Finite Group Databasebeta

← #29601511

Subgroups — #29601511

Order 15616.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C2×#16839641C211yesmaximal, characteristic
3C2×#16839639C211yesmaximal, characteristic
4C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
5C2×C4×#11758198C211yesmaximal, characteristic, complemented
6C22×#14519684C211yesmaximal, characteristic, complemented
7#21444057C211yesmaximal, characteristic, complemented
8#21444055C211yesmaximal, characteristic, complemented
9#21444054C211yesmaximal, characteristic, complemented
10#21444052C211yesmaximal, characteristic, complemented
11#21444043C211yesmaximal, characteristic, complemented
12#21444041C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14C4×#14519684C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519737—24no—
21C2×#14519737—24no—
22C2×#14519737C418yescomplemented
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839641C418yescomplemented
34#16839639C418yescomplemented
35C22⋊C4×Dic61—24no—
36C4×#11758198—24no—
37C2×#14519684—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
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C24×C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C42×C61C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic
57C4×C22⋊C4×C61—24no—
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⋊D61C2×C414yes—
67C22×C22⋊D61C2×C414yes—
68C23×Dic61—22no—
69C23×Dic61—22no—
70C23×Dic61—22no—
71C23×Dic61—22no—
72C23×Dic61—22no—
73C23×Dic61—22no—
74C23×Dic61—22no—
75C23×Dic61—22no—
76C23×Dic61—41no—
77C23×Dic61—41no—
78C23×Dic61—41no—
79C23×Dic61—41no—
80C23×Dic61C2×C414yes—
81C23×Dic61C2×C414yescomplemented
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—41no—
94C22×C4×D61—41no—
95C22×C4×D61C2×C414yescomplemented
96#14519737—232no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196C2×C414yescomplemented
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—22no—
102C2×C22⋊Dic61C2×C414yescomplemented
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198C2×C414yescomplemented
114C2×#11758198C2×C414yescomplemented
115C2×#11758198C2×C414yescomplemented
116C2×#11758198C2×C414yescomplemented
117C2×#11758198C2×C414yescomplemented
118C2×C4×Dic61—22no—
119C2×C4×Dic61—22no—
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61—22no—
123C2×C4×Dic61—22no—
124C2×C4×Dic61—41no—
125C2×C4×Dic61—41no—
126C2×C4×Dic61C2×C414yescomplemented
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—41no—
135#14519684—41no—
136#14519684C2×C414yescomplemented
137#14519684C2×C414yescomplemented
138#14519684C2×C414yescomplemented
139#14519684C2×C414yescomplemented
140#14519684D414yescomplemented
141C25×C61C2311yescharacteristic
142C23×C4×C61—22no—
143C23×C4×C61—22no—
144C23×C4×C61—22no—
145C23×C4×C61—22no—
146C23×C4×C61—41no—
147C23×C4×C61—41no—
148C23×C4×C61C2×C414yescomplemented
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61C2×C414yes—
158C2×C22⋊C4×C61C2×C414yescomplemented
159C2×C22⋊C4×C61D414yes—
160C2×C22⋊C4×C61D414yes—
161C2×C42×C61—22no—
162C2×C42×C61—22no—
163C2×C42×C61—22no—
164C2×C42×C61—22no—
165C2×C42×C61—41no—
166C2×C42×C61—41no—
167#95×C61—22no—
168#95×C61—22no—
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×C61C22×C412yes—
178C24×C61C22×C412yes—
179C24×C61C22×C412yes—
180C24×C61C2×D412yes—
181C24×C61C2×D412yes—
182C24×C61#4112yes—
183C24×C61#4112yes—
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×D61C22×C412yes—
199C23×D61C22×C412yes—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
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—28no—
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—28no—
232C22×C4×C61—44no—
233C22×C4×C61—44no—
234C22×C4×C61—44no—
235C22×C4×C61—44no—
236C22×C4×C61—44no—
237C22×C4×C61C22×C412yes—
238C22×C4×C61C22×C412yes—
239C22×C4×C61C22×C412yes—
240C22×C4×C61C22×C412yes—
241C22×C4×C61C22×C412yes—
242C22×C4×C61C22×C412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×D412yes—
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⋊D61C42116yescomplemented
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—28no—
269C22×Dic61—28no—
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×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61—28no—
295C22×Dic61—28no—
296C22×Dic61—44no—
297C22×Dic61—44no—
298C22×Dic61—44no—
299C22×Dic61—44no—
300C22×Dic61—44no—
301C22×Dic61—44no—
302C22×Dic61—44no—
303C22×Dic61—44no—
304C22×Dic61—44no—
305C22×Dic61—44no—
306C22×Dic61C22×C412yes—
307C22×Dic61C22×C412yes—
308C22×Dic61C22×C412yes—
309C22×Dic61C22×C412yes—
310C22×Dic61C22×C412yes—
311C22×Dic61C22×C412yes—
312C22×Dic61C22×C412yes—
313C22×Dic61C22×C412yes—
314C22×Dic61C22×C412yes—
315C22×Dic61C2×D412yes—
316C22×Dic61C2×D412yes—
317C22×Dic61#4112yes—
318C22×Dic61#4112yes—
319C2×C4×D61—28no—
320C2×C4×D61—28no—
321C2×C4×D61—44no—
322C2×C4×D61—44no—
323C2×C4×D61—44no—
324C2×C4×D61—44no—
325C2×C4×D61—44no—
326C22⋊C4×C61—28no—
327C22⋊C4×C61C22⋊C4116yescomplemented
328C42×C61—44no—
329C42×C61—44no—
330C22⋊Dic61—28no—
331#11758198—28no—
332#11758198—28no—
333#11758198—28no—
334#11758198—44no—
335#11758198—44no—
336#11758196—28no—
337C4×Dic61—28no—
338C4×Dic61—44no—
339C4×Dic61—44no—
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—22no—
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×C61C2×C4214yes—
369C23×C61C2×C22⋊C414yes—
370C23×C61#11714yes—
371C23×C61C4×D414yes—
372C23×C61C4×D414yes—
373C23×C61C4×D414yes—
374C23×C61C4×D414yes—
375C23×C61C23×C411yescharacteristic
376C23×C61C23×C411yescharacteristic
377C23×C61C23×C411yescharacteristic
378C23×C61C22×D411yescharacteristic
379C23×C61C22×D411yescharacteristic
380C23×C61C22×D411yescharacteristic
381C23×C61C2×#4111yescharacteristic
382C23×C61C2×#4111yescharacteristic
383C23×C61C2×#4111yescharacteristic
384C23×C61C2×#4111yescharacteristic
385C23×C61C2×#4111yescharacteristic
386C23×C61H(5,𝔽2)11yescharacteristic
387C23×C61H(5,𝔽2)11yescharacteristic
388C23×C61H(5,𝔽2)11yescharacteristic
389C23×C612−1+411yescharacteristic
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—22no—
401C22×D61—22no—
402C22×D61—22no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
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×D61—41no—
417C22×D61—41no—
418C22×D61—41no—
419C22×D61—41no—
420C22×D61—41no—
421C22×D61—41no—
422C22×D61—41no—
423C22×D61—41no—
424C22×D61C2×C4214yes—
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—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—22no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—22no—
443C2×C4×C61—22no—
444C2×C4×C61—22no—
445C2×C4×C61—22no—
446C2×C4×C61—22no—
447C2×C4×C61—22no—
448C2×C4×C61—22no—
449C2×C4×C61—22no—
450C2×C4×C61—22no—
451C2×C4×C61—22no—
452C2×C4×C61—416no—
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—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61C2×C22⋊C414yes—
466C2×C4×C61C2×C22⋊C414yes—
467C2×C4×C61C4×D414yescomplemented
468C22⋊D61—232no—
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—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—22no—
485C2×Dic61—22no—
486C2×Dic61—22no—
487C2×Dic61—22no—
488C2×Dic61—22no—
489C2×Dic61—22no—
490C2×Dic61—22no—
491C2×Dic61—22no—
492C2×Dic61—22no—
493C2×Dic61—22no—
494C2×Dic61—22no—
495C2×Dic61—22no—
496C2×Dic61—22no—
497C2×Dic61—22no—
498C2×Dic61—22no—
499C2×Dic61—416no—
500C2×Dic61—416no—
501C2×Dic61—41no—
502C2×Dic61—41no—
503C2×Dic61—41no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61—41no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61—41no—
514C2×Dic61—41no—
515C2×Dic61—41no—
516C2×Dic61—41no—
517C2×Dic61C2×C4214yes—
518C2×Dic61C4×D414yes—
519C2×Dic61C4×D414yescomplemented
520C4×D61—416no—
521#13813—611nomaximal, Sylow
522C22×C61—24no—
523C22×C61—24no—
524C22×C61—24no—
525C22×C61—24no—
526C22×C61—24no—
527C22×C61—24no—
528C22×C61—24no—
529C22×C61—24no—
530C22×C61—24no—
531C22×C61—24no—
532C22×C61—24no—
533C22×C61—24no—
534C22×C61—24no—
535C22×C61—24no—
536C22×C61C4×C22⋊C418yescomplemented
537C22×C61C22×C4211yescharacteristic
538C22×C61C22×C22⋊C411yescharacteristic
539C22×C61C2×#11711yescharacteristic
540C22×C61C2×C4×D411yescharacteristic
541C22×C61C2×C4×D411yescharacteristic
542C22×C61C2×C4×D411yescharacteristic
543C22×C61C2×C4×D411yescharacteristic
544C22×C61C2×C4×D411yescharacteristic
545C22×C61C2×C4×D411yescharacteristic
546C22×C61C2×C4×D411yescharacteristic
547C22×C61C4×#4111yescharacteristic
548C22×C61C4×#4111yescharacteristic
549C22×C61C4×#4111yescharacteristic
550C22×C61#51811yescharacteristic
551C22×C61#51811yescharacteristic
552C22×C61#51811yescharacteristic
553C22×C61#52011yescharacteristic
554C22×C61#52011yescharacteristic
555C22×C61#52011yescharacteristic
556C22×C61D4211yescharacteristic
557C22×C61D4211yescharacteristic
558C22×C61#54611yescharacteristic
559C22×C61#54611yescharacteristic
560C22×C61#54611yescharacteristic
561C22×C61#54611yescharacteristic
562C22×C61#54611yescharacteristic
563C22×C61#54711yescharacteristic
564C22×C61#54711yescharacteristic
565C22×C61#54811yescharacteristic
566C22×C61#55111yescharacteristic
567C22×C61#55111yescharacteristic
568C22×C61#55211yescharacteristic
569C22×C61#55311yescharacteristic
570C22×C61#55311yescharacteristic
571C22×C61#55311yescharacteristic
572C2×D61—24no—
573C2×D61—24no—
574C2×D61—24no—
575C2×D61—42no—
576C2×D61—42no—
577C2×D61—42no—
578C2×D61—42no—
579C2×D61—42no—
580C2×D61—42no—
581C2×D61—42no—
582C2×D61—42no—
583C2×D61—42no—
584C2×D61—42no—
585C2×D61—42no—
586C2×D61—42no—
587C4×C61—24no—
588C4×C61—24no—
589C4×C61—24no—
590C4×C61—42no—
591C4×C61—42no—
592C4×C61—42no—
593Dic61—24no—
594Dic61—24no—
595Dic61—24no—
596Dic61—42no—
597Dic61—42no—
598Dic61—42no—
599Dic61—42no—
600C22×C4×D4—611no—
601C2×#386—611no—
602C2×#386—611no—
603C2×C4×C22⋊C4—611no—
604C2×C4×C22⋊C4—611no—
605C2×C4×C22⋊C4D6111yescharacteristic, complemented
606C22×#95—611no—
607#1437—611no—
608#1437—611no—
609#1436—611no—
610#1436—611no—
611#1434—611no—
612C22⋊#95—611no—
613C22⋊#95—611no—
614C4×#95—611no—
615C2×C61—28no—
616C2×C61C2×C4×C22⋊C411yescharacteristic
617C2×C61C42×D411yescharacteristic
618C2×C61#227511yescharacteristic
619C2×C61D4×C22⋊C411yescharacteristic
620C2×C61#233911yescharacteristic
621C2×C61#235211yescharacteristic
622C2×C61#235311yescharacteristic
623C2×C61#235811yescharacteristic
624C2×C61#235811yescharacteristic
625C2×C61#235911yescharacteristic
626C2×C61#235911yescharacteristic
627C2×C61#236111yescharacteristic
628C2×C61#236111yescharacteristic
629C2×C61#236411yescharacteristic
630C2×C61#236411yescharacteristic
631D61—44no—
632C23×D4—611no—
633C24×C4—611no—
634C24×C4—611no—
635C24×C4—611no—
636C24×C4C2×D6111yescharacteristic
637C2×C4×D4—618no—
638C2×C4×D4—1224no—
639C2×C4×D4—1224no—
640C22×C4⋊C4—611no—
641C22×C22⋊C4—611no—
642C22×C22⋊C4—611no—
643C22×C22⋊C4—611no—
644C22×C22⋊C4—611no—
645C22×C22⋊C4—611no—
646C22×C22⋊C4—611no—
647C22×C22⋊C4C2×D6111yescharacteristic
648C22×C22⋊C4C2×D6111yescharacteristic
649C22×C42—611no—
650C22×C42—611no—
651C22×C42—611no—
652C22×C42C2×D6111yescharacteristic
653C22×C42C2×D6111yescharacteristic
654#386—618no—
655#386—618no—
656C4×C22⋊C4—24no—
657C4×C22⋊C4—1224no—
658C4×C22⋊C4—1224no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95—611no—
663C2×#95—611no—
664C2×#95—611no—
665C2×#95—611no—
666C2×#95—611no—
667C2×#95—611no—
668C2×#95—611no—
669C2×#95—611no—
670C2×#95—611no—
671C2×#95—611no—
672C2×#95—611no—
673C2×#95—1224no—
674C2×#95C2×D6111yescharacteristic
675C2×#95C2×D6111yescharacteristic
676C61#1381311yescharacteristic, complemented, Sylow
677C25—611no—
678C25C22×D6111yescharacteristic
679C22×D4—614no—
680C22×D4—614no—
681C22×D4—614no—
682C22×D4—1222no—
683C22×D4—1222no—
684C22×D4—1222no—
685C22×D4—1222no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—611no—
693C23×C4—611no—
694C23×C4—611no—
695C23×C4—611no—
696C23×C4—611no—
697C23×C4—611no—
698C23×C4—611no—
699C23×C4—614no—
700C23×C4—614no—
701C23×C4—614no—
702C23×C4—1222no—
703C23×C4—1222no—
704C23×C4—1222no—
705C23×C4—1222no—
706C23×C4—1222no—
707C23×C4—1222no—
708C23×C4—1222no—
709C23×C4—1222no—
710C23×C4—1222no—
711C23×C4—1222no—
712C23×C4—1222no—
713C23×C4—1222no—
714C23×C4—2441no—
715C23×C4—2441no—
716C23×C4—2441no—
717C23×C4—2441no—
718C23×C4—2441no—
719C23×C4—2441no—
720C23×C4C4×D6114yescomplemented
721C23×C4C22×D6111yescharacteristic
722C23×C4C22×D6111yescharacteristic
723C23×C4C22×D6111yescharacteristic
724C23×C4C22×D6111yescharacteristic
725C23×C4C22×D6111yescharacteristic
726C23×C4C22×D6111yescharacteristic
727C4×D4—12232no—
728C2×C4⋊C4—614no—
729C2×C4⋊C4—1222no—
730C2×C4⋊C4—1222no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—614no—
734C2×C22⋊C4—614no—
735C2×C22⋊C4—614no—
736C2×C22⋊C4—614no—
737C2×C22⋊C4—614no—
738C2×C22⋊C4—614no—
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—2441no—
748C2×C22⋊C4—2441no—
749C2×C22⋊C4—2441no—
750C2×C22⋊C4—2441no—
751C2×C22⋊C4C4×D6114yes—
752C2×C22⋊C4C4×D6114yescomplemented
753C2×C22⋊C4D24414yes—
754C2×C22⋊C4C22⋊D6114yes—
755C2×C42—22no—
756C2×C42—22no—
757C2×C42—22no—
758C2×C42—22no—
759C2×C42—41no—
760C2×C42—41no—
761C2×C42—614no—
762C2×C42—1222no—
763C2×C42—1222no—
764C2×C42—1222no—
765C2×C42—1222no—
766C2×C42—1222no—
767C2×C42—1222no—
768C2×C42—2441no—
769C2×C42—2441no—
770#95—22no—
771#95—22no—
772#95—614no—
773#95—614no—
774#95—614no—
775#95—614no—
776#95—614no—
777#95—1222no—
778#95—1222no—
779#95—1222no—
780#95—1222no—
781#95—1222no—
782#95—1222no—
783#95—1222no—
784#95—2441no—
785#95—2441no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—612no—
795C24—612no—
796C24—612no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24—1221no—
801C24—1221no—
802C24—1221no—
803C24—1221no—
804C24—1221no—
805C24—1221no—
806C24—1221no—
807C24—1221no—
808C24—1221no—
809C24C2×C4×D6112yes—
810C24C2×C4×D6112yes—
811C24C2×C4×D6112yes—
812C24C2×D24412yes—
813C24#1175822212yes—
814C24#1175822212yes—
815C24C2×C22⋊D6112yes—
816C24C23×D6111yescharacteristic
817C2×D4—6116no—
818C2×D4—1228no—
819C2×D4—1228no—
820C2×D4—1228no—
821C2×D4—1228no—
822C2×D4—1228no—
823C2×D4—1228no—
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—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
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—612no—
871C22×C4—612no—
872C22×C4—612no—
873C22×C4—612no—
874C22×C4—1228no—
875C22×C4—1228no—
876C22×C4—1228no—
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—1221no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1221no—
911C22×C4—1221no—
912C22×C4—1221no—
913C22×C4—1228no—
914C22×C4—1228no—
915C22×C4—1228no—
916C22×C4—2444no—
917C22×C4—2444no—
918C22×C4—2444no—
919C22×C4—2444no—
920C22×C4—2444no—
921C22×C4—2444no—
922C22×C4—2444no—
923C22×C4—2444no—
924C22×C4—2444no—
925C22×C4—2444no—
926C22×C4—2444no—
927C22×C4—2444no—
928C22×C4—2444no—
929C22×C4—2444no—
930C22×C4—2444no—
931C22×C4C2×C4×D6112yes—
932C22×C4C2×C4×D6112yes—
933C22×C4C2×C4×D6112yes—
934C22×C4C2×C4×D6112yes—
935C22×C4C2×C4×D6112yes—
936C22×C4C2×C4×D6112yes—
937C22×C4C2×D24412yes—
938C22×C4C2×D24412yes—
939C22×C4D4×D6112yes—
940C22×C4#1175822412yes—
941C22×C4C2×C22⋊D6112yes—
942C22×C4C2×C22⋊D6112yes—
943C4⋊C4—1228no—
944C22⋊C4—28no—
945C22⋊C4—1228no—
946C22⋊C4—1228no—
947C22⋊C4—1228no—
948C22⋊C4—1228no—
949C22⋊C4—2444no—
950C22⋊C4—2444no—
951C22⋊C4#11758198116yescomplemented
952C42—44no—
953C42—44no—
954C42—1228no—
955C42—2444no—
956C42—2444no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—614no—
986C23—1222no—
987C23—1222no—
988C23—1222no—
989C23—1222no—
990C23—1222no—
991C23—1222no—
992C23—1222no—
993C23—1222no—
994C23—1222no—
995C23—1222no—
996C23—1222no—
997C23—1222no—
998C23—1222no—
999C23—1222no—
1000C23—1222no—
1001C23—1222no—
1002C23—1222no—
1003C23—1222no—
1004C23—2441no—
1005C23—2441no—
1006C23—2441no—
1007C23—2441no—
1008C23—2441no—
1009C23—2441no—
1010C23—2441no—
1011C23—2441no—
1012C23—2441no—
1013C23—2441no—
1014C23—2441no—
1015C23—2441no—
1016C23—2441no—
1017C23—2441no—
1018C23—2441no—
1019C23—2441no—
1020C23C42×D6114yes—
1021C23C2×#1175819814yes—
1022C23#1451973414yes—
1023C23C4×C22⋊D6114yes—
1024C23C4×C22⋊D6114yes—
1025C23C4×D24414yes—
1026C23C4×D24414yes—
1027C23C22×C4×D6111yescharacteristic
1028C23C22×C4×D6111yescharacteristic
1029C23C22×C4×D6111yescharacteristic
1030C23C2×D4×D6111yescharacteristic
1031C23C22×C22⋊D6111yescharacteristic
1032C23C22×D24411yescharacteristic
1033C23#41×D6111yescharacteristic
1034C23#41×D6111yescharacteristic
1035C23C2×#1175822411yescharacteristic
1036C23C2×#1175822211yescharacteristic
1037C23C2×#1175822211yescharacteristic
1038C23#1451982211yescharacteristic
1039C23#1451982211yescharacteristic
1040C23#1451982311yescharacteristic
1041C23#1451982411yescharacteristic
1042D4—12232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—416no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—614no—
1084C2×C4—614no—
1085C2×C4—614no—
1086C2×C4—1222no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—1222no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—1222no—
1098C2×C4—1222no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—1222no—
1104C2×C4—1222no—
1105C2×C4—1222no—
1106C2×C4—1222no—
1107C2×C4—1222no—
1108C2×C4—1222no—
1109C2×C4—1222no—
1110C2×C4—1222no—
1111C2×C4—1222no—
1112C2×C4—1222no—
1113C2×C4—1222no—
1114C2×C4—1222no—
1115C2×C4—1222no—
1116C2×C4—24416no—
1117C2×C4—24416no—
1118C2×C4—24416no—
1119C2×C4—2441no—
1120C2×C4—2441no—
1121C2×C4—2441no—
1122C2×C4—2441no—
1123C2×C4—2441no—
1124C2×C4—2441no—
1125C2×C4—2441no—
1126C2×C4—2441no—
1127C2×C4—2441no—
1128C2×C4—2441no—
1129C2×C4—2441no—
1130C2×C4—2441no—
1131C2×C4—2441no—
1132C2×C4—2441no—
1133C2×C4—2441no—
1134C2×C4—2441no—
1135C2×C4C2×#1175819814yes—
1136C2×C4C2×#1175819814yes—
1137C2×C4#1451973714yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—1224no—
1153C22—1224no—
1154C22—1224no—
1155C22—2442no—
1156C22—2442no—
1157C22—2442no—
1158C22—2442no—
1159C22—2442no—
1160C22—2442no—
1161C22—2442no—
1162C22—2442no—
1163C22—2442no—
1164C22—2442no—
1165C22—2442no—
1166C22—2442no—
1167C22C4×#1175819818yescomplemented
1168C22C2×C42×D6111yescharacteristic
1169C22C22×#1175819811yescharacteristic
1170C22C2×#1451973411yescharacteristic
1171C22C4×D4×D6111yescharacteristic
1172C22C4×D4×D6111yescharacteristic
1173C22C2×#1451973711yescharacteristic
1174C22C2×C4×C22⋊D6111yescharacteristic
1175C22C2×C4×C22⋊D6111yescharacteristic
1176C22C2×C4×D24411yescharacteristic
1177C22C2×C4×D24411yescharacteristic
1178C22C4×#1175822411yescharacteristic
1179C22C4×#1175822411yescharacteristic
1180C22#1684023011yescharacteristic
1181C22#1684023411yescharacteristic
1182C22#1684023411yescharacteristic
1183C22#1684023511yescharacteristic
1184C22#1684024111yescharacteristic
1185C22#1684024111yescharacteristic
1186C22#1684024211yescharacteristic
1187C22D4×C22⋊D6111yescharacteristic
1188C22D4×D24411yescharacteristic
1189C22#1684040011yescharacteristic
1190C22#1684040211yescharacteristic
1191C22#1684040611yescharacteristic
1192C22#1684040711yescharacteristic
1193C22#1684040711yescharacteristic
1194C22#1684041111yescharacteristic
1195C22#1684041611yescharacteristic
1196C22#1684042111yescharacteristic
1197C22#1684043611yescharacteristic
1198C22#1684043811yescharacteristic
1199C22#1684044511yescharacteristic
1200C22#1684045811yescharacteristic
1201C22#1684046111yescharacteristic
1202C22#1684046111yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—1224no—
1210C4—1224no—
1211C4—1224no—
1212C4—2442no—
1213C4—2442no—
1214C4—2442no—
1215C4—2442no—
1216C2—28no—
1217C2—2444no—
1218C2C2×C4×#1175819811yescharacteristic
1219C2C4×#1451973711yescharacteristic
1220C2#2144817811yescharacteristic
1221C2D4×#1175819811yescharacteristic
1222C2#2144864411yescharacteristic
1223C2#2144874211yescharacteristic
1224C2#2144875311yescharacteristic
1225C2#2144879811yescharacteristic
1226C2#2144880111yescharacteristic
1227C2#2144881111yescharacteristic
1228C2#2144881311yescharacteristic
1229C2#2144883311yescharacteristic
1230C2#2144883611yescharacteristic
1231C2#2144886411yescharacteristic
1232C2#2144886911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#13813
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic61C2semidirect
5. C2×C4×#11758198C2semidirect
6. C22×#14519684C2semidirect
7. #21444057C2semidirect
8. #21444055C2semidirect
9. #21444054C2semidirect
10. #21444052C2semidirect
11. #21444043C2semidirect
12. #21444041C2semidirect
13. #21444040C2semidirect
14. C4×#14519684C2semidirect
15. C2×C4×C22⋊C4×C61C2semidirect
22. C2×#14519737C4semidirect
33. #16839641C4semidirect
34. #16839639C4semidirect
81. C23×Dic61C2×C4semidirect
95. C22×C4×D61C2×C4semidirect
99. C2×#11758196C2×C4semidirect
102. C2×C22⋊Dic61C2×C4semidirect
113. C2×#11758198C2×C4semidirect
114. C2×#11758198C2×C4semidirect
115. C2×#11758198C2×C4semidirect
116. C2×#11758198C2×C4semidirect
117. C2×#11758198C2×C4semidirect
126. C2×C4×Dic61C2×C4semidirect
136. #14519684C2×C4semidirect
137. #14519684C2×C4semidirect
138. #14519684C2×C4semidirect
139. #14519684C2×C4semidirect
140. #14519684D4semidirect
148. C23×C4×C61C2×C4semidirect
158. C2×C22⋊C4×C61C2×C4semidirect
255. C2×C22⋊D61C42semidirect
327. C22⋊C4×C61C22⋊C4semidirect
467. C2×C4×C61C4×D4semidirect
519. C2×Dic61C4×D4semidirect
536. C22×C61C4×C22⋊C4semidirect
605. C2×C4×C22⋊C4D61semidirect
676. C61#13813semidirect
720. C23×C4C4×D61semidirect
752. C2×C22⋊C4C4×D61semidirect
951. C22⋊C4#11758198semidirect
1137. C2×C4#14519737semidirect
1167. C22C4×#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396412
C2×#168396392
C2×C22⋊C4×Dic612
C2×C4×#117581982
C22×#145196842
#214440572
#214440552
#214440542
#214440522
#214440432
#214440412
#214440402
C4×#145196842
C2×C4×C22⋊C4×C612
#1381361