Finite Group Databasebeta

← #30548501

Subgroups — #30548501

Order 15616.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459208C211yesmaximal, characteristic, complemented
2C2×#16840244C211yesmaximal, characteristic, complemented
3#21456095C214yesmaximal, complemented
4#21456080C214yesmaximal, complemented
5#21456032C214yesmaximal, complemented
6#21456017C214yesmaximal, complemented
7#21455740C212yesmaximal, complemented
8#21455624C211yesmaximal, characteristic, complemented
9#21455618C211yesmaximal, characteristic, complemented
10#21455279C211yesmaximal, characteristic, complemented
11#21455060C212yesmaximal, complemented
12#137×Dic61C212yesmaximal, complemented
13#21454632C212yesmaximal, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3037C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C2×#14519802C2212yes—
18#16840381C2212yescomplemented
19#16840381C2212yescomplemented
20#16840373C2212yescomplemented
21#16840366C2212yescomplemented
22#16840357—21no—
23#16840357—21no—
24#16840349—21no—
25#16840349—21no—
26#16840319C2211yescharacteristic
27#16840292—22no—
28#16840292—22no—
29#16840269C2212yes—
30#16840244—22no—
31#16840244—22no—
32#16840244C2214yes—
33#16840244C2214yes—
34#41×Dic61C2212yes—
35C2×Q8×Dic61C2211yescharacteristic
36C2×C4×D244—21no—
37C2×C4×D244C2211yescharacteristic
38C2×#14519739—21no—
39C2×#14519739C2211yescharacteristic
40C2×#14519734—21no—
41C2×#14519734C2211yescharacteristic
42C2×C4⋊C4×D61—21no—
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840096C2214yescomplemented
45#16840091C2214yescomplemented
46#16840079C2214yescomplemented
47#16840074C2214yescomplemented
48#16840069C2214yescomplemented
49#16840063C2214yescomplemented
50#16840057C2212yescomplemented
51#16840053C2212yescomplemented
52#16840047C2212yescomplemented
53#16840043C2212yescomplemented
54#16839974C2214yescomplemented
55#16839964C2212yescomplemented
56#16839954C2212yescomplemented
57#16839923C2214yes—
58#16839923C2214yes—
59#16839906C2214yes—
60#16839906C2214yes—
61#16839871C2214yescomplemented
62#16839869C2214yescomplemented
63#16839865C2214yescomplemented
64#16839863C2214yescomplemented
65Q16×Dic61C2214yescomplemented
66SD16×Dic61C2214yescomplemented
67#16839847C2214yescomplemented
68#16839842C2214yescomplemented
69#16839822C2214yescomplemented
70#16839822C2214yescomplemented
71#16839804C2212yes—
72#16839802C2212yes—
73#16839786C2211yescharacteristic
74#16839771C2212yes—
75#16839768C2212yes—
76#16839763C2212yes—
77#16839725C2212yes—
78M16×Dic61C2212yes—
79C2×#137×C61C2212yes—
80C61×#532C2211yescharacteristic
81C2×C4×Q8×C61C2211yescharacteristic
82C61×#464C2214yescomplemented
83C61×#462C2212yescomplemented
84C61×#460C2212yescomplemented
85C61×#423C2211yescharacteristic
86C61×#417C2212yes—
87C2×#11758226—24no—
88C2×#11758226—24no—
89C2×#11758226—22no—
90C2×#11758226C2314yes—
91C22×D244—21no—
92C22×D244C2311yescharacteristic
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98#14519802—28no—
99C2×#11758201C2314yes—
100C2×#11758199C2314yes—
101C2×#11758194C2312yes—
102#14519777C2311yescharacteristic
103#14519777C2311yescharacteristic
104#14519772—22no—
105#14519772—22no—
106#14519770—22no—
107#14519770—22no—
108#14519769C2312yes—
109#14519767—22no—
110#14519767—22no—
111#14519763—22no—
112#14519763—22no—
113#14519761—22no—
114#14519761—22no—
115#14519758—22no—
116#14519758—22no—
117#14519758—22no—
118#14519756—21no—
119#14519756—21no—
120#14519754—22no—
121#14519754—22no—
122#14519753C2312yes—
123#14519753C2312yes—
124#14519749—22no—
125#14519749—22no—
126#14519748C2312yes—
127#14519748C2312yes—
128#14519745—22no—
129Q8×Dic61—22no—
130Q8×Dic61C2314yes—
131Q8×Dic61C2312yes—
132Q8×Dic61C2312yes—
133C4×Dic122—21no—
134C4×Dic122—21no—
135C4×D244—21no—
136C4×D244—21no—
137C4×D244—24no—
138C4×D244—24no—
139C4×D244C2312yes—
140C4×D244C2312yes—
141D4×Dic61—22no—
142D4×Dic61—22no—
143D4×Dic61C2312yes—
144D4×Dic61C2312yes—
145#14519739—24no—
146#14519739—24no—
147#14519739—22no—
148#14519739C2314yes—
149C4×C22⋊D61—22no—
150C4×C22⋊D61—22no—
151#14519736—22no—
152#14519736C2312yes—
153#14519734—24no—
154#14519734—24no—
155#14519734D412yes—
156#14519734D412yes—
157#14519734C2312yes—
158#14519734C2312yes—
159C2×C4⋊Dic61—21no—
160C2×C4⋊Dic61C2311yescharacteristic
161C2×#11758196—21no—
162C2×#11758196D411yescharacteristic
163C2×#11758196D411yescharacteristic
164C4⋊C4×D61—22no—
165C4⋊C4×D61—24no—
166C4⋊C4×D61—24no—
167C4⋊C4×D61C2314yes—
168C2×#11758198—21no—
169C2×#11758198—21no—
170C2×#11758198D411yescharacteristic
171C2×#11758198D411yescharacteristic
172C2×C4×Dic61—21no—
173C2×C4×Dic61—22no—
174C2×C4×Dic61C2311yescharacteristic
175#14519711C2314yes—
176#14519710C2314yes—
177#14519709C2314yes—
178#14519708C2314yes—
179C4⋊#92418C2312yes—
180C4⋊#92418C2312yes—
181#14519701C2314yes—
182#14519701C2314yes—
183#14519701C2314yes—
184#14519699C2314yes—
185#14519699C2314yes—
186#14519698C2314yes—
187#14519689C2314yes—
188#14519689C2314yes—
189#14519687C2314yes—
190C8×Dic61C2314yes—
191C2×#41×C61C2312yes—
192C22×Q8×C61C2311yescharacteristic
193#137×C61—28no—
194C2×Q16×C61C2314yes—
195C2×SD16×C61C2314yes—
196C2×M16×C61C2312yes—
197C4⋊Q8×C61C2311yescharacteristic
198#127×C61C2311yescharacteristic
199#124×C61C2312yes—
200#121×C61—21no—
201#121×C61—21no—
202C4×Q8×C61—21no—
203C4×Q8×C61—21no—
204C4×Q8×C61C2312yes—
205C4×Q8×C61C2312yes—
206C4×D4×C61—21no—
207C4×D4×C61—21no—
208C2×C4⋊C4×C61—21no—
209C2×C4⋊C4×C61C2311yescharacteristic
210C2×C42×C61—21no—
211C2×C42×C61C2311yescharacteristic
212C4⋊C8×C61C2312yes—
213C4⋊C8×C61C2312yes—
214#103×C61C2314yes—
215#102×C61C2314yes—
216C23×D61—21no—
217C23×D61C2×D411yescharacteristic
218#41×C61—24no—
219#41×C61—24no—
220C2×Q8×C61—21no—
221C2×Q8×C61—22no—
222C2×Q8×C61#4114yes—
223C2×Q8×C61C2412yes—
224C2×Q8×C61C2412yes—
225C2×D4×C61—22no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61C2412yes—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—22no—
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C2×C22⋊D61—22no—
236C2×C22⋊D61—22no—
237C22×Dic61—21no—
238C22×Dic61—22no—
239C22×Dic61—22no—
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243#11758226—216no—
244#11758226—28no—
245#11758226—28no—
246C2×D244—28no—
247C2×D244—24no—
248C2×D244—21no—
249C2×D244—22no—
250C2×D244#4114yes—
251C2×D244C2412yes—
252C2×C4×D61—28no—
253C2×C4×D61—22no—
254C2×C4×D61—22no—
255C2×C4×D61—24no—
256C2×C4×D61—24no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—24no—
260C2×C4×D61—82no—
261C2×C4×D61—82no—
262C2×C4×D61—82no—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2412yes—
265C2×Dic122—21no—
266C2×Dic122—21no—
267Q16×C61—28no—
268SD16×C61—28no—
269M16×C61—24no—
270C2×C8×C61C2414yes—
271C4⋊C4×C61—22no—
272C4⋊C4×C61—22no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61C2412yes—
277C22⋊C4×C61—22no—
278C22⋊C4×C61—22no—
279C42×C61—22no—
280C42×C61—22no—
281C42×C61C2×D411yescharacteristic
282C42×C61C2×D411yescharacteristic
283C42×C61C2411yescharacteristic
284C42×C61C2411yescharacteristic
285C22⋊Dic61—22no—
286C22⋊Dic61—22no—
287C22⋊Dic61—22no—
288C22⋊Dic61—22no—
289C22⋊Dic61—22no—
290#11758201—28no—
291#11758199—28no—
292#11758198—22no—
293#11758198—22no—
294#11758198—22no—
295#11758198—22no—
296#11758198—24no—
297#11758198C2×D412yes—
298#11758198C2×D412yes—
299#11758198C2×D412yes—
300#11758198C2×D412yes—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—24no—
305C4⋊Dic61—22no—
306C4⋊Dic61—22no—
307C4⋊Dic61C2412yes—
308C4⋊Dic61C2412yes—
309C4⋊Dic61C2412yes—
310#11758196—22no—
311#11758196—22no—
312#11758196—24no—
313#11758196—22no—
314#11758196—22no—
315#11758196C2×D412yes—
316#11758196C2×D412yes—
317#11758196C2×D412yes—
318#11758196C2×D412yes—
319C4×Dic61—22no—
320C4×Dic61—24no—
321C4×Dic61—22no—
322C4×Dic61—22no—
323C4×Dic61C2×D412yes—
324C4×Dic61C2412yes—
325#11758194—24no—
326C2×#92418C2414yes—
327C23×C61—22no—
328C23×C61C22×D411yescharacteristic
329C22×D61—22no—
330C22×D61—24no—
331C22×D61—22no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61C22×D412yes—
337Q8×C61—24no—
338Q8×C61—22no—
339Q8×C61—22no—
340Q8×C61—22no—
341Q8×C61C2×#4114yes—
342D4×C61—22no—
343D4×C61—22no—
344D4×C61—44no—
345D4×C61—81no—
346D4×C61—81no—
347C2×C4×C61—24no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—42no—
354C2×C4×C61—44no—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C2×#4112yes—
361C2×C4×C61C2×#4112yes—
362C2×C4×C61C2511yescharacteristic
363C22⋊D61—82no—
364C22⋊D61—82no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—42no—
372C2×Dic61—82no—
373C2×Dic61—82no—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376C2×Dic61C22×D412yes—
377D244—216no—
378D244—24no—
379D244—22no—
380D244C2×#4114yes—
381C4×D61—216no—
382C4×D61—24no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—84no—
386C4×D61—82no—
387C4×D61—82no—
388C4×D61—84no—
389Dic122—81no—
390Dic122—81no—
391C8×C61—24no—
392#92418—24no—
393#60565—611nomaximal, Sylow
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61#52512yes—
400C22×C61C23×D411yescharacteristic
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—24no—
405C2×D61—44no—
406C2×D61—48no—
407C2×D61—42no—
408C2×D61—42no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—24no—
414C4×C61—42no—
415C4×C61—42no—
416C4×C61#52512yes—
417C4×C61C22×#4111yescharacteristic
418C4×C61C22×#4111yescharacteristic
419Dic61—22no—
420Dic61—22no—
421Dic61—22no—
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425#3455—611no—
426C2×#520—611no—
427#3125—614no—
428#3124—614no—
429#3120—614no—
430#3119—614no—
431#3092—612no—
432#3078—611no—
433#3077—611no—
434#3037D6111yescharacteristic, complemented
435#3036—611no—
436#3005—612no—
437C4×#137—612no—
438C4×AGL(1,ℤ/8)—612no—
439#2921—611no—
440C2×C61—22no—
441C2×C61—82no—
442C2×C61C2×#52511yescharacteristic
443C2×C61#358511yescharacteristic
444C2×C61#358611yescharacteristic
445D61—42no—
446D61—44no—
447C22×#41—611no—
448C2×#137C2×D6112yes—
449C2×AGL(1,ℤ/8)—612no—
450#542—612no—
451#542—612no—
452#541—612no—
453#540—612no—
454#539—1221no—
455#539—1221no—
456#538—1221no—
457#538—1221no—
458#533—611no—
459#532C2×D6111yescharacteristic
460#529—1222no—
461#529—1222no—
462#525—612no—
463#520—614no—
464#520—614no—
465#520—1222no—
466#520—1222no—
467C4×#41—612no—
468C2×C4×Q8—611no—
469C2×C4×Q8C2×D6111yescharacteristic
470C2×C4×D4—611no—
471C2×C4×D4—611no—
472C2×C4×D4—1221no—
473C2×C4×D4—1221no—
474C2×#117—611no—
475C2×#117—1221no—
476C22×C4⋊C4—611no—
477C22×C4⋊C4—1221no—
478#484—614no—
479#483—614no—
480#481—614no—
481#480—614no—
482#479—614no—
483#478—614no—
484#477—612no—
485#476—612no—
486#475—612no—
487#474—612no—
488#464C2×D6114yescomplemented
489#463—614no—
490#462C2×D6112yescomplemented
491#461—612no—
492#460C2×D6112yescomplemented
493#459—612no—
494#452—614no—
495#452—614no—
496#449—614no—
497#449—614no—
498#442—614no—
499#441—614no—
500#440—614no—
501#440—614no—
502C4×Q16—614no—
503C4×SD16—614no—
504C4×SD16—614no—
505C4×D8—614no—
506#433—614no—
507#433—614no—
508#428—612no—
509#428—612no—
510#423—611no—
511#423C2×D6111yescharacteristic
512#419—612no—
513#418—612no—
514#417—612no—
515#417C2×D6112yes—
516#407—612no—
517C4×M16—612no—
518C61#6056511yescharacteristic, complemented, Sylow
519C2×#41—614no—
520C2×#41—1222no—
521C2×#41—1224no—
522C2×#41—1224no—
523C2×#41C22×D6112yes—
524C22×Q8C22×D6111yescharacteristic
525C22×D4—611no—
526C22×D4—1221no—
527C23×C4—611no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4—1221no—
532#137—28no—
533AGL(1,ℤ/8)—1228no—
534C2×Q16C22×D6114yes—
535C2×SD16—614no—
536C2×SD16C22×D6114yes—
537C2×D8—614no—
538C2×M16—612no—
539C2×M16C22×D6112yes—
540C4⋊Q8—611no—
541C4⋊Q8—611no—
542C4⋊Q8C22×D6111yescharacteristic
543#127C22×D6111yescharacteristic
544#126—1222no—
545#126—1222no—
546#126—1222no—
547#126—1222no—
548#125—612no—
549#125—1222no—
550#125—1222no—
551#124—1222no—
552#124—1222no—
553#124C22×D6112yes—
554#123—1222no—
555#123—1222no—
556#123—1222no—
557#123—1222no—
558#123—1222no—
559C22⋊Q8—612no—
560C22⋊Q8—612no—
561C22⋊Q8—1222no—
562C22⋊Q8—1222no—
563C22⋊Q8—1221no—
564C22⋊Q8—1221no—
565#121—21no—
566#121—21no—
567#121—612no—
568#121—612no—
569#121—1222no—
570#121—1222no—
571#120—1222no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8—614no—
575C4×Q8—612no—
576C4×Q8—612no—
577C4×Q8—1222no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8C22×D6112yes—
581C4×Q8C22×D6112yes—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—612no—
585C4×D4—612no—
586C4×D4—614no—
587C4×D4—612no—
588C4×D4—612no—
589C4×D4—1224no—
590C4×D4—1224no—
591C4×D4—1222no—
592C4×D4—1224no—
593C4×D4—1224no—
594C4×D4—1222no—
595C4×D4—1222no—
596C4×D4—1222no—
597C4×D4—1222no—
598C4×D4—1221no—
599C4×D4—1221no—
600#117—612no—
601#117—612no—
602#117—612no—
603#117—612no—
604#117—612no—
605#117—1224no—
606#117—1224no—
607#117—1222no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—614no—
613C2×C4⋊C4—1224no—
614C2×C4⋊C4—1224no—
615C2×C4⋊C4—1222no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4C22×D6111yescharacteristic
619C2×C22⋊C4—611no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C42—21no—
624C2×C42—611no—
625C2×C42—1222no—
626C2×C42—1221no—
627C2×C42C22×D6111yescharacteristic
628#107—614no—
629#107—614no—
630#106—614no—
631#106—614no—
632C4⋊C8—612no—
633C4⋊C8—612no—
634C4⋊C8C22×D6112yes—
635C4⋊C8C22×D6112yes—
636#103—614no—
637#103—614no—
638#103—614no—
639#103C22×D6114yes—
640#102—614no—
641#102—614no—
642#102—614no—
643#102C22×D6114yes—
644C22⋊C8—614no—
645C22⋊C8—614no—
646#97—614no—
647C4×C8—614no—
648C24—611no—
649C24—1221no—
650#41—24no—
651#41—24no—
652#41—1228no—
653#41—12216no—
654#41—1228no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—1221no—
658C2×Q8—1221no—
659C2×Q8#1175822414yes—
660C2×Q8C23×D6112yes—
661C2×Q8C23×D6112yes—
662C2×D4—22no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—614no—
666C2×D4—612no—
667C2×D4—1224no—
668C2×D4—1228no—
669C2×D4—1222no—
670C2×D4—1222no—
671C2×D4—1221no—
672C2×D4—1222no—
673C2×D4C23×D6112yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—1224no—
683C22×C4—1224no—
684C22×C4—1228no—
685C22×C4—1224no—
686C22×C4—1222no—
687C22×C4—1222no—
688C22×C4—1222no—
689C22×C4—1222no—
690C22×C4—1221no—
691C22×C4—1222no—
692C22×C4—1222no—
693C22×C4—4882no—
694C22×C4—4882no—
695C22×C4—4882no—
696C22×C4D4×D6111yescharacteristic
697C22×C4D4×D6111yescharacteristic
698C22×C4C23×D6111yescharacteristic
699Q16—28no—
700SD16—28no—
701SD16—1228no—
702D8—1228no—
703M16—24no—
704M16—1224no—
705C2×C8—614no—
706C2×C8C23×D6114yes—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—612no—
713C4⋊C4—612no—
714C4⋊C4—612no—
715C4⋊C4—612no—
716C4⋊C4—612no—
717C4⋊C4—612no—
718C4⋊C4—612no—
719C4⋊C4—1224no—
720C4⋊C4—1224no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4—1222no—
724C4⋊C4—1222no—
725C4⋊C4—1221no—
726C4⋊C4—1222no—
727C4⋊C4—1222no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4C23×D6112yes—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—612no—
734C22⋊C4—612no—
735C22⋊C4—612no—
736C22⋊C4—612no—
737C22⋊C4—1224no—
738C22⋊C4—1222no—
739C22⋊C4—1222no—
740C22⋊C4—1222no—
741C22⋊C4—1222no—
742C22⋊C4—1222no—
743C22⋊C4—1222no—
744C22⋊C4—1222no—
745C22⋊C4—1222no—
746C22⋊C4—1222no—
747C42—22no—
748C42—22no—
749C42—612no—
750C42—612no—
751C42—1224no—
752C42—1222no—
753C42—1222no—
754C42—1222no—
755C42D4×D6111yescharacteristic
756C42D4×D6111yescharacteristic
757C42C23×D6111yescharacteristic
758C42C23×D6111yescharacteristic
759C23—22no—
760C23—612no—
761C23—1224no—
762C23—1222no—
763C23—1222no—
764C23—2441no—
765C23—2441no—
766C23—2442no—
767C23—2442no—
768C23C2×D4×D6111yescharacteristic
769Q8—24no—
770Q8—22no—
771Q8—22no—
772Q8—22no—
773Q8—4881no—
774Q8—4881no—
775Q8C2×#1175822414yes—
776D4—22no—
777D4—22no—
778D4—44no—
779D4—81no—
780D4—81no—
781D4—614no—
782D4—12216no—
783D4—1224no—
784D4—1222no—
785D4—4882no—
786D4—4882no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—612no—
796C2×C4—612no—
797C2×C4—612no—
798C2×C4—12216no—
799C2×C4—1222no—
800C2×C4—1224no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—4882no—
807C2×C4—4882no—
808C2×C4—4884no—
809C2×C4—4884no—
810C2×C4—4882no—
811C2×C4—4882no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2442no—
815C2×C4C2×D4×D6111yescharacteristic
816C2×C4C2×D4×D6111yescharacteristic
817C2×C4C2×D4×D6111yescharacteristic
818C2×C4C2×D4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4#41×D6112yes—
821C2×C4C2×#1175822412yes—
822C2×C4C24×D6111yescharacteristic
823C8—24no—
824C8—1224no—
825C22—21no—
826C22—21no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—1224no—
831C22—1222no—
832C22—1222no—
833C22—1222no—
834C22—2444no—
835C22—2448no—
836C22—2442no—
837C22—2442no—
838C22#1684027212yes—
839C22C22×D4×D6111yescharacteristic
840C4—24no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—42no—
846C4—42no—
847C4—1222no—
848C4—1222no—
849C4—1222no—
850C4—2442no—
851C4—2442no—
852C4—2442no—
853C4#1684027212yes—
854C4C2×#41×D6111yescharacteristic
855C4C22×#1175822411yescharacteristic
856C2—22no—
857C2—82no—
858C2—2442no—
859C2—2444no—
860C2C2×#1684027211yescharacteristic
861C2#2146059611yescharacteristic
862C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3037C2
socleC22×C61C23×D4
hypercenter#3037D61
hypocenterC61#60565
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
1. #21459208C2semidirect
2. C2×#16840244C2semidirect
3. #21456095C2semidirect
4. #21456080C2semidirect
5. #21456032C2semidirect
6. #21456017C2semidirect
7. #21455740C2semidirect
8. #21455624C2semidirect
9. #21455618C2semidirect
10. #21455279C2semidirect
11. #21455060C2semidirect
12. #137×Dic61C2semidirect
13. #21454632C2semidirect
14. #21454456C2semidirect
15. C61×#3037C2semidirect
18. #16840381C22semidirect
19. #16840381C22semidirect
20. #16840373C22semidirect
21. #16840366C22semidirect
44. #16840096C22semidirect
45. #16840091C22semidirect
46. #16840079C22semidirect
47. #16840074C22semidirect
48. #16840069C22semidirect
49. #16840063C22semidirect
50. #16840057C22semidirect
51. #16840053C22semidirect
52. #16840047C22semidirect
53. #16840043C22semidirect
54. #16839974C22semidirect
55. #16839964C22semidirect
56. #16839954C22semidirect
61. #16839871C22semidirect
62. #16839869C22semidirect
63. #16839865C22semidirect
64. #16839863C22semidirect
65. Q16×Dic61C22semidirect
66. SD16×Dic61C22semidirect
67. #16839847C22semidirect
68. #16839842C22semidirect
69. #16839822C22semidirect
70. #16839822C22semidirect
82. C61×#464C22semidirect
83. C61×#462C22semidirect
84. C61×#460C22semidirect
434. #3037D61semidirect
488. #464C2×D61semidirect
490. #462C2×D61semidirect
492. #460C2×D61semidirect
518. C61#60565semidirect

Maximal subgroups

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

subgroupindex
#214592082
C2×#168402442
#214560952
#214560802
#214560322
#214560172
#214557402
#214556242
#214556182
#214552792
#214550602
#137×Dic612
#214546322
#214544562
C61×#30372
#6056561