Finite Group Databasebeta

← #29607349

Subgroups — #29607349

Order 15616.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839665C211yesmaximal, characteristic, complemented
2C2×#16839655C211yesmaximal, characteristic, complemented
3C2×#16839642C211yesmaximal, characteristic, complemented
4C2×#16839642C211yesmaximal, characteristic, complemented
5C2×#16839637C211yesmaximal, characteristic, complemented
6C2×#16839622C211yesmaximal, characteristic, complemented
7#21444072C211yesmaximal, characteristic, complemented
8#21444064C211yesmaximal, characteristic, complemented
9#21444064C211yesmaximal, characteristic, complemented
10#21444060C211yesmaximal, characteristic, complemented
11#21444060C211yesmaximal, characteristic, complemented
12#21444060C211yesmaximal, characteristic, complemented
13#21444051C211yesmaximal, characteristic, complemented
14#21444042C211yesmaximal, characteristic, complemented
15C22×#121×C61C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839665—24no—
33#16839655—24no—
34#16839642—24no—
35#16839642—24no—
36#16839637—24no—
37#16839622—24no—
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C23×D4×C61C2211yescharacteristic
51C23×D4×C61C2211yescharacteristic
52C23×D4×C61C2211yescharacteristic
53C24×C4×C61C2211yescharacteristic
54C2×#121×C61—24no—
55C2×#121×C61—24no—
56C2×#121×C61C418yescomplemented
57C22×C4⋊C4×C61C2211yescharacteristic
58C22×C22⋊C4×C61C2211yescharacteristic
59C22×C22⋊C4×C61C2211yescharacteristic
60C23×Dic61—22no—
61C23×Dic61—22no—
62C23×Dic61—22no—
63C23×Dic61—41no—
64C23×Dic61—41no—
65C23×Dic61—41no—
66C23×Dic61—41no—
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—41no—
82C2×C4⋊Dic61—41no—
83C2×C4⋊Dic61—41no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—22no—
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—41no—
99C2×C22⋊Dic61—41no—
100C2×C22⋊Dic61—41no—
101C2×C22⋊Dic61—41no—
102C2×C22⋊Dic61—41no—
103C2×C22⋊Dic61—41no—
104C2×C22⋊Dic61—41no—
105C2×C22⋊Dic61—41no—
106C2×C22⋊Dic61—41no—
107C2×C22⋊Dic61—41no—
108C2×C22⋊Dic61—41no—
109C2×C22⋊Dic61—41no—
110C2×C22⋊Dic61—41no—
111C2×C22⋊Dic61—41no—
112C2×C22⋊Dic61—41no—
113C2×C22⋊Dic61—41no—
114C2×C22⋊Dic61—41no—
115C2×C22⋊Dic61—41no—
116C2×C22⋊Dic61D414yescomplemented
117C2×C4×Dic61—22no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—41no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—41no—
130#14519684—41no—
131#14519684D414yescomplemented
132C25×C61C2311yescharacteristic
133C25×C61C2311yescharacteristic
134C25×C61C2311yescharacteristic
135C22×D4×C61—22no—
136C22×D4×C61—22no—
137C22×D4×C61—22no—
138C22×D4×C61—22no—
139C22×D4×C61—22no—
140C22×D4×C61—22no—
141C22×D4×C61—22no—
142C22×D4×C61—22no—
143C22×D4×C61—22no—
144C22×D4×C61—22no—
145C22×D4×C61—22no—
146C22×D4×C61—22no—
147C22×D4×C61—41no—
148C22×D4×C61—41no—
149C22×D4×C61—41no—
150C22×D4×C61—41no—
151C22×D4×C61—41no—
152C22×D4×C61—41no—
153C22×D4×C61C2×C414yes—
154C22×D4×C61C2×C414yes—
155C22×D4×C61C2×C414yescomplemented
156C23×C4×C61—22no—
157C23×C4×C61—22no—
158C23×C4×C61—22no—
159C23×C4×C61—22no—
160C23×C4×C61—41no—
161C23×C4×C61—41no—
162C23×C4×C61C2×C414yescomplemented
163C23×C4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167#121×C61—232no—
168C2×C4⋊C4×C61—22no—
169C2×C4⋊C4×C61—22no—
170C2×C4⋊C4×C61C2×C414yescomplemented
171C2×C22⋊C4×C61—22no—
172C2×C22⋊C4×C61—22no—
173C2×C22⋊C4×C61C2×C414yes—
174C2×C22⋊C4×C61C2×C414yescomplemented
175C2×C22⋊C4×C61D414yes—
176C2×C22⋊C4×C61D414yes—
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×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61—21no—
193C24×C61—21no—
194C24×C61—21no—
195C24×C61—21no—
196C24×C61—21no—
197C24×C61—21no—
198C24×C61—21no—
199C24×C61—21no—
200C24×C61—21no—
201C24×C61—21no—
202C24×C61—21no—
203C24×C61—21no—
204C24×C61—21no—
205C24×C61—21no—
206C24×C61—21no—
207C24×C61—21no—
208C24×C61—21no—
209C24×C61—21no—
210C24×C61—21no—
211C24×C61—21no—
212C24×C61—21no—
213C24×C61—21no—
214C24×C61—21no—
215C24×C61C22×C412yes—
216C24×C61C22×C412yes—
217C24×C61C22×C412yes—
218C24×C61C2×D412yes—
219C24×C61C2×D412yes—
220C24×C61C2×D412yes—
221C24×C61#4112yes—
222C24×C61C2411yescharacteristic
223C2×D4×C61—28no—
224C2×D4×C61—28no—
225C2×D4×C61—28no—
226C2×D4×C61—28no—
227C2×D4×C61—28no—
228C2×D4×C61—28no—
229C2×D4×C61—44no—
230C2×D4×C61—44no—
231C2×D4×C61—44no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—44no—
235C2×D4×C61—44no—
236C2×D4×C61—44no—
237C2×D4×C61—44no—
238C2×D4×C61—44no—
239C2×D4×C61—44no—
240C2×D4×C61—44no—
241C2×D4×C61—44no—
242C2×D4×C61—44no—
243C2×D4×C61—44no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—28no—
263C22×C4×C61—28no—
264C22×C4×C61—44no—
265C22×C4×C61—44no—
266C22×C4×C61—44no—
267C22×C4×C61—44no—
268C22×C4×C61—44no—
269C22×C4×C61C22×C412yes—
270C22×C4×C61C22×C412yes—
271C22×C4×C61C22×C412yes—
272C22×C4×C61C22×C412yes—
273C22×C4×C61C2×D412yes—
274C22×C4×C61C2×D412yes—
275C22×C4×C61C2×D412yes—
276C22×C4×C61C2×D412yes—
277C22×C4×C61C2×D412yes—
278C22×C4×C61#4112yes—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61—21no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61—21no—
320C22×Dic61—21no—
321C22×Dic61—21no—
322C22×Dic61—21no—
323C22×Dic61—21no—
324C22×Dic61—21no—
325C22×Dic61—21no—
326C22×Dic61—21no—
327C22×Dic61—21no—
328C22×Dic61—21no—
329C22×Dic61—21no—
330C22×Dic61—21no—
331C22×Dic61—44no—
332C22×Dic61—44no—
333C22×Dic61—44no—
334C22×Dic61—44no—
335C22×Dic61—44no—
336C22×Dic61—44no—
337C22×Dic61—44no—
338C22×Dic61C2×D412yes—
339C22×Dic61C2×D412yes—
340C22×Dic61C2×D412yes—
341C22×Dic61C2×D412yes—
342C4⋊C4×C61—28no—
343C22⋊C4×C61—28no—
344C22⋊C4×C61C22⋊C4116yescomplemented
345C22⋊Dic61—44no—
346C22⋊Dic61—44no—
347C22⋊Dic61—44no—
348C22⋊Dic61—44no—
349C22⋊Dic61—44no—
350C22⋊Dic61—44no—
351C22⋊Dic61—44no—
352C22⋊Dic61—44no—
353C22⋊Dic61—44no—
354C22⋊Dic61—44no—
355C22⋊Dic61—44no—
356C4⋊Dic61—44no—
357C4⋊Dic61—44no—
358C4⋊Dic61—44no—
359C4×Dic61—44no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—22no—
376C23×C61—22no—
377C23×C61—22no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—22no—
386C23×C61—22no—
387C23×C61—22no—
388C23×C61—22no—
389C23×C61—22no—
390C23×C61—22no—
391C23×C61—22no—
392C23×C61—22no—
393C23×C61—22no—
394C23×C61—22no—
395C23×C61—22no—
396C23×C61—22no—
397C23×C61—22no—
398C23×C61—22no—
399C23×C61—22no—
400C23×C61—22no—
401C23×C61—22no—
402C23×C61—22no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61—41no—
406C23×C61—41no—
407C23×C61—41no—
408C23×C61—41no—
409C23×C61—41no—
410C23×C61—41no—
411C23×C61—41no—
412C23×C61—41no—
413C23×C61—41no—
414C23×C61—41no—
415C23×C61—41no—
416C23×C61—41no—
417C23×C61—41no—
418C23×C61—41no—
419C23×C61—41no—
420C23×C61—41no—
421C23×C61—41no—
422C23×C61—41no—
423C23×C61—41no—
424C23×C61—41no—
425C23×C61—41no—
426C23×C61—41no—
427C23×C61—41no—
428C23×C61—41no—
429C23×C61—41no—
430C23×C61—41no—
431C23×C61—41no—
432C23×C61—41no—
433C23×C61—41no—
434C23×C61—41no—
435C23×C61—41no—
436C23×C61—41no—
437C23×C61—41no—
438C23×C61—41no—
439C23×C61—41no—
440C23×C61—41no—
441C23×C61—41no—
442C23×C61—41no—
443C23×C61—41no—
444C23×C61—41no—
445C23×C61—41no—
446C23×C61—41no—
447C23×C61—41no—
448C23×C61—41no—
449C23×C61—41no—
450C23×C61—41no—
451C23×C61—41no—
452C23×C61—41no—
453C23×C61—41no—
454C23×C61—41no—
455C23×C61—41no—
456C23×C61—41no—
457C23×C61—41no—
458C23×C61—41no—
459C23×C61—41no—
460C23×C61—41no—
461C23×C61—41no—
462C23×C61—41no—
463C23×C61C2×C22⋊C414yes—
464C23×C61C4×D414yes—
465C23×C61C23×C411yescharacteristic
466C23×C61C22×D411yescharacteristic
467C23×C61C22×D411yescharacteristic
468C23×C61C22×D411yescharacteristic
469C23×C61C22×D411yescharacteristic
470C23×C61C2×#4111yescharacteristic
471C23×C61C2×#4111yescharacteristic
472C23×C61H(5,𝔽2)11yescharacteristic
473C23×C61H(5,𝔽2)11yescharacteristic
474C23×C61H(5,𝔽2)11yescharacteristic
475C23×C61H(5,𝔽2)11yescharacteristic
476C23×C61H(5,𝔽2)11yescharacteristic
477C23×C61H(5,𝔽2)11yescharacteristic
478C23×C612−1+411yescharacteristic
479C23×C612−1+411yescharacteristic
480D4×C61—416no—
481D4×C61—416no—
482D4×C61—416no—
483C2×C4×C61—22no—
484C2×C4×C61—22no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—22no—
489C2×C4×C61—22no—
490C2×C4×C61—22no—
491C2×C4×C61—22no—
492C2×C4×C61—22no—
493C2×C4×C61—22no—
494C2×C4×C61—22no—
495C2×C4×C61—22no—
496C2×C4×C61—22no—
497C2×C4×C61—22no—
498C2×C4×C61—22no—
499C2×C4×C61—22no—
500C2×C4×C61—22no—
501C2×C4×C61—22no—
502C2×C4×C61—22no—
503C2×C4×C61—22no—
504C2×C4×C61—416no—
505C2×C4×C61—41no—
506C2×C4×C61—41no—
507C2×C4×C61—41no—
508C2×C4×C61—41no—
509C2×C4×C61C2×C22⋊C414yes—
510C2×C4×C61C2×C22⋊C414yes—
511C2×C4×C61C4×D414yes—
512C2×Dic61—22no—
513C2×Dic61—22no—
514C2×Dic61—22no—
515C2×Dic61—22no—
516C2×Dic61—22no—
517C2×Dic61—22no—
518C2×Dic61—22no—
519C2×Dic61—22no—
520C2×Dic61—22no—
521C2×Dic61—22no—
522C2×Dic61—22no—
523C2×Dic61—22no—
524C2×Dic61—416no—
525C2×Dic61—41no—
526C2×Dic61—41no—
527C2×Dic61—41no—
528C2×Dic61—41no—
529C2×Dic61—41no—
530C2×Dic61—41no—
531C2×Dic61—41no—
532C2×Dic61—41no—
533C2×Dic61—41no—
534C2×Dic61—41no—
535C2×Dic61—41no—
536C2×Dic61—41no—
537C2×Dic61—41no—
538C2×Dic61—41no—
539C2×Dic61—41no—
540C2×Dic61—41no—
541C2×Dic61—41no—
542C2×Dic61—41no—
543C2×Dic61—41no—
544C2×Dic61—41no—
545C2×Dic61—41no—
546C2×Dic61—41no—
547C2×Dic61—41no—
548C2×Dic61—41no—
549C2×Dic61—41no—
550C2×Dic61—41no—
551C2×Dic61—41no—
552C2×Dic61—41no—
553C2×Dic61—41no—
554C2×Dic61—41no—
555C2×Dic61—41no—
556C2×Dic61—41no—
557C2×Dic61—41no—
558C2×Dic61—41no—
559C2×Dic61—41no—
560C2×Dic61—41no—
561C2×Dic61—41no—
562C2×Dic61—41no—
563C2×Dic61—41no—
564C2×Dic61—41no—
565C2×Dic61—41no—
566C2×Dic61—41no—
567C2×Dic61—41no—
568C2×Dic61—41no—
569#14361—611nomaximal, Sylow
570C22×C61—24no—
571C22×C61—24no—
572C22×C61—24no—
573C22×C61—24no—
574C22×C61—24no—
575C22×C61—24no—
576C22×C61—42no—
577C22×C61—42no—
578C22×C61—42no—
579C22×C61—42no—
580C22×C61—42no—
581C22×C61—42no—
582C22×C61—42no—
583C22×C61—42no—
584C22×C61—42no—
585C22×C61—42no—
586C22×C61—42no—
587C22×C61—42no—
588C22×C61—42no—
589C22×C61—42no—
590C22×C61—42no—
591C22×C61—42no—
592C22×C61—42no—
593C22×C61—42no—
594C22×C61—42no—
595C22×C61—42no—
596C22×C61—42no—
597C22×C61—42no—
598C22×C61—42no—
599C22×C61—42no—
600C22×C61—42no—
601C22×C61—42no—
602C22×C61—42no—
603C22×C61—42no—
604C22×C61—42no—
605C22×C61—42no—
606C22×C61—42no—
607C22×C61—81no—
608C22×C61—81no—
609C22×C61—81no—
610C22×C61—81no—
611C22×C61—81no—
612C22×C61—81no—
613C22×C61—81no—
614C22×C61—81no—
615C22×C61C22×C22⋊C411yescharacteristic
616C22×C61C2×C4×D411yescharacteristic
617C22×C61C2×C4×D411yescharacteristic
618C22×C61#51811yescharacteristic
619C22×C61#51811yescharacteristic
620C22×C61#52011yescharacteristic
621C22×C61#52011yescharacteristic
622C22×C61#53411yescharacteristic
623C22×C61#53511yescharacteristic
624C22×C61#53511yescharacteristic
625C22×C61#53611yescharacteristic
626C22×C61#53711yescharacteristic
627C22×C61#53711yescharacteristic
628C22×C61#53711yescharacteristic
629C22×C61#53711yescharacteristic
630C22×C61#53811yescharacteristic
631C22×C61#53911yescharacteristic
632C22×C61#54011yescharacteristic
633C22×C61#54211yescharacteristic
634C22×C61D4211yescharacteristic
635C22×C61D4211yescharacteristic
636C22×C61D4211yescharacteristic
637C22×C61D4211yescharacteristic
638C22×C61D4211yescharacteristic
639C22×C61#54611yescharacteristic
640C22×C61#54611yescharacteristic
641C22×C61#54611yescharacteristic
642C22×C61#54611yescharacteristic
643C22×C61#54711yescharacteristic
644C22×C61#54811yescharacteristic
645C22×C61#55311yescharacteristic
646C22×C61#56011yescharacteristic
647C22×C61#56011yescharacteristic
648C22×C61#56211yescharacteristic
649C22×C61#56211yescharacteristic
650C4×C61—24no—
651C4×C61—24no—
652C4×C61—24no—
653C4×C61—42no—
654Dic61—42no—
655Dic61—42no—
656Dic61—42no—
657Dic61—42no—
658Dic61—81no—
659Dic61—81no—
660Dic61—81no—
661Dic61—81no—
662C22×#121D6111yescharacteristic
663C2×#390—611no—
664C2×#388—611no—
665C2×#386—611no—
666C2×#386—611no—
667C2×#385—611no—
668C2×#380—611no—
669#1441—611no—
670#1439—611no—
671#1439—611no—
672#1438—611no—
673#1438—611no—
674#1438—611no—
675#1436—611no—
676C22⋊#95—611no—
677C2×C61—44no—
678C2×C61—44no—
679C2×C61—82no—
680C2×C61#231111yescharacteristic
681C2×C61#232411yescharacteristic
682C2×C61#232511yescharacteristic
683C2×C61D4×C22⋊C411yescharacteristic
684C2×C61D4×C22⋊C411yescharacteristic
685C2×C61#236111yescharacteristic
686C2×C61#237711yescharacteristic
687C2×C61#266911yescharacteristic
688C2×C61#267111yescharacteristic
689C2×C61#267211yescharacteristic
690C2×C61#267511yescharacteristic
691C2×C61#267611yescharacteristic
692C2×C61#268111yescharacteristic
693C2×C61#269111yescharacteristic
694C2×C61#270311yescharacteristic
695C23×D4C2×D6111yescharacteristic
696C23×D4C2×D6111yescharacteristic
697C23×D4C2×D6111yescharacteristic
698C24×C4—611no—
699C24×C4C2×D6111yescharacteristic
700C2×#121—24no—
701C2×#121—24no—
702C2×#121Dic6118yescomplemented
703C22×C4⋊C4—611no—
704C22×C4⋊C4—611no—
705C22×C4⋊C4—611no—
706C22×C4⋊C4C2×D6111yescharacteristic
707C22×C22⋊C4—611no—
708C22×C22⋊C4—611no—
709C22×C22⋊C4—611no—
710C22×C22⋊C4—611no—
711C22×C22⋊C4—611no—
712C22×C22⋊C4—611no—
713C22×C22⋊C4—611no—
714C22×C22⋊C4—611no—
715C22×C22⋊C4—611no—
716C22×C22⋊C4—611no—
717C22×C22⋊C4—611no—
718C22×C22⋊C4C2×D6111yescharacteristic
719C22×C22⋊C4C2×D6111yescharacteristic
720C22×C42—611no—
721#390—1224no—
722#388—1224no—
723#386—1224no—
724#386—1224no—
725#385—1224no—
726#380—1224no—
727C2×#95—611no—
728C2×#95—611no—
729C2×#95—611no—
730C2×#95—611no—
731C2×#95—611no—
732C2×#95—611no—
733C2×#95—611no—
734C2×#95—611no—
735C2×#95—611no—
736C2×#95—611no—
737C2×#95—611no—
738C2×#95—611no—
739C61#1436111yescharacteristic, complemented, Sylow
740C25C22×D6111yescharacteristic
741C25C22×D6111yescharacteristic
742C25C22×D6111yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4—41no—
761C22×D4C2×Dic6114yes—
762C22×D4C2×Dic6114yes—
763C22×D4C2×Dic6114yescomplemented
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—41no—
769C23×C4—41no—
770C23×C4—611no—
771C23×C4—611no—
772C23×C4—611no—
773C23×C4—611no—
774C23×C4—611no—
775C23×C4—611no—
776C23×C4—611no—
777C23×C4—611no—
778C23×C4—1222no—
779C23×C4—1222no—
780C23×C4—1222no—
781C23×C4—2441no—
782C23×C4—2441no—
783C23×C4—2441no—
784C23×C4—2441no—
785C23×C4C2×Dic6114yescomplemented
786C23×C4C22×D6111yescharacteristic
787C23×C4C22×D6111yescharacteristic
788C23×C4C22×D6111yescharacteristic
789C23×C4C22×D6111yescharacteristic
790#121—232no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—1222no—
794C2×C4⋊C4—1222no—
795C2×C4⋊C4—1222no—
796C2×C4⋊C4—1222no—
797C2×C4⋊C4—1222no—
798C2×C4⋊C4—1222no—
799C2×C4⋊C4—2441no—
800C2×C4⋊C4—2441no—
801C2×C4⋊C4—2441no—
802C2×C4⋊C4C2×Dic6114yescomplemented
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—614no—
806C2×C22⋊C4—1222no—
807C2×C22⋊C4—1222no—
808C2×C22⋊C4—1222no—
809C2×C22⋊C4—1222no—
810C2×C22⋊C4—1222no—
811C2×C22⋊C4—1222no—
812C2×C22⋊C4—1222no—
813C2×C22⋊C4—1222no—
814C2×C22⋊C4—1222no—
815C2×C22⋊C4—1222no—
816C2×C22⋊C4—1222no—
817C2×C22⋊C4—1222no—
818C2×C22⋊C4—1222no—
819C2×C22⋊C4—1222no—
820C2×C22⋊C4—2441no—
821C2×C22⋊C4—2441no—
822C2×C22⋊C4—2441no—
823C2×C22⋊C4—2441no—
824C2×C22⋊C4—2441no—
825C2×C22⋊C4—2441no—
826C2×C22⋊C4—2441no—
827C2×C22⋊C4—2441no—
828C2×C22⋊C4—2441no—
829C2×C22⋊C4—2441no—
830C2×C22⋊C4—2441no—
831C2×C22⋊C4—2441no—
832C2×C22⋊C4—2441no—
833C2×C22⋊C4—2441no—
834C2×C22⋊C4—2441no—
835C2×C22⋊C4—2441no—
836C2×C22⋊C4—2441no—
837C2×C22⋊C4—2441no—
838C2×C22⋊C4C2×Dic6114yes—
839C2×C22⋊C4C2×Dic6114yescomplemented
840C2×C22⋊C4C22⋊D6114yes—
841C2×C22⋊C4C22⋊D6114yes—
842C2×C42—1222no—
843C2×C42—1222no—
844C2×C42—2441no—
845#95—614no—
846#95—1222no—
847#95—1222no—
848#95—1222no—
849#95—1222no—
850#95—1222no—
851#95—1222no—
852#95—1222no—
853#95—1222no—
854#95—1222no—
855#95—2441no—
856#95—2441no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24D4×D6112yes—
896C24#1175822412yes—
897C24C22×Dic6112yes—
898C24C22×Dic6112yes—
899C24C22×Dic6112yes—
900C24C2×C22⋊D6112yes—
901C24C2×C22⋊D6112yes—
902C24C23×D6111yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—28no—
943C22×C4—28no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—612no—
950C22×C4—612no—
951C22×C4—612no—
952C22×C4—612no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1221no—
977C22×C4—1221no—
978C22×C4—1221no—
979C22×C4—1221no—
980C22×C4—1221no—
981C22×C4—1221no—
982C22×C4—1221no—
983C22×C4—1221no—
984C22×C4—1221no—
985C22×C4—1221no—
986C22×C4—1221no—
987C22×C4—1221no—
988C22×C4—1221no—
989C22×C4—1221no—
990C22×C4—1221no—
991C22×C4—1221no—
992C22×C4—1221no—
993C22×C4—1221no—
994C22×C4—1221no—
995C22×C4—1221no—
996C22×C4—1221no—
997C22×C4—1221no—
998C22×C4—1221no—
999C22×C4—1221no—
1000C22×C4—1221no—
1001C22×C4—1221no—
1002C22×C4—1221no—
1003C22×C4—1221no—
1004C22×C4—1221no—
1005C22×C4—2444no—
1006C22×C4—2444no—
1007C22×C4—2444no—
1008C22×C4—2444no—
1009C22×C4—2444no—
1010C22×C4—2444no—
1011C22×C4—2444no—
1012C22×C4D4×D6112yes—
1013C22×C4#1175822412yes—
1014C22×C4C22×Dic6112yes—
1015C22×C4C22×Dic6112yes—
1016C22×C4C22×Dic6112yes—
1017C22×C4C22×Dic6112yes—
1018C22×C4C2×C22⋊D6112yes—
1019C22×C4C2×C22⋊D6112yes—
1020C22×C4C2×C22⋊D6112yes—
1021C22×C4C2×C22⋊D6112yes—
1022C4⋊C4—28no—
1023C4⋊C4—2444no—
1024C4⋊C4—2444no—
1025C4⋊C4—2444no—
1026C22⋊C4—28no—
1027C22⋊C4—2444no—
1028C22⋊C4—2444no—
1029C22⋊C4—2444no—
1030C22⋊C4—2444no—
1031C22⋊C4—2444no—
1032C22⋊C4—2444no—
1033C22⋊C4—2444no—
1034C22⋊C4—2444no—
1035C22⋊C4—2444no—
1036C22⋊C4—2444no—
1037C22⋊C4—2444no—
1038C22⋊C4C22⋊Dic61116yescomplemented
1039C42—2444no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23C2×C22⋊Dic6114yes—
1144C23D4×Dic6114yes—
1145C23C23×Dic6111yescharacteristic
1146C23C2×D4×D6111yescharacteristic
1147C23C2×D4×D6111yescharacteristic
1148C23C22×C22⋊D6111yescharacteristic
1149C23C22×C22⋊D6111yescharacteristic
1150C23C2×#1175822411yescharacteristic
1151C23C2×#1175822411yescharacteristic
1152C23#1451982211yescharacteristic
1153C23#1451982211yescharacteristic
1154C23#1451982211yescharacteristic
1155C23#1451982211yescharacteristic
1156C23#1451982311yescharacteristic
1157C23#1451982311yescharacteristic
1158C23#1451982411yescharacteristic
1159C23#1451982411yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—416no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—1222no—
1190C2×C4—1222no—
1191C2×C4—1222no—
1192C2×C4—1222no—
1193C2×C4—1222no—
1194C2×C4—1222no—
1195C2×C4—1222no—
1196C2×C4—1222no—
1197C2×C4—1222no—
1198C2×C4—1222no—
1199C2×C4—1222no—
1200C2×C4—1222no—
1201C2×C4—2441no—
1202C2×C4—2441no—
1203C2×C4—2441no—
1204C2×C4—2441no—
1205C2×C4—2441no—
1206C2×C4—2441no—
1207C2×C4—2441no—
1208C2×C4—2441no—
1209C2×C4—2441no—
1210C2×C4—2441no—
1211C2×C4—2441no—
1212C2×C4—2441no—
1213C2×C4—2441no—
1214C2×C4—2441no—
1215C2×C4—2441no—
1216C2×C4—2441no—
1217C2×C4—2441no—
1218C2×C4—2441no—
1219C2×C4—2441no—
1220C2×C4—2441no—
1221C2×C4—2441no—
1222C2×C4—2441no—
1223C2×C4—2441no—
1224C2×C4—2441no—
1225C2×C4—2441no—
1226C2×C4—2441no—
1227C2×C4—2441no—
1228C2×C4—2441no—
1229C2×C4—24416no—
1230C2×C4—2441no—
1231C2×C4—2441no—
1232C2×C4—2441no—
1233C2×C4—2441no—
1234C2×C4—2441no—
1235C2×C4—2441no—
1236C2×C4—2441no—
1237C2×C4—2441no—
1238C2×C4—2441no—
1239C2×C4—2441no—
1240C2×C4—2441no—
1241C2×C4—2441no—
1242C2×C4—2441no—
1243C2×C4—2441no—
1244C2×C4—2441no—
1245C2×C4—2441no—
1246C2×C4C2×C22⋊Dic6114yes—
1247C2×C4C2×C22⋊Dic6114yes—
1248C2×C4D4×Dic6114yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C22⋊Dic6111yescharacteristic
1295C22C2×D4×Dic6111yescharacteristic
1296C22C2×D4×Dic6111yescharacteristic
1297C22#1684023711yescharacteristic
1298C22#1684023711yescharacteristic
1299C22#1684024511yescharacteristic
1300C22#1684024511yescharacteristic
1301C22#1684032011yescharacteristic
1302C22#1684032611yescharacteristic
1303C22#1684032811yescharacteristic
1304C22#1684033311yescharacteristic
1305C22#1684033911yescharacteristic
1306C22#1684034011yescharacteristic
1307C22#1684034011yescharacteristic
1308C22#1684034111yescharacteristic
1309C22#1684034911yescharacteristic
1310C22#1684035711yescharacteristic
1311C22#1684036511yescharacteristic
1312C22#1684037911yescharacteristic
1313C22D4×C22⋊D6111yescharacteristic
1314C22D4×C22⋊D6111yescharacteristic
1315C22D4×C22⋊D6111yescharacteristic
1316C22D4×C22⋊D6111yescharacteristic
1317C22#1684039611yescharacteristic
1318C22#1684040611yescharacteristic
1319C22#1684040611yescharacteristic
1320C22#1684040611yescharacteristic
1321C22#1684040611yescharacteristic
1322C22#1684041211yescharacteristic
1323C22#1684041811yescharacteristic
1324C22#1684046411yescharacteristic
1325C22#1684050011yescharacteristic
1326C22#1684050011yescharacteristic
1327C22#1684050711yescharacteristic
1328C22#1684050711yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—42no—
1333C4—4881no—
1334C4—4881no—
1335C4—4881no—
1336C4—4881no—
1337C4—2442no—
1338C4—2442no—
1339C4—2442no—
1340C4—2442no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2#2144841111yescharacteristic
1345C2#2144851411yescharacteristic
1346C2#2144852411yescharacteristic
1347C2D4×C22⋊Dic6111yescharacteristic
1348C2D4×C22⋊Dic6111yescharacteristic
1349C2#2144883911yescharacteristic
1350C2#2144897611yescharacteristic
1351C2#2145203111yescharacteristic
1352C2#2145205011yescharacteristic
1353C2#2145206411yescharacteristic
1354C2#2145210911yescharacteristic
1355C2#2145212011yescharacteristic
1356C2#2145216511yescharacteristic
1357C2#2145229611yescharacteristic
1358C2#2145245811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
Fitting, prime radicalC22×#121×C61C2
socle, cosocleC24×C61C24
hypercenterC22×#121D61
hypocenterC61#14361
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16839665C2semidirect
2. C2×#16839655C2semidirect
3. C2×#16839642C2semidirect
4. C2×#16839642C2semidirect
5. C2×#16839637C2semidirect
6. C2×#16839622C2semidirect
7. #21444072C2semidirect
8. #21444064C2semidirect
9. #21444064C2semidirect
10. #21444060C2semidirect
11. #21444060C2semidirect
12. #21444060C2semidirect
13. #21444051C2semidirect
14. #21444042C2semidirect
56. C2×#121×C61C4semidirect
116. C2×C22⋊Dic61D4semidirect
131. #14519684D4semidirect
155. C22×D4×C61C2×C4semidirect
162. C23×C4×C61C2×C4semidirect
170. C2×C4⋊C4×C61C2×C4semidirect
174. C2×C22⋊C4×C61C2×C4semidirect
344. C22⋊C4×C61C22⋊C4semidirect
702. C2×#121Dic61semidirect
739. C61#14361semidirect
763. C22×D4C2×Dic61semidirect
785. C23×C4C2×Dic61semidirect
802. C2×C4⋊C4C2×Dic61semidirect
839. C2×C22⋊C4C2×Dic61semidirect
1038. C22⋊C4C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396652
C2×#168396552
C2×#168396422
C2×#168396372
C2×#168396222
#214440722
#214440642
#214440602
#214440512
#214440422
C22×#121×C612
#1436161