Finite Group Databasebeta

← #29603157

Subgroups — #29603157

Order 15616.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519750C211yesmaximal, characteristic
2C2×#16839664C211yesmaximal, characteristic, complemented
3C2×#16839662C211yesmaximal, characteristic, complemented
4C2×#16839662C211yesmaximal, characteristic, complemented
5C2×#16839662C211yesmaximal, characteristic, complemented
6C2×#16839659C211yesmaximal, characteristic, complemented
7C2×#16839621C211yesmaximal, characteristic, complemented
8C2×C4×#11758196C211yesmaximal, characteristic, complemented
9C2×#16839609C211yesmaximal, characteristic, complemented
10#21444064C211yesmaximal, characteristic, complemented
11#21444063C211yesmaximal, characteristic, complemented
12#21444059C211yesmaximal, characteristic, complemented
13#21444058C211yesmaximal, characteristic, complemented
14#21444055C211yesmaximal, characteristic, complemented
15C61×#1437C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519750—24no—
21C2×#14519750—24no—
22C2×#14519750C418yescomplemented
23C22×C4⋊Dic61C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42#16839664—24no—
43#16839662—24no—
44#16839662—24no—
45#16839662—24no—
46#16839659—24no—
47#16839621—24no—
48C4×#11758196—24no—
49#16839609—24no—
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C22×C42×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C2×#95×C61C2211yescharacteristic
61C2×#95×C61C2211yescharacteristic
62C24×D61C2311yescharacteristic
63C24×D61C2311yescharacteristic
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—41no—
69C22×D244—41no—
70C22×D244C2×C414yes—
71C22×C22⋊D61—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61—22no—
74C22×C22⋊D61—22no—
75C22×C22⋊D61—22no—
76C22×C22⋊D61—22no—
77C22×C22⋊D61—22no—
78C22×C22⋊D61—22no—
79C22×C22⋊D61—22no—
80C22×C22⋊D61—22no—
81C22×C22⋊D61—41no—
82C22×C22⋊D61—41no—
83C22×C22⋊D61C2×C414yes—
84C22×C22⋊D61C2×C414yes—
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
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×D61C2×C414yes—
98#14519750—232no—
99C2×C4⋊Dic61—22no—
100C2×C4⋊Dic61—22no—
101C2×C4⋊Dic61—41no—
102C2×#11758196—22no—
103C2×#11758196—22no—
104C2×#11758196—22no—
105C2×#11758196—22no—
106C2×#11758196—22no—
107C2×#11758196—22no—
108C2×#11758196—22no—
109C2×#11758196—41no—
110C2×#11758196C2×C414yes—
111C2×#11758196D414yes—
112C2×#11758196D414yes—
113C2×#11758196D414yescomplemented
114C2×C22⋊Dic61—22no—
115C2×C22⋊Dic61—22no—
116C2×C22⋊Dic61—22no—
117C2×C22⋊Dic61—41no—
118C2×C22⋊Dic61—41no—
119C2×C22⋊Dic61—41no—
120C2×#11758198—22no—
121C2×#11758198—22no—
122C2×#11758198—22no—
123C2×#11758198—22no—
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198—22no—
130C2×#11758198—22no—
131C2×#11758198—22no—
132C2×#11758198—22no—
133C2×#11758198—22no—
134C2×#11758198—22no—
135C2×#11758198—22no—
136C2×#11758198—22no—
137C2×#11758198—22no—
138C2×#11758198—22no—
139C2×#11758198—41no—
140C2×#11758198—41no—
141C2×#11758198—41no—
142C2×#11758198—41no—
143C2×#11758198—41no—
144C2×#11758198—41no—
145C2×#11758198C2×C414yes—
146C2×#11758198D414yescomplemented
147C2×C4×Dic61—22no—
148C2×C4×Dic61—22no—
149C2×C4×Dic61—22no—
150C2×C4×Dic61—22no—
151C2×C4×Dic61—22no—
152C2×C4×Dic61—22no—
153C2×C4×Dic61—22no—
154C2×C4×Dic61—41no—
155C2×C4×Dic61D414yescomplemented
156#14519684—22no—
157#14519684—22no—
158#14519684—22no—
159#14519684—22no—
160#14519684—22no—
161C25×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C2×C22⋊C4×C61—22no—
169C2×C22⋊C4×C61—22no—
170C2×C22⋊C4×C61—22no—
171C2×C22⋊C4×C61—22no—
172C2×C22⋊C4×C61—22no—
173C2×C22⋊C4×C61—22no—
174C2×C22⋊C4×C61—22no—
175C2×C22⋊C4×C61—41no—
176C2×C22⋊C4×C61C2×C414yes—
177C2×C42×C61—22no—
178C2×C42×C61—22no—
179C2×C42×C61—41no—
180#95×C61—22no—
181#95×C61—22no—
182#95×C61—22no—
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×C61C22×C412yes—
198C24×C61C2411yescharacteristic
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
206C23×D61—21no—
207C23×D61—21no—
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×D61—21no—
221C23×D61—21no—
222C23×D61—21no—
223C23×D61—21no—
224C23×D61—21no—
225C23×D61C22×C412yes—
226C23×D61C22×C412yes—
227C23×D61C2×D412yes—
228C23×D61#4112yes—
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—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×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61C22×C412yes—
263C22×C4×C61C22×C412yes—
264C22×C4×C61C2×D412yes—
265C22×C4×C61C2×D412yes—
266C22×C4×C61C2×D412yes—
267C22×C4×C61C2×D412yes—
268C22×C4×C61C2×D412yes—
269C22×C4×C61#4112yes—
270C22×C4×C61#4112yes—
271C2×C22⋊D61—28no—
272C2×C22⋊D61—28no—
273C2×C22⋊D61—28no—
274C2×C22⋊D61—28no—
275C2×C22⋊D61—28no—
276C2×C22⋊D61—44no—
277C2×C22⋊D61—44no—
278C2×C22⋊D61—44no—
279C2×C22⋊D61—44no—
280C2×C22⋊D61—44no—
281C2×C22⋊D61—44no—
282C2×C22⋊D61—44no—
283C2×C22⋊D61—44no—
284C2×C22⋊D61—44no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61—21no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—21no—
314C22×Dic61C22×C412yes—
315C22×Dic61C22×C412yes—
316C22×Dic61C2×D412yes—
317C22×Dic61C2×D412yes—
318C22×Dic61C2×D412yes—
319C22×Dic61C2×D412yes—
320C22×Dic61C2×D412yes—
321C22×Dic61C2×D412yes—
322C22×Dic61C2×D412yes—
323C22×Dic61C2×D412yes—
324C22×Dic61C2×D412yes—
325C22×Dic61#4112yes—
326C22×Dic61#4112yes—
327C2×D244—28no—
328C2×D244—28no—
329C2×D244—44no—
330C2×D244—44no—
331C2×D244—44no—
332C2×D244—44no—
333C2×D244—44no—
334C2×C4×D61—28no—
335C2×C4×D61—28no—
336C2×C4×D61—28no—
337C2×C4×D61—44no—
338C2×C4×D61—44no—
339C2×C4×D61—44no—
340C2×C4×D61—44no—
341C22⋊C4×C61—28no—
342C22⋊C4×C61—44no—
343C22⋊C4×C61—44no—
344C42×C61—44no—
345C22⋊Dic61—44no—
346C22⋊Dic61—44no—
347#11758198—28no—
348#11758198—28no—
349#11758198—28no—
350#11758198—44no—
351#11758198—44no—
352#11758198—44no—
353#11758198—44no—
354#11758198—44no—
355#11758198—44no—
356C4⋊Dic61—44no—
357#11758196—28no—
358#11758196—44no—
359#11758196—44no—
360#11758196C22⋊C4116yescomplemented
361C4×Dic61—28no—
362C4×Dic61—44no—
363C4×Dic61—44no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61—41no—
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×C61C23×C411yescharacteristic
400C23×C61C22×D411yescharacteristic
401C23×C61C22×D411yescharacteristic
402C23×C61C22×D411yescharacteristic
403C23×C61C22×D411yescharacteristic
404C23×C61C22×D411yescharacteristic
405C23×C61C2×#4111yescharacteristic
406C23×C61C2×#4111yescharacteristic
407C23×C61C2×#4111yescharacteristic
408C23×C61C2×#4111yescharacteristic
409C23×C61C2×#4111yescharacteristic
410C23×C61H(5,𝔽2)11yescharacteristic
411C23×C61H(5,𝔽2)11yescharacteristic
412C23×C61H(5,𝔽2)11yescharacteristic
413C23×C612−1+411yescharacteristic
414C22×D61—22no—
415C22×D61—22no—
416C22×D61—22no—
417C22×D61—22no—
418C22×D61—22no—
419C22×D61—22no—
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—22no—
423C22×D61—22no—
424C22×D61—22no—
425C22×D61—22no—
426C22×D61—22no—
427C22×D61—22no—
428C22×D61—22no—
429C22×D61—22no—
430C22×D61—22no—
431C22×D61—22no—
432C22×D61—22no—
433C22×D61—22no—
434C22×D61—22no—
435C22×D61—22no—
436C22×D61—22no—
437C22×D61—22no—
438C22×D61—22no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—41no—
451C22×D61—41no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61—41no—
455C22×D61—41no—
456C22×D61—41no—
457C22×D61—41no—
458C22×D61—41no—
459C22×D61—41no—
460C22×D61—41no—
461C22×D61—41no—
462C22×D61—41no—
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×D61—41no—
480C22×D61—41no—
481C22×D61—41no—
482C22×D61—41no—
483C22×D61C4×D414yes—
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—22no—
500C2×C4×C61—22no—
501C2×C4×C61—22no—
502C2×C4×C61—22no—
503C2×C4×C61—22no—
504C2×C4×C61—22no—
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×C61—41no—
515C2×C4×C61—41no—
516C2×C4×C61—41no—
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×C61C2×C22⋊C414yes—
525C2×C4×C61#12114yescomplemented
526C22⋊D61—416no—
527C22⋊D61—416no—
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—22no—
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×Dic61C2×C22⋊C414yes—
563C2×Dic61C2×C22⋊C414yes—
564C2×Dic61C4×D414yes—
565C2×Dic61C4×D414yes—
566C2×Dic61#12114yes—
567C2×Dic61#12114yes—
568C2×Dic61#12414yes—
569C2×Dic61#12714yes—
570D244—416no—
571C4×D61—416no—
572#13998—611nomaximal, Sylow
573C22×C61—42no—
574C22×C61—42no—
575C22×C61—42no—
576C22×C61—42no—
577C22×C61—42no—
578C22×C61—42no—
579C22×C61—42no—
580C22×C61—81no—
581C22×C61—81no—
582C22×C61—81no—
583C22×C61—81no—
584C22×C61—81no—
585C22×C61—81no—
586C22×C61—81no—
587C22×C61—81no—
588C22×C61C22×C22⋊C411yescharacteristic
589C22×C61C2×C4×D411yescharacteristic
590C22×C61C2×C4×D411yescharacteristic
591C22×C61C2×C4×D411yescharacteristic
592C22×C61C4×#4111yescharacteristic
593C22×C61#51811yescharacteristic
594C22×C61#52011yescharacteristic
595C22×C61C2×#12111yescharacteristic
596C22×C61C2×#12111yescharacteristic
597C22×C61C2×#12111yescharacteristic
598C22×C61#52511yescharacteristic
599C22×C61C2×#12411yescharacteristic
600C22×C61#52911yescharacteristic
601C22×C61C2×#12711yescharacteristic
602C22×C61#53211yescharacteristic
603C22×C61#53511yescharacteristic
604C22×C61#53711yescharacteristic
605C22×C61#54011yescharacteristic
606C22×C61#54211yescharacteristic
607C22×C61D4211yescharacteristic
608C22×C61D4211yescharacteristic
609C22×C61D4211yescharacteristic
610C22×C61#54611yescharacteristic
611C22×C61#54611yescharacteristic
612C22×C61#54611yescharacteristic
613C22×C61#54711yescharacteristic
614C22×C61#54811yescharacteristic
615C22×C61#54811yescharacteristic
616C22×C61#54811yescharacteristic
617C22×C61#55011yescharacteristic
618C22×C61#55011yescharacteristic
619C22×C61#55011yescharacteristic
620C22×C61#55311yescharacteristic
621C22×C61#55311yescharacteristic
622C22×C61#55511yescharacteristic
623C2×D61—24no—
624C2×D61—24no—
625C2×D61—24no—
626C2×D61—42no—
627C2×D61—42no—
628C2×D61—42no—
629C2×D61—42no—
630C2×D61—42no—
631C2×D61—42no—
632C2×D61—42no—
633C2×D61—42no—
634C2×D61—42no—
635C2×D61—42no—
636C2×D61—42no—
637C2×D61—42no—
638C2×D61—42no—
639C2×D61—42no—
640C2×D61—42no—
641C2×D61—42no—
642C2×D61—42no—
643C2×D61—42no—
644C2×D61—42no—
645C2×D61—81no—
646C2×D61—81no—
647C2×D61—81no—
648C2×D61—81no—
649C2×D61—81no—
650C2×D61—81no—
651C2×D61—81no—
652C2×D61—81no—
653C4×C61—24no—
654C4×C61—24no—
655C4×C61—42no—
656C4×C61—42no—
657C4×C61—42no—
658C4×C61—81no—
659Dic61—24no—
660Dic61—42no—
661Dic61—42no—
662Dic61—42no—
663Dic61—81no—
664Dic61#39018yescomplemented
665C22×#121—611no—
666C2×#390—611no—
667C2×#390—611no—
668C2×#390—611no—
669C2×#390—611no—
670C2×#389—611no—
671C2×#380—611no—
672C2×C4×C4⋊C4—611no—
673C2×C4×C22⋊C4—611no—
674#1439—611no—
675#1439—611no—
676#1438—611no—
677#1438—611no—
678#1437—611no—
679#1437D6111yescharacteristic, complemented
680C2×C61—82no—
681C2×C61C2×#39011yescharacteristic
682C2×C61C4×#12111yescharacteristic
683C2×C61#232411yescharacteristic
684C2×C61D4×C22⋊C411yescharacteristic
685C2×C61#234111yescharacteristic
686C2×C61#236111yescharacteristic
687C2×C61#236311yescharacteristic
688C2×C61#241411yescharacteristic
689C2×C61#241611yescharacteristic
690C2×C61#242611yescharacteristic
691C2×C61#242811yescharacteristic
692C2×C61#249011yescharacteristic
693C2×C61#249111yescharacteristic
694C2×C61#254011yescharacteristic
695C2×C61#254111yescharacteristic
696D61—44no—
697D61—82no—
698C23×D4—611no—
699C23×D4—611no—
700C23×D4—611no—
701C24×C4—611no—
702C2×#121—618no—
703C2×#121—1224no—
704C2×#121—1224no—
705C22×C4⋊C4—611no—
706C22×C4⋊C4—611no—
707C22×C4⋊C4—611no—
708C22×C4⋊C4—611no—
709C22×C4⋊C4—611no—
710C22×C22⋊C4—611no—
711C22×C22⋊C4—611no—
712C22×C22⋊C4—611no—
713C22×C22⋊C4—611no—
714C22×C22⋊C4—611no—
715C22×C22⋊C4—611no—
716C22×C22⋊C4—611no—
717C22×C22⋊C4—611no—
718C22×C22⋊C4—611no—
719C22×C22⋊C4—611no—
720C22×C22⋊C4—611no—
721C22×C22⋊C4C2×D6111yescharacteristic
722C22×C22⋊C4C2×D6111yescharacteristic
723C22×C22⋊C4C2×D6111yescharacteristic
724C22×C42—611no—
725C22×C42—611no—
726C22×C42—611no—
727C22×C42C2×D6111yescharacteristic
728#390—1224no—
729#390—1224no—
730#390—1224no—
731#390—1224no—
732#389—1224no—
733#380—1224no—
734C4×C4⋊C4—1224no—
735C4×C22⋊C4—1224no—
736C2×#95—611no—
737C2×#95—611no—
738C2×#95—611no—
739C2×#95—611no—
740C2×#95—611no—
741C2×#95C2×D6111yescharacteristic
742C2×#95C2×D6111yescharacteristic
743C2×#95C2×D6111yescharacteristic
744C61#1399811yescharacteristic, complemented, Sylow
745C25—611no—
746C25—611no—
747C25C22×D6111yescharacteristic
748C22×D4—614no—
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—1222no—
760C22×D4—1222no—
761C22×D4—1222no—
762C22×D4—1222no—
763C22×D4—1222no—
764C22×D4—1222no—
765C22×D4—2441no—
766C22×D4—2441no—
767C22×D4—2441no—
768C22×D4—2441no—
769C23×C4—611no—
770C23×C4—611no—
771C23×C4—611no—
772C23×C4—611no—
773C23×C4—611no—
774C23×C4—614no—
775C23×C4—611no—
776C23×C4—1222no—
777C23×C4—1222no—
778C23×C4—1222no—
779C23×C4—1222no—
780C23×C4—1222no—
781C23×C4—1222no—
782C23×C4C22×D6111yescharacteristic
783C23×C4C22×D6111yescharacteristic
784C23×C4C22×D6111yescharacteristic
785C23×C4C22×D6111yescharacteristic
786C23×C4C22×D6111yescharacteristic
787C23×C4C22×D6111yescharacteristic
788#121—12232no—
789C2×C4⋊C4—614no—
790C2×C4⋊C4—614no—
791C2×C4⋊C4—614no—
792C2×C4⋊C4—614no—
793C2×C4⋊C4—1222no—
794C2×C4⋊C4—1222no—
795C2×C4⋊C4—1222no—
796C2×C4⋊C4—1222no—
797C2×C4⋊C4—1222no—
798C2×C4⋊C4—1222no—
799C2×C4⋊C4—1222no—
800C2×C4⋊C4—1222no—
801C2×C4⋊C4—1222no—
802C2×C4⋊C4—2441no—
803C2×C4⋊C4—2441no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—614no—
813C2×C22⋊C4—614no—
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—1222no—
830C2×C22⋊C4—1222no—
831C2×C22⋊C4—1222no—
832C2×C22⋊C4—1222no—
833C2×C22⋊C4—1222no—
834C2×C22⋊C4—1222no—
835C2×C22⋊C4—1222no—
836C2×C22⋊C4—2441no—
837C2×C22⋊C4—2441no—
838C2×C22⋊C4—2441no—
839C2×C22⋊C4—2441no—
840C2×C22⋊C4—2441no—
841C2×C22⋊C4—2441no—
842C2×C22⋊C4—2441no—
843C2×C22⋊C4—2441no—
844C2×C22⋊C4—2441no—
845C2×C22⋊C4C4×D6114yes—
846C2×C42—22no—
847C2×C42—22no—
848C2×C42—41no—
849C2×C42—614no—
850C2×C42—1222no—
851C2×C42—1222no—
852C2×C42—1222no—
853C2×C42—1222no—
854C2×C42—1222no—
855C2×C42—1222no—
856C2×C42—1222no—
857C2×C42—2441no—
858#95—22no—
859#95—22no—
860#95—22no—
861#95—1222no—
862#95—1222no—
863#95—1222no—
864#95—1222no—
865#95—1222no—
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—612no—
881C24—612no—
882C24—612no—
883C24—612no—
884C24—1221no—
885C24—1221no—
886C24—1221no—
887C24—1221no—
888C24—1221no—
889C24—1221no—
890C24—1221no—
891C24—1221no—
892C24—1221no—
893C24—1221no—
894C24—1221no—
895C24—1221no—
896C24—1221no—
897C24—1221no—
898C24—1221no—
899C24—1221no—
900C24—1221no—
901C24—1221no—
902C24—1221no—
903C24—1221no—
904C24—1221no—
905C24—1221no—
906C24—1221no—
907C24—1221no—
908C24—1221no—
909C24—1221no—
910C24C2×C4×D6112yes—
911C24C23×D6111yescharacteristic
912C2×D4—1228no—
913C2×D4—1228no—
914C2×D4—1228no—
915C2×D4—1228no—
916C2×D4—1228no—
917C2×D4—1228no—
918C2×D4—1228no—
919C2×D4—2444no—
920C2×D4—2444no—
921C2×D4—2444no—
922C2×D4—2444no—
923C2×D4—2444no—
924C2×D4—2444no—
925C2×D4—2444no—
926C2×D4—2444no—
927C2×D4—2444no—
928C2×D4—2444no—
929C2×D4—2444no—
930C2×D4—2444no—
931C2×D4—2444no—
932C2×D4—2444no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—612no—
967C22×C4—612no—
968C22×C4—612no—
969C22×C4—612no—
970C22×C4—612no—
971C22×C4—612no—
972C22×C4—612no—
973C22×C4—612no—
974C22×C4—612no—
975C22×C4—612no—
976C22×C4—612no—
977C22×C4—612no—
978C22×C4—612no—
979C22×C4—1228no—
980C22×C4—1228no—
981C22×C4—1228no—
982C22×C4—1221no—
983C22×C4—1221no—
984C22×C4—1221no—
985C22×C4—1221no—
986C22×C4—1221no—
987C22×C4—1221no—
988C22×C4—1221no—
989C22×C4—1221no—
990C22×C4—1221no—
991C22×C4—1221no—
992C22×C4—1221no—
993C22×C4—1221no—
994C22×C4—1221no—
995C22×C4—1221no—
996C22×C4—1221no—
997C22×C4—1221no—
998C22×C4—1221no—
999C22×C4—1221no—
1000C22×C4—1221no—
1001C22×C4—1221no—
1002C22×C4—1221no—
1003C22×C4—1221no—
1004C22×C4—1221no—
1005C22×C4—1221no—
1006C22×C4—1221no—
1007C22×C4—1221no—
1008C22×C4—1221no—
1009C22×C4—1221no—
1010C22×C4—1221no—
1011C22×C4—2444no—
1012C22×C4—2444no—
1013C22×C4—2444no—
1014C22×C4—2444no—
1015C22×C4C2×C4×D6112yes—
1016C22×C4C2×C4×D6112yes—
1017C22×C4#1175822212yes—
1018C22×C4#1175822212yes—
1019C22×C4D4×D6112yes—
1020C22×C4D4×D6112yes—
1021C22×C4D4×D6112yes—
1022C22×C4D4×D6112yes—
1023C22×C4D4×D6112yes—
1024C4⋊C4—6116no—
1025C4⋊C4—1228no—
1026C4⋊C4—2444no—
1027C4⋊C4—2444no—
1028C4⋊C4—2444no—
1029C22⋊C4—28no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—1228no—
1033C22⋊C4—1228no—
1034C22⋊C4—1228no—
1035C22⋊C4—2444no—
1036C22⋊C4—2444no—
1037C22⋊C4—2444no—
1038C22⋊C4—2444no—
1039C22⋊C4—2444no—
1040C22⋊C4—2444no—
1041C22⋊C4—2444no—
1042C22⋊C4—2444no—
1043C42—44no—
1044C42—1228no—
1045C42—2444no—
1046C42—2444no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
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—614no—
1083C23—1222no—
1084C23—1222no—
1085C23—1222no—
1086C23—1222no—
1087C23—1222no—
1088C23—1222no—
1089C23—1222no—
1090C23—1222no—
1091C23—1222no—
1092C23—1222no—
1093C23—1222no—
1094C23—1222no—
1095C23—1222no—
1096C23—1222no—
1097C23—1222no—
1098C23—1222no—
1099C23—1222no—
1100C23—1222no—
1101C23—1222no—
1102C23—1222no—
1103C23—1222no—
1104C23—1222no—
1105C23—1222no—
1106C23—1222no—
1107C23—1222no—
1108C23—2441no—
1109C23—2441no—
1110C23—2441no—
1111C23—2441no—
1112C23—2441no—
1113C23—2441no—
1114C23—2441no—
1115C23—2441no—
1116C23—2441no—
1117C23—2441no—
1118C23—2441no—
1119C23—2441no—
1120C23—2441no—
1121C23—2441no—
1122C23—2441no—
1123C23—2441no—
1124C23—2441no—
1125C23—2441no—
1126C23—2441no—
1127C23—2441no—
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—
1144C23—2441no—
1145C23—2441no—
1146C23—2441no—
1147C23—2441no—
1148C23—2441no—
1149C23—2441no—
1150C23—2441no—
1151C23—2441no—
1152C23C22×C4×D6111yescharacteristic
1153C23C2×D4×D6111yescharacteristic
1154C23C2×D4×D6111yescharacteristic
1155C23C2×D4×D6111yescharacteristic
1156C23C2×D4×D6111yescharacteristic
1157C23C2×D4×D6111yescharacteristic
1158C23#41×D6111yescharacteristic
1159C23#41×D6111yescharacteristic
1160C23#41×D6111yescharacteristic
1161C23C2×#1175822211yescharacteristic
1162C23C2×#1175822211yescharacteristic
1163C23#1451982211yescharacteristic
1164C23#1451982311yescharacteristic
1165C23#1451982311yescharacteristic
1166C23#1451982411yescharacteristic
1167D4—24416no—
1168D4—24416no—
1169D4—24416no—
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—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—614no—
1211C2×C4—614no—
1212C2×C4—614no—
1213C2×C4—614no—
1214C2×C4—614no—
1215C2×C4—614no—
1216C2×C4—614no—
1217C2×C4—614no—
1218C2×C4—1222no—
1219C2×C4—1222no—
1220C2×C4—1222no—
1221C2×C4—1222no—
1222C2×C4—1222no—
1223C2×C4—1222no—
1224C2×C4—1222no—
1225C2×C4—1222no—
1226C2×C4—1222no—
1227C2×C4—1222no—
1228C2×C4—1222no—
1229C2×C4—1222no—
1230C2×C4—1222no—
1231C2×C4—1222no—
1232C2×C4—1222no—
1233C2×C4—24416no—
1234C2×C4—2441no—
1235C2×C4—2441no—
1236C2×C4—2441no—
1237C2×C4—2441no—
1238C2×C4—2441no—
1239C2×C4—2441no—
1240C2×C4—2441no—
1241C2×C4—2441no—
1242C2×C4—2441no—
1243C2×C4—2441no—
1244C2×C4—2441no—
1245C2×C4—2441no—
1246C2×C4—2441no—
1247C2×C4—2441no—
1248C2×C4—2441no—
1249C2×C4—2441no—
1250C2×C4—2441no—
1251C2×C4—2441no—
1252C2×C4—2441no—
1253C2×C4C22⋊C4×D6114yes—
1254C2×C4#1451975014yescomplemented
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—1224no—
1271C22—1224no—
1272C22—1224no—
1273C22—4881no—
1274C22—4881no—
1275C22—4881no—
1276C22—4881no—
1277C22—4881no—
1278C22—4881no—
1279C22—4881no—
1280C22—4881no—
1281C22—2442no—
1282C22—2442no—
1283C22—2442no—
1284C22—2442no—
1285C22—2442no—
1286C22—2442no—
1287C22—2442no—
1288C22—2442no—
1289C22—2442no—
1290C22—2442no—
1291C22—2442no—
1292C22—2442no—
1293C22—2442no—
1294C22—2442no—
1295C22—2442no—
1296C22—2442no—
1297C22—2442no—
1298C22—2442no—
1299C22—2442no—
1300C22C2×C22⋊C4×D6111yescharacteristic
1301C22C4×D4×D6111yescharacteristic
1302C22C4×D4×D6111yescharacteristic
1303C22C4×D4×D6111yescharacteristic
1304C22C4×#1175822211yescharacteristic
1305C22#1684023411yescharacteristic
1306C22#1684024211yescharacteristic
1307C22#121×D6111yescharacteristic
1308C22#121×D6111yescharacteristic
1309C22C2×#1451975011yescharacteristic
1310C22#1684027111yescharacteristic
1311C22#124×D6111yescharacteristic
1312C22#1684029011yescharacteristic
1313C22#127×D6111yescharacteristic
1314C22#1684030911yescharacteristic
1315C22#1684033011yescharacteristic
1316C22#1684033911yescharacteristic
1317C22#1684036411yescharacteristic
1318C22#1684037811yescharacteristic
1319C22#1684039411yescharacteristic
1320C22#1684039611yescharacteristic
1321C22#1684039611yescharacteristic
1322C22#1684040111yescharacteristic
1323C22#1684040211yescharacteristic
1324C22#1684040411yescharacteristic
1325C22#1684041011yescharacteristic
1326C22#1684042011yescharacteristic
1327C22#1684042111yescharacteristic
1328C22#1684042111yescharacteristic
1329C22#1684043311yescharacteristic
1330C22#1684043311yescharacteristic
1331C22#1684043311yescharacteristic
1332C22#1684046111yescharacteristic
1333C22#1684046311yescharacteristic
1334C22#1684047511yescharacteristic
1335C4—24no—
1336C4—24no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—81no—
1341C4—618no—
1342C4—1224no—
1343C4—4881no—
1344C4—2442no—
1345C4—2442no—
1346C4—2442no—
1347C2—82no—
1348C2—4882no—
1349C2—2444no—
1350C2#390×D6111yescharacteristic
1351C2C4×#1451975011yescharacteristic
1352C2#2144850711yescharacteristic
1353C2#2144863711yescharacteristic
1354C2#2144865911yescharacteristic
1355C2#2144883211yescharacteristic
1356C2#2144885811yescharacteristic
1357C2#2144923611yescharacteristic
1358C2#2144925811yescharacteristic
1359C2#2144938411yescharacteristic
1360C2#2144940611yescharacteristic
1361C2#2145017011yescharacteristic
1362C2#2145018111yescharacteristic
1363C2#2145075611yescharacteristic
1364C2#2145076411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1437C2
socle, cosocleC24×C61C24
prime radicalC22×#14519750C2
hypercenter#1437D61
hypocenterC61#13998
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#16839664C2semidirect
3. C2×#16839662C2semidirect
4. C2×#16839662C2semidirect
5. C2×#16839662C2semidirect
6. C2×#16839659C2semidirect
7. C2×#16839621C2semidirect
8. C2×C4×#11758196C2semidirect
9. C2×#16839609C2semidirect
10. #21444064C2semidirect
11. #21444063C2semidirect
12. #21444059C2semidirect
13. #21444058C2semidirect
14. #21444055C2semidirect
15. C61×#1437C2semidirect
22. C2×#14519750C4semidirect
113. C2×#11758196D4semidirect
146. C2×#11758198D4semidirect
155. C2×C4×Dic61D4semidirect
360. #11758196C22⋊C4semidirect
525. C2×C4×C61#121semidirect
664. Dic61#390semidirect
679. #1437D61semidirect
744. C61#13998semidirect
1254. C2×C4#14519750semidirect

Maximal subgroups

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

subgroupindex
C22×#145197502
C2×#168396642
C2×#168396622
C2×#168396592
C2×#168396212
C2×C4×#117581962
C2×#168396092
#214440642
#214440632
#214440592
#214440582
#214440552
C61×#14372
#1399861