Finite Group Databasebeta

← #30547711

Subgroups — #30547711

Order 15616.

2006 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459635C211yesmaximal, characteristic, complemented
2C4×#14519824C211yesmaximal, characteristic
3#21455674C212yesmaximal, complemented
4#21455665C214yesmaximal, complemented
5#21455659C212yesmaximal, complemented
6#21455654C214yesmaximal, complemented
7#21455631C212yesmaximal, complemented
8#21455626C211yesmaximal, characteristic, complemented
9#21455625C212yesmaximal, complemented
10#21455608C212yesmaximal, complemented
11#21455607C211yesmaximal, characteristic, complemented
12C2×#16840054C211yesmaximal, characteristic, complemented
13#477×D61C212yesmaximal, complemented
14#21454418C212yesmaximal, complemented
15#21454388C211yesmaximal, characteristic, complemented
16#21454350C212yesmaximal
17C61×#3079C211yesmaximal, characteristic, complemented
18C2×#14519824C2211yescharacteristic
19C2×#14519785C2212yes—
20#16840492—21no—
21#16840487—21no—
22#16840473—21no—
23#16840467—22no—
24#16840427—21no—
25Q8×C22⋊D61—22no—
26#16840393C2212yes—
27#16840389C2214yes—
28#16840319C2211yescharacteristic
29#16840317C2212yes—
30C4⋊Q8×D61C2212yes—
31#16840245C2211yescharacteristic
32#16840243C2212yes—
33#16840242—21no—
34#16840242C2211yescharacteristic
35#16840241—22no—
36#16840241C2212yes—
37#16840239—21no—
38#16840239C2211yescharacteristic
39#16840238C2212yes—
40C4×#11758222—21no—
41C4×#11758222C2211yescharacteristic
42C4×#11758224—22no—
43C4×#11758224C2212yes—
44C2×C4×Dic122—21no—
45C2×C4×Dic122C2211yescharacteristic
46C4×Q8×D61C2212yes—
47#16840072C2214yes—
48#16840070C2214yes—
49#16840069C2212yes—
50#16840068C2214yes—
51#16840067C2214yes—
52#16840064C2214yes—
53#16840062C2212yes—
54#16840058C2212yes—
55#16840057C2211yescharacteristic
56#16840056C2214yes—
57#16840055C2214yes—
58#16840054C2212yes—
59#16840054C2214yes—
60#16840054C2212yes—
61#16840052C2211yescharacteristic
62#16840048C2212yes—
63#16840047C2211yescharacteristic
64#16840046C2214yes—
65#16840042C2211yescharacteristic
66#16840040C2214yes—
67#16839804C2212yes—
68#16839803C2214yes—
69#16839801C2214yes—
70#16839798C2212yes—
71#16839797C2214yes—
72C2×#14519710C2212yes—
73#107×D61C2214yes—
74#16839790C2212yes—
75#16839787C2214yes—
76#16839784C2212yes—
77C2×C4⋊#92418C2211yescharacteristic
78C4⋊C8×D61C2212yes—
79#16839772C2212yes—
80#16839769C2214yes—
81#16839760C2214yes—
82#16839758C2212yes—
83#16839755C2214yes—
84C2×#14519700C2212yes—
85#103×D61C2214yes—
86C2×C4⋊Q8×C61C2211yescharacteristic
87C4×#41×C61C2211yescharacteristic
88C61×#477C2212yes—
89C61×#476C2212yes—
90C61×#475C2212yes—
91C61×#474C2212yes—
92C61×#428C2212yes—
93C61×#423C2211yescharacteristic
94C61×#417C2212yes—
95#14519824—24no—
96#14519824Q818yescomplemented
97C2×#11758222—21no—
98C2×#11758222C2311yescharacteristic
99C2×#11758224—22no—
100C2×#11758224C2312yes—
101C22×Dic122—21no—
102C22×Dic122C2311yescharacteristic
103C2×Q8×D61—22no—
104C2×Q8×D61C2312yes—
105#14519785—28no—
106C2×#11758189C2314yes—
107C22×#92418C2312yes—
108C2×C8×D61C2314yes—
109#14519777C2311yescharacteristic
110#14519777C2311yescharacteristic
111#14519776—22no—
112#14519776—22no—
113#14519776C2314yes—
114#14519775—24no—
115#14519775—22no—
116#14519769C2312yes—
117#14519768—22no—
118#14519768C2314yes—
119#14519767—24no—
120#14519757—22no—
121#14519756—21no—
122#14519756—21no—
123#14519756—24no—
124#14519755—24no—
125#14519753—22no—
126#14519753—24no—
127Q8×Dic61—22no—
128Q8×Dic61C2312yes—
129C4×Dic122—21no—
130C4×Dic122—21no—
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122—21no—
134C4×Dic122—21no—
135C4×Dic122—21no—
136C4×Dic122—22no—
137C4×Dic122—22no—
138C4×Dic122D411yescharacteristic
139C4×Dic122D411yescharacteristic
140C4×Dic122C2312yes—
141C4×Dic122C2312yes—
142#14519742—22no—
143#14519742—22no—
144#14519742—22no—
145#14519742—22no—
146#14519742C2312yes—
147#14519742C2312yes—
148C4×D244—21no—
149C4×D244D411yescharacteristic
150C4×D244D411yescharacteristic
151D4×Dic61—22no—
152D4×Dic61C2312yes—
153#14519739—22no—
154C4×C22⋊D61—24no—
155C4×C22⋊D61—22no—
156C4×C22⋊D61—22no—
157C4×C22⋊D61D412yes—
158C4×C22⋊D61D412yes—
159#14519737—22no—
160#14519737—22no—
161#14519737—22no—
162#14519736—21no—
163#14519736C2312yes—
164#14519736C2311yescharacteristic
165#14519735—22no—
166#14519735C2312yes—
167#14519735C2314yes—
168#14519734—22no—
169#14519734C2312yes—
170#14519733—22no—
171#14519733—22no—
172#14519733—22no—
173C2×C4⋊Dic61—21no—
174C2×C4⋊Dic61C2311yescharacteristic
175C2×#11758196—21no—
176C2×#11758196—22no—
177C4⋊C4×D61—22no—
178C4⋊C4×D61—22no—
179C4⋊C4×D61C2312yes—
180C4⋊C4×D61C2314yes—
181C2×C4×Dic61—21no—
182C2×C4×Dic61—22no—
183C42×D61—22no—
184C42×D61C2312yes—
185#14519711C2314yes—
186#14519710C2314yes—
187#14519710C2312yes—
188#14519710C2312yes—
189#14519710C2314yes—
190#14519709C2314yes—
191#14519708C2312yes—
192#14519708C2312yes—
193C4⋊#92418C2311yescharacteristic
194C4⋊#92418C2311yescharacteristic
195C4⋊#92418C2312yes—
196#14519706C2314yes—
197#14519706C2314yes—
198#14519702C2314yes—
199#14519702C2314yes—
200#14519701C2312yes—
201#14519701C2312yes—
202#14519700C2314yes—
203#14519700C2314yes—
204#14519698C2312yes—
205#14519698C2312yes—
206C2×#41×C61C2311yescharacteristic
207C22×Q8×C61—21no—
208C2×M16×C61C2312yes—
209C4⋊Q8×C61—21no—
210C4⋊Q8×C61—21no—
211C4⋊Q8×C61C2312yes—
212C4⋊Q8×C61C2312yes—
213C4×Q8×C61C2311yescharacteristic
214C4×Q8×C61C2311yescharacteristic
215C4×D4×C61—21no—
216C4×D4×C61—21no—
217C4×D4×C61C2311yescharacteristic
218C4×D4×C61C2311yescharacteristic
219#117×C61—21no—
220#117×C61C2311yescharacteristic
221C2×C4⋊C4×C61—21no—
222C2×C4⋊C4×C61C2312yes—
223C2×C42×C61—21no—
224C2×C42×C61C2311yescharacteristic
225#107×C61C2314yes—
226#106×C61C2314yes—
227C4⋊C8×C61C2312yes—
228C4⋊C8×C61C2312yes—
229#103×C61C2314yes—
230#102×C61C2314yes—
231#41×C61—22no—
232#41×C61C2×Q814yescomplemented
233C2×Q8×C61—22no—
234C2×Q8×C61—22no—
235C2×Q8×C61—82no—
236C2×Q8×C61C2411yescharacteristic
237C2×D4×C61—21no—
238C2×D4×C61C2411yescharacteristic
239C22×C4×C61—21no—
240C22×C4×C61—22no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2411yescharacteristic
246C2×C22⋊D61—22no—
247C2×C22⋊D61C2×D412yes—
248C22×Dic61—21no—
249C22×Dic61—22no—
250C22×Dic61—21no—
251C22×Dic61—22no—
252Q8×D61—24no—
253Q8×D61—84no—
254Q8×D61C2×Q818yescomplemented
255#11758224—216no—
256#11758224—24no—
257#11758224C2×Q818yescomplemented
258#11758222—28no—
259#11758222C2×Q814yes—
260#11758222#4114yes—
261C2×D244C2×D411yescharacteristic
262C2×C4×D61—22no—
263C2×C4×D61—24no—
264C2×C4×D61—22no—
265C2×C4×D61C2×D412yes—
266C2×C4×D61C2×D412yes—
267C2×C4×D61C2412yes—
268C2×Dic122—21no—
269C2×Dic122—22no—
270C2×Dic122—22no—
271C2×Dic122—28no—
272C2×Dic122—21no—
273C2×Dic122—21no—
274C2×Dic122—24no—
275C2×Dic122C2×D411yescharacteristic
276C2×Dic122C2×Q814yescomplemented
277C2×Dic122C2412yes—
278M16×C61—24no—
279C2×C8×C61C2414yes—
280C4⋊C4×C61—22no—
281C4⋊C4×C61—22no—
282C4⋊C4×C61—22no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61C2414yes—
286C4⋊C4×C61C2411yescharacteristic
287C4⋊C4×C61C2411yescharacteristic
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C42×C61—21no—
292C42×C61—21no—
293C42×C61—21no—
294C42×C61C2×D411yescharacteristic
295C42×C61C2×D411yescharacteristic
296C42×C61C2411yescharacteristic
297C42×C61C2411yescharacteristic
298C22⋊Dic61—22no—
299C22⋊Dic61—22no—
300C22⋊Dic61C2×D412yes—
301#11758198—22no—
302#11758198—24no—
303#11758198C2×D412yes—
304#11758198C2×D412yes—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61—22no—
309C4⋊Dic61—24no—
310C4⋊Dic61C2×D411yescharacteristic
311C4⋊Dic61C2×D411yescharacteristic
312C4⋊Dic61C2412yes—
313C4⋊Dic61C2412yes—
314C4⋊Dic61C2412yes—
315#11758196—22no—
316#11758196—22no—
317#11758196—22no—
318#11758196—22no—
319#11758196—22no—
320#11758196—24no—
321#11758196—22no—
322#11758196—24no—
323#11758196—22no—
324#11758196—24no—
325#11758196C2×D412yes—
326#11758196C2×D412yes—
327C4×Dic61—22no—
328C4×Dic61—22no—
329C4×Dic61—22no—
330C4×Dic61—22no—
331C4×Dic61—22no—
332C4×Dic61—22no—
333C4×Dic61—22no—
334C4×Dic61—24no—
335C4×Dic61C2×D412yes—
336C4×Dic61C2×D412yes—
337C4×Dic61C2412yes—
338C2×#92418—24no—
339C2×#92418C2412yes—
340C2×#92418C2412yes—
341#11758189—28no—
342C8×D61—28no—
343C23×C61—21no—
344C23×C61C22×D411yescharacteristic
345C22×D61C22×D412yes—
346Q8×C61—21no—
347Q8×C61—44no—
348Q8×C61—82no—
349Q8×C61C22×Q812yes—
350D4×C61—24no—
351D4×C61—21no—
352D4×C61C22×Q812yes—
353C2×C4×C61—21no—
354C2×C4×C61—24no—
355C2×C4×C61—22no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—24no—
359C2×C4×C61—41no—
360C2×C4×C61—42no—
361C2×C4×C61—81no—
362C2×C4×C61—82no—
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×Q812yes—
369C2×C4×C61C2×#4112yes—
370C2×C4×C61C2511yescharacteristic
371C22⋊D61—28no—
372C22⋊D61C22⋊Q818yes—
373C2×Dic61—24no—
374C2×Dic61—22no—
375C2×Dic61—28no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—82no—
380C2×Dic61—81no—
381C2×Dic61C22×D412yes—
382C2×Dic61C22×D412yes—
383C2×Dic61C22×D412yes—
384D244C22⋊Q814yes—
385C4×D61—28no—
386C4×D61—24no—
387C4×D61—42no—
388C4×D61—82no—
389C4×D61—84no—
390C4×D61C22×Q814yes—
391C4×D61C2×#4114yes—
392Dic122—24no—
393Dic122—22no—
394Dic122—28no—
395Dic122—42no—
396Dic122—42no—
397Dic122—84no—
398Dic122C22⋊Q814yes—
399Dic122C22×Q814yes—
400C8×C61—24no—
401#92418—22no—
402#92418—22no—
403#60498—611nomaximal, Sylow
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—22no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61C2×C22⋊Q812yes—
410C22×C61C23×D411yescharacteristic
411C2×D61—22no—
412C2×D61—22no—
413C2×D61C2×C22⋊Q814yes—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—22no—
417C4×C61—21no—
418C4×C61—44no—
419C4×C61—41no—
420C4×C61—41no—
421C4×C61C2×C22⋊Q812yes—
422C4×C61#57812yes—
423C4×C61C23×Q811yescharacteristic
424C4×C61C22×#4111yescharacteristic
425Dic61—22no—
426Dic61—24no—
427Dic61—22no—
428Dic61—42no—
429Dic61—42no—
430Dic61—42no—
431Dic61C2×C22⋊Q814yes—
432#3503—611no—
433C4×2−1+4—611no—
434#3083—614no—
435#3083—612no—
436#3082—614no—
437#3082—612no—
438#3079—612no—
439#3079D6111yescharacteristic, complemented
440#3078—612no—
441#3078—611no—
442#3076—612no—
443#3076—611no—
444C2×#477—612no—
445C2×#477—611no—
446#2913—612no—
447#2906—611no—
448#2898—612no—
449C2×C61—22no—
450C2×C61—42no—
451C2×C61C22×C22⋊Q811yescharacteristic
452C2×C61C2×#57811yescharacteristic
453C2×C61#358511yescharacteristic
454D61—24no—
455C2×2−1+4—611no—
456C2×#131—612no—
457Q82—1221no—
458#557—1221no—
459#554—1222no—
460#554—1221no—
461D4×Q8—1221no—
462D4×Q8—1222no—
463#544—614no—
464#544—612no—
465#533—612no—
466#533—611no—
467C2×C4⋊Q8—612no—
468C2×C4⋊Q8C2×D6111yescharacteristic
469#520—611no—
470#520—612no—
471#520—611no—
472#520—612no—
473#520—1221no—
474#520—1222no—
475#519—612no—
476#519—611no—
477#519—1221no—
478C4×#41—611no—
479C4×#41—612no—
480C4×#41—1221no—
481C4×#41—1222no—
482C4×#41C2×D6111yescharacteristic
483C2×C4×Q8—612no—
484C2×C4×Q8—611no—
485C2×C4×Q8—1221no—
486#479—612no—
487#479—614no—
488#479—614no—
489#479—614no—
490#479—614no—
491#478—612no—
492#478—614no—
493#477—612no—
494#477—612no—
495#477—614no—
496#477—611no—
497#477—614no—
498#477—612no—
499#477—614no—
500#477C2×D6112yes—
501#476—611no—
502#476C2×D6112yes—
503#475—611no—
504#475—614no—
505#475—612no—
506#475C2×D6112yes—
507#474—611no—
508#474—614no—
509#474C2×D6112yes—
510#428—612no—
511#428—614no—
512#428—614no—
513#428C2×D6112yes—
514#427—612no—
515#427—614no—
516C2×#107—612no—
517C2×#107—614no—
518#424—612no—
519#424—614no—
520#423—612no—
521#423C2×D6111yescharacteristic
522C2×C4⋊C8—611no—
523C2×C4⋊C8—612no—
524#419—612no—
525#419—614no—
526#417—614no—
527#417C2×D6112yes—
528#416—612no—
529#416—614no—
530C2×#103—612no—
531C2×#103—614no—
532C61#6049811yescharacteristic, complemented, Sylow
5332−1+4—618no—
5342−1+4—1224no—
535C2×#41—611no—
536C2×#41—612no—
537C2×#41—1221no—
538C2×#41—1222no—
539C2×#41C22×D6111yescharacteristic
540C22×Q8—21no—
541C22×Q8—612no—
542C22×Q8—611no—
543C22×Q8—1221no—
544C22×Q8—1222no—
545#131—1228no—
546C2×M16—614no—
547C2×M16C22×D6112yes—
548C22×C8—612no—
549C22×C8—614no—
550C4⋊Q8—21no—
551C4⋊Q8—21no—
552C4⋊Q8—614no—
553C4⋊Q8—611no—
554C4⋊Q8—611no—
555C4⋊Q8—1222no—
556C4⋊Q8—1222no—
557C4⋊Q8—1222no—
558C4⋊Q8—1224no—
559C4⋊Q8C22×D6112yes—
560C4⋊Q8C22×D6112yes—
561#125—614no—
562#125—612no—
563#125—1224no—
564#125—1222no—
565C22⋊Q8—1224no—
566C22⋊Q8—1224no—
567C22⋊Q8—1224no—
568C22⋊Q8—1222no—
569C22⋊Q8—1222no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—612no—
575C4×Q8—612no—
576C4×Q8—612no—
577C4×Q8—612no—
578C4×Q8—612no—
579C4×Q8—1222no—
580C4×Q8—1221no—
581C4×Q8—1222no—
582C4×Q8—1221no—
583C4×Q8—1221no—
584C4×Q8—1222no—
585C4×Q8—1222no—
586C4×Q8—1222no—
587C4×Q8—1222no—
588C4×Q8—1222no—
589C4×Q8—1221no—
590C4×Q8—1221no—
591C4×Q8—1221no—
592C4×Q8—1221no—
593C4×Q8C22×D6111yescharacteristic
594C4×Q8C22×D6111yescharacteristic
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—612no—
598C4×D4—612no—
599C4×D4—612no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—1221no—
603C4×D4—1222no—
604C4×D4—1222no—
605C4×D4—1222no—
606C4×D4—1222no—
607C4×D4—1222no—
608C4×D4—1222no—
609C4×D4—1222no—
610C4×D4—1224no—
611C4×D4C22×D6111yescharacteristic
612C4×D4C22×D6111yescharacteristic
613#117—21no—
614#117—611no—
615#117—612no—
616#117—612no—
617#117—612no—
618#117—614no—
619#117—1222no—
620#117—1222no—
621#117—1222no—
622#117—1222no—
623#117—1222no—
624#117—1221no—
625#117C22×D6111yescharacteristic
626C2×C4⋊C4—21no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—612no—
629C2×C4⋊C4—614no—
630C2×C4⋊C4—1222no—
631C2×C4⋊C4—1222no—
632C2×C4⋊C4—1222no—
633C2×C4⋊C4—1221no—
634C2×C4⋊C4—1221no—
635C2×C4⋊C4C22×D6112yes—
636C2×C42—21no—
637C2×C42—612no—
638C2×C42—1222no—
639C2×C42—1222no—
640C2×C42—1221no—
641C2×C42C22×D6111yescharacteristic
642#107—614no—
643#107—612no—
644#107—614no—
645#107—614no—
646#107—612no—
647#107C22×D6114yes—
648#106—614no—
649#106—612no—
650#106—612no—
651#106C22×D6114yes—
652C4⋊C8—614no—
653C4⋊C8—614no—
654C4⋊C8—611no—
655C4⋊C8—611no—
656C4⋊C8—612no—
657C4⋊C8C22×D6112yes—
658C4⋊C8C22×D6112yes—
659#103—612no—
660#103—612no—
661#103—614no—
662#103—614no—
663#103—614no—
664#103—614no—
665#103C22×D6114yes—
666#102—612no—
667#102—612no—
668#102C22×D6114yes—
669#41—22no—
670#41—614no—
671#41—614no—
672#41—618no—
673#41—1228no—
674#41—1224no—
675#41—12216no—
676#41Q8×D6114yescomplemented
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—82no—
680C2×Q8—611no—
681C2×Q8—618no—
682C2×Q8—614no—
683C2×Q8—612no—
684C2×Q8—1222no—
685C2×Q8—1224no—
686C2×Q8—1228no—
687C2×Q8—1224no—
688C2×Q8—1221no—
689C2×Q8—1221no—
690C2×Q8—1221no—
691C2×Q8—1222no—
692C2×Q8—4884no—
693C2×Q8C23×D6111yescharacteristic
694C2×D4—21no—
695C2×D4—612no—
696C2×D4—611no—
697C2×D4—1222no—
698C2×D4C23×D6111yescharacteristic
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1224no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4D4×D6111yescharacteristic
714C22×C4D4×D6111yescharacteristic
715C22×C4C23×D6111yescharacteristic
716M16—24no—
717M16—1228no—
718C2×C8—612no—
719C2×C8—612no—
720C2×C8—1228no—
721C2×C8—1224no—
722C2×C8C23×D6114yes—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—612no—
729C4⋊C4—611no—
730C4⋊C4—612no—
731C4⋊C4—611no—
732C4⋊C4—612no—
733C4⋊C4—612no—
734C4⋊C4—612no—
735C4⋊C4—1222no—
736C4⋊C4—1224no—
737C4⋊C4—1222no—
738C4⋊C4—1222no—
739C4⋊C4—1224no—
740C4⋊C4—1222no—
741C4⋊C4—1224no—
742C4⋊C4—1224no—
743C4⋊C4—1221no—
744C4⋊C4—1222no—
745C4⋊C4—1222no—
746C4⋊C4—1221no—
747C4⋊C4—1222no—
748C4⋊C4—1222no—
749C4⋊C4—1221no—
750C4⋊C4C23×D6114yes—
751C4⋊C4C23×D6111yescharacteristic
752C4⋊C4C23×D6111yescharacteristic
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—612no—
757C22⋊C4—612no—
758C22⋊C4—612no—
759C22⋊C4—1222no—
760C22⋊C4—1224no—
761C22⋊C4—1222no—
762C22⋊C4—1222no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—612no—
767C42—612no—
768C42—612no—
769C42—1222no—
770C42—1222no—
771C42—1222no—
772C42—1222no—
773C42—1224no—
774C42—1222no—
775C42—1222no—
776C42—1222no—
777C42D4×D6111yescharacteristic
778C42D4×D6111yescharacteristic
779C42C23×D6111yescharacteristic
780C42C23×D6111yescharacteristic
781C23—21no—
782C23—612no—
783C23C2×D4×D6111yescharacteristic
784Q8—21no—
785Q8—44no—
786Q8—82no—
787Q8—614no—
788Q8—614no—
789Q8—1228no—
790Q8—1224no—
791Q8—1222no—
792Q8—4884no—
793Q8—2442no—
794Q8—2442no—
795Q8C2×Q8×D6112yes—
796D4—24no—
797D4—21no—
798D4—618no—
799D4—614no—
800D4—1228no—
801D4C2×Q8×D6112yes—
802C2×C4—21no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—24no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—81no—
811C2×C4—82no—
812C2×C4—612no—
813C2×C4—614no—
814C2×C4—614no—
815C2×C4—612no—
816C2×C4—612no—
817C2×C4—1228no—
818C2×C4—1228no—
819C2×C4—1224no—
820C2×C4—1222no—
821C2×C4—1224no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—4882no—
826C2×C4—4884no—
827C2×C4—4882no—
828C2×C4—4881no—
829C2×C4—2442no—
830C2×C4C2×D4×D6111yescharacteristic
831C2×C4C2×D4×D6111yescharacteristic
832C2×C4C2×D4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4C2×Q8×D6112yes—
836C2×C4#41×D6112yes—
837C2×C4C24×D6111yescharacteristic
838C8—24no—
839C8—1222no—
840C8—1222no—
841C22—21no—
842C22—21no—
843C22—22no—
844C22—41no—
845C22—41no—
846C22—614no—
847C22—1222no—
848C22—1222no—
849C22C22⋊Q8×D6112yes—
850C22C22×D4×D6111yescharacteristic
851C4—22no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—41no—
856C4—41no—
857C4—44no—
858C4—614no—
859C4—1224no—
860C4—1222no—
861C4—1222no—
862C4—2442no—
863C4—2442no—
864C4—2442no—
865C4C22⋊Q8×D6112yes—
866C4#1684057812yes—
867C4C22×Q8×D6111yescharacteristic
868C4C2×#41×D6111yescharacteristic
869C2—22no—
870C2—42no—
871C2—1224no—
872C2C2×C22⋊Q8×D6111yescharacteristic
873C2C2×#1684057811yescharacteristic
874C2#2146059511yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3079C2
socleC22×C61C23×D4
prime radicalC2×#14519824C22
hypercenter#3079D61
hypocenterC61#60498
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #21459635C2semidirect
3. #21455674C2semidirect
4. #21455665C2semidirect
5. #21455659C2semidirect
6. #21455654C2semidirect
7. #21455631C2semidirect
8. #21455626C2semidirect
9. #21455625C2semidirect
10. #21455608C2semidirect
11. #21455607C2semidirect
12. C2×#16840054C2semidirect
13. #477×D61C2semidirect
14. #21454418C2semidirect
15. #21454388C2semidirect
17. C61×#3079C2semidirect
96. #14519824Q8semidirect
232. #41×C61C2×Q8semidirect
254. Q8×D61C2×Q8semidirect
257. #11758224C2×Q8semidirect
276. C2×Dic122C2×Q8semidirect
439. #3079D61semidirect
532. C61#60498semidirect
676. #41Q8×D61semidirect

Maximal subgroups

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

subgroupindex
#214596352
C4×#145198242
#214556742
#214556652
#214556592
#214556542
#214556312
#214556262
#214556252
#214556082
#214556072
C2×#168400542
#477×D612
#214544182
#214543882
#214543502
C61×#30792
#6049861