Finite Group Databasebeta

← #29605351

Subgroups — #29605351

Order 15616.

2854 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D244C211yesmaximal, characteristic, complemented
2C2×#16839671C211yesmaximal, characteristic
3C2×#16839641C212yesmaximal, complemented
4C2×#16839638C212yesmaximal, complemented
5#21444075C211yesmaximal, characteristic, complemented
6#21444064C211yesmaximal, characteristic, complemented
7#21444059C211yesmaximal, characteristic, complemented
8#21444057C212yesmaximal, complemented
9#21444046C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C22⋊D61C2212yes—
14C23×C4×D61C2212yes—
15C2×C4×D244—28no—
16C2×C4×D244—24no—
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23#16839671C418yescomplemented
24#16839641—28no—
25#16839638—28no—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C24×C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2211yescharacteristic
36C22×C42×C61C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C4×C22⋊C4×C61—24no—
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2211yescharacteristic
41C24×D61C2312yes—
42C22×D244—24no—
43C22×D244—24no—
44C22×D244—22no—
45C22×D244—22no—
46C22×D244C2×C414yescomplemented
47C22×C22⋊D61—24no—
48C22×C22⋊D61—24no—
49C22×C22⋊D61—24no—
50C22×C22⋊D61—24no—
51C22×C22⋊D61—42no—
52C22×C22⋊D61—42no—
53C22×C22⋊D61C2×C418yescomplemented
54C23×Dic61C2312yes—
55C23×Dic61C2312yes—
56C23×Dic61C2312yes—
57C22×C4×D61—24no—
58C22×C4×D61—24no—
59C22×C4×D61—24no—
60C22×C4×D61—24no—
61C22×C4×D61—24no—
62C22×C4×D61—42no—
63C22×C4×D61—42no—
64C4×D244—232no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61—24no—
67C2×C22⋊Dic61—24no—
68C2×C22⋊Dic61—24no—
69C2×C22⋊Dic61—42no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—24no—
75C2×#11758198—24no—
76C2×#11758198—42no—
77C2×#11758198—42no—
78C2×#11758198—42no—
79C2×#11758198—42no—
80C2×#11758198C2×C418yescomplemented
81C2×#11758198D418yescomplemented
82#14519684—24no—
83#14519684—24no—
84#14519684—24no—
85#14519684—22no—
86#14519684—24no—
87#14519684—42no—
88#14519684C2×C414yescomplemented
89C25×C61C2311yescharacteristic
90C23×C4×C61—22no—
91C23×C4×C61—22no—
92C23×C4×C61—22no—
93C23×C4×C61—24no—
94C23×C4×C61—42no—
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C2×C22⋊C4×C61—22no—
102C2×C22⋊C4×C61—22no—
103C2×C22⋊C4×C61—22no—
104C2×C22⋊C4×C61—22no—
105C2×C22⋊C4×C61C2×C414yescomplemented
106C2×C22⋊C4×C61D414yescomplemented
107C2×C42×C61—24no—
108C2×C42×C61—22no—
109C2×C42×C61—42no—
110C2×C42×C61D414yescomplemented
111#95×C61—22no—
112#95×C61—22no—
113C24×C61—22no—
114C24×C61—21no—
115C24×C61—22no—
116C24×C61—21no—
117C24×C61—21no—
118C24×C61—21no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61C22×C412yes—
122C24×C61C2×D412yes—
123C24×C61#4112yes—
124C24×C61C2411yescharacteristic
125C23×D61—22no—
126C23×D61—22no—
127C23×D61—22no—
128C23×D61—22no—
129C23×D61—22no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61C22×C414yes—
138C23×D61C2×D414yes—
139C23×D61#4114yes—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—28no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—22no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—48no—
161C22×C4×C61—48no—
162C22×C4×C61—44no—
163C22×C4×C61—44no—
164C22×C4×C61C22×C412yes—
165C22×C4×C61C22×C412yes—
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D414yes—
169C22×C4×C61C2×D412yes—
170C22×C4×C61C2×D412yes—
171C22×C4×C61C2×D412yes—
172C22×C4×C61#4112yes—
173C22×C4×C61#4112yes—
174C22×C4×C61#4112yes—
175C2×C22⋊D61—216no—
176C2×C22⋊D61—216no—
177C2×C22⋊D61—48no—
178C2×C22⋊D61—48no—
179C2×C22⋊D61—48no—
180C2×C22⋊D61—48no—
181C2×C22⋊D61—48no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61C22×C414yes—
202C22×Dic61C2×D414yes—
203C2×D244—28no—
204C2×D244—216no—
205C2×D244—28no—
206C2×D244—216no—
207C2×D244—28no—
208C2×C4×D61—216no—
209C2×C4×D61—48no—
210C2×C4×D61—48no—
211C2×C4×D61—48no—
212C2×C4×D61—48no—
213C2×C4×D61—48no—
214C2×C4×D61—48no—
215C22⋊C4×C61—28no—
216C22⋊C4×C61—28no—
217C42×C61—28no—
218C42×C61—44no—
219C22⋊Dic61—48no—
220#11758198—216no—
221#11758198—48no—
222#11758198—48no—
223#11758198—48no—
224C4⋊Dic61—28no—
225C23×C61—22no—
226C23×C61—24no—
227C23×C61—22no—
228C23×C61—24no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—24no—
234C23×C61—24no—
235C23×C61—24no—
236C23×C61—24no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—42no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—42no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61—42no—
246C23×C61—42no—
247C23×C61C4×D414yescomplemented
248C23×C61C23×C411yescharacteristic
249C23×C61C22×D411yescharacteristic
250C23×C61C22×D412yes—
251C23×C61C22×D411yescharacteristic
252C23×C61C2×#4111yescharacteristic
253C23×C61C2×#4112yes—
254C23×C61C2×#4111yescharacteristic
255C23×C61C2×#4111yescharacteristic
256C23×C61C2×#4111yescharacteristic
257C23×C61H(5,𝔽2)12yes—
258C23×C61H(5,𝔽2)12yes—
259C22×D61—24no—
260C22×D61—24no—
261C22×D61—24no—
262C22×D61—24no—
263C22×D61—24no—
264C22×D61—24no—
265C22×D61—24no—
266C22×D61—24no—
267C22×D61—24no—
268C22×D61—24no—
269C22×D61—24no—
270C22×D61—24no—
271C22×D61—24no—
272C22×D61—24no—
273C22×D61—24no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61C4×D418yes—
294C2×C4×C61—24no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—24no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—24no—
303C2×C4×C61—24no—
304C2×C4×C61—24no—
305C2×C4×C61—24no—
306C2×C4×C61—22no—
307C2×C4×C61—24no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—24no—
311C2×C4×C61—24no—
312C2×C4×C61—416no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61C4×D414yes—
323C2×C4×C61#12014yes—
324C2×C4×C61#12114yes—
325C22⋊D61—432no—
326C2×Dic61—24no—
327C2×Dic61—24no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—24no—
331C2×Dic61—24no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347D244—232no—
348C4×D61—432no—
349#14175—611nomaximal, Sylow
350C22×C61—28no—
351C22×C61—24no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—44no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—44no—
358C22×C61—44no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61C2×C4×D412yes—
362C22×C61C2×C4×D411yescharacteristic
363C22×C61C2×C4×D411yescharacteristic
364C22×C61C4×#4111yescharacteristic
365C22×C61#51812yes—
366C22×C61C2×#12011yescharacteristic
367C22×C61C2×#12111yescharacteristic
368C22×C61#52511yescharacteristic
369C22×C61#52512yes—
370C22×C61#52511yescharacteristic
371C22×C61#52911yescharacteristic
372C22×C61#53211yescharacteristic
373C22×C61#53511yescharacteristic
374C22×C61#53511yescharacteristic
375C22×C61#54012yes—
376C22×C61D4212yes—
377C22×C61#54612yes—
378C22×C61#54612yes—
379C22×C61#54612yes—
380C22×C61#54612yes—
381C22×C61#55112yes—
382C22×C61#55312yes—
383C22×C61#55312yes—
384C2×D61—28no—
385C2×D61—28no—
386C2×D61—28no—
387C2×D61—44no—
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61—44no—
392C2×D61—44no—
393C2×D61—44no—
394C2×D61—44no—
395C2×D61—44no—
396C2×D61—44no—
397C2×D61—44no—
398C2×D61—44no—
399C4×C61—24no—
400C4×C61—24no—
401C4×C61—24no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—42no—
405Dic61—44no—
406Dic61—44no—
407Dic61—82no—
408C22×C4×D4—611no—
409C2×#392—611no—
410C2×#386—612no—
411C2×#386—612no—
412C2×C4×C22⋊C4D6111yescharacteristic, complemented
413#1442—611no—
414#1439—611no—
415#1438—611no—
416#1437—612no—
417#1434—611no—
418C22⋊#95—612no—
419C2×C61—44no—
420C2×C61C4×#12011yescharacteristic
421C2×C61C4×#12111yescharacteristic
422C2×C61#232811yescharacteristic
423C2×C61#235812yes—
424C2×C61#236412yes—
425C2×C61#240411yescharacteristic
426C2×C61#240811yescharacteristic
427C2×C61#245712yes—
428C2×C61#246412yes—
429C2×C61#253511yescharacteristic
430C2×C61#259811yescharacteristic
431D61—48no—
432C23×D4—612no—
433C23×D4—611no—
434C24×C4—612no—
435C24×C4C2×D6111yescharacteristic
436C2×C4×D4—1228no—
437C2×C4×D4—1224no—
438C22×C4⋊C4—611no—
439C22×C22⋊C4—612no—
440C22×C22⋊C4—612no—
441C22×C22⋊C4—612no—
442C22×C22⋊C4—612no—
443C22×C22⋊C4—612no—
444C22×C22⋊C4C2×D6111yescharacteristic
445C22×C22⋊C4C2×D6111yescharacteristic
446C22×C42C2×D6111yescharacteristic
447C22×C42C2×D6111yescharacteristic
448#392—618no—
449#386—1228no—
450#386—1228no—
451C4×C22⋊C4—24no—
452C2×#95—611no—
453C2×#95—612no—
454C2×#95—612no—
455C2×#95—612no—
456C2×#95—611no—
457C2×#95—612no—
458C2×#95—612no—
459C2×#95C2×D6111yescharacteristic
460C2×#95C2×D6111yescharacteristic
461C61#1417511yescharacteristic, complemented, Sylow
462C25—612no—
463C25C22×D6111yescharacteristic
464C22×D4—618no—
465C22×D4—614no—
466C22×D4—1224no—
467C22×D4—1224no—
468C22×D4—1224no—
469C22×D4—1224no—
470C22×D4—1224no—
471C22×D4—1224no—
472C22×D4—1222no—
473C22×D4—1222no—
474C22×D4—2442no—
475C22×D4—2442no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—612no—
482C23×C4—612no—
483C23×C4—612no—
484C23×C4—1224no—
485C23×C4—1224no—
486C23×C4—1224no—
487C23×C4—1224no—
488C23×C4—1224no—
489C23×C4—2442no—
490C23×C4—2442no—
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6111yescharacteristic
494C23×C4C22×D6111yescharacteristic
495C23×C4C22×D6111yescharacteristic
496C23×C4C22×D6111yescharacteristic
497C4×D4—12232no—
498C2×C4⋊C4—1224no—
499C2×C4⋊C4—1222no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—618no—
505C2×C22⋊C4—618no—
506C2×C22⋊C4—1224no—
507C2×C22⋊C4—1224no—
508C2×C22⋊C4—1224no—
509C2×C22⋊C4—1224no—
510C2×C22⋊C4—1224no—
511C2×C22⋊C4—1224no—
512C2×C22⋊C4—1224no—
513C2×C22⋊C4—1224no—
514C2×C22⋊C4—2442no—
515C2×C22⋊C4—2442no—
516C2×C22⋊C4—2442no—
517C2×C22⋊C4—2442no—
518C2×C22⋊C4—2442no—
519C2×C22⋊C4C4×D6114yescomplemented
520C2×C22⋊C4D24414yescomplemented
521C2×C42—24no—
522C2×C42—22no—
523C2×C42—42no—
524C2×C42C22⋊D6114yescomplemented
525#95—22no—
526#95—22no—
527#95—614no—
528#95—1224no—
529#95—1224no—
530#95—1224no—
531#95—1222no—
532#95—1224no—
533#95—2442no—
534C24—22no—
535C24—21no—
536C24—22no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—22no—
541C24—22no—
542C24—614no—
543C24—614no—
544C24—614no—
545C24—1222no—
546C24—1222no—
547C24—1222no—
548C24—1222no—
549C24—1222no—
550C24—1222no—
551C24—1222no—
552C24—1222no—
553C24—1222no—
554C24—1222no—
555C24—1222no—
556C24—1222no—
557C24C2×C4×D6112yes—
558C24C2×D24412yes—
559C24#1175822212yes—
560C24C23×D6111yescharacteristic
561C2×D4—12216no—
562C2×D4—1228no—
563C2×D4—1228no—
564C2×D4—12216no—
565C2×D4—12216no—
566C2×D4—12216no—
567C2×D4—1228no—
568C2×D4—2448no—
569C2×D4—2448no—
570C2×D4—2448no—
571C2×D4—2448no—
572C2×D4—2448no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—614no—
598C22×C4—614no—
599C22×C4—12216no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—2448no—
620C22×C4—2448no—
621C22×C4—2448no—
622C22×C4—2448no—
623C22×C4—2448no—
624C22×C4—2448no—
625C22×C4C2×C4×D6112yes—
626C22×C4C2×C4×D6112yes—
627C22×C4C2×D24412yes—
628C22×C4C2×D24412yes—
629C22×C4#1175822212yes—
630C22×C4#1175822212yes—
631C22×C4#1175822212yes—
632C22×C4D4×D6114yes—
633C22×C4C2×C22⋊D6112yes—
634C22×C4C2×C22⋊D6112yes—
635C22×C4C2×C22⋊D6112yes—
636C4⋊C4—1228no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—12216no—
640C22⋊C4—2448no—
641C22⋊C4—2448no—
642C22⋊C4—2448no—
643C22⋊C4—2448no—
644C42—28no—
645C42—44no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—42no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—42no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—618no—
669C23—1224no—
670C23—1224no—
671C23—1224no—
672C23—1224no—
673C23—1224no—
674C23—1224no—
675C23—1224no—
676C23—1224no—
677C23—1224no—
678C23—1224no—
679C23—1224no—
680C23—1224no—
681C23—1224no—
682C23—1224no—
683C23—1224no—
684C23—1224no—
685C23—1224no—
686C23—1224no—
687C23—2442no—
688C23—2442no—
689C23—2442no—
690C23—2442no—
691C23—2442no—
692C23—2442no—
693C23—2442no—
694C23—2442no—
695C23—2442no—
696C23—2442no—
697C23—2442no—
698C23—2442no—
699C23—2442no—
700C23—2442no—
701C23—2442no—
702C23—2442no—
703C23C4×D24414yescomplemented
704C23C22×C4×D6111yescharacteristic
705C23C2×D4×D6112yes—
706C23C22×C22⋊D6111yescharacteristic
707C23C22×D24411yescharacteristic
708C23#41×D6112yes—
709C23C2×#1175822211yescharacteristic
710C23C2×#1175822211yescharacteristic
711C23C2×#1175822211yescharacteristic
712C23C2×#1175822211yescharacteristic
713C23#1451982212yes—
714C23#1451982312yes—
715D4—12232no—
716D4—24432no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—416no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—1224no—
746C2×C4—1224no—
747C2×C4—1224no—
748C2×C4—1224no—
749C2×C4—1224no—
750C2×C4—1224no—
751C2×C4—24432no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4C4×C22⋊D6114yes—
768C2×C4#1451974514yes—
769C2×C4#1451975114yes—
770C22—28no—
771C22—24no—
772C22—42no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—44no—
781C22—1228no—
782C22—1228no—
783C22—1228no—
784C22—2444no—
785C22—2444no—
786C22—2444no—
787C22—2444no—
788C22—2444no—
789C22—2444no—
790C22—2444no—
791C22—2444no—
792C22—2444no—
793C22—2444no—
794C22—2444no—
795C22—2444no—
796C22C4×D4×D6112yes—
797C22C2×C4×C22⋊D6111yescharacteristic
798C22C2×C4×D24411yescharacteristic
799C22C4×#1175822211yescharacteristic
800C22#1684023412yes—
801C22C2×#1451974511yescharacteristic
802C22C2×#1451975111yescharacteristic
803C22#1684026911yescharacteristic
804C22#1684027112yes—
805C22#1684027311yescharacteristic
806C22#1684029611yescharacteristic
807C22#1684031211yescharacteristic
808C22#1684032611yescharacteristic
809C22#1684032911yescharacteristic
810C22#1684036312yes—
811C22D4×D24412yes—
812C22#1684040212yes—
813C22#1684040212yes—
814C22#1684040712yes—
815C22#1684040812yes—
816C22#1684043612yes—
817C22#1684045612yes—
818C22#1684046212yes—
819C4—24no—
820C4—24no—
821C4—24no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—4882no—
826C4—2444no—
827C4—2444no—
828C2—44no—
829C2—2448no—
830C2C4×#1451974511yescharacteristic
831C2C4×#1451975111yescharacteristic
832C2#2144854111yescharacteristic
833C2#2144880112yes—
834C2#2144887012yes—
835C2#2144913811yescharacteristic
836C2#2144917511yescharacteristic
837C2#2144972612yes—
838C2#2144982512yes—
839C2#2145071611yescharacteristic
840C2#2145138511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC2×#16839671C2
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#14175
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D244C2semidirect
3. C2×#16839641C2semidirect
4. C2×#16839638C2semidirect
5. #21444075C2semidirect
6. #21444064C2semidirect
7. #21444059C2semidirect
8. #21444057C2semidirect
9. #21444046C2semidirect
10. #21444040C2semidirect
11. C2×C4×C22⋊C4×C61C2semidirect
23. #16839671C4semidirect
46. C22×D244C2×C4semidirect
53. C22×C22⋊D61C2×C4semidirect
80. C2×#11758198C2×C4semidirect
81. C2×#11758198D4semidirect
88. #14519684C2×C4semidirect
105. C2×C22⋊C4×C61C2×C4semidirect
106. C2×C22⋊C4×C61D4semidirect
110. C2×C42×C61D4semidirect
247. C23×C61C4×D4semidirect
412. C2×C4×C22⋊C4D61semidirect
461. C61#14175semidirect
519. C2×C22⋊C4C4×D61semidirect
520. C2×C22⋊C4D244semidirect
524. C2×C42C22⋊D61semidirect
703. C23C4×D244semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2442
C2×#168396712
C2×#168396412
C2×#168396382
#214440752
#214440642
#214440592
#214440572
#214440462
#214440402
C2×C4×C22⋊C4×C612
#1417561