C2×#4111yescharacteristic
330C23×C61H(5,𝔽2)11yescharacteristic
331C23×C612−1+411yescharacteristic
332C23×C612−1+411yescharacteristic
333C23×C612−1+411yescharacteristic
334C2×C4×C61—232no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61C4×D414yes—
375C2×C4×C61C4×D414yes—
376C2×C4×C61#12014yes—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61#11714yescomplemented
433#14072—611nomaximal, Sylow
434C22×C61—24no—
435C22×C61—24no—
436C22×C61—24no—
437C22×C61—42no—
438C22×C61—42no—
439C22×C61—42no—
440C22×C61—42no—
441C22×C61—42no—
442C22×C61—42no—
443C22×C61—42no—
444C22×C61—42no—
445C22×C61—42no—
446C22×C61—42no—
447C22×C61—42no—
448C22×C61—42no—
449C22×C61C2×#11711yescharacteristic
450C22×C61C2×C4×D411yescharacteristic
451C22×C61C2×C4×D411yescharacteristic
452C22×C61C2×C4×D411yescharacteristic
453C22×C61C4×#4111yescharacteristic
454C22×C61#51911yescharacteristic
455C22×C61#52011yescharacteristic
456C22×C61C2×#12011yescharacteristic
457C22×C61#52511yescharacteristic
458C22×C61#52511yescharacteristic
459C22×C61#52511yescharacteristic
460C22×C61#52911yescharacteristic
461C22×C61#52911yescharacteristic
462C22×C61#53211yescharacteristic
463C22×C61#53211yescharacteristic
464C22×C61#53611yescharacteristic
465C22×C61#53711yescharacteristic
466C22×C61#54111yescharacteristic
467C22×C61#54211yescharacteristic
468C22×C61#54611yescharacteristic
469C22×C61#54611yescharacteristic
470C22×C61#54711yescharacteristic
471C22×C61#54711yescharacteristic
472C22×C61#54711yescharacteristic
473C22×C61#54711yescharacteristic
474C22×C61#54811yescharacteristic
475C22×C61#54811yescharacteristic
476C22×C61#55111yescharacteristic
477C22×C61#55211yescharacteristic
478C22×C61#55211yescharacteristic
479C22×C61#55211yescharacteristic
480C22×C61#55211yescharacteristic
481C22×C61#55211yescharacteristic
482C22×C61#55311yescharacteristic
483C22×C61#55611yescharacteristic
484C4×C61—24no—
485C4×C61—24no—
486C4×C61—24no—
487C4×C61—42no—
488C4×C61—42no—
489C4×C61—42no—
490Dic61—24no—
491Dic61—42no—
492Dic61—42no—
493Dic61—42no—
494Dic61—42no—
495Dic61—42no—
496Dic61—81no—
497Dic61—81no—
498C22×#117D6111yescharacteristic
499C2×#389—611no—
500C2×#388—611no—
501C2×#387—611no—
502C2×#385—611no—
503#1442—611no—
504#1441—611no—
505#1440—611no—
506#1439—611no—
507#1437—611no—
508#1436—611no—
509#1436—611no—
510#1436—611no—
511C22⋊#95—611no—
512C4×#95—611no—
513C2×C61—44no—
514C2×C61#229311yescharacteristic
515C2×C61C4×#12011yescharacteristic
516C2×C61#232311yescharacteristic
517C2×C61#234411yescharacteristic
518C2×C61#235211yescharacteristic
519C2×C61#235911yescharacteristic
520C2×C61#236211yescharacteristic
521C2×C61#243011yescharacteristic
522C2×C61#243211yescharacteristic
523C2×C61#247011yescharacteristic
524C2×C61#247511yescharacteristic
525C2×C61#247711yescharacteristic
526C2×C61#247811yescharacteristic
527C2×C61#260111yescharacteristic
528C2×C61#261111yescharacteristic
529C24×C4C2×D6111yescharacteristic
530C2×#117—24no—
531C2×#117—24no—
532C2×#117—24no—
533C22×C4⋊C4—611no—
534C22×C4⋊C4—611no—
535C22×C4⋊C4—611no—
536C22×C4⋊C4—611no—
537C22×C4⋊C4C2×D6111yescharacteristic
538C22×C4⋊C4C2×D6111yescharacteristic
539C22×C22⋊C4—611no—
540C22×C22⋊C4—611no—
541C22×C22⋊C4—611no—
542C22×C22⋊C4—611no—
543C22×C22⋊C4C2×D6111yescharacteristic
544C22×C22⋊C4C2×D6111yescharacteristic
545C22×C42—611no—
546C22×C42—611no—
547C22×C42C2×D6111yescharacteristic
548C22×C42C2×D6111yescharacteristic
549#389—1224no—
550#388—1224no—
551#387—1224no—
552#385—618no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95—611no—
565C2×#95—611no—
566C2×#95—611no—
567C2×#95—611no—
568C2×#95—611no—
569C2×#95—611no—
570C2×#95—611no—
571C61#1407211yescharacteristic, complemented, Sylow
572C25C22×D6111yescharacteristic
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—611no—
586C23×C4—611no—
587C23×C4C4×D6114yes—
588C23×C4C22×D6111yescharacteristic
589C23×C4C22×D6111yescharacteristic
590C23×C4C22×D6111yescharacteristic
591C23×C4C22×D6111yescharacteristic
592C23×C4C22×D6111yescharacteristic
593C23×C4C22×D6111yescharacteristic
594#117—232no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—614no—
601C2×C4⋊C4—614no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—2441no—
612C2×C4⋊C4C22⋊D6114yes—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—614no—
619C2×C22⋊C4—614no—
620C2×C22⋊C4—1222no—
621C2×C22⋊C4—1222no—
622C2×C22⋊C4—1222no—
623C2×C22⋊C4—1222no—
624C2×C22⋊C4—1222no—
625C2×C22⋊C4—1222no—
626C2×C22⋊C4—1222no—
627C2×C22⋊C4—1222no—
628C2×C22⋊C4—2441no—
629C2×C22⋊C4—2441no—
630C2×C22⋊C4C22⋊D6114yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—1222no—
637C2×C42—1222no—
638C2×C42—1222no—
639C2×C42—1222no—
640C2×C42—2441no—
641C2×C42—2441no—
642C2×C42C22⋊D6114yes—
643#95—614no—
644#95—614no—
645#95—1222no—
646#95—1222no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650#95—1222no—
651#95—1222no—
652#95—1222no—
653#95—1222no—
654#95—1222no—
655#95—1222no—
656#95—1222no—
657#95—1222no—
658#95—1222no—
659#95—1222no—
660#95—2441no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24C2×C4×D6112yes—
674C24#1175822212yes—
675C24C2×C22⋊D6112yes—
676C24C23×D6111yescharacteristic
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—28no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—612no—
715C22×C4—612no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—612no—
719C22×C4—612no—
720C22×C4—612no—
721C22×C4—612no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4C2×C4×D6112yes—
771C22×C4C2×C4×D6112yes—
772C22×C4#1175822212yes—
773C22×C4#1175822212yes—
774C22×C4C2×C22⋊D6112yes—
775C22×C4C2×C22⋊D6112yes—
776C22×C4C2×C22⋊D6112yes—
777C22×C4C2×C22⋊D6112yes—
778C22×C4C2×C22⋊D6112yes—
779C22×C4C2×C22⋊D6112yes—
780C22×C4C2×C22⋊D6112yes—
781C22×C4C2×C22⋊D6112yes—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—1228no—
785C4⋊C4—1228no—
786C4⋊C4—2444no—
787C4⋊C4—2444no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—1228no—
791C22⋊C4—1228no—
792C22⋊C4—2444no—
793C22⋊C4—2444no—
794C42—28no—
795C42—28no—
796C42—2444no—
797C42—2444no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23C4×C22⋊D6114yes—
833C23C22×C4×D6111yescharacteristic
834C23C22×C22⋊D6111yescharacteristic
835C23C22×C22⋊D6111yescharacteristic
836C23C22×C22⋊D6111yescharacteristic
837C23#41×D6111yescharacteristic
838C23#41×D6111yescharacteristic
839C23#41×D6111yescharacteristic
840C23#41×D6111yescharacteristic
841C23C2×#1175822211yescharacteristic
842C23C2×#1175822211yescharacteristic
843C23C2×#1175822211yescharacteristic
844C23#1451982311yescharacteristic
845C23#1451982411yescharacteristic
846C23#1451982411yescharacteristic
847C23#1451982411yescharacteristic
848C2×C4—232no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—614no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1222no—
907C2×C4—1222no—
908C2×C4—1222no—
909C2×C4—1222no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4C4×C22⋊D6114yes—
945C2×C4C4×C22⋊D6114yes—
946C2×C4#1451974614yes—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22#117×D6111yescharacteristic
963C22C2×C4×C22⋊D6111yescharacteristic
964C22C2×C4×C22⋊D6111yescharacteristic
965C22C2×C4×C22⋊D6111yescharacteristic
966C22#1684023011yescharacteristic
967C22#1684023911yescharacteristic
968C22#1684024211yescharacteristic
969C22C2×#1451974611yescharacteristic
970C22#1684027311yescharacteristic
971C22#1684027311yescharacteristic
972C22#1684027311yescharacteristic
973C22#1684029011yescharacteristic
974C22#1684029011yescharacteristic
975C22#1684030811yescharacteristic
976C22#1684030811yescharacteristic
977C22#1684033311yescharacteristic
978C22#1684034011yescharacteristic
979C22#1684037411yescharacteristic
980C22#1684038311yescharacteristic
981C22#1684040011yescharacteristic
982C22#1684040011yescharacteristic
983C22#1684041111yescharacteristic
984C22#1684041111yescharacteristic
985C22#1684041111yescharacteristic
986C22#1684041111yescharacteristic
987C22#1684041911yescharacteristic
988C22#1684041911yescharacteristic
989C22#1684043611yescharacteristic
990C22#1684044511yescharacteristic
991C22#1684044511yescharacteristic
992C22#1684044511yescharacteristic
993C22#1684045111yescharacteristic
994C22#1684045111yescharacteristic
995C22#1684045611yescharacteristic
996C22#1684048011yescharacteristic
997C4—24no—
998C4—24no—
999C4—24no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—1224no—
1004C4—4881no—
1005C4—4881no—
1006C4—2442no—
1007C4—2442no—
1008C4—2442no—
1009C4—2442no—
1010C4—2442no—
1011C2—44no—
1012C2#2144827811yescharacteristic
1013C2C4×#1451974611yescharacteristic
1014C2#2144850111yescharacteristic
1015C2#2144868911yescharacteristic
1016C2#2144874911yescharacteristic
1017C2#2144881111yescharacteristic
1018C2#2144884611yescharacteristic
1019C2#2144942311yescharacteristic
1020C2#2144944311yescharacteristic
1021C2#2144990911yescharacteristic
1022C2#2144998411yescharacteristic
1023C2#2145001411yescharacteristic
1024C2#2145002911yescharacteristic
1025C2#2145141611yescharacteristic
1026C2#2145151711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×#117×C61C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC22×#117D61
hypocenterC61#14072
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C2×#16839657C2semidirect
3. C2×#16839646C2semidirect
5. #21444078C2semidirect
6. #21444069C2semidirect
10. #21444052C2semidirect
11. #21444052C2semidirect
12. #21444051C2semidirect
14. C4×#14519684C2semidirect
29. #16839635C4semidirect
432. C2×Dic61#117semidirect
571. C61#14072semidirect

Maximal subgroups

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

subgroupindex
C2×#168396572
C2×#168396562
C2×#168396462
C2×#168396352
#214440782
#214440692
#214440662
#214440622
#214440562
#214440522
#214440512
#214440422
C4×#145196842
C22×#117×C612
#1407261