Finite Group Databasebeta

← #30571175

Subgroups — #30571175

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
2C2×#16840485C211yesmaximal, characteristic, complemented
3#21458900C214yesmaximal, complemented
4#21458887C214yesmaximal, complemented
5#21458663C214yesmaximal, complemented
6#21458648C214yesmaximal, complemented
7#21456848C212yesmaximal, complemented
8#21456824C211yesmaximal, characteristic, complemented
9#21456808C211yesmaximal, characteristic
10#21456786C212yesmaximal, complemented
11#21455959C212yesmaximal, complemented
12#21455950C211yesmaximal, characteristic, complemented
13#21455942C211yesmaximal, characteristic, complemented
14#21455901C212yesmaximal, complemented
15C61×#2983C211yesmaximal, characteristic, complemented
16#16840497C2212yescomplemented
17#16840490C2212yescomplemented
18#16840485—22no—
19#16840485—22no—
20#16840485C2214yes—
21#16840485C2214yes—
22#16840485C2212yescomplemented
23#16840484—22no—
24#16840472C2212yescomplemented
25#16840453—22no—
26#16840359—21no—
27#16840359—21no—
28#16840336—21no—
29#16840319C2211yescharacteristic
30#16840312C2211yescharacteristic
31C2×#14519777C2211yescharacteristic
32#16840296C2212yes—
33#16840296C2212yes—
34C2×#14519772—21no—
35C2×#14519772—21no—
36C2×#14519765C2211yescharacteristic
37C2×#14519765C2211yescharacteristic
38C2×#14519753—21no—
39#16840243—21no—
40C2×C4×Dic122C2211yescharacteristic
41C2×C4×Dic122C2211yescharacteristic
42C2×C4×D244C2211yescharacteristic
43C2×#14519735—21no—
44#16840156C2212yes—
45#16840156C2214yescomplemented
46#16840151C2212yes—
47#16840146C2214yes—
48#16840131C2214yescomplemented
49#16840122C2212yes—
50#16840122C2212yes—
51#16840117C2214yes—
52#16840093C2212yes—
53#16840076C2212yes—
54#16840070C2214yescomplemented
55#16840063C2214yes—
56#16840058C2212yescomplemented
57#16840048C2212yescomplemented
58#16839985C2214yes—
59#16839985C2214yes—
60#16839985C2214yescomplemented
61#16839978C2214yes—
62#16839978C2214yes—
63#16839978C2214yes—
64#16839973C2212yescomplemented
65#16839973C2214yescomplemented
66#16839968C2214yescomplemented
67#16839963C2212yescomplemented
68#16839920C2212yes—
69#16839920C2212yes—
70#16839915C2212yes—
71#16839903C2212yes—
72#16839903C2212yes—
73#16839898C2212yes—
74#16839875C2214yes—
75#16839870C2214yescomplemented
76#16839864C2214yes—
77#16839864C2214yescomplemented
78C4×Dic244C2214yescomplemented
79C4×#11758190C2214yescomplemented
80C2×C4×Q8×C61C2211yescharacteristic
81C61×#446C2214yescomplemented
82C61×#446C2214yescomplemented
83C61×#432C2211yescharacteristic
84C61×#432C2211yescharacteristic
85C61×#432C2212yes—
86C61×#431C2212yes—
87C2×#11758222—21no—
88C22×Dic122C2311yescharacteristic
89C22×Dic122C2311yescharacteristic
90C22×D244C2311yescharacteristic
91C22×C4×D61—21no—
92C2×Dic244C2314yes—
93C2×Dic244C2314yes—
94C2×#11758190C2314yes—
95C2×#11758190C2314yes—
96C2×#11758190C2314yes—
97C2×D488C2314yes—
98#14519777—22no—
99#14519777C2314yes—
100#14519777C2311yescharacteristic
101#14519777C2311yescharacteristic
102#14519777C2311yescharacteristic
103#14519775—22no—
104#14519774C2311yescharacteristic
105#14519772—22no—
106#14519772—22no—
107#14519772—24no—
108#14519772—24no—
109#14519772—24no—
110#14519772—24no—
111#14519771—22no—
112#14519771—22no—
113#14519769—21no—
114#14519769C2312yes—
115#14519769C2312yes—
116#14519767—22no—
117#14519767—22no—
118#14519766—22no—
119#14519765—21no—
120#14519765—22no—
121#14519765—21no—
122#14519765—21no—
123#14519765C2312yes—
124#14519765C2314yes—
125#14519765C2312yes—
126#14519765C2312yes—
127#14519765C2312yes—
128#14519762—22no—
129#14519762—22no—
130#14519760—22no—
131#14519760—22no—
132#14519756—21no—
133#14519756C2312yes—
134#14519755—22no—
135#14519755—22no—
136#14519753—22no—
137#14519753—22no—
138#14519753—24no—
139#14519753—24no—
140#14519751—21no—
141#14519751C2312yes—
142C4×Dic122—22no—
143C4×Dic122—21no—
144C4×Dic122—21no—
145C4×Dic122—21no—
146C4×Dic122C2312yes—
147C4×Dic122C2312yes—
148C4×Dic122C2314yes—
149C4×Dic122C2312yes—
150C4×Dic122C2312yes—
151C4×Dic122C2312yes—
152#14519742—22no—
153C4×D244—21no—
154C4×D244—22no—
155C4×D244C2312yes—
156C4×D244C2312yes—
157C4×D244C2312yes—
158C4×D244C2314yes—
159#14519739—22no—
160C4×C22⋊D61—22no—
161C4×C22⋊D61—22no—
162#14519736—21no—
163#14519735—22no—
164#14519735—24no—
165#14519735—24no—
166#14519734—22no—
167#14519734—22no—
168C2×C4⋊Dic61—21no—
169C2×C4⋊Dic61—21no—
170C2×C4⋊Dic61C2311yescharacteristic
171C2×#11758196—21no—
172C2×#11758196—21no—
173C4⋊C4×D61—22no—
174C2×#11758198—21no—
175C2×#11758198—21no—
176C2×#11758198—21no—
177C2×#11758198—21no—
178C2×#11758198—21no—
179C2×C4×Dic61—21no—
180C2×C4×Dic61—21no—
181#14519711C2314yes—
182#14519709C2314yes—
183#14519702C2314yes—
184#14519702C2314yes—
185#14519702C2314yes—
186#14519702C2314yes—
187#14519702C2314yes—
188#14519699C2314yes—
189#14519699C2314yes—
190#14519699C2314yes—
191C22×Q8×C61D411yescharacteristic
192C4×Q8×C61D412yes—
193C4×Q8×C61D412yes—
194C4×Q8×C61C2312yes—
195C4×Q8×C61C2312yes—
196C2×C4⋊C4×C61D411yescharacteristic
197C2×C4⋊C4×C61D411yescharacteristic
198C2×C4⋊C4×C61D411yescharacteristic
199C2×C42×C61C2311yescharacteristic
200C2×C42×C61C2311yescharacteristic
201C2×C42×C61C2311yescharacteristic
202C4⋊C8×C61C2312yes—
203C4⋊C8×C61C2314yes—
204C4⋊C8×C61C2312yes—
205C4⋊C8×C61C2314yes—
206C22⋊C8×C61C2312yes—
207C22⋊C8×C61C2312yes—
208#97×C61C2314yes—
209#97×C61C2312yes—
210#97×C61C2312yes—
211C4×C8×C61C2314yes—
212C23×D61—21no—
213C2×Q8×C61—42no—
214C2×Q8×C61C2×D412yes—
215C2×Q8×C61C2×D412yes—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2411yescharacteristic
223C2×C22⋊D61—22no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227#11758222—44no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—42no—
232C2×D244C2412yes—
233C2×D244C2412yes—
234C2×C4×D61—24no—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—44no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—42no—
244C2×Dic122—42no—
245C2×Dic122C2412yes—
246C2×Dic122C2412yes—
247C2×Dic122C2412yes—
248C2×C8×C61C2414yes—
249C2×C8×C61C2414yes—
250C4⋊C4×C61C2×D412yes—
251C4⋊C4×C61C2×D412yes—
252C4⋊C4×C61C2×D412yes—
253C4⋊C4×C61C2×D412yes—
254C4⋊C4×C61C2×D412yes—
255C4⋊C4×C61C2×D412yes—
256C42×C61C2×D412yes—
257C42×C61C2×D412yes—
258C42×C61C2×D411yescharacteristic
259C42×C61C2×D411yescharacteristic
260C42×C61C2412yes—
261C42×C61C2412yes—
262C42×C61C2411yescharacteristic
263C42×C61C2411yescharacteristic
264C22⋊Dic61—22no—
265#11758198—24no—
266#11758198—22no—
267#11758198—22no—
268#11758198—24no—
269#11758198—22no—
270#11758198—24no—
271#11758198—22no—
272#11758198—22no—
273#11758198—22no—
274#11758198—22no—
275#11758198—22no—
276#11758198—22no—
277#11758198—22no—
278#11758198—22no—
279#11758198—22no—
280C4⋊Dic61—21no—
281C4⋊Dic61—24no—
282C4⋊Dic61—24no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61C2412yes—
288C4⋊Dic61C2412yes—
289C4⋊Dic61C2412yes—
290#11758196—22no—
291#11758196—22no—
292#11758196—22no—
293#11758196—24no—
294#11758196—22no—
295#11758196—22no—
296#11758196—22no—
297#11758196—22no—
298#11758196—22no—
299#11758196—22no—
300#11758196—22no—
301C4×Dic61—24no—
302C4×Dic61—22no—
303C4×Dic61—22no—
304C4×Dic61—22no—
305C4×Dic61—22no—
306C4×Dic61—22no—
307Dic244—44no—
308Dic244—44no—
309D488—44no—
310#11758190—44no—
311#11758190—44no—
312#11758190—44no—
313C23×C61C22×D411yescharacteristic
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61—42no—
319Q8×C61—42no—
320Q8×C61—42no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61C22×D412yes—
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C22×D412yes—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C2511yescharacteristic
338C22⋊D61—44no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348D244—24no—
349D244—24no—
350D244—42no—
351D244—42no—
352D244—81no—
353C4×D61—48no—
354C4×D61—44no—
355C4×D61—82no—
356C4×D61—82no—
357Dic122—22no—
358Dic122—24no—
359Dic122—24no—
360Dic122—22no—
361Dic122—42no—
362Dic122—42no—
363Dic122—42no—
364Dic122—81no—
365C8×C61—24no—
366C8×C61—24no—
367#61894—611nomaximal, Sylow
368C22×C61—21no—
369C22×C61—21no—
370C22×C61#57512yes—
371C22×C61C23×D411yescharacteristic
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—84no—
379C4×C61—21no—
380C4×C61—22no—
381C4×C61—22no—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—22no—
386C4×C61—21no—
387C4×C61—22no—
388C4×C61#58512yes—
389Dic61—42no—
390Dic61—42no—
391Dic61—42no—
392Dic61—42no—
393Dic61—42no—
394Dic61—42no—
395#3507—611no—
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#2983D6111yescharacteristic, complemented
410C2×C61—22no—
411C2×C61#348711yescharacteristic
412C2×C61C2×#57511yescharacteristic
413C2×C61#358611yescharacteristic
414D61—82no—
415D61—82no—
416#559—612no—
417#557—612no—
418#556—614no—
419#556—614no—
420#556—612no—
421#556—1222no—
422#556—1222no—
423#556—1222no—
424#554—612no—
425#552—1222no—
426#539—1221no—
427#539—1221no—
428#536—1221no—
429#533—611no—
430#532—611no—
431C2×C4⋊Q8—611no—
432#529—612no—
433#529—612no—
434C2×#126—1221no—
435C2×#126—1221no—
436C2×#124—611no—
437C2×#124—611no—
438C2×C22⋊Q8—1221no—
439#520—1221no—
440C2×C4×Q8—611no—
441C2×C4×Q8—611no—
442C2×C4×Q8C2×D6111yescharacteristic
443C2×C4×D4—611no—
444C2×#117—1221no—
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—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#446C2×D6114yescomplemented
476#446C2×D6114yescomplemented
477#442—614no—
478#441—614no—
479#440—614no—
480#440—614no—
481C4×Q16—614no—
482C4×SD16—614no—
483#432C2×D6111yescharacteristic
484#432C2×D6111yescharacteristic
485#432C2×D6112yes—
486#431C2×D6112yes—
487C61#6189411yescharacteristic, complemented, Sylow
488C2×#41—1221no—
489C22×Q8—611no—
490C22×Q8—611no—
491C22×Q8D24411yescharacteristic
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—611no—
501C4⋊Q8—611no—
502C4⋊Q8—614no—
503C4⋊Q8—611no—
504C4⋊Q8—1222no—
505C4⋊Q8—1222no—
506#127—611no—
507#126—1224no—
508#126—1224no—
509#126—1224no—
510#126—1224no—
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—612no—
521#124—614no—
522#124—612no—
523#124—612no—
524#124—612no—
525#124—1222no—
526#124—1222no—
527#124—1221no—
528#124—1221no—
529#124—1221no—
530#123—1222no—
531#123—1222no—
532#123—1222no—
533#123—1222no—
534C22⋊Q8—612no—
535C22⋊Q8—1224no—
536C22⋊Q8—1224no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539C22⋊Q8—1221no—
540C22⋊Q8—1222no—
541C22⋊Q8—1222no—
542#121—612no—
543#121—1221no—
544C4×Q8—614no—
545C4×Q8—612no—
546C4×Q8—612no—
547C4×Q8—612no—
548C4×Q8—612no—
549C4×Q8—612no—
550C4×Q8—1222no—
551C4×Q8—1222no—
552C4×Q8—1221no—
553C4×Q8—1221no—
554C4×Q8—1221no—
555C4×Q8D24412yes—
556C4×Q8D24412yes—
557C4×Q8C22×D6112yes—
558C4×Q8C22×D6112yes—
559C4×D4—614no—
560C4×D4—612no—
561C4×D4—612no—
562C4×D4—612no—
563C4×D4—1222no—
564C4×D4—1222no—
565C4×D4—1222no—
566C4×D4—1222no—
567C4×D4—1221no—
568#117—1221no—
569#117—1224no—
570#117—1224no—
571#117—1222no—
572#117—1222no—
573#117—1222no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1222no—
580C2×C4⋊C4D24411yescharacteristic
581C2×C4⋊C4D24411yescharacteristic
582C2×C4⋊C4D24411yescharacteristic
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⋊C8C22×D6114yes—
596C4⋊C8C22×D6112yes—
597C4⋊C8C22×D6114yes—
598C4⋊C8C22×D6112yes—
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⋊C8C22×D6112yes—
608C22⋊C8C22×D6112yes—
609#97C22×D6112yes—
610#97C22×D6114yes—
611#97C22×D6112yes—
612C4×C8C22×D6114yes—
613C24—1221no—
614#41—2444no—
615C2×Q8—42no—
616C2×Q8—612no—
617C2×Q8—612no—
618C2×Q8—612no—
619C2×Q8—1221no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—2442no—
624C2×Q8—2442no—
625C2×Q8C2×D24412yes—
626C2×Q8C2×D24412yes—
627C2×D4—612no—
628C2×D4—612no—
629C2×D4—1222no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—2442no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1224no—
641C22×C4—2444no—
642C22×C4C2×D24411yescharacteristic
643C22×C4C2×D24411yescharacteristic
644C22×C4C2×D24411yescharacteristic
645C22×C4C2×D24411yescharacteristic
646C22×C4C2×D24411yescharacteristic
647C22×C4C2×D24411yescharacteristic
648C22×C4C23×D6111yescharacteristic
649Q16—2444no—
650Q16—2444no—
651SD16—2444no—
652SD16—2444no—
653SD16—2444no—
654D8—2444no—
655C2×C8C23×D6114yes—
656C2×C8C23×D6114yes—
657C4⋊C4—612no—
658C4⋊C4—612no—
659C4⋊C4—612no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4—1222no—
665C4⋊C4—1224no—
666C4⋊C4—1222no—
667C4⋊C4—1224no—
668C4⋊C4—1224no—
669C4⋊C4—1222no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1222no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4C2×D24412yes—
679C4⋊C4C2×D24412yes—
680C4⋊C4C2×D24412yes—
681C4⋊C4C2×D24412yes—
682C4⋊C4C2×D24412yes—
683C4⋊C4C2×D24412yes—
684C22⋊C4—1222no—
685C22⋊C4—1224no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4—1224no—
689C22⋊C4—1222no—
690C22⋊C4—1224no—
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—1224no—
701C42—1222no—
702C42—1222no—
703C42—1222no—
704C42—1222no—
705C42—1222no—
706C42C2×D24412yes—
707C42C2×D24412yes—
708C42C2×D24411yescharacteristic
709C42C2×D24411yescharacteristic
710C42C23×D6112yes—
711C42C23×D6112yes—
712C42C23×D6111yescharacteristic
713C42C23×D6111yescharacteristic
714C23—1222no—
715C23—1222no—
716C23—2442no—
717C23—2442no—
718C23—2442no—
719C23C22×D24411yescharacteristic
720Q8—42no—
721Q8—42no—
722Q8—1222no—
723Q8—1224no—
724Q8—1224no—
725Q8—1222no—
726Q8—4881no—
727Q8—2442no—
728Q8—2442no—
729Q8—2442no—
730D4—1224no—
731D4—1224no—
732D4—4881no—
733D4—2442no—
734D4—2442no—
735D4—2444no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—4882no—
750C2×C4—4882no—
751C2×C4—2448no—
752C2×C4—2444no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4C22×D24412yes—
757C2×C4C22×D24411yescharacteristic
758C2×C4C22×D24411yescharacteristic
759C2×C4C22×D24411yescharacteristic
760C2×C4C22×D24412yes—
761C2×C4C22×D24411yescharacteristic
762C2×C4C22×D24412yes—
763C2×C4C22×D24412yes—
764C2×C4C22×D24411yescharacteristic
765C2×C4C24×D6111yescharacteristic
766C8—24no—
767C8—24no—
768C22—21no—
769C22—21no—
770C22—4884no—
771C22—2442no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22#1684056212yes—
778C22C23×D24411yescharacteristic
779C4—21no—
780C4—22no—
781C4—21no—
782C4—21no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—21no—
787C4—21no—
788C4—2442no—
789C4—2442no—
790C4—2442no—
791C4—2442no—
792C4—2442no—
793C4—2442no—
794C4#1684059912yes—
795C2—22no—
796C2—4882no—
797C2—4882no—
798C2#2145947811yescharacteristic
799C2C2×#1684056211yescharacteristic
800C2#2146060711yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2983C2
socleC22×C61C23×D4
prime radical#21456808C2
hypercenter#2983D61
hypocenterC61#61894
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2983

Complements

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

NH ≅ G/Ntype
1. #21459684C2semidirect
2. C2×#16840485C2semidirect
3. #21458900C2semidirect
4. #21458887C2semidirect
5. #21458663C2semidirect
6. #21458648C2semidirect
7. #21456848C2semidirect
8. #21456824C2semidirect
10. #21456786C2semidirect
11. #21455959C2semidirect
12. #21455950C2semidirect
13. #21455942C2semidirect
14. #21455901C2semidirect
15. C61×#2983C2semidirect
16. #16840497C22semidirect
17. #16840490C22semidirect
22. #16840485C22semidirect
24. #16840472C22semidirect
45. #16840156C22semidirect
48. #16840131C22semidirect
54. #16840070C22semidirect
56. #16840058C22semidirect
57. #16840048C22semidirect
60. #16839985C22semidirect
64. #16839973C22semidirect
65. #16839973C22semidirect
66. #16839968C22semidirect
67. #16839963C22semidirect
75. #16839870C22semidirect
77. #16839864C22semidirect
78. C4×Dic244C22semidirect
79. C4×#11758190C22semidirect
81. C61×#446C22semidirect
82. C61×#446C22semidirect
409. #2983D61semidirect
475. #446C2×D61semidirect
476. #446C2×D61semidirect
487. C61#61894semidirect

Maximal subgroups

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

subgroupindex
#214596842
C2×#168404852
#214589002
#214588872
#214586632
#214586482
#214568482
#214568242
#214568082
#214567862
#214559592
#214559502
#214559422
#214559012
C61×#29832
#6189461