Finite Group Databasebeta

← #29603145

Subgroups — #29603145

Order 15616.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519753C211yesmaximal, characteristic
2C2×#16839669C211yesmaximal, characteristic, complemented
3C2×#16839660C211yesmaximal, characteristic, complemented
4C2×#16839619C211yesmaximal, characteristic
5C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
6C2×C4×#11758198C211yesmaximal, characteristic
7#21444085C212yesmaximal, complemented
8#21444063C212yesmaximal
9#21444055C212yesmaximal
10#21444047C212yesmaximal, complemented
11C2×C61×#391C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C2×#14519753—24no—
14C2×#14519753—24no—
15C2×#14519753C418yescomplemented
16C22×C4⋊Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2212yes—
19C22×#11758196C2212yes—
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C2212yes—
25C22×C4×Dic61C2211yescharacteristic
26#16839669—24no—
27#16839660—24no—
28#16839619—24no—
29C4⋊C4×Dic61—24no—
30C4×#11758198—24no—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2212yes—
36C2×#14519684C2211yescharacteristic
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×Dic61C2311yescharacteristic
48C23×Dic61C2312yes—
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—
58C2×C4⋊Dic61—22no—
59C2×C4⋊Dic61—22no—
60C2×C4⋊Dic61—22no—
61C2×C4⋊Dic61C2×C414yes—
62C2×C4⋊Dic61D414yes—
63C2×C4⋊Dic61D414yes—
64C2×#11758196—24no—
65C2×#11758196—24no—
66C2×#11758196—24no—
67C2×#11758196—24no—
68C2×#11758196—42no—
69C2×#11758196C2×C418yes—
70C2×#11758198—22no—
71C2×#11758198—22no—
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—24no—
78C2×#11758198—24no—
79C2×#11758198—42no—
80C2×#11758198C2×C418yes—
81C2×#11758198Q814yescomplemented
82C2×C4×Dic61—22no—
83C2×C4×Dic61—22no—
84C2×C4×Dic61—24no—
85C2×C4×Dic61—24no—
86C2×C4×Dic61—42no—
87C2×C4×Dic61D414yes—
88#14519684—24no—
89#14519684—22no—
90#14519684—22no—
91#14519684—24no—
92#14519684—24no—
93#14519684—24no—
94#14519684—24no—
95C22×Q8×C61—22no—
96C22×Q8×C61—22no—
97C22×Q8×C61—22no—
98C22×Q8×C61—22no—
99C22×Q8×C61—22no—
100C22×Q8×C61—22no—
101C22×Q8×C61C2×C414yes—
102C23×C4×C61C2312yes—
103C23×C4×C61C2312yes—
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61D414yes—
110C2×C42×C61—22no—
111C2×C42×C61—22no—
112C2×C42×C61—22no—
113#95×C61—24no—
114#95×C61—24no—
115C24×C61C2411yescharacteristic
116C23×D61—21no—
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×D61C22×C412yes—
129C23×D61C2×Q812yes—
130C23×D61#4112yes—
131C2×Q8×C61—28no—
132C2×Q8×C61—28no—
133C2×Q8×C61—28no—
134C2×Q8×C61—44no—
135C2×Q8×C61—44no—
136C2×Q8×C61—44no—
137C2×Q8×C61—44no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—21no—
158C22×C4×C61—22no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61C22×C414yes—
163C22×C4×C61C22×C412yes—
164C22×C4×C61C2×D414yes—
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×Q812yes—
170C22×C4×C61#4112yes—
171C22×C4×C61#4112yes—
172C22×C4×C61#4112yes—
173C22×Dic61—21no—
174C22×Dic61—22no—
175C22×Dic61—21no—
176C22×Dic61—22no—
177C22×Dic61—21no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61C22×C412yes—
201C22×Dic61C22×C414yes—
202C22×Dic61C2×D412yes—
203C22×Dic61C2×D414yes—
204C22×Dic61C2×D414yes—
205C22×Dic61C2×D412yes—
206C22×Dic61C2×Q812yes—
207C22×Dic61#4112yes—
208C2×C4×D61—28no—
209C2×C4×D61—28no—
210C2×C4×D61—28no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
214C2×C4×D61—44no—
215C4⋊C4×C61—28no—
216C42×C61—44no—
217#11758198—28no—
218#11758198—216no—
219#11758198—28no—
220#11758198—48no—
221C4⋊Dic61—44no—
222C4⋊Dic61C22⋊C4116yescomplemented
223#11758196—216no—
224#11758196—48no—
225C4×Dic61—28no—
226C4×Dic61—48no—
227C23×C61C23×C411yescharacteristic
228C23×C61C22×D411yescharacteristic
229C23×C61C22×D411yescharacteristic
230C23×C61C22×D411yescharacteristic
231C23×C61C22×D411yescharacteristic
232C23×C61C22×Q811yescharacteristic
233C23×C61C2×#4111yescharacteristic
234C23×C61C2×#4111yescharacteristic
235C23×C61C2×#4111yescharacteristic
236C23×C61C2×#4111yescharacteristic
237C23×C61C2×#4111yescharacteristic
238C23×C61H(5,𝔽2)11yescharacteristic
239C23×C612−1+411yescharacteristic
240C23×C612−1+411yescharacteristic
241C23×C612−1+411yescharacteristic
242C22×D61—22no—
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—41no—
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×D61C4×Q814yes—
277Q8×C61—416no—
278C2×C4×C61—24no—
279C2×C4×C61—24no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—24no—
286C2×C4×C61—24no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—42no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—42no—
305C2×C4×C61—41no—
306C2×C4×C61C2×C22⋊C414yes—
307C2×C4×C61C4×D414yes—
308C2×C4×C61C4×D414yes—
309C2×C4×C61#12114yes—
310C2×C4×C61#12114yes—
311C2×C4×C61#12414yes—
312C2×C4×C61#12714yes—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—24no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61C2×C22⋊C418yes—
347C2×Dic61C22⋊Q814yescomplemented
348C4×D61—416no—
349#13997—611nomaximal, Sylow
350C22×C61C22×C22⋊C411yescharacteristic
351C22×C61C2×C4×D411yescharacteristic
352C22×C61C2×C4×D411yescharacteristic
353C22×C61C2×C4×Q811yescharacteristic
354C22×C61C4×#4111yescharacteristic
355C22×C61#51911yescharacteristic
356C22×C61#52011yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C22×C61C2×#12111yescharacteristic
359C22×C61C2×C22⋊Q811yescharacteristic
360C22×C61#52511yescharacteristic
361C22×C61C2×#12411yescharacteristic
362C22×C61#52911yescharacteristic
363C22×C61C2×#12711yescharacteristic
364C22×C61#53311yescharacteristic
365C22×C61#53611yescharacteristic
366C22×C61#53711yescharacteristic
367C22×C61#54111yescharacteristic
368C22×C61#54211yescharacteristic
369C22×C61#54611yescharacteristic
370C22×C61#54611yescharacteristic
371C22×C61#54611yescharacteristic
372C22×C61#54711yescharacteristic
373C22×C61#54711yescharacteristic
374C22×C61#54711yescharacteristic
375C22×C61#54811yescharacteristic
376C22×C61#54811yescharacteristic
377C22×C61#54811yescharacteristic
378C22×C61D4×Q811yescharacteristic
379C22×C61D4×Q811yescharacteristic
380C22×C61D4×Q811yescharacteristic
381C22×C61#55211yescharacteristic
382C22×C61#55211yescharacteristic
383C22×C61#55411yescharacteristic
384C22×C61#55611yescharacteristic
385C2×D61—24no—
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—42no—
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—
400C4×C61—44no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61—44no—
404C4×C61#39018yes—
405Dic61—28no—
406Dic61—24no—
407Dic61—42no—
408Dic61—42no—
409Dic61—82no—
410C22×C22⋊Q8—611no—
411C2×#391—611no—
412C2×#391D6111yescharacteristic, complemented
413C2×#389—611no—
414C2×#380—611no—
415C2×C4×C4⋊C4—611no—
416C2×C4×C22⋊C4—611no—
417#1445—612no—
418#1439—612no—
419#1437—612no—
420C4⋊#95—612no—
421C2×C61C2×#39011yescharacteristic
422C2×C61C4×C22⋊Q811yescharacteristic
423C2×C61#232311yescharacteristic
424C2×C61#233911yescharacteristic
425C2×C61Q8×C22⋊C411yescharacteristic
426C2×C61#236011yescharacteristic
427C2×C61#236211yescharacteristic
428C2×C61#241511yescharacteristic
429C2×C61#241711yescharacteristic
430C2×C61#242711yescharacteristic
431C2×C61#242911yescharacteristic
432C2×C61#248911yescharacteristic
433C2×C61#249211yescharacteristic
434C2×C61#254011yescharacteristic
435C2×C61#254211yescharacteristic
436D61—44no—
437C23×Q8C2×D6111yescharacteristic
438C24×C4—611no—
439C2×C22⋊Q8—618no—
440C2×C22⋊Q8—1224no—
441C2×C22⋊Q8—1224no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—612no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—612no—
446C22×C4⋊C4C2×D6111yescharacteristic
447C22×C22⋊C4—612no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—612no—
451C22×C42—611no—
452C22×C42—612no—
453C22×C42C2×D6111yescharacteristic
454#391—24no—
455#391—1224no—
456#389—1224no—
457#380—1224no—
458C4×C4⋊C4—1224no—
459C4×C22⋊C4—1224no—
460C2×#95—611no—
461C2×#95—612no—
462C2×#95—612no—
463C2×#95—612no—
464C2×#95—612no—
465C2×#95—612no—
466C2×#95—611no—
467C2×#95C2×D6112yes—
468C2×#95C2×D6112yes—
469C61#1399711yescharacteristic, complemented, Sylow
470C25—611no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8—22no—
477C22×Q8C4×D6114yes—
478C23×C4—612no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—614no—
483C23×C4—612no—
484C23×C4—1222no—
485C23×C4—1222no—
486C23×C4—1222no—
487C23×C4—1222no—
488C23×C4—1222no—
489C23×C4—1222no—
490C23×C4C22×D6112yes—
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6112yes—
494C23×C4C22×D6111yescharacteristic
495C22⋊Q8—12232no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—614no—
499C2×C4⋊C4—614no—
500C2×C4⋊C4—614no—
501C2×C4⋊C4—618no—
502C2×C4⋊C4—1224no—
503C2×C4⋊C4—1224no—
504C2×C4⋊C4—1224no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1224no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—2442no—
510C2×C4⋊C4C22⋊D6114yes—
511C2×C22⋊C4—618no—
512C2×C22⋊C4—614no—
513C2×C22⋊C4—1224no—
514C2×C22⋊C4—1224no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—1222no—
517C2×C22⋊C4—1222no—
518C2×C22⋊C4—1222no—
519C2×C22⋊C4—1222no—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4—1224no—
522C2×C22⋊C4—2442no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—614no—
527C2×C42—1222no—
528C2×C42—1222no—
529C2×C42—1224no—
530C2×C42—1224no—
531C2×C42—2442no—
532#95—24no—
533#95—24no—
534#95—1222no—
535#95—1222no—
536#95—1224no—
537#95—1224no—
538#95—1224no—
539#95—1224no—
540#95—1224no—
541C24—612no—
542C24—612no—
543C24—612no—
544C24—1221no—
545C24—1221no—
546C24—1221no—
547C24—1221no—
548C24—1221no—
549C24—1221no—
550C24—1221no—
551C24—1221no—
552C24—1221no—
553C24—1221no—
554C24—1221no—
555C24—1221no—
556C24C23×D6111yescharacteristic
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—614no—
589C22×C4—612no—
590C22×C4—614no—
591C22×C4—614no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—1221no—
597C22×C4—1222no—
598C22×C4—1221no—
599C22×C4—1222no—
600C22×C4—1221no—
601C22×C4—1222no—
602C22×C4—1221no—
603C22×C4—1222no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1228no—
617C22×C4—1228no—
618C22×C4—1228no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—2444no—
627C22×C4—2444no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4C2×C4×D6114yes—
631C22×C4C2×C4×D6112yes—
632C22×C4#1175822212yes—
633C22×C4D4×D6112yes—
634C22×C4D4×D6112yes—
635C22×C4D4×D6112yes—
636C22×C4#1175822412yes—
637C22×C4Q8×D6112yes—
638C22×C4#1175822612yes—
639C22×C4C2×C22⋊D6114yes—
640C22×C4C2×C22⋊D6112yes—
641C4⋊C4—28no—
642C4⋊C4—6116no—
643C4⋊C4—12216no—
644C4⋊C4—2448no—
645C4⋊C4—2444no—
646C22⋊C4—1228no—
647C22⋊C4—12216no—
648C22⋊C4—1228no—
649C22⋊C4—2448no—
650C42—44no—
651C42—1228no—
652C42—2448no—
653C23—614no—
654C23—1222no—
655C23—1222no—
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—2441no—
673C23—2441no—
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—
688C23C22×C4×D6111yescharacteristic
689C23C2×D4×D6111yescharacteristic
690C23C2×D4×D6111yescharacteristic
691C23C2×D4×D6111yescharacteristic
692C23C22×C22⋊D6111yescharacteristic
693C23C2×Q8×D6111yescharacteristic
694C23#41×D6111yescharacteristic
695C23#41×D6111yescharacteristic
696C23C2×#1175822411yescharacteristic
697C23C2×#1175822211yescharacteristic
698C23C2×#1175822611yescharacteristic
699C23#1451982311yescharacteristic
700C23#1451982411yescharacteristic
701C23#1451982511yescharacteristic
702C23#1451982511yescharacteristic
703Q8—416no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—618no—
733C2×C4—614no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1224no—
737C2×C4—1224no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1224no—
741C2×C4—1222no—
742C2×C4—1224no—
743C2×C4—1224no—
744C2×C4—1224no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—24416no—
768C2×C4C22⋊C4×D6114yes—
769C2×C4#1451973714yes—
770C2×C4C4×C22⋊D6114yes—
771C2×C4#1451974914yes—
772C2×C4#1451975014yes—
773C2×C4#1451976314yes—
774C2×C4#1451977314yes—
775C22—1224no—
776C22—1224no—
777C22—1224no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22C2×C22⋊C4×D6111yescharacteristic
791C22C2×#1451973711yescharacteristic
792C22C2×C4×C22⋊D6111yescharacteristic
793C22C4×Q8×D6111yescharacteristic
794C22C4×#1175822611yescharacteristic
795C22#1684023811yescharacteristic
796C22#1684024411yescharacteristic
797C22C2×#1451974911yescharacteristic
798C22C2×#1451975011yescharacteristic
799C22C22⋊Q8×D6111yescharacteristic
800C22#1684027511yescharacteristic
801C22C2×#1451976311yescharacteristic
802C22#1684029111yescharacteristic
803C22C2×#1451977311yescharacteristic
804C22#1684031711yescharacteristic
805C22#1684033511yescharacteristic
806C22#1684034211yescharacteristic
807C22#1684037311yescharacteristic
808C22#1684038111yescharacteristic
809C22#1684040011yescharacteristic
810C22#1684040311yescharacteristic
811C22#1684040511yescharacteristic
812C22#1684041111yescharacteristic
813C22#1684041411yescharacteristic
814C22#1684041511yescharacteristic
815C22#1684042011yescharacteristic
816C22#1684042211yescharacteristic
817C22#1684042311yescharacteristic
818C22#1684042511yescharacteristic
819C22Q8×C22⋊D6111yescharacteristic
820C22#1684042711yescharacteristic
821C22#1684045311yescharacteristic
822C22#1684045311yescharacteristic
823C22#1684047211yescharacteristic
824C22#1684048511yescharacteristic
825C4—42no—
826C4—42no—
827C4—44no—
828C4—44no—
829C4—1224no—
830C4—1228no—
831C4—4882no—
832C4—2442no—
833C4—2442no—
834C4#1683966218yes—
835C2—2444no—
836C2C2×#1683966211yescharacteristic
837C2#2144835711yescharacteristic
838C2#2144850411yescharacteristic
839C2#2144864811yescharacteristic
840C2#2144865311yescharacteristic
841C2#2144882011yescharacteristic
842C2#2144884211yescharacteristic
843C2#2144925111yescharacteristic
844C2#2144927311yescharacteristic
845C2#2144939911yescharacteristic
846C2#2144942111yescharacteristic
847C2#2145015811yescharacteristic
848C2#2145019111yescharacteristic
849C2#2145075711yescharacteristic
850C2#2145076911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#391C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×#391D61
hypocenterC61#13997
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#16839669C2semidirect
3. C2×#16839660C2semidirect
5. C2×C4⋊C4×Dic61C2semidirect
7. #21444085C2semidirect
10. #21444047C2semidirect
11. C2×C61×#391C2semidirect
15. C2×#14519753C4semidirect
81. C2×#11758198Q8semidirect
222. C4⋊Dic61C22⋊C4semidirect
347. C2×Dic61C22⋊Q8semidirect
412. C2×#391D61semidirect
469. C61#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#145197532
C2×#168396692
C2×#168396602
C2×#168396192
C2×C4⋊C4×Dic612
C2×C4×#117581982
#214440852
#214440632
#214440552
#214440472
C2×C61×#3912
#1399761