Finite Group Databasebeta

← #29602810

Subgroups — #29602810

Order 15616.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519753C211yesmaximal, characteristic
2C22×Q8×Dic61C211yesmaximal, characteristic, complemented
3C2×#16839619C211yesmaximal, characteristic
4C2×C4×#11758198C211yesmaximal, characteristic
5#21444073C212yesmaximal, complemented
6#21444065C212yesmaximal
7#21444055C212yesmaximal
8#21444054C212yesmaximal, complemented
9#21444049C211yesmaximal, characteristic, complemented
10#21444048C211yesmaximal, characteristic, complemented
11C2×C61×#391C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C2×#14519753—24no—
14C2×#14519753—24no—
15C2×#14519753C418yescomplemented
16C2×Q8×Dic61—24no—
17C2×Q8×Dic61—24no—
18C2×Q8×Dic61—24no—
19C22×C4⋊Dic61C2212yes—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2212yes—
25C22×#11758198C2212yes—
26C22×#11758198C2211yescharacteristic
27C22×C4×Dic61C2212yes—
28C22×C4×Dic61C2211yescharacteristic
29#16839619—24no—
30C4×#11758198—24no—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C23×Q8×C61C2211yescharacteristic
39C22×C4⋊C4×C61C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic
41C61×#391—24no—
42C2×#95×C61C2212yes—
43C2×#95×C61C2212yes—
44C24×D61C2311yescharacteristic
45C23×Dic61C2312yes—
46C23×Dic61C2311yescharacteristic
47C23×Dic61C2312yes—
48C23×Dic61C2311yescharacteristic
49C23×Dic61C2311yescharacteristic
50C22×C4×D61—22no—
51C22×C4×D61—22no—
52C22×C4×D61—22no—
53C22×C4×D61—22no—
54C22×C4×D61—22no—
55C22×C4×D61—22no—
56C22×C4×D61C2×C414yes—
57#14519753—232no—
58Q8×Dic61—232no—
59C2×C4⋊Dic61—24no—
60C2×C4⋊Dic61—22no—
61C2×C4⋊Dic61—22no—
62C2×C4⋊Dic61—22no—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61—24no—
65C2×C4⋊Dic61—24no—
66C2×C4⋊Dic61C2×C414yes—
67C2×C4⋊Dic61D414yes—
68C2×#11758196—24no—
69C2×#11758196—24no—
70C2×#11758196C2×C418yes—
71C2×#11758198—22no—
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198—24no—
79C2×#11758198—24no—
80C2×#11758198—42no—
81C2×#11758198C2×C418yes—
82C2×#11758198Q814yescomplemented
83C2×C4×Dic61—24no—
84C2×C4×Dic61—22no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61—24no—
87C2×C4×Dic61—24no—
88C2×C4×Dic61D414yes—
89#14519684—24no—
90#14519684—22no—
91#14519684—22no—
92#14519684—24no—
93#14519684—24no—
94#14519684—42no—
95#14519684—42no—
96C22×Q8×C61—22no—
97C22×Q8×C61—22no—
98C22×Q8×C61—22no—
99C22×Q8×C61—22no—
100C22×Q8×C61C2×C414yes—
101C22×Q8×C61D414yes—
102C22×Q8×C61D414yes—
103C23×C4×C61C2312yes—
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2312yes—
107C23×C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61—22no—
110C2×C4⋊C4×C61—22no—
111C2×C42×C61—22no—
112C2×C42×C61—22no—
113C2×C42×C61—22no—
114#95×C61—24no—
115#95×C61—24no—
116C24×C61C2411yescharacteristic
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—21no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61—21no—
125C23×D61—21no—
126C23×D61—21no—
127C23×D61—21no—
128C23×D61—21no—
129C23×D61C22×C412yes—
130C23×D61C2×Q812yes—
131C23×D61#4112yes—
132C2×Q8×C61—28no—
133C2×Q8×C61—28no—
134C2×Q8×C61—28no—
135C2×Q8×C61—28no—
136C2×Q8×C61—28no—
137C2×Q8×C61—28no—
138C2×Q8×C61C22⋊C4116yescomplemented
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
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—22no—
161C22×C4×C61—22no—
162C22×C4×C61C22×C414yes—
163C22×C4×C61C22×C412yes—
164C22×C4×C61C2×D414yes—
165C22×C4×C61C2×D414yes—
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×D412yes—
170C22×C4×C61C2×Q812yes—
171C22×C4×C61#4112yes—
172C22×C4×C61#4112yes—
173C22×C4×C61#4112yes—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—22no—
183C22×Dic61—21no—
184C22×Dic61—22no—
185C22×Dic61—21no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—21no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—21no—
201C22×Dic61—22no—
202C22×Dic61C22×C412yes—
203C22×Dic61C22×C414yes—
204C22×Dic61C2×D414yes—
205C22×Dic61C2×D412yes—
206C22×Dic61C2×D412yes—
207C22×Dic61C2×Q812yes—
208C22×Dic61#4112yes—
209C2×C4×D61—28no—
210C2×C4×D61—28no—
211C2×C4×D61—28no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
214C2×C4×D61—44no—
215C2×C4×D61—44no—
216C4⋊C4×C61—44no—
217C42×C61—44no—
218#11758198—28no—
219#11758198—216no—
220#11758198—28no—
221#11758198—48no—
222C4⋊Dic61—216no—
223C4⋊Dic61—28no—
224C4⋊Dic61—28no—
225#11758196—216no—
226C4×Dic61—216no—
227C4×Dic61—28no—
228C23×C61C23×C411yescharacteristic
229C23×C61C22×D411yescharacteristic
230C23×C61C22×D411yescharacteristic
231C23×C61C22×D411yescharacteristic
232C23×C61C22×D411yescharacteristic
233C23×C61C22×Q811yescharacteristic
234C23×C61C2×#4111yescharacteristic
235C23×C61C2×#4111yescharacteristic
236C23×C61C2×#4111yescharacteristic
237C23×C61C2×#4111yescharacteristic
238C23×C61C2×#4111yescharacteristic
239C23×C61H(5,𝔽2)11yescharacteristic
240C23×C612−1+411yescharacteristic
241C23×C612−1+411yescharacteristic
242C23×C612−1+411yescharacteristic
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61C4×Q814yescomplemented
278Q8×C61—232no—
279C2×C4×C61—24no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—24no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61C2×C22⋊C418yes—
307C2×C4×C61C2×C22⋊C414yes—
308C2×C4×C61C4×D414yes—
309C2×C4×C61C4×D414yes—
310C2×C4×C61#12014yes—
311C2×C4×C61#12114yes—
312C2×C4×C61#12114yes—
313C2×C4×C61#12314yes—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—24no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—24no—
325C2×Dic61—24no—
326C2×Dic61—24no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—24no—
331C2×Dic61—24no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—41no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—41no—
348C2×Dic61C22⋊Q814yescomplemented
349C4×D61—416no—
350#13969—611nomaximal, Sylow
351C22×C61C22×C22⋊C411yescharacteristic
352C22×C61C2×C4×D411yescharacteristic
353C22×C61C2×C4×D411yescharacteristic
354C22×C61C2×C4×Q811yescharacteristic
355C22×C61C4×#4111yescharacteristic
356C22×C61#51911yescharacteristic
357C22×C61#52011yescharacteristic
358C22×C61C2×#12011yescharacteristic
359C22×C61C2×#12111yescharacteristic
360C22×C61C2×#12111yescharacteristic
361C22×C61C2×C22⋊Q811yescharacteristic
362C22×C61C2×#12311yescharacteristic
363C22×C61#52511yescharacteristic
364C22×C61#52911yescharacteristic
365C22×C61#53311yescharacteristic
366C22×C61#53611yescharacteristic
367C22×C61#53711yescharacteristic
368C22×C61#54111yescharacteristic
369C22×C61#54211yescharacteristic
370C22×C61#54611yescharacteristic
371C22×C61#54711yescharacteristic
372C22×C61#54811yescharacteristic
373C22×C61#54811yescharacteristic
374C22×C61#54811yescharacteristic
375C22×C61#54811yescharacteristic
376C22×C61#54811yescharacteristic
377C22×C61D4×Q811yescharacteristic
378C22×C61D4×Q811yescharacteristic
379C22×C61D4×Q811yescharacteristic
380C22×C61#55011yescharacteristic
381C22×C61#55011yescharacteristic
382C22×C61#55211yescharacteristic
383C22×C61#55211yescharacteristic
384C22×C61#55411yescharacteristic
385C22×C61#55611yescharacteristic
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—24no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C4×C61—28no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—82no—
405C4×C61#38618yes—
406Dic61—24no—
407Dic61—44no—
408Dic61—42no—
409Dic61—44no—
410Dic61—42no—
411C22×C22⋊Q8—611no—
412C22×C4×Q8—611no—
413C2×#391D6111yescharacteristic, complemented
414C2×#380—611no—
415C2×C4×C22⋊C4—611no—
416#1441—612no—
417#1439—612no—
418#1437—612no—
419#1436—612no—
420C4⋊#95—611no—
421C4⋊#95—611no—
422C2×C61C2×#38611yescharacteristic
423C2×C61C4×C22⋊Q811yescharacteristic
424C2×C61#232311yescharacteristic
425C2×C61Q8×C22⋊C411yescharacteristic
426C2×C61#234111yescharacteristic
427C2×C61#236011yescharacteristic
428C2×C61#236211yescharacteristic
429C2×C61#240711yescharacteristic
430C2×C61#240911yescharacteristic
431C2×C61#242111yescharacteristic
432C2×C61#242311yescharacteristic
433C2×C61#242611yescharacteristic
434C2×C61#242911yescharacteristic
435C2×C61#253611yescharacteristic
436C2×C61#253811yescharacteristic
437D61—44no—
438C23×Q8C2×D6111yescharacteristic
439C24×C4—611no—
440C2×C22⋊Q8—618no—
441C2×C22⋊Q8—1224no—
442C2×C22⋊Q8—1224no—
443C2×C4×Q8—1224no—
444C2×C4×Q8—1224no—
445C2×C4×Q8—1224no—
446C22×C4⋊C4—612no—
447C22×C4⋊C4—611no—
448C22×C4⋊C4—611no—
449C22×C4⋊C4—612no—
450C22×C4⋊C4C2×D6111yescharacteristic
451C22×C22⋊C4—612no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—612no—
455C22×C42—611no—
456C22×C42—612no—
457C22×C42C2×D6111yescharacteristic
458#391—24no—
459#380—1224no—
460C4×C22⋊C4—1224no—
461C2×#95—612no—
462C2×#95—612no—
463C2×#95—611no—
464C2×#95—612no—
465C2×#95—611no—
466C2×#95—612no—
467C2×#95—612no—
468C2×#95C2×D6112yes—
469C2×#95C2×D6112yes—
470C61#1396911yescharacteristic, complemented, Sylow
471C25—611no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8C4×D6114yes—
477C22×Q8D24414yes—
478C22×Q8C22⋊D6114yes—
479C23×C4—611no—
480C23×C4—612no—
481C23×C4—611no—
482C23×C4—612no—
483C23×C4—611no—
484C23×C4—614no—
485C23×C4—1222no—
486C23×C4—1222no—
487C23×C4—1222no—
488C23×C4—1222no—
489C23×C4—1222no—
490C23×C4—1222no—
491C23×C4C22×D6112yes—
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6111yescharacteristic
494C23×C4C22×D6112yes—
495C23×C4C22×D6111yescharacteristic
496C22⋊Q8—12232no—
497C4×Q8—12232no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—618no—
502C2×C4⋊C4—614no—
503C2×C4⋊C4—614no—
504C2×C4⋊C4—1224no—
505C2×C4⋊C4—1224no—
506C2×C4⋊C4—1224no—
507C2×C4⋊C4—1222no—
508C2×C4⋊C4—1224no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1224no—
512C2×C4⋊C4—1222no—
513C2×C22⋊C4—618no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—1222no—
517C2×C22⋊C4—1222no—
518C2×C22⋊C4—1222no—
519C2×C22⋊C4—1224no—
520C2×C22⋊C4—1222no—
521C2×C22⋊C4—1224no—
522C2×C22⋊C4—1224no—
523C2×C22⋊C4—1224no—
524C2×C22⋊C4—2442no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—614no—
529C2×C42—1224no—
530C2×C42—1224no—
531C2×C42—1224no—
532C2×C42—1222no—
533C2×C42—1222no—
534#95—24no—
535#95—24no—
536#95—1222no—
537#95—1222no—
538#95—1224no—
539#95—1224no—
540#95—1224no—
541#95—2442no—
542#95—2442no—
543C24—612no—
544C24—612no—
545C24—612no—
546C24—1221no—
547C24—1221no—
548C24—1221no—
549C24—1221no—
550C24—1221no—
551C24—1221no—
552C24—1221no—
553C24—1221no—
554C24—1221no—
555C24—1221no—
556C24—1221no—
557C24—1221no—
558C24C23×D6111yescharacteristic
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—28no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8—28no—
565C2×Q8#11758198116yescomplemented
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—612no—
590C22×C4—612no—
591C22×C4—612no—
592C22×C4—614no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—614no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1222no—
603C22×C4—1221no—
604C22×C4—1222no—
605C22×C4—1221no—
606C22×C4—1222no—
607C22×C4—1221no—
608C22×C4—1222no—
609C22×C4—1221no—
610C22×C4—1222no—
611C22×C4—1221no—
612C22×C4—1222no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1221no—
618C22×C4—1222no—
619C22×C4—1221no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1221no—
623C22×C4—1222no—
624C22×C4—1228no—
625C22×C4—1228no—
626C22×C4—1228no—
627C22×C4—2444no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4—2444no—
631C22×C4C2×C4×D6114yes—
632C22×C4C2×C4×D6112yes—
633C22×C4C2×D24414yes—
634C22×C4C2×D24412yes—
635C22×C4D4×D6112yes—
636C22×C4D4×D6112yes—
637C22×C4#1175822412yes—
638C22×C4#1175822412yes—
639C22×C4Q8×D6112yes—
640C22×C4#1175822612yes—
641C22×C4C2×C22⋊D6114yes—
642C22×C4C2×C22⋊D6112yes—
643C4⋊C4—44no—
644C4⋊C4—12216no—
645C4⋊C4—12216no—
646C4⋊C4—1228no—
647C4⋊C4—1228no—
648C22⋊C4—1228no—
649C22⋊C4—1228no—
650C22⋊C4—12216no—
651C22⋊C4—2448no—
652C42—44no—
653C42—12216no—
654C42—1228no—
655C23—614no—
656C23—1222no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23C22×C4×D6111yescharacteristic
691C23C2×D4×D6111yescharacteristic
692C23C2×D4×D6111yescharacteristic
693C23C22×C22⋊D6111yescharacteristic
694C23C22×D24411yescharacteristic
695C23C2×Q8×D6111yescharacteristic
696C23#41×D6111yescharacteristic
697C23#41×D6111yescharacteristic
698C23C2×#1175822411yescharacteristic
699C23C2×#1175822411yescharacteristic
700C23C2×#1175822611yescharacteristic
701C23#1451982311yescharacteristic
702C23#1451982411yescharacteristic
703C23#1451982511yescharacteristic
704C23#1451982511yescharacteristic
705Q8—232no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—614no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1224no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1224no—
745C2×C4—1224no—
746C2×C4—1224no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1224no—
751C2×C4—1224no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2442no—
761C2×C4—2441no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2441no—
767C2×C4—2442no—
768C2×C4—24416no—
769C2×C4C2×#1175819818yes—
770C2×C4C2×#1175819814yes—
771C2×C4#1451973714yes—
772C2×C4#1451973714yes—
773C2×C4#1451974714yes—
774C2×C4#1451974914yes—
775C2×C4#1451974914yes—
776C2×C4#1451976114yes—
777C22—1224no—
778C22—1224no—
779C22—1224no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22C22×#1175819811yescharacteristic
793C22C2×#1451973711yescharacteristic
794C22C2×#1451973711yescharacteristic
795C22C4×Q8×D6111yescharacteristic
796C22C4×#1175822611yescharacteristic
797C22#1684023811yescharacteristic
798C22#1684024411yescharacteristic
799C22C2×#1451974711yescharacteristic
800C22C2×#1451974911yescharacteristic
801C22C2×#1451974911yescharacteristic
802C22C22⋊Q8×D6111yescharacteristic
803C22C2×#1451976111yescharacteristic
804C22#1684027511yescharacteristic
805C22#1684029111yescharacteristic
806C22#1684031711yescharacteristic
807C22#1684033511yescharacteristic
808C22#1684034211yescharacteristic
809C22#1684037311yescharacteristic
810C22#1684038111yescharacteristic
811C22#1684040511yescharacteristic
812C22#1684041511yescharacteristic
813C22#1684041911yescharacteristic
814C22#1684042011yescharacteristic
815C22#1684042311yescharacteristic
816C22#1684042411yescharacteristic
817C22#1684042411yescharacteristic
818C22Q8×C22⋊D6111yescharacteristic
819C22#1684042711yescharacteristic
820C22Q8×D24411yescharacteristic
821C22#1684043111yescharacteristic
822C22#1684043411yescharacteristic
823C22#1684044611yescharacteristic
824C22#1684045411yescharacteristic
825C22#1684047011yescharacteristic
826C22#1684048311yescharacteristic
827C4—28no—
828C4—42no—
829C4—42no—
830C4—82no—
831C4—1224no—
832C4—2442no—
833C4—2442no—
834C4—2444no—
835C4—2444no—
836C4#1683963918yes—
837C2—2444no—
838C2C2×#1683963911yescharacteristic
839C2#2144835711yescharacteristic
840C2#2144850411yescharacteristic
841C2Q8×#1175819811yescharacteristic
842C2#2144865711yescharacteristic
843C2#2144882911yescharacteristic
844C2#2144885111yescharacteristic
845C2#2144916711yescharacteristic
846C2#2144918211yescharacteristic
847C2#2144932011yescharacteristic
848C2#2144934211yescharacteristic
849C2#2144938811yescharacteristic
850C2#2144942111yescharacteristic
851C2#2145072611yescharacteristic
852C2#2145073811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#391C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×#391D61
hypocenterC61#13969
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic61C2semidirect
5. #21444073C2semidirect
8. #21444054C2semidirect
9. #21444049C2semidirect
10. #21444048C2semidirect
11. C2×C61×#391C2semidirect
15. C2×#14519753C4semidirect
82. C2×#11758198Q8semidirect
138. C2×Q8×C61C22⋊C4semidirect
277. C22×D61C4×Q8semidirect
348. C2×Dic61C22⋊Q8semidirect
413. C2×#391D61semidirect
470. C61#13969semidirect
565. C2×Q8#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145197532
C22×Q8×Dic612
C2×#168396192
C2×C4×#117581982
#214440732
#214440652
#214440552
#214440542
#214440492
#214440482
C2×C61×#3912
#1396961