Finite Group Databasebeta

← #29603462

Subgroups — #29603462

Order 15616.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519748C211yesmaximal, characteristic
2C22×C4×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839638C211yesmaximal, characteristic, complemented
4C2×#16839638C211yesmaximal, characteristic, complemented
5C2×#16839638C211yesmaximal, characteristic, complemented
6C2×#95×D61C211yesmaximal, characteristic, complemented
7#21444071C211yesmaximal, characteristic, complemented
8#21444066C211yesmaximal, characteristic, complemented
9#21444062C211yesmaximal, characteristic, complemented
10#21444060C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444042C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519748—24no—
22C2×#14519748—24no—
23C2×#14519748C418yescomplemented
24C2×C4×C22⋊D61—24no—
25C2×C4×C22⋊D61—24no—
26C2×C4×C22⋊D61—24no—
27C22×C4⋊Dic61C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38#16839638—24no—
39#16839638—24no—
40#16839638—24no—
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53#95×D61—24no—
54C23×D4×C61C2211yescharacteristic
55C24×C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C22×C22⋊C4×C61C2211yescharacteristic
59C61×#386—24no—
60C2×#95×C61C2211yescharacteristic
61C2×#95×C61C2211yescharacteristic
62C24×D61C2311yescharacteristic
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61—22no—
66C22×C22⋊D61—22no—
67C22×C22⋊D61—22no—
68C22×C22⋊D61—22no—
69C22×C22⋊D61—22no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61C2×C414yes—
74C22×C22⋊D61C2×C414yescomplemented
75C22×C22⋊D61D414yes—
76C22×C22⋊D61D414yes—
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—22no—
94C22×C4×D61—22no—
95C22×C4×D61—22no—
96C22×C4×D61—22no—
97C22×C4×D61—41no—
98C22×C4×D61—41no—
99C22×C4×D61—41no—
100C22×C4×D61—41no—
101C22×C4×D61—41no—
102C22×C4×D61—41no—
103C22×C4×D61C2×C414yescomplemented
104C22×C4×D61D414yescomplemented
105#14519748—232no—
106C4×C22⋊D61—232no—
107C2×C4⋊Dic61—22no—
108C2×C4⋊Dic61—22no—
109C2×C4⋊Dic61C2×C414yescomplemented
110C2×#11758196—22no—
111C2×#11758196—22no—
112C2×#11758196—22no—
113C2×C22⋊Dic61—22no—
114C2×C22⋊Dic61—22no—
115C2×C22⋊Dic61—22no—
116C2×C22⋊Dic61—22no—
117C2×C22⋊Dic61—22no—
118C2×C22⋊Dic61—22no—
119C2×C22⋊Dic61—22no—
120C2×C22⋊Dic61—22no—
121C2×C22⋊Dic61—22no—
122C2×C22⋊Dic61—22no—
123C2×C22⋊Dic61—22no—
124C2×C22⋊Dic61—22no—
125C2×C22⋊Dic61—41no—
126C2×C22⋊Dic61—41no—
127C2×C22⋊Dic61—41no—
128C2×C22⋊Dic61—41no—
129C2×C22⋊Dic61C2×C414yescomplemented
130C2×C22⋊Dic61C2×C414yescomplemented
131C2×#11758198—22no—
132C2×#11758198—22no—
133C2×#11758198—22no—
134C2×#11758198—22no—
135C2×#11758198—22no—
136C2×#11758198D414yescomplemented
137C2×C4×Dic61—22no—
138C2×C4×Dic61—22no—
139C2×C4×Dic61—22no—
140#14519684—22no—
141#14519684—22no—
142#14519684—22no—
143#14519684—22no—
144#14519684—22no—
145#14519684—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684—22no—
149#14519684—22no—
150#14519684—41no—
151#14519684—41no—
152C25×C61C2311yescharacteristic
153C25×C61C2311yescharacteristic
154C22×D4×C61—22no—
155C22×D4×C61—22no—
156C22×D4×C61—22no—
157C22×D4×C61—22no—
158C22×D4×C61—41no—
159C22×D4×C61—41no—
160C22×D4×C61C2×C414yescomplemented
161C23×C4×C61—22no—
162C23×C4×C61—22no—
163C23×C4×C61—22no—
164C23×C4×C61—22no—
165C23×C4×C61—22no—
166C23×C4×C61—41no—
167C23×C4×C61—41no—
168C23×C4×C61C2311yescharacteristic
169C23×C4×C61C2311yescharacteristic
170C23×C4×C61C2311yescharacteristic
171C23×C4×C61C2311yescharacteristic
172C23×C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—22no—
174C2×C22⋊C4×C61—22no—
175C2×C22⋊C4×C61—22no—
176C2×C22⋊C4×C61—22no—
177C2×C22⋊C4×C61—22no—
178C2×C22⋊C4×C61—22no—
179C2×C22⋊C4×C61—22no—
180C2×C22⋊C4×C61—41no—
181C2×C22⋊C4×C61—41no—
182#95×C61—22no—
183#95×C61D414yescomplemented
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×C61C22×C412yes—
211C24×C61C22×C412yes—
212C24×C61C2×D412yes—
213C24×C61C2×D412yes—
214C24×C61C2411yescharacteristic
215C23×D61—21no—
216C23×D61—21no—
217C23×D61—21no—
218C23×D61—21no—
219C23×D61—21no—
220C23×D61—21no—
221C23×D61—21no—
222C23×D61—21no—
223C23×D61C22×C412yes—
224C23×D61C2×D412yes—
225C23×D61C2×D412yes—
226C23×D61C2×D412yes—
227C23×D61C2×D412yes—
228C23×D61#4112yes—
229C23×D61#4112yes—
230C2×D4×C61—28no—
231C2×D4×C61—28no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—44no—
235C2×D4×C61—44no—
236C2×D4×C61—44no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—28no—
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—44no—
266C22×C4×C61—44no—
267C22×C4×C61—44no—
268C22×C4×C61—44no—
269C22×C4×C61—44no—
270C22×C4×C61—44no—
271C22×C4×C61C22×C412yes—
272C22×C4×C61C2×D412yes—
273C22×C4×C61C2×D412yes—
274C22×C4×C61C2×D412yes—
275C22×C4×C61C2×D412yes—
276C22×C4×C61C2×D412yes—
277C22×C4×C61#4112yes—
278C22×C4×C61#4112yes—
279C2×C22⋊D61—28no—
280C2×C22⋊D61—28no—
281C2×C22⋊D61—28no—
282C2×C22⋊D61—28no—
283C2×C22⋊D61—28no—
284C2×C22⋊D61—28no—
285C2×C22⋊D61—28no—
286C2×C22⋊D61—28no—
287C2×C22⋊D61—28no—
288C2×C22⋊D61—44no—
289C2×C22⋊D61—44no—
290C2×C22⋊D61—44no—
291C2×C22⋊D61—44no—
292C2×C22⋊D61C22⋊C4116yescomplemented
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—21no—
332C22×Dic61—21no—
333C22×Dic61—21no—
334C22×Dic61C22×C412yes—
335C22×Dic61C22×C412yes—
336C22×Dic61C22×C412yes—
337C22×Dic61C2×D412yes—
338C22×Dic61C2×D412yes—
339C22×Dic61C2×D412yes—
340C22×Dic61C2×D412yes—
341C22×Dic61#4112yes—
342C2×C4×D61—28no—
343C2×C4×D61—28no—
344C2×C4×D61—28no—
345C2×C4×D61—28no—
346C2×C4×D61—28no—
347C2×C4×D61—44no—
348C2×C4×D61—44no—
349C2×C4×D61—44no—
350C2×C4×D61—44no—
351C2×C4×D61—44no—
352C2×C4×D61—44no—
353C2×C4×D61—44no—
354C2×C4×D61—44no—
355C2×C4×D61—44no—
356C2×C4×D61—44no—
357C2×C4×D61—44no—
358C2×C4×D61—44no—
359C2×C4×D61—44no—
360C2×C4×D61—44no—
361C2×C4×D61—44no—
362C2×C4×D61—44no—
363C22⋊C4×C61—44no—
364C22⋊C4×C61—44no—
365C22⋊C4×C61—44no—
366C22⋊Dic61—28no—
367C22⋊Dic61—28no—
368C22⋊Dic61—28no—
369C22⋊Dic61—44no—
370C22⋊Dic61—44no—
371C22⋊Dic61—44no—
372#11758198—28no—
373#11758198—44no—
374C4⋊Dic61—28no—
375#11758196—28no—
376C4×Dic61—28no—
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—41no—
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×C61C2×C22⋊C414yes—
447C23×C61C23×C411yescharacteristic
448C23×C61C22×D411yescharacteristic
449C23×C61C22×D411yescharacteristic
450C23×C61C22×D411yescharacteristic
451C23×C61C22×D411yescharacteristic
452C23×C61C22×D411yescharacteristic
453C23×C61C2×#4111yescharacteristic
454C23×C61C2×#4111yescharacteristic
455C23×C61C2×#4111yescharacteristic
456C23×C61C2×#4111yescharacteristic
457C23×C61C2×#4111yescharacteristic
458C23×C61H(5,𝔽2)11yescharacteristic
459C23×C61H(5,𝔽2)11yescharacteristic
460C23×C61H(5,𝔽2)11yescharacteristic
461C23×C612−1+411yescharacteristic
462C22×D61—22no—
463C22×D61—22no—
464C22×D61—22no—
465C22×D61—22no—
466C22×D61—22no—
467C22×D61—22no—
468C22×D61—22no—
469C22×D61—22no—
470C22×D61—22no—
471C22×D61—22no—
472C22×D61—22no—
473C22×D61—22no—
474C22×D61—22no—
475C22×D61—22no—
476C22×D61—22no—
477C22×D61—22no—
478C22×D61—22no—
479C22×D61—22no—
480C22×D61—22no—
481C22×D61—22no—
482C22×D61—22no—
483C22×D61—22no—
484C22×D61—22no—
485C22×D61—22no—
486C22×D61—22no—
487C22×D61—22no—
488C22×D61—22no—
489C22×D61—22no—
490C22×D61C2×C22⋊C414yes—
491C22×D61C4×D414yes—
492C22×D61C4×D414yes—
493C22×D61#12014yes—
494C22×D61#12114yes—
495C22×D61#12114yes—
496C22×D61#12314yes—
497D4×C61—416no—
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—22no—
505C2×C4×C61—22no—
506C2×C4×C61—22no—
507C2×C4×C61—22no—
508C2×C4×C61—22no—
509C2×C4×C61—22no—
510C2×C4×C61—22no—
511C2×C4×C61—22no—
512C2×C4×C61—22no—
513C2×C4×C61—22no—
514C2×C4×C61—22no—
515C2×C4×C61—22no—
516C2×C4×C61—416no—
517C2×C4×C61—41no—
518C2×C4×C61—41no—
519C2×C4×C61—41no—
520C2×C4×C61—41no—
521C2×C4×C61—41no—
522C2×C4×C61—41no—
523C2×C4×C61—41no—
524C2×C4×C61—41no—
525C2×C4×C61—41no—
526C2×C4×C61—41no—
527C2×C4×C61—41no—
528C2×C4×C61—41no—
529C2×C4×C61—41no—
530C2×C4×C61—41no—
531C2×C4×C61—41no—
532C2×C4×C61C4×D414yescomplemented
533C2×C4×C61#12114yescomplemented
534C22⋊D61—232no—
535C22⋊D61—416no—
536C2×Dic61—22no—
537C2×Dic61—22no—
538C2×Dic61—22no—
539C2×Dic61—22no—
540C2×Dic61—22no—
541C2×Dic61—22no—
542C2×Dic61—22no—
543C2×Dic61—22no—
544C2×Dic61—22no—
545C2×Dic61—22no—
546C2×Dic61—22no—
547C2×Dic61—22no—
548C2×Dic61—22no—
549C2×Dic61—22no—
550C2×Dic61—22no—
551C2×Dic61—22no—
552C2×Dic61—22no—
553C2×Dic61—22no—
554C2×Dic61—22no—
555C2×Dic61—22no—
556C2×Dic61—22no—
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—
570C2×Dic61—41no—
571C2×Dic61—41no—
572C2×Dic61—41no—
573C2×Dic61—41no—
574C2×Dic61—41no—
575C2×Dic61—41no—
576C2×Dic61—41no—
577C2×Dic61—41no—
578C2×Dic61—41no—
579C2×Dic61—41no—
580C2×Dic61—41no—
581C2×Dic61—41no—
582C2×Dic61—41no—
583C2×Dic61—41no—
584C2×Dic61C2×C22⋊C414yes—
585C4×D61—416no—
586C4×D61—416no—
587C4×D61—416no—
588#14023—611nomaximal, Sylow
589C22×C61—24no—
590C22×C61—24no—
591C22×C61—24no—
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—81no—
612C22×C61—81no—
613C22×C61—81no—
614C22×C61—81no—
615C22×C61—81no—
616C22×C61—81no—
617C22×C61—81no—
618C22×C61—81no—
619C22×C61C22×C22⋊C411yescharacteristic
620C22×C61C2×C4×D411yescharacteristic
621C22×C61C2×C4×D411yescharacteristic
622C22×C61C2×C4×D411yescharacteristic
623C22×C61C4×#4111yescharacteristic
624C22×C61#51811yescharacteristic
625C22×C61#52011yescharacteristic
626C22×C61C2×#12011yescharacteristic
627C22×C61C2×#12111yescharacteristic
628C22×C61C2×#12111yescharacteristic
629C22×C61C2×#12111yescharacteristic
630C22×C61C2×#12311yescharacteristic
631C22×C61#52511yescharacteristic
632C22×C61#52911yescharacteristic
633C22×C61#53211yescharacteristic
634C22×C61#53411yescharacteristic
635C22×C61#53711yescharacteristic
636C22×C61#53811yescharacteristic
637C22×C61#53911yescharacteristic
638C22×C61D4211yescharacteristic
639C22×C61D4211yescharacteristic
640C22×C61D4211yescharacteristic
641C22×C61#54611yescharacteristic
642C22×C61#54611yescharacteristic
643C22×C61#54611yescharacteristic
644C22×C61#54611yescharacteristic
645C22×C61#54611yescharacteristic
646C22×C61#54611yescharacteristic
647C22×C61#54711yescharacteristic
648C22×C61#54711yescharacteristic
649C22×C61#54711yescharacteristic
650C22×C61#54811yescharacteristic
651C22×C61#55311yescharacteristic
652C22×C61#55311yescharacteristic
653C22×C61#55311yescharacteristic
654C2×D61—24no—
655C2×D61—24no—
656C2×D61—24no—
657C2×D61—24no—
658C2×D61—24no—
659C2×D61—24no—
660C2×D61—24no—
661C2×D61—24no—
662C2×D61—24no—
663C2×D61—24no—
664C2×D61—24no—
665C2×D61—24no—
666C2×D61—24no—
667C2×D61—24no—
668C2×D61#38618yescomplemented
669C4×C61—24no—
670C4×C61—24no—
671C4×C61—42no—
672C4×C61—42no—
673C4×C61—81no—
674Dic61—24no—
675Dic61—42no—
676Dic61—42no—
677Dic61—42no—
678Dic61—42no—
679Dic61—42no—
680Dic61—81no—
681C22×#121—611no—
682C22×C4×D4—611no—
683C2×#386—611no—
684C2×#386—611no—
685C2×#386—611no—
686C2×#386D6111yescharacteristic, complemented
687C22×#95—611no—
688#1441—611no—
689#1440—611no—
690#1439—611no—
691#1438—611no—
692#1437—611no—
693#1436—611no—
694C22⋊#95—611no—
695C22⋊#95—611no—
696C2×C61—44no—
697C2×C61—82no—
698C2×C61C2×#38611yescharacteristic
699C2×C61C4×#12111yescharacteristic
700C2×C61#232511yescharacteristic
701C2×C61D4×C22⋊C411yescharacteristic
702C2×C61#233911yescharacteristic
703C2×C61#236111yescharacteristic
704C2×C61#236411yescharacteristic
705C2×C61#241011yescharacteristic
706C2×C61#241611yescharacteristic
707C2×C61#242411yescharacteristic
708C2×C61#242511yescharacteristic
709C2×C61#243011yescharacteristic
710C2×C61#244311yescharacteristic
711C2×C61#244411yescharacteristic
712C2×C61#254311yescharacteristic
713D61—28no—
714C23×D4—611no—
715C23×D4—611no—
716C23×D4C2×D6111yescharacteristic
717C24×C4—611no—
718C24×C4—611no—
719C24×C4—611no—
720C24×C4C2×D6111yescharacteristic
721C2×#121—618no—
722C2×#121—1224no—
723C2×#121—1224no—
724C2×C4×D4—1224no—
725C2×C4×D4—1224no—
726C2×C4×D4—1224no—
727C22×C4⋊C4—611no—
728C22×C4⋊C4—611no—
729C22×C22⋊C4—611no—
730C22×C22⋊C4—611no—
731C22×C22⋊C4—611no—
732C22×C22⋊C4—611no—
733C22×C22⋊C4—611no—
734C22×C22⋊C4—611no—
735C22×C22⋊C4—611no—
736C22×C22⋊C4—611no—
737C22×C22⋊C4C2×D6111yescharacteristic
738C22×C22⋊C4C2×D6111yescharacteristic
739C22×C22⋊C4C2×D6111yescharacteristic
740C22×C42—611no—
741#386—24no—
742#386—1224no—
743#386—1224no—
744#386—1224no—
745C2×#95—611no—
746C2×#95—611no—
747C2×#95—611no—
748C2×#95—611no—
749C2×#95—611no—
750C2×#95—611no—
751C2×#95—611no—
752C2×#95—611no—
753C2×#95—611no—
754C2×#95—611no—
755C2×#95—611no—
756C2×#95—611no—
757C2×#95—1224no—
758C2×#95C2×D6111yescharacteristic
759C2×#95C2×D6111yescharacteristic
760C61#1402311yescharacteristic, complemented, Sylow
761C25—611no—
762C25C22×D6111yescharacteristic
763C25C22×D6111yescharacteristic
764C22×D4—22no—
765C22×D4—22no—
766C22×D4—22no—
767C22×D4—22no—
768C22×D4—41no—
769C22×D4—41no—
770C22×D4—614no—
771C22×D4—614no—
772C22×D4—614no—
773C22×D4—614no—
774C22×D4—1222no—
775C22×D4—1222no—
776C22×D4—1222no—
777C22×D4—1222no—
778C22×D4—1222no—
779C22×D4—1222no—
780C22×D4—1222no—
781C22×D4—1222no—
782C22×D4—1222no—
783C22×D4—1222no—
784C22×D4C4×D6114yescomplemented
785C23×C4—22no—
786C23×C4—22no—
787C23×C4—22no—
788C23×C4—22no—
789C23×C4—22no—
790C23×C4—41no—
791C23×C4—41no—
792C23×C4—611no—
793C23×C4—611no—
794C23×C4—611no—
795C23×C4—611no—
796C23×C4—611no—
797C23×C4—611no—
798C23×C4—614no—
799C23×C4—614no—
800C23×C4—611no—
801C23×C4—1222no—
802C23×C4—1222no—
803C23×C4—1222no—
804C23×C4—1222no—
805C23×C4—1222no—
806C23×C4—1222no—
807C23×C4—1222no—
808C23×C4—1222no—
809C23×C4—1222no—
810C23×C4—1222no—
811C23×C4—1222no—
812C23×C4—1222no—
813C23×C4—1222no—
814C23×C4—2441no—
815C23×C4—2441no—
816C23×C4—2441no—
817C23×C4—2441no—
818C23×C4—2441no—
819C23×C4—2441no—
820C23×C4C22×D6111yescharacteristic
821C23×C4C22×D6111yescharacteristic
822C23×C4C22×D6111yescharacteristic
823C23×C4C22×D6111yescharacteristic
824C23×C4C22×D6111yescharacteristic
825#121—12232no—
826C4×D4—12232no—
827C2×C4⋊C4—614no—
828C2×C4⋊C4—1222no—
829C2×C4⋊C4—1222no—
830C2×C4⋊C4—1222no—
831C2×C4⋊C4—1222no—
832C2×C4⋊C4—1222no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—22no—
838C2×C22⋊C4—22no—
839C2×C22⋊C4—22no—
840C2×C22⋊C4—41no—
841C2×C22⋊C4—41no—
842C2×C22⋊C4—614no—
843C2×C22⋊C4—614no—
844C2×C22⋊C4—614no—
845C2×C22⋊C4—1222no—
846C2×C22⋊C4—1222no—
847C2×C22⋊C4—1222no—
848C2×C22⋊C4—1222no—
849C2×C22⋊C4—1222no—
850C2×C22⋊C4—1222no—
851C2×C22⋊C4—1222no—
852C2×C22⋊C4—1222no—
853C2×C22⋊C4—1222no—
854C2×C22⋊C4—1222no—
855C2×C22⋊C4—1222no—
856C2×C22⋊C4—1222no—
857C2×C22⋊C4—1222no—
858C2×C22⋊C4—1222no—
859C2×C22⋊C4—1222no—
860C2×C22⋊C4—1222no—
861C2×C22⋊C4—1222no—
862C2×C22⋊C4—2441no—
863C2×C22⋊C4—2441no—
864C2×C22⋊C4—2441no—
865C2×C22⋊C4—2441no—
866C2×C42—1222no—
867C2×C42—1222no—
868C2×C42—1222no—
869#95—22no—
870#95—1222no—
871#95—1222no—
872#95—1222no—
873#95—1222no—
874#95—1222no—
875#95—1222no—
876#95—1222no—
877#95—1222no—
878#95—1222no—
879#95—1222no—
880#95—2441no—
881#95—2441no—
882#95C22⋊D6114yescomplemented
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—21no—
903C24—21no—
904C24—21no—
905C24—21no—
906C24—21no—
907C24—21no—
908C24—21no—
909C24—612no—
910C24—612no—
911C24—612no—
912C24—612no—
913C24—612no—
914C24—612no—
915C24—612no—
916C24—1221no—
917C24—1221no—
918C24—1221no—
919C24—1221no—
920C24—1221no—
921C24—1221no—
922C24—1221no—
923C24—1221no—
924C24C2×C4×D6112yes—
925C24C2×C4×D6112yes—
926C24D4×D6112yes—
927C24D4×D6112yes—
928C24C23×D6111yescharacteristic
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—6116no—
937C2×D4—1228no—
938C2×D4—1228no—
939C2×D4—1228no—
940C2×D4—1228no—
941C2×D4—1228no—
942C2×D4—1228no—
943C2×D4—1228no—
944C2×D4—1228no—
945C2×D4—1228no—
946C2×D4—2444no—
947C2×D4—2444no—
948C2×D4—2444no—
949C2×D4—2444no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—28no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—612no—
985C22×C4—612no—
986C22×C4—612no—
987C22×C4—612no—
988C22×C4—612no—
989C22×C4—612no—
990C22×C4—612no—
991C22×C4—612no—
992C22×C4—1228no—
993C22×C4—1228no—
994C22×C4—1228no—
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×C4—1221no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1221no—
1014C22×C4—1221no—
1015C22×C4—1221no—
1016C22×C4—1221no—
1017C22×C4—1221no—
1018C22×C4—1221no—
1019C22×C4—1221no—
1020C22×C4—1221no—
1021C22×C4—1221no—
1022C22×C4—1221no—
1023C22×C4—1221no—
1024C22×C4—1221no—
1025C22×C4—1221no—
1026C22×C4—1221no—
1027C22×C4—1221no—
1028C22×C4—1221no—
1029C22×C4—1228no—
1030C22×C4—1228no—
1031C22×C4—1221no—
1032C22×C4—1221no—
1033C22×C4—1221no—
1034C22×C4—1221no—
1035C22×C4—1221no—
1036C22×C4—1221no—
1037C22×C4—1221no—
1038C22×C4—2444no—
1039C22×C4—2444no—
1040C22×C4—2444no—
1041C22×C4—2444no—
1042C22×C4—2444no—
1043C22×C4—2444no—
1044C22×C4—2444no—
1045C22×C4—2444no—
1046C22×C4—2444no—
1047C22×C4—2444no—
1048C22×C4—2444no—
1049C22×C4—2444no—
1050C22×C4—2444no—
1051C22×C4—2444no—
1052C22×C4—2444no—
1053C22×C4—2444no—
1054C22×C4C2×C4×D6112yes—
1055C22×C4#1175822212yes—
1056C22×C4D4×D6112yes—
1057C22×C4D4×D6112yes—
1058C22×C4#1175822412yes—
1059C22×C4C2×C22⋊D6112yes—
1060C22×C4C2×C22⋊D6112yes—
1061C22×C4C2×C22⋊D6112yes—
1062C4⋊C4—1228no—
1063C4⋊C4—1228no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—1228no—
1068C22⋊C4—1228no—
1069C22⋊C4—1228no—
1070C22⋊C4—1228no—
1071C22⋊C4—2444no—
1072C22⋊C4—2444no—
1073C22⋊C4—2444no—
1074C22⋊C4—2444no—
1075C42—1228no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
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—
1143C23—41no—
1144C23—41no—
1145C23—614no—
1146C23—614no—
1147C23—614no—
1148C23—614no—
1149C23—614no—
1150C23—614no—
1151C23—614no—
1152C23—1222no—
1153C23—1222no—
1154C23—1222no—
1155C23—1222no—
1156C23—1222no—
1157C23—1222no—
1158C23—1222no—
1159C23—1222no—
1160C23—1222no—
1161C23—1222no—
1162C23—1222no—
1163C23—1222no—
1164C23—1222no—
1165C23—1222no—
1166C23—1222no—
1167C23—1222no—
1168C23—1222no—
1169C23—1222no—
1170C23—1222no—
1171C23—1222no—
1172C23—1222no—
1173C23—1222no—
1174C23—1222no—
1175C23—1222no—
1176C23—1222no—
1177C23—1222no—
1178C23—1222no—
1179C23—1222no—
1180C23C22⋊C4×D6114yes—
1181C23C22×C4×D6111yescharacteristic
1182C23C2×D4×D6111yescharacteristic
1183C23C2×D4×D6111yescharacteristic
1184C23C2×D4×D6111yescharacteristic
1185C23C2×D4×D6111yescharacteristic
1186C23C22×C22⋊D6111yescharacteristic
1187C23#41×D6111yescharacteristic
1188C23#41×D6111yescharacteristic
1189C23#41×D6111yescharacteristic
1190C23C2×#1175822411yescharacteristic
1191C23C2×#1175822211yescharacteristic
1192C23#1451982211yescharacteristic
1193C23#1451982211yescharacteristic
1194C23#1451982211yescharacteristic
1195C23#1451982411yescharacteristic
1196D4—416no—
1197D4—12232no—
1198D4—24416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—416no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—614no—
1234C2×C4—1222no—
1235C2×C4—1222no—
1236C2×C4—1222no—
1237C2×C4—1222no—
1238C2×C4—1222no—
1239C2×C4—1222no—
1240C2×C4—1222no—
1241C2×C4—1222no—
1242C2×C4—1222no—
1243C2×C4—1222no—
1244C2×C4—1222no—
1245C2×C4—1222no—
1246C2×C4—1222no—
1247C2×C4—1222no—
1248C2×C4—1222no—
1249C2×C4—1222no—
1250C2×C4—1222no—
1251C2×C4—1222no—
1252C2×C4—1222no—
1253C2×C4—1222no—
1254C2×C4—1222no—
1255C2×C4—24416no—
1256C2×C4—24416no—
1257C2×C4—24416no—
1258C2×C4—2441no—
1259C2×C4—2441no—
1260C2×C4—2441no—
1261C2×C4—2441no—
1262C2×C4—2441no—
1263C2×C4—2441no—
1264C2×C4—2441no—
1265C2×C4—2441no—
1266C2×C4—2441no—
1267C2×C4—2441no—
1268C2×C4—2441no—
1269C2×C4—2441no—
1270C2×C4—2441no—
1271C2×C4—2441no—
1272C2×C4—2441no—
1273C2×C4—2441no—
1274C2×C4—2441no—
1275C2×C4—2441no—
1276C2×C4—2441no—
1277C2×C4—2441no—
1278C2×C4—2441no—
1279C2×C4—2441no—
1280C2×C4—2441no—
1281C2×C4—2441no—
1282C2×C4—2441no—
1283C2×C4—2441no—
1284C2×C4—2441no—
1285C2×C4C4×C22⋊D6114yescomplemented
1286C2×C4#1451974814yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—618no—
1318C22—1224no—
1319C22—1224no—
1320C22—1224no—
1321C22—1224no—
1322C22—1224no—
1323C22—1224no—
1324C22—1224no—
1325C22—1224no—
1326C22—1224no—
1327C22—1224no—
1328C22—1224no—
1329C22—1224no—
1330C22—1224no—
1331C22—1224no—
1332C22C2×C22⋊C4×D6111yescharacteristic
1333C22C4×D4×D6111yescharacteristic
1334C22C4×D4×D6111yescharacteristic
1335C22C2×C4×C22⋊D6111yescharacteristic
1336C22C4×#1175822411yescharacteristic
1337C22#1684023511yescharacteristic
1338C22#1684024111yescharacteristic
1339C22#120×D6111yescharacteristic
1340C22#121×D6111yescharacteristic
1341C22#121×D6111yescharacteristic
1342C22C2×#1451974811yescharacteristic
1343C22#123×D6111yescharacteristic
1344C22#1684026911yescharacteristic
1345C22#1684029411yescharacteristic
1346C22#1684030911yescharacteristic
1347C22#1684032211yescharacteristic
1348C22#1684034111yescharacteristic
1349C22#1684034411yescharacteristic
1350C22#1684035511yescharacteristic
1351C22D4×C22⋊D6111yescharacteristic
1352C22D4×C22⋊D6111yescharacteristic
1353C22D4×C22⋊D6111yescharacteristic
1354C22#1684039911yescharacteristic
1355C22#1684039911yescharacteristic
1356C22#1684040111yescharacteristic
1357C22#1684040211yescharacteristic
1358C22#1684040211yescharacteristic
1359C22#1684040911yescharacteristic
1360C22#1684041011yescharacteristic
1361C22#1684041211yescharacteristic
1362C22#1684041711yescharacteristic
1363C22#1684041911yescharacteristic
1364C22#1684045711yescharacteristic
1365C22#1684045911yescharacteristic
1366C22#1684046211yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—81no—
1372C4—1224no—
1373C4—4881no—
1374C4—2442no—
1375C4—2442no—
1376C4—2442no—
1377C4—2442no—
1378C4—2442no—
1379C2—44no—
1380C2—82no—
1381C2—1228no—
1382C2#386×D6111yescharacteristic
1383C2C4×#1451974811yescharacteristic
1384C2#2144852111yescharacteristic
1385C2C22⋊C4×C22⋊D6111yescharacteristic
1386C2#2144864511yescharacteristic
1387C2#2144883111yescharacteristic
1388C2#2144886811yescharacteristic
1389C2#2144918911yescharacteristic
1390C2#2144925511yescharacteristic
1391C2#2144935211yescharacteristic
1392C2#2144936911yescharacteristic
1393C2#2144942611yescharacteristic
1394C2#2144955111yescharacteristic
1395C2#2144956611yescharacteristic
1396C2#2145077811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#386C2
socle, cosocleC24×C61C24
prime radicalC22×#14519748C2
hypercenterC2×#386D61
hypocenterC61#14023
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D61C2semidirect
3. C2×#16839638C2semidirect
4. C2×#16839638C2semidirect
5. C2×#16839638C2semidirect
6. C2×#95×D61C2semidirect
7. #21444071C2semidirect
8. #21444066C2semidirect
9. #21444062C2semidirect
10. #21444060C2semidirect
11. #21444056C2semidirect
12. #21444053C2semidirect
13. #21444042C2semidirect
14. #21444040C2semidirect
15. C2×C61×#386C2semidirect
23. C2×#14519748C4semidirect
74. C22×C22⋊D61C2×C4semidirect
103. C22×C4×D61C2×C4semidirect
104. C22×C4×D61D4semidirect
109. C2×C4⋊Dic61C2×C4semidirect
129. C2×C22⋊Dic61C2×C4semidirect
130. C2×C22⋊Dic61C2×C4semidirect
136. C2×#11758198D4semidirect
160. C22×D4×C61C2×C4semidirect
183. #95×C61D4semidirect
292. C2×C22⋊D61C22⋊C4semidirect
532. C2×C4×C61C4×D4semidirect
533. C2×C4×C61#121semidirect
668. C2×D61#386semidirect
686. C2×#386D61semidirect
760. C61#14023semidirect
784. C22×D4C4×D61semidirect
882. #95C22⋊D61semidirect
1285. C2×C4C4×C22⋊D61semidirect
1286. C2×C4#14519748semidirect

Maximal subgroups

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

subgroupindex
C22×#145197482
C22×C4×C22⋊D612
C2×#168396382
C2×#95×D612
#214440712
#214440662
#214440622
#214440602
#214440562
#214440532
#214440422
#214440402
C2×C61×#3862
#1402361