Finite Group Databasebeta

← #30571172

Subgroups — #30571172

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
1#21459684C211yesmaximal, characteristic, complemented
2#21458894C214yesmaximal, complemented
3#21458885C214yesmaximal, complemented
4#21458655C214yesmaximal, complemented
5#21458640C214yesmaximal, complemented
6#21456846C212yesmaximal, complemented
7#21456822C211yesmaximal, characteristic, complemented
8#21456806C211yesmaximal, characteristic
9#21456784C212yesmaximal, complemented
10#21455957C212yesmaximal, complemented
11#21455949C211yesmaximal, characteristic, complemented
12#21455941C211yesmaximal, characteristic, complemented
13#21455899C212yesmaximal, complemented
14#21454904C211yesmaximal, characteristic, complemented
15C2×C61×#556C211yesmaximal, characteristic, complemented
16#16840497C2212yescomplemented
17#16840490C2212yescomplemented
18#16840485C2212yescomplemented
19#16840484—22no—
20#16840472C2212yescomplemented
21#16840453—22no—
22#16840359—21no—
23#16840359—21no—
24#16840336—21no—
25#16840319C2211yescharacteristic
26#16840312C2211yescharacteristic
27#16840296C2212yes—
28#16840296C2212yes—
29#16840243—21no—
30#16840157C2212yes—
31#16840154C2214yescomplemented
32#16840152C2212yes—
33#16840144C2214yes—
34#16840130C2214yescomplemented
35#16840121C2212yes—
36#16840121C2212yes—
37#16840116C2214yes—
38#16840092C2212yes—
39#16840075C2212yes—
40#16840069C2214yescomplemented
41#16840062C2214yes—
42#16840057C2212yescomplemented
43#16840047C2212yescomplemented
44#16839984C2214yescomplemented
45#16839981C2214yes—
46#16839981C2214yes—
47#16839977C2214yes—
48#16839974C2214yes—
49#16839974C2214yes—
50#16839972C2212yescomplemented
51#16839969C2214yescomplemented
52#16839964C2214yescomplemented
53#16839962C2212yescomplemented
54#16839918C2212yes—
55#16839918C2212yes—
56#16839913C2212yes—
57#16839901C2212yes—
58#16839901C2212yes—
59#16839896C2212yes—
60#16839893C2214yescomplemented
61#16839893C2214yescomplemented
62#16839872C2214yes—
63#16839867C2214yescomplemented
64#16839862C2214yes—
65#16839860C2214yescomplemented
66C4×#11758202C2214yescomplemented
67C4×#11758201C2214yescomplemented
68#16839819C2211yescharacteristic
69#16839819C2211yescharacteristic
70#16839819C2212yes—
71#16839815C2212yes—
72C61×#556—22no—
73C61×#556—22no—
74C61×#556C2214yes—
75C61×#556C2214yes—
76C2×C4⋊Q8×C61C2211yescharacteristic
77C2×#126×C61—21no—
78C2×#126×C61—21no—
79C2×#124×C61C2211yescharacteristic
80C2×#124×C61C2211yescharacteristic
81C2×C22⋊Q8×C61—21no—
82C2×C4×Q8×C61C2211yescharacteristic
83C2×C4×Q8×C61C2211yescharacteristic
84C2×C4×Q8×C61C2211yescharacteristic
85C2×C4×D4×C61C2211yescharacteristic
86C2×#117×C61—21no—
87C2×#11758222—21no—
88C2×#11758202C2314yes—
89C2×#11758202C2314yes—
90C2×#11758200C2314yes—
91C2×#11758201C2314yes—
92C2×#11758201C2314yes—
93C2×#11758199C2314yes—
94#14519777C2311yescharacteristic
95#14519777C2311yescharacteristic
96#14519777C2311yescharacteristic
97#14519775—22no—
98#14519774C2311yescharacteristic
99#14519772—22no—
100#14519772—22no—
101#14519771—22no—
102#14519771—22no—
103#14519769—21no—
104#14519769C2312yes—
105#14519769C2312yes—
106#14519767—22no—
107#14519767—22no—
108#14519766—22no—
109#14519765—21no—
110#14519765C2312yes—
111#14519765C2312yes—
112#14519762—22no—
113#14519762—22no—
114#14519760—22no—
115#14519760—22no—
116#14519756—21no—
117#14519756C2312yes—
118#14519755—22no—
119#14519755—22no—
120#14519753—22no—
121#14519753—22no—
122#14519751—21no—
123#14519751C2312yes—
124C4×Dic122—21no—
125C4×Dic122C2312yes—
126C4×Dic122C2312yes—
127C4×Dic122C2312yes—
128#14519742—22no—
129C4×D244—21no—
130C4×D244C2312yes—
131C4×D244C2312yes—
132C4×D244C2312yes—
133#14519739—22no—
134C4×C22⋊D61—22no—
135C4×C22⋊D61—22no—
136#14519736—21no—
137#14519735—22no—
138#14519734—22no—
139#14519734—22no—
140C4⋊C4×D61—22no—
141#14519710C2314yes—
142#14519708C2314yes—
143C4⋊#92418C2312yes—
144C4⋊#92418C2314yes—
145C4⋊#92418C2312yes—
146C4⋊#92418C2314yes—
147#14519701C2314yes—
148#14519701C2314yes—
149#14519701C2314yes—
150#14519701C2314yes—
151#14519700C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154#14519697C2314yes—
155C22⋊#92418C2312yes—
156C22⋊#92418C2312yes—
157#14519688C2312yes—
158#14519688C2314yes—
159#14519688C2312yes—
160C4×#92418C2314yes—
161C22×Q8×C61D411yescharacteristic
162C22×Q8×C61C2311yescharacteristic
163C22×Q8×C61C2311yescharacteristic
164C22×D4×C61C2311yescharacteristic
165C23×C4×C61—21no—
166C4⋊Q8×C61—22no—
167C4⋊Q8×C61C2314yes—
168#126×C61—24no—
169#126×C61—24no—
170#126×C61—24no—
171#126×C61—24no—
172#124×C61—22no—
173#124×C61—21no—
174#124×C61—21no—
175#124×C61C2312yes—
176#124×C61C2314yes—
177#124×C61C2312yes—
178C22⋊Q8×C61—24no—
179C22⋊Q8×C61—24no—
180C4×Q8×C61—22no—
181C4×Q8×C61—21no—
182C4×Q8×C61—21no—
183C4×Q8×C61D412yes—
184C4×Q8×C61D412yes—
185C4×Q8×C61C2312yes—
186C4×Q8×C61C2312yes—
187C4×Q8×C61C2314yes—
188C4×Q8×C61C2312yes—
189C4×Q8×C61C2312yes—
190C4×D4×C61—22no—
191C4×D4×C61C2314yes—
192#117×C61—24no—
193#117×C61—24no—
194C2×C4⋊C4×C61—21no—
195C2×C4⋊C4×C61—21no—
196C2×C4⋊C4×C61—21no—
197C2×C4⋊C4×C61—21no—
198C2×C4⋊C4×C61D411yescharacteristic
199C2×C4⋊C4×C61D411yescharacteristic
200C2×C4⋊C4×C61D411yescharacteristic
201C2×C4⋊C4×C61C2311yescharacteristic
202C2×C22⋊C4×C61—21no—
203C2×C22⋊C4×C61—21no—
204C2×C22⋊C4×C61—21no—
205C2×C22⋊C4×C61—21no—
206C2×C22⋊C4×C61—21no—
207C2×C42×C61—21no—
208C2×C42×C61—21no—
209C2×C42×C61C2311yescharacteristic
210C2×C42×C61C2311yescharacteristic
211C2×C42×C61C2311yescharacteristic
212C24×C61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61—42no—
216C2×Q8×C61—42no—
217C2×Q8×C61—42no—
218C2×Q8×C61C2×D412yes—
219C2×Q8×C61C2×D412yes—
220C2×Q8×C61C2412yes—
221C2×Q8×C61C2412yes—
222C2×D4×C61—21no—
223C2×D4×C61—42no—
224C2×D4×C61C2412yes—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—24no—
229C22×C4×C61—44no—
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2411yescharacteristic
237C2×C22⋊D61—22no—
238#11758222—44no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244C2412yes—
242C2×C4×D61—22no—
243C2×C4×D61—22no—
244C2×C4×D61—22no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122C2412yes—
248C4⋊C4×C61—24no—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C2×D412yes—
255C4⋊C4×C61C2×D412yes—
256C4⋊C4×C61C2×D412yes—
257C4⋊C4×C61C2×D412yes—
258C4⋊C4×C61C2×D412yes—
259C4⋊C4×C61C2×D412yes—
260C4⋊C4×C61C2412yes—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—22no—
266C22⋊C4×C61—24no—
267C22⋊C4×C61—22no—
268C42×C61—24no—
269C42×C61—22no—
270C42×C61—22no—
271C42×C61C2×D412yes—
272C42×C61C2×D412yes—
273C42×C61C2×D411yescharacteristic
274C42×C61C2×D411yescharacteristic
275C42×C61C2412yes—
276C42×C61C2412yes—
277C42×C61C2411yescharacteristic
278C42×C61C2411yescharacteristic
279C22⋊Dic61—22no—
280#11758202—44no—
281#11758202—44no—
282#11758201—44no—
283#11758201—44no—
284#11758200—44no—
285#11758199—44no—
286#11758198—22no—
287#11758198—22no—
288#11758198—22no—
289#11758198—22no—
290#11758198—22no—
291#11758198—22no—
292#11758198—22no—
293#11758198—22no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61C2412yes—
299C4⋊Dic61C2412yes—
300#11758196—22no—
301#11758196—22no—
302#11758196—22no—
303#11758196—22no—
304#11758196—22no—
305#11758196—22no—
306#11758196—22no—
307#11758196—22no—
308C4×Dic61—22no—
309C4×Dic61—22no—
310C4×Dic61—22no—
311C2×#92418C2414yes—
312C2×#92418C2414yes—
313C23×C61—22no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61C22×D411yescharacteristic
318C22×D61—22no—
319Q8×C61—22no—
320Q8×C61—24no—
321Q8×C61—22no—
322Q8×C61—42no—
323Q8×C61—42no—
324Q8×C61—42no—
325Q8×C61—42no—
326D4×C61—24no—
327D4×C61—42no—
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—48no—
339C2×C4×C61—42no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D412yes—
344C2×C4×C61C22×D412yes—
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D412yes—
348C2×C4×C61C22×D412yes—
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C2511yescharacteristic
352C22⋊D61—44no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356D244—24no—
357D244—42no—
358D244—81no—
359C4×D61—44no—
360C4×D61—82no—
361C4×D61—82no—
362Dic122—24no—
363Dic122—42no—
364Dic122—81no—
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—84no—
374C22×C61#57512yes—
375C22×C61C23×D411yescharacteristic
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C4×C61—21no—
380C4×C61—22no—
381C4×C61—22no—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61#58512yes—
392Dic61—42no—
393Dic61—42no—
394Dic61—42no—
395#3507—611no—
396C2×#556D6111yescharacteristic, complemented
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#559—612no—
417#557—612no—
418#556—22no—
419#556—22no—
420#556—612no—
421#556—1222no—
422#556C2×D6114yes—
423#556C2×D6114yes—
424#554—612no—
425#552—1222no—
426#539—1221no—
427#539—1221no—
428#536—1221no—
429#533—611no—
430#532—611no—
431C2×C4⋊Q8C2×D6111yescharacteristic
432#529—612no—
433#529—612no—
434C2×#126—21no—
435C2×#126—21no—
436C2×#124C2×D6111yescharacteristic
437C2×#124C2×D6111yescharacteristic
438C2×C22⋊Q8—21no—
439#520—1221no—
440C2×C4×Q8C2×D6111yescharacteristic
441C2×C4×Q8C2×D6111yescharacteristic
442C2×C4×Q8C2×D6111yescharacteristic
443C2×C4×D4C2×D6111yescharacteristic
444C2×#117—21no—
445#497—614no—
446#497—612no—
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—614no—
466#462—612no—
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—1221no—
489C22×Q8C22⋊D6111yescharacteristic
490C22×Q8C22×D6111yescharacteristic
491C22×Q8C22×D6111yescharacteristic
492C22×D4C22×D6111yescharacteristic
493C23×C4—21no—
494C2×Q16—614no—
495C2×Q16—614no—
496C2×SD16—614no—
497C2×SD16—614no—
498C2×SD16—614no—
499C2×D8—614no—
500C4⋊Q8—22no—
501C4⋊Q8—611no—
502C4⋊Q8—611no—
503C4⋊Q8—611no—
504C4⋊Q8—1222no—
505C4⋊Q8C22×D6114yes—
506#127—611no—
507#126—24no—
508#126—24no—
509#126—24no—
510#126—24no—
511#126—1222no—
512#126—1222no—
513#126—1222no—
514#126—1222no—
515#125—612no—
516#125—612no—
517#125—1222no—
518#125—1222no—
519#125—1221no—
520#124—22no—
521#124—21no—
522#124—21no—
523#124—612no—
524#124—612no—
525#124—1222no—
526#124—1221no—
527#124C22×D6112yes—
528#124C22×D6114yes—
529#124C22×D6112yes—
530#123—1222no—
531#123—1222no—
532#123—1222no—
533#123—1222no—
534C22⋊Q8—24no—
535C22⋊Q8—24no—
536C22⋊Q8—612no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539C22⋊Q8—1221no—
540C22⋊Q8—1222no—
541C22⋊Q8—1222no—
542#121—612no—
543#121—1221no—
544C4×Q8—22no—
545C4×Q8—21no—
546C4×Q8—21no—
547C4×Q8—612no—
548C4×Q8—612no—
549C4×Q8—612no—
550C4×Q8—1222no—
551C4×Q8—1221no—
552C4×Q8C22⋊D6112yes—
553C4×Q8C22⋊D6112yes—
554C4×Q8C22×D6114yes—
555C4×Q8C22×D6112yes—
556C4×Q8C22×D6112yes—
557C4×Q8C22×D6112yes—
558C4×Q8C22×D6112yes—
559C4×D4—22no—
560C4×D4—612no—
561C4×D4—612no—
562C4×D4—612no—
563C4×D4—1222no—
564C4×D4—1222no—
565C4×D4—1222no—
566C4×D4—1221no—
567C4×D4C22×D6114yes—
568#117—24no—
569#117—24no—
570#117—1221no—
571#117—1222no—
572#117—1222no—
573#117—1222no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—1222no—
579C2×C4⋊C4C22⋊D6111yescharacteristic
580C2×C4⋊C4C22⋊D6111yescharacteristic
581C2×C4⋊C4C22⋊D6111yescharacteristic
582C2×C4⋊C4C22×D6111yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C42—21no—
589C2×C42—21no—
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—21no—
614#41—2444no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—42no—
618C2×Q8—42no—
619C2×Q8—42no—
620C2×Q8—612no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8C2×C22⋊D6112yes—
624C2×Q8C2×C22⋊D6112yes—
625C2×Q8C23×D6112yes—
626C2×Q8C23×D6112yes—
627C2×D4—21no—
628C2×D4—42no—
629C2×D4—612no—
630C2×D4—1222no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4C23×D6112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
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—24no—
658C4⋊C4—22no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—612no—
664C4⋊C4—612no—
665C4⋊C4—1221no—
666C4⋊C4—1222no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1222no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4C2×C22⋊D6112yes—
678C4⋊C4C2×C22⋊D6112yes—
679C4⋊C4C2×C22⋊D6112yes—
680C4⋊C4C2×C22⋊D6112yes—
681C4⋊C4C2×C22⋊D6112yes—
682C4⋊C4C2×C22⋊D6112yes—
683C4⋊C4C23×D6112yes—
684C22⋊C4—24no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—24no—
688C22⋊C4—22no—
689C22⋊C4—24no—
690C22⋊C4—22no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4—1222no—
696C22⋊C4—1222no—
697C22⋊C4—1222no—
698C22⋊C4—1222no—
699C22⋊C4—1222no—
700C42—24no—
701C42—22no—
702C42—22no—
703C42—1222no—
704C42—1222no—
705C42—1222no—
706C42C2×C22⋊D6112yes—
707C42C2×C22⋊D6112yes—
708C42C2×C22⋊D6111yescharacteristic
709C42C2×C22⋊D6111yescharacteristic
710C42C23×D6112yes—
711C42C23×D6111yescharacteristic
712C42C23×D6112yes—
713C42C23×D6111yescharacteristic
714C23—22no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—1222no—
719C23C22×C22⋊D6111yescharacteristic
720Q8—22no—
721Q8—24no—
722Q8—22no—
723Q8—42no—
724Q8—42no—
725Q8—42no—
726Q8—42no—
727Q8—1224no—
728Q8—4881no—
729Q8—2442no—
730D4—24no—
731D4—42no—
732D4—1224no—
733D4—4881no—
734D4—2442no—
735D4—2444no—
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—48no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—4882no—
754C2×C4—4882no—
755C2×C4—2444no—
756C2×C4C22×C22⋊D6112yes—
757C2×C4C22×C22⋊D6111yescharacteristic
758C2×C4C22×C22⋊D6111yescharacteristic
759C2×C4C22×C22⋊D6111yescharacteristic
760C2×C4C22×C22⋊D6112yes—
761C2×C4C22×C22⋊D6111yescharacteristic
762C2×C4C22×C22⋊D6112yes—
763C2×C4C22×C22⋊D6111yescharacteristic
764C2×C4C22×C22⋊D6112yes—
765C2×C4C24×D6111yescharacteristic
766C8—1224no—
767C8—1224no—
768C22—21no—
769C22—21no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—84no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22#1684056012yes—
778C22C23×C22⋊D6111yescharacteristic
779C4—21no—
780C4—22no—
781C4—21no—
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#1684059812yes—
795C2—22no—
796C2—82no—
797C2—4882no—
798C2#2145947711yescharacteristic
799C2C2×#1684056011yescharacteristic
800C2#2146060611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#556C2
socleC22×C61C23×D4
prime radical#21456806C2
hypercenterC2×#556D61
hypocenterC61#61894
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #21459684C2semidirect
2. #21458894C2semidirect
3. #21458885C2semidirect
4. #21458655C2semidirect
5. #21458640C2semidirect
6. #21456846C2semidirect
7. #21456822C2semidirect
9. #21456784C2semidirect
10. #21455957C2semidirect
11. #21455949C2semidirect
12. #21455941C2semidirect
13. #21455899C2semidirect
14. #21454904C2semidirect
15. C2×C61×#556C2semidirect
16. #16840497C22semidirect
17. #16840490C22semidirect
18. #16840485C22semidirect
20. #16840472C22semidirect
31. #16840154C22semidirect
34. #16840130C22semidirect
40. #16840069C22semidirect
42. #16840057C22semidirect
43. #16840047C22semidirect
44. #16839984C22semidirect
50. #16839972C22semidirect
51. #16839969C22semidirect
52. #16839964C22semidirect
53. #16839962C22semidirect
60. #16839893C22semidirect
61. #16839893C22semidirect
63. #16839867C22semidirect
65. #16839860C22semidirect
66. C4×#11758202C22semidirect
67. C4×#11758201C22semidirect
396. C2×#556D61semidirect
487. C61#61894semidirect

Maximal subgroups

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

subgroupindex
#214596842
#214588942
#214588852
#214586552
#214586402
#214568462
#214568222
#214568062
#214567842
#214559572
#214559492
#214559412
#214558992
#214549042
C2×C61×#5562
#6189461