Finite Group Databasebeta

← #29607394

Subgroups — #29607394

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839669C211yesmaximal, characteristic, complemented
2C2×#16839655C211yesmaximal, characteristic
3C2×#16839655C211yesmaximal, characteristic
4C2×#16839625C211yesmaximal, characteristic
5#21444090C211yesmaximal, characteristic, complemented
6#21444087C211yesmaximal, characteristic, complemented
7#21444072C211yesmaximal, characteristic, complemented
8#21444072C211yesmaximal, characteristic, complemented
9#21444068C211yesmaximal, characteristic
10#21444068C211yesmaximal, characteristic
11#21444051C211yesmaximal, characteristic, complemented
12#21444051C211yesmaximal, characteristic, complemented
13#21444048C211yesmaximal, characteristic, complemented
14#21444042C211yesmaximal, characteristic
15C22×C22⋊Q8×C61C211yesmaximal, characteristic
16C22×C4⋊Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24#16839669—24no—
25#16839655—24no—
26#16839655—24no—
27#16839625—24no—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2211yescharacteristic
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
48C23×Q8×C61C2211yescharacteristic
49C24×C4×C61C2211yescharacteristic
50C2×C22⋊Q8×C61—24no—
51C2×C22⋊Q8×C61—24no—
52C2×C22⋊Q8×C61C418yescomplemented
53C22×C4⋊C4×C61C2211yescharacteristic
54C22×C4⋊C4×C61C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C2×C4⋊Dic61—22no—
67C2×C4⋊Dic61—22no—
68C2×C4⋊Dic61—22no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—41no—
71C2×C4⋊Dic61—41no—
72C2×C22⋊Dic61—22no—
73C2×C22⋊Dic61—22no—
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61—22no—
76C2×C22⋊Dic61—22no—
77C2×C22⋊Dic61—22no—
78C2×C22⋊Dic61—22no—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—41no—
81C2×C22⋊Dic61—41no—
82C2×C22⋊Dic61—41no—
83C2×C22⋊Dic61—41no—
84C2×C4×Dic61—22no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61—22no—
87C2×C4×Dic61—22no—
88C2×C4×Dic61—41no—
89C2×C4×Dic61—41no—
90#14519684—22no—
91#14519684—22no—
92#14519684—22no—
93#14519684—22no—
94#14519684—22no—
95#14519684—22no—
96#14519684—22no—
97#14519684—22no—
98#14519684—22no—
99#14519684—22no—
100#14519684—22no—
101#14519684—22no—
102#14519684—22no—
103#14519684—41no—
104#14519684—41no—
105#14519684—41no—
106#14519684—41no—
107#14519684—41no—
108#14519684—41no—
109#14519684D414yes—
110C25×C61C2311yescharacteristic
111C22×Q8×C61—22no—
112C22×Q8×C61—22no—
113C22×Q8×C61—22no—
114C22×Q8×C61—22no—
115C22×Q8×C61—41no—
116C22×Q8×C61—41no—
117C22×Q8×C61C2×C414yes—
118C23×C4×C61—22no—
119C23×C4×C61—22no—
120C23×C4×C61—22no—
121C23×C4×C61—22no—
122C23×C4×C61—41no—
123C23×C4×C61—41no—
124C23×C4×C61C2×C414yes—
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C22⋊Q8×C61—232no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—22no—
134C2×C4⋊C4×C61—22no—
135C2×C4⋊C4×C61—22no—
136C2×C4⋊C4×C61—22no—
137C2×C4⋊C4×C61—22no—
138C2×C4⋊C4×C61C2×C414yes—
139C2×C4⋊C4×C61C2×C414yes—
140C2×C4⋊C4×C61C2×C414yes—
141C2×C22⋊C4×C61—22no—
142C2×C22⋊C4×C61—22no—
143C2×C22⋊C4×C61C2×C414yes—
144C2×C22⋊C4×C61C2×C414yes—
145C2×C22⋊C4×C61D414yes—
146C2×C22⋊C4×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×C61C2×D412yes—
162C24×C61C2411yescharacteristic
163C2×Q8×C61—28no—
164C2×Q8×C61—28no—
165C2×Q8×C61—44no—
166C2×Q8×C61—44no—
167C2×Q8×C61—44no—
168C2×Q8×C61—44no—
169C2×Q8×C61—44no—
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—21no—
181C22×C4×C61—21no—
182C22×C4×C61—28no—
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—28no—
202C22×C4×C61—44no—
203C22×C4×C61—44no—
204C22×C4×C61—44no—
205C22×C4×C61—44no—
206C22×C4×C61—44no—
207C22×C4×C61C22×C412yes—
208C22×C4×C61C22×C412yes—
209C22×C4×C61C22×C412yes—
210C22×C4×C61C22×C412yes—
211C22×C4×C61C22×C412yes—
212C22×C4×C61C22×C412yes—
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2×D412yes—
218C22×C4×C61#4112yes—
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×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×Dic61C2×D412yes—
272C22×Dic61C2×D412yes—
273C22×Dic61#4112yes—
274C22×Dic61#4112yes—
275C4⋊C4×C61—28no—
276C4⋊C4×C61—28no—
277C4⋊C4×C61—28no—
278C22⋊C4×C61—28no—
279C22⋊C4×C61C22⋊C4116yes—
280C22⋊Dic61—44no—
281C22⋊Dic61—44no—
282C22⋊Dic61—44no—
283C22⋊Dic61—44no—
284C4⋊Dic61—44no—
285C4⋊Dic61—44no—
286C4×Dic61—44no—
287C4×Dic61—44no—
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—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
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×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61C2×C22⋊C414yes—
323C23×C61C23×C411yescharacteristic
324C23×C61C22×D411yescharacteristic
325C23×C61C22×D411yescharacteristic
326C23×C61C22×D411yescharacteristic
327C23×C61C2×#4111yescharacteristic
328C23×C61C2×#4111yescharacteristic
329C23×C61C2×#4111yescharacteristic
330C23×C61H(5,𝔽2)11yescharacteristic
331C23×C61H(5,𝔽2)11yescharacteristic
332C23×C61H(5,𝔽2)11yescharacteristic
333C23×C612−1+411yescharacteristic
334C23×C612−1+411yescharacteristic
335C23×C612−1+411yescharacteristic
336C23×C612−1+411yescharacteristic
337C23×C612−1+411yescharacteristic
338Q8×C61—416no—
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—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—416no—
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×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61C2×C22⋊C414yes—
380C2×C4×C61C2×C22⋊C414yes—
381C2×C4×C61C4×D414yes—
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—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
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—41no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438#14364—611nomaximal, Sylow
439C22×C61—24no—
440C22×C61—24no—
441C22×C61—24no—
442C22×C61—42no—
443C22×C61—42no—
444C22×C61—42no—
445C22×C61—42no—
446C22×C61—42no—
447C22×C61—42no—
448C22×C61—42no—
449C22×C61—42no—
450C22×C61—42no—
451C22×C61—42no—
452C22×C61—42no—
453C22×C61—42no—
454C22×C61C22×C22⋊C411yescharacteristic
455C22×C61C2×C4×D411yescharacteristic
456C22×C61C4×#4111yescharacteristic
457C22×C61#51811yescharacteristic
458C22×C61#51911yescharacteristic
459C22×C61#51911yescharacteristic
460C22×C61#52011yescharacteristic
461C22×C61#53611yescharacteristic
462C22×C61#53611yescharacteristic
463C22×C61#53611yescharacteristic
464C22×C61#53611yescharacteristic
465C22×C61#53611yescharacteristic
466C22×C61#53711yescharacteristic
467C22×C61#53911yescharacteristic
468C22×C61#53911yescharacteristic
469C22×C61#54111yescharacteristic
470C22×C61#54211yescharacteristic
471C22×C61#54211yescharacteristic
472C22×C61#54211yescharacteristic
473C22×C61D4211yescharacteristic
474C22×C61D4211yescharacteristic
475C22×C61#54611yescharacteristic
476C22×C61#54611yescharacteristic
477C22×C61#54611yescharacteristic
478C22×C61#54611yescharacteristic
479C22×C61#54711yescharacteristic
480C22×C61#54711yescharacteristic
481C22×C61#54711yescharacteristic
482C22×C61#54811yescharacteristic
483C22×C61#55211yescharacteristic
484C22×C61#55611yescharacteristic
485C22×C61#56211yescharacteristic
486C22×C61#56211yescharacteristic
487C22×C61#56311yescharacteristic
488C22×C61#56311yescharacteristic
489C4×C61—24no—
490C4×C61—24no—
491C4×C61—24no—
492C4×C61—42no—
493C4×C61—42no—
494C4×C61—42no—
495Dic61—42no—
496Dic61—42no—
497Dic61—42no—
498Dic61—42no—
499Dic61—81no—
500Dic61—81no—
501Dic61—81no—
502Dic61—81no—
503C22×C22⋊Q8D6111yescharacteristic
504C2×#391—611no—
505C2×#388—611no—
506C2×#388—611no—
507C2×#381—611no—
508#1446—611no—
509#1445—611no—
510#1441—611no—
511#1441—611no—
512#1440—611no—
513#1440—611no—
514#1436—611no—
515#1436—611no—
516C4⋊#95—611no—
517C22⋊#95—611no—
518C2×C61—44no—
519C2×C61#231011yescharacteristic
520C2×C61#232311yescharacteristic
521C2×C61#233211yescharacteristic
522C2×C61D4×C22⋊C411yescharacteristic
523C2×C61#233911yescharacteristic
524C2×C61#236211yescharacteristic
525C2×C61#237811yescharacteristic
526C2×C61#267211yescharacteristic
527C2×C61#267411yescharacteristic
528C2×C61#268011yescharacteristic
529C2×C61#268111yescharacteristic
530C2×C61#268711yescharacteristic
531C2×C61#268911yescharacteristic
532C2×C61#269811yescharacteristic
533C2×C61#270011yescharacteristic
534C23×Q8C2×D6111yescharacteristic
535C24×C4C2×D6111yescharacteristic
536C2×C22⋊Q8—24no—
537C2×C22⋊Q8—24no—
538C2×C22⋊Q8Dic6118yescomplemented
539C22×C4⋊C4—611no—
540C22×C4⋊C4—611no—
541C22×C4⋊C4C2×D6111yescharacteristic
542C22×C4⋊C4C2×D6111yescharacteristic
543C22×C4⋊C4C2×D6111yescharacteristic
544C22×C22⋊C4—611no—
545C22×C22⋊C4—611no—
546C22×C22⋊C4—611no—
547C22×C22⋊C4—611no—
548C22×C22⋊C4C2×D6111yescharacteristic
549C22×C22⋊C4C2×D6111yescharacteristic
550C22×C42—611no—
551C22×C42—611no—
552#391—1224no—
553#388—1224no—
554#388—1224no—
555#381—1224no—
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—
571C2×#95—611no—
572C2×#95—611no—
573C2×#95—611no—
574C2×#95—611no—
575C2×#95—611no—
576C61#1436411yescharacteristic, complemented, Sylow
577C25C22×D6111yescharacteristic
578C22×Q8—22no—
579C22×Q8—22no—
580C22×Q8—22no—
581C22×Q8—22no—
582C22×Q8—41no—
583C22×Q8—41no—
584C22×Q8C2×Dic6114yes—
585C23×C4—22no—
586C23×C4—22no—
587C23×C4—22no—
588C23×C4—22no—
589C23×C4—41no—
590C23×C4—41no—
591C23×C4—611no—
592C23×C4—611no—
593C23×C4—611no—
594C23×C4—611no—
595C23×C4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4C2×Dic6114yes—
600C23×C4C22×D6111yescharacteristic
601C23×C4C22×D6111yescharacteristic
602C23×C4C22×D6111yescharacteristic
603C23×C4C22×D6111yescharacteristic
604C23×C4C22×D6111yescharacteristic
605C23×C4C22×D6111yescharacteristic
606C22⋊Q8—232no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—1222no—
614C2×C4⋊C4—1222no—
615C2×C4⋊C4—1222no—
616C2×C4⋊C4—1222no—
617C2×C4⋊C4—2441no—
618C2×C4⋊C4—2441no—
619C2×C4⋊C4C2×Dic6114yes—
620C2×C4⋊C4C2×Dic6114yes—
621C2×C4⋊C4C2×Dic6114yes—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—1222no—
625C2×C22⋊C4—1222no—
626C2×C22⋊C4—1222no—
627C2×C22⋊C4—1222no—
628C2×C22⋊C4—1222no—
629C2×C22⋊C4—1222no—
630C2×C22⋊C4—1222no—
631C2×C22⋊C4—1222no—
632C2×C22⋊C4—2441no—
633C2×C22⋊C4—2441no—
634C2×C22⋊C4—2441no—
635C2×C22⋊C4—2441no—
636C2×C22⋊C4C2×Dic6114yes—
637C2×C22⋊C4C2×Dic6114yes—
638C2×C22⋊C4C22⋊D6114yes—
639C2×C22⋊C4C22⋊D6114yes—
640C2×C42—1222no—
641C2×C42—1222no—
642C2×C42—1222no—
643C2×C42—1222no—
644C2×C42—2441no—
645C2×C42—2441no—
646#95—614no—
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—
661#95—2441no—
662#95—2441no—
663#95—2441no—
664#95—2441no—
665#95—2441no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24C22×Dic6112yes—
679C24C2×C22⋊D6112yes—
680C24C2×C22⋊D6112yes—
681C24C23×D6111yescharacteristic
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
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—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—612no—
727C22×C4—612no—
728C22×C4—612no—
729C22×C4—612no—
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×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
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×C4D4×D6112yes—
783C22×C4#1175822412yes—
784C22×C4C22×Dic6112yes—
785C22×C4C22×Dic6112yes—
786C22×C4C22×Dic6112yes—
787C22×C4C22×Dic6112yes—
788C22×C4C22×Dic6112yes—
789C22×C4C22×Dic6112yes—
790C22×C4C2×C22⋊D6112yes—
791C22×C4C2×C22⋊D6112yes—
792C22×C4C2×C22⋊D6112yes—
793C22×C4C2×C22⋊D6112yes—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—2444no—
798C4⋊C4—2444no—
799C22⋊C4—28no—
800C22⋊C4—2444no—
801C22⋊C4—2444no—
802C22⋊C4—2444no—
803C22⋊C4—2444no—
804C22⋊C4C22⋊Dic61116yes—
805C42—2444no—
806C42—2444no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23C2×C22⋊Dic6114yes—
842C23C23×Dic6111yescharacteristic
843C23C2×D4×D6111yescharacteristic
844C23C22×C22⋊D6111yescharacteristic
845C23C22×C22⋊D6111yescharacteristic
846C23#41×D6111yescharacteristic
847C23#41×D6111yescharacteristic
848C23C2×#1175822411yescharacteristic
849C23#1451982211yescharacteristic
850C23#1451982211yescharacteristic
851C23#1451982311yescharacteristic
852C23#1451982411yescharacteristic
853C23#1451982511yescharacteristic
854C23#1451982511yescharacteristic
855C23#1451982511yescharacteristic
856C23#1451982511yescharacteristic
857Q8—416no—
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—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—416no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
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×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4—2441no—
953C2×C4—2441no—
954C2×C4C2×C22⋊Dic6114yes—
955C2×C4C2×C22⋊Dic6114yes—
956C2×C4D4×Dic6114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C22⋊Dic6111yescharacteristic
973C22C2×D4×Dic6111yescharacteristic
974C22#41×Dic6111yescharacteristic
975C22#1684023711yescharacteristic
976C22#1684024011yescharacteristic
977C22#1684024011yescharacteristic
978C22#1684024511yescharacteristic
979C22#1684033511yescharacteristic
980C22#1684033611yescharacteristic
981C22#1684033611yescharacteristic
982C22#1684033611yescharacteristic
983C22#1684033611yescharacteristic
984C22#1684034211yescharacteristic
985C22#1684035811yescharacteristic
986C22#1684035811yescharacteristic
987C22#1684037211yescharacteristic
988C22#1684038211yescharacteristic
989C22#1684038211yescharacteristic
990C22#1684038511yescharacteristic
991C22D4×C22⋊D6111yescharacteristic
992C22D4×C22⋊D6111yescharacteristic
993C22#1684040011yescharacteristic
994C22#1684040011yescharacteristic
995C22#1684040611yescharacteristic
996C22#1684040611yescharacteristic
997C22#1684041111yescharacteristic
998C22#1684041111yescharacteristic
999C22#1684041411yescharacteristic
1000C22#1684042211yescharacteristic
1001C22#1684044611yescharacteristic
1002C22#1684048311yescharacteristic
1003C22#1684050811yescharacteristic
1004C22#1684050811yescharacteristic
1005C22#1684051311yescharacteristic
1006C22#1684051311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—4881no—
1014C4—4881no—
1015C4—4881no—
1016C4—4881no—
1017C4—2442no—
1018C4—2442no—
1019C4—2442no—
1020C4—2442no—
1021C2—44no—
1022C2#2144840511yescharacteristic
1023C2#2144850311yescharacteristic
1024C2#2144857711yescharacteristic
1025C2D4×C22⋊Dic6111yescharacteristic
1026C2#2144864911yescharacteristic
1027C2#2144885011yescharacteristic
1028C2#2144898511yescharacteristic
1029C2#2145206611yescharacteristic
1030C2#2145209611yescharacteristic
1031C2#2145215811yescharacteristic
1032C2#2145216711yescharacteristic
1033C2#2145223611yescharacteristic
1034C2#2145226611yescharacteristic
1035C2#2145238911yescharacteristic
1036C2#2145241311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×C22⋊Q8×C61C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC22×C22⋊Q8D61
hypocenterC61#14364
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16839669C2semidirect
5. #21444090C2semidirect
6. #21444087C2semidirect
7. #21444072C2semidirect
8. #21444072C2semidirect
11. #21444051C2semidirect
12. #21444051C2semidirect
13. #21444048C2semidirect
52. C2×C22⋊Q8×C61C4semidirect
538. C2×C22⋊Q8Dic61semidirect
576. C61#14364semidirect

Maximal subgroups

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

subgroupindex
C2×#168396692
C2×#168396552
C2×#168396252
#214440902
#214440872
#214440722
#214440682
#214440512
#214440482
#214440422
C22×C22⋊Q8×C612
#1436461