Finite Group Databasebeta

← #29611258

Subgroups — #29611258

Order 15616.

2574 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D61C211yesmaximal, characteristic
2C2×#16839661C211yesmaximal, characteristic, complemented
3C2×#16839660C211yesmaximal, characteristic, complemented
4C2×#16839636C212yesmaximal
5C2×#16839619C211yesmaximal, characteristic
6C2×#16839619C211yesmaximal, characteristic
7#21444054C212yesmaximal, complemented
8#21444053C212yesmaximal, complemented
9#21444048C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal
11C61×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C22×C4⋊Dic61C2212yes—
16C22×C4⋊Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×C4×Dic61C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24C2×C42×D61—24no—
25C2×C42×D61—24no—
26C2×C42×D61—24no—
27#16839661—24no—
28#16839660—24no—
29#16839636—28no—
30#16839619—24no—
31#16839619C418yescomplemented
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C4⋊C4×C61C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic
41C2×#95×C61C2212yes—
42C2×#95×C61C2212yes—
43C24×D61C2311yescharacteristic
44C23×Dic61C2312yes—
45C23×Dic61C2312yes—
46C23×Dic61C2311yescharacteristic
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2311yescharacteristic
49C22×C4×D61—22no—
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×D61—22no—
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—22no—
61C22×C4×D61—22no—
62C22×C4×D61—22no—
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61C2×C414yes—
66C22×C4×D61D414yes—
67C22×C4×D61D414yes—
68C22×C4×D61Q814yes—
69C22×C4×D61Q814yes—
70C2×C4⋊Dic61—22no—
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—22no—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—24no—
76C2×C4⋊Dic61—24no—
77C2×C4⋊Dic61—24no—
78C2×C4⋊Dic61C2×C414yescomplemented
79C2×#11758196—24no—
80C2×#11758196—24no—
81C2×#11758196—24no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—24no—
87C2×#11758198C2×C418yes—
88C2×C4×Dic61—22no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61—22no—
91C2×C4×Dic61—22no—
92C2×C4×Dic61—22no—
93C2×C4×Dic61—22no—
94C2×C4×Dic61—22no—
95C2×C4×Dic61—22no—
96C2×C4×Dic61D414yes—
97C42×D61—232no—
98#14519684—24no—
99#14519684—24no—
100#14519684—24no—
101#14519684—24no—
102#14519684—24no—
103#14519684C2×C418yescomplemented
104C23×C4×C61C2312yes—
105C23×C4×C61C2312yes—
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61—22no—
110C2×C4⋊C4×C61—22no—
111C2×C4⋊C4×C61—22no—
112C2×C4⋊C4×C61—22no—
113C2×C4⋊C4×C61—22no—
114C2×C4⋊C4×C61C2×C414yescomplemented
115C2×C42×C61—22no—
116C2×C42×C61—22no—
117C2×C42×C61D414yes—
118#95×C61—24no—
119#95×C61—24no—
120C24×C61C2411yescharacteristic
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×D412yes—
131C23×D61C2×D412yes—
132C23×D61C2×Q812yes—
133C23×D61C2×Q812yes—
134C23×D61#4112yes—
135C23×D61#4112yes—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
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—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61C22×C414yes—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2×Q812yes—
166C22×C4×C61C2×Q812yes—
167C22×C4×C61#4112yes—
168C22×C4×C61#4112yes—
169C22×C4×C61#4112yes—
170C22×C4×C61#4112yes—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
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—21no—
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×Dic61C22×C414yes—
197C22×Dic61C22×C412yes—
198C22×Dic61C2×D412yes—
199C22×Dic61C2×D412yes—
200C22×Dic61C2×D412yes—
201C22×Dic61C2×D412yes—
202C22×Dic61C2×Q812yes—
203C22×Dic61C2×Q812yes—
204C22×Dic61#4112yes—
205C22×Dic61#4112yes—
206C2×C4×D61—28no—
207C2×C4×D61—28no—
208C2×C4×D61—28no—
209C2×C4×D61—28no—
210C2×C4×D61—28no—
211C2×C4×D61—28no—
212C2×C4×D61—28no—
213C2×C4×D61—28no—
214C2×C4×D61—28no—
215C2×C4×D61—28no—
216C2×C4×D61—28no—
217C2×C4×D61—28no—
218C2×C4×D61—28no—
219C2×C4×D61—28no—
220C2×C4×D61—28no—
221C2×C4×D61—28no—
222C2×C4×D61—28no—
223C2×C4×D61—28no—
224C2×C4×D61—28no—
225C2×C4×D61—28no—
226C2×C4×D61C4⋊C4116yescomplemented
227C4⋊C4×C61—28no—
228C4⋊C4×C61—44no—
229C42×C61—28no—
230#11758198—216no—
231#11758198—48no—
232C4⋊Dic61—28no—
233C4⋊Dic61—44no—
234C4⋊Dic61—48no—
235#11758196—48no—
236C4×Dic61—28no—
237C4×Dic61—28no—
238C4×Dic61—28no—
239C23×C61C23×C411yescharacteristic
240C23×C61C22×D411yescharacteristic
241C23×C61C22×D411yescharacteristic
242C23×C61C22×D411yescharacteristic
243C23×C61C22×D411yescharacteristic
244C23×C61C22×Q811yescharacteristic
245C23×C61C22×Q811yescharacteristic
246C23×C61C2×#4111yescharacteristic
247C23×C61C2×#4111yescharacteristic
248C23×C61C2×#4111yescharacteristic
249C23×C61C2×#4111yescharacteristic
250C23×C61C2×#4111yescharacteristic
251C23×C61C2×#4111yescharacteristic
252C23×C61C2×#4111yescharacteristic
253C23×C61C2×#4111yescharacteristic
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61C2×C4⋊C414yes—
283C22×D61C4×D414yes—
284C22×D61C4×Q814yes—
285C22×D61#12114yes—
286C22×D61C22⋊Q814yes—
287C22×D61#12514yes—
288C22×D61C4⋊Q814yes—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—24no—
302C2×C4×C61—24no—
303C2×C4×C61—24no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61C2×C4⋊C414yes—
316C2×C4×C61C4×D414yes—
317C2×C4×C61C4×D414yes—
318C2×C4×C61#12014yes—
319C2×C4×C61#12114yes—
320C2×C4×C61C22⋊Q814yes—
321C2×C4×C61C22⋊Q814yes—
322C2×C4×C61C22⋊Q814yes—
323C2×C4×C61#12314yes—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—24no—
343C2×Dic61—24no—
344C2×Dic61—24no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61—42no—
356C2×Dic61C2×C4⋊C414yes—
357C2×Dic61#12114yes—
358C2×Dic61C22⋊Q814yes—
359C4×D61—232no—
360C4×D61—232no—
361C4×D61—232no—
362#14697—611nomaximal, Sylow
363C22×C61C22×C4⋊C411yescharacteristic
364C22×C61C2×C4×D411yescharacteristic
365C22×C61C2×C4×D411yescharacteristic
366C22×C61C2×C4×D411yescharacteristic
367C22×C61C2×C4×Q811yescharacteristic
368C22×C61C4×#4111yescharacteristic
369C22×C61C4×#4111yescharacteristic
370C22×C61C2×#12011yescharacteristic
371C22×C61C2×#12111yescharacteristic
372C22×C61C2×#12111yescharacteristic
373C22×C61C2×#12111yescharacteristic
374C22×C61C2×C22⋊Q811yescharacteristic
375C22×C61C2×C22⋊Q811yescharacteristic
376C22×C61C2×C22⋊Q811yescharacteristic
377C22×C61C2×C22⋊Q811yescharacteristic
378C22×C61C2×C22⋊Q811yescharacteristic
379C22×C61C2×#12311yescharacteristic
380C22×C61#52511yescharacteristic
381C22×C61#52511yescharacteristic
382C22×C61#52511yescharacteristic
383C22×C61#52511yescharacteristic
384C22×C61#52511yescharacteristic
385C22×C61#52511yescharacteristic
386C22×C61C2×#12511yescharacteristic
387C22×C61#52911yescharacteristic
388C22×C61#52911yescharacteristic
389C22×C61#52911yescharacteristic
390C22×C61#52911yescharacteristic
391C22×C61C2×C4⋊Q811yescharacteristic
392C22×C61#53211yescharacteristic
393C22×C61#53211yescharacteristic
394C22×C61#53311yescharacteristic
395C22×C61#53311yescharacteristic
396C22×C61#53311yescharacteristic
397C22×C61#53311yescharacteristic
398C2×D61—24no—
399C2×D61—24no—
400C2×D61—24no—
401C2×D61—24no—
402C2×D61—24no—
403C2×D61—24no—
404C2×D61—24no—
405C2×D61—24no—
406C2×D61—24no—
407C2×D61—24no—
408C2×D61—24no—
409C2×D61—24no—
410C2×D61—24no—
411C2×D61—24no—
412C2×D61#38918yescomplemented
413C4×C61—24no—
414C4×C61—24no—
415C4×C61—44no—
416C4×C61—82no—
417C4×C61#38518yescomplemented
418Dic61—24no—
419Dic61—24no—
420Dic61—24no—
421Dic61—44no—
422Dic61—82no—
423C23×C42—611no—
424C2×#389—611no—
425C2×#389—611no—
426C2×#385—612no—
427C2×#380—611no—
428C2×#380—611no—
429#1436—612no—
430#1436—612no—
431C4⋊#95—611no—
432C4⋊#95D6111yescharacteristic, complemented
433C22⋊#95—612no—
434C2×C61C2×#38511yescharacteristic
435C2×C61C2×#38911yescharacteristic
436C2×C61#229611yescharacteristic
437C2×C61C4×#12111yescharacteristic
438C2×C61C4×#12111yescharacteristic
439C2×C61C4×C22⋊Q811yescharacteristic
440C2×C61C4×C22⋊Q811yescharacteristic
441C2×C61#284711yescharacteristic
442C2×C61#284811yescharacteristic
443C2×C61#285111yescharacteristic
444C2×C61#285111yescharacteristic
445C2×C61#285411yescharacteristic
446C2×C61#285511yescharacteristic
447C2×C61#285711yescharacteristic
448C2×C61#285711yescharacteristic
449D61—28no—
450C24×C4—611no—
451C24×C4—611no—
452C24×C4—611no—
453C22×C4⋊C4—611no—
454C22×C4⋊C4—612no—
455C22×C4⋊C4—612no—
456C22×C4⋊C4—611no—
457C22×C4⋊C4C2×D6111yescharacteristic
458C22×C4⋊C4C2×D6111yescharacteristic
459C22×C22⋊C4—612no—
460C22×C22⋊C4—612no—
461C22×C42—611no—
462C22×C42—611no—
463C22×C42—611no—
464C22×C42—1224no—
465C22×C42—1224no—
466C22×C42—1224no—
467C22×C42C2×D6111yescharacteristic
468#389—1224no—
469#389—1224no—
470#385—1228no—
471#380—618no—
472#380—1224no—
473C2×#95—612no—
474C2×#95—612no—
475C2×#95—612no—
476C2×#95—612no—
477C2×#95—612no—
478C2×#95—612no—
479C2×#95C2×D6112yes—
480C2×#95C2×D6112yes—
481C61#1469711yescharacteristic, complemented, Sylow
482C25—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—614no—
487C23×C4—614no—
488C23×C4—614no—
489C23×C4—612no—
490C23×C4—614no—
491C23×C4—614no—
492C23×C4—612no—
493C23×C4—1222no—
494C23×C4—1222no—
495C23×C4—1222no—
496C23×C4—1222no—
497C23×C4—1222no—
498C23×C4—1222no—
499C23×C4—1222no—
500C23×C4—1222no—
501C23×C4—1222no—
502C23×C4—1222no—
503C23×C4—1222no—
504C23×C4—1222no—
505C23×C4—1222no—
506C23×C4—1222no—
507C23×C4—1222no—
508C23×C4—1222no—
509C23×C4C22×D6112yes—
510C23×C4C22×D6112yes—
511C23×C4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513C23×C4C22×D6111yescharacteristic
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—614no—
520C2×C4⋊C4—1222no—
521C2×C4⋊C4—1222no—
522C2×C4⋊C4—1224no—
523C2×C4⋊C4—1224no—
524C2×C4⋊C4—1224no—
525C2×C4⋊C4—1224no—
526C2×C4⋊C4—1222no—
527C2×C4⋊C4—1222no—
528C2×C4⋊C4—1224no—
529C2×C4⋊C4—1222no—
530C2×C4⋊C4—1224no—
531C2×C4⋊C4C4×D6114yescomplemented
532C2×C22⋊C4—618no—
533C2×C22⋊C4—1224no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4—1224no—
536C2×C22⋊C4—1224no—
537C2×C22⋊C4—1224no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—614no—
541C2×C42—12232no—
542C2×C42—1222no—
543C2×C42—1222no—
544C2×C42—1222no—
545C2×C42—1222no—
546C2×C42—1222no—
547C2×C42—1222no—
548C2×C42—1222no—
549C2×C42—1222no—
550C2×C42D24414yes—
551#95—24no—
552#95—24no—
553#95—618no—
554#95—1224no—
555#95—1224no—
556#95—1224no—
557#95—1224no—
558#95—1224no—
559C24—612no—
560C24—612no—
561C24—612no—
562C24—612no—
563C24—612no—
564C24—612no—
565C24—612no—
566C24—1221no—
567C24—1221no—
568C24—1221no—
569C24—1221no—
570C24—1221no—
571C24—1221no—
572C24—1221no—
573C24—1221no—
574C24C23×D6111yescharacteristic
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—6116no—
606C22×C4—614no—
607C22×C4—1228no—
608C22×C4—1228no—
609C22×C4—1228no—
610C22×C4—1228no—
611C22×C4—1228no—
612C22×C4—1228no—
613C22×C4—1228no—
614C22×C4—1228no—
615C22×C4—1228no—
616C22×C4—1228no—
617C22×C4—1228no—
618C22×C4—1228no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1228no—
632C22×C4—1228no—
633C22×C4—1228no—
634C22×C4—1228no—
635C22×C4—1228no—
636C22×C4—1228no—
637C22×C4—1228no—
638C22×C4—1228no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4C2×C4×D6114yes—
653C22×C4C2×C4×D6112yes—
654C22×C4C2×D24412yes—
655C22×C4C2×D24412yes—
656C22×C4C2×D24412yes—
657C22×C4#1175822212yes—
658C22×C4D4×D6112yes—
659C22×C4D4×D6112yes—
660C22×C4D4×D6112yes—
661C22×C4#1175822412yes—
662C22×C4#1175822412yes—
663C22×C4Q8×D6112yes—
664C22×C4Q8×D6112yes—
665C22×C4#1175822612yes—
666C4⋊C4—28no—
667C4⋊C4—44no—
668C4⋊C4—1228no—
669C4⋊C4—2448no—
670C4⋊C4—2444no—
671C4⋊C4—2448no—
672C22⋊C4—12216no—
673C22⋊C4—2448no—
674C42—28no—
675C42—1228no—
676C42—1228no—
677C42—1228no—
678C23—614no—
679C23—614no—
680C23—614no—
681C23—614no—
682C23—614no—
683C23—614no—
684C23—614no—
685C23—1222no—
686C23—1222no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—1222no—
707C23—1222no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—1222no—
712C23—1222no—
713C23C22×C4×D6111yescharacteristic
714C23C2×D4×D6111yescharacteristic
715C23C2×D4×D6111yescharacteristic
716C23C2×D4×D6111yescharacteristic
717C23C22×D24411yescharacteristic
718C23C2×Q8×D6111yescharacteristic
719C23C2×Q8×D6111yescharacteristic
720C23#41×D6111yescharacteristic
721C23#41×D6111yescharacteristic
722C23#41×D6111yescharacteristic
723C23#41×D6111yescharacteristic
724C23C2×#1175822411yescharacteristic
725C23C2×#1175822411yescharacteristic
726C23C2×#1175822211yescharacteristic
727C23C2×#1175822611yescharacteristic
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—614no—
755C2×C4—614no—
756C2×C4—614no—
757C2×C4—12232no—
758C2×C4—12232no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—12232no—
778C2×C4—1224no—
779C2×C4—1224no—
780C2×C4—1224no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4—2442no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4—2442no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4C4⋊C4×D6114yes—
793C2×C4#1451973714yes—
794C2×C4C4×D24414yes—
795C2×C4#1451974714yes—
796C2×C4#1451975214yes—
797C2×C4#1451975514yes—
798C2×C4#1451975714yes—
799C2×C4#1451975714yes—
800C2×C4#1451975914yes—
801C22—618no—
802C22—1224no—
803C22—1224no—
804C22—1224no—
805C22—1224no—
806C22—1224no—
807C22—1224no—
808C22—1224no—
809C22—1224no—
810C22—1224no—
811C22—1224no—
812C22—1224no—
813C22—1224no—
814C22—1224no—
815C22—1224no—
816C22C2×C4⋊C4×D6111yescharacteristic
817C22C4×D4×D6111yescharacteristic
818C22C2×#1451973711yescharacteristic
819C22C2×C4×D24411yescharacteristic
820C22C4×Q8×D6111yescharacteristic
821C22C4×#1175822411yescharacteristic
822C22C4×#1175822611yescharacteristic
823C22C2×#1451974711yescharacteristic
824C22#121×D6111yescharacteristic
825C22#121×D6111yescharacteristic
826C22C2×#1451975211yescharacteristic
827C22C22⋊Q8×D6111yescharacteristic
828C22C22⋊Q8×D6111yescharacteristic
829C22C2×#1451975511yescharacteristic
830C22C2×#1451975711yescharacteristic
831C22C2×#1451975711yescharacteristic
832C22C2×#1451975911yescharacteristic
833C22#1684027211yescharacteristic
834C22#1684027211yescharacteristic
835C22#1684027411yescharacteristic
836C22#1684027411yescharacteristic
837C22#1684027511yescharacteristic
838C22#1684027511yescharacteristic
839C22#125×D6111yescharacteristic
840C22#1684029111yescharacteristic
841C22#1684029111yescharacteristic
842C22#1684029411yescharacteristic
843C22#1684029911yescharacteristic
844C22C4⋊Q8×D6111yescharacteristic
845C22#1684030911yescharacteristic
846C22#1684031011yescharacteristic
847C22#1684031611yescharacteristic
848C22#1684031711yescharacteristic
849C22#1684031711yescharacteristic
850C22#1684031811yescharacteristic
851C4—24no—
852C4—24no—
853C4—44no—
854C4—82no—
855C4—1224no—
856C4—1224no—
857C4—1224no—
858C4—4882no—
859C4—2444no—
860C4#1683963618yescomplemented
861C2—1228no—
862C2C2×#1683963611yescharacteristic
863C2#389×D6111yescharacteristic
864C2#2144830011yescharacteristic
865C2C4×#1451975211yescharacteristic
866C2#2144833511yescharacteristic
867C2C4×#1451975711yescharacteristic
868C2#2144835711yescharacteristic
869C2#2145410211yescharacteristic
870C2#2145410711yescharacteristic
871C2#2145412811yescharacteristic
872C2#2145413011yescharacteristic
873C2#2145414911yescharacteristic
874C2#2145416011yescharacteristic
875C2#2145417011yescharacteristic
876C2#2145417211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC4⋊#95D61
hypocenterC61#14697
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16839661C2semidirect
3. C2×#16839660C2semidirect
7. #21444054C2semidirect
8. #21444053C2semidirect
9. #21444048C2semidirect
11. C61×C4⋊#95C2semidirect
31. #16839619C4semidirect
78. C2×C4⋊Dic61C2×C4semidirect
103. #14519684C2×C4semidirect
114. C2×C4⋊C4×C61C2×C4semidirect
226. C2×C4×D61C4⋊C4semidirect
412. C2×D61#389semidirect
417. C4×C61#385semidirect
432. C4⋊#95D61semidirect
481. C61#14697semidirect
531. C2×C4⋊C4C4×D61semidirect
860. C4#16839636semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D612
C2×#168396612
C2×#168396602
C2×#168396362
C2×#168396192
#214440542
#214440532
#214440482
#214440402
C61×C4⋊#952
#1469761