Finite Group Databasebeta

← #30571164

Subgroups — #30571164

Order 15616.

1730 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840485C211yesmaximal, characteristic, complemented
2#21458894C214yesmaximal, complemented
3#21458879C214yesmaximal, complemented
4#21458661C214yesmaximal, complemented
5#21458646C214yesmaximal, complemented
6#21456843C212yesmaximal, complemented
7#21456818C211yesmaximal, characteristic, complemented
8#21456802C211yesmaximal, characteristic
9#21456780C212yesmaximal, complemented
10#21455953C212yesmaximal, complemented
11#21455945C211yesmaximal, characteristic, complemented
12#21455937C211yesmaximal, characteristic, complemented
13#21455895C212yesmaximal, complemented
14#21454904C211yesmaximal, characteristic, complemented
15C61×#3507C211yesmaximal, characteristic, complemented
16#16840485—22no—
17#16840485—22no—
18#16840485C2214yes—
19#16840485C2214yes—
20C2×#14519777C2211yescharacteristic
21C2×#14519772—21no—
22C2×#14519772—21no—
23C2×#14519765C2211yescharacteristic
24C2×#14519765C2211yescharacteristic
25C2×#14519753—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×#14519735—21no—
30#16840157C2214yescomplemented
31#16840154C2212yes—
32#16840149C2212yes—
33#16840144C2214yes—
34#16840132C2214yescomplemented
35#16840124C2212yes—
36#16840124C2212yes—
37#16840119C2214yes—
38#16840090C2212yes—
39#16840073C2212yes—
40#16840066C2214yescomplemented
41#16840059C2214yes—
42#16840054C2212yescomplemented
43#16840044C2212yescomplemented
44#16839984C2214yes—
45#16839984C2214yes—
46#16839981C2214yescomplemented
47#16839977C2214yes—
48#16839977C2214yes—
49#16839974C2214yes—
50#16839972C2214yescomplemented
51#16839969C2212yescomplemented
52#16839967C2214yescomplemented
53#16839959C2212yescomplemented
54#16839917C2212yes—
55#16839917C2212yes—
56#16839912C2212yes—
57#16839900C2212yes—
58#16839900C2212yes—
59#16839895C2212yes—
60#16839893C2214yescomplemented
61#16839893C2214yescomplemented
62#16839872C2214yes—
63#16839867C2214yescomplemented
64#16839862C2214yescomplemented
65#16839860C2214yes—
66C4×#11758202C2214yescomplemented
67C4×#11758200C2214yescomplemented
68#16839819C2211yescharacteristic
69#16839819C2211yescharacteristic
70#16839819C2212yes—
71#16839815C2212yes—
72C61×#559C2212yescomplemented
73C61×#557C2212yescomplemented
74C61×#556—22no—
75C61×#556C2212yescomplemented
76C61×#554C2212yescomplemented
77C61×#552—22no—
78C61×#539—21no—
79C61×#539—21no—
80C61×#536—21no—
81C61×#533C2211yescharacteristic
82C61×#532C2211yescharacteristic
83C61×#529C2212yes—
84C61×#529C2212yes—
85C61×#520—21no—
86C2×C4×Q8×C61C2211yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2311yescharacteristic
89C22×D244C2311yescharacteristic
90C22×C4×D61—21no—
91C2×#11758202C2314yes—
92C2×#11758202C2314yes—
93C2×#11758200C2314yes—
94C2×#11758200C2314yes—
95C2×#11758201C2314yes—
96C2×#11758199C2314yes—
97#14519777—22no—
98#14519777C2314yes—
99#14519772—24no—
100#14519772—24no—
101#14519772—24no—
102#14519772—24no—
103#14519765—22no—
104#14519765—21no—
105#14519765—21no—
106#14519765C2312yes—
107#14519765C2314yes—
108#14519765C2312yes—
109#14519753—24no—
110#14519753—24no—
111C4×Dic122—22no—
112C4×Dic122—21no—
113C4×Dic122—21no—
114C4×Dic122C2312yes—
115C4×Dic122C2312yes—
116C4×Dic122C2314yes—
117C4×D244—22no—
118C4×D244C2314yes—
119#14519735—24no—
120#14519735—24no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758198—21no—
127C2×#11758198—21no—
128C2×#11758198—21no—
129C2×#11758198—21no—
130C2×#11758198—21no—
131C2×C4×Dic61—21no—
132C2×C4×Dic61—21no—
133#14519710C2314yes—
134#14519708C2314yes—
135C4⋊#92418C2312yes—
136C4⋊#92418C2314yes—
137C4⋊#92418C2312yes—
138C4⋊#92418C2314yes—
139#14519701C2314yes—
140#14519700C2314yes—
141#14519700C2314yes—
142#14519700C2314yes—
143#14519700C2314yes—
144#14519698C2314yes—
145#14519697C2314yes—
146#14519697C2314yes—
147C22⋊#92418C2312yes—
148C22⋊#92418C2312yes—
149#14519688C2314yes—
150#14519688C2312yes—
151#14519688C2312yes—
152C4×#92418C2314yes—
153C2×#41×C61—21no—
154C22×Q8×C61D411yescharacteristic
155C4⋊Q8×C61—22no—
156C4⋊Q8×C61C2311yescharacteristic
157C4⋊Q8×C61C2311yescharacteristic
158C4⋊Q8×C61C2311yescharacteristic
159#127×C61C2311yescharacteristic
160#126×C61—22no—
161#126×C61—22no—
162#126×C61—22no—
163#126×C61—22no—
164#125×C61—22no—
165#125×C61—22no—
166#125×C61—21no—
167#125×C61C2312yes—
168#125×C61C2312yes—
169#124×C61—22no—
170#124×C61—21no—
171#124×C61C2312yes—
172#124×C61C2312yes—
173#123×C61—22no—
174#123×C61—22no—
175#123×C61—22no—
176#123×C61—22no—
177C22⋊Q8×C61—22no—
178C22⋊Q8×C61—22no—
179C22⋊Q8×C61—21no—
180C22⋊Q8×C61—22no—
181C22⋊Q8×C61—22no—
182C22⋊Q8×C61C2312yes—
183#121×C61—21no—
184#121×C61C2312yes—
185C4×Q8×C61—22no—
186C4×Q8×C61—21no—
187C4×Q8×C61D412yes—
188C4×Q8×C61D412yes—
189C4×Q8×C61C2312yes—
190C4×Q8×C61C2312yes—
191C4×Q8×C61C2312yes—
192C4×Q8×C61C2312yes—
193C4×Q8×C61C2312yes—
194C4×D4×C61—22no—
195C4×D4×C61—22no—
196C4×D4×C61—22no—
197C4×D4×C61—21no—
198C4×D4×C61C2312yes—
199C4×D4×C61C2312yes—
200C4×D4×C61C2312yes—
201#117×C61—21no—
202#117×C61—22no—
203#117×C61—22no—
204#117×C61—22no—
205C2×C4⋊C4×C61—22no—
206C2×C4⋊C4×C61D411yescharacteristic
207C2×C4⋊C4×C61D411yescharacteristic
208C2×C4⋊C4×C61D411yescharacteristic
209C2×C42×C61C2311yescharacteristic
210C2×C42×C61C2311yescharacteristic
211C2×C42×C61C2311yescharacteristic
212C23×D61—21no—
213#41×C61—44no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—42no—
217C2×Q8×C61C2×D412yes—
218C2×Q8×C61C2×D412yes—
219C2×Q8×C61C2412yes—
220C2×D4×C61—22no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61C2412yes—
224C22×C4×C61—22no—
225C22×C4×C61—22no—
226C22×C4×C61—22no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C2×D244—21no—
238C2×D244—42no—
239C2×D244C2412yes—
240C2×C4×D61—24no—
241C2×C4×D61—44no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—42no—
245C2×Dic122—42no—
246C2×Dic122C2412yes—
247C2×Dic122C2412yes—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—22no—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—22no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—22no—
258C4⋊C4×C61—22no—
259C4⋊C4×C61—22no—
260C4⋊C4×C61C2×D412yes—
261C4⋊C4×C61C2×D412yes—
262C4⋊C4×C61C2×D412yes—
263C4⋊C4×C61C2×D412yes—
264C4⋊C4×C61C2×D412yes—
265C4⋊C4×C61C2×D412yes—
266C4⋊C4×C61C2412yes—
267C4⋊C4×C61C2412yes—
268C22⋊C4×C61—22no—
269C22⋊C4×C61—22no—
270C22⋊C4×C61—22no—
271C22⋊C4×C61—22no—
272C22⋊C4×C61—22no—
273C22⋊C4×C61—22no—
274C22⋊C4×C61—22no—
275C22⋊C4×C61—22no—
276C22⋊C4×C61—22no—
277C42×C61—22no—
278C42×C61—22no—
279C42×C61—22no—
280C42×C61C2×D412yes—
281C42×C61C2×D412yes—
282C42×C61C2×D411yescharacteristic
283C42×C61C2×D411yescharacteristic
284C42×C61C2411yescharacteristic
285C42×C61C2412yes—
286C42×C61C2412yes—
287C42×C61C2411yescharacteristic
288#11758202—44no—
289#11758202—44no—
290#11758201—44no—
291#11758200—44no—
292#11758200—44no—
293#11758199—44no—
294#11758198—24no—
295#11758198—22no—
296#11758198—22no—
297#11758198—24no—
298#11758198—22no—
299#11758198—24no—
300#11758198—22no—
301C4⋊Dic61—24no—
302C4⋊Dic61—24no—
303C4⋊Dic61—21no—
304C4⋊Dic61C2412yes—
305#11758196—22no—
306#11758196—24no—
307#11758196—22no—
308C4×Dic61—24no—
309C4×Dic61—22no—
310C4×Dic61—22no—
311C2×#92418C2414yes—
312C2×#92418C2414yes—
313C23×C61—22no—
314C23×C61C22×D411yescharacteristic
315C22×D61—22no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61—42no—
319Q8×C61—24no—
320Q8×C61—42no—
321Q8×C61—42no—
322Q8×C61—42no—
323Q8×C61—81no—
324D4×C61—24no—
325D4×C61—42no—
326D4×C61—44no—
327D4×C61—81no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—44no—
339C2×C4×C61—82no—
340C2×C4×C61—82no—
341C2×C4×C61C22×D412yes—
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D412yes—
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D412yes—
348C2×C4×C61C22×D412yes—
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C2511yescharacteristic
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—42no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357D244—24no—
358D244—42no—
359C4×D61—48no—
360Dic122—22no—
361Dic122—24no—
362Dic122—22no—
363Dic122—42no—
364Dic122—42no—
365#92418—24no—
366#92418—24no—
367#61894—611nomaximal, Sylow
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61#57512yes—
374C22×C61C23×D411yescharacteristic
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—84no—
379C4×C61—22no—
380C4×C61—22no—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—22no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—22no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61#58512yes—
392Dic61—42no—
393Dic61—42no—
394Dic61—42no—
395#3507D6111yescharacteristic, complemented
396C2×#556—611no—
397#3402—614no—
398#3401—614no—
399#3377—614no—
400#3376—614no—
401#3218—612no—
402#3215—611no—
403#3213—611no—
404#3211—612no—
405#3114—612no—
406#3113—611no—
407#3112—611no—
408#3108—612no—
409#2983—611no—
410C2×C61—22no—
411C2×C61—82no—
412C2×C61#348711yescharacteristic
413C2×C61C2×#57511yescharacteristic
414C2×C61#358611yescharacteristic
415D61—82no—
416#559C2×D6112yescomplemented
417#557C2×D6112yescomplemented
418#556—22no—
419#556—614no—
420#556—614no—
421#556—1222no—
422#556—1222no—
423#556C2×D6112yescomplemented
424#554C2×D6112yescomplemented
425#552—22no—
426#539—21no—
427#539—21no—
428#536—21no—
429#533C2×D6111yescharacteristic
430#532C2×D6111yescharacteristic
431C2×C4⋊Q8—611no—
432#529C2×D6112yes—
433#529C2×D6112yes—
434C2×#126—1221no—
435C2×#126—1221no—
436C2×#124—611no—
437C2×#124—611no—
438C2×C22⋊Q8—1221no—
439#520—21no—
440C2×C4×Q8—611no—
441C2×C4×Q8—611no—
442C2×C4×Q8C2×D6111yescharacteristic
443C2×C4×D4—611no—
444C2×#117—1221no—
445#497—612no—
446#497—614no—
447#496—612no—
448#495—614no—
449#491—614no—
450#489—612no—
451#489—612no—
452#488—614no—
453#483—612no—
454#480—612no—
455#479—614no—
456#478—614no—
457#477—612no—
458#475—612no—
459#464—614no—
460#464—614no—
461#464—614no—
462#463—614no—
463#463—614no—
464#463—614no—
465#462—612no—
466#462—614no—
467#461—614no—
468#460—612no—
469#451—612no—
470#451—612no—
471#450—612no—
472#448—612no—
473#448—612no—
474#447—612no—
475#446—614no—
476#446—614no—
477#442—614no—
478#441—614no—
479#440—614no—
480#440—614no—
481C4×Q16—614no—
482C4×SD16—614no—
483#432—611no—
484#432—611no—
485#432—612no—
486#431—612no—
487C61#6189411yescharacteristic, complemented, Sylow
488C2×#41—21no—
489C22×Q8—611no—
490C22×Q8—611no—
491C22×Q8C22⋊D6111yescharacteristic
492C22×D4—611no—
493C23×C4—1221no—
494C2×Q16—614no—
495C2×Q16—614no—
496C2×SD16—614no—
497C2×SD16—614no—
498C2×SD16—614no—
499C2×D8—614no—
500C4⋊Q8—22no—
501C4⋊Q8—614no—
502C4⋊Q8—1222no—
503C4⋊Q8C22×D6111yescharacteristic
504C4⋊Q8C22×D6111yescharacteristic
505C4⋊Q8C22×D6111yescharacteristic
506#127C22×D6111yescharacteristic
507#126—22no—
508#126—22no—
509#126—22no—
510#126—22no—
511#126—1224no—
512#126—1224no—
513#126—1224no—
514#126—1224no—
515#125—22no—
516#125—22no—
517#125—21no—
518#125C22×D6112yes—
519#125C22×D6112yes—
520#124—22no—
521#124—21no—
522#124—612no—
523#124—614no—
524#124—612no—
525#124—1222no—
526#124—1221no—
527#124—1221no—
528#124C22×D6112yes—
529#124C22×D6112yes—
530#123—22no—
531#123—22no—
532#123—22no—
533#123—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8—21no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—1224no—
540C22⋊Q8—1224no—
541C22⋊Q8C22×D6112yes—
542#121—21no—
543#121C22×D6112yes—
544C4×Q8—22no—
545C4×Q8—21no—
546C4×Q8—614no—
547C4×Q8—612no—
548C4×Q8—612no—
549C4×Q8—1222no—
550C4×Q8—1221no—
551C4×Q8—1221no—
552C4×Q8C22⋊D6112yes—
553C4×Q8C22⋊D6112yes—
554C4×Q8C22×D6112yes—
555C4×Q8C22×D6112yes—
556C4×Q8C22×D6112yes—
557C4×Q8C22×D6112yes—
558C4×Q8C22×D6112yes—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—21no—
563C4×D4—614no—
564C4×D4—1222no—
565C4×D4C22×D6112yes—
566C4×D4C22×D6112yes—
567C4×D4C22×D6112yes—
568#117—21no—
569#117—22no—
570#117—22no—
571#117—22no—
572#117—1224no—
573#117—1224no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4C22⋊D6111yescharacteristic
581C2×C4⋊C4C22⋊D6111yescharacteristic
582C2×C4⋊C4C22⋊D6111yescharacteristic
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C42—1221no—
589C2×C42—1221no—
590C2×C42C22×D6111yescharacteristic
591C2×C42C22×D6111yescharacteristic
592C2×C42C22×D6111yescharacteristic
593#107—614no—
594#106—614no—
595C4⋊C8—614no—
596C4⋊C8—612no—
597C4⋊C8—614no—
598C4⋊C8—612no—
599#103—614no—
600#103—614no—
601#103—614no—
602#103—614no—
603#103—614no—
604#102—614no—
605#102—614no—
606#102—614no—
607C22⋊C8—612no—
608C22⋊C8—612no—
609#97—612no—
610#97—614no—
611#97—612no—
612C4×C8—614no—
613C24—1221no—
614#41—44no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—42no—
618C2×Q8—612no—
619C2×Q8—612no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—2442no—
623C2×Q8—2442no—
624C2×Q8C2×C22⋊D6112yes—
625C2×Q8C2×C22⋊D6112yes—
626C2×Q8C23×D6112yes—
627C2×D4—22no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—612no—
631C2×D4—1221no—
632C2×D4—2442no—
633C2×D4C23×D6112yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1224no—
641C22×C4—2444no—
642C22×C4C2×C22⋊D6111yescharacteristic
643C22×C4C2×C22⋊D6111yescharacteristic
644C22×C4C2×C22⋊D6111yescharacteristic
645C22×C4C2×C22⋊D6111yescharacteristic
646C22×C4C2×C22⋊D6111yescharacteristic
647C22×C4C2×C22⋊D6111yescharacteristic
648C22×C4C23×D6111yescharacteristic
649Q16—2444no—
650Q16—2444no—
651SD16—2444no—
652SD16—2444no—
653SD16—2444no—
654D8—2444no—
655C2×C8—614no—
656C2×C8—614no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—612no—
670C4⋊C4—1221no—
671C4⋊C4—1222no—
672C4⋊C4—1224no—
673C4⋊C4—1222no—
674C4⋊C4—1224no—
675C4⋊C4—1224no—
676C4⋊C4C2×C22⋊D6112yes—
677C4⋊C4C2×C22⋊D6112yes—
678C4⋊C4C2×C22⋊D6112yes—
679C4⋊C4C2×C22⋊D6112yes—
680C4⋊C4C2×C22⋊D6112yes—
681C4⋊C4C2×C22⋊D6112yes—
682C4⋊C4C23×D6112yes—
683C4⋊C4C23×D6112yes—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—1224no—
694C22⋊C4—1222no—
695C22⋊C4—1222no—
696C22⋊C4—1224no—
697C22⋊C4—1222no—
698C22⋊C4—1224no—
699C22⋊C4—1222no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—1224no—
704C42—1222no—
705C42—1222no—
706C42C2×C22⋊D6112yes—
707C42C2×C22⋊D6112yes—
708C42C2×C22⋊D6111yescharacteristic
709C42C2×C22⋊D6111yescharacteristic
710C42C23×D6112yes—
711C42C23×D6112yes—
712C42C23×D6111yescharacteristic
713C42C23×D6111yescharacteristic
714C23—22no—
715C23—1222no—
716C23—2442no—
717C23—2442no—
718C23—2442no—
719C23C22×C22⋊D6111yescharacteristic
720Q8—24no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—81no—
725Q8—1222no—
726Q8—1224no—
727Q8—1222no—
728Q8—2442no—
729Q8—2442no—
730D4—24no—
731D4—42no—
732D4—44no—
733D4—81no—
734D4—1224no—
735D4—2442no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—44no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—2448no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4C22×C22⋊D6111yescharacteristic
757C2×C4C22×C22⋊D6112yes—
758C2×C4C22×C22⋊D6112yes—
759C2×C4C22×C22⋊D6111yescharacteristic
760C2×C4C22×C22⋊D6111yescharacteristic
761C2×C4C22×C22⋊D6111yescharacteristic
762C2×C4C22×C22⋊D6112yes—
763C2×C4C22×C22⋊D6112yes—
764C2×C4C22×C22⋊D6111yescharacteristic
765C2×C4C24×D6111yescharacteristic
766C8—1224no—
767C8—1224no—
768C22—21no—
769C22—21no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—4884no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22#1684056012yes—
778C22C23×C22⋊D6111yescharacteristic
779C4—21no—
780C4—21no—
781C4—22no—
782C4—21no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—21no—
787C4—21no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—2442no—
792C4—2442no—
793C4—2442no—
794C4#1684059912yes—
795C2—22no—
796C2—82no—
797C2—4882no—
798C2#2145947411yescharacteristic
799C2C2×#1684056011yescharacteristic
800C2#2146060511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3507C2
socleC22×C61C23×D4
prime radical#21456802C2
hypercenter#3507D61
hypocenterC61#61894
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. C2×#16840485C2semidirect
2. #21458894C2semidirect
3. #21458879C2semidirect
4. #21458661C2semidirect
5. #21458646C2semidirect
6. #21456843C2semidirect
7. #21456818C2semidirect
9. #21456780C2semidirect
10. #21455953C2semidirect
11. #21455945C2semidirect
12. #21455937C2semidirect
13. #21455895C2semidirect
14. #21454904C2semidirect
15. C61×#3507C2semidirect
30. #16840157C22semidirect
34. #16840132C22semidirect
40. #16840066C22semidirect
42. #16840054C22semidirect
43. #16840044C22semidirect
46. #16839981C22semidirect
50. #16839972C22semidirect
51. #16839969C22semidirect
52. #16839967C22semidirect
53. #16839959C22semidirect
60. #16839893C22semidirect
61. #16839893C22semidirect
63. #16839867C22semidirect
64. #16839862C22semidirect
66. C4×#11758202C22semidirect
67. C4×#11758200C22semidirect
72. C61×#559C22semidirect
73. C61×#557C22semidirect
75. C61×#556C22semidirect
76. C61×#554C22semidirect
395. #3507D61semidirect
416. #559C2×D61semidirect
417. #557C2×D61semidirect
423. #556C2×D61semidirect
424. #554C2×D61semidirect
487. C61#61894semidirect

Maximal subgroups

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

subgroupindex
C2×#168404852
#214588942
#214588792
#214586612
#214586462
#214568432
#214568182
#214568022
#214567802
#214559532
#214559452
#214559372
#214558952
#214549042
C61×#35072
#6189461