Finite Group Databasebeta

← #29603409

Subgroups — #29603409

Order 15616.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic
3C2×#16839662C211yesmaximal, characteristic
4C2×#16839659C211yesmaximal, characteristic, complemented
5C2×#16839636C211yesmaximal, characteristic, complemented
6C2×#16839635C211yesmaximal, characteristic, complemented
7C2×#16839613C211yesmaximal, characteristic, complemented
8#21444064C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444063C211yesmaximal, characteristic, complemented
11#21444062C211yesmaximal, characteristic, complemented
12#21444047C211yesmaximal, characteristic, complemented
13#21444047C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C2×C4×C22⋊D61—24no—
19C2×C4×C22⋊D61—24no—
20C2×C4×C22⋊D61—24no—
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39#16839662—24no—
40#16839662C418yescomplemented
41#16839659—24no—
42#16839636—24no—
43#16839635—24no—
44#16839613—24no—
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C24×C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61C2×C414yes—
66C22×C22⋊D61D414yes—
67C22×C22⋊D61Q814yes—
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C4×C22⋊D61—232no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—41no—
86C2×#11758196—22no—
87C2×#11758196—22no—
88C2×#11758196—22no—
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196—22no—
93C2×#11758196—22no—
94C2×#11758196—22no—
95C2×#11758196—22no—
96C2×#11758196—22no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—22no—
100C2×#11758196—41no—
101C2×#11758196C2×C414yescomplemented
102C2×#11758196D414yes—
103C2×#11758196D414yescomplemented
104C2×C22⋊Dic61—22no—
105C2×C22⋊Dic61—22no—
106C2×C22⋊Dic61—22no—
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
109C2×C22⋊Dic61—22no—
110C2×C22⋊Dic61—22no—
111C2×C22⋊Dic61—41no—
112C2×C22⋊Dic61C2×C414yescomplemented
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—22no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×#11758198—22no—
122C2×#11758198—41no—
123C2×#11758198—41no—
124C2×#11758198—41no—
125C2×#11758198—41no—
126C2×#11758198C2×C414yescomplemented
127C2×#11758198C2×C414yescomplemented
128C2×C4×Dic61—22no—
129C2×C4×Dic61—22no—
130C2×C4×Dic61—22no—
131C2×C4×Dic61—22no—
132C2×C4×Dic61—22no—
133C2×C4×Dic61—22no—
134C2×C4×Dic61—22no—
135C2×C4×Dic61C2×C414yescomplemented
136C2×C4×Dic61D414yes—
137#14519684—22no—
138#14519684—22no—
139#14519684—22no—
140#14519684—22no—
141#14519684—22no—
142#14519684—41no—
143#14519684—41no—
144#14519684—41no—
145C25×C61C2311yescharacteristic
146C23×C4×C61—22no—
147C23×C4×C61—22no—
148C23×C4×C61—22no—
149C23×C4×C61—22no—
150C23×C4×C61—22no—
151C23×C4×C61—41no—
152C23×C4×C61—41no—
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C2×C22⋊C4×C61—22no—
160C2×C22⋊C4×C61—22no—
161C2×C22⋊C4×C61—41no—
162C2×C22⋊C4×C61—41no—
163C2×C22⋊C4×C61—41no—
164C2×C22⋊C4×C61C2×C414yescomplemented
165#95×C61—22no—
166#95×C61—22no—
167#95×C61—22no—
168#95×C61—41no—
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×C61C22×C412yes—
182C24×C61C2×D412yes—
183C24×C61C2×Q812yes—
184C24×C61C2411yescharacteristic
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61C22×C412yes—
198C23×D61C2×D412yes—
199C23×D61C2×Q812yes—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—28no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—44no—
237C22×C4×C61—44no—
238C22×C4×C61—44no—
239C22×C4×C61—44no—
240C22×C4×C61—44no—
241C22×C4×C61—44no—
242C22×C4×C61C22×C412yes—
243C22×C4×C61C22×C412yes—
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61#4112yes—
248C22×C4×C61#4112yes—
249C2×C22⋊D61—28no—
250C2×C22⋊D61—28no—
251C2×C22⋊D61—28no—
252C2×C22⋊D61—28no—
253C2×C22⋊D61—28no—
254C2×C22⋊D61—28no—
255C2×C22⋊D61C4⋊C4116yescomplemented
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×Dic61—21no—
272C22×Dic61—21no—
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×Dic61C22×C412yes—
292C22×Dic61C22×C412yes—
293C22×Dic61C22×C412yes—
294C22×Dic61C2×D412yes—
295C22×Dic61C2×D412yes—
296C22×Dic61C2×D412yes—
297C22×Dic61C2×D412yes—
298C22×Dic61C2×D412yes—
299C22×Dic61C2×D412yes—
300C22×Dic61C2×D412yes—
301C22×Dic61C2×Q812yes—
302C22×Dic61#4112yes—
303C22×Dic61#4112yes—
304C22×Dic61#4112yes—
305C2×C4×D61—28no—
306C2×C4×D61—44no—
307C2×C4×D61—44no—
308C2×C4×D61—44no—
309C2×C4×D61—44no—
310C2×C4×D61—44no—
311C2×C4×D61—44no—
312C22⋊C4×C61—44no—
313C22⋊C4×C61—44no—
314C22⋊Dic61—28no—
315C22⋊Dic61—28no—
316C22⋊Dic61—44no—
317#11758198—28no—
318#11758198—28no—
319#11758198—44no—
320#11758198—44no—
321#11758198—44no—
322C4⋊Dic61—44no—
323#11758196—28no—
324#11758196—28no—
325#11758196—28no—
326#11758196—28no—
327#11758196—44no—
328#11758196—44no—
329C4×Dic61—28no—
330C4×Dic61—28no—
331C4×Dic61—44no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61C2×C4⋊C414yes—
367C23×C61C23×C411yescharacteristic
368C23×C61C22×D411yescharacteristic
369C23×C61C22×D411yescharacteristic
370C23×C61C22×D411yescharacteristic
371C23×C61C22×D411yescharacteristic
372C23×C61C22×Q811yescharacteristic
373C23×C61C2×#4111yescharacteristic
374C23×C61C2×#4111yescharacteristic
375C23×C61C2×#4111yescharacteristic
376C23×C61C2×#4111yescharacteristic
377C23×C61C2×#4111yescharacteristic
378C23×C61H(5,𝔽2)11yescharacteristic
379C23×C61H(5,𝔽2)11yescharacteristic
380C23×C61H(5,𝔽2)11yescharacteristic
381C23×C612−1+411yescharacteristic
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61—41no—
408C22×D61—41no—
409C22×D61—41no—
410C22×D61—41no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61C2×C4⋊C414yes—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—416no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61#12114yes—
460C22⋊D61—232no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—22no—
472C2×Dic61—22no—
473C2×Dic61—22no—
474C2×Dic61—22no—
475C2×Dic61—22no—
476C2×Dic61—22no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C2×Dic61—41no—
499C2×Dic61—41no—
500C2×Dic61—41no—
501C2×Dic61—41no—
502C2×Dic61C2×C4⋊C414yes—
503C2×Dic61C4×D414yes—
504C2×Dic61C4×D414yes—
505C2×Dic61C4×D414yescomplemented
506C2×Dic61#12014yes—
507C2×Dic61C22⋊Q814yes—
508C2×Dic61C22⋊Q814yes—
509C2×Dic61#12314yes—
510C4×D61—416no—
511#14018—611nomaximal, Sylow
512C22×C61—24no—
513C22×C61—24no—
514C22×C61—24no—
515C22×C61—42no—
516C22×C61—42no—
517C22×C61—42no—
518C22×C61—42no—
519C22×C61—42no—
520C22×C61—42no—
521C22×C61—42no—
522C22×C61—42no—
523C22×C61—42no—
524C22×C61—42no—
525C22×C61—42no—
526C22×C61—42no—
527C22×C61C22×C4⋊C411yescharacteristic
528C22×C61C2×C4×D411yescharacteristic
529C22×C61C2×C4×D411yescharacteristic
530C22×C61C2×C4×D411yescharacteristic
531C22×C61C4×#4111yescharacteristic
532C22×C61#51811yescharacteristic
533C22×C61#52011yescharacteristic
534C22×C61C2×#12011yescharacteristic
535C22×C61C2×#12111yescharacteristic
536C22×C61C2×C22⋊Q811yescharacteristic
537C22×C61C2×C22⋊Q811yescharacteristic
538C22×C61C2×#12311yescharacteristic
539C22×C61#52511yescharacteristic
540C22×C61#52911yescharacteristic
541C22×C61#53211yescharacteristic
542C22×C61#53511yescharacteristic
543C22×C61#53711yescharacteristic
544C22×C61#54011yescharacteristic
545C22×C61#54211yescharacteristic
546C22×C61D4211yescharacteristic
547C22×C61D4211yescharacteristic
548C22×C61#54611yescharacteristic
549C22×C61#54611yescharacteristic
550C22×C61#54611yescharacteristic
551C22×C61#54711yescharacteristic
552C22×C61#54811yescharacteristic
553C22×C61D4×Q811yescharacteristic
554C22×C61#55011yescharacteristic
555C22×C61#55011yescharacteristic
556C22×C61#55411yescharacteristic
557C22×C61#55411yescharacteristic
558C22×C61#55411yescharacteristic
559C22×C61#55611yescharacteristic
560C22×C61#55911yescharacteristic
561C22×C61#55911yescharacteristic
562C2×D61—24no—
563C2×D61—24no—
564C2×D61—24no—
565C2×D61—42no—
566C2×D61—42no—
567C2×D61—42no—
568C2×D61—42no—
569C2×D61—42no—
570C2×D61—42no—
571C2×D61—42no—
572C2×D61—42no—
573C2×D61—42no—
574C2×D61—42no—
575C2×D61—42no—
576C2×D61—42no—
577C4×C61—24no—
578C4×C61—42no—
579C4×C61—42no—
580C4×C61—42no—
581C4×C61—42no—
582C4×C61—81no—
583Dic61—24no—
584Dic61—42no—
585Dic61—42no—
586Dic61—42no—
587Dic61—42no—
588Dic61—81no—
589Dic61#38518yescomplemented
590C22×C4×D4—611no—
591C2×#390—611no—
592C2×#390—611no—
593C2×#389—611no—
594C2×#385—611no—
595C2×#385—611no—
596C2×C4×C4⋊C4—611no—
597#1439—611no—
598#1439—611no—
599#1439—611no—
600#1439—611no—
601C4⋊#95—611no—
602C4⋊#95—611no—
603C22⋊#95—611no—
604C22⋊#95D6111yescharacteristic, complemented
605C2×C61—44no—
606C2×C61C2×#38511yescharacteristic
607C2×C61C4×#12111yescharacteristic
608C2×C61#232411yescharacteristic
609C2×C61D4×C4⋊C411yescharacteristic
610C2×C61#234911yescharacteristic
611C2×C61#236611yescharacteristic
612C2×C61#236711yescharacteristic
613C2×C61#240711yescharacteristic
614C2×C61#240811yescharacteristic
615C2×C61#244511yescharacteristic
616C2×C61#244711yescharacteristic
617C2×C61#245211yescharacteristic
618C2×C61#245411yescharacteristic
619C2×C61#253811yescharacteristic
620C2×C61#258011yescharacteristic
621D61—44no—
622C23×D4—611no—
623C24×C4—611no—
624C24×C4C2×D6111yescharacteristic
625C2×C4×D4—1224no—
626C2×C4×D4—1224no—
627C2×C4×D4—1224no—
628C22×C4⋊C4—611no—
629C22×C4⋊C4—611no—
630C22×C4⋊C4—611no—
631C22×C4⋊C4—611no—
632C22×C4⋊C4—611no—
633C22×C4⋊C4—611no—
634C22×C4⋊C4—611no—
635C22×C22⋊C4—611no—
636C22×C22⋊C4—611no—
637C22×C22⋊C4—611no—
638C22×C22⋊C4—611no—
639C22×C22⋊C4—611no—
640C22×C22⋊C4—611no—
641C22×C22⋊C4—611no—
642C22×C22⋊C4—611no—
643C22×C22⋊C4C2×D6111yescharacteristic
644C22×C22⋊C4C2×D6111yescharacteristic
645C22×C42—611no—
646C22×C42—611no—
647C22×C42—611no—
648#390—618no—
649#390—1224no—
650#389—1224no—
651#385—1224no—
652#385—1224no—
653C4×C4⋊C4—1224no—
654C2×#95—611no—
655C2×#95—611no—
656C2×#95—611no—
657C2×#95—611no—
658C2×#95—611no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95C2×D6111yescharacteristic
663C2×#95C2×D6111yescharacteristic
664C2×#95C2×D6111yescharacteristic
665C2×#95C2×D6111yescharacteristic
666C61#1401811yescharacteristic, complemented, Sylow
667C25—611no—
668C25C22×D6111yescharacteristic
669C22×D4—614no—
670C22×D4—614no—
671C22×D4—614no—
672C22×D4—1222no—
673C22×D4—1222no—
674C22×D4—1222no—
675C22×D4—1222no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—22no—
679C23×C4—22no—
680C23×C4—22no—
681C23×C4—41no—
682C23×C4—41no—
683C23×C4—611no—
684C23×C4—611no—
685C23×C4—611no—
686C23×C4—611no—
687C23×C4—611no—
688C23×C4—611no—
689C23×C4—611no—
690C23×C4—1222no—
691C23×C4—1222no—
692C23×C4—1222no—
693C23×C4—1222no—
694C23×C4—1222no—
695C23×C4—2441no—
696C23×C4—2441no—
697C23×C4C22×D6111yescharacteristic
698C23×C4C22×D6111yescharacteristic
699C23×C4C22×D6111yescharacteristic
700C23×C4C22×D6111yescharacteristic
701C23×C4C22×D6111yescharacteristic
702C23×C4C22×D6111yescharacteristic
703C4×D4—12232no—
704C2×C4⋊C4—614no—
705C2×C4⋊C4—614no—
706C2×C4⋊C4—614no—
707C2×C4⋊C4—1222no—
708C2×C4⋊C4—1222no—
709C2×C4⋊C4—1222no—
710C2×C4⋊C4—1222no—
711C2×C4⋊C4—1222no—
712C2×C4⋊C4—1222no—
713C2×C4⋊C4—1222no—
714C2×C4⋊C4—1222no—
715C2×C4⋊C4—1222no—
716C2×C4⋊C4—1222no—
717C2×C4⋊C4—1222no—
718C2×C4⋊C4—1222no—
719C2×C4⋊C4—1222no—
720C2×C4⋊C4—1222no—
721C2×C4⋊C4—1222no—
722C2×C4⋊C4—1222no—
723C2×C4⋊C4—2441no—
724C2×C4⋊C4—2441no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—614no—
731C2×C22⋊C4—614no—
732C2×C22⋊C4—614no—
733C2×C22⋊C4—1222no—
734C2×C22⋊C4—1222no—
735C2×C22⋊C4—1222no—
736C2×C22⋊C4—1222no—
737C2×C22⋊C4—1222no—
738C2×C22⋊C4—1222no—
739C2×C22⋊C4—1222no—
740C2×C22⋊C4—1222no—
741C2×C22⋊C4—1222no—
742C2×C22⋊C4—1222no—
743C2×C22⋊C4—1222no—
744C2×C22⋊C4—1222no—
745C2×C22⋊C4—1222no—
746C2×C22⋊C4—1222no—
747C2×C22⋊C4—1222no—
748C2×C22⋊C4—1222no—
749C2×C22⋊C4—2441no—
750C2×C22⋊C4—2441no—
751C2×C22⋊C4—2441no—
752C2×C22⋊C4—2441no—
753C2×C22⋊C4—2441no—
754C2×C22⋊C4C4×D6114yescomplemented
755C2×C42—614no—
756C2×C42—614no—
757C2×C42—1222no—
758C2×C42—1222no—
759C2×C42—1222no—
760C2×C42—1222no—
761C2×C42—1222no—
762C2×C42—1222no—
763C2×C42—1222no—
764#95—22no—
765#95—22no—
766#95—22no—
767#95—41no—
768#95—1222no—
769#95—1222no—
770#95—1222no—
771#95—1222no—
772#95—1222no—
773#95—2441no—
774#95—2441no—
775#95—2441no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—612no—
789C24—612no—
790C24—612no—
791C24—1221no—
792C24—1221no—
793C24—1221no—
794C24—1221no—
795C24—1221no—
796C24—1221no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24—1221no—
802C24—1221no—
803C24C2×C4×D6112yes—
804C24D4×D6112yes—
805C24Q8×D6112yes—
806C24C23×D6111yescharacteristic
807C2×D4—6116no—
808C2×D4—1228no—
809C2×D4—1228no—
810C2×D4—1228no—
811C2×D4—1228no—
812C2×D4—1228no—
813C2×D4—1228no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—28no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—612no—
857C22×C4—612no—
858C22×C4—612no—
859C22×C4—612no—
860C22×C4—612no—
861C22×C4—612no—
862C22×C4—612no—
863C22×C4—612no—
864C22×C4—612no—
865C22×C4—612no—
866C22×C4—612no—
867C22×C4—612no—
868C22×C4—612no—
869C22×C4—612no—
870C22×C4—1228no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—2444no—
907C22×C4—2444no—
908C22×C4—2444no—
909C22×C4—2444no—
910C22×C4—2444no—
911C22×C4—2444no—
912C22×C4C2×C4×D6112yes—
913C22×C4C2×C4×D6112yes—
914C22×C4#1175822212yes—
915C22×C4#1175822212yes—
916C22×C4D4×D6112yes—
917C22×C4D4×D6112yes—
918C22×C4D4×D6112yes—
919C4⋊C4—1228no—
920C4⋊C4—1228no—
921C4⋊C4—1228no—
922C4⋊C4—1228no—
923C4⋊C4—2444no—
924C4⋊C4—2444no—
925C4⋊C4—2444no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—1228no—
929C22⋊C4—1228no—
930C22⋊C4—1228no—
931C22⋊C4—1228no—
932C22⋊C4—2444no—
933C22⋊C4—2444no—
934C22⋊C4—2444no—
935C22⋊C4—2444no—
936C42—1228no—
937C42—1228no—
938C42—2444no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—614no—
974C23—1222no—
975C23—1222no—
976C23—1222no—
977C23—1222no—
978C23—1222no—
979C23—1222no—
980C23—1222no—
981C23—1222no—
982C23—1222no—
983C23—1222no—
984C23—1222no—
985C23—1222no—
986C23—1222no—
987C23—1222no—
988C23—1222no—
989C23—1222no—
990C23—1222no—
991C23—1222no—
992C23—2441no—
993C23—2441no—
994C23—2441no—
995C23—2441no—
996C23—2441no—
997C23—2441no—
998C23—2441no—
999C23—2441no—
1000C23—2441no—
1001C23—2441no—
1002C23—2441no—
1003C23—2441no—
1004C23—2441no—
1005C23—2441no—
1006C23—2441no—
1007C23—2441no—
1008C23C4⋊C4×D6114yes—
1009C23C22×C4×D6111yescharacteristic
1010C23C2×D4×D6111yescharacteristic
1011C23C2×D4×D6111yescharacteristic
1012C23C2×D4×D6111yescharacteristic
1013C23C2×D4×D6111yescharacteristic
1014C23C2×Q8×D6111yescharacteristic
1015C23#41×D6111yescharacteristic
1016C23#41×D6111yescharacteristic
1017C23#41×D6111yescharacteristic
1018C23C2×#1175822211yescharacteristic
1019C23C2×#1175822211yescharacteristic
1020C23#1451982211yescharacteristic
1021C23#1451982211yescharacteristic
1022C23#1451982211yescharacteristic
1023C23#1451982411yescharacteristic
1024D4—12232no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—416no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—614no—
1068C2×C4—614no—
1069C2×C4—614no—
1070C2×C4—614no—
1071C2×C4—614no—
1072C2×C4—614no—
1073C2×C4—614no—
1074C2×C4—614no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1222no—
1078C2×C4—1222no—
1079C2×C4—1222no—
1080C2×C4—1222no—
1081C2×C4—1222no—
1082C2×C4—1222no—
1083C2×C4—1222no—
1084C2×C4—1222no—
1085C2×C4—1222no—
1086C2×C4—1222no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—24416no—
1094C2×C4—2441no—
1095C2×C4—2441no—
1096C2×C4—2441no—
1097C2×C4—2441no—
1098C2×C4—2441no—
1099C2×C4—2441no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4—2441no—
1103C2×C4—2441no—
1104C2×C4—2441no—
1105C2×C4—2441no—
1106C2×C4—2441no—
1107C2×C4—2441no—
1108C2×C4—2441no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4—2441no—
1112C2×C4—2441no—
1113C2×C4—2441no—
1114C2×C4—2441no—
1115C2×C4—2441no—
1116C2×C4—2441no—
1117C2×C4#1451975014yes—
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—1224no—
1134C22—1224no—
1135C22—1224no—
1136C22—2442no—
1137C22—2442no—
1138C22—2442no—
1139C22—2442no—
1140C22—2442no—
1141C22—2442no—
1142C22—2442no—
1143C22—2442no—
1144C22—2442no—
1145C22—2442no—
1146C22—2442no—
1147C22—2442no—
1148C22C2×C4⋊C4×D6111yescharacteristic
1149C22C4×D4×D6111yescharacteristic
1150C22C4×D4×D6111yescharacteristic
1151C22C4×D4×D6111yescharacteristic
1152C22C4×#1175822211yescharacteristic
1153C22#1684023511yescharacteristic
1154C22#1684024111yescharacteristic
1155C22#120×D6111yescharacteristic
1156C22C2×#1451975011yescharacteristic
1157C22C22⋊Q8×D6111yescharacteristic
1158C22C22⋊Q8×D6111yescharacteristic
1159C22#123×D6111yescharacteristic
1160C22#1684027111yescharacteristic
1161C22#1684029011yescharacteristic
1162C22#1684030911yescharacteristic
1163C22#1684032711yescharacteristic
1164C22#1684034111yescharacteristic
1165C22#1684036211yescharacteristic
1166C22#1684038011yescharacteristic
1167C22#1684039411yescharacteristic
1168C22#1684039411yescharacteristic
1169C22#1684040211yescharacteristic
1170C22#1684040211yescharacteristic
1171C22#1684040211yescharacteristic
1172C22#1684041011yescharacteristic
1173C22#1684042111yescharacteristic
1174C22#1684042511yescharacteristic
1175C22#1684043011yescharacteristic
1176C22#1684043011yescharacteristic
1177C22#1684046611yescharacteristic
1178C22#1684046711yescharacteristic
1179C22#1684046711yescharacteristic
1180C22#1684048011yescharacteristic
1181C22#1684049511yescharacteristic
1182C22#1684049611yescharacteristic
1183C4—24no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—618no—
1190C4—1224no—
1191C4—4881no—
1192C4—2442no—
1193C4—2442no—
1194C4—2442no—
1195C4—2442no—
1196C2—44no—
1197C2—2444no—
1198C2#385×D6111yescharacteristic
1199C2C4×#1451975011yescharacteristic
1200C2#2144850911yescharacteristic
1201C2#2144871711yescharacteristic
1202C2#2144872611yescharacteristic
1203C2#2144888211yescharacteristic
1204C2#2144889111yescharacteristic
1205C2#2144916111yescharacteristic
1206C2#2144917411yescharacteristic
1207C2#2144958111yescharacteristic
1208C2#2144960511yescharacteristic
1209C2#2144966611yescharacteristic
1210C2#2144969011yescharacteristic
1211C2#2145074311yescharacteristic
1212C2#2145117611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22⋊#95D61
hypocenterC61#14018
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#16839659C2semidirect
5. C2×#16839636C2semidirect
6. C2×#16839635C2semidirect
7. C2×#16839613C2semidirect
8. #21444064C2semidirect
9. #21444063C2semidirect
10. #21444063C2semidirect
11. #21444062C2semidirect
12. #21444047C2semidirect
13. #21444047C2semidirect
14. #21444040C2semidirect
15. C61×C22⋊#95C2semidirect
40. #16839662C4semidirect
101. C2×#11758196C2×C4semidirect
103. C2×#11758196D4semidirect
112. C2×C22⋊Dic61C2×C4semidirect
126. C2×#11758198C2×C4semidirect
127. C2×#11758198C2×C4semidirect
135. C2×C4×Dic61C2×C4semidirect
164. C2×C22⋊C4×C61C2×C4semidirect
255. C2×C22⋊D61C4⋊C4semidirect
505. C2×Dic61C4×D4semidirect
589. Dic61#385semidirect
604. C22⋊#95D61semidirect
666. C61#14018semidirect
754. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C2×#168396622
C2×#168396592
C2×#168396362
C2×#168396352
C2×#168396132
#214440642
#214440632
#214440622
#214440472
#214440402
C61×C22⋊#952
#1401861