Finite Group Databasebeta

← #29681558

Subgroups — #29681558

Order 15616.

1708 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic, complemented
2#21459152C211yesmaximal, characteristic
3C2×#16839780C211yesmaximal, characteristic, complemented
4C2×#16839778C211yesmaximal, characteristic, complemented
5C2×#16839735C211yesmaximal, characteristic, complemented
6#21446201C218yesmaximal, complemented
7#21445529C211yesmaximal, characteristic, complemented
8C61×#1733C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C22×#11758222C2211yescharacteristic
11#16840528—22no—
12#16840528—22no—
13#16840528—22no—
14#16840528C2214yescomplemented
15C2×#14519785—22no—
16C2×#14519783—22no—
17C22×#11758194C2211yescharacteristic
18C2×M16×D61—22no—
19#16840343—22no—
20#16840338C412yescomplemented
21#16840338C412yescomplemented
22#16840331C412yescomplemented
23#16840331C412yescomplemented
24#16840324—22no—
25#16840312C2214yes—
26#16840274—22no—
27#16840274—22no—
28C2×#14519736C2211yescharacteristic
29#16839780—22no—
30#16839780C2214yescomplemented
31#16839778—22no—
32#16839778C2214yescomplemented
33C2×#14519705—22no—
34C2×#14519703—22no—
35#16839735—22no—
36#16839735C2214yescomplemented
37C2×#14519691—22no—
38#16839522C2214yescomplemented
39C22×M16×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C2×#117×C61C2211yescharacteristic
42C61×#339C2214yescomplemented
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222C2×C412yes—
62C2×#11758222C2×C412yes—
63C2×#11758222D412yes—
64C2×#11758222D412yes—
65C2×#11758222C2312yes—
66C2×#11758222C2312yes—
67C22×Dic122C2×C411yescharacteristic
68C22×Dic122C2×C411yescharacteristic
69C22×D244C2×C411yescharacteristic
70C22×D244C2×C411yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61D412yes—
73C22×C4×D61—21no—
74C22×C4×D61D412yes—
75#14519785—28no—
76#14519785—28no—
77#14519783—28no—
78#14519783—28no—
79C2×#11758194—21no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82C2×#11758194D412yescomplemented
83C2×#11758194D412yescomplemented
84C2×#11758194C2312yes—
85C2×#11758189—24no—
86M16×D61—28no—
87M16×D61—28no—
88C22×#92418—21no—
89C2×C8×D61—24no—
90#14519777C2×C414yescomplemented
91#14519774C2×C414yescomplemented
92#14519765C2×C414yescomplemented
93#14519765C2×C414yescomplemented
94#14519761—24no—
95#14519761—24no—
96#14519757—24no—
97#14519757—24no—
98#14519752—24no—
99#14519752—24no—
100#14519751—28no—
101#14519747—24no—
102#14519747—24no—
103C4×D244—28no—
104#14519736—21no—
105#14519736—21no—
106#14519736—21no—
107#14519736C2312yes—
108C2×C4⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C4×Dic61—21no—
111#14519705—28no—
112#14519703—28no—
113#14519691—28no—
114C23×C4×C61C2311yescharacteristic
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61D412yescomplemented
119C2×M16×C61D412yescomplemented
120C2×M16×C61C2312yes—
121C22×C8×C61—21no—
122#117×C61—21no—
123#117×C61—21no—
124#117×C61—21no—
125#117×C61—21no—
126#117×C61—21no—
127#117×C61C2×C412yes—
128#117×C61C2×C412yes—
129#117×C61C2312yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C42×C61—21no—
135C2×C42×C61C2312yes—
136C24×C61C2×D411yescharacteristic
137C23×D61—21no—
138C23×D61C22⋊C412yes—
139C22×C4×C61—22no—
140C22×C4×C61—41no—
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C22×C4×C61C2411yescharacteristic
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—41no—
162C2×C22⋊D61—41no—
163C2×C22⋊D61—41no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61C22⋊C414yes—
166C2×C22⋊D61C2×D414yes—
167C22×Dic61—21no—
168C22×Dic61—41no—
169C22×Dic61C22⋊C412yes—
170#11758222—22no—
171#11758222—22no—
172#11758222—22no—
173#11758222—22no—
174#11758222—22no—
175#11758222—22no—
176#11758222—22no—
177#11758222—22no—
178#11758222—22no—
179#11758222—22no—
180#11758222—22no—
181#11758222—22no—
182#11758222—22no—
183#11758222—22no—
184#11758222—22no—
185#11758222—22no—
186#11758222—22no—
187#11758222—22no—
188#11758222—22no—
189#11758222—22no—
190#11758222—22no—
191#11758222—22no—
192#11758222—22no—
193#11758222—22no—
194#11758222—41no—
195#11758222—41no—
196#11758222—41no—
197#11758222—41no—
198#11758222—41no—
199#11758222—41no—
200#11758222—41no—
201#11758222—41no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—28no—
212C2×D244C22⋊C412yes—
213C2×D244C22×C412yes—
214C2×D244C22×C412yes—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—41no—
222C2×C4×D61—41no—
223C2×C4×D61—41no—
224C2×C4×D61—41no—
225C2×C4×D61C22⋊C414yes—
226C2×C4×D61C2×D414yes—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122C22⋊C412yes—
237C2×Dic122C22×C412yes—
238C2×Dic122C22×C412yes—
239M16×C61—22no—
240M16×C61—22no—
241M16×C61—22no—
242M16×C61C2×D414yes—
243C2×C8×C61—22no—
244C2×C8×C61—22no—
245C2×C8×C61—22no—
246C4⋊C4×C61—22no—
247C4⋊C4×C61—22no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—41no—
250C22⋊C4×C61—22no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—41no—
254C42×C61—22no—
255C42×C61—22no—
256C42×C61—41no—
257C42×C61C22×C414yes—
258C22⋊Dic61—22no—
259C22⋊Dic61—41no—
260#11758198—28no—
261#11758198—28no—
262C4⋊Dic61—28no—
263C4⋊Dic61—22no—
264C4⋊Dic61—41no—
265C4×Dic61—22no—
266C4×Dic61—41no—
267#11758194—22no—
268#11758194—22no—
269#11758194—22no—
270#11758194C2×D414yes—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418—22no—
274#11758189—216no—
275C8×D61—216no—
276C23×C61—81no—
277C23×C61C2×C22⋊C411yescharacteristic
278C23×C61C2×C22⋊C411yescharacteristic
279C23×C61#12111yescharacteristic
280C23×C61#12111yescharacteristic
281C23×C61#12111yescharacteristic
282C23×C61#12111yescharacteristic
283C23×C61C22×D411yescharacteristic
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—82no—
290C22×D61—82no—
291C22×D61C2×C22⋊C414yes—
292C2×C4×C61—24no—
293C2×C4×C61—42no—
294C2×C4×C61—82no—
295C2×C4×C61—82no—
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C4×D411yescharacteristic
302C2×C4×C61C4×D411yescharacteristic
303C2×C4×C61C4×D411yescharacteristic
304C2×C4×C61C4×D411yescharacteristic
305C2×C4×C61C4×D411yescharacteristic
306C2×C4×C61#12011yescharacteristic
307C2×C4×C61#12011yescharacteristic
308C2×C4×C61#12011yescharacteristic
309C2×C4×C61#12011yescharacteristic
310C2×C4×C61#12111yescharacteristic
311C2×C4×C61#12111yescharacteristic
312C2×C4×C61#12111yescharacteristic
313C2×C4×C61#12111yescharacteristic
314C2×C4×C61#12311yescharacteristic
315C2×C4×C61#12311yescharacteristic
316C2×C4×C61#12311yescharacteristic
317C2×C4×C61#12311yescharacteristic
318C2×C4×C61C23×C411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C2×#4111yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C22⋊D61—24no—
325C22⋊D61—24no—
326C22⋊D61—24no—
327C22⋊D61—24no—
328C22⋊D61—42no—
329C22⋊D61—42no—
330C22⋊D61—42no—
331C22⋊D61—42no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—42no—
338C2×Dic61—82no—
339C2×Dic61C2×C22⋊C414yes—
340D244—22no—
341D244—22no—
342D244—22no—
343D244—22no—
344D244—22no—
345D244—22no—
346D244—41no—
347D244—41no—
348D244—88no—
349C4×D61—24no—
350C4×D61—24no—
351C4×D61—24no—
352C4×D61—24no—
353C4×D61—42no—
354C4×D61—42no—
355C4×D61—42no—
356C4×D61—42no—
357Dic122—22no—
358Dic122—22no—
359Dic122—22no—
360Dic122—22no—
361Dic122—22no—
362Dic122—22no—
363Dic122—41no—
364Dic122—41no—
365C8×C61—24no—
366#92418—24no—
367#20947—611nomaximal, Sylow
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61#38611yescharacteristic
376C22×C61#38611yescharacteristic
377C22×C61#38611yescharacteristic
378C22×C61#38611yescharacteristic
379C22×C61C22×C22⋊C411yescharacteristic
380C22×C61C2×#12111yescharacteristic
381C22×C61C2×#12111yescharacteristic
382C2×D61—24no—
383C2×D61—44no—
384C2×D61—44no—
385C2×D61—44no—
386C2×D61—42no—
387C2×D61—82no—
388C2×D61—82no—
389C2×D61—82no—
390C4×C61—44no—
391C4×C61—82no—
392C4×C61#38611yescharacteristic
393C4×C61#38611yescharacteristic
394C4×C61#38611yescharacteristic
395C4×C61#38611yescharacteristic
396C4×C61C2×C4×D411yescharacteristic
397C4×C61C2×C4×D411yescharacteristic
398C4×C61C2×#12011yescharacteristic
399C4×C61C2×#12311yescharacteristic
400Dic61—24no—
401Dic61—42no—
402Dic61—82no—
403C2×#568—611no—
404#3449—611no—
405C2×#421—611no—
406C2×#421—611no—
407C2×#410—611no—
408#1884—618no—
409#1733—611no—
410#1733D6111yescharacteristic, complemented
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61—21no—
415C2×C61—21no—
416C2×C61—21no—
417C2×C61—21no—
418C2×C61C2×#38611yescharacteristic
419D61—44no—
420D61—82no—
421C22×#41—611no—
422C22×#41—611no—
423#568—614no—
424#568—1222no—
425#568—1222no—
426#568—1222no—
427C2×#131—1222no—
428C2×#131—1222no—
429C22×M16—611no—
430C22×M16—1222no—
431C22×M16C2×D6111yescharacteristic
432#537—1222no—
433#536—612no—
434#536—612no—
435#535—612no—
436#535—612no—
437#534—1222no—
438#532—614no—
439#525—1222no—
440#525—1222no—
441C2×#117—611no—
442C2×#117C2×D6111yescharacteristic
443C2×#117C2×D6111yescharacteristic
444#421—614no—
445#421—614no—
446#421—1222no—
447#421—1222no—
448C2×#104—1222no—
449C2×#104—1222no—
450#410—614no—
451#410—1222no—
452C2×#99—1222no—
453#339—614no—
454#339C2×D6114yescomplemented
455C61#2094711yescharacteristic, complemented, Sylow
456C2×#41—612no—
457C2×#41—612no—
458C2×#41—612no—
459C2×#41—612no—
460C2×#41—612no—
461C2×#41—612no—
462C2×#41—1221no—
463C2×#41—1221no—
464C2×#41—1221no—
465C2×#41—1221no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—1221no—
469C2×#41—1221no—
470C2×#41—1221no—
471C2×#41—1221no—
472C2×#41—1221no—
473C2×#41—1221no—
474C2×#41—1221no—
475C2×#41—1221no—
476C2×#41—1221no—
477C2×#41—1221no—
478C2×#41—1221no—
479C2×#41—1221no—
480C22×Q8—611no—
481C22×Q8—611no—
482C22×D4—612no—
483C22×D4—611no—
484C22×D4—611no—
485C22×D4—1221no—
486C23×C4—612no—
487C23×C4—1221no—
488C23×C4C22×D6111yescharacteristic
489#131—1228no—
490#131—1228no—
491#131—1228no—
492#131—1228no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—612no—
497C2×M16—612no—
498C2×M16—612no—
499C2×M16—1224no—
500C2×M16—1228no—
501C2×M16—1228no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16D24412yescomplemented
506C2×M16D24412yescomplemented
507C2×M16C22×D6112yes—
508C22×C8—21no—
509C22×C8—1224no—
510C22×C8—1221no—
511C4⋊Q8—614no—
512#127—614no—
513#124—614no—
514#124—614no—
515#123—1224no—
516#123—1224no—
517C22⋊Q8—1224no—
518C22⋊Q8—1224no—
519#121—1224no—
520#121—1224no—
521#121—1228no—
522#120—1224no—
523#120—1224no—
524C4×D4—1228no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—21no—
529#117—21no—
530#117—612no—
531#117—1221no—
532#117—1221no—
533#117—1221no—
534#117C4×D6112yes—
535#117C4×D6112yes—
536#117C22×D6112yes—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—1221no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—1221no—
543C2×C42—21no—
544C2×C42—1221no—
545C2×C42C22×D6112yes—
546#104—1228no—
547#104—1228no—
548#99—1228no—
549C24—612no—
550C24—1221no—
551C24D4×D6111yescharacteristic
552#41—1222no—
553#41—1222no—
554#41—1222no—
555#41—1222no—
556#41—1222no—
557#41—1222no—
558#41—1222no—
559#41—1222no—
560#41—1222no—
561#41—1222no—
562#41—1222no—
563#41—1222no—
564#41—1222no—
565#41—1222no—
566#41—1222no—
567#41—1222no—
568#41—1222no—
569#41—1222no—
570#41—1222no—
571#41—1222no—
572#41—1222no—
573#41—1222no—
574#41—1222no—
575#41—1222no—
576#41—2441no—
577#41—2441no—
578#41—2441no—
579#41—2441no—
580#41—2441no—
581#41—2441no—
582#41—2441no—
583#41—2441no—
584C2×Q8—612no—
585C2×Q8—612no—
586C2×Q8—612no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×D4—614no—
597C2×D4—614no—
598C2×D4—612no—
599C2×D4—612no—
600C2×D4—612no—
601C2×D4—1228no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—1222no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—2441no—
618C2×D4—2441no—
619C2×D4—2441no—
620C2×D4—2441no—
621C22×C4—22no—
622C22×C4—41no—
623C22×C4—612no—
624C22×C4—614no—
625C22×C4—614no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1221no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—2441no—
634C22×C4—2441no—
635C22×C4—2441no—
636C22×C4—2441no—
637C22×C4—2441no—
638C22×C4C2×C4×D6111yescharacteristic
639C22×C4C2×C4×D6111yescharacteristic
640C22×C4C2×D24411yescharacteristic
641C22×C4C2×D24411yescharacteristic
642C22×C4#1175822211yescharacteristic
643C22×C4#1175822211yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4D4×D6111yescharacteristic
646C22×C4D4×D6111yescharacteristic
647C22×C4D4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4#1175822611yescharacteristic
650C22×C4#1175822611yescharacteristic
651C22×C4C23×D6111yescharacteristic
652M16—22no—
653M16—22no—
654M16—22no—
655M16—614no—
656M16—12216no—
657M16—1222no—
658M16—1222no—
659M16—1222no—
660M16C2×D24414yes—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—12216no—
665C2×C8—1222no—
666C2×C8—1222no—
667C2×C8—1222no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—41no—
672C4⋊C4—1228no—
673C4⋊C4—1222no—
674C4⋊C4—2441no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—1228no—
680C22⋊C4—1228no—
681C22⋊C4—1222no—
682C22⋊C4—2441no—
683C42—22no—
684C42—22no—
685C42—41no—
686C42—1222no—
687C42—2441no—
688C42C2×C4×D6114yes—
689C23—81no—
690C23—614no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—4882no—
695C23—4882no—
696C23—2441no—
697C23—2441no—
698C23C22⋊C4×D6111yescharacteristic
699C23C22⋊C4×D6111yescharacteristic
700C23#1451975011yescharacteristic
701C23#1451975011yescharacteristic
702C23#1451975211yescharacteristic
703C23#1451975211yescharacteristic
704C23C2×D4×D6111yescharacteristic
705Q8—1222no—
706Q8—1222no—
707Q8—1222no—
708Q8—1222no—
709Q8—1222no—
710Q8—1222no—
711Q8—2441no—
712Q8—2441no—
713D4—1224no—
714D4—1224no—
715D4—1224no—
716D4—1224no—
717D4—1222no—
718D4—1222no—
719D4—1222no—
720D4—1222no—
721D4—1222no—
722D4—1222no—
723D4—4888no—
724D4—2442no—
725D4—2442no—
726D4—2442no—
727D4—2442no—
728D4—2441no—
729D4—2441no—
730C2×C4—24no—
731C2×C4—42no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—614no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1224no—
738C2×C4—1224no—
739C2×C4—1224no—
740C2×C4—1224no—
741C2×C4—1222no—
742C2×C4—4882no—
743C2×C4—2442no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4C22⋊C4×D6111yescharacteristic
751C2×C4C22⋊C4×D6111yescharacteristic
752C2×C4#1451973911yescharacteristic
753C2×C4#1451973911yescharacteristic
754C2×C4#1451973911yescharacteristic
755C2×C4#1451973911yescharacteristic
756C2×C4C4×D24411yescharacteristic
757C2×C4C4×D24411yescharacteristic
758C2×C4C4×D24411yescharacteristic
759C2×C4C4×D24411yescharacteristic
760C2×C4#1451974711yescharacteristic
761C2×C4#1451974711yescharacteristic
762C2×C4#1451974711yescharacteristic
763C2×C4#1451974711yescharacteristic
764C2×C4#1451975011yescharacteristic
765C2×C4#1451975011yescharacteristic
766C2×C4#1451975211yescharacteristic
767C2×C4#1451975211yescharacteristic
768C2×C4#1451976211yescharacteristic
769C2×C4#1451976211yescharacteristic
770C2×C4#1451976211yescharacteristic
771C2×C4#1451976211yescharacteristic
772C2×C4C22×C4×D6111yescharacteristic
773C2×C4C2×D4×D6111yescharacteristic
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4C22×D24411yescharacteristic
776C2×C4C2×#1175822211yescharacteristic
777C2×C4C2×#1175822611yescharacteristic
778C8—24no—
779C8—1224no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—1224no—
788C22—4882no—
789C22—4882no—
790C22—4882no—
791C22—2444no—
792C22—2444no—
793C22—2444no—
794C22—2442no—
795C22#1683964011yescharacteristic
796C22#1683964011yescharacteristic
797C22#1683964011yescharacteristic
798C22#1683964011yescharacteristic
799C22C2×C22⋊C4×D6111yescharacteristic
800C22C2×#1451975011yescharacteristic
801C22C2×#1451975211yescharacteristic
802C4—44no—
803C4—82no—
804C4—1224no—
805C4—4882no—
806C4—2442no—
807C4#1683964011yescharacteristic
808C4#1683964011yescharacteristic
809C4#1683964011yescharacteristic
810C4#1683964011yescharacteristic
811C4C2×#1451973911yescharacteristic
812C4C2×C4×D24411yescharacteristic
813C4C2×#1451974711yescharacteristic
814C4C2×#1451976211yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—4882no—
823C2—2444no—
824C2C2×#1683964011yescharacteristic
subgroupG/H
centerC4C2×#14519747
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1733C2
socleC2×C61C2×#386
prime radical#21459152C2
cosocleC22×C4×C61C24
hypercenter#1733D61
hypocenterC61#20947
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839780C2semidirect
4. C2×#16839778C2semidirect
5. C2×#16839735C2semidirect
6. #21446201C2semidirect
7. #21445529C2semidirect
8. C61×#1733C2semidirect
14. #16840528C22semidirect
20. #16840338C4semidirect
21. #16840338C4semidirect
22. #16840331C4semidirect
23. #16840331C4semidirect
30. #16839780C22semidirect
32. #16839778C22semidirect
36. #16839735C22semidirect
38. #16839522C22semidirect
42. C61×#339C22semidirect
82. C2×#11758194D4semidirect
83. C2×#11758194D4semidirect
90. #14519777C2×C4semidirect
91. #14519774C2×C4semidirect
92. #14519765C2×C4semidirect
93. #14519765C2×C4semidirect
118. C2×M16×C61D4semidirect
119. C2×M16×C61D4semidirect
410. #1733D61semidirect
454. #339C2×D61semidirect
455. C61#20947semidirect
505. C2×M16D244semidirect
506. C2×M16D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
#214591522
C2×#168397802
C2×#168397782
C2×#168397352
#214462012
#214455292
C61×#17332
#2094761