Finite Group Databasebeta

← #30548529

Subgroups — #30548529

Order 15616.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840383C211yesmaximal, characteristic, complemented
2#21459020C211yesmaximal, characteristic, complemented
3#21456098C214yesmaximal, complemented
4#21456083C214yesmaximal, complemented
5#21456050C214yesmaximal, complemented
6#21456005C214yesmaximal, complemented
7#21455768C211yesmaximal, characteristic, complemented
8#21455760C211yesmaximal, characteristic, complemented
9#21455635C212yesmaximal, complemented
10#21455314C212yesmaximal, complemented
11#21455081C211yesmaximal, characteristic, complemented
12#21455073C211yesmaximal, characteristic
13C4×#14519810C212yesmaximal, complemented
14C4×#14519805C212yesmaximal, complemented
15C61×#2921C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519810C2212yes—
18C2×#14519805C2212yes—
19#16840383—22no—
20#16840383—22no—
21#16840383C2214yes—
22#16840383C2214yescomplemented
23C2×#14519777C2211yescharacteristic, complemented
24C2×#14519772—21no—
25C2×#14519765C2211yescharacteristic, complemented
26C2×#14519763—21no—
27C2×#14519759—21no—
28C2×#14519756C2211yescharacteristic
29C2×#14519755—21no—
30C2×#14519751C2211yescharacteristic
31#16840243—21no—
32#16840243—21no—
33#16840242C2212yescomplemented
34#16840242C2212yescomplemented
35#16840239C2212yescomplemented
36#16840236C2212yescomplemented
37#16840235—21no—
38#16840235—21no—
39C4×#11758222C2212yes—
40C4×#11758222C2212yes—
41#16840230—22no—
42C2×C4×Dic122C2211yescharacteristic, complemented
43C2×C4×D244C2211yescharacteristic, complemented
44C2×#14519736C2211yescharacteristic
45#117×D61—22no—
46#16840104C2214yescomplemented
47#16840098C2212yescomplemented
48#16840093C2212yescomplemented
49#16840087C2214yes—
50#16840081C2212yescomplemented
51#16840076C2212yescomplemented
52#16840058C2214yescomplemented
53#16840053C2214yescomplemented
54#16840048C2214yescomplemented
55#16840043C2214yescomplemented
56#16839985C2214yescomplemented
57#16839985C2214yescomplemented
58#16839978C2214yescomplemented
59#16839978C2214yescomplemented
60#16839926C2214yescomplemented
61#16839920C2212yescomplemented
62#16839915C2212yescomplemented
63#16839909C2214yes—
64#16839903C2212yes—
65#16839898C2212yes—
66#16839875C2214yescomplemented
67#16839870C2214yescomplemented
68#16839864C2214yescomplemented
69#16839864C2214yescomplemented
70C4×Dic244C2214yescomplemented
71C4×#11758190C2214yescomplemented
72C4×#11758190C2214yescomplemented
73C4×D488C2214yescomplemented
74#16839804C2212yescomplemented
75#16839804C2212yescomplemented
76#16839772C2212yescomplemented
77#16839768C2212yescomplemented
78#16839764C2212yes—
79#16839764C2212yes—
80C2×#117×C61C2211yescharacteristic
81C61×#433C2214yescomplemented
82C61×#433C2214yescomplemented
83C61×#423C2212yescomplemented
84C61×#407C2211yescharacteristic
85C61×#407C2211yescharacteristic
86C4×M16×C61C2212yescomplemented
87C2×#11758222—21no—
88C2×#11758222—21no—
89C2×#11758222—28no—
90C2×#11758222C2312yes—
91C2×#11758222C2312yes—
92C22×Dic122—21no—
93C22×Dic122C2311yescharacteristic
94C22×Dic122C2311yescharacteristic
95C22×D244C2311yescharacteristic
96C22×D244C2311yescharacteristic
97C22×C22⋊D61—21no—
98C22×C22⋊D61—21no—
99C22×C4×D61—21no—
100C22×C4×D61—21no—
101#14519810—28no—
102#14519805—28no—
103C2×Dic244C2314yes—
104C2×#11758190C2314yes—
105C2×#11758190C2314yes—
106C2×D488C2314yes—
107#14519777—22no—
108#14519777C2314yes—
109#14519772—24no—
110#14519772—24no—
111#14519765—22no—
112#14519765C2314yes—
113#14519763—24no—
114#14519763—24no—
115#14519759—24no—
116#14519759—24no—
117#14519756—21no—
118#14519756—21no—
119#14519756C2312yes—
120#14519756C2312yes—
121#14519755—24no—
122#14519755—24no—
123#14519751—21no—
124#14519751—21no—
125#14519751C2312yes—
126#14519751C2312yes—
127C4×Dic122—22no—
128C4×Dic122C2314yes—
129C4×Dic122C2312yes—
130C4×Dic122C2312yes—
131C4×Dic122C2312yes—
132C4×Dic122C2312yes—
133#14519742—22no—
134#14519742—22no—
135C4×D244—22no—
136C4×D244C2314yes—
137C4×D244C2312yes—
138C4×D244C2312yes—
139C4×D244C2312yes—
140C4×D244C2312yes—
141#14519739—22no—
142#14519739—22no—
143C4×C22⋊D61—22no—
144C4×C22⋊D61—22no—
145C4×C22⋊D61—22no—
146C4×C22⋊D61—22no—
147#14519737—22no—
148#14519737—22no—
149#14519737—22no—
150#14519737—22no—
151#14519736—21no—
152#14519736—21no—
153#14519736C2312yes—
154#14519736C2312yes—
155#14519735—22no—
156#14519735—22no—
157#14519734—22no—
158#14519734—22no—
159#14519733—22no—
160#14519733—22no—
161C2×C4⋊Dic61—21no—
162C2×C4⋊Dic61C2311yescharacteristic
163C2×C4⋊Dic61C2311yescharacteristic
164C2×C4⋊Dic61C2311yescharacteristic
165C2×C4⋊Dic61C2311yescharacteristic
166C2×#11758196—21no—
167C2×#11758196—21no—
168C4⋊C4×D61—22no—
169C4⋊C4×D61—22no—
170C2×C22⋊Dic61—21no—
171C2×C22⋊Dic61—21no—
172C2×#11758198—21no—
173C2×#11758198—21no—
174C2×#11758198—21no—
175C2×#11758198—21no—
176C22⋊C4×D61—22no—
177C22⋊C4×D61—22no—
178C2×C4×Dic61—21no—
179C2×C4×Dic61—21no—
180C42×D61—22no—
181C42×D61—22no—
182#14519711C2314yes—
183#14519711C2314yes—
184#14519709C2314yes—
185#14519709C2314yes—
186#14519702C2314yes—
187#14519702C2314yes—
188#14519702C2314yes—
189#14519702C2314yes—
190#14519699C2314yes—
191#14519699C2314yes—
192#14519699C2314yes—
193#14519699C2314yes—
194C23×C4×C61C2311yescharacteristic
195C2×M16×C61C2312yes—
196C2×M16×C61C2312yes—
197#117×C61D412yes—
198#117×C61D412yes—
199#117×C61C2312yes—
200#117×C61C2312yes—
201C2×C4⋊C4×C61D411yescharacteristic
202C2×C4⋊C4×C61D411yescharacteristic
203C2×C22⋊C4×C61D411yescharacteristic
204C2×C22⋊C4×C61D411yescharacteristic
205C2×C42×C61C2311yescharacteristic
206C2×C42×C61C2311yescharacteristic
207C4⋊C8×C61C2314yes—
208C4⋊C8×C61C2314yes—
209C22⋊C8×C61C2312yes—
210C22⋊C8×C61C2312yes—
211C22⋊C8×C61C2312yes—
212C22⋊C8×C61C2312yes—
213#97×C61C2314yes—
214C4×C8×C61C2314yes—
215C24×C61C2×D411yescharacteristic
216C23×D61—21no—
217C23×D61—21no—
218C22×C4×C61—24no—
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C22×C4×C61C2411yescharacteristic
229C2×C22⋊D61—28no—
230C2×C22⋊D61—22no—
231C2×C22⋊D61—22no—
232C2×C22⋊D61—22no—
233C2×C22⋊D61—22no—
234C2×C22⋊D61—82no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241#11758222—28no—
242#11758222—28no—
243#11758222—24no—
244#11758222—24no—
245#11758222—24no—
246#11758222#4118yes—
247C2×D244—21no—
248C2×D244—24no—
249C2×D244—24no—
250C2×D244—21no—
251C2×D244C2412yes—
252C2×D244C2412yes—
253C2×C4×D61—28no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—24no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—82no—
262C2×Dic122—21no—
263C2×Dic122—24no—
264C2×Dic122—24no—
265C2×Dic122—21no—
266C2×Dic122—24no—
267C2×Dic122—82no—
268C2×Dic122C2412yes—
269C2×Dic122C2412yes—
270M16×C61—24no—
271M16×C61—24no—
272C2×C8×C61C2414yes—
273C2×C8×C61C2414yes—
274C4⋊C4×C61C2×D412yes—
275C4⋊C4×C61C2×D412yes—
276C4⋊C4×C61C2×D412yes—
277C4⋊C4×C61C2×D412yes—
278C22⋊C4×C61C2×D412yes—
279C22⋊C4×C61C2×D412yes—
280C22⋊C4×C61C2×D412yes—
281C22⋊C4×C61C2×D412yes—
282C42×C61C2×D412yes—
283C42×C61C2×D412yes—
284C42×C61C2412yes—
285C42×C61C2412yes—
286C22⋊Dic61—22no—
287C22⋊Dic61—22no—
288C22⋊Dic61—22no—
289C22⋊Dic61—22no—
290#11758198—22no—
291#11758198—22no—
292#11758198—22no—
293#11758198—22no—
294#11758198—24no—
295#11758198—22no—
296#11758198—22no—
297#11758198—24no—
298#11758198—24no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61—24no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61C2412yes—
305C4⋊Dic61C2412yes—
306C4⋊Dic61C2412yes—
307C4⋊Dic61C2412yes—
308#11758196—22no—
309#11758196—22no—
310#11758196—22no—
311#11758196—22no—
312#11758196—24no—
313#11758196—22no—
314#11758196—22no—
315C4×Dic61—22no—
316C4×Dic61—22no—
317C4×Dic61—22no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320C4×Dic61—22no—
321C4×Dic61—24no—
322Dic244—28no—
323D488—28no—
324#11758190—28no—
325#11758190—28no—
326C23×C61—22no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61C22×D411yescharacteristic
330C23×C61C22×D411yescharacteristic
331C23×C61C22×D411yescharacteristic
332C22×D61—22no—
333C22×D61—24no—
334C22×D61—22no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—81no—
339C22×D61—81no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61C22×D412yes—
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C2×#4114yes—
357C2×C4×C61C2511yescharacteristic
358C22⋊D61—28no—
359C22⋊D61—28no—
360C22⋊D61—82no—
361C22⋊D61—82no—
362C2×Dic61—24no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—42no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C2×Dic61—81no—
373C2×Dic61—81no—
374D244—24no—
375D244—22no—
376D244—24no—
377D244—42no—
378D244C2×#4114yes—
379C4×D61—28no—
380C4×D61—28no—
381C4×D61—82no—
382C4×D61—82no—
383C4×D61—82no—
384C4×D61—82no—
385C4×D61—84no—
386Dic122—24no—
387Dic122—22no—
388Dic122—24no—
389Dic122—42no—
390Dic122—84no—
391Dic122C2×#4114yes—
392C8×C61—24no—
393C8×C61—24no—
394#60567—611nomaximal, Sylow
395C22×C61—21no—
396C22×C61—21no—
397C22×C61—21no—
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—82no—
404C22×C61#52512yes—
405C22×C61C23×D411yescharacteristic
406C2×D61—24no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—84no—
413C2×D61—84no—
414C4×C61—22no—
415C4×C61—22no—
416C4×C61—22no—
417C4×C61—22no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61#52512yes—
421C4×C61C22×#4112yes—
422Dic61—24no—
423Dic61—42no—
424Dic61—42no—
425Dic61—42no—
426Dic61—42no—
427Dic61—42no—
428C2×#542—611no—
429#3428—611no—
430#3125—614no—
431#3124—614no—
432#3121—614no—
433#3118—614no—
434#3095—611no—
435#3094—611no—
436#3079—612no—
437#3040—612no—
438#3007—611no—
439#3006—611no—
440C4×#137—612no—
441C4×AGL(1,ℤ/8)—612no—
442#2921D6111yescharacteristic, complemented
443C2×C61—22no—
444C2×C61—41no—
445C2×C61—41no—
446C2×C61C2×#52511yescharacteristic
447C2×C61#358511yescharacteristic
448C2×C61#358611yescharacteristic
449D61—44no—
450D61—82no—
451C22×#41—611no—
452C2×#137—612no—
453C2×AGL(1,ℤ/8)—612no—
454#542—614no—
455#542—614no—
456#542—1222no—
457#542—1222no—
458C2×C4⋊Q8—611no—
459C2×#126—1221no—
460C2×#124—611no—
461C2×#124—1221no—
462C2×#123—1221no—
463C2×C22⋊Q8—611no—
464C2×C22⋊Q8—1221no—
465C2×#121—611no—
466#520—612no—
467#520—612no—
468#520—1221no—
469#520—1221no—
470#519—612no—
471#518—612no—
472#518—1221no—
473#518—1221no—
474C4×#41—612no—
475C4×#41—612no—
476C4×#41—1222no—
477C2×C4×Q8—611no—
478C2×C4×D4—611no—
479C2×#117—611no—
480C2×#117—1222no—
481C2×#117C2×D6111yescharacteristic
482#485—614no—
483#484—612no—
484#483—612no—
485#482—614no—
486#481—612no—
487#480—612no—
488#477—614no—
489#476—614no—
490#475—614no—
491#474—614no—
492#464—614no—
493#464—614no—
494#463—614no—
495#463—614no—
496#452—614no—
497#451—612no—
498#450—612no—
499#449—614no—
500#448—612no—
501#447—612no—
502#442—614no—
503#441—614no—
504#440—614no—
505#440—614no—
506C4×Q16—614no—
507C4×SD16—614no—
508C4×SD16—614no—
509C4×D8—614no—
510#433C2×D6114yescomplemented
511#433C2×D6114yescomplemented
512#428—612no—
513#428—612no—
514#423C2×D6112yescomplemented
515#419—612no—
516#418—612no—
517#417—612no—
518#417—612no—
519#407C2×D6111yescharacteristic
520#407C2×D6111yescharacteristic
521C4×M16C2×D6112yescomplemented
522C61#6056711yescharacteristic, complemented, Sylow
523C2×#41—612no—
524C2×#41—612no—
525C2×#41—1228no—
526C2×#41—1221no—
527C2×#41—1221no—
528C22×Q8—611no—
529C22×Q8—611no—
530C22×Q8—1221no—
531C22×D4—611no—
532C22×D4—611no—
533C22×D4—1221no—
534C22×D4—1221no—
535C23×C4—1221no—
536C23×C4—1221no—
537C23×C4C22×D6111yescharacteristic
538#137—1228no—
539AGL(1,ℤ/8)—1228no—
540C2×Q16—614no—
541C2×SD16—614no—
542C2×SD16—614no—
543C2×D8—614no—
544C2×M16C22×D6112yes—
545C2×M16C22×D6112yes—
546C4⋊Q8—614no—
547C4⋊Q8—1222no—
548#126—1224no—
549#126—1224no—
550#124—614no—
551#124—1224no—
552#124—1224no—
553#124—1222no—
554#123—1224no—
555#123—1224no—
556C22⋊Q8—612no—
557C22⋊Q8—612no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1224no—
561C22⋊Q8—1224no—
562#121—612no—
563#121—612no—
564#121—1221no—
565#121—1221no—
566C4×Q8—614no—
567C4×Q8—612no—
568C4×Q8—612no—
569C4×Q8—612no—
570C4×Q8—612no—
571C4×Q8—1222no—
572C4×Q8—1222no—
573C4×Q8—1222no—
574C4×D4—614no—
575C4×D4—612no—
576C4×D4—612no—
577C4×D4—612no—
578C4×D4—612no—
579C4×D4—1222no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4—1222no—
583C4×D4—1222no—
584C4×D4—1222no—
585C4×D4—1222no—
586C4×D4—1222no—
587C4×D4—1222no—
588C4×D4—1222no—
589C4×D4—1222no—
590#117—612no—
591#117—612no—
592#117—1221no—
593#117—1221no—
594#117—1222no—
595#117—1222no—
596#117—1222no—
597#117—1222no—
598#117—1222no—
599#117—1222no—
600#117D24412yes—
601#117D24412yes—
602#117C22×D6112yes—
603#117C22×D6112yes—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4D24411yescharacteristic
614C2×C4⋊C4D24411yescharacteristic
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C22⋊C4—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1222no—
622C2×C22⋊C4—1222no—
623C2×C22⋊C4D24411yescharacteristic
624C2×C22⋊C4D24411yescharacteristic
625C2×C42—1221no—
626C2×C42—1221no—
627C2×C42—1222no—
628C2×C42—1222no—
629C2×C42C22×D6111yescharacteristic
630C2×C42C22×D6111yescharacteristic
631#107—614no—
632#107—614no—
633#106—614no—
634#106—614no—
635C4⋊C8C22×D6114yes—
636C4⋊C8C22×D6114yes—
637#103—614no—
638#103—614no—
639#103—614no—
640#103—614no—
641#102—614no—
642#102—614no—
643#102—614no—
644#102—614no—
645C22⋊C8C22×D6112yes—
646C22⋊C8C22×D6112yes—
647C22⋊C8C22×D6112yes—
648C22⋊C8C22×D6112yes—
649#97C22×D6114yes—
650C4×C8C22×D6114yes—
651C24—1221no—
652C24—1221no—
653C24C2×D24411yescharacteristic
654#41—618no—
655#41—1224no—
656#41—1224no—
657#41—1228no—
658#41—1228no—
659#41—1224no—
660C2×Q8—612no—
661C2×Q8—612no—
662C2×Q8—1224no—
663C2×Q8—1221no—
664C2×Q8—1224no—
665C2×Q8—1221no—
666C2×Q8—1224no—
667C2×Q8—4882no—
668C2×D4—612no—
669C2×D4—612no—
670C2×D4—1224no—
671C2×D4—1228no—
672C2×D4—1222no—
673C2×D4—1222no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1224no—
679C2×D4—4882no—
680C22×C4—24no—
681C22×C4—1228no—
682C22×C4—1221no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—1222no—
693C22×C4—1222no—
694C22×C4—1224no—
695C22×C4—4882no—
696C22×C4C2×D24411yescharacteristic
697C22×C4C2×D24411yescharacteristic
698C22×C4C2×D24411yescharacteristic
699C22×C4C2×D24411yescharacteristic
700C22×C4C2×D24411yescharacteristic
701C22×C4C2×D24411yescharacteristic
702C22×C4C2×D24411yescharacteristic
703C22×C4C23×D6111yescharacteristic
704C22×C4C23×D6111yescharacteristic
705C22×C4C23×D6111yescharacteristic
706Q16—1228no—
707SD16—1228no—
708SD16—1228no—
709D8—1228no—
710M16—24no—
711M16—24no—
712C2×C8C23×D6114yes—
713C2×C8C23×D6114yes—
714C4⋊C4—612no—
715C4⋊C4—612no—
716C4⋊C4—612no—
717C4⋊C4—612no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1222no—
723C4⋊C4—1222no—
724C4⋊C4—1222no—
725C4⋊C4—1222no—
726C4⋊C4—1224no—
727C4⋊C4—1222no—
728C4⋊C4—1222no—
729C4⋊C4—1224no—
730C4⋊C4C2×D24412yes—
731C4⋊C4C2×D24412yes—
732C4⋊C4C2×D24412yes—
733C4⋊C4C2×D24412yes—
734C22⋊C4—1222no—
735C22⋊C4—1222no—
736C22⋊C4—1222no—
737C22⋊C4—1222no—
738C22⋊C4—1222no—
739C22⋊C4—1222no—
740C22⋊C4—1222no—
741C22⋊C4—1222no—
742C22⋊C4—1224no—
743C22⋊C4—1222no—
744C22⋊C4—1222no—
745C22⋊C4—1224no—
746C22⋊C4—1224no—
747C22⋊C4C2×D24412yes—
748C22⋊C4C2×D24412yes—
749C22⋊C4C2×D24412yes—
750C22⋊C4C2×D24412yes—
751C42—1222no—
752C42—1222no—
753C42—1222no—
754C42—1222no—
755C42—1222no—
756C42—1222no—
757C42—1224no—
758C42C2×D24412yes—
759C42C2×D24412yes—
760C42C23×D6112yes—
761C42C23×D6112yes—
762C23—22no—
763C23—41no—
764C23—41no—
765C23—1224no—
766C23—1222no—
767C23—1222no—
768C23—4881no—
769C23—4881no—
770C23—2442no—
771C23—2442no—
772C23—2442no—
773C23C22×D24411yescharacteristic
774C23C22×D24411yescharacteristic
775C23C22×D24411yescharacteristic
776Q8—614no—
777Q8—1224no—
778Q8—1222no—
779Q8—1224no—
780Q8—4884no—
781Q8—2442no—
782D4—614no—
783D4—1224no—
784D4—1228no—
785D4—1228no—
786D4—1222no—
787D4—1224no—
788D4—4882no—
789D4—4882no—
790D4—2442no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—1228no—
801C2×C4—1224no—
802C2×C4—1222no—
803C2×C4—1228no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—4882no—
810C2×C4—4882no—
811C2×C4—4882no—
812C2×C4—4882no—
813C2×C4—4884no—
814C2×C4—4881no—
815C2×C4—4881no—
816C2×C4—2442no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4C22×D24412yes—
820C2×C4C22×D24411yescharacteristic
821C2×C4C22×D24412yes—
822C2×C4C22×D24412yes—
823C2×C4C22×D24412yes—
824C2×C4C22×D24411yescharacteristic
825C2×C4C22×D24411yescharacteristic
826C2×C4#41×D6114yes—
827C2×C4C24×D6111yescharacteristic
828C8—24no—
829C8—24no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—82no—
839C22—1224no—
840C22—4884no—
841C22—4884no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22—2442no—
846C22—2442no—
847C22#1684027412yes—
848C22C23×D24411yescharacteristic
849C4—21no—
850C4—21no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—1224no—
856C4—2442no—
857C4—2442no—
858C4—2442no—
859C4—2442no—
860C4—2442no—
861C4#1684027412yes—
862C4C2×#41×D6112yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—4882no—
867C2—2444no—
868C2C2×#1684027411yescharacteristic
869C2#2146060011yescharacteristic
870C2#2146060711yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2921C2
socleC22×C61C23×D4
prime radical#21455073C2
hypercenter#2921D61
hypocenterC61#60567
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. C2×#16840383C2semidirect
2. #21459020C2semidirect
3. #21456098C2semidirect
4. #21456083C2semidirect
5. #21456050C2semidirect
6. #21456005C2semidirect
7. #21455768C2semidirect
8. #21455760C2semidirect
9. #21455635C2semidirect
10. #21455314C2semidirect
11. #21455081C2semidirect
13. C4×#14519810C2semidirect
14. C4×#14519805C2semidirect
15. C61×#2921C2semidirect
22. #16840383C22semidirect
23. C2×#14519777C22semidirect
25. C2×#14519765C22semidirect
33. #16840242C22semidirect
34. #16840242C22semidirect
35. #16840239C22semidirect
36. #16840236C22semidirect
42. C2×C4×Dic122C22semidirect
43. C2×C4×D244C22semidirect
46. #16840104C22semidirect
47. #16840098C22semidirect
48. #16840093C22semidirect
50. #16840081C22semidirect
51. #16840076C22semidirect
52. #16840058C22semidirect
53. #16840053C22semidirect
54. #16840048C22semidirect
55. #16840043C22semidirect
56. #16839985C22semidirect
57. #16839985C22semidirect
58. #16839978C22semidirect
59. #16839978C22semidirect
60. #16839926C22semidirect
61. #16839920C22semidirect
62. #16839915C22semidirect
66. #16839875C22semidirect
67. #16839870C22semidirect
68. #16839864C22semidirect
69. #16839864C22semidirect
70. C4×Dic244C22semidirect
71. C4×#11758190C22semidirect
72. C4×#11758190C22semidirect
73. C4×D488C22semidirect
74. #16839804C22semidirect
75. #16839804C22semidirect
76. #16839772C22semidirect
77. #16839768C22semidirect
81. C61×#433C22semidirect
82. C61×#433C22semidirect
83. C61×#423C22semidirect
86. C4×M16×C61C22semidirect
442. #2921D61semidirect
510. #433C2×D61semidirect
511. #433C2×D61semidirect
514. #423C2×D61semidirect
521. C4×M16C2×D61semidirect
522. C61#60567semidirect

Maximal subgroups

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

subgroupindex
C2×#168403832
#214590202
#214560982
#214560832
#214560502
#214560052
#214557682
#214557602
#214556352
#214553142
#214550812
#214550732
C4×#145198102
C4×#145198052
C61×#29212
#6056761