Finite Group Databasebeta

← #29604521

Subgroups — #29604521

Order 15616.

2690 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519749C211yesmaximal, characteristic
2C2×#16839652C211yesmaximal, characteristic, complemented
3C2×#16839638C211yesmaximal, characteristic, complemented
4C2×#16839638C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
6C2×C4×#11758198C211yesmaximal, characteristic, complemented
7#21444069C211yesmaximal, characteristic, complemented
8#21444060C211yesmaximal, characteristic, complemented
9#21444058C211yesmaximal, characteristic, complemented
10#21444058C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444056C211yesmaximal, characteristic, complemented
13#21444052C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C2×C61×#390C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519749—24no—
21C2×#14519749—24no—
22C2×#14519749C418yescomplemented
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839652—24no—
36#16839638—24no—
37#16839638—24no—
38C22⋊C4×Dic61—24no—
39C4×#11758198—24no—
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C23×D4×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C22×C42×C61C2211yescharacteristic
59C61×#390—24no—
60C24×D61C2311yescharacteristic
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
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—41no—
70C22×C22⋊D61—41no—
71C22×C22⋊D61—41no—
72C22×C22⋊D61—41no—
73C22×C22⋊D61C2×C414yes—
74C22×C22⋊D61C2×C414yes—
75C23×Dic61—22no—
76C23×Dic61—22no—
77C23×Dic61—22no—
78C23×Dic61—22no—
79C23×Dic61—41no—
80C23×Dic61—41no—
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—22no—
94C22×C4×D61—41no—
95C22×C4×D61—41no—
96#14519749—232no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196C2×C414yescomplemented
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—22no—
102C2×C22⋊Dic61—22no—
103C2×C22⋊Dic61—22no—
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—41no—
111C2×C22⋊Dic61—41no—
112C2×C22⋊Dic61—41no—
113C2×C22⋊Dic61—41no—
114C2×C22⋊Dic61C2×C414yescomplemented
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×#11758198C2×C414yes—
125C2×#11758198D414yes—
126C2×#11758198D414yes—
127C2×C4×Dic61—22no—
128C2×C4×Dic61—22no—
129C2×C4×Dic61—22no—
130C2×C4×Dic61—22no—
131C2×C4×Dic61—41no—
132C2×C4×Dic61—41no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684—22no—
140#14519684—22no—
141#14519684—22no—
142#14519684—41no—
143#14519684—41no—
144#14519684D414yescomplemented
145C25×C61C2311yescharacteristic
146C25×C61C2311yescharacteristic
147C22×D4×C61—22no—
148C22×D4×C61—22no—
149C22×D4×C61—22no—
150C22×D4×C61—22no—
151C22×D4×C61—41no—
152C22×D4×C61—41no—
153C22×D4×C61C2×C414yescomplemented
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C2×C4⋊C4×C61—22no—
160C2×C4⋊C4×C61—22no—
161C2×C4⋊C4×C61—41no—
162C2×C22⋊C4×C61—22no—
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—22no—
165C2×C22⋊C4×C61—22no—
166C2×C22⋊C4×C61—22no—
167C2×C22⋊C4×C61—22no—
168C2×C22⋊C4×C61—22no—
169C2×C22⋊C4×C61—22no—
170C2×C22⋊C4×C61—22no—
171C2×C22⋊C4×C61—41no—
172C2×C22⋊C4×C61—41no—
173C2×C22⋊C4×C61D414yescomplemented
174C2×C42×C61—22no—
175C2×C42×C61—22no—
176C2×C42×C61—41no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61—21no—
193C24×C61—21no—
194C24×C61—21no—
195C24×C61—21no—
196C24×C61—21no—
197C24×C61—21no—
198C24×C61—21no—
199C24×C61—21no—
200C24×C61—21no—
201C24×C61—21no—
202C24×C61—21no—
203C24×C61C22×C412yes—
204C24×C61C22×C412yes—
205C24×C61C2×D412yes—
206C24×C61#4112yes—
207C24×C61C2411yescharacteristic
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211C23×D61—21no—
212C23×D61—21no—
213C23×D61—21no—
214C23×D61—21no—
215C23×D61—21no—
216C23×D61—21no—
217C23×D61—21no—
218C23×D61—21no—
219C23×D61—21no—
220C23×D61C22×C412yes—
221C23×D61C2×D412yes—
222C23×D61C2×D412yes—
223C2×D4×C61—28no—
224C2×D4×C61—28no—
225C2×D4×C61—44no—
226C2×D4×C61—44no—
227C2×D4×C61—44no—
228C2×D4×C61—44no—
229C2×D4×C61—44no—
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—21no—
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—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×C61C22×C412yes—
258C22×C4×C61C2×D412yes—
259C22×C4×C61C2×D412yes—
260C22×C4×C61C2×D412yes—
261C22×C4×C61C2×D412yes—
262C22×C4×C61C2×D412yes—
263C22×C4×C61#4112yes—
264C22×C4×C61#4112yes—
265C2×C22⋊D61—28no—
266C2×C22⋊D61—28no—
267C2×C22⋊D61—28no—
268C2×C22⋊D61—28no—
269C2×C22⋊D61—44no—
270C2×C22⋊D61—44no—
271C2×C22⋊D61—44no—
272C2×C22⋊D61—44no—
273C2×C22⋊D61—44no—
274C2×C22⋊D61—44no—
275C2×C22⋊D61—44no—
276C2×C22⋊D61—44no—
277C2×C22⋊D61—44no—
278C2×C22⋊D61—44no—
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—28no—
312C22×Dic61—28no—
313C22×Dic61—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61—21no—
320C22×Dic61—44no—
321C22×Dic61—44no—
322C22×Dic61—44no—
323C22×Dic61—44no—
324C22×Dic61—44no—
325C22×Dic61C22×C412yes—
326C22×Dic61C22×C412yes—
327C22×Dic61C22×C412yes—
328C22×Dic61C2×D412yes—
329C22×Dic61C2×D412yes—
330C22×Dic61C2×D412yes—
331C22×Dic61C2×D412yes—
332C22×Dic61#4112yes—
333C22×Dic61#4112yes—
334C22×Dic61#4112yes—
335C2×C4×D61—28no—
336C2×C4×D61—44no—
337C2×C4×D61—44no—
338C2×C4×D61—44no—
339C2×C4×D61—44no—
340C2×C4×D61—44no—
341C2×C4×D61—44no—
342C4⋊C4×C61—44no—
343C22⋊C4×C61—28no—
344C22⋊C4×C61—44no—
345C22⋊C4×C61—44no—
346C22⋊C4×C61—44no—
347C42×C61—44no—
348C22⋊Dic61—28no—
349C22⋊Dic61—28no—
350C22⋊Dic61—44no—
351C22⋊Dic61—44no—
352C22⋊Dic61—44no—
353#11758198—28no—
354#11758198—44no—
355#11758198—44no—
356#11758198C22⋊C4116yescomplemented
357#11758196—28no—
358C4×Dic61—44no—
359C4×Dic61—44no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—22no—
376C23×C61—22no—
377C23×C61—22no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—41no—
388C23×C61—41no—
389C23×C61—41no—
390C23×C61—41no—
391C23×C61—41no—
392C23×C61—41no—
393C23×C61—41no—
394C23×C61—41no—
395C23×C61—41no—
396C23×C61—41no—
397C23×C61—41no—
398C23×C61—41no—
399C23×C61—41no—
400C23×C61—41no—
401C23×C61—41no—
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×C61C4×D414yes—
430C23×C61C23×C411yescharacteristic
431C23×C61C22×D411yescharacteristic
432C23×C61C22×D411yescharacteristic
433C23×C61C22×D411yescharacteristic
434C23×C61C22×D411yescharacteristic
435C23×C61C2×#4111yescharacteristic
436C23×C61C2×#4111yescharacteristic
437C23×C61C2×#4111yescharacteristic
438C23×C61C2×#4111yescharacteristic
439C23×C61C2×#4111yescharacteristic
440C23×C61C2×#4111yescharacteristic
441C23×C61H(5,𝔽2)11yescharacteristic
442C23×C61H(5,𝔽2)11yescharacteristic
443C23×C61H(5,𝔽2)11yescharacteristic
444C23×C61H(5,𝔽2)11yescharacteristic
445C22×D61—22no—
446C22×D61—22no—
447C22×D61—22no—
448C22×D61—22no—
449C22×D61—22no—
450C22×D61—22no—
451C22×D61—22no—
452C22×D61—22no—
453C22×D61—22no—
454C22×D61—22no—
455C22×D61—22no—
456C22×D61—22no—
457C22×D61—22no—
458C22×D61—22no—
459C22×D61—22no—
460C22×D61—22no—
461C22×D61—22no—
462C22×D61—22no—
463C22×D61—41no—
464C22×D61—41no—
465C22×D61—41no—
466C22×D61—41no—
467C22×D61—41no—
468C22×D61—41no—
469C22×D61—41no—
470C22×D61—41no—
471C22×D61—41no—
472C22×D61—41no—
473C22×D61—41no—
474C22×D61—41no—
475C22×D61—41no—
476C22×D61—41no—
477C22×D61—41no—
478C22×D61—41no—
479C22×D61C2×C22⋊C414yes—
480D4×C61—416no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—22no—
484C2×C4×C61—22no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—22no—
489C2×C4×C61—22no—
490C2×C4×C61—22no—
491C2×C4×C61—22no—
492C2×C4×C61—22no—
493C2×C4×C61—22no—
494C2×C4×C61—22no—
495C2×C4×C61—22no—
496C2×C4×C61—22no—
497C2×C4×C61—22no—
498C2×C4×C61—22no—
499C2×C4×C61—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×C4×C61C2×C22⋊C414yes—
515C2×C4×C61#12114yescomplemented
516C22⋊D61—416no—
517C22⋊D61—416no—
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—22no—
533C2×Dic61—22no—
534C2×Dic61—22no—
535C2×Dic61—22no—
536C2×Dic61—22no—
537C2×Dic61—22no—
538C2×Dic61—22no—
539C2×Dic61—22no—
540C2×Dic61—22no—
541C2×Dic61—22no—
542C2×Dic61—416no—
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×Dic61C2×C22⋊C414yes—
567C2×Dic61C4×D414yes—
568C4×D61—416no—
569#14100—611nomaximal, Sylow
570C22×C61—24no—
571C22×C61—24no—
572C22×C61—24no—
573C22×C61—42no—
574C22×C61—42no—
575C22×C61—42no—
576C22×C61—42no—
577C22×C61—42no—
578C22×C61—42no—
579C22×C61—42no—
580C22×C61—42no—
581C22×C61—42no—
582C22×C61—42no—
583C22×C61—42no—
584C22×C61—42no—
585C22×C61—42no—
586C22×C61—42no—
587C22×C61—42no—
588C22×C61—42no—
589C22×C61—42no—
590C22×C61—42no—
591C22×C61—42no—
592C22×C61—81no—
593C22×C61—81no—
594C22×C61—81no—
595C22×C61—81no—
596C22×C61—81no—
597C22×C61—81no—
598C22×C61—81no—
599C22×C61—81no—
600C22×C61C22×C22⋊C411yescharacteristic
601C22×C61C2×C4×D411yescharacteristic
602C22×C61C2×C4×D411yescharacteristic
603C22×C61C4×#4111yescharacteristic
604C22×C61C4×#4111yescharacteristic
605C22×C61#51811yescharacteristic
606C22×C61#51811yescharacteristic
607C22×C61C2×#12111yescharacteristic
608C22×C61#52511yescharacteristic
609C22×C61#52511yescharacteristic
610C22×C61#52511yescharacteristic
611C22×C61#52911yescharacteristic
612C22×C61#53211yescharacteristic
613C22×C61#53211yescharacteristic
614C22×C61#53211yescharacteristic
615C22×C61#53811yescharacteristic
616C22×C61#53811yescharacteristic
617C22×C61#54011yescharacteristic
618C22×C61#54011yescharacteristic
619C22×C61D4211yescharacteristic
620C22×C61D4211yescharacteristic
621C22×C61D4211yescharacteristic
622C22×C61D4211yescharacteristic
623C22×C61#54611yescharacteristic
624C22×C61#54611yescharacteristic
625C22×C61#54611yescharacteristic
626C22×C61#54611yescharacteristic
627C22×C61#54611yescharacteristic
628C22×C61#54611yescharacteristic
629C22×C61#54611yescharacteristic
630C22×C61#55011yescharacteristic
631C22×C61#55311yescharacteristic
632C22×C61#55311yescharacteristic
633C22×C61#55311yescharacteristic
634C22×C61#55511yescharacteristic
635C2×D61—24no—
636C2×D61—24no—
637C2×D61—24no—
638C2×D61—42no—
639C2×D61—42no—
640C2×D61—42no—
641C2×D61—42no—
642C2×D61—42no—
643C2×D61—42no—
644C2×D61—42no—
645C2×D61—42no—
646C2×D61—42no—
647C2×D61—42no—
648C2×D61—42no—
649C2×D61—42no—
650C4×C61—24no—
651C4×C61—24no—
652C4×C61—42no—
653C4×C61—42no—
654C4×C61—81no—
655Dic61—24no—
656Dic61—24no—
657Dic61—42no—
658Dic61—42no—
659Dic61—42no—
660Dic61—42no—
661Dic61—81no—
662C22×#121—611no—
663C2×#390D6111yescharacteristic, complemented
664C2×#388—611no—
665C2×#386—611no—
666C2×#386—611no—
667C2×C4×C22⋊C4—611no—
668C2×C4×C22⋊C4—611no—
669#1441—611no—
670#1438—611no—
671#1438—611no—
672#1438—611no—
673#1437—611no—
674#1437—611no—
675#1436—611no—
676C22⋊#95—611no—
677C2×C61—44no—
678C2×C61—82no—
679C2×C61#229711yescharacteristic
680C2×C61C4×#12111yescharacteristic
681C2×C61#233311yescharacteristic
682C2×C61D4×C22⋊C411yescharacteristic
683C2×C61D4×C22⋊C411yescharacteristic
684C2×C61#236311yescharacteristic
685C2×C61#236411yescharacteristic
686C2×C61#242411yescharacteristic
687C2×C61#242811yescharacteristic
688C2×C61#245611yescharacteristic
689C2×C61#246411yescharacteristic
690C2×C61#246411yescharacteristic
691C2×C61#247611yescharacteristic
692C2×C61#255511yescharacteristic
693C2×C61#255911yescharacteristic
694D61—44no—
695C23×D4—611no—
696C23×D4—611no—
697C23×D4C2×D6111yescharacteristic
698C24×C4—611no—
699C24×C4—611no—
700C2×#121—618no—
701C2×#121—1224no—
702C2×#121—1224no—
703C22×C4⋊C4—611no—
704C22×C4⋊C4C2×D6111yescharacteristic
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⋊C4—611no—
713C22×C22⋊C4—611no—
714C22×C22⋊C4C2×D6111yescharacteristic
715C22×C22⋊C4C2×D6111yescharacteristic
716C22×C22⋊C4C2×D6111yescharacteristic
717C22×C22⋊C4C2×D6111yescharacteristic
718C22×C42—611no—
719C22×C42—611no—
720C22×C42C2×D6111yescharacteristic
721#390—24no—
722#388—1224no—
723#386—1224no—
724#386—1224no—
725C4×C22⋊C4—1224no—
726C4×C22⋊C4—1224no—
727C2×#95—611no—
728C2×#95—611no—
729C2×#95—611no—
730C2×#95—611no—
731C2×#95—611no—
732C2×#95—611no—
733C2×#95—611no—
734C2×#95—611no—
735C2×#95—611no—
736C2×#95—611no—
737C2×#95—611no—
738C2×#95—611no—
739C61#1410011yescharacteristic, complemented, Sylow
740C25—611no—
741C25C22×D6111yescharacteristic
742C25C22×D6111yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—614no—
750C22×D4—614no—
751C22×D4—1222no—
752C22×D4—1222no—
753C22×D4—1222no—
754C22×D4—1222no—
755C22×D4—1222no—
756C22×D4—1222no—
757C22×D4—1222no—
758C22×D4—1222no—
759C22×D4—2441no—
760C22×D4—2441no—
761C22×D4—2441no—
762C22×D4—2441no—
763C22×D4C4×D6114yescomplemented
764C23×C4—611no—
765C23×C4—611no—
766C23×C4—611no—
767C23×C4—611no—
768C23×C4—611no—
769C23×C4—611no—
770C23×C4—614no—
771C23×C4—611no—
772C23×C4—1222no—
773C23×C4—1222no—
774C23×C4—1222no—
775C23×C4—1222no—
776C23×C4—1222no—
777C23×C4—1222no—
778C23×C4—1222no—
779C23×C4—1222no—
780C23×C4—1222no—
781C23×C4—2441no—
782C23×C4—2441no—
783C23×C4—2441no—
784C23×C4—2441no—
785C23×C4C22×D6111yescharacteristic
786C23×C4C22×D6111yescharacteristic
787C23×C4C22×D6111yescharacteristic
788C23×C4C22×D6111yescharacteristic
789C23×C4C22×D6111yescharacteristic
790#121—12232no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—41no—
794C2×C4⋊C4—614no—
795C2×C4⋊C4—1222no—
796C2×C4⋊C4—1222no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—614no—
809C2×C22⋊C4—614no—
810C2×C22⋊C4—614no—
811C2×C22⋊C4—614no—
812C2×C22⋊C4—1222no—
813C2×C22⋊C4—1222no—
814C2×C22⋊C4—1222no—
815C2×C22⋊C4—1222no—
816C2×C22⋊C4—1222no—
817C2×C22⋊C4—1222no—
818C2×C22⋊C4—1222no—
819C2×C22⋊C4—1222no—
820C2×C22⋊C4—1222no—
821C2×C22⋊C4—1222no—
822C2×C22⋊C4—1222no—
823C2×C22⋊C4—1222no—
824C2×C22⋊C4—1222no—
825C2×C22⋊C4—1222no—
826C2×C22⋊C4—1222no—
827C2×C22⋊C4—1222no—
828C2×C22⋊C4—1222no—
829C2×C22⋊C4—2441no—
830C2×C22⋊C4—2441no—
831C2×C22⋊C4—2441no—
832C2×C22⋊C4—2441no—
833C2×C22⋊C4—2441no—
834C2×C22⋊C4—2441no—
835C2×C22⋊C4C22⋊D6114yescomplemented
836C2×C42—22no—
837C2×C42—22no—
838C2×C42—41no—
839C2×C42—1222no—
840C2×C42—1222no—
841C2×C42—1222no—
842C2×C42—1222no—
843C2×C42—2441no—
844C2×C42—2441no—
845#95—614no—
846#95—1222no—
847#95—1222no—
848#95—1222no—
849#95—1222no—
850#95—1222no—
851#95—1222no—
852#95—1222no—
853#95—1222no—
854#95—1222no—
855#95—2441no—
856#95—2441no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—612no—
884C24—612no—
885C24—612no—
886C24—1221no—
887C24—1221no—
888C24—1221no—
889C24—1221no—
890C24—1221no—
891C24—1221no—
892C24—1221no—
893C24—1221no—
894C24—1221no—
895C24—1221no—
896C24—1221no—
897C24—1221no—
898C24C2×C4×D6112yes—
899C24C2×C4×D6112yes—
900C24#1175822212yes—
901C24C2×C22⋊D6112yes—
902C24C23×D6111yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—1228no—
911C2×D4—1228no—
912C2×D4—1228no—
913C2×D4—1228no—
914C2×D4—2444no—
915C2×D4—2444no—
916C2×D4—2444no—
917C2×D4—2444no—
918C2×D4—2444no—
919C2×D4—2444no—
920C2×D4—2444no—
921C2×D4—2444no—
922C2×D4—2444no—
923C2×D4—2444no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—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—612no—
952C22×C4—612no—
953C22×C4—612no—
954C22×C4—612no—
955C22×C4—612no—
956C22×C4—612no—
957C22×C4—612no—
958C22×C4—612no—
959C22×C4—612no—
960C22×C4—612no—
961C22×C4—1228no—
962C22×C4—1228no—
963C22×C4—1228no—
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—2444no—
1004C22×C4—2444no—
1005C22×C4—2444no—
1006C22×C4—2444no—
1007C22×C4—2444no—
1008C22×C4—2444no—
1009C22×C4—2444no—
1010C22×C4—2444no—
1011C22×C4—2444no—
1012C22×C4—2444no—
1013C22×C4—2444no—
1014C22×C4C2×C4×D6112yes—
1015C22×C4D4×D6112yes—
1016C22×C4D4×D6112yes—
1017C22×C4D4×D6112yes—
1018C22×C4#1175822412yes—
1019C22×C4#1175822412yes—
1020C22×C4C2×C22⋊D6112yes—
1021C22×C4C2×C22⋊D6112yes—
1022C4⋊C4—44no—
1023C4⋊C4—1228no—
1024C22⋊C4—28no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—6116no—
1029C22⋊C4—1228no—
1030C22⋊C4—1228no—
1031C22⋊C4—1228no—
1032C22⋊C4—2444no—
1033C22⋊C4—2444no—
1034C22⋊C4—2444no—
1035C22⋊C4—2444no—
1036C22⋊C4—2444no—
1037C42—44no—
1038C42—2444no—
1039C42—2444no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—614no—
1110C23—1222no—
1111C23—1222no—
1112C23—1222no—
1113C23—1222no—
1114C23—1222no—
1115C23—1222no—
1116C23—1222no—
1117C23—1222no—
1118C23—1222no—
1119C23—1222no—
1120C23—1222no—
1121C23—1222no—
1122C23—1222no—
1123C23—1222no—
1124C23—1222no—
1125C23—1222no—
1126C23—1222no—
1127C23—1222no—
1128C23—2441no—
1129C23—2441no—
1130C23—2441no—
1131C23—2441no—
1132C23—2441no—
1133C23—2441no—
1134C23—2441no—
1135C23—2441no—
1136C23—2441no—
1137C23—2441no—
1138C23—2441no—
1139C23—2441no—
1140C23—2441no—
1141C23—2441no—
1142C23—2441no—
1143C23—2441no—
1144C23C4×C22⋊D6114yes—
1145C23C22×C4×D6111yescharacteristic
1146C23C2×D4×D6111yescharacteristic
1147C23C2×D4×D6111yescharacteristic
1148C23C2×D4×D6111yescharacteristic
1149C23C22×C22⋊D6111yescharacteristic
1150C23#41×D6111yescharacteristic
1151C23#41×D6111yescharacteristic
1152C23#41×D6111yescharacteristic
1153C23C2×#1175822411yescharacteristic
1154C23C2×#1175822411yescharacteristic
1155C23C2×#1175822211yescharacteristic
1156C23#1451982211yescharacteristic
1157C23#1451982211yescharacteristic
1158C23#1451982211yescharacteristic
1159C23#1451982311yescharacteristic
1160D4—416no—
1161D4—24416no—
1162D4—24416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—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—614no—
1197C2×C4—614no—
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—1222no—
1215C2×C4—1222no—
1216C2×C4—1222no—
1217C2×C4—1222no—
1218C2×C4—1222no—
1219C2×C4—1222no—
1220C2×C4—1222no—
1221C2×C4—1222no—
1222C2×C4—24416no—
1223C2×C4—24416no—
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×C4C22⋊C4×D6114yes—
1248C2×C4#1451974914yescomplemented
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—1224no—
1280C22—1224no—
1281C22—1224no—
1282C22—2442no—
1283C22—2442no—
1284C22—2442no—
1285C22—2442no—
1286C22—2442no—
1287C22—2442no—
1288C22—2442no—
1289C22—2442no—
1290C22—2442no—
1291C22—2442no—
1292C22—2442no—
1293C22—2442no—
1294C22C2×C22⋊C4×D6111yescharacteristic
1295C22C4×D4×D6111yescharacteristic
1296C22C2×C4×C22⋊D6111yescharacteristic
1297C22C4×#1175822411yescharacteristic
1298C22C4×#1175822411yescharacteristic
1299C22#1684023411yescharacteristic
1300C22#1684023511yescharacteristic
1301C22C2×#1451974911yescharacteristic
1302C22#1684027111yescharacteristic
1303C22#1684027211yescharacteristic
1304C22#1684027211yescharacteristic
1305C22#1684029211yescharacteristic
1306C22#1684030811yescharacteristic
1307C22#1684031011yescharacteristic
1308C22#1684031111yescharacteristic
1309C22#1684034611yescharacteristic
1310C22#1684034911yescharacteristic
1311C22#1684036211yescharacteristic
1312C22#1684036611yescharacteristic
1313C22D4×C22⋊D6111yescharacteristic
1314C22D4×C22⋊D6111yescharacteristic
1315C22#1684039611yescharacteristic
1316C22#1684039711yescharacteristic
1317C22#1684040011yescharacteristic
1318C22#1684040111yescharacteristic
1319C22#1684040211yescharacteristic
1320C22#1684040211yescharacteristic
1321C22#1684040511yescharacteristic
1322C22#1684040611yescharacteristic
1323C22#1684040911yescharacteristic
1324C22#1684043211yescharacteristic
1325C22#1684045511yescharacteristic
1326C22#1684045811yescharacteristic
1327C22#1684046111yescharacteristic
1328C22#1684047411yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—42no—
1332C4—42no—
1333C4—81no—
1334C4—1224no—
1335C4—1224no—
1336C4—4881no—
1337C4—2442no—
1338C4—2442no—
1339C4—2442no—
1340C4—2442no—
1341C2—44no—
1342C2—82no—
1343C2—2444no—
1344C2#2144830611yescharacteristic
1345C2C4×#1451974911yescharacteristic
1346C2#2144857811yescharacteristic
1347C2C22⋊C4×C22⋊D6111yescharacteristic
1348C2#2144864011yescharacteristic
1349C2#2144885411yescharacteristic
1350C2#2144886411yescharacteristic
1351C2#2144936111yescharacteristic
1352C2#2144941011yescharacteristic
1353C2#2144971711yescharacteristic
1354C2#2144983011yescharacteristic
1355C2#2144983111yescharacteristic
1356C2#2145001011yescharacteristic
1357C2#2145089011yescharacteristic
1358C2#2145095311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#390C2
socle, cosocleC24×C61C24
prime radicalC22×#14519749C2
hypercenterC2×#390D61
hypocenterC61#14100
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#16839652C2semidirect
3. C2×#16839638C2semidirect
4. C2×#16839638C2semidirect
5. C2×C22⋊C4×Dic61C2semidirect
6. C2×C4×#11758198C2semidirect
7. #21444069C2semidirect
8. #21444060C2semidirect
9. #21444058C2semidirect
10. #21444058C2semidirect
11. #21444056C2semidirect
12. #21444056C2semidirect
13. #21444052C2semidirect
14. #21444041C2semidirect
15. C2×C61×#390C2semidirect
22. C2×#14519749C4semidirect
81. C23×Dic61C2×C4semidirect
99. C2×#11758196C2×C4semidirect
114. C2×C22⋊Dic61C2×C4semidirect
144. #14519684D4semidirect
153. C22×D4×C61C2×C4semidirect
173. C2×C22⋊C4×C61D4semidirect
356. #11758198C22⋊C4semidirect
515. C2×C4×C61#121semidirect
663. C2×#390D61semidirect
739. C61#14100semidirect
763. C22×D4C4×D61semidirect
835. C2×C22⋊C4C22⋊D61semidirect
1248. C2×C4#14519749semidirect

Maximal subgroups

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

subgroupindex
C22×#145197492
C2×#168396522
C2×#168396382
C2×C22⋊C4×Dic612
C2×C4×#117581982
#214440692
#214440602
#214440582
#214440562
#214440522
#214440412
C2×C61×#3902
#1410061