Finite Group Databasebeta

← #29611498

Subgroups — #29611498

Order 15616.

3494 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839685C212yesmaximal, complemented
2C2×#16839635C211yesmaximal, characteristic, complemented
3C2×#16839635C211yesmaximal, characteristic, complemented
4C2×#16839622C211yesmaximal, characteristic, complemented
5C2×#16839618C211yesmaximal, characteristic
6C2×#16839618C211yesmaximal, characteristic
7#21444064C212yesmaximal, complemented
8#21444062C212yesmaximal, complemented
9#21444062C212yesmaximal, complemented
10#21444042C211yesmaximal, characteristic, complemented
11C23×C22⋊C4×C61C211yesmaximal, characteristic
12C22×C4⋊Dic61C2212yescomplemented
13C22×#11758196C2211yescharacteristic, complemented
14C22×#11758196C2212yescomplemented
15C22×#11758196C2211yescharacteristic, complemented
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2212yes—
19C22×C22⋊Dic61C2212yes—
20C22×C22⋊Dic61C2212yes—
21C22×C22⋊Dic61C2212yes—
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24#16839685—28no—
25#16839635—24no—
26#16839635—24no—
27#16839622—24no—
28#16839618—24no—
29#16839618—24no—
30C2×#14519684C2212yescomplemented
31C2×#14519684C2211yescharacteristic, complemented
32C2×#14519684C2212yescomplemented
33C2×#14519684C2211yescharacteristic, complemented
34C2×#14519684C2212yescomplemented
35C2×#14519684C2212yescomplemented
36C26×C61C2211yescharacteristic
37C24×C4×C61C2211yescharacteristic
38C24×C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61—24no—
40C22×C22⋊C4×C61—28no—
41C22×C22⋊C4×C61C2212yes—
42C22×C22⋊C4×C61C2212yes—
43C23×Dic61C2311yescharacteristic
44C23×Dic61C2312yes—
45C23×Dic61C2311yescharacteristic
46C23×Dic61C2311yescharacteristic
47C23×Dic61C2312yes—
48C23×Dic61C2311yescharacteristic
49C2×C4⋊Dic61—24no—
50C2×C4⋊Dic61—24no—
51C2×C4⋊Dic61—42no—
52C2×#11758196—24no—
53C2×#11758196—24no—
54C2×#11758196—22no—
55C2×#11758196—22no—
56C2×#11758196—24no—
57C2×#11758196—42no—
58C2×#11758196—42no—
59C2×C22⋊Dic61—22no—
60C2×C22⋊Dic61—22no—
61C2×C22⋊Dic61—22no—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61—24no—
64C2×C22⋊Dic61—24no—
65C2×C22⋊Dic61—22no—
66C2×C22⋊Dic61—22no—
67C2×C22⋊Dic61—22no—
68C2×C22⋊Dic61—22no—
69C2×C22⋊Dic61—24no—
70C2×C22⋊Dic61—24no—
71C2×C22⋊Dic61—22no—
72C2×C22⋊Dic61—22no—
73C2×C22⋊Dic61—24no—
74C2×C22⋊Dic61—24no—
75C2×C22⋊Dic61—24no—
76C2×C22⋊Dic61—24no—
77C2×C22⋊Dic61—42no—
78C2×C22⋊Dic61—42no—
79C2×C22⋊Dic61—42no—
80C2×C22⋊Dic61—42no—
81C2×C22⋊Dic61D414yes—
82C2×C22⋊Dic61D414yes—
83#14519684—24no—
84#14519684—22no—
85#14519684—22no—
86#14519684—24no—
87#14519684—24no—
88#14519684—42no—
89C25×C61—24no—
90C25×C61—22no—
91C25×C61—24no—
92C25×C61—22no—
93C25×C61—22no—
94C25×C61—22no—
95C25×C61—22no—
96C25×C61—22no—
97C25×C61—42no—
98C25×C61—42no—
99C25×C61Q814yes—
100C25×C61C2312yes—
101C25×C61C2311yescharacteristic
102C23×C4×C61—22no—
103C23×C4×C61—22no—
104C23×C4×C61—22no—
105C23×C4×C61—24no—
106C23×C4×C61—24no—
107C23×C4×C61—22no—
108C23×C4×C61—22no—
109C23×C4×C61—42no—
110C23×C4×C61—42no—
111C23×C4×C61D414yes—
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2312yes—
114C23×C4×C61C2311yescharacteristic
115C2×C22⋊C4×C61—232no—
116C2×C22⋊C4×C61—24no—
117C2×C22⋊C4×C61—24no—
118C2×C22⋊C4×C61—24no—
119C2×C22⋊C4×C61—24no—
120C2×C22⋊C4×C61—24no—
121C2×C22⋊C4×C61D418yes—
122C24×C61—22no—
123C24×C61—22no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61—28no—
127C24×C61—28no—
128C24×C61—216no—
129C24×C61—216no—
130C24×C61—28no—
131C24×C61—22no—
132C24×C61—22no—
133C24×C61—22no—
134C24×C61—22no—
135C24×C61—22no—
136C24×C61—22no—
137C24×C61—22no—
138C24×C61—22no—
139C24×C61—22no—
140C24×C61—22no—
141C24×C61—22no—
142C24×C61—22no—
143C24×C61—28no—
144C24×C61—28no—
145C24×C61—48no—
146C24×C61—48no—
147C24×C61—48no—
148C24×C61—48no—
149C24×C61—48no—
150C24×C61—48no—
151C24×C61—48no—
152C24×C61—48no—
153C24×C61—48no—
154C24×C61—44no—
155C24×C61—44no—
156C24×C61—48no—
157C24×C61—44no—
158C24×C61—44no—
159C24×C61—44no—
160C24×C61—44no—
161C24×C61C2×D414yes—
162C24×C61C2×D412yes—
163C24×C61C2×D412yes—
164C24×C61C2×D412yes—
165C24×C61C2×Q814yes—
166C24×C61C2×Q812yes—
167C24×C61#4114yes—
168C24×C61#4112yes—
169C24×C61#4112yes—
170C24×C61#4112yes—
171C24×C61C2411yescharacteristic
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—22no—
175C22×C4×C61—28no—
176C22×C4×C61—28no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—21no—
181C22×C4×C61—22no—
182C22×C4×C61—21no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—28no—
188C22×C4×C61—44no—
189C22×C4×C61—48no—
190C22×C4×C61—48no—
191C22×C4×C61—48no—
192C22×C4×C61—48no—
193C22×C4×C61—44no—
194C22×C4×C61—44no—
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2×D414yes—
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2×D414yes—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—21no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—21no—
218C22×Dic61—22no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—22no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—22no—
230C22×Dic61C2×D412yes—
231C22×Dic61C2×D414yes—
232C22×Dic61C2×D412yes—
233C22⋊C4×C61—216no—
234C22⋊C4×C61—216no—
235C22⋊Dic61—28no—
236C22⋊Dic61—28no—
237C22⋊Dic61—48no—
238C22⋊Dic61—48no—
239C22⋊Dic61—48no—
240C22⋊Dic61—48no—
241C22⋊Dic61—44no—
242C22⋊Dic61—44no—
243C4⋊Dic61—48no—
244#11758196—48no—
245#11758196—44no—
246#11758196—44no—
247C23×C61—22no—
248C23×C61—24no—
249C23×C61—22no—
250C23×C61—24no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—24no—
254C23×C61—24no—
255C23×C61—24no—
256C23×C61—24no—
257C23×C61—24no—
258C23×C61—24no—
259C23×C61—24no—
260C23×C61—24no—
261C23×C61—24no—
262C23×C61—24no—
263C23×C61—232no—
264C23×C61—24no—
265C23×C61—24no—
266C23×C61—24no—
267C23×C61—24no—
268C23×C61—24no—
269C23×C61—24no—
270C23×C61—24no—
271C23×C61—24no—
272C23×C61—24no—
273C23×C61—24no—
274C23×C61—24no—
275C23×C61—24no—
276C23×C61—24no—
277C23×C61—24no—
278C23×C61—24no—
279C23×C61—24no—
280C23×C61—24no—
281C23×C61—24no—
282C23×C61—432no—
283C23×C61—432no—
284C23×C61—416no—
285C23×C61—416no—
286C23×C61—416no—
287C23×C61—416no—
288C23×C61—432no—
289C23×C61—432no—
290C23×C61—416no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—416no—
308C23×C61#12114yes—
309C23×C61#12114yes—
310C23×C61#12114yes—
311C23×C61C22⋊Q818yes—
312C23×C61C22⋊Q814yes—
313C23×C61C22⋊Q814yes—
314C23×C61C22⋊Q814yes—
315C23×C61#12614yes—
316C23×C61C22×D411yescharacteristic
317C23×C61C22×D412yes—
318C23×C61C22×D411yescharacteristic
319C23×C61C22×D411yescharacteristic
320C23×C61C22×Q811yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61C2×#4112yes—
325C23×C61H(5,𝔽2)12yes—
326C23×C61H(5,𝔽2)12yes—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—24no—
330C2×C4×C61—24no—
331C2×C4×C61—24no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—24no—
336C2×C4×C61—24no—
337C2×C4×C61—416no—
338C2×C4×C61—416no—
339C2×C4×C61—42no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61#12014yes—
346C2×Dic61—22no—
347C2×Dic61—24no—
348C2×Dic61—22no—
349C2×Dic61—24no—
350C2×Dic61—24no—
351C2×Dic61—24no—
352C2×Dic61—24no—
353C2×Dic61—41no—
354C2×Dic61—42no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—42no—
359C2×Dic61—42no—
360C2×Dic61—42no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—42no—
367C2×Dic61—41no—
368C2×Dic61—42no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61—42no—
378C2×Dic61—42no—
379C2×Dic61—42no—
380#14726—611nomaximal, Sylow
381C22×C61—24no—
382C22×C61—24no—
383C22×C61—24no—
384C22×C61—24no—
385C22×C61—24no—
386C22×C61—28no—
387C22×C61—28no—
388C22×C61—28no—
389C22×C61—28no—
390C22×C61—24no—
391C22×C61—28no—
392C22×C61—28no—
393C22×C61—28no—
394C22×C61—464no—
395C22×C61—44no—
396C22×C61—44no—
397C22×C61—44no—
398C22×C61—44no—
399C22×C61—44no—
400C22×C61—44no—
401C22×C61—44no—
402C22×C61—44no—
403C22×C61—44no—
404C22×C61—44no—
405C22×C61—44no—
406C22×C61—44no—
407C22×C61#39618yescomplemented
408C22×C61C2×#12011yescharacteristic
409C22×C61C2×#12111yescharacteristic
410C22×C61C2×#12111yescharacteristic
411C22×C61C2×#12111yescharacteristic
412C22×C61C2×C22⋊Q811yescharacteristic
413C22×C61C2×C22⋊Q811yescharacteristic
414C22×C61C2×C22⋊Q811yescharacteristic
415C22×C61C2×C22⋊Q812yes—
416C22×C61#52511yescharacteristic
417C22×C61#52512yes—
418C22×C61C2×#12611yescharacteristic
419C22×C61#53411yescharacteristic
420C22×C61#53511yescharacteristic
421C22×C61#53812yes—
422C22×C61#54312yes—
423C22×C61D4212yes—
424C22×C61D4212yes—
425C22×C61#54612yes—
426C22×C61#54612yes—
427C22×C61#54612yes—
428C22×C61#54612yes—
429C22×C61#55112yes—
430C22×C61#55112yes—
431C4×C61—24no—
432C4×C61—44no—
433C4×C61—42no—
434Dic61—42no—
435Dic61—44no—
436Dic61—42no—
437Dic61—81no—
438Dic61—81no—
439Dic61—82no—
440C23×C22⋊C4D6111yescharacteristic
441C2×#396—612no—
442C2×#385—611no—
443C2×#385—611no—
444C2×#380—611no—
445C2×#379—611no—
446C2×#379—611no—
447#1439—612no—
448#1439—612no—
449#1439—612no—
450C22⋊#95—611no—
451C2×C61—28no—
452C2×C61—48no—
453C2×C61C2×#39611yescharacteristic
454C2×C61#240811yescharacteristic
455C2×C61#241011yescharacteristic
456C2×C61#241111yescharacteristic
457C2×C61#242412yes—
458C2×C61#243712yes—
459C2×C61#243712yes—
460C2×C61#248012yes—
461C2×C61#253411yescharacteristic
462C2×C61#262611yescharacteristic
463C2×C61#284811yescharacteristic
464C26C2×D6111yescharacteristic
465C24×C4C2×D6111yescharacteristic
466C24×C4C2×D6111yescharacteristic
467C22×C4⋊C4—611no—
468C22×C4⋊C4—612no—
469C22×C4⋊C4—612no—
470C22×C4⋊C4—611no—
471C22×C22⋊C4—24no—
472C22×C22⋊C4—28no—
473C22×C22⋊C4—611no—
474C22×C22⋊C4—611no—
475C22×C22⋊C4—611no—
476C22×C22⋊C4—611no—
477C22×C22⋊C4—612no—
478C22×C22⋊C4—612no—
479C22×C22⋊C4—612no—
480C22×C22⋊C4—612no—
481C22×C22⋊C4C2×D6112yes—
482C22×C22⋊C4C2×D6112yes—
483#396—1228no—
484#385—1224no—
485#385—1224no—
486#380—1224no—
487#379—1224no—
488#379—1224no—
489C2×#95—612no—
490C2×#95—612no—
491C2×#95—612no—
492C2×#95—611no—
493C2×#95—611no—
494C2×#95—612no—
495C61#1472611yescharacteristic, complemented, Sylow
496C25—24no—
497C25—22no—
498C25—24no—
499C25—22no—
500C25—22no—
501C25—22no—
502C25—22no—
503C25—22no—
504C25—42no—
505C25—42no—
506C25Dic12214yes—
507C25C22×D6112yes—
508C25C22×D6111yescharacteristic
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—22no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—22no—
515C23×C4—22no—
516C23×C4—42no—
517C23×C4—42no—
518C23×C4—611no—
519C23×C4—612no—
520C23×C4—611no—
521C23×C4—611no—
522C23×C4—612no—
523C23×C4—611no—
524C23×C4C22⋊D6114yes—
525C23×C4C22×D6111yescharacteristic
526C23×C4C22×D6112yes—
527C23×C4C22×D6111yescharacteristic
528C2×C4⋊C4—1224no—
529C2×C4⋊C4—1224no—
530C2×C4⋊C4—1222no—
531C2×C4⋊C4—1222no—
532C2×C4⋊C4—1224no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4—1224no—
535C2×C4⋊C4—2442no—
536C2×C4⋊C4—2442no—
537C2×C4⋊C4—2442no—
538C2×C22⋊C4—232no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—1222no—
547C2×C22⋊C4—1222no—
548C2×C22⋊C4—1222no—
549C2×C22⋊C4—1222no—
550C2×C22⋊C4—1224no—
551C2×C22⋊C4—1224no—
552C2×C22⋊C4—1224no—
553C2×C22⋊C4—1224no—
554C2×C22⋊C4—1224no—
555C2×C22⋊C4—1224no—
556C2×C22⋊C4—1222no—
557C2×C22⋊C4—1222no—
558C2×C22⋊C4—1222no—
559C2×C22⋊C4—1222no—
560C2×C22⋊C4—1222no—
561C2×C22⋊C4—1222no—
562C2×C22⋊C4—1224no—
563C2×C22⋊C4—1224no—
564C2×C22⋊C4—2442no—
565C2×C22⋊C4—2442no—
566C2×C22⋊C4—2442no—
567C2×C22⋊C4—2442no—
568C2×C22⋊C4C22⋊D6118yes—
569#95—1224no—
570#95—1224no—
571#95—1222no—
572#95—1222no—
573#95—1224no—
574#95—2442no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—28no—
580C24—216no—
581C24—28no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—216no—
595C24—28no—
596C24—28no—
597C24—28no—
598C24—48no—
599C24—48no—
600C24—48no—
601C24—48no—
602C24—48no—
603C24—48no—
604C24—48no—
605C24—48no—
606C24—48no—
607C24—44no—
608C24—44no—
609C24—48no—
610C24—44no—
611C24—44no—
612C24—44no—
613C24—44no—
614C24C2×Dic12214yes—
615C24C2×Dic12212yes—
616C24#1175822214yes—
617C24#1175822212yes—
618C24D4×D6112yes—
619C24D4×D6112yes—
620C24#1175822412yes—
621C24#1175822412yes—
622C24C2×C22⋊D6114yes—
623C24C2×C22⋊D6112yes—
624C24C23×D6111yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—28no—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—28no—
640C22×C4—28no—
641C22×C4—44no—
642C22×C4—48no—
643C22×C4—48no—
644C22×C4—48no—
645C22×C4—48no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—612no—
649C22×C4—614no—
650C22×C4—612no—
651C22×C4—1222no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1222no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1222no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1222no—
669C22×C4—1221no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1222no—
681C22×C4—1222no—
682C22×C4C2×C22⋊D6112yes—
683C22×C4C2×C22⋊D6114yes—
684C22×C4C2×C22⋊D6112yes—
685C22×C4C2×C22⋊D6114yes—
686C4⋊C4—2448no—
687C4⋊C4—2448no—
688C4⋊C4—2444no—
689C4⋊C4—2444no—
690C22⋊C4—216no—
691C22⋊C4—216no—
692C22⋊C4—1228no—
693C22⋊C4—1228no—
694C22⋊C4—2448no—
695C22⋊C4—2448no—
696C22⋊C4—2448no—
697C22⋊C4—2448no—
698C22⋊C4—2444no—
699C22⋊C4—2444no—
700C23—22no—
701C23—24no—
702C23—24no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—232no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—432no—
736C23—432no—
737C23—432no—
738C23—416no—
739C23—432no—
740C23—416no—
741C23—416no—
742C23—416no—
743C23—416no—
744C23—416no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23#1451974814yes—
762C23#1451974914yes—
763C23#1451975014yes—
764C23#1451975414yes—
765C23#1451975414yes—
766C23#1451975618yes—
767C23#1451975614yes—
768C23#1451977014yes—
769C23C2×D4×D6111yescharacteristic
770C23C2×D4×D6111yescharacteristic
771C23C22×C22⋊D6111yescharacteristic
772C23C22×C22⋊D6112yes—
773C23C22×Dic12211yescharacteristic
774C23C2×#1175822411yescharacteristic
775C23C2×#1175822411yescharacteristic
776C23C2×#1175822211yescharacteristic
777C23C2×#1175822212yes—
778C23#1451982212yes—
779C23#1451982212yes—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—416no—
791C2×C4—416no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1224no—
801C2×C4—1224no—
802C2×C4—1224no—
803C2×C4—1224no—
804C2×C4—1224no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2442no—
809C2×C4—2442no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2442no—
814C2×C4—2442no—
815C2×C4—2442no—
816C2×C4—2442no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4—2442no—
820C2×C4—2442no—
821C2×C4—2442no—
822C2×C4—2441no—
823C2×C4—2442no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2442no—
828C2×C4—2442no—
829C2×C4—2442no—
830C2×C4—2442no—
831C2×C4—2442no—
832C2×C4#1451974614yes—
833C22—28no—
834C22—28no—
835C22—24no—
836C22—28no—
837C22—24no—
838C22—28no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—28no—
844C22—28no—
845C22—28no—
846C22—464no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22#1683968518yescomplemented
860C22C2×#1451974611yescharacteristic
861C22C2×#1451974811yescharacteristic
862C22C2×#1451974911yescharacteristic
863C22C2×#1451975011yescharacteristic
864C22C2×#1451975411yescharacteristic
865C22C2×#1451975411yescharacteristic
866C22C2×#1451975612yes—
867C22C2×#1451975611yescharacteristic
868C22#1684027312yes—
869C22#1684027311yescharacteristic
870C22C2×#1451977011yescharacteristic
871C22#1684032111yescharacteristic
872C22#1684032911yescharacteristic
873C22#1684035012yes—
874C22#1684038812yes—
875C22D4×C22⋊D6112yes—
876C22D4×C22⋊D6112yes—
877C22#1684040212yes—
878C22#1684040212yes—
879C22#1684040612yes—
880C22#1684040612yes—
881C22#1684043812yes—
882C22#1684043812yes—
883C4—24no—
884C4—44no—
885C4—42no—
886C4—4882no—
887C4—4881no—
888C4—4881no—
889C4—2444no—
890C4—2442no—
891C4—2442no—
892C2—28no—
893C2—48no—
894C2C2×#1683968511yescharacteristic
895C2#2144916911yescharacteristic
896C2#2144919311yescharacteristic
897C2#2144920411yescharacteristic
898C2#2144935512yes—
899C2#2144948012yes—
900C2#2144948012yes—
901C2#2145005912yes—
902C2#2145070911yescharacteristic
903C2#2145162411yescharacteristic
904C2#2145410611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, cosocleC24×C61C24
FittingC23×C22⋊C4×C61C2
prime radicalC26×C61C22
hypercenterC23×C22⋊C4D61
hypocenterC61#14726
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16839685C2semidirect
2. C2×#16839635C2semidirect
3. C2×#16839635C2semidirect
4. C2×#16839622C2semidirect
7. #21444064C2semidirect
8. #21444062C2semidirect
9. #21444062C2semidirect
10. #21444042C2semidirect
12. C22×C4⋊Dic61C22semidirect
13. C22×#11758196C22semidirect
14. C22×#11758196C22semidirect
15. C22×#11758196C22semidirect
30. C2×#14519684C22semidirect
31. C2×#14519684C22semidirect
32. C2×#14519684C22semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
35. C2×#14519684C22semidirect
407. C22×C61#396semidirect
495. C61#14726semidirect
859. C22#16839685semidirect

Maximal subgroups

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

subgroupindex
C2×#168396852
C2×#168396352
C2×#168396222
C2×#168396182
#214440642
#214440622
#214440422
C23×C22⋊C4×C612
#1472661