Finite Group Databasebeta

← #29611466

Subgroups — #29611466

Order 15616.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic, complemented
2C22×D4×Dic61C211yesmaximal, characteristic
3C2×#16839683C211yesmaximal, characteristic, complemented
4C2×#16839674C211yesmaximal, characteristic, complemented
5C2×#16839637C211yesmaximal, characteristic, complemented
6C2×#16839634C211yesmaximal, characteristic, complemented
7#21444071C211yesmaximal, characteristic, complemented
8#21444064C211yesmaximal, characteristic, complemented
9#21444062C211yesmaximal, characteristic, complemented
10#21444062C211yesmaximal, characteristic, complemented
11#21444060C211yesmaximal, characteristic
12#21444053C211yesmaximal, characteristic, complemented
13#21444050C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C61×#1438C211yesmaximal, characteristic
16C23×Dic122C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C2×#14519754—24no—
20C2×#14519754—24no—
21C2×#14519754—24no—
22C2×D4×Dic61—24no—
23C2×D4×Dic61—24no—
24C2×D4×Dic61—24no—
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×C4⋊Dic61C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×C22⋊Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38#16839683—24no—
39#16839674—24no—
40#16839637—24no—
41#16839634—24no—
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C23×D4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C22×C22⋊C4×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C2×#95×C61C2211yescharacteristic
61C22×Dic122—22no—
62C22×Dic122—22no—
63C22×Dic122—22no—
64C22×Dic122—22no—
65C22×Dic122—22no—
66C22×Dic122—41no—
67C22×Dic122—41no—
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—22no—
77C23×Dic61—41no—
78C23×Dic61—41no—
79C23×Dic61—41no—
80C23×Dic61—41no—
81C23×Dic61D414yes—
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90#14519754—232no—
91D4×Dic61—232no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61—22no—
96C2×C4⋊Dic61—22no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—41no—
99C2×C4⋊Dic61D414yes—
100C2×C4⋊Dic61D414yescomplemented
101C2×#11758196—22no—
102C2×#11758196—22no—
103C2×#11758196—22no—
104C2×#11758196—22no—
105C2×#11758196—22no—
106C2×#11758196—22no—
107C2×#11758196—22no—
108C2×#11758196—41no—
109C2×#11758196D414yescomplemented
110C2×C22⋊Dic61—22no—
111C2×C22⋊Dic61—22no—
112C2×C22⋊Dic61—22no—
113C2×C22⋊Dic61—22no—
114C2×C22⋊Dic61—22no—
115C2×C22⋊Dic61—22no—
116C2×C22⋊Dic61—22no—
117C2×C22⋊Dic61—22no—
118C2×C22⋊Dic61—22no—
119C2×C22⋊Dic61—22no—
120C2×C22⋊Dic61—22no—
121C2×C22⋊Dic61—22no—
122C2×C22⋊Dic61—22no—
123C2×C22⋊Dic61—22no—
124C2×C22⋊Dic61—22no—
125C2×C22⋊Dic61—41no—
126C2×C22⋊Dic61—41no—
127C2×C22⋊Dic61D414yes—
128C2×C4×Dic61—22no—
129C2×C4×Dic61—22no—
130C2×C4×Dic61—22no—
131#14519684—22no—
132#14519684—22no—
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—22no—
143C25×C61C2311yescharacteristic
144C25×C61C2311yescharacteristic
145C22×D4×C61—22no—
146C22×D4×C61—22no—
147C22×D4×C61—22no—
148C22×D4×C61—22no—
149C22×D4×C61—22no—
150C22×D4×C61—22no—
151C22×D4×C61Q814yescomplemented
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C2×C22⋊C4×C61—22no—
158C2×C22⋊C4×C61—22no—
159C2×C22⋊C4×C61—22no—
160C2×C22⋊C4×C61—22no—
161C2×C22⋊C4×C61—22no—
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—41no—
168C2×C22⋊C4×C61—41no—
169#95×C61—22no—
170#95×C61—22no—
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×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×C61C2×D412yes—
196C24×C61C2×D412yes—
197C24×C61C2×Q812yes—
198C24×C61C2×Q812yes—
199C24×C61#4112yes—
200C24×C61#4112yes—
201C24×C61C2411yescharacteristic
202C2×D4×C61—28no—
203C2×D4×C61—28no—
204C2×D4×C61—28no—
205C2×D4×C61—28no—
206C2×D4×C61—28no—
207C2×D4×C61—28no—
208C2×D4×C61—28no—
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—21no—
237C22×C4×C61—21no—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×Q812yes—
242C22×C4×C61#4112yes—
243C22×C4×C61#4112yes—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—28no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
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—28no—
284C22×Dic61—28no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—21no—
292C22×Dic61—44no—
293C22×Dic61—44no—
294C22×Dic61—44no—
295C22×Dic61—44no—
296C22×Dic61—44no—
297C22×Dic61—44no—
298C22×Dic61—44no—
299C22×Dic61—44no—
300C22×Dic61—44no—
301C22×Dic61—44no—
302C22×Dic61—44no—
303C22×Dic61C2×D412yes—
304C22×Dic61C2×D412yes—
305C22×Dic61C2×D412yes—
306C22×Dic61C2×D412yes—
307C22×Dic61C2×D412yes—
308C22×Dic61C2×D412yes—
309C22×Dic61C2×D412yes—
310C22×Dic61C2×D412yes—
311C22×Dic61C2×D412yes—
312C22×Dic61C2×D412yes—
313C22×Dic61#4112yes—
314C2×Dic122—28no—
315C2×Dic122—44no—
316C2×Dic122—44no—
317C2×Dic122—44no—
318C2×Dic122—44no—
319C2×Dic122—44no—
320C2×Dic122—44no—
321C22⋊C4×C61—28no—
322C22⋊C4×C61—28no—
323C22⋊C4×C61—44no—
324C22⋊C4×C61—44no—
325C22⋊Dic61—28no—
326C22⋊Dic61—28no—
327C22⋊Dic61—28no—
328C22⋊Dic61—28no—
329C22⋊Dic61—44no—
330C22⋊Dic61—44no—
331C4⋊Dic61—28no—
332C4⋊Dic61—28no—
333C4⋊Dic61—44no—
334#11758196—28no—
335#11758196—28no—
336#11758196—44no—
337C4×Dic61—28no—
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—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×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—22no—
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×C61—41no—
400C23×C61—41no—
401C23×C61—41no—
402C23×C61—41no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61—41no—
406C23×C61C22⋊Q814yes—
407C23×C61C22⋊Q814yescomplemented
408C23×C61C22×D411yescharacteristic
409C23×C61C22×D411yescharacteristic
410C23×C61C22×D411yescharacteristic
411C23×C61C22×D411yescharacteristic
412C23×C61C22×D411yescharacteristic
413C23×C61C22×Q811yescharacteristic
414C23×C61C2×#4111yescharacteristic
415C23×C61C2×#4111yescharacteristic
416C23×C61C2×#4111yescharacteristic
417C23×C61C2×#4111yescharacteristic
418C23×C61C2×#4111yescharacteristic
419C23×C61H(5,𝔽2)11yescharacteristic
420C23×C61H(5,𝔽2)11yescharacteristic
421C23×C612−1+411yescharacteristic
422C23×C612−1+411yescharacteristic
423D4×C61—232no—
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—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
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×C61C22⋊Q814yescomplemented
459C2×Dic61—22no—
460C2×Dic61—22no—
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—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—22no—
485C2×Dic61—22no—
486C2×Dic61—416no—
487C2×Dic61—416no—
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×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#12014yes—
516C2×Dic61#12014yes—
517Dic122—416no—
518#14723—611nomaximal, Sylow
519C22×C61—24no—
520C22×C61—24no—
521C22×C61—24no—
522C22×C61—24no—
523C22×C61—24no—
524C22×C61—24no—
525C22×C61—42no—
526C22×C61—42no—
527C22×C61—42no—
528C22×C61—42no—
529C22×C61—42no—
530C22×C61—42no—
531C22×C61—42no—
532C22×C61—42no—
533C22×C61—42no—
534C22×C61—42no—
535C22×C61—42no—
536C22×C61—42no—
537C22×C61—42no—
538C22×C61—42no—
539C22×C61—42no—
540C22×C61—42no—
541C22×C61—42no—
542C22×C61—42no—
543C22×C61—42no—
544C22×C61—42no—
545C22×C61—42no—
546C22×C61—42no—
547C22×C61—42no—
548C22×C61—42no—
549C22×C61C2×#12011yescharacteristic
550C22×C61C2×#12011yescharacteristic
551C22×C61C2×C22⋊Q811yescharacteristic
552C22×C61C2×C22⋊Q811yescharacteristic
553C22×C61C2×C22⋊Q811yescharacteristic
554C22×C61#52511yescharacteristic
555C22×C61#52511yescharacteristic
556C22×C61#52511yescharacteristic
557C22×C61#52511yescharacteristic
558C22×C61#52511yescharacteristic
559C22×C61#53211yescharacteristic
560C22×C61#53211yescharacteristic
561C22×C61#53211yescharacteristic
562C22×C61#53411yescharacteristic
563C22×C61#53611yescharacteristic
564C22×C61#53911yescharacteristic
565C22×C61#53911yescharacteristic
566C22×C61#54211yescharacteristic
567C22×C61#54211yescharacteristic
568C22×C61D4211yescharacteristic
569C22×C61D4211yescharacteristic
570C22×C61D4211yescharacteristic
571C22×C61D4211yescharacteristic
572C22×C61#54711yescharacteristic
573C22×C61#54711yescharacteristic
574C22×C61#54811yescharacteristic
575C22×C61#54811yescharacteristic
576C22×C61#54811yescharacteristic
577C22×C61#54811yescharacteristic
578C22×C61D4×Q811yescharacteristic
579C22×C61D4×Q811yescharacteristic
580C22×C61#55111yescharacteristic
581C22×C61#55111yescharacteristic
582C22×C61#55411yescharacteristic
583C22×C61#55411yescharacteristic
584C4×C61—24no—
585C4×C61—42no—
586C4×C61—42no—
587C4×C61—42no—
588C4×C61—81no—
589Dic61—24no—
590Dic61—24no—
591Dic61—42no—
592Dic61—42no—
593Dic61—42no—
594Dic61—42no—
595Dic61—42no—
596Dic61—81no—
597C22×C22⋊Q8—611no—
598C22×C4×D4—611no—
599C2×#395—611no—
600C2×#393—611no—
601C2×#385—611no—
602C2×#385—611no—
603#1441—611no—
604#1439—611no—
605#1439—611no—
606#1439—611no—
607#1438—611no—
608#1438D6111yescharacteristic
609#1436—611no—
610#1436—611no—
611C22⋊#95—611no—
612C2×C61—44no—
613C2×C61—44no—
614C2×C61#238811yescharacteristic
615C2×C61#240311yescharacteristic
616C2×C61#240911yescharacteristic
617C2×C61#243211yescharacteristic
618C2×C61#244911yescharacteristic
619C2×C61#244911yescharacteristic
620C2×C61#245211yescharacteristic
621C2×C61#245211yescharacteristic
622C2×C61#246111yescharacteristic
623C2×C61#246111yescharacteristic
624C2×C61#246311yescharacteristic
625C2×C61#246311yescharacteristic
626C2×C61#256411yescharacteristic
627C2×C61#263811yescharacteristic
628C2×C61#284811yescharacteristic
629C23×Q8—611no—
630C23×D4C2×D6111yescharacteristic
631C24×C4—611no—
632C24×C4—611no—
633C2×C22⋊Q8—1224no—
634C2×C22⋊Q8—1224no—
635C2×C22⋊Q8—1224no—
636C2×C4×D4—1224no—
637C2×C4×D4—1224no—
638C2×C4×D4—1224no—
639C22×C4⋊C4—611no—
640C22×C4⋊C4—611no—
641C22×C4⋊C4—611no—
642C22×C4⋊C4—611no—
643C22×C4⋊C4—611no—
644C22×C4⋊C4—611no—
645C22×C22⋊C4—611no—
646C22×C22⋊C4—611no—
647C22×C22⋊C4—611no—
648C22×C22⋊C4—611no—
649C22×C22⋊C4—611no—
650C22×C22⋊C4—611no—
651C22×C22⋊C4C2×D6111yescharacteristic
652C22×C22⋊C4C2×D6111yescharacteristic
653C22×C22⋊C4C2×D6111yescharacteristic
654C22×C22⋊C4C2×D6111yescharacteristic
655C22×C42—611no—
656#395—1224no—
657#393—1224no—
658#385—1224no—
659#385—1224no—
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×#95C2×D6111yescharacteristic
673C2×#95C2×D6111yescharacteristic
674C61#1472311yescharacteristic, complemented, Sylow
675C25C22×D6111yescharacteristic
676C25C22×D6111yescharacteristic
677C22×Q8—1222no—
678C22×Q8—1222no—
679C22×Q8—1222no—
680C22×Q8—1222no—
681C22×Q8—1222no—
682C22×Q8—2441no—
683C22×Q8—2441no—
684C22×D4—22no—
685C22×D4—22no—
686C22×D4—22no—
687C22×D4—22no—
688C22×D4—22no—
689C22×D4—22no—
690C22×D4Dic12214yescomplemented
691C23×C4—611no—
692C23×C4—611no—
693C23×C4—611no—
694C23×C4—611no—
695C23×C4—611no—
696C23×C4—611no—
697C23×C4—611no—
698C23×C4—614no—
699C23×C4—611no—
700C23×C4—1222no—
701C23×C4—1222no—
702C23×C4—1222no—
703C23×C4—1222no—
704C23×C4—1222no—
705C23×C4—1222no—
706C23×C4—1222no—
707C23×C4—1222no—
708C23×C4—1222no—
709C23×C4—2441no—
710C23×C4—2441no—
711C23×C4—2441no—
712C23×C4—2441no—
713C23×C4C22×D6111yescharacteristic
714C23×C4C22×D6111yescharacteristic
715C23×C4C22×D6111yescharacteristic
716C23×C4C22×D6111yescharacteristic
717C23×C4C22×D6111yescharacteristic
718C22⋊Q8—12232no—
719C4×D4—12232no—
720C2×C4⋊C4—614no—
721C2×C4⋊C4—614no—
722C2×C4⋊C4—614no—
723C2×C4⋊C4—1222no—
724C2×C4⋊C4—1222no—
725C2×C4⋊C4—1222no—
726C2×C4⋊C4—1222no—
727C2×C4⋊C4—1222no—
728C2×C4⋊C4—1222no—
729C2×C4⋊C4—1222no—
730C2×C4⋊C4—1222no—
731C2×C4⋊C4—1222no—
732C2×C4⋊C4—1222no—
733C2×C4⋊C4—1222no—
734C2×C4⋊C4—1222no—
735C2×C4⋊C4—1222no—
736C2×C4⋊C4—2441no—
737C2×C4⋊C4—2441no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—41no—
750C2×C22⋊C4—614no—
751C2×C22⋊C4—1222no—
752C2×C22⋊C4—1222no—
753C2×C22⋊C4—1222no—
754C2×C22⋊C4—1222no—
755C2×C22⋊C4—1222no—
756C2×C22⋊C4—1222no—
757C2×C22⋊C4—1222no—
758C2×C22⋊C4—1222no—
759C2×C22⋊C4—1222no—
760C2×C22⋊C4—1222no—
761C2×C22⋊C4—1222no—
762C2×C22⋊C4—1222no—
763C2×C22⋊C4—1222no—
764C2×C22⋊C4—1222no—
765C2×C22⋊C4—1222no—
766C2×C22⋊C4—2441no—
767C2×C22⋊C4—2441no—
768C2×C42—1222no—
769C2×C42—1222no—
770C2×C42—1222no—
771#95—22no—
772#95—22no—
773#95—1222no—
774#95—1222no—
775#95—1222no—
776#95—1222no—
777#95—1222no—
778#95—1222no—
779#95—1222no—
780#95—1222no—
781#95—1222no—
782#95—1222no—
783#95—1222no—
784#95—1222no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24C2×Dic12212yes—
810C24C2×Dic12212yes—
811C24D4×D6112yes—
812C24D4×D6112yes—
813C24#1175822412yes—
814C24#1175822412yes—
815C24C23×D6111yescharacteristic
816C2×Q8—1228no—
817C2×Q8—2444no—
818C2×Q8—2444no—
819C2×Q8—2444no—
820C2×Q8—2444no—
821C2×Q8—2444no—
822C2×Q8—2444no—
823C2×D4—28no—
824C2×D4—28no—
825C2×D4—28no—
826C2×D4—28no—
827C2×D4—28no—
828C2×D4—28no—
829C2×D4—28no—
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—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
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—1228no—
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—1228no—
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—1221no—
914C22×C4—1221no—
915C22×C4—1221no—
916C22×C4—1221no—
917C22×C4—1221no—
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×C4C2×Dic12212yes—
930C22×C4D4×D6112yes—
931C22×C4D4×D6112yes—
932C22×C4D4×D6112yes—
933C22×C4#1175822412yes—
934C22×C4#1175822412yes—
935C4⋊C4—1228no—
936C4⋊C4—1228no—
937C4⋊C4—1228no—
938C4⋊C4—1228no—
939C4⋊C4—2444no—
940C4⋊C4—2444no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—1228no—
946C22⋊C4—1228no—
947C22⋊C4—1228no—
948C22⋊C4—1228no—
949C22⋊C4—2444no—
950C22⋊C4—2444no—
951C42—1228no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
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—22no—
986C23—22no—
987C23—22no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23#1451975414yes—
1021C23#1451975414yescomplemented
1022C23C2×D4×D6111yescharacteristic
1023C23C2×D4×D6111yescharacteristic
1024C23C2×D4×D6111yescharacteristic
1025C23C2×D4×D6111yescharacteristic
1026C23C2×D4×D6111yescharacteristic
1027C23C22×Dic12211yescharacteristic
1028C23#41×D6111yescharacteristic
1029C23C2×#1175822411yescharacteristic
1030C23C2×#1175822411yescharacteristic
1031C23C2×#1175822411yescharacteristic
1032C23C2×#1175822411yescharacteristic
1033C23#1451982211yescharacteristic
1034C23#1451982311yescharacteristic
1035C23#1451982411yescharacteristic
1036C23#1451982411yescharacteristic
1037Q8—24416no—
1038D4—232no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
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—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—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
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—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—24416no—
1103C2×C4—24416no—
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—2441no—
1118C2×C4—2441no—
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#1451975414yescomplemented
1132C22—24no—
1133C22—24no—
1134C22—24no—
1135C22—24no—
1136C22—24no—
1137C22—24no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22#120×D6111yescharacteristic
1163C22#120×D6111yescharacteristic
1164C22C2×#1451975411yescharacteristic
1165C22C2×#1451975411yescharacteristic
1166C22C2×#1451975411yescharacteristic
1167C22#1684026811yescharacteristic
1168C22#1684026811yescharacteristic
1169C22#1684026811yescharacteristic
1170C22#1684026811yescharacteristic
1171C22#1684027211yescharacteristic
1172C22#1684030711yescharacteristic
1173C22#1684030711yescharacteristic
1174C22#1684031011yescharacteristic
1175C22#1684032011yescharacteristic
1176C22#1684033411yescharacteristic
1177C22#1684035611yescharacteristic
1178C22#1684035711yescharacteristic
1179C22#1684037911yescharacteristic
1180C22#1684038111yescharacteristic
1181C22#1684039411yescharacteristic
1182C22#1684039611yescharacteristic
1183C22#1684039611yescharacteristic
1184C22#1684039711yescharacteristic
1185C22#1684041011yescharacteristic
1186C22#1684041211yescharacteristic
1187C22#1684041811yescharacteristic
1188C22#1684041811yescharacteristic
1189C22#1684041811yescharacteristic
1190C22#1684042011yescharacteristic
1191C22D4×Dic12211yescharacteristic
1192C22D4×Dic12211yescharacteristic
1193C22#1684043511yescharacteristic
1194C22#1684044311yescharacteristic
1195C22#1684046911yescharacteristic
1196C22#1684047111yescharacteristic
1197C4—24no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—81no—
1202C4—1224no—
1203C4—1224no—
1204C4—4881no—
1205C4—2442no—
1206C4—2442no—
1207C4—2442no—
1208C4—2442no—
1209C4—2442no—
1210C2—44no—
1211C2—44no—
1212C2#2144903111yescharacteristic
1213C2#2144912811yescharacteristic
1214C2#2144918111yescharacteristic
1215C2#2144944211yescharacteristic
1216C2#2144963211yescharacteristic
1217C2#2144963411yescharacteristic
1218C2#2144967111yescharacteristic
1219C2#2144967211yescharacteristic
1220C2#2144977911yescharacteristic
1221C2#2144978111yescharacteristic
1222C2#2144980911yescharacteristic
1223C2#2144981111yescharacteristic
1224C2#2145100311yescharacteristic
1225C2#2145173511yescharacteristic
1226C2#2145410411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, cosocleC24×C61C24
FittingC61×#1438C2
prime radicalC23×D4×C61C22
hypercenter#1438D61
hypocenterC61#14723
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×#14519754C2semidirect
3. C2×#16839683C2semidirect
4. C2×#16839674C2semidirect
5. C2×#16839637C2semidirect
6. C2×#16839634C2semidirect
7. #21444071C2semidirect
8. #21444064C2semidirect
9. #21444062C2semidirect
10. #21444062C2semidirect
12. #21444053C2semidirect
13. #21444050C2semidirect
14. #21444041C2semidirect
100. C2×C4⋊Dic61D4semidirect
109. C2×#11758196D4semidirect
151. C22×D4×C61Q8semidirect
407. C23×C61C22⋊Q8semidirect
458. C2×C4×C61C22⋊Q8semidirect
674. C61#14723semidirect
690. C22×D4Dic122semidirect
1021. C23#14519754semidirect
1131. C2×C4#14519754semidirect

Maximal subgroups

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

subgroupindex
C22×#145197542
C22×D4×Dic612
C2×#168396832
C2×#168396742
C2×#168396372
C2×#168396342
#214440712
#214440642
#214440622
#214440602
#214440532
#214440502
#214440412
C61×#14382
#1472361