Finite Group Databasebeta

← #30575630

Subgroups — #30575630

Order 15616.

1728 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
1#21459412C211yesmaximal, characteristic
2#21458706C212yesmaximal, complemented
3#21458515C212yesmaximal, complemented
4#21458245C212yesmaximal, complemented
5#21458198C214yesmaximal, complemented
6#21457752C212yesmaximal, complemented
7#21457700C214yesmaximal, complemented
8#21457150C212yesmaximal, complemented
9#21457131C211yesmaximal, characteristic, complemented
10#21456998C212yesmaximal, complemented
11#21456940C211yesmaximal, characteristic, complemented
12#21455884C212yesmaximal, complemented
13#21455854C211yesmaximal, characteristic, complemented
14#21455601C212yesmaximal, complemented
15C2×#16840044C211yesmaximal, characteristic, complemented
16#21454930C211yesmaximal, characteristic, complemented
17C61×#3509C211yesmaximal, characteristic, complemented
18#16840497C2211yescharacteristic
19#16840495—21no—
20#16840490C2211yescharacteristic
21#16840484—21no—
22#16840482C2211yescharacteristic
23#16840461—22no—
24#16840458C2212yes—
25#16840433C2211yescharacteristic
26#16840421C2212yes—
27#16840312C2211yescharacteristic
28#16840308—21no—
29#16840296C2212yes—
30#16840290—22no—
31C4×#11758222C2212yes—
32#16840230—21no—
33C2×C4×Dic122C2211yescharacteristic
34#16840165C2212yes—
35#16840161C2214yes—
36#16840119C2214yes—
37#16840110C2212yes—
38#16840103C2214yes—
39#16840100C2214yes—
40#16840095C2212yes—
41#16840086C2214yes—
42#16840075C2214yes—
43#16840069C2214yes—
44#16840066C2214yes—
45#16840059C2214yes—
46#16840054C2211yescharacteristic
47#16840054C2211yescharacteristic
48#16840049C2212yes—
49#16840047C2212yes—
50#16840044C2212yes—
51#16840044C2212yes—
52#16840044C2212yes—
53#16840044C2212yes—
54#16840039C2212yes—
55#16840039C2212yes—
56#16840001C2214yes—
57#16839993C2214yes—
58#16839993C2214yes—
59#16839984C2214yes—
60#16839969C2211yescharacteristic
61#16839969C2211yescharacteristic
62#16839964C2212yes—
63#16839962C2212yes—
64#16839922C2214yes—
65#16839917C2212yes—
66Q8×#92418C2212yes—
67C4×#11758202C2214yes—
68C4×#11758202C2212yes—
69C4×#11758202C2212yes—
70C4×#11758201C2214yes—
71D4×#92418C2214yes—
72D4×#92418C2212yes—
73#16839815C2212yes—
74#16839815C2211yescharacteristic
75#16839798C2214yes—
76C2×#14519708C2212yes—
77C2×C4⋊#92418C2211yescharacteristic
78C2×C4⋊#92418C2212yes—
79#16839756C2214yes—
80C2×#14519700C2212yes—
81C61×#557—21no—
82C61×#557C2212yes—
83C61×#556—21no—
84C61×#556C2212yes—
85C61×#552—22no—
86C61×#552C2214yes—
87C61×#541—22no—
88C61×#536—21no—
89C61×#533C2212yes—
90C61×#533C2211yescharacteristic
91C61×#533C2212yes—
92C2×C4⋊Q8×C61C2211yescharacteristic
93C61×#519—21no—
94C4×#41×C61C2211yescharacteristic
95C2×#11758222—21no—
96C2×#11758222C2312yes—
97C22×Dic122C2311yescharacteristic
98C2×#11758202C2312yes—
99C2×#11758202C2312yes—
100C2×#11758201C2314yes—
101C22×#92418C2312yes—
102C22×#92418C2314yes—
103#14519777C2311yescharacteristic
104#14519775—21no—
105#14519774C2311yescharacteristic
106#14519773—21no—
107#14519772—22no—
108#14519771—22no—
109#14519770—22no—
110#14519769C2312yes—
111#14519767—22no—
112#14519766—21no—
113#14519765—21no—
114#14519765C2312yes—
115#14519764—21no—
116#14519763—22no—
117#14519762—22no—
118#14519760—22no—
119#14519759—22no—
120#14519756C2312yes—
121#14519755—22no—
122#14519751—21no—
123#14519751C2312yes—
124#14519751C2312yes—
125#14519750—22no—
126#14519749—22no—
127#14519749—22no—
128C4×Dic122—21no—
129C4×Dic122—21no—
130C4×Dic122C2311yescharacteristic
131C4×Dic122C2311yescharacteristic
132C4×Dic122C2311yescharacteristic
133C4×Dic122C2311yescharacteristic
134C4×Dic122C2312yes—
135#14519742—21no—
136#14519742—21no—
137C4×D244—21no—
138C4×D244C2312yes—
139C4×D244C2312yes—
140#14519739—21no—
141#14519739—21no—
142C4×C22⋊D61—22no—
143C4×C22⋊D61—22no—
144C4×C22⋊D61—22no—
145#14519737—22no—
146#14519737—22no—
147#14519736C2312yes—
148#14519734—22no—
149#14519734—22no—
150C2×C4⋊Dic61C2311yescharacteristic
151C2×#11758196—21no—
152C2×C4×Dic61—21no—
153C42×D61—22no—
154#14519710C2314yes—
155#14519710C2314yes—
156#14519710C2312yes—
157#14519710C2312yes—
158#14519708C2314yes—
159#14519708C2314yes—
160#14519708C2314yes—
161C4⋊#92418C2312yes—
162C4⋊#92418C2312yes—
163C4⋊#92418C2311yescharacteristic
164C4⋊#92418C2311yescharacteristic
165C4⋊#92418C2314yes—
166#14519701C2314yes—
167#14519701C2312yes—
168#14519701C2312yes—
169#14519700C2314yes—
170#14519700C2314yes—
171#14519700C2312yes—
172#14519700C2312yes—
173#14519697C2314yes—
174#14519697C2314yes—
175#14519697C2314yes—
176C22⋊#92418C2312yes—
177C22⋊#92418C2314yes—
178C4×#92418C2314yes—
179C4×#92418C2312yes—
180C2×#41×C61D411yescharacteristic
181C22×Q8×C61—21no—
182C4⋊Q8×C61—22no—
183C4⋊Q8×C61—21no—
184C4⋊Q8×C61—21no—
185C4⋊Q8×C61C2311yescharacteristic
186C4⋊Q8×C61C2312yes—
187C4⋊Q8×C61C2312yes—
188C4⋊Q8×C61C2311yescharacteristic
189#126×C61—24no—
190#126×C61—24no—
191#125×C61—24no—
192#125×C61—24no—
193#125×C61—21no—
194#125×C61—22no—
195#125×C61C2314yes—
196#124×C61—22no—
197#123×C61—24no—
198C22⋊Q8×C61—22no—
199C22⋊Q8×C61—22no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61—22no—
202C22⋊Q8×C61C2312yes—
203C22⋊Q8×C61C2314yes—
204C4×Q8×C61—22no—
205C4×Q8×C61—22no—
206C4×Q8×C61—22no—
207C4×Q8×C61—22no—
208C4×Q8×C61—22no—
209C4×Q8×C61—21no—
210C4×Q8×C61D411yescharacteristic
211C4×Q8×C61C2314yes—
212C4×Q8×C61C2312yes—
213C4×Q8×C61C2311yescharacteristic
214C4×D4×C61D412yes—
215C4×D4×C61D411yescharacteristic
216C4×D4×C61C2312yes—
217C4×D4×C61C2311yescharacteristic
218#117×C61—21no—
219#117×C61—22no—
220#117×C61—24no—
221#117×C61D412yes—
222#117×C61D411yescharacteristic
223#117×C61C2314yes—
224C2×C4⋊C4×C61—21no—
225C2×C4⋊C4×C61C2312yes—
226C2×C42×C61C2311yescharacteristic
227C2×C42×C61C2312yes—
228#41×C61—24no—
229C2×Q8×C61—21no—
230C2×Q8×C61—22no—
231C2×Q8×C61—22no—
232C2×Q8×C61—44no—
233C2×Q8×C61C2×D411yescharacteristic
234C2×Q8×C61C2412yes—
235C2×D4×C61C2×D412yes—
236C2×D4×C61C2×D411yescharacteristic
237C22×C4×C61—22no—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2411yescharacteristic
243C22×C4×C61C2412yes—
244C2×C22⋊D61—22no—
245C2×C22⋊D61—22no—
246C2×C22⋊D61—22no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249#11758222—24no—
250#11758222—42no—
251#11758222—44no—
252C2×D244—21no—
253C2×D244—21no—
254C2×D244C2412yes—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×Dic122—22no—
259C2×Dic122—21no—
260C2×Dic122—21no—
261C2×Dic122—41no—
262C2×Dic122C2411yescharacteristic
263C2×Dic122C2411yescharacteristic
264C4⋊C4×C61—22no—
265C4⋊C4×C61—22no—
266C4⋊C4×C61—22no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—24no—
271C4⋊C4×C61—24no—
272C4⋊C4×C61—24no—
273C4⋊C4×C61—22no—
274C4⋊C4×C61—24no—
275C4⋊C4×C61—22no—
276C4⋊C4×C61C2×D411yescharacteristic
277C4⋊C4×C61C2×D412yes—
278C4⋊C4×C61C2×D411yescharacteristic
279C4⋊C4×C61C2×D412yes—
280C4⋊C4×C61C2414yes—
281C4⋊C4×C61C2412yes—
282C22⋊C4×C61—22no—
283C22⋊C4×C61—24no—
284C22⋊C4×C61—24no—
285C22⋊C4×C61C2×D412yes—
286C22⋊C4×C61C2×D412yes—
287C22⋊C4×C61C2×D412yes—
288C42×C61—24no—
289C42×C61—24no—
290C42×C61—22no—
291C42×C61C2×D412yes—
292C42×C61C2×D411yescharacteristic
293C42×C61C2×D412yes—
294C42×C61C2×D411yescharacteristic
295C42×C61C2411yescharacteristic
296C42×C61C2412yes—
297C42×C61C2411yescharacteristic
298C22⋊Dic61—22no—
299C22⋊Dic61—22no—
300#11758202—24no—
301#11758202—42no—
302#11758201—44no—
303#11758198—22no—
304#11758198—22no—
305#11758198—22no—
306#11758198—22no—
307#11758198—22no—
308#11758198—22no—
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61C2411yescharacteristic
312C4⋊Dic61C2411yescharacteristic
313C4⋊Dic61C2412yes—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—22no—
319#11758196—22no—
320#11758196—22no—
321#11758196—22no—
322C4×Dic61—21no—
323C4×Dic61—22no—
324C4×Dic61—22no—
325C4×Dic61—21no—
326C4×Dic61—21no—
327C4×Dic61—21no—
328C2×#92418—42no—
329C2×#92418—44no—
330C2×#92418C2412yes—
331C2×#92418C2412yes—
332C2×#92418C2414yes—
333C23×C61C22×D412yes—
334C23×C61C22×D411yescharacteristic
335C22×D61—22no—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—22no—
339Q8×C61—42no—
340Q8×C61—44no—
341Q8×C61—44no—
342D4×C61—24no—
343D4×C61—22no—
344C2×C4×C61—24no—
345C2×C4×C61—21no—
346C2×C4×C61—22no—
347C2×C4×C61—21no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—24no—
352C2×C4×C61—42no—
353C2×C4×C61—41no—
354C2×C4×C61—44no—
355C2×C4×C61#13514yes—
356C2×C4×C61C22×D412yes—
357C2×C4×C61C22×D412yes—
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D412yes—
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C2511yescharacteristic
365C22⋊D61—44no—
366C22⋊D61—44no—
367C22⋊D61—82no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—22no—
372C2×Dic61—21no—
373C2×Dic61—42no—
374C2×Dic61—81no—
375D244—22no—
376D244—22no—
377D244—42no—
378D244—81no—
379C4×D61—44no—
380C4×D61—44no—
381C4×D61—82no—
382Dic122—21no—
383Dic122—21no—
384Dic122—21no—
385Dic122—42no—
386Dic122—42no—
387Dic1222−1+412yes—
388#92418—22no—
389#92418—24no—
390#92418—22no—
391#62101—611nomaximal, Sylow
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61C2×#13512yes—
398C22×C61C23×D411yescharacteristic
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—42no—
402C4×C61—22no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—22no—
407C4×C61—22no—
408C4×C61—42no—
409C4×C61—42no—
410C4×C61—44no—
411C4×C61C2×#13512yes—
412C4×C61C2×#13512yes—
413C4×C61C2×2−1+411yescharacteristic
414C4×C61#58511yescharacteristic
415Dic61—22no—
416Dic61—41no—
417Dic61—41no—
418Dic61—41no—
419Dic61—42no—
420#3509D6111yescharacteristic, complemented
421#3480—611no—
422#3383—612no—
423#3365—612no—
424#3342—612no—
425#3337—614no—
426#3304—612no—
427#3300—614no—
428#3248—612no—
429#3246—611no—
430#3233—612no—
431#3226—611no—
432#3107—612no—
433#3104—611no—
434#3076—612no—
435C2×#475—611no—
436#2988—611no—
437C2×C61—22no—
438C2×C61—42no—
439C2×C61#348911yescharacteristic
440C2×C61C22×#13511yescharacteristic
441C2×C61#358611yescharacteristic
442D61—82no—
443#559—611no—
444#559—1221no—
445#557—21no—
446#557—611no—
447#557C2×D6112yes—
448#556—21no—
449#556—611no—
450#556—1221no—
451#556C2×D6112yes—
452#553—612no—
453#553—1222no—
454#552—22no—
455#552C2×D6114yes—
456#550—611no—
457#548—612no—
458#541—22no—
459#536—21no—
460#533C2×D6111yescharacteristic
461#533C2×D6112yes—
462#533C2×D6112yes—
463#532—611no—
464#532—1221no—
465C2×C4⋊Q8C2×D6111yescharacteristic
466#529—612no—
467#529—1222no—
468#519—21no—
469C4×#41—612no—
470C4×#41—1221no—
471C4×#41C2×D6111yescharacteristic
472C2×C4×Q8—611no—
473#500—612no—
474#499—614no—
475#488—614no—
476#486—612no—
477#485—614no—
478#485—614no—
479#484—612no—
480#482—614no—
481#480—614no—
482#479—614no—
483#479—614no—
484#478—614no—
485#477—611no—
486#477—611no—
487#476—612no—
488#475—612no—
489#475—612no—
490#475—612no—
491#475—612no—
492#475—612no—
493#474—612no—
494#474—612no—
495#467—614no—
496#465—614no—
497#465—614no—
498#464—614no—
499#462—611no—
500#462—611no—
501#461—612no—
502#460—612no—
503#452—614no—
504#451—612no—
505C8×Q8—612no—
506C4×Q16—612no—
507C4×Q16—612no—
508C4×Q16—614no—
509C4×SD16—614no—
510C8×D4—614no—
511C8×D4—612no—
512#431—611no—
513#431—612no—
514#427—614no—
515C2×#106—612no—
516C2×C4⋊C8—611no—
517C2×C4⋊C8—612no—
518#416—614no—
519C2×#103—612no—
520C61#6210111yescharacteristic, complemented, Sylow
521C2×#41—612no—
522C2×#41—1221no—
523C2×#41C22⋊D6111yescharacteristic
524C22×Q8—21no—
525C22×Q8—611no—
526C2×Q16—612no—
527C2×Q16—612no—
528C2×SD16—614no—
529C22×C8—612no—
530C22×C8—614no—
531C4⋊Q8—22no—
532C4⋊Q8—21no—
533C4⋊Q8—21no—
534C4⋊Q8—611no—
535C4⋊Q8—1221no—
536C4⋊Q8C22×D6111yescharacteristic
537C4⋊Q8C22×D6112yes—
538C4⋊Q8C22×D6112yes—
539C4⋊Q8C22×D6111yescharacteristic
540#127—611no—
541#127—1221no—
542#126—24no—
543#126—24no—
544#126—1222no—
545#126—1222no—
546#126—1222no—
547#125—24no—
548#125—24no—
549#125—21no—
550#125—22no—
551#125—612no—
552#125—1222no—
553#125C22×D6114yes—
554#124—22no—
555#124—612no—
556#124—1221no—
557#124—1221no—
558#124—1222no—
559#124—1221no—
560#123—24no—
561#123—1222no—
562#123—1222no—
563#123—1222no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—21no—
567C22⋊Q8—22no—
568C22⋊Q8—612no—
569C22⋊Q8—1222no—
570C22⋊Q8C22×D6112yes—
571C22⋊Q8C22×D6114yes—
572#121—612no—
573#121—612no—
574#121—1222no—
575#121—1222no—
576#121—1221no—
577#121—1222no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—21no—
584C4×Q8—611no—
585C4×Q8—611no—
586C4×Q8—611no—
587C4×Q8—611no—
588C4×Q8—612no—
589C4×Q8—1221no—
590C4×Q8—1221no—
591C4×Q8—1221no—
592C4×Q8—1221no—
593C4×Q8C22⋊D6111yescharacteristic
594C4×Q8C22×D6114yes—
595C4×Q8C22×D6112yes—
596C4×Q8C22×D6111yescharacteristic
597C4×D4—612no—
598C4×D4—612no—
599C4×D4—1222no—
600C4×D4—1222no—
601C4×D4—1222no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1222no—
605C4×D4—1222no—
606C4×D4—1221no—
607C4×D4C22⋊D6112yes—
608C4×D4C22⋊D6111yescharacteristic
609C4×D4C22×D6112yes—
610C4×D4C22×D6111yescharacteristic
611#117—21no—
612#117—22no—
613#117—24no—
614#117—612no—
615#117—1222no—
616#117—1222no—
617#117C22⋊D6111yescharacteristic
618#117C22⋊D6112yes—
619#117C22×D6114yes—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—1221no—
623C2×C4⋊C4C22×D6112yes—
624C2×C42—1221no—
625C2×C42—1222no—
626C2×C42C22×D6111yescharacteristic
627C2×C42C22×D6112yes—
628#107—612no—
629#107—614no—
630#107—614no—
631#107—612no—
632#106—614no—
633#106—614no—
634#106—614no—
635C4⋊C8—612no—
636C4⋊C8—611no—
637C4⋊C8—612no—
638C4⋊C8—614no—
639C4⋊C8—611no—
640#103—612no—
641#103—614no—
642#103—612no—
643#103—614no—
644#103—614no—
645#103—612no—
646#103—612no—
647#102—614no—
648#102—614no—
649#102—614no—
650C22⋊C8—612no—
651C22⋊C8—614no—
652C4×C8—614no—
653C4×C8—612no—
654#41—24no—
655#41—1224no—
656#41—2442no—
657#41—2444no—
658C2×Q8—21no—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—44no—
662C2×Q8—611no—
663C2×Q8—611no—
664C2×Q8—1222no—
665C2×Q8—1221no—
666C2×Q8—1221no—
667C2×Q8—2441no—
668C2×Q8C2×C22⋊D6111yescharacteristic
669C2×Q8C23×D6112yes—
670C2×D4—612no—
671C2×D4—1222no—
672C2×D4—1222no—
673C2×D4—1222no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4C2×C22⋊D6112yes—
677C2×D4C2×C22⋊D6111yescharacteristic
678C22×C4—22no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1222no—
682C22×C4—1222no—
683C22×C4—1222no—
684C22×C4C2×C22⋊D6112yes—
685C22×C4C2×C22⋊D6111yescharacteristic
686C22×C4C2×C22⋊D6112yes—
687C22×C4C2×C22⋊D6111yescharacteristic
688C22×C4C23×D6111yescharacteristic
689C22×C4C23×D6112yes—
690Q16—1224no—
691Q16—2442no—
692SD16—2444no—
693C2×C8—612no—
694C2×C8—612no—
695C2×C8—614no—
696C2×C8—2442no—
697C2×C8—2444no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—24no—
707C4⋊C4—22no—
708C4⋊C4—24no—
709C4⋊C4—22no—
710C4⋊C4—611no—
711C4⋊C4—611no—
712C4⋊C4—612no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1222no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1221no—
723C4⋊C4C2×C22⋊D6111yescharacteristic
724C4⋊C4C2×C22⋊D6111yescharacteristic
725C4⋊C4C2×C22⋊D6112yes—
726C4⋊C4C2×C22⋊D6112yes—
727C4⋊C4C23×D6114yes—
728C4⋊C4C23×D6112yes—
729C22⋊C4—22no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—1222no—
733C22⋊C4—1222no—
734C22⋊C4—1222no—
735C22⋊C4—1222no—
736C22⋊C4—1222no—
737C22⋊C4—1222no—
738C22⋊C4—1222no—
739C22⋊C4—1222no—
740C22⋊C4C2×C22⋊D6112yes—
741C22⋊C4C2×C22⋊D6112yes—
742C22⋊C4C2×C22⋊D6112yes—
743C42—24no—
744C42—24no—
745C42—22no—
746C42—1221no—
747C42—1222no—
748C42—1221no—
749C42—1222no—
750C42—1221no—
751C42—1221no—
752C42C2×C22⋊D6112yes—
753C42C2×C22⋊D6112yes—
754C42C2×C22⋊D6111yescharacteristic
755C42C2×C22⋊D6111yescharacteristic
756C42C23×D6112yes—
757C42C23×D6111yescharacteristic
758C42C23×D6111yescharacteristic
759C23—1222no—
760C23C22×C22⋊D6112yes—
761C23C22×C22⋊D6111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—44no—
767Q8—44no—
768Q8—612no—
769Q8—1221no—
770Q8—1221no—
771Q8—1221no—
772Q8—2442no—
773Q8—2442no—
774D4—24no—
775D4—22no—
776D4—1222no—
777D4—1222no—
778D4—4881no—
779D4—4882no—
780D4—2444no—
781D4—2444no—
782D4—2442no—
783C2×C4—24no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—44no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1222no—
798C2×C4—1221no—
799C2×C4—4882no—
800C2×C4—4881no—
801C2×C4—2444no—
802C2×C4—2442no—
803C2×C4—2444no—
804C2×C4#1451979714yes—
805C2×C4C22×C22⋊D6112yes—
806C2×C4C22×C22⋊D6112yes—
807C2×C4C22×C22⋊D6111yescharacteristic
808C2×C4C22×C22⋊D6111yescharacteristic
809C2×C4C22×C22⋊D6112yes—
810C2×C4C22×C22⋊D6111yescharacteristic
811C2×C4C22×C22⋊D6111yescharacteristic
812C2×C4C22×C22⋊D6111yescharacteristic
813C2×C4C24×D6111yescharacteristic
814C8—1222no—
815C8—1224no—
816C8—1222no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—2442no—
823C22—2442no—
824C22—2442no—
825C22C2×#1451979712yes—
826C22C23×C22⋊D6111yescharacteristic
827C4—22no—
828C4—21no—
829C4—22no—
830C4—21no—
831C4—22no—
832C4—21no—
833C4—42no—
834C4—44no—
835C4—42no—
836C4—1222no—
837C4—2441no—
838C4—2442no—
839C4—2441no—
840C4—2441no—
841C4C2×#1451979712yes—
842C4C2×#1451979712yes—
843C42−1+4×D6111yescharacteristic
844C4#1684059911yescharacteristic
845C2—22no—
846C2—42no—
847C2—4882no—
848C2#2145949211yescharacteristic
849C2C22×#1451979711yescharacteristic
850C2#2146060611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3509C2
socleC22×C61C23×D4
prime radical#21459412C2
hypercenter#3509D61
hypocenterC61#62101
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3509

Complements

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

NH ≅ G/Ntype
2. #21458706C2semidirect
3. #21458515C2semidirect
4. #21458245C2semidirect
5. #21458198C2semidirect
6. #21457752C2semidirect
7. #21457700C2semidirect
8. #21457150C2semidirect
9. #21457131C2semidirect
10. #21456998C2semidirect
11. #21456940C2semidirect
12. #21455884C2semidirect
13. #21455854C2semidirect
14. #21455601C2semidirect
15. C2×#16840044C2semidirect
16. #21454930C2semidirect
17. C61×#3509C2semidirect
420. #3509D61semidirect
520. C61#62101semidirect

Maximal subgroups

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

subgroupindex
#214594122
#214587062
#214585152
#214582452
#214581982
#214577522
#214577002
#214571502
#214571312
#214569982
#214569402
#214558842
#214558542
#214556012
C2×#168400442
#214549302
C61×#35092
#6210161