Finite Group Databasebeta

← #30548491

Subgroups — #30548491

Order 15616.

2218 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459211C211yesmaximal, characteristic, complemented
2C2×#16840234C211yesmaximal, characteristic, complemented
3#21456073C214yesmaximal, complemented
4#21456064C214yesmaximal, complemented
5#21456010C214yesmaximal, complemented
6#21456008C214yesmaximal, complemented
7#21455753C212yesmaximal, complemented
8#21455612C211yesmaximal, characteristic, complemented
9#21455285C211yesmaximal, characteristic, complemented
10#21455283C211yesmaximal, characteristic, complemented
11#21455048C212yesmaximal, complemented
12#21454626C212yesmaximal, complemented
13#21454623C212yesmaximal, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3077C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C2×#14519805C2212yes—
18C2×#14519803C2212yes—
19#16840386C2212yescomplemented
20#16840386C2212yescomplemented
21#16840375C2212yescomplemented
22#16840368C2212yescomplemented
23#16840361—21no—
24#16840361—21no—
25#16840352—21no—
26#16840352—21no—
27#16840312C2211yescharacteristic, complemented
28#16840299—22no—
29#16840299—22no—
30#16840274C2212yes—
31#16840234—22no—
32#16840234—22no—
33#16840234C2214yes—
34#16840234C2214yes—
35#16840230C2212yescomplemented
36C2×C4×D244C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×#14519739C2211yescharacteristic
39C2×C4×C22⋊D61—21no—
40C2×#14519737—21no—
41C2×#14519735C2211yescharacteristic
42C2×#14519734C2211yescharacteristic
43C22×#11758198—21no—
44C2×C22⋊C4×D61—21no—
45#16840106C2214yescomplemented
46#16840105C2214yescomplemented
47#16840089C2214yescomplemented
48#16840088C2214yescomplemented
49#16840059C2214yescomplemented
50#16840049C2212yescomplemented
51#16840039C2212yescomplemented
52#16839978C2214yescomplemented
53#16839977C2214yescomplemented
54#16839968C2212yescomplemented
55#16839967C2212yescomplemented
56#16839958C2212yescomplemented
57#16839957C2212yescomplemented
58#16839914C2214yes—
59#16839914C2214yes—
60#16839897C2214yes—
61#16839897C2214yes—
62#16839873C2214yescomplemented
63#16839871C2214yescomplemented
64#16839861C2214yescomplemented
65#16839859C2214yescomplemented
66#16839853C2214yescomplemented
67#16839849C2214yescomplemented
68#16839844C2214yescomplemented
69#16839842C2214yescomplemented
70#16839822C2214yescomplemented
71#16839822C2214yescomplemented
72#16839805C2212yescomplemented
73#16839786C2211yescharacteristic, complemented
74#16839766C2212yes—
75#16839764C2212yescomplemented
76#16839761C2212yescomplemented
77#16839725C2212yes—
78M16×Dic61C2212yescomplemented
79C61×#533C2211yescharacteristic, complemented
80C2×C4×D4×C61C2211yescharacteristic
81C61×#478C2214yescomplemented
82C61×#476C2212yescomplemented
83C61×#474C2212yescomplemented
84C61×#428C2212yescomplemented
85C61×#423C2211yescharacteristic, complemented
86C61×#418C2212yes—
87C24×D61—21no—
88C2×#11758222C2312yes—
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C2×D4×D61—24no—
92C2×D4×D61—24no—
93C2×D4×D61—22no—
94C2×D4×D61C2314yes—
95C23×Dic61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C22×C4×D61C2311yescharacteristic
99#14519805—28no—
100#14519803—28no—
101C2×#11758190C2314yes—
102C2×#11758200C2314yes—
103C2×D488C2314yes—
104C2×#11758199C2314yes—
105C2×#11758194C2312yes—
106#14519777C2311yescharacteristic, complemented
107#14519774C2311yescharacteristic, complemented
108#14519772—22no—
109#14519772—22no—
110#14519772—22no—
111#14519772—22no—
112#14519768—22no—
113#14519768—22no—
114#14519766—22no—
115#14519766—22no—
116#14519765C2312yescomplemented
117#14519762—22no—
118#14519762—22no—
119#14519762—22no—
120#14519762—22no—
121#14519761—22no—
122#14519757C2312yes—
123#14519757C2312yes—
124#14519753—22no—
125#14519753—22no—
126#14519752—22no—
127#14519752—22no—
128#14519752C2312yes—
129#14519752C2312yes—
130#14519751—21no—
131#14519751—21no—
132#14519747—22no—
133#14519742C2312yescomplemented
134#14519742C2312yescomplemented
135C4×D244—22no—
136C4×D244—22no—
137C4×D244—21no—
138C4×D244—21no—
139C4×D244—21no—
140C4×D244—21no—
141C4×D244C2312yes—
142C4×D244C2312yes—
143D4×Dic61—22no—
144D4×Dic61C2314yes—
145#14519739—22no—
146#14519739C2314yes—
147#14519739C2312yescomplemented
148#14519739C2312yescomplemented
149C4×C22⋊D61—24no—
150C4×C22⋊D61—24no—
151#14519737—22no—
152#14519737—22no—
153#14519737—24no—
154#14519737—24no—
155#14519735—22no—
156#14519735C2314yes—
157#14519734—22no—
158#14519734D412yes—
159#14519734D412yes—
160#14519734C2312yes—
161#14519734C2312yes—
162C2×C4⋊Dic61C2311yescharacteristic
163C2×#11758196D411yescharacteristic
164C2×#11758196D411yescharacteristic
165C2×C22⋊Dic61—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198—24no—
170C2×#11758198—24no—
171C2×#11758198D411yescharacteristic
172C2×#11758198D411yescharacteristic
173C22⋊C4×D61—24no—
174C22⋊C4×D61—24no—
175C2×C4×Dic61—21no—
176C2×C4×Dic61C2311yescharacteristic
177C42×D61—22no—
178#14519710C2314yescomplemented
179#14519708C2314yescomplemented
180C4⋊#92418C2312yescomplemented
181C4⋊#92418C2312yescomplemented
182#14519702C2314yescomplemented
183#14519700C2314yescomplemented
184#14519699C2314yescomplemented
185#14519697C2314yes—
186#14519697C2314yes—
187#14519697C2314yescomplemented
188#14519689C2314yes—
189#14519689C2314yes—
190#14519687C2314yescomplemented
191C8×Dic61C2314yescomplemented
192C22×D4×C61C2311yescharacteristic
193C23×C4×C61—21no—
194C2×M16×C61C2312yes—
195C4⋊Q8×C61C2311yescharacteristic, complemented
196C4⋊Q8×C61C2311yescharacteristic, complemented
197#125×C61C2312yescomplemented
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61—21no—
200C4×Q8×C61—21no—
201C4×Q8×C61—21no—
202C4×D4×C61—21no—
203C4×D4×C61—21no—
204C4×D4×C61C2312yes—
205C4×D4×C61C2312yes—
206#117×C61C2312yes—
207C2×C4⋊C4×C61C2311yescharacteristic
208C2×C22⋊C4×C61—21no—
209C2×C42×C61C2311yescharacteristic
210#107×C61C2314yescomplemented
211#106×C61C2314yescomplemented
212C4⋊C8×C61C2312yescomplemented
213C4⋊C8×C61C2312yescomplemented
214#102×C61C2314yes—
215#102×C61C2314yes—
216C24×C61—21no—
217C23×D61—21no—
218C23×D61—28no—
219C23×D61—24no—
220C23×D61—82no—
221C23×D61—82no—
222C23×D61C2×D411yescharacteristic
223C2×Q8×C61—21no—
224C2×Q8×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—22no—
227C2×D4×C61#4114yes—
228C2×D4×C61C2412yes—
229C22×C4×C61—21no—
230C22×C4×C61—22no—
231C22×C4×C61—22no—
232C22×C4×C61—82no—
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C2×C22⋊D61—28no—
237C2×C22⋊D61—22no—
238C2×C22⋊D61—24no—
239C22×Dic61—21no—
240C22×Dic61—24no—
241C22×Dic61—82no—
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244C22×Dic61C2×D411yescharacteristic
245D4×D61—216no—
246D4×D61—28no—
247D4×D61—28no—
248#11758222—24no—
249#11758222—24no—
250C2×D244—21no—
251C2×D244—22no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—21no—
255C2×D244—21no—
256C2×D244#4114yes—
257C2×D244C2412yes—
258C2×D244C2412yes—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—22no—
263C2×C4×D61—22no—
264C2×C4×D61—24no—
265C2×C4×D61—22no—
266C2×C4×D61—22no—
267C2×C4×D61—82no—
268C2×C4×D61—82no—
269C2×C4×D61C2×D412yes—
270C2×C4×D61C2412yes—
271C2×Dic122C2412yes—
272M16×C61—24no—
273C2×C8×C61C2414yes—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—22no—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C2412yes—
280C4⋊C4×C61C2412yes—
281C4⋊C4×C61C2412yes—
282C22⋊C4×C61—22no—
283C22⋊C4×C61—22no—
284C22⋊C4×C61—22no—
285C42×C61—22no—
286C42×C61C2×D411yescharacteristic
287C42×C61C2×D411yescharacteristic
288C42×C61C2411yescharacteristic
289C42×C61C2411yescharacteristic
290C22⋊Dic61—24no—
291#11758200—28no—
292#11758199—28no—
293#11758198—24no—
294#11758198—22no—
295#11758198—22no—
296#11758198—22no—
297#11758198—22no—
298#11758198—22no—
299#11758198—22no—
300#11758198—24no—
301#11758198—22no—
302#11758198—22no—
303#11758198—22no—
304#11758198—22no—
305#11758198C2×D412yes—
306#11758198C2×D412yes—
307#11758198C2×D412yes—
308#11758198C2×D412yes—
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61—22no—
313C4⋊Dic61—22no—
314C4⋊Dic61C2412yes—
315#11758196—22no—
316#11758196—22no—
317#11758196C2×D412yes—
318#11758196C2×D412yes—
319#11758196C2×D412yes—
320#11758196C2×D412yes—
321C4×Dic61—22no—
322C4×Dic61—22no—
323C4×Dic61—24no—
324C4×Dic61C2×D412yes—
325C4×Dic61C2412yes—
326#11758194—24no—
327C2×#92418C2414yes—
328D488—28no—
329#11758190—28no—
330C23×C61—24no—
331C23×C61—22no—
332C23×C61—42no—
333C23×C61—42no—
334C23×C61C22×D411yescharacteristic
335C22×D61—22no—
336C22×D61—24no—
337C22×D61—22no—
338C22×D61—216no—
339C22×D61—22no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—84no—
345C22×D61—84no—
346C22×D61—816no—
347C22×D61C22×D412yes—
348Q8×C61—81no—
349Q8×C61—81no—
350D4×C61—24no—
351D4×C61—22no—
352D4×C61C2×#4114yes—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—42no—
359C2×C4×C61—82no—
360C2×C4×C61—82no—
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C2×#4112yes—
367C2×C4×C61C2×#4112yes—
368C2×C4×C61C2511yescharacteristic
369C22⋊D61—216no—
370C22⋊D61—44no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—42no—
377C2×Dic61—84no—
378C2×Dic61C22×D412yes—
379C2×Dic61C22×D412yes—
380C2×Dic61C22×D412yes—
381D244—24no—
382D244—22no—
383D244—22no—
384D244—22no—
385D244—81no—
386D244—81no—
387D244—82no—
388D244—82no—
389D244C2×#4114yes—
390C4×D61—24no—
391C4×D61—22no—
392C4×D61—22no—
393C4×D61—44no—
394C4×D61—82no—
395C4×D61—82no—
396C4×D61—84no—
397C4×D61—82no—
398C4×D61—82no—
399Dic122—22no—
400Dic122—22no—
401C8×C61—24no—
402#92418—24no—
403#60564—611nomaximal, Sylow
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—24no—
407C22×C61—48no—
408C22×C61—42no—
409C22×C61—42no—
410C22×C61#52512yes—
411C22×C61C23×D411yescharacteristic
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—24no—
416C2×D61—48no—
417C2×D61—44no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—816no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—42no—
429C4×C61—42no—
430C4×C61—42no—
431C4×C61#52512yes—
432C4×C61C22×#4111yescharacteristic
433C4×C61C22×#4111yescharacteristic
434Dic61—22no—
435Dic61—22no—
436Dic61—22no—
437Dic61—42no—
438Dic61—42no—
439#3455—611no—
440C2×#518—611no—
441#3123—614no—
442#3122—614no—
443#3118—614no—
444#3118—614no—
445#3093—612no—
446#3077—611no—
447#3077D6111yescharacteristic, complemented
448#3036—611no—
449#3036—611no—
450#3003—612no—
451C4×AGL(1,ℤ/8)—612no—
452C4×AGL(1,ℤ/8)—612no—
453#2921—611no—
454C2×C61—22no—
455C2×C61—44no—
456C2×C61C2×#52511yescharacteristic
457C2×C61#358511yescharacteristic
458C2×C61#358511yescharacteristic
459D61—42no—
460D61—44no—
461D61—82no—
462C23×D4—611no—
463C2×AGL(1,ℤ/8)—612no—
464C2×AGL(1,ℤ/8)—612no—
465#542—612no—
466#542—612no—
467#541—612no—
468#540—612no—
469#539—1221no—
470#539—1221no—
471#538—1221no—
472#538—1221no—
473#533C2×D6111yescharacteristic, complemented
474#532—611no—
475#529—1222no—
476#529—1222no—
477#525—612no—
478#518—614no—
479#518—614no—
480#518—1222no—
481#518—1222no—
482C4×#41—612no—
483C2×C4×D4—611no—
484C2×C4×D4—611no—
485C2×C4×D4—611no—
486C2×C4×D4—1221no—
487C2×C4×D4—1221no—
488C2×C4×D4C2×D6111yescharacteristic
489C2×#117—611no—
490C2×#117—611no—
491C22×C22⋊C4—1221no—
492C22×C22⋊C4—1221no—
493#485—614no—
494#485—614no—
495#482—614no—
496#482—614no—
497#478—614no—
498#478C2×D6114yescomplemented
499#476—612no—
500#476C2×D6112yescomplemented
501#474—612no—
502#474C2×D6112yescomplemented
503#463—614no—
504#463—614no—
505#461—612no—
506#461—612no—
507#459—612no—
508#459—612no—
509#450—614no—
510#450—614no—
511#447—614no—
512#447—614no—
513#442—614no—
514#442—614no—
515#440—614no—
516#440—614no—
517C4×SD16—614no—
518C4×SD16—614no—
519C4×D8—614no—
520C4×D8—614no—
521#433—614no—
522#433—614no—
523#428—612no—
524#428C2×D6112yescomplemented
525#423—611no—
526#423C2×D6111yescharacteristic, complemented
527#418—612no—
528#418C2×D6112yes—
529#417—612no—
530#417—612no—
531#407—612no—
532C4×M16—612no—
533C61#6056411yescharacteristic, complemented, Sylow
534C25—1221no—
535C2×#41—612no—
536C22×D4—614no—
537C22×D4—611no—
538C22×D4—1222no—
539C22×D4—1221no—
540C22×D4—1224no—
541C22×D4—1224no—
542C22×D4C22×D6111yescharacteristic
543C23×C4—21no—
544C23×C4—611no—
545C23×C4—1221no—
546C23×C4—1221no—
547C23×C4—1221no—
548AGL(1,ℤ/8)—1228no—
549AGL(1,ℤ/8)—1228no—
550C2×SD16—614no—
551C2×SD16—614no—
552C2×D8—614no—
553C2×D8—614no—
554C2×M16—612no—
555C2×M16C22×D6112yes—
556C4⋊Q8—611no—
557C4⋊Q8C22×D6111yescharacteristic, complemented
558C4⋊Q8C22×D6111yescharacteristic, complemented
559#127—611no—
560#126—1222no—
561#126—1222no—
562#126—1222no—
563#126—1222no—
564#125—1222no—
565#125—1222no—
566#125C22×D6112yescomplemented
567#124—612no—
568#124—1222no—
569#124—1222no—
570#123—1222no—
571#123—1222no—
572#123—1222no—
573#123—1222no—
574#123—1222no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—612no—
578C22⋊Q8—612no—
579C22⋊Q8—1222no—
580C22⋊Q8—1222no—
581#121—612no—
582#121—612no—
583#121—1222no—
584#121—1222no—
585#121—1221no—
586#121—1221no—
587#120—1222no—
588C4×Q8—21no—
589C4×Q8—21no—
590C4×Q8—612no—
591C4×Q8—612no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—614no—
595C4×D4—614no—
596C4×D4—612no—
597C4×D4—612no—
598C4×D4—612no—
599C4×D4—612no—
600C4×D4—1222no—
601C4×D4—1222no—
602C4×D4—1222no—
603C4×D4—1222no—
604C4×D4—1224no—
605C4×D4—1224no—
606C4×D4—1222no—
607C4×D4—1222no—
608C4×D4—1224no—
609C4×D4—1224no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4C22×D6112yes—
615C4×D4C22×D6112yes—
616#117—612no—
617#117—612no—
618#117—612no—
619#117—612no—
620#117—614no—
621#117—1222no—
622#117—1222no—
623#117C22×D6112yes—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4C22×D6111yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—611no—
630C2×C22⋊C4—611no—
631C2×C22⋊C4—1224no—
632C2×C22⋊C4—1224no—
633C2×C22⋊C4—1224no—
634C2×C22⋊C4—1224no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C42—611no—
640C2×C42—1222no—
641C2×C42—1221no—
642C2×C42C22×D6111yescharacteristic
643#107—614no—
644#107C22×D6114yescomplemented
645#106—614no—
646#106C22×D6114yescomplemented
647C4⋊C8—612no—
648C4⋊C8—612no—
649C4⋊C8C22×D6112yescomplemented
650C4⋊C8C22×D6112yescomplemented
651#103—614no—
652#103—614no—
653#102—614no—
654#102—614no—
655#102—614no—
656#102—614no—
657#102C22×D6114yes—
658#102C22×D6114yes—
659C22⋊C8—614no—
660C22⋊C8—614no—
661#97—614no—
662C4×C8—614no—
663C24—21no—
664C24—611no—
665C24—1224no—
666C24—1228no—
667C24—1221no—
668C24—4882no—
669C24—4882no—
670#41—1224no—
671#41—1224no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—612no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—614no—
678C2×D4—612no—
679C2×D4—612no—
680C2×D4—1222no—
681C2×D4—1222no—
682C2×D4—1224no—
683C2×D4—1228no—
684C2×D4—12216no—
685C2×D4—1228no—
686C2×D4—1228no—
687C2×D4—1222no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—1222no—
692C2×D4#1175822614yes—
693C2×D4C23×D6112yes—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—82no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—1222no—
704C22×C4—1222no—
705C22×C4—1224no—
706C22×C4—1224no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1221no—
710C22×C4—1222no—
711C22×C4—1222no—
712C22×C4—1222no—
713C22×C4—4882no—
714C22×C4—4882no—
715C22×C4—4882no—
716C22×C4D4×D6111yescharacteristic
717C22×C4D4×D6111yescharacteristic
718C22×C4C23×D6111yescharacteristic
719SD16—1228no—
720SD16—1228no—
721D8—1228no—
722D8—1228no—
723M16—24no—
724M16—1224no—
725C2×C8—614no—
726C2×C8C23×D6114yes—
727C4⋊C4—21no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—612no—
733C4⋊C4—612no—
734C4⋊C4—612no—
735C4⋊C4—612no—
736C4⋊C4—612no—
737C4⋊C4—1222no—
738C4⋊C4—1222no—
739C4⋊C4—1222no—
740C4⋊C4—1222no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4C23×D6112yes—
745C4⋊C4C23×D6112yes—
746C4⋊C4C23×D6112yes—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—612no—
751C22⋊C4—612no—
752C22⋊C4—612no—
753C22⋊C4—612no—
754C22⋊C4—1224no—
755C22⋊C4—1222no—
756C22⋊C4—1222no—
757C22⋊C4—1222no—
758C22⋊C4—1222no—
759C22⋊C4—1224no—
760C22⋊C4—1222no—
761C22⋊C4—1222no—
762C22⋊C4—1224no—
763C22⋊C4—1222no—
764C22⋊C4—1222no—
765C22⋊C4—1222no—
766C22⋊C4—1222no—
767C42—22no—
768C42—612no—
769C42—612no—
770C42—1224no—
771C42—1222no—
772C42—1222no—
773C42D4×D6111yescharacteristic
774C42D4×D6111yescharacteristic
775C42C23×D6111yescharacteristic
776C42C23×D6111yescharacteristic
777C23—24no—
778C23—22no—
779C23—42no—
780C23—42no—
781C23—612no—
782C23—12216no—
783C23—1222no—
784C23—1224no—
785C23—1222no—
786C23—1222no—
787C23—4884no—
788C23—4884no—
789C23—48816no—
790C23—2441no—
791C23—2441no—
792C23—2442no—
793C23—2442no—
794C23C2×D4×D6111yescharacteristic
795Q8—81no—
796Q8—81no—
797Q8—1222no—
798Q8—1222no—
799D4—24no—
800D4—22no—
801D4—614no—
802D4—12216no—
803D4—1224no—
804D4—1222no—
805D4—1222no—
806D4—1222no—
807D4—4881no—
808D4—4881no—
809D4—4882no—
810D4—4882no—
811D4—2444no—
812D4C2×#1175822614yes—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—82no—
820C2×C4—82no—
821C2×C4—612no—
822C2×C4—612no—
823C2×C4—612no—
824C2×C4—1222no—
825C2×C4—1224no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—4882no—
831C2×C4—4882no—
832C2×C4—4882no—
833C2×C4—4882no—
834C2×C4—4884no—
835C2×C4—4884no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2442no—
839C2×C4—2444no—
840C2×C4C2×D4×D6111yescharacteristic
841C2×C4C2×D4×D6111yescharacteristic
842C2×C4C2×D4×D6111yescharacteristic
843C2×C4C2×D4×D6111yescharacteristic
844C2×C4C2×D4×D6111yescharacteristic
845C2×C4#41×D6112yes—
846C2×C4C2×#1175822612yes—
847C2×C4C24×D6111yescharacteristic
848C8—24no—
849C8—1224no—
850C22—21no—
851C22—21no—
852C22—24no—
853C22—48no—
854C22—42no—
855C22—42no—
856C22—1222no—
857C22—1222no—
858C22—1222no—
859C22—1224no—
860C22—48816no—
861C22—2444no—
862C22—2448no—
863C22—2442no—
864C22—2442no—
865C22—2442no—
866C22—2442no—
867C22—2442no—
868C22#1684027512yes—
869C22C22×D4×D6111yescharacteristic
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—1222no—
878C4—1222no—
879C4—1222no—
880C4—2442no—
881C4—2442no—
882C4#1684027512yes—
883C4C2×#41×D6111yescharacteristic
884C4C22×#1175822611yescharacteristic
885C2—22no—
886C2—44no—
887C2—4882no—
888C2—2442no—
889C2—2444no—
890C2C2×#1684027511yescharacteristic
891C2#2146059511yescharacteristic
892C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3077C2
socleC22×C61C23×D4
hypercenter#3077D61
hypocenterC61#60564
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #21459211C2semidirect
2. C2×#16840234C2semidirect
3. #21456073C2semidirect
4. #21456064C2semidirect
5. #21456010C2semidirect
6. #21456008C2semidirect
7. #21455753C2semidirect
8. #21455612C2semidirect
9. #21455285C2semidirect
10. #21455283C2semidirect
11. #21455048C2semidirect
12. #21454626C2semidirect
13. #21454623C2semidirect
14. #21454456C2semidirect
15. C61×#3077C2semidirect
19. #16840386C22semidirect
20. #16840386C22semidirect
21. #16840375C22semidirect
22. #16840368C22semidirect
27. #16840312C22semidirect
35. #16840230C22semidirect
45. #16840106C22semidirect
46. #16840105C22semidirect
47. #16840089C22semidirect
48. #16840088C22semidirect
49. #16840059C22semidirect
50. #16840049C22semidirect
51. #16840039C22semidirect
52. #16839978C22semidirect
53. #16839977C22semidirect
54. #16839968C22semidirect
55. #16839967C22semidirect
56. #16839958C22semidirect
57. #16839957C22semidirect
62. #16839873C22semidirect
63. #16839871C22semidirect
64. #16839861C22semidirect
65. #16839859C22semidirect
66. #16839853C22semidirect
67. #16839849C22semidirect
68. #16839844C22semidirect
69. #16839842C22semidirect
70. #16839822C22semidirect
71. #16839822C22semidirect
72. #16839805C22semidirect
73. #16839786C22semidirect
75. #16839764C22semidirect
76. #16839761C22semidirect
78. M16×Dic61C22semidirect
79. C61×#533C22semidirect
81. C61×#478C22semidirect
82. C61×#476C22semidirect
83. C61×#474C22semidirect
84. C61×#428C22semidirect
85. C61×#423C22semidirect
106. #14519777C23semidirect
107. #14519774C23semidirect
116. #14519765C23semidirect
133. #14519742C23semidirect
134. #14519742C23semidirect
147. #14519739C23semidirect
148. #14519739C23semidirect
178. #14519710C23semidirect
179. #14519708C23semidirect
180. C4⋊#92418C23semidirect
181. C4⋊#92418C23semidirect
182. #14519702C23semidirect
183. #14519700C23semidirect
184. #14519699C23semidirect
187. #14519697C23semidirect
190. #14519687C23semidirect
191. C8×Dic61C23semidirect
195. C4⋊Q8×C61C23semidirect
196. C4⋊Q8×C61C23semidirect
197. #125×C61C23semidirect
210. #107×C61C23semidirect
211. #106×C61C23semidirect
212. C4⋊C8×C61C23semidirect
213. C4⋊C8×C61C23semidirect
447. #3077D61semidirect
473. #533C2×D61semidirect
498. #478C2×D61semidirect
500. #476C2×D61semidirect
502. #474C2×D61semidirect
524. #428C2×D61semidirect
526. #423C2×D61semidirect
533. C61#60564semidirect
557. C4⋊Q8C22×D61semidirect
558. C4⋊Q8C22×D61semidirect
566. #125C22×D61semidirect
644. #107C22×D61semidirect
646. #106C22×D61semidirect
649. C4⋊C8C22×D61semidirect
650. C4⋊C8C22×D61semidirect

Maximal subgroups

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

subgroupindex
#214592112
C2×#168402342
#214560732
#214560642
#214560102
#214560082
#214557532
#214556122
#214552852
#214552832
#214550482
#214546262
#214546232
#214544562
C61×#30772
#6056461