Finite Group Databasebeta

← #30571141

Subgroups — #30571141

Order 15616.

1770 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459624C211yesmaximal, characteristic, complemented
2C2×#16840495C211yesmaximal, characteristic
3#21458873C214yesmaximal, complemented
4#21458867C214yesmaximal, complemented
5#21458636C214yesmaximal, complemented
6#21458634C214yesmaximal, complemented
7#21456824C211yesmaximal, characteristic, complemented
8#21456819C212yesmaximal, complemented
9#21456818C211yesmaximal, characteristic, complemented
10#21456758C212yesmaximal
11#21455918C211yesmaximal, characteristic, complemented
12#21455915C212yesmaximal, complemented
13#21455855C212yesmaximal, complemented
14#21454903C211yesmaximal, characteristic, complemented
15C61×#3110C211yesmaximal, characteristic, complemented
16#16840495—22no—
17#16840495—22no—
18#16840495C2214yes—
19#16840495C2214yes—
20Q8×Dic122C2212yescomplemented
21#16840492C2212yescomplemented
22#16840490—22no—
23#16840490C2212yescomplemented
24#16840489—22no—
25#16840487C2212yescomplemented
26#16840391—21no—
27#16840391—21no—
28#16840390—21no—
29#16840319C2211yescharacteristic
30#16840314C2212yes—
31#16840314C2212yes—
32C2×#14519773C2211yescharacteristic
33C2×#14519765C2211yescharacteristic
34C2×#14519764C2211yescharacteristic
35C2×#14519763—21no—
36C2×#14519760—21no—
37C2×#14519759—21no—
38#16840239—21no—
39C2×C4×Dic122C2211yescharacteristic
40C2×#14519742C2211yescharacteristic
41C2×#14519739C2211yescharacteristic
42C2×C4×C22⋊D61—21no—
43#16840156C2212yescomplemented
44#16840154C2212yescomplemented
45#16840153C2214yescomplemented
46#16840133C2214yes—
47#16840124C2212yescomplemented
48#16840122C2212yescomplemented
49#16840120C2214yescomplemented
50#16840107C2214yes—
51#16840097C2212yes—
52#16840056C2214yescomplemented
53#16840042C2212yescomplemented
54#16840041C2214yescomplemented
55#16839985C2214yescomplemented
56#16839984C2214yescomplemented
57#16839983C2214yescomplemented
58#16839982C2214yescomplemented
59#16839971C2214yescomplemented
60#16839967C2212yescomplemented
61#16839966C2214yescomplemented
62#16839961C2214yes—
63#16839960C2214yes—
64#16839920C2212yes—
65#16839917C2212yes—
66#16839915C2212yes—
67#16839913C2212yes—
68#16839912C2212yes—
69#16839891C2214yescomplemented
70#16839890C2214yescomplemented
71#16839865C2214yescomplemented
72#16839862C2214yescomplemented
73#16839861C2214yescomplemented
74#16839856C2214yescomplemented
75#16839854C2214yescomplemented
76#16839819C2211yescharacteristic
77#16839816C2212yes—
78#16839812C2212yes—
79C61×#533C2211yescharacteristic
80C2×C4×D4×C61C2211yescharacteristic
81C61×#484C2212yes—
82C61×#474C2212yescomplemented
83C61×#461C2212yescomplemented
84C61×#450C2212yes—
85C61×#440C2214yescomplemented
86C61×#432C2211yescharacteristic
87C22×Dic122D411yescharacteristic
88C22×Dic122C2311yescharacteristic
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C4×D61—21no—
93C2×Dic244C2314yes—
94C2×#11758202C2314yes—
95C2×#11758190C2314yes—
96C2×#11758200C2314yes—
97C2×#11758201C2314yes—
98#14519777—22no—
99#14519777C2311yescharacteristic
100#14519777C2311yescharacteristic
101#14519776—22no—
102#14519776—22no—
103#14519776—22no—
104#14519776C2312yes—
105#14519776C2312yes—
106#14519775—22no—
107#14519775—22no—
108#14519775C2312yes—
109#14519775C2312yes—
110#14519773—22no—
111#14519773C2314yes—
112#14519769—21no—
113#14519769—22no—
114#14519768—22no—
115#14519767—22no—
116#14519767—22no—
117#14519767—22no—
118#14519767—22no—
119#14519767—22no—
120#14519767—22no—
121#14519765—21no—
122#14519765—21no—
123#14519765C2312yes—
124#14519765C2312yes—
125#14519764—22no—
126#14519764C2314yes—
127#14519763—24no—
128#14519763—24no—
129#14519760—24no—
130#14519760—24no—
131#14519759—24no—
132#14519759—24no—
133#14519756—21no—
134#14519756C2312yes—
135#14519754—22no—
136#14519754—22no—
137Q8×Dic61C2312yes—
138Q8×Dic61C2312yes—
139C4×Dic122—22no—
140C4×Dic122—22no—
141C4×Dic122—21no—
142C4×Dic122D412yes—
143C4×Dic122D412yes—
144C4×Dic122C2312yes—
145C4×Dic122C2312yes—
146C4×Dic122C2312yes—
147#14519742—22no—
148#14519742—22no—
149#14519742—22no—
150#14519742—22no—
151#14519742—22no—
152#14519742C2312yes—
153#14519742C2314yes—
154#14519742C2312yes—
155#14519739—22no—
156#14519739C2314yes—
157C4×C22⋊D61—24no—
158C4×C22⋊D61—24no—
159#14519736—21no—
160#14519733—22no—
161#14519733—22no—
162C2×C4⋊Dic61D411yescharacteristic
163C2×#11758196—21no—
164C2×#11758196D411yescharacteristic
165C2×#11758196D411yescharacteristic
166C2×C22⋊Dic61—21no—
167C2×C22⋊Dic61—21no—
168C2×#11758198—21no—
169C2×#11758198—21no—
170C2×#11758198—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61C2311yescharacteristic
173C2×C4×Dic61C2311yescharacteristic
174#14519710C2314yes—
175C4⋊#92418C2312yes—
176#14519706C2314yes—
177#14519706C2314yes—
178#14519702C2314yes—
179#14519700C2314yes—
180#14519700C2314yes—
181#14519699C2314yes—
182#14519698C2314yes—
183#14519697C2314yes—
184C22⋊#92418C2312yes—
185#14519688C2312yes—
186#14519687C2314yes—
187C8×Dic61C2314yes—
188C22×D4×C61C2311yescharacteristic
189C23×C4×C61—21no—
190C2×SD16×C61C2314yes—
191C4⋊Q8×C61C2311yescharacteristic
192C4⋊Q8×C61C2311yescharacteristic
193#125×C61—21no—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61C2312yes—
196C4×Q8×C61—21no—
197C4×Q8×C61C2312yes—
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200C4×D4×C61C2312yes—
201C4×D4×C61C2312yes—
202#117×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61—21no—
205C2×C42×C61C2311yescharacteristic
206#107×C61C2314yes—
207C4⋊C8×C61C2312yes—
208#103×C61C2314yes—
209#102×C61C2314yes—
210C22⋊C8×C61C2312yes—
211#97×C61C2312yes—
212C24×C61—21no—
213C23×D61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61C2412yes—
216C2×D4×C61—21no—
217C2×D4×C61—42no—
218C2×D4×C61C2412yes—
219C22×C4×C61—21no—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—82no—
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2411yescharacteristic
226C2×C22⋊D61—24no—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—82no—
230C22×Dic61—21no—
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C2×D244—21no—
236C2×D244—42no—
237C2×D244C2412yes—
238C2×C4×D61—24no—
239C2×C4×D61—82no—
240C2×Dic122—24no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—22no—
244C2×Dic122—22no—
245C2×Dic122—42no—
246C2×Dic122C2×D412yes—
247C2×Dic122C2×D412yes—
248C2×Dic122C2412yes—
249C2×Dic122C2412yes—
250SD16×C61—44no—
251C2×C8×C61C2414yes—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—22no—
257C4⋊C4×C61—22no—
258C4⋊C4×C61C2412yes—
259C4⋊C4×C61C2412yes—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—22no—
263C42×C61—22no—
264C42×C61C2×D411yescharacteristic
265C42×C61C2×D411yescharacteristic
266C42×C61C2411yescharacteristic
267C42×C61C2411yescharacteristic
268C22⋊Dic61—22no—
269C22⋊Dic61—24no—
270C22⋊Dic61—24no—
271#11758202—44no—
272#11758201—44no—
273#11758200—44no—
274#11758198—22no—
275#11758198—22no—
276#11758198—22no—
277#11758198—22no—
278#11758198—24no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—22no—
283C4⋊Dic61—22no—
284C4⋊Dic61C2×D412yes—
285C4⋊Dic61C2×D412yes—
286C4⋊Dic61C2412yes—
287#11758196—22no—
288#11758196—22no—
289#11758196—24no—
290#11758196—22no—
291#11758196—22no—
292#11758196—22no—
293#11758196—22no—
294#11758196—22no—
295#11758196—22no—
296#11758196—22no—
297#11758196—22no—
298#11758196C2×D412yes—
299#11758196C2×D412yes—
300#11758196C2×D412yes—
301#11758196C2×D412yes—
302C4×Dic61—22no—
303C4×Dic61—24no—
304C4×Dic61—22no—
305C4×Dic61—22no—
306C4×Dic61—22no—
307C4×Dic61—22no—
308C4×Dic61C2×D412yes—
309C4×Dic61C2×D412yes—
310C4×Dic61C2412yes—
311C4×Dic61C2412yes—
312C2×#92418C2414yes—
313Dic244—44no—
314#11758190—44no—
315C23×C61—22no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61C22×D411yescharacteristic
320C22×D61—22no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61—42no—
324Q8×C61—24no—
325Q8×C61—81no—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—42no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—41no—
335C2×C4×C61—42no—
336C2×C4×C61—82no—
337C2×C4×C61—82no—
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C2511yescharacteristic
344C22⋊D61—48no—
345C22⋊D61—84no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—42no—
353C2×Dic61#13714yes—
354C2×Dic61C22×D412yes—
355C2×Dic61C22×D412yes—
356C2×Dic61C22×D412yes—
357C2×Dic61C22×D412yes—
358D244—24no—
359D244—42no—
360C4×D61—84no—
361Dic122—24no—
362Dic122—24no—
363Dic122—24no—
364Dic122—24no—
365Dic122—42no—
366Dic122—82no—
367Dic122—82no—
368Dic122—81no—
369C8×C61—24no—
370#92418—24no—
371#61892—611nomaximal, Sylow
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—84no—
378C22×C61C2×#13712yes—
379C22×C61C23×D411yescharacteristic
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—84no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61#58512yes—
393Dic61—22no—
394Dic61—22no—
395Dic61—22no—
396Dic61—42no—
397Dic61—42no—
398Dic61—42no—
399Dic61C2×#13714yes—
400#3502—611no—
401C2×#559—611no—
402#3400—614no—
403#3400—614no—
404#3375—614no—
405#3375—614no—
406#3215—612no—
407#3215—611no—
408#3215—611no—
409#3208—612no—
410#3110—612no—
411#3110—611no—
412#3110D6111yescharacteristic, complemented
413#3104—612no—
414#2983—611no—
415C2×C61—22no—
416C2×C61—82no—
417C2×C61#348711yescharacteristic
418C2×C61C22×#13711yescharacteristic
419C2×C61#358511yescharacteristic
420D61—82no—
421#559—614no—
422#559—614no—
423#559—1222no—
424#559—1222no—
425Q82—612no—
426Q82—612no—
427#557—612no—
428#557—612no—
429#557—1222no—
430#557—1222no—
431#544—1221no—
432#544—1221no—
433#544—1221no—
434#533—612no—
435#533—612no—
436#533—611no—
437#533C2×D6111yescharacteristic
438C2×#127—611no—
439C2×#124—611no—
440C2×#124—611no—
441C2×#124—1221no—
442C2×#123—1221no—
443C2×#123—1221no—
444#519—1221no—
445C2×C4×Q8—611no—
446C2×C4×Q8—611no—
447C2×C4×D4—611no—
448C2×C4×D4—1221no—
449C2×C4×D4C2×D6111yescharacteristic
450#497—614no—
451#497—612no—
452#497—612no—
453#492—614no—
454#489—612no—
455#489—614no—
456#489—612no—
457#486—614no—
458#484—612no—
459#484C2×D6112yes—
460#477—614no—
461#474—612no—
462#474—614no—
463#474C2×D6112yescomplemented
464#464—614no—
465#464—614no—
466#464—614no—
467#464—614no—
468#462—614no—
469#461—612no—
470#461—614no—
471#461C2×D6112yescomplemented
472#460—614no—
473#460—614no—
474#451—612no—
475#451—612no—
476#450—612no—
477#450—612no—
478#450—612no—
479#450C2×D6112yes—
480#446—614no—
481#446—614no—
482#440—614no—
483#440—614no—
484#440—614no—
485#440C2×D6114yescomplemented
486C4×Q16—614no—
487C4×Q16—614no—
488#432—611no—
489#432—612no—
490#432C2×D6111yescharacteristic
491#431—612no—
492C61#6189211yescharacteristic, complemented, Sylow
493C22×Q8—611no—
494C22×Q8—611no—
495C22×D4—611no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4C22×D6111yescharacteristic
499C23×C4—21no—
500C23×C4—1221no—
501C2×Q16—614no—
502C2×Q16—614no—
503C2×SD16—614no—
504C2×SD16—614no—
505C2×SD16—614no—
506C2×SD16C22×D6114yes—
507C4⋊Q8—612no—
508C4⋊Q8—612no—
509C4⋊Q8—612no—
510C4⋊Q8—612no—
511C4⋊Q8—611no—
512C4⋊Q8—611no—
513C4⋊Q8—1222no—
514C4⋊Q8—1222no—
515C4⋊Q8—1222no—
516C4⋊Q8—1222no—
517C4⋊Q8—1222no—
518C4⋊Q8—1222no—
519C4⋊Q8C22×D6111yescharacteristic
520C4⋊Q8C22×D6111yescharacteristic
521#127—614no—
522#127—1222no—
523#125—21no—
524#125—1222no—
525#125—1222no—
526#125—1222no—
527#125—1222no—
528#125—1222no—
529#125—1222no—
530#125—1222no—
531#125—1222no—
532#125—1221no—
533#124—614no—
534#124—612no—
535#124—612no—
536#124—1222no—
537#124—1224no—
538#124—1224no—
539#124—1221no—
540#124—1221no—
541#123—1224no—
542#123—1224no—
543#123—1224no—
544#123—1224no—
545C22⋊Q8—21no—
546C22⋊Q8—612no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549C22⋊Q8—1221no—
550C22⋊Q8C22×D6112yes—
551C4×Q8—21no—
552C4×Q8—612no—
553C4×Q8—612no—
554C4×Q8—612no—
555C4×Q8—612no—
556C4×Q8—612no—
557C4×Q8—612no—
558C4×Q8—614no—
559C4×Q8—612no—
560C4×Q8—612no—
561C4×Q8—612no—
562C4×Q8—1222no—
563C4×Q8—1222no—
564C4×Q8—1222no—
565C4×Q8—1222no—
566C4×Q8—1222no—
567C4×Q8—1222no—
568C4×Q8—1222no—
569C4×Q8—1221no—
570C4×Q8C22×D6112yes—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—614no—
574C4×D4—1222no—
575C4×D4—1224no—
576C4×D4—1224no—
577C4×D4C22×D6112yes—
578C4×D4C22×D6112yes—
579#117—21no—
580#117—1222no—
581#117—1222no—
582#117—1221no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—1221no—
587C2×C4⋊C4C22×D6111yescharacteristic
588C2×C22⋊C4—21no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C42—611no—
595C2×C42—611no—
596C2×C42—1221no—
597C2×C42C22×D6111yescharacteristic
598#107—614no—
599#107C22×D6114yes—
600C4⋊C8—614no—
601C4⋊C8—614no—
602C4⋊C8—612no—
603C4⋊C8C22×D6112yes—
604#103—614no—
605#103—614no—
606#103—614no—
607#103C22×D6114yes—
608#102—614no—
609#102—614no—
610#102—614no—
611#102C22×D6114yes—
612C22⋊C8—612no—
613C22⋊C8C22×D6112yes—
614#97—614no—
615#97—612no—
616#97C22×D6112yes—
617C4×C8—614no—
618C24—21no—
619C24—1221no—
620C2×Q8—21no—
621C2×Q8—612no—
622C2×Q8—612no—
623C2×Q8—612no—
624C2×Q8—612no—
625C2×Q8—1224no—
626C2×Q8—1222no—
627C2×Q8—1222no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—2442no—
631C2×Q8C23×D6112yes—
632C2×D4—21no—
633C2×D4—42no—
634C2×D4—612no—
635C2×D4—1224no—
636C2×D4—1224no—
637C2×D4—1221no—
638C2×D4—4882no—
639C2×D4—2442no—
640C2×D4—2444no—
641C2×D4C23×D6112yes—
642C22×C4—21no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—82no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—1224no—
651C22×C4—1221no—
652C22×C4—4882no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656Q16—2444no—
657Q16—2444no—
658SD16—44no—
659SD16—2444no—
660SD16—2444no—
661SD16—2444no—
662C2×C8—614no—
663C2×C8C23×D6114yes—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—612no—
671C4⋊C4—612no—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—612no—
675C4⋊C4—612no—
676C4⋊C4—612no—
677C4⋊C4—1224no—
678C4⋊C4—1222no—
679C4⋊C4—1222no—
680C4⋊C4—1222no—
681C4⋊C4—1222no—
682C4⋊C4—1222no—
683C4⋊C4—1222no—
684C4⋊C4—1222no—
685C4⋊C4—1222no—
686C4⋊C4—1222no—
687C4⋊C4—1222no—
688C4⋊C4—1222no—
689C4⋊C4—1222no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4C23×D6112yes—
694C4⋊C4C23×D6112yes—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—1222no—
702C22⋊C4—1222no—
703C22⋊C4—1222no—
704C22⋊C4—1222no—
705C22⋊C4—1222no—
706C42—22no—
707C42—612no—
708C42—612no—
709C42—612no—
710C42—612no—
711C42—1224no—
712C42—1222no—
713C42—1222no—
714C42—1222no—
715C42—1222no—
716C42—1222no—
717C42D4×D6111yescharacteristic
718C42D4×D6111yescharacteristic
719C42C23×D6111yescharacteristic
720C42C23×D6111yescharacteristic
721C23—22no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—1222no—
726C23—2442no—
727C23—2442no—
728C23—2442no—
729C23C2×D4×D6111yescharacteristic
730Q8—24no—
731Q8—81no—
732Q8—1224no—
733Q8—1224no—
734Q8—1224no—
735Q8—1224no—
736Q8—4881no—
737Q8—4882no—
738Q8—4882no—
739Q8—2442no—
740D4—22no—
741D4—22no—
742D4—42no—
743D4—1224no—
744D4—4884no—
745D4—2442no—
746D4—2448no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4—614no—
757C2×C4—612no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—612no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—4884no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2442no—
769C2×C4C2×D4×D6111yescharacteristic
770C2×C4C2×D4×D6111yescharacteristic
771C2×C4C2×D4×D6111yescharacteristic
772C2×C4C2×D4×D6111yescharacteristic
773C2×C4C2×D4×D6111yescharacteristic
774C2×C4C24×D6111yescharacteristic
775C8—24no—
776C8—1224no—
777C22—21no—
778C22—21no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—84no—
783C22—4884no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22#137×D6112yes—
788C22C22×D4×D6111yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—614no—
798C4—1222no—
799C4—1222no—
800C4—1222no—
801C4—2442no—
802C4—2442no—
803C4—2442no—
804C4#1684059812yes—
805C2—22no—
806C2—82no—
807C2—4882no—
808C2#2145947311yescharacteristic
809C2C2×#137×D6111yescharacteristic
810C2#2146059511yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3110C2
socleC22×C61C23×D4
prime radicalC2×#14519773C22
hypercenter#3110D61
hypocenterC61#61892
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3110

Complements

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

NH ≅ G/Ntype
1. #21459624C2semidirect
3. #21458873C2semidirect
4. #21458867C2semidirect
5. #21458636C2semidirect
6. #21458634C2semidirect
7. #21456824C2semidirect
8. #21456819C2semidirect
9. #21456818C2semidirect
11. #21455918C2semidirect
12. #21455915C2semidirect
13. #21455855C2semidirect
14. #21454903C2semidirect
15. C61×#3110C2semidirect
20. Q8×Dic122C22semidirect
21. #16840492C22semidirect
23. #16840490C22semidirect
25. #16840487C22semidirect
43. #16840156C22semidirect
44. #16840154C22semidirect
45. #16840153C22semidirect
47. #16840124C22semidirect
48. #16840122C22semidirect
49. #16840120C22semidirect
52. #16840056C22semidirect
53. #16840042C22semidirect
54. #16840041C22semidirect
55. #16839985C22semidirect
56. #16839984C22semidirect
57. #16839983C22semidirect
58. #16839982C22semidirect
59. #16839971C22semidirect
60. #16839967C22semidirect
61. #16839966C22semidirect
69. #16839891C22semidirect
70. #16839890C22semidirect
71. #16839865C22semidirect
72. #16839862C22semidirect
73. #16839861C22semidirect
74. #16839856C22semidirect
75. #16839854C22semidirect
82. C61×#474C22semidirect
83. C61×#461C22semidirect
85. C61×#440C22semidirect
412. #3110D61semidirect
463. #474C2×D61semidirect
471. #461C2×D61semidirect
485. #440C2×D61semidirect
492. C61#61892semidirect

Maximal subgroups

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

subgroupindex
#214596242
C2×#168404952
#214588732
#214588672
#214586362
#214586342
#214568242
#214568192
#214568182
#214567582
#214559182
#214559152
#214558552
#214549032
C61×#31102
#6189261