Finite Group Databasebeta

← #29707862

Subgroups — #29707862

Order 15616.

1332 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840562C211yesmaximal, characteristic
2C2×#16839778C211yesmaximal, characteristic, complemented
3#21454339C211yesmaximal, characteristic, complemented
4C2×#16839744C211yesmaximal, characteristic, complemented
5C2×#16839744C211yesmaximal, characteristic, complemented
6#21447101C214yesmaximal, complemented
7#21447094C214yesmaximal, complemented
8C2×#16839534C211yesmaximal, characteristic, complemented
9C2×C61×#430C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11C22×#11758222C2211yescharacteristic
12#16840562—22no—
13#16840562—22no—
14#16840562—22no—
15#16840562—22no—
16C2×#14519810—21no—
17C2×#14519810C2212yes—
18C2×#14519805—21no—
19C2×#14519805C2212yes—
20C2×#14519799—22no—
21C22×#11758194C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23#16839778—22no—
24#16839778C2214yes—
25C2×#14519703—22no—
26#16839772C2212yescomplemented
27#16839768C2212yescomplemented
28#16839764—22no—
29#16839759—22no—
30#16839744—22no—
31#16839744—22no—
32#16839744—22no—
33#16839744C2214yes—
34C2×#14519695—21no—
35C2×#14519695C2212yescomplemented
36C2×#14519693—21no—
37C2×#14519693C2212yescomplemented
38#16839534C2214yescomplemented
39C22×M16×C61C2211yescharacteristic
40C22×M16×C61C2211yescharacteristic
41C22×M16×C61C2211yescharacteristic
42C61×#430—22no—
43C61×#430C2214yescomplemented
44C2×#108×C61—22no—
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×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222—21no—
64C2×#11758222—21no—
65C2×#11758222D412yes—
66C2×#11758222D412yes—
67C2×#11758222D412yes—
68C2×#11758222C2312yes—
69C22×Dic122D411yescharacteristic
70C22×Dic122C2311yescharacteristic
71C22×D244D411yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77#14519810—24no—
78#14519810—24no—
79#14519810—24no—
80#14519810—24no—
81#14519805—24no—
82#14519805—24no—
83#14519805—24no—
84#14519805—24no—
85#14519799—28no—
86#14519799—28no—
87C2×Dic244—22no—
88C2×#11758190—22no—
89C2×#11758190—22no—
90C2×D488—22no—
91C2×#11758194—21no—
92C2×#11758194—21no—
93C2×#11758194—21no—
94C2×#11758194—21no—
95C2×#11758194—21no—
96C2×#11758194C2312yes—
97C22×#92418—21no—
98#14519736—21no—
99#14519736—21no—
100#14519736—21no—
101#14519736C2312yes—
102C2×C4⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C4×Dic61—21no—
105#14519703—28no—
106#14519702—24no—
107#14519699—24no—
108#14519695—24no—
109#14519695—24no—
110#14519693—24no—
111#14519693—24no—
112C23×C4×C61C2311yescharacteristic
113C2×M16×C61—21no—
114C2×M16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61—21no—
120C2×M16×C61—21no—
121C2×M16×C61—21no—
122C2×M16×C61—21no—
123C2×M16×C61—21no—
124C2×M16×C61D412yes—
125C2×M16×C61D412yes—
126C2×M16×C61D412yes—
127C2×M16×C61D412yes—
128C2×M16×C61C2312yes—
129C2×M16×C61C2312yes—
130C2×M16×C61C2312yes—
131C22×C8×C61—21no—
132C22×C8×C61—21no—
133C22×C8×C61—21no—
134#108×C61—28no—
135C24×C61#4111yescharacteristic
136C23×D61—21no—
137C23×D61—21no—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C22×C4×C61#4111yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C22×C4×C61#4111yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—41no—
157C2×C22⋊D61—41no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—41no—
162C2×C22⋊D61—41no—
163C2×C22⋊D61—41no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—41no—
167#11758222—22no—
168#11758222—22no—
169#11758222—22no—
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—41no—
184#11758222—41no—
185#11758222—41no—
186#11758222—41no—
187#11758222—41no—
188#11758222—41no—
189#11758222—41no—
190#11758222—41no—
191#11758222—41no—
192#11758222—41no—
193#11758222—41no—
194#11758222—41no—
195#11758222—41no—
196#11758222—41no—
197#11758222—41no—
198#11758222—41no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244C2×D412yes—
210C2×D244C2×D412yes—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—41no—
216C2×C4×D61—41no—
217C2×C4×D61—41no—
218C2×C4×D61—41no—
219C2×C4×D61—41no—
220C2×C4×D61—41no—
221C2×C4×D61—41no—
222C2×C4×D61—41no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122C2×D412yes—
234C2×Dic122C2×D412yes—
235M16×C61—22no—
236M16×C61—22no—
237M16×C61—22no—
238M16×C61—22no—
239M16×C61—22no—
240M16×C61—22no—
241M16×C61—22no—
242M16×C61—22no—
243M16×C61—41no—
244M16×C61—41no—
245M16×C61C2×D414yes—
246M16×C61C2×D414yes—
247C2×C8×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61—22no—
250C2×C8×C61—22no—
251C2×C8×C61—22no—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61—41no—
255C2×C8×C61—41no—
256C22⋊Dic61—22no—
257C22⋊Dic61—41no—
258C4⋊Dic61—22no—
259C4⋊Dic61—41no—
260C4×Dic61—22no—
261C4×Dic61—41no—
262#11758194—22no—
263#11758194—22no—
264#11758194—41no—
265#11758194—41no—
266C2×#92418—22no—
267C2×#92418—41no—
268C2×#92418—41no—
269Dic244—28no—
270D488—28no—
271#11758190—28no—
272#11758190—28no—
273C23×C61—81no—
274C23×C61#12111yescharacteristic
275C23×C61#12111yescharacteristic
276C23×C61#12311yescharacteristic
277C23×C61#12311yescharacteristic
278C23×C61#12411yescharacteristic
279C23×C61#12411yescharacteristic
280C23×C61C2×#4111yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—82no—
288C22×D61—82no—
289C2×C4×C61#12011yescharacteristic
290C2×C4×C61#12011yescharacteristic
291C2×C4×C61#12011yescharacteristic
292C2×C4×C61#12011yescharacteristic
293C2×C4×C61#12111yescharacteristic
294C2×C4×C61#12111yescharacteristic
295C2×C4×C61#12111yescharacteristic
296C2×C4×C61#12111yescharacteristic
297C2×C4×C61#12111yescharacteristic
298C2×C4×C61#12111yescharacteristic
299C2×C4×C61#12111yescharacteristic
300C2×C4×C61#12111yescharacteristic
301C2×C4×C61#12111yescharacteristic
302C2×C4×C61#12111yescharacteristic
303C2×C4×C61#12311yescharacteristic
304C2×C4×C61#12311yescharacteristic
305C2×C4×C61#12311yescharacteristic
306C2×C4×C61#12311yescharacteristic
307C2×C4×C61#12311yescharacteristic
308C2×C4×C61#12311yescharacteristic
309C2×C4×C61#12411yescharacteristic
310C2×C4×C61#12411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C22⋊D61—42no—
318C22⋊D61—42no—
319C22⋊D61—42no—
320C22⋊D61—42no—
321C22⋊D61—42no—
322C22⋊D61—42no—
323C22⋊D61—42no—
324C22⋊D61—42no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—42no—
332C2×Dic61—82no—
333D244—22no—
334D244—22no—
335D244—22no—
336D244—22no—
337D244—41no—
338D244—41no—
339D244—41no—
340D244—41no—
341C4×D61—42no—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61—42no—
346C4×D61—42no—
347C4×D61—42no—
348C4×D61—42no—
349Dic122—22no—
350Dic122—22no—
351Dic122—22no—
352Dic122—22no—
353Dic122—41no—
354Dic122—41no—
355Dic122—41no—
356Dic122—41no—
357C8×C61—24no—
358C8×C61—24no—
359C8×C61—42no—
360#92418—42no—
361#23525—611nomaximal, Sylow
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61#39411yescharacteristic
370C22×C61#39411yescharacteristic
371C22×C61#39411yescharacteristic
372C22×C61#39411yescharacteristic
373C22×C61C2×#12111yescharacteristic
374C22×C61C2×#12311yescharacteristic
375C22×C61C2×#12411yescharacteristic
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—82no—
379C2×D61—82no—
380C2×D61—82no—
381C2×D61—82no—
382C2×D61—82no—
383C2×D61—82no—
384C4×C61#39411yescharacteristic
385C4×C61#39411yescharacteristic
386C4×C61#39411yescharacteristic
387C4×C61#39411yescharacteristic
388C4×C61C2×#12011yescharacteristic
389C4×C61C2×#12111yescharacteristic
390C4×C61C2×#12111yescharacteristic
391C4×C61C2×#12311yescharacteristic
392Dic61—42no—
393Dic61—42no—
394Dic61—82no—
395C2×#575—611no—
396C2×#430D6111yescharacteristic, complemented
397C2×#421—611no—
398#2896—611no—
399C2×#413—611no—
400C2×#413—611no—
401#2049—614no—
402#2048—614no—
403C2×#344—611no—
404C2×C61—21no—
405C2×C61—21no—
406C2×C61—21no—
407C2×C61—21no—
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61C2×#39411yescharacteristic
412D61—82no—
413D61—82no—
414C22×#41—611no—
415C22×#41—611no—
416#575—1222no—
417#575—1222no—
418#575—1222no—
419#575—1222no—
420C2×#137—612no—
421C2×#137—1221no—
422C2×AGL(1,ℤ/8)—612no—
423C2×AGL(1,ℤ/8)—1221no—
424C2×#135—1222no—
425C22×M16—611no—
426C22×M16C2×D6111yescharacteristic
427C22×M16C2×D6111yescharacteristic
428C22×M16C2×D6111yescharacteristic
429C2×#117—611no—
430#430—22no—
431#430C2×D6114yescomplemented
432C2×#108—22no—
433#421—614no—
434#421—1222no—
435C2×#104—1222no—
436#419—612no—
437#418—612no—
438#417—1222no—
439#416—1222no—
440#413—614no—
441#413—1222no—
442#413—1222no—
443#413—1222no—
444C2×#101—612no—
445C2×#101—1221no—
446C2×#100—612no—
447C2×#100—1221no—
448#344—614no—
449C61#2352511yescharacteristic, complemented, Sylow
450C2×#41—612no—
451C2×#41—612no—
452C2×#41—612no—
453C2×#41—612no—
454C2×#41—1221no—
455C2×#41—1221no—
456C2×#41—1221no—
457C2×#41—1221no—
458C2×#41—1221no—
459C2×#41—1221no—
460C2×#41—1221no—
461C2×#41—1221no—
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—
474C22×Q8—611no—
475C22×Q8—611no—
476C22×D4—611no—
477C22×D4—611no—
478C22×D4—1221no—
479C22×D4—1221no—
480C23×C4—1221no—
481C23×C4—1221no—
482C23×C4C22×D6111yescharacteristic
483#137—1224no—
484#137—1224no—
485#137—1224no—
486#137—1224no—
487AGL(1,ℤ/8)—1224no—
488AGL(1,ℤ/8)—1224no—
489AGL(1,ℤ/8)—1224no—
490AGL(1,ℤ/8)—1224no—
491#135—1228no—
492#135—1228no—
493C2×Q16—1222no—
494C2×SD16—1222no—
495C2×SD16—1222no—
496C2×D8—1222no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—612no—
509C2×M16—1221no—
510C2×M16—1221no—
511C2×M16—1221no—
512C2×M16—1221no—
513C2×M16—1221no—
514C2×M16D24412yes—
515C2×M16D24412yes—
516C2×M16C22⋊D6112yes—
517C2×M16C22⋊D6112yes—
518C2×M16C22×D6112yes—
519C2×M16C22×D6112yes—
520C2×M16C22×D6112yes—
521C22×C8—21no—
522C22×C8—21no—
523C22×C8—21no—
524C22×C8—1221no—
525#117—612no—
526#117—1221no—
527#117—1221no—
528#117—1221no—
529C2×C4⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C42—1221no—
532#108—28no—
533#104—1228no—
534#103—1224no—
535#102—1224no—
536#101—1224no—
537#101—1224no—
538#100—1224no—
539#100—1224no—
540C24—1221no—
541C24—1221no—
542C24#1175822611yescharacteristic
543#41—1222no—
544#41—1222no—
545#41—1222no—
546#41—1222no—
547#41—1222no—
548#41—1222no—
549#41—1222no—
550#41—1222no—
551#41—1222no—
552#41—1222no—
553#41—1222no—
554#41—1222no—
555#41—1222no—
556#41—1222no—
557#41—1222no—
558#41—1222no—
559#41—2441no—
560#41—2441no—
561#41—2441no—
562#41—2441no—
563#41—2441no—
564#41—2441no—
565#41—2441no—
566#41—2441no—
567#41—2441no—
568#41—2441no—
569#41—2441no—
570#41—2441no—
571#41—2441no—
572#41—2441no—
573#41—2441no—
574#41—2441no—
575C2×Q8—612no—
576C2×Q8—612no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—1221no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×D4—612no—
588C2×D4—612no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—1221no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—2441no—
604C2×D4—2441no—
605C2×D4—2441no—
606C2×D4—2441no—
607C2×D4—2441no—
608C2×D4—2441no—
609C2×D4—2441no—
610C2×D4—2441no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—2441no—
618C22×C4—2441no—
619C22×C4—2441no—
620C22×C4—2441no—
621C22×C4—2441no—
622C22×C4—2441no—
623C22×C4—2441no—
624C22×C4—2441no—
625C22×C4—2441no—
626C22×C4C2×D24411yescharacteristic
627C22×C4C2×D24411yescharacteristic
628C22×C4#1175822211yescharacteristic
629C22×C4#1175822211yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4D4×D6111yescharacteristic
632C22×C4D4×D6111yescharacteristic
633C22×C4D4×D6111yescharacteristic
634C22×C4#1175822611yescharacteristic
635C22×C4#1175822611yescharacteristic
636C22×C4#1175822611yescharacteristic
637C22×C4C2×C22⋊D6111yescharacteristic
638C22×C4C2×C22⋊D6111yescharacteristic
639C22×C4C23×D6111yescharacteristic
640Q16—1228no—
641SD16—1228no—
642SD16—1228no—
643D8—1228no—
644M16—22no—
645M16—22no—
646M16—22no—
647M16—22no—
648M16—22no—
649M16—22no—
650M16—22no—
651M16—22no—
652M16—41no—
653M16—41no—
654M16—1222no—
655M16—1222no—
656M16—2441no—
657M16—2441no—
658M16C2×D24414yes—
659M16C2×C22⋊D6114yes—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—41no—
668C2×C8—41no—
669C2×C8—1222no—
670C2×C8—2441no—
671C2×C8—2441no—
672C4⋊C4—1222no—
673C4⋊C4—2441no—
674C22⋊C4—1222no—
675C22⋊C4—2441no—
676C42—1222no—
677C42—2441no—
678C23—81no—
679C23—1222no—
680C23—1222no—
681C23—4882no—
682C23—4882no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23#1451975211yescharacteristic
688C23#1451975211yescharacteristic
689C23#1451976211yescharacteristic
690C23#1451976211yescharacteristic
691C23#1451976611yescharacteristic
692C23#1451976611yescharacteristic
693C23C2×#1175822611yescharacteristic
694Q8—1222no—
695Q8—1222no—
696Q8—1222no—
697Q8—1222no—
698Q8—2441no—
699Q8—2441no—
700Q8—2441no—
701Q8—2441no—
702D4—1222no—
703D4—1222no—
704D4—1222no—
705D4—1222no—
706D4—2442no—
707D4—2442no—
708D4—2442no—
709D4—2442no—
710D4—2442no—
711D4—2442no—
712D4—2442no—
713D4—2442no—
714D4—2441no—
715D4—2441no—
716D4—2441no—
717D4—2441no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—4882no—
721C2×C4—2442no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4#1451974511yescharacteristic
735C2×C4#1451974511yescharacteristic
736C2×C4#1451974511yescharacteristic
737C2×C4#1451974511yescharacteristic
738C2×C4#1451975111yescharacteristic
739C2×C4#1451975111yescharacteristic
740C2×C4#1451975111yescharacteristic
741C2×C4#1451975111yescharacteristic
742C2×C4#1451975211yescharacteristic
743C2×C4#1451975211yescharacteristic
744C2×C4#1451975211yescharacteristic
745C2×C4#1451975211yescharacteristic
746C2×C4#1451975211yescharacteristic
747C2×C4#1451975211yescharacteristic
748C2×C4#1451976211yescharacteristic
749C2×C4#1451976211yescharacteristic
750C2×C4#1451976211yescharacteristic
751C2×C4#1451976211yescharacteristic
752C2×C4#1451976211yescharacteristic
753C2×C4#1451976211yescharacteristic
754C2×C4#1451976611yescharacteristic
755C2×C4#1451976611yescharacteristic
756C2×C4C2×D4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4C22×C22⋊D6111yescharacteristic
759C2×C4C22×D24411yescharacteristic
760C2×C4C2×#1175822211yescharacteristic
761C2×C4C2×#1175822611yescharacteristic
762C8—24no—
763C8—24no—
764C8—42no—
765C8—2442no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—4882no—
774C22—4882no—
775C22—4882no—
776C22—4882no—
777C22—4882no—
778C22—4882no—
779C22—2442no—
780C22—2442no—
781C22#1683967911yescharacteristic
782C22#1683967911yescharacteristic
783C22#1683967911yescharacteristic
784C22#1683967911yescharacteristic
785C22C2×#1451975211yescharacteristic
786C22C2×#1451976211yescharacteristic
787C22C2×#1451976611yescharacteristic
788C4—4882no—
789C4—2442no—
790C4—2442no—
791C4#1683967911yescharacteristic
792C4#1683967911yescharacteristic
793C4#1683967911yescharacteristic
794C4#1683967911yescharacteristic
795C4C2×#1451974511yescharacteristic
796C4C2×#1451975111yescharacteristic
797C4C2×#1451975211yescharacteristic
798C4C2×#1451976211yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—4882no—
807C2—4882no—
808C2C2×#1683967911yescharacteristic
subgroupG/H
centerC4#16839679
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#430C2
socleC2×C61C2×#394
prime radicalC2×#16840562C2
hypercenterC2×#430D61
hypocenterC61#23525
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
2. C2×#16839778C2semidirect
3. #21454339C2semidirect
4. C2×#16839744C2semidirect
5. C2×#16839744C2semidirect
6. #21447101C2semidirect
7. #21447094C2semidirect
8. C2×#16839534C2semidirect
9. C2×C61×#430C2semidirect
26. #16839772C22semidirect
27. #16839768C22semidirect
35. C2×#14519695C22semidirect
37. C2×#14519693C22semidirect
38. #16839534C22semidirect
43. C61×#430C22semidirect
396. C2×#430D61semidirect
431. #430C2×D61semidirect
449. C61#23525semidirect

Maximal subgroups

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

subgroupindex
C2×#168405622
C2×#168397782
#214543392
C2×#168397442
#214471012
#214470942
C2×#168395342
C2×C61×#4302
#2352561