Finite Group Databasebeta

← #29607405

Subgroups — #29607405

Order 15616.

2854 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839656C211yesmaximal, characteristic, complemented
2C2×#16839650C211yesmaximal, characteristic, complemented
3C2×#16839618C211yesmaximal, characteristic
4C2×#16839618C211yesmaximal, characteristic
5#21444066C211yesmaximal, characteristic, complemented
6#21444066C211yesmaximal, characteristic, complemented
7#21444062C211yesmaximal, characteristic, complemented
8#21444062C211yesmaximal, characteristic, complemented
9#21444062C211yesmaximal, characteristic, complemented
10#21444062C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444056C211yesmaximal, characteristic, complemented
13#21444056C211yesmaximal, characteristic, complemented
14#21444056C211yesmaximal, characteristic, complemented
15C2×C61×#379C211yesmaximal, characteristic
16C22×#11758196C2211yescharacteristic, complemented
17C22×#11758196C2211yescharacteristic, complemented
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C22⋊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×C4×Dic61C2211yescharacteristic, complemented
31C22×C4×Dic61C2211yescharacteristic, complemented
32#16839656—24no—
33#16839650—24no—
34#16839618—24no—
35#16839618C418yescomplemented
36C2×#14519684C2211yescharacteristic, complemented
37C2×#14519684C2211yescharacteristic, complemented
38C2×#14519684C2211yescharacteristic, complemented
39C2×#14519684C2211yescharacteristic, complemented
40C2×#14519684C2211yescharacteristic, complemented
41C2×#14519684C2211yescharacteristic, complemented
42C2×#14519684C2211yescharacteristic, complemented
43C2×#14519684C2211yescharacteristic, complemented
44C2×#14519684C2211yescharacteristic, complemented
45C2×#14519684C2211yescharacteristic, complemented
46C2×#14519684C2211yescharacteristic, complemented
47C2×#14519684C2211yescharacteristic, complemented
48C26×C61C2211yescharacteristic
49C22×C22⋊C4×C61C2211yescharacteristic
50C22×C22⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C61×#379—24no—
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C2×#11758196—22no—
65C2×#11758196—22no—
66C2×#11758196—41no—
67C2×#11758196—41no—
68C2×#11758196—41no—
69C2×#11758196—41no—
70C2×C22⋊Dic61—22no—
71C2×C22⋊Dic61—22no—
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—22no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—41no—
84C2×C22⋊Dic61—41no—
85C2×C22⋊Dic61—41no—
86C2×C22⋊Dic61—41no—
87C2×C22⋊Dic61—41no—
88C2×C22⋊Dic61—41no—
89C2×C22⋊Dic61—41no—
90C2×C22⋊Dic61—41no—
91C2×C22⋊Dic61—41no—
92C2×C22⋊Dic61—41no—
93C2×C22⋊Dic61—41no—
94C2×C22⋊Dic61—41no—
95C2×C22⋊Dic61—41no—
96C2×C22⋊Dic61—41no—
97C2×C22⋊Dic61—41no—
98C2×C22⋊Dic61—41no—
99C2×C22⋊Dic61C2×C414yes—
100C2×C22⋊Dic61C2×C414yes—
101C2×C22⋊Dic61C2×C414yes—
102C2×C22⋊Dic61C2×C414yes—
103C2×C22⋊Dic61C2×C414yes—
104C2×C22⋊Dic61C2×C414yes—
105C2×C22⋊Dic61D414yes—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—41no—
109C2×C4×Dic61—41no—
110C2×C4×Dic61—41no—
111C2×C4×Dic61—41no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—22no—
116#14519684—41no—
117#14519684—41no—
118#14519684—41no—
119#14519684—41no—
120#14519684—41no—
121#14519684—41no—
122#14519684—41no—
123#14519684—41no—
124C25×C61—22no—
125C25×C61—22no—
126C25×C61—22no—
127C25×C61—22no—
128C25×C61—22no—
129C25×C61—22no—
130C25×C61—41no—
131C25×C61—41no—
132C25×C61—41no—
133C25×C61—41no—
134C25×C61—41no—
135C25×C61—41no—
136C25×C61—41no—
137C25×C61—41no—
138C25×C61C2×C414yes—
139C25×C61C2311yescharacteristic
140C25×C61C2311yescharacteristic
141C25×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61—22no—
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61—41no—
156C2×C22⋊C4×C61—41no—
157C2×C22⋊C4×C61—41no—
158C2×C22⋊C4×C61—41no—
159C2×C22⋊C4×C61—41no—
160C2×C22⋊C4×C61—41no—
161C2×C22⋊C4×C61—41no—
162C2×C22⋊C4×C61—41no—
163C2×C22⋊C4×C61D414yes—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×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—28no—
201C24×C61—28no—
202C24×C61—28no—
203C24×C61—44no—
204C24×C61—44no—
205C24×C61—44no—
206C24×C61—44no—
207C24×C61—44no—
208C24×C61—44no—
209C24×C61—44no—
210C24×C61—44no—
211C24×C61—44no—
212C24×C61—44no—
213C24×C61—44no—
214C24×C61—44no—
215C24×C61—44no—
216C24×C61—44no—
217C24×C61—44no—
218C24×C61—44no—
219C24×C61—44no—
220C24×C61—44no—
221C24×C61—44no—
222C24×C61—44no—
223C24×C61—44no—
224C24×C61—44no—
225C24×C61—44no—
226C24×C61—44no—
227C24×C61—44no—
228C24×C61—44no—
229C24×C61—44no—
230C24×C61—44no—
231C24×C61—44no—
232C24×C61—44no—
233C24×C61—44no—
234C24×C61—44no—
235C24×C61C22×C412yes—
236C24×C61C22×C412yes—
237C24×C61C22×C412yes—
238C24×C61C2×D412yes—
239C24×C61C2×D412yes—
240C24×C61#4112yes—
241C24×C61#4112yes—
242C24×C61#4112yes—
243C24×C61#4112yes—
244C24×C61C2411yescharacteristic
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—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61—21no—
271C22×C4×C61C2×D412yes—
272C22×C4×C61C2×D412yes—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×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×Dic61C22×C412yes—
324C22×Dic61C22×C412yes—
325C22×Dic61C22×C412yes—
326C22×Dic61C22×C412yes—
327C22×Dic61C2×D412yes—
328C22×Dic61C2×D412yes—
329C22⋊C4×C61—44no—
330C22⋊C4×C61—44no—
331C22⋊C4×C61—44no—
332C22⋊C4×C61—44no—
333C22⋊C4×C61—44no—
334C22⋊C4×C61—44no—
335C22⋊Dic61—28no—
336C22⋊Dic61—28no—
337C22⋊Dic61—44no—
338C22⋊Dic61—44no—
339C22⋊Dic61—44no—
340C22⋊Dic61—44no—
341C22⋊Dic61—44no—
342C22⋊Dic61—44no—
343C22⋊Dic61—44no—
344C22⋊Dic61—44no—
345C22⋊Dic61—44no—
346C22⋊Dic61—44no—
347#11758196—44no—
348#11758196—44no—
349C4×Dic61—44no—
350C4×Dic61—44no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
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—22no—
404C23×C61—22no—
405C23×C61—416no—
406C23×C61—416no—
407C23×C61—416no—
408C23×C61—416no—
409C23×C61—416no—
410C23×C61—416no—
411C23×C61—416no—
412C23×C61—416no—
413C23×C61—416no—
414C23×C61—416no—
415C23×C61—416no—
416C23×C61—416no—
417C23×C61—416no—
418C23×C61—416no—
419C23×C61—416no—
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×C61—41no—
464C23×C61—41no—
465C23×C61—41no—
466C23×C61—41no—
467C23×C61—41no—
468C23×C61#11714yes—
469C23×C61C4×D414yes—
470C23×C61C4×D414yes—
471C23×C61C23×C411yescharacteristic
472C23×C61C22×D411yescharacteristic
473C23×C61C22×D411yescharacteristic
474C23×C61C2×#4111yescharacteristic
475C23×C61C2×#4111yescharacteristic
476C23×C61C2×#4111yescharacteristic
477C23×C61C2×#4111yescharacteristic
478C23×C61H(5,𝔽2)11yescharacteristic
479C23×C61H(5,𝔽2)11yescharacteristic
480C23×C61H(5,𝔽2)11yescharacteristic
481C23×C61H(5,𝔽2)11yescharacteristic
482C23×C61H(5,𝔽2)11yescharacteristic
483C23×C61H(5,𝔽2)11yescharacteristic
484C23×C61H(5,𝔽2)11yescharacteristic
485C23×C61H(5,𝔽2)11yescharacteristic
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—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61—41no—
496C2×C4×C61—41no—
497C2×C4×C61—41no—
498C2×C4×C61—41no—
499C2×C4×C61—41no—
500C2×C4×C61—41no—
501C2×C4×C61—41no—
502C2×C4×C61—41no—
503C2×C4×C61—41no—
504C2×C4×C61—41no—
505C2×C4×C61—41no—
506C2×C4×C61—41no—
507C2×C4×C61—41no—
508C2×C4×C61—41no—
509C2×C4×C61—41no—
510C2×C4×C61—41no—
511C2×C4×C61—41no—
512C2×C4×C61—41no—
513C2×C4×C61—41no—
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—22no—
525C2×Dic61—22no—
526C2×Dic61—22no—
527C2×Dic61—22no—
528C2×Dic61—22no—
529C2×Dic61—22no—
530C2×Dic61—22no—
531C2×Dic61—22no—
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—
569C2×Dic61—41no—
570#14365—611nomaximal, Sylow
571C22×C61—24no—
572C22×C61—24no—
573C22×C61—24no—
574C22×C61—24no—
575C22×C61—24no—
576C22×C61—24no—
577C22×C61—24no—
578C22×C61—24no—
579C22×C61—24no—
580C22×C61—464no—
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—42no—
608C22×C61—42no—
609C22×C61—42no—
610C22×C61—42no—
611C22×C61—42no—
612C22×C61—42no—
613C22×C61—42no—
614C22×C61—42no—
615C22×C61—42no—
616C22×C61—42no—
617C22×C61C2×#11711yescharacteristic
618C22×C61C2×C4×D411yescharacteristic
619C22×C61C2×C4×D411yescharacteristic
620C22×C61#51811yescharacteristic
621C22×C61#51811yescharacteristic
622C22×C61#51811yescharacteristic
623C22×C61#51811yescharacteristic
624C22×C61#53411yescharacteristic
625C22×C61#53411yescharacteristic
626C22×C61#53511yescharacteristic
627C22×C61#53511yescharacteristic
628C22×C61#53811yescharacteristic
629C22×C61#53811yescharacteristic
630C22×C61#53811yescharacteristic
631C22×C61#53811yescharacteristic
632C22×C61#53811yescharacteristic
633C22×C61#53811yescharacteristic
634C22×C61#53811yescharacteristic
635C22×C61#53811yescharacteristic
636C22×C61D4211yescharacteristic
637C22×C61#54611yescharacteristic
638C22×C61#54611yescharacteristic
639C22×C61#54611yescharacteristic
640C22×C61#54611yescharacteristic
641C22×C61#54611yescharacteristic
642C22×C61#54611yescharacteristic
643C22×C61#55111yescharacteristic
644C22×C61#55111yescharacteristic
645C22×C61#55111yescharacteristic
646C22×C61#55111yescharacteristic
647C22×C61#55111yescharacteristic
648C22×C61#56011yescharacteristic
649C22×C61#56011yescharacteristic
650C22×C61#56011yescharacteristic
651C22×C61H(3,𝔽4)11yescharacteristic
652C4×C61—42no—
653C4×C61—42no—
654C4×C61—81no—
655C4×C61—81no—
656Dic61—42no—
657Dic61—42no—
658Dic61—42no—
659Dic61—42no—
660Dic61—42no—
661Dic61—42no—
662Dic61—81no—
663Dic61—81no—
664C2×#388—611no—
665C2×#388—611no—
666C2×#379—611no—
667C2×#379—611no—
668C2×#379D6111yescharacteristic
669#1440—611no—
670#1440—611no—
671#1439—611no—
672#1439—611no—
673#1439—611no—
674#1439—611no—
675#1437—611no—
676#1437—611no—
677#1437—611no—
678#1437—611no—
679C2×C61—44no—
680C2×C61—44no—
681C2×C61—44no—
682C2×C61#231211yescharacteristic
683C2×C61#232111yescharacteristic
684C2×C61#232111yescharacteristic
685C2×C61#234211yescharacteristic
686C2×C61#234211yescharacteristic
687C2×C61#235811yescharacteristic
688C2×C61#237511yescharacteristic
689C2×C61#267811yescharacteristic
690C2×C61#267811yescharacteristic
691C2×C61#268411yescharacteristic
692C2×C61#268411yescharacteristic
693C2×C61#268511yescharacteristic
694C2×C61#268511yescharacteristic
695C2×C61#273511yescharacteristic
696C2×C61#273511yescharacteristic
697C26C2×D6111yescharacteristic
698C22×C4⋊C4—611no—
699C22×C4⋊C4—611no—
700C22×C22⋊C4—611no—
701C22×C22⋊C4—611no—
702C22×C22⋊C4—611no—
703C22×C22⋊C4—611no—
704C22×C22⋊C4—611no—
705C22×C22⋊C4—611no—
706C22×C22⋊C4—611no—
707C22×C22⋊C4—611no—
708C22×C22⋊C4—611no—
709C22×C22⋊C4—611no—
710C22×C22⋊C4—611no—
711C22×C22⋊C4—611no—
712C22×C22⋊C4C2×D6111yescharacteristic
713C22×C22⋊C4C2×D6111yescharacteristic
714C22×C22⋊C4C2×D6111yescharacteristic
715C22×C22⋊C4C2×D6111yescharacteristic
716C22×C22⋊C4C2×D6111yescharacteristic
717C22×C22⋊C4C2×D6111yescharacteristic
718C22×C42—611no—
719C22×C42—611no—
720#388—1224no—
721#388—1224no—
722#379—24no—
723#379—618no—
724#379—1224no—
725C2×#95—611no—
726C2×#95—611no—
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—
737C61#1436511yescharacteristic, complemented, Sylow
738C25—22no—
739C25—22no—
740C25—22no—
741C25—22no—
742C25—22no—
743C25—22no—
744C25—41no—
745C25—41no—
746C25—41no—
747C25—41no—
748C25—41no—
749C25—41no—
750C25—41no—
751C25—41no—
752C25C4×D6114yes—
753C25C22×D6111yescharacteristic
754C25C22×D6111yescharacteristic
755C25C22×D6111yescharacteristic
756C23×C4—611no—
757C23×C4—611no—
758C23×C4—611no—
759C23×C4—611no—
760C23×C4—611no—
761C23×C4—611no—
762C23×C4—611no—
763C23×C4—611no—
764C23×C4C22×D6111yescharacteristic
765C23×C4C22×D6111yescharacteristic
766C23×C4C22×D6111yescharacteristic
767C23×C4C22×D6111yescharacteristic
768C2×C4⋊C4—1222no—
769C2×C4⋊C4—1222no—
770C2×C4⋊C4—2441no—
771C2×C4⋊C4—2441no—
772C2×C4⋊C4—2441no—
773C2×C4⋊C4—2441no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—614no—
792C2×C22⋊C4—614no—
793C2×C22⋊C4—614no—
794C2×C22⋊C4—614no—
795C2×C22⋊C4—614no—
796C2×C22⋊C4—614no—
797C2×C22⋊C4—614no—
798C2×C22⋊C4—1222no—
799C2×C22⋊C4—1222no—
800C2×C22⋊C4—1222no—
801C2×C22⋊C4—1222no—
802C2×C22⋊C4—1222no—
803C2×C22⋊C4—1222no—
804C2×C22⋊C4—1222no—
805C2×C22⋊C4—1222no—
806C2×C22⋊C4—1222no—
807C2×C22⋊C4—1222no—
808C2×C22⋊C4—1222no—
809C2×C22⋊C4—1222no—
810C2×C22⋊C4—1222no—
811C2×C22⋊C4—2441no—
812C2×C22⋊C4—2441no—
813C2×C22⋊C4—2441no—
814C2×C22⋊C4—2441no—
815C2×C22⋊C4—2441no—
816C2×C22⋊C4—2441no—
817C2×C22⋊C4—2441no—
818C2×C22⋊C4—2441no—
819C2×C22⋊C4—2441no—
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⋊C4C22⋊D6114yes—
828C2×C42—1222no—
829C2×C42—1222no—
830C2×C42—2441no—
831C2×C42—2441no—
832C2×C42—2441no—
833C2×C42—2441no—
834#95—1222no—
835#95—1222no—
836#95—1222no—
837#95—1222no—
838#95—2441no—
839#95—2441no—
840#95—2441no—
841#95—2441no—
842#95—2441no—
843#95—2441no—
844#95—2441no—
845#95—2441no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
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—28no—
883C24—28no—
884C24—28no—
885C24—44no—
886C24—44no—
887C24—44no—
888C24—44no—
889C24—44no—
890C24—44no—
891C24—44no—
892C24—44no—
893C24—44no—
894C24—44no—
895C24—44no—
896C24—44no—
897C24—44no—
898C24—44no—
899C24—44no—
900C24—44no—
901C24—44no—
902C24—44no—
903C24—44no—
904C24—44no—
905C24—44no—
906C24—44no—
907C24—44no—
908C24—44no—
909C24—44no—
910C24—44no—
911C24—44no—
912C24—44no—
913C24—44no—
914C24—44no—
915C24—44no—
916C24—44no—
917C24C2×C4×D6112yes—
918C24C2×C4×D6112yes—
919C24C2×C4×D6112yes—
920C24#1175822212yes—
921C24D4×D6112yes—
922C24#1175822412yes—
923C24#1175822412yes—
924C24#1175822412yes—
925C24C2×C22⋊D6112yes—
926C24C23×D6111yescharacteristic
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—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—612no—
954C22×C4—612no—
955C22×C4—612no—
956C22×C4—612no—
957C22×C4—612no—
958C22×C4—612no—
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—1221no—
1006C22×C4—1221no—
1007C22×C4—1221no—
1008C22×C4—1221no—
1009C22×C4C2×C22⋊D6112yes—
1010C22×C4C2×C22⋊D6112yes—
1011C4⋊C4—2444no—
1012C4⋊C4—2444no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—1228no—
1020C22⋊C4—1228no—
1021C22⋊C4—2444no—
1022C22⋊C4—2444no—
1023C22⋊C4—2444no—
1024C22⋊C4—2444no—
1025C22⋊C4—2444no—
1026C22⋊C4—2444no—
1027C22⋊C4—2444no—
1028C22⋊C4—2444no—
1029C22⋊C4—2444no—
1030C22⋊C4—2444no—
1031C42—2444no—
1032C42—2444no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
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—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—416no—
1088C23—416no—
1089C23—416no—
1090C23—416no—
1091C23—416no—
1092C23—416no—
1093C23—416no—
1094C23—416no—
1095C23—416no—
1096C23—416no—
1097C23—416no—
1098C23—416no—
1099C23—416no—
1100C23—416no—
1101C23—416no—
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—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23#1451973314yes—
1151C23#1451973714yes—
1152C23C4×C22⋊D6114yes—
1153C23C22×C4×D6111yescharacteristic
1154C23C2×D4×D6111yescharacteristic
1155C23C22×C22⋊D6111yescharacteristic
1156C23C2×#1175822411yescharacteristic
1157C23C2×#1175822411yescharacteristic
1158C23C2×#1175822411yescharacteristic
1159C23C2×#1175822211yescharacteristic
1160C23#1451982211yescharacteristic
1161C23#1451982211yescharacteristic
1162C23#1451982211yescharacteristic
1163C23#1451982211yescharacteristic
1164C23#1451982211yescharacteristic
1165C23#1451982211yescharacteristic
1166C23#1451982211yescharacteristic
1167C23#1451982211yescharacteristic
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—1222no—
1197C2×C4—1222no—
1198C2×C4—1222no—
1199C2×C4—1222no—
1200C2×C4—1222no—
1201C2×C4—1222no—
1202C2×C4—1222no—
1203C2×C4—1222no—
1204C2×C4—1222no—
1205C2×C4—1222no—
1206C2×C4—1222no—
1207C2×C4—1222no—
1208C2×C4—1222no—
1209C2×C4—1222no—
1210C2×C4—1222no—
1211C2×C4—1222no—
1212C2×C4—1222no—
1213C2×C4—1222no—
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—2441no—
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×C4—2441no—
1247C2×C4—2441no—
1248C2×C4—2441no—
1249C2×C4—2441no—
1250C2×C4—2441no—
1251C2×C4—2441no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—464no—
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—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22C2×#1451973311yescharacteristic
1299C22C2×#1451973711yescharacteristic
1300C22C2×C4×C22⋊D6111yescharacteristic
1301C22#1684023511yescharacteristic
1302C22#1684023511yescharacteristic
1303C22#1684023511yescharacteristic
1304C22#1684023511yescharacteristic
1305C22#1684032111yescharacteristic
1306C22#1684032211yescharacteristic
1307C22#1684032711yescharacteristic
1308C22#1684032911yescharacteristic
1309C22#1684034711yescharacteristic
1310C22#1684034711yescharacteristic
1311C22#1684034711yescharacteristic
1312C22#1684034711yescharacteristic
1313C22#1684034711yescharacteristic
1314C22#1684034711yescharacteristic
1315C22#1684035011yescharacteristic
1316C22#1684035011yescharacteristic
1317C22D4×C22⋊D6111yescharacteristic
1318C22#1684039911yescharacteristic
1319C22#1684039911yescharacteristic
1320C22#1684040211yescharacteristic
1321C22#1684040611yescharacteristic
1322C22#1684040611yescharacteristic
1323C22#1684040611yescharacteristic
1324C22#1684043811yescharacteristic
1325C22#1684043811yescharacteristic
1326C22#1684043811yescharacteristic
1327C22#1684044311yescharacteristic
1328C22#1684044311yescharacteristic
1329C22#1684050111yescharacteristic
1330C22#1684050111yescharacteristic
1331C22#1684050111yescharacteristic
1332C22#1684050511yescharacteristic
1333C4—42no—
1334C4—42no—
1335C4—81no—
1336C4—81no—
1337C4—4881no—
1338C4—4881no—
1339C4—2442no—
1340C4—2442no—
1341C4—2442no—
1342C4—2442no—
1343C4—2442no—
1344C4—2442no—
1345C2—44no—
1346C2—44no—
1347C2—44no—
1348C2#2144841511yescharacteristic
1349C2#2144847411yescharacteristic
1350C2#2144847711yescharacteristic
1351C2#2144866411yescharacteristic
1352C2#2144867011yescharacteristic
1353C2#2144879811yescharacteristic
1354C2#2144895811yescharacteristic
1355C2#2145214011yescharacteristic
1356C2#2145214411yescharacteristic
1357C2#2145219711yescharacteristic
1358C2#2145219911yescharacteristic
1359C2#2145220611yescharacteristic
1360C2#2145221011yescharacteristic
1361C2#2145285611yescharacteristic
1362C2#2145286011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#379C2
socle, cosocleC24×C61C24
prime radicalC26×C61C22
hypercenterC2×#379D61
hypocenterC61#14365
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C2×#16839656C2semidirect
2. C2×#16839650C2semidirect
5. #21444066C2semidirect
6. #21444066C2semidirect
7. #21444062C2semidirect
8. #21444062C2semidirect
9. #21444062C2semidirect
10. #21444062C2semidirect
11. #21444056C2semidirect
12. #21444056C2semidirect
13. #21444056C2semidirect
14. #21444056C2semidirect
16. C22×#11758196C22semidirect
17. C22×#11758196C22semidirect
30. C22×C4×Dic61C22semidirect
31. C22×C4×Dic61C22semidirect
35. #16839618C4semidirect
36. C2×#14519684C22semidirect
37. C2×#14519684C22semidirect
38. C2×#14519684C22semidirect
39. C2×#14519684C22semidirect
40. C2×#14519684C22semidirect
41. C2×#14519684C22semidirect
42. C2×#14519684C22semidirect
43. C2×#14519684C22semidirect
44. C2×#14519684C22semidirect
45. C2×#14519684C22semidirect
46. C2×#14519684C22semidirect
47. C2×#14519684C22semidirect
737. C61#14365semidirect

Maximal subgroups

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

subgroupindex
C2×#168396562
C2×#168396502
C2×#168396182
#214440662
#214440622
#214440562
C2×C61×#3792
#1436561