Finite Group Databasebeta

← #30552424

Subgroups — #30552424

Order 15616.

1682 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459571C211yesmaximal, characteristic
2C2×#16840390C211yesmaximal, characteristic, complemented
3#21457119C214yesmaximal, complemented
4#21457089C214yesmaximal, complemented
5#21457042C212yesmaximal, complemented
6#21457027C212yesmaximal, complemented
7#21456989C212yesmaximal, complemented
8#21456965C212yesmaximal, complemented
9#21456350C212yesmaximal, complemented
10#21456186C212yesmaximal, complemented
11#21455768C211yesmaximal, characteristic, complemented
12#21455744C211yesmaximal, characteristic
13#21455734C211yesmaximal, characteristic
14C2×#16840093C211yesmaximal, characteristic, complemented
15#21455683C212yesmaximal, complemented
16#21455662C212yesmaximal, complemented
17C61×#2924C211yesmaximal, characteristic, complemented
18#16840480—21no—
19#16840467—21no—
20#16840451—21no—
21#16840447—21no—
22#16840445—22no—
23#16840438—22no—
24#16840390—21no—
25#16840390—21no—
26#16840390—22no—
27#16840390C2212yes—
28#16840390C2212yes—
29#16840390C2214yes—
30#16840390C2211yescharacteristic
31#16840383C2212yes—
32#16840374C2212yes—
33#16840338C2211yescharacteristic
34#16840319C2212yes—
35C2×#14519777C2212yes—
36C2×#14519776—21no—
37#16840296C2212yes—
38C2×#14519769C2212yes—
39C2×#14519768—21no—
40#16840273C2211yescharacteristic
41C2×#14519756C2211yescharacteristic
42C2×#14519754—22no—
43#16840242C2211yescharacteristic
44#16840239C2211yescharacteristic
45C2×#14519736C2211yescharacteristic
46C22×C4⋊Dic61C2211yescharacteristic
47#16840171C2214yescomplemented
48#16840171C2214yescomplemented
49#16840164C2214yescomplemented
50#16840160C2214yescomplemented
51#16840131C2214yescomplemented
52#16840122C2214yescomplemented
53#16840117C2214yescomplemented
54#16840113C2214yescomplemented
55#16840104C2212yes—
56#16840104C2214yes—
57#16840098C2212yes—
58#16840098C2211yescharacteristic
59#16840098C2212yes—
60#16840093C2211yescharacteristic
61#16840093C2212yes—
62#16840093C2212yes—
63#16840093C2212yes—
64#16840093C2212yes—
65#16840093C2214yes—
66#16840087C2212yes—
67#16840081C2211yescharacteristic
68#16840081C2212yes—
69#16840076C2212yes—
70#16840076C2211yescharacteristic
71#16840070C2214yescomplemented
72#16840070C2214yescomplemented
73#16840070C2214yescomplemented
74#16840063C2214yescomplemented
75#16840058C2214yescomplemented
76#16840053C2214yescomplemented
77#16840048C2214yescomplemented
78#16840048C2214yescomplemented
79#16839804C2212yes—
80#16839804C2212yes—
81#16839800C2212yes—
82C2×#14519709C2212yes—
83#16839772C2212yes—
84#16839764C2212yes—
85#16839759C2212yes—
86C2×#14519702C2212yes—
87C2×#117×C61C2211yescharacteristic
88C61×#433C2214yes—
89C61×#432C2212yes—
90C61×#431C2212yes—
91C61×#424C2212yes—
92C61×#407C2211yescharacteristic
93C2×C22⋊C8×C61C2211yescharacteristic
94C61×#405C2212yes—
95C2×#11758222C2311yescharacteristic
96C22×Dic122—22no—
97C22×Dic122C2311yescharacteristic
98C23×Dic61—21no—
99#14519777—22no—
100#14519777—22no—
101#14519777C2312yes—
102#14519777C2314yes—
103#14519777C2314yes—
104#14519777C2312yes—
105#14519776—21no—
106#14519776—22no—
107#14519776—22no—
108#14519776—24no—
109#14519772—22no—
110#14519771—22no—
111#14519770—22no—
112#14519770—22no—
113#14519769—22no—
114#14519769—22no—
115#14519769—22no—
116#14519769C2314yes—
117#14519769C2314yes—
118#14519769C2312yes—
119#14519768—21no—
120#14519768—22no—
121#14519768—24no—
122#14519768—22no—
123#14519767—22no—
124#14519767—22no—
125#14519765C2312yes—
126#14519763—22no—
127#14519761—22no—
128#14519760—21no—
129#14519760—22no—
130#14519759—22no—
131#14519757—21no—
132#14519757—21no—
133#14519756—21no—
134#14519756—21no—
135#14519756—22no—
136#14519756C2312yes—
137#14519756C2312yes—
138#14519756C2311yescharacteristic
139#14519756C2311yescharacteristic
140#14519755—22no—
141#14519754—24no—
142#14519754—24no—
143#14519754—24no—
144#14519754—24no—
145#14519754—22no—
146#14519751C2311yescharacteristic
147#14519751C2311yescharacteristic
148#14519746—21no—
149C4×Dic122—22no—
150C4×Dic122C2312yes—
151C4×Dic122C2312yes—
152C4×Dic122C2312yes—
153#14519742—21no—
154#14519742—21no—
155C4×D244C2312yes—
156C4×C22⋊D61—21no—
157C4×C22⋊D61—21no—
158C4×C22⋊D61—22no—
159#14519737—22no—
160#14519736—21no—
161#14519736—21no—
162#14519736—22no—
163#14519736C2312yes—
164#14519736C2312yes—
165#14519736C2311yescharacteristic
166#14519735—21no—
167#14519734—22no—
168#14519733—22no—
169C2×C4⋊Dic61—21no—
170C2×C4⋊Dic61—21no—
171C2×C4⋊Dic61—21no—
172C2×C4⋊Dic61—22no—
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2312yes—
175C2×C4⋊Dic61C2312yes—
176C2×C4⋊Dic61C2311yescharacteristic
177C2×C4⋊Dic61C2311yescharacteristic
178C2×C4⋊Dic61C2311yescharacteristic
179C2×#11758196—22no—
180C2×#11758196—22no—
181C2×#11758196—21no—
182C4⋊C4×D61—21no—
183C2×C22⋊Dic61—21no—
184C2×C22⋊Dic61—21no—
185C2×C4×Dic61—21no—
186#14519711C2312yes—
187#14519711C2312yes—
188#14519711C2314yes—
189#14519711C2314yes—
190#14519709C2312yes—
191#14519709C2314yes—
192#14519709C2314yes—
193#14519709C2314yes—
194#14519709C2314yes—
195#14519709C2312yes—
196#14519702C2314yes—
197#14519702C2314yes—
198#14519702C2312yes—
199#14519702C2312yes—
200#14519702C2314yes—
201#14519702C2314yes—
202#14519702C2314yes—
203#14519699C2312yes—
204#14519699C2312yes—
205#14519699C2314yes—
206C23×C4×C61C2311yescharacteristic
207C2×M16×C61C2312yes—
208C22×C8×C61C2312yes—
209#117×C61D411yescharacteristic
210#117×C61D411yescharacteristic
211#117×C61D412yes—
212#117×C61C2311yescharacteristic
213#117×C61C2311yescharacteristic
214#117×C61C2312yes—
215C2×C4⋊C4×C61D411yescharacteristic
216C2×C4⋊C4×C61D411yescharacteristic
217C2×C22⋊C4×C61D412yes—
218C2×C42×C61C2312yes—
219C4⋊C8×C61C2314yes—
220C4⋊C8×C61C2314yes—
221C22⋊C8×C61C2311yescharacteristic
222C22⋊C8×C61C2311yescharacteristic
223C22⋊C8×C61C2312yes—
224C22⋊C8×C61C2312yes—
225C22⋊C8×C61C2312yes—
226#97×C61C2314yes—
227C4×C8×C61C2314yes—
228C24×C61C2×D411yescharacteristic
229C22×C4×C61—24no—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2411yescharacteristic
236C22×C4×C61C2411yescharacteristic
237C22×C4×C61C2411yescharacteristic
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C22×Dic61—22no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—22no—
246C22×Dic61—22no—
247C22×Dic61—21no—
248C22×Dic61—82no—
249#11758222—24no—
250C2×D244C2411yescharacteristic
251C2×C4×D61—21no—
252C2×C4×D61—22no—
253C2×Dic122—24no—
254C2×Dic122—21no—
255C2×Dic122—24no—
256C2×Dic122—24no—
257C2×Dic122—22no—
258C2×Dic122—84no—
259C2×Dic122C2412yes—
260C2×Dic122C2411yescharacteristic
261M16×C61—24no—
262C2×C8×C61—24no—
263C2×C8×C61C2412yes—
264C2×C8×C61C2414yes—
265C2×C8×C61C2412yes—
266C4⋊C4×C61C2×D411yescharacteristic
267C4⋊C4×C61C2×D411yescharacteristic
268C4⋊C4×C61C2×D412yes—
269C4⋊C4×C61C2×D411yescharacteristic
270C4⋊C4×C61C2×D411yescharacteristic
271C4⋊C4×C61C2×D412yes—
272C22⋊C4×C61C2×D412yes—
273C22⋊C4×C61C2×D412yes—
274C22⋊C4×C61C2×D412yes—
275C22⋊C4×C61C2×D412yes—
276C42×C61C2×D412yes—
277C42×C61C2×D412yes—
278C42×C61C2412yes—
279C42×C61C2412yes—
280C22⋊Dic61—22no—
281C22⋊Dic61—22no—
282C22⋊Dic61—22no—
283C22⋊Dic61—22no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287#11758198—21no—
288#11758198—22no—
289#11758198—22no—
290#11758198—21no—
291#11758198—22no—
292C4⋊Dic61—21no—
293C4⋊Dic61—22no—
294C4⋊Dic61—22no—
295C4⋊Dic61—22no—
296C4⋊Dic61—24no—
297C4⋊Dic61—24no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—22no—
301C4⋊Dic61—22no—
302C4⋊Dic61—22no—
303C4⋊Dic61C2414yes—
304C4⋊Dic61C2412yes—
305C4⋊Dic61C2412yes—
306C4⋊Dic61C2412yes—
307C4⋊Dic61C2411yescharacteristic
308C4⋊Dic61C2411yescharacteristic
309#11758196—22no—
310#11758196—22no—
311#11758196—24no—
312#11758196—24no—
313#11758196—24no—
314#11758196—24no—
315#11758196—22no—
316#11758196—22no—
317#11758196—22no—
318#11758196—22no—
319#11758196—21no—
320#11758196—22no—
321#11758196—21no—
322C4×Dic61—22no—
323C4×Dic61—22no—
324C4×Dic61—22no—
325C4×Dic61—22no—
326C4×Dic61—22no—
327C4×Dic61—21no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—41no—
331C23×C61C22×D411yescharacteristic
332C23×C61C22×D411yescharacteristic
333C23×C61C22×D411yescharacteristic
334C22×D61—21no—
335C2×C4×C61—22no—
336C2×C4×C61—24no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—42no—
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D412yes—
344C2×C4×C61C22×D412yes—
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D412yes—
347C2×C4×C61C22×D412yes—
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C612−1+414yes—
350C2×C4×C61C2511yescharacteristic
351C22⋊D61—42no—
352C22⋊D61—42no—
353C22⋊D61—81no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—22no—
357C2×Dic61—21no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—24no—
362C2×Dic61—42no—
363C2×Dic61—42no—
364C2×Dic61—42no—
365C2×Dic61—44no—
366C2×Dic61—81no—
367C2×Dic61—82no—
368C2×Dic61—82no—
369D244—22no—
370C4×D61—42no—
371C4×D61—82no—
372Dic122—24no—
373Dic122—22no—
374Dic122—42no—
375Dic122—82no—
376Dic122—84no—
377Dic122—84no—
378C8×C61—22no—
379C8×C61—22no—
380C8×C61—24no—
381#60872—611nomaximal, Sylow
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—44no—
390C22×C61#53612yes—
391C22×C61#57712yes—
392C22×C61C23×D411yescharacteristic
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—22no—
401C4×C61—22no—
402C4×C61#53612yes—
403C4×C61C2×2−1+412yes—
404Dic61—41no—
405Dic61—42no—
406Dic61—42no—
407Dic61—42no—
408Dic61—41no—
409Dic61—42no—
410Dic61—44no—
411Dic61—41no—
412#3495—611no—
413C2×#544—611no—
414#3244—614no—
415#3242—614no—
416#3238—612no—
417#3236—612no—
418#3232—612no—
419#3229—612no—
420#3163—612no—
421#3137—612no—
422#3095—611no—
423#3092—611no—
424#3091—611no—
425C2×#483—611no—
426#3084—612no—
427#3082—612no—
428#2924D6111yescharacteristic, complemented
429C2×C61—22no—
430C2×C61—22no—
431C2×C61—41no—
432C2×C61C2×#53611yescharacteristic
433C2×C61C2×#57711yescharacteristic
434C2×C61#358611yescharacteristic
435D61—81no—
436#556—1221no—
437#554—1221no—
438#552—1221no—
439#552—1222no—
440#552—1221no—
441#551—1222no—
442#544—612no—
443#544—612no—
444#544—611no—
445#544—614no—
446#544—1222no—
447#544—1221no—
448#544—1221no—
449#542—612no—
450#541—612no—
451#536—611no—
452#533—612no—
453C2×C4⋊Q8—612no—
454C2×C4⋊Q8—1221no—
455#529—612no—
456C2×#125—612no—
457C2×#125—1221no—
458#525—611no—
459C2×C22⋊Q8—611no—
460C2×C22⋊Q8—1222no—
461#520—611no—
462#519—611no—
463C2×#117—611no—
464C2×#117C2×D6111yescharacteristic
465C22×C4⋊C4—611no—
466#501—614no—
467#501—614no—
468#499—614no—
469#498—614no—
470#491—614no—
471#489—614no—
472#488—614no—
473#487—614no—
474#485—612no—
475#485—614no—
476#484—611no—
477#484—612no—
478#484—612no—
479#483—612no—
480#483—612no—
481#483—614no—
482#483—611no—
483#483—612no—
484#483—612no—
485#482—612no—
486#481—611no—
487#481—612no—
488#480—611no—
489#480—612no—
490#479—614no—
491#479—614no—
492#479—614no—
493#478—614no—
494#477—614no—
495#476—614no—
496#475—614no—
497#475—614no—
498#433C2×D6114yes—
499#432C2×D6112yes—
500#431C2×D6112yes—
501#428—612no—
502#428—612no—
503#427—612no—
504C2×#106—612no—
505#424C2×D6112yes—
506#419—612no—
507#417—612no—
508#416—612no—
509C2×#103—612no—
510#407C2×D6111yescharacteristic
511C2×C22⋊C8C2×D6111yescharacteristic
512#405C2×D6112yes—
513C61#6087211yescharacteristic, complemented, Sylow
514C2×#41—611no—
515C22×Q8—611no—
516C22×Q8—1222no—
517C23×C4—1221no—
518C23×C4C22×D6111yescharacteristic
519C2×M16C22×D6112yes—
520C22×C8C22×D6112yes—
521C4⋊Q8—614no—
522C4⋊Q8—614no—
523C4⋊Q8—612no—
524C4⋊Q8—612no—
525C4⋊Q8—1222no—
526C4⋊Q8—1222no—
527C4⋊Q8—1224no—
528C4⋊Q8—1221no—
529C4⋊Q8—1222no—
530C4⋊Q8—1222no—
531#126—1222no—
532#126—1222no—
533#126—1222no—
534#126—1222no—
535#125—614no—
536#125—614no—
537#125—612no—
538#125—1222no—
539#125—1224no—
540#125—1222no—
541#125—1222no—
542#125—1222no—
543#125—1221no—
544#125—1222no—
545#125—1222no—
546#125—1222no—
547#124—612no—
548#124—1222no—
549#123—1221no—
550#123—1222no—
551#123—1222no—
552#123—1222no—
553C22⋊Q8—612no—
554C22⋊Q8—612no—
555C22⋊Q8—611no—
556C22⋊Q8—611no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1222no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8—1222no—
563C22⋊Q8—1224no—
564C22⋊Q8—1224no—
565C22⋊Q8—1224no—
566C22⋊Q8—1224no—
567C22⋊Q8—1222no—
568#121—611no—
569#121—611no—
570#120—1221no—
571C4×Q8—612no—
572C4×Q8—612no—
573C4×Q8—612no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1222no—
577C4×D4—612no—
578C4×D4—1221no—
579C4×D4—1221no—
580C4×D4—1222no—
581C4×D4—1222no—
582#117—612no—
583#117—612no—
584#117—611no—
585#117—1221no—
586#117—1221no—
587#117—1222no—
588#117—1221no—
589#117—1222no—
590#117—1222no—
591#117D24411yescharacteristic
592#117D24412yes—
593#117D24411yescharacteristic
594#117C22×D6111yescharacteristic
595#117C22×D6111yescharacteristic
596#117C22×D6112yes—
597C2×C4⋊C4—612no—
598C2×C4⋊C4—612no—
599C2×C4⋊C4—612no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4D24411yescharacteristic
612C2×C4⋊C4D24411yescharacteristic
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4D24412yes—
616C2×C42—1221no—
617C2×C42C22×D6112yes—
618#107—612no—
619#107—612no—
620#107—614no—
621#107—614no—
622#106—614no—
623#106—614no—
624#106—612no—
625#106—612no—
626#106—614no—
627#106—614no—
628C4⋊C8C22×D6114yes—
629C4⋊C8C22×D6114yes—
630#103—614no—
631#103—614no—
632#103—612no—
633#103—612no—
634#103—614no—
635#103—614no—
636#103—614no—
637#102—612no—
638#102—612no—
639#102—614no—
640C22⋊C8C22×D6111yescharacteristic
641C22⋊C8C22×D6111yescharacteristic
642C22⋊C8C22×D6112yes—
643C22⋊C8C22×D6112yes—
644C22⋊C8C22×D6112yes—
645#97C22×D6114yes—
646C4×C8C22×D6114yes—
647C24C2×D24411yescharacteristic
648#41—1224no—
649C2×Q8—612no—
650C2×Q8—611no—
651C2×Q8—1222no—
652C2×Q8—1224no—
653C2×Q8—1224no—
654C2×Q8—1221no—
655C2×Q8—1224no—
656C2×Q8—4884no—
657C2×D4—611no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1221no—
661C22×C4—24no—
662C22×C4—1221no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1222no—
669C22×C4—1222no—
670C22×C4—1221no—
671C22×C4—4882no—
672C22×C4C2×D24411yescharacteristic
673C22×C4C2×D24412yes—
674C22×C4C2×D24411yescharacteristic
675C22×C4C2×D24411yescharacteristic
676C22×C4C2×D24412yes—
677C22×C4C23×D6111yescharacteristic
678C22×C4C23×D6111yescharacteristic
679C22×C4C23×D6111yescharacteristic
680M16—24no—
681C2×C8—24no—
682C2×C8C23×D6112yes—
683C2×C8C23×D6114yes—
684C2×C8C23×D6112yes—
685C4⋊C4—614no—
686C4⋊C4—612no—
687C4⋊C4—612no—
688C4⋊C4—612no—
689C4⋊C4—611no—
690C4⋊C4—611no—
691C4⋊C4—1222no—
692C4⋊C4—1222no—
693C4⋊C4—1222no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1222no—
698C4⋊C4—1222no—
699C4⋊C4—1222no—
700C4⋊C4—1224no—
701C4⋊C4—1224no—
702C4⋊C4—1224no—
703C4⋊C4—1224no—
704C4⋊C4—1224no—
705C4⋊C4—1224no—
706C4⋊C4—1222no—
707C4⋊C4—1222no—
708C4⋊C4—1222no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1222no—
712C4⋊C4—1222no—
713C4⋊C4—1222no—
714C4⋊C4—1222no—
715C4⋊C4C2×D24411yescharacteristic
716C4⋊C4C2×D24411yescharacteristic
717C4⋊C4C2×D24412yes—
718C4⋊C4C2×D24411yescharacteristic
719C4⋊C4C2×D24411yescharacteristic
720C4⋊C4C2×D24412yes—
721C22⋊C4—1222no—
722C22⋊C4—1222no—
723C22⋊C4—1222no—
724C22⋊C4—1222no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1222no—
730C22⋊C4—1222no—
731C22⋊C4—1221no—
732C22⋊C4—1222no—
733C22⋊C4C2×D24412yes—
734C22⋊C4C2×D24412yes—
735C22⋊C4C2×D24412yes—
736C22⋊C4C2×D24412yes—
737C42—1222no—
738C42—1222no—
739C42—1221no—
740C42—1222no—
741C42—1222no—
742C42—1222no—
743C42C2×D24412yes—
744C42C2×D24412yes—
745C42C23×D6112yes—
746C42C23×D6112yes—
747C23—22no—
748C23—22no—
749C23—41no—
750C23—1221no—
751C23C22×D24411yescharacteristic
752C23C22×D24411yescharacteristic
753C23C22×D24411yescharacteristic
754Q8—1224no—
755Q8—1222no—
756Q8—4882no—
757Q8—4884no—
758Q8—4884no—
759Q8—2442no—
760D4—1222no—
761D4—4881no—
762D4—2442no—
763D4—2442no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—42no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1221no—
777C2×C4—1222no—
778C2×C4—1224no—
779C2×C4—4882no—
780C2×C4—4881no—
781C2×C4—4882no—
782C2×C4—4882no—
783C2×C4—2442no—
784C2×C4—2444no—
785C2×C4—2442no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4C22×D24412yes—
789C2×C4C22×D24411yescharacteristic
790C2×C4C22×D24412yes—
791C2×C4C22×D24411yescharacteristic
792C2×C4C22×D24412yes—
793C2×C4C22×D24412yes—
794C2×C4C22×D24411yescharacteristic
795C2×C4#1451982414yes—
796C2×C4C24×D6111yescharacteristic
797C8—22no—
798C8—22no—
799C8—24no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—44no—
808C22—2441no—
809C22—2441no—
810C22—2441no—
811C22#1684033812yes—
812C22#1684057412yes—
813C22C23×D24411yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—21no—
819C4—21no—
820C4—2444no—
821C4—2442no—
822C4—2441no—
823C4—2442no—
824C4—2442no—
825C4—2441no—
826C4—2441no—
827C4—2442no—
828C4#1684033812yes—
829C4C2×#1451982412yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—4881no—
834C2C2×#1684033811yescharacteristic
835C2C2×#1684057411yescharacteristic
836C2#2146060711yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2924C2
socleC22×C61C23×D4
prime radical#16840273C22
hypercenter#2924D61
hypocenterC61#60872
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. C2×#16840390C2semidirect
3. #21457119C2semidirect
4. #21457089C2semidirect
5. #21457042C2semidirect
6. #21457027C2semidirect
7. #21456989C2semidirect
8. #21456965C2semidirect
9. #21456350C2semidirect
10. #21456186C2semidirect
11. #21455768C2semidirect
14. C2×#16840093C2semidirect
15. #21455683C2semidirect
16. #21455662C2semidirect
17. C61×#2924C2semidirect
47. #16840171C22semidirect
48. #16840171C22semidirect
49. #16840164C22semidirect
50. #16840160C22semidirect
51. #16840131C22semidirect
52. #16840122C22semidirect
53. #16840117C22semidirect
54. #16840113C22semidirect
71. #16840070C22semidirect
72. #16840070C22semidirect
73. #16840070C22semidirect
74. #16840063C22semidirect
75. #16840058C22semidirect
76. #16840053C22semidirect
77. #16840048C22semidirect
78. #16840048C22semidirect
428. #2924D61semidirect
513. C61#60872semidirect

Maximal subgroups

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

subgroupindex
#214595712
C2×#168403902
#214571192
#214570892
#214570422
#214570272
#214569892
#214569652
#214563502
#214561862
#214557682
#214557442
#214557342
C2×#168400932
#214556832
#214556622
C61×#29242
#6087261