Finite Group Databasebeta

← #30564915

Subgroups — #30564915

Order 15616.

2126 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459658C211yesmaximal, characteristic, complemented
2#21457915C214yesmaximal, complemented
3#21457795C214yesmaximal, complemented
4#21457370C214yesmaximal, complemented
5#21457345C214yesmaximal, complemented
6#21456846C212yesmaximal, complemented
7#21456640C211yesmaximal, characteristic, complemented
8#21456621C211yesmaximal, characteristic, complemented
9#21456600C212yesmaximal, complemented
10#21455957C212yesmaximal, complemented
11#21455079C211yesmaximal, characteristic, complemented
12#21455071C211yesmaximal, characteristic, complemented
13#21455037C212yesmaximal, complemented
14#21454848C211yesmaximal, characteristic, complemented
15C2×C61×#547C211yesmaximal, characteristic, complemented
16C2×#14519807C2212yescomplemented
17C2×#14519802C2212yescomplemented
18C2×#14519797C2214yescomplemented
19#16840461—22no—
20#16840458C2212yescomplemented
21#16840452C2212yescomplemented
22#16840441—22no—
23#16840421C2212yescomplemented
24#16840408C2212yescomplemented
25#16840359—21no—
26#16840350—21no—
27#16840321—21no—
28#16840296C2212yes—
29#16840273C2212yes—
30C2×#14519756C2211yescharacteristic
31C2×#14519751C2211yescharacteristic
32#16840235—21no—
33#16840154C2214yescomplemented
34#16840130C2214yescomplemented
35#16840100C2214yescomplemented
36#16840095C2212yescomplemented
37#16840092C2212yescomplemented
38#16840090C2212yescomplemented
39#16840075C2212yes—
40#16840062C2214yescomplemented
41#16840018C2214yescomplemented
42#16840010C2214yescomplemented
43#16840001C2214yescomplemented
44#16839993C2214yescomplemented
45#16839977C2214yescomplemented
46#16839969C2214yescomplemented
47#16839964C2214yescomplemented
48#16839924C2214yescomplemented
49#16839924C2214yescomplemented
50#16839922C2214yescomplemented
51#16839918C2212yescomplemented
52#16839918C2212yescomplemented
53#16839917C2212yescomplemented
54#16839913C2212yescomplemented
55#16839912C2212yescomplemented
56#16839907C2214yescomplemented
57#16839907C2214yescomplemented
58#16839901C2212yes—
59#16839901C2212yes—
60#16839896C2212yes—
61#16839872C2214yescomplemented
62#16839862C2214yescomplemented
63#16839834C2214yescomplemented
64#16839834C2214yescomplemented
65#16839819C2212yescomplemented
66#16839763C2212yescomplemented
67#16839763C2212yescomplemented
68#16839758C2214yescomplemented
69#16839726C2211yescharacteristic
70#16839726C2211yescharacteristic
71C2×C22⋊#92418C2212yescomplemented
72C22×#41×C61C2211yescharacteristic
73C22×#41×C61C2211yescharacteristic, complemented
74C61×#547—22no—
75C61×#547—22no—
76C61×#547C2214yes—
77C61×#547C2214yescomplemented
78C2×C4⋊Q8×C61C2211yescharacteristic, complemented
79C2×#123×C61—21no—
80C2×#123×C61—21no—
81C2×C22⋊Q8×C61C2211yescharacteristic
82C2×C22⋊Q8×C61C2211yescharacteristic, complemented
83C2×#121×C61—21no—
84C2×C4×D4×C61C2211yescharacteristic
85C2×C4×D4×C61C2211yescharacteristic, complemented
86C22×C4⋊C4×C61—21no—
87C2×#11758222C2312yes—
88C22×Dic122C2311yescharacteristic
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91#14519807—44no—
92#14519802—44no—
93#14519797—48no—
94C2×#11758202C2314yes—
95C2×#11758202C2314yes—
96C2×#11758200C2314yes—
97C2×#11758201C2314yes—
98C2×#11758201C2314yes—
99C2×#11758199C2314yes—
100C2×#11758194C2312yes—
101C2×#11758194C2312yes—
102C22×#92418C2314yes—
103#14519772—22no—
104#14519771—22no—
105#14519770—22no—
106#14519769C2312yes—
107#14519767—22no—
108#14519765C2312yes—
109#14519763—22no—
110#14519762—22no—
111#14519760—22no—
112#14519760—22no—
113#14519759—22no—
114#14519758—22no—
115#14519756—21no—
116#14519756—21no—
117#14519756C2312yes—
118#14519756C2312yes—
119#14519756C2312yes—
120#14519755—22no—
121#14519751—21no—
122#14519751—21no—
123#14519751C2312yes—
124#14519751C2312yes—
125#14519751C2312yes—
126#14519750—22no—
127#14519749—22no—
128#14519749—22no—
129#14519746—22no—
130#14519745—22no—
131C4×Dic122C2312yes—
132C4×D244C2312yes—
133C4×C22⋊D61—22no—
134C4×C22⋊D61—22no—
135C4×C22⋊D61—22no—
136#14519737—22no—
137#14519737—22no—
138#14519736C2312yes—
139#14519734—22no—
140#14519733—22no—
141C2×C4⋊Dic61C2311yescharacteristic
142C2×C4⋊Dic61C2311yescharacteristic
143C2×#11758196—21no—
144C2×C22⋊Dic61—21no—
145C2×#11758198—21no—
146C22⋊C4×D61—22no—
147#14519710C2314yes—
148#14519708C2314yes—
149C4⋊#92418C2314yes—
150#14519701C2314yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519701C2314yes—
154#14519700C2314yes—
155#14519698C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158C22⋊#92418C2312yes—
159C22⋊#92418C2312yes—
160C22⋊#92418C2314yes—
161C22⋊#92418C2312yes—
162C22⋊#92418C2312yes—
163#14519688C2314yes—
164C2×#41×C61—21no—
165C2×#41×C61—21no—
166C2×#41×C61—22no—
167C2×#41×C61—44no—
168C2×#41×C61—44no—
169C2×#41×C61C2312yes—
170C2×#41×C61C2314yes—
171C2×#41×C61C2312yes—
172C22×Q8×C61C2311yescharacteristic
173C22×Q8×C61C2311yescharacteristic
174C22×D4×C61—21no—
175C22×D4×C61—21no—
176C22×D4×C61D411yescharacteristic
177C22×D4×C61C2311yescharacteristic
178C23×C4×C61—21no—
179C23×C4×C61—21no—
180C23×C4×C61—21no—
181C23×C4×C61C2311yescharacteristic
182C23×C4×C61C2311yescharacteristic
183C4⋊Q8×C61—22no—
184C4⋊Q8×C61C2314yes—
185#123×C61—24no—
186#123×C61—24no—
187#123×C61—24no—
188#123×C61—24no—
189C22⋊Q8×C61—21no—
190C22⋊Q8×C61—21no—
191C22⋊Q8×C61—22no—
192C22⋊Q8×C61C2312yes—
193C22⋊Q8×C61C2314yes—
194C22⋊Q8×C61C2312yes—
195#121×C61—24no—
196#121×C61—24no—
197C4×D4×C61—22no—
198C4×D4×C61D412yes—
199C4×D4×C61D412yes—
200C4×D4×C61C2314yes—
201C4×D4×C61C2312yes—
202C4×D4×C61C2312yes—
203C2×C4⋊C4×C61—21no—
204C2×C4⋊C4×C61—21no—
205C2×C4⋊C4×C61—21no—
206C2×C4⋊C4×C61—21no—
207C2×C4⋊C4×C61—24no—
208C2×C4⋊C4×C61—24no—
209C2×C4⋊C4×C61D411yescharacteristic
210C2×C4⋊C4×C61C2311yescharacteristic
211C2×C22⋊C4×C61—21no—
212C2×C22⋊C4×C61—21no—
213C2×C22⋊C4×C61—21no—
214C2×C22⋊C4×C61D411yescharacteristic
215C2×C22⋊C4×C61D411yescharacteristic
216C2×C42×C61C2311yescharacteristic
217C24×C61—21no—
218C24×C61C2×D411yescharacteristic
219C24×C61C2×D411yescharacteristic
220C23×D61—21no—
221#41×C61—28no—
222#41×C61—24no—
223#41×C61—24no—
224#41×C61—44no—
225#41×C61—42no—
226#41×C61—42no—
227#41×C61—44no—
228#41×C61—44no—
229#41×C61—48no—
230C2×Q8×C61—21no—
231C2×Q8×C61—21no—
232C2×Q8×C61—42no—
233C2×Q8×C61—42no—
234C2×Q8×C61C2412yes—
235C2×Q8×C61C2412yes—
236C2×D4×C61—24no—
237C2×D4×C61—22no—
238C2×D4×C61—24no—
239C2×D4×C61—22no—
240C2×D4×C61—21no—
241C2×D4×C61—42no—
242C2×D4×C61—44no—
243C2×D4×C61—44no—
244C2×D4×C61C2×D412yes—
245C2×D4×C61C2×D412yes—
246C2×D4×C61C2412yes—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—24no—
251C22×C4×C61—24no—
252C22×C4×C61—22no—
253C22×C4×C61—22no—
254C22×C4×C61—42no—
255C22×C4×C61—42no—
256C22×C4×C61—44no—
257C22×C4×C61—44no—
258C22×C4×C61—44no—
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2×D411yescharacteristic
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D412yes—
266C22×C4×C61C2411yescharacteristic
267C22×C4×C61C2411yescharacteristic
268C22×C4×C61C2412yes—
269C22×C4×C61C2411yescharacteristic
270C2×C22⋊D61—22no—
271C2×C22⋊D61—22no—
272C2×C22⋊D61—22no—
273C2×C22⋊D61—22no—
274C2×C22⋊D61—44no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278#11758222—44no—
279C2×D244—21no—
280C2×D244—42no—
281C2×D244C2412yes—
282C2×C4×D61—22no—
283C2×C4×D61—22no—
284C2×Dic122—21no—
285C2×Dic122—42no—
286C2×Dic122C2412yes—
287C4⋊C4×C61—24no—
288C4⋊C4×C61—24no—
289C4⋊C4×C61—22no—
290C4⋊C4×C61—22no—
291C4⋊C4×C61—24no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61C2×D412yes—
294C4⋊C4×C61C2×D412yes—
295C4⋊C4×C61C2412yes—
296C22⋊C4×C61—22no—
297C22⋊C4×C61—24no—
298C22⋊C4×C61—22no—
299C22⋊C4×C61—24no—
300C22⋊C4×C61C2×D412yes—
301C22⋊C4×C61C2×D412yes—
302C22⋊C4×C61C2×D412yes—
303C22⋊C4×C61C2×D412yes—
304C42×C61C2×D412yes—
305C42×C61C2412yes—
306C22⋊Dic61—22no—
307C22⋊Dic61—22no—
308C22⋊Dic61—22no—
309C22⋊Dic61—22no—
310#11758202—44no—
311#11758202—44no—
312#11758201—44no—
313#11758201—44no—
314#11758200—28no—
315#11758199—28no—
316#11758198—22no—
317#11758198—22no—
318#11758198—22no—
319#11758198—22no—
320#11758198—22no—
321#11758198—22no—
322C4⋊Dic61—21no—
323C4⋊Dic61—21no—
324C4⋊Dic61C2412yes—
325C4⋊Dic61C2412yes—
326#11758196—22no—
327#11758196—22no—
328#11758196—22no—
329#11758196—22no—
330#11758196—22no—
331#11758196—22no—
332C4×Dic61—22no—
333C4×Dic61—22no—
334#11758194—42no—
335#11758194—42no—
336C2×#92418—44no—
337C2×#92418C2414yes—
338C2×#92418C2414yes—
339C23×C61—24no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—42no—
348C23×C61—42no—
349C23×C61C22×D411yescharacteristic
350C23×C61C22×D412yes—
351C23×C61C22×D411yescharacteristic
352C23×C61C22×D411yescharacteristic
353C22×D61—22no—
354C22×D61—42no—
355C22×D61—81no—
356C22×D61—81no—
357Q8×C61—22no—
358Q8×C61—24no—
359Q8×C61—22no—
360Q8×C61—42no—
361Q8×C61—42no—
362D4×C61—24no—
363D4×C61—22no—
364D4×C61—42no—
365D4×C61—42no—
366D4×C61—44no—
367D4×C61—48no—
368D4×C61—44no—
369D4×C61H(5,𝔽2)14yes—
370C2×C4×C61—22no—
371C2×C4×C61—24no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—42no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—44no—
385C2×C4×C61—48no—
386C2×C4×C61—44no—
387C2×C4×C61—48no—
388C2×C4×C61—42no—
389C2×C4×C61—42no—
390C2×C4×C61—42no—
391C2×C4×C61C22×D412yes—
392C2×C4×C61C22×D412yes—
393C2×C4×C61C22×D411yescharacteristic
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D412yes—
396C2×C4×C61C22×D411yescharacteristic
397C2×C4×C61C2511yescharacteristic
398C22⋊D61—44no—
399C22⋊D61—44no—
400C22⋊D61—82no—
401C22⋊D61—82no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—42no—
406C2×Dic61—81no—
407C2×Dic61—81no—
408D244—24no—
409D244—81no—
410C4×D61—82no—
411C4×D61—82no—
412Dic122—24no—
413Dic122—81no—
414#92418—24no—
415#92418—24no—
416#61575—611nomaximal, Sylow
417C22×C61—21no—
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—22no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—22no—
424C22×C61—21no—
425C22×C61—24no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—22no—
429C22×C61—48no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—82no—
433C22×C61—82no—
434C22×C61#57512yes—
435C22×C61C23×D411yescharacteristic
436C2×D61—42no—
437C2×D61—42no—
438C2×D61—42no—
439C2×D61—162no—
440C4×C61—22no—
441C4×C61—21no—
442C4×C61—22no—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—22no—
446C4×C61—42no—
447C4×C61—42no—
448C4×C61—42no—
449C4×C61C2×H(5,𝔽2)12yes—
450Dic61—42no—
451Dic61—42no—
452Dic61—42no—
453#3505—611no—
454C2×#547D6111yescharacteristic, complemented
455#3315—614no—
456#3307—614no—
457#3269—614no—
458#3267—614no—
459#3218—612no—
460#3195—611no—
461#3193—611no—
462#3190—612no—
463#3114—612no—
464#3007—611no—
465#3006—611no—
466#3002—612no—
467#2973—611no—
468C2×C61—22no—
469C2×C61—41no—
470C2×C61—41no—
471C2×C61—42no—
472C2×C61—44no—
473C2×C61#348411yescharacteristic
474C2×C61C2×#57511yescharacteristic
475C2×C61#358611yescharacteristic
476D61—82no—
477C22×#41C2×D6111yescharacteristic
478C22×#41C2×D6111yescharacteristic, complemented
479C2×#137—612no—
480C2×AGL(1,ℤ/8)—612no—
481C2×#135—614no—
482#553—612no—
483#553—1222no—
484#552—612no—
485#551—1222no—
486#548—612no—
487#547—22no—
488#547—22no—
489#547C2×D6114yes—
490#547C2×D6114yescomplemented
491#546—612no—
492#539—1221no—
493#538—1221no—
494#534—1221no—
495C2×C4⋊Q8C2×D6111yescharacteristic, complemented
496#529—612no—
497#525—612no—
498C2×#123—21no—
499C2×#123—21no—
500C2×C22⋊Q8—611no—
501C2×C22⋊Q8C2×D6111yescharacteristic
502C2×C22⋊Q8C2×D6111yescharacteristic, complemented
503C2×#121—21no—
504C2×#121—611no—
505#518—1221no—
506C2×C4×D4C2×D6111yescharacteristic
507C2×C4×D4C2×D6111yescharacteristic, complemented
508C22×C4⋊C4—21no—
509#497—614no—
510#491—614no—
511#485—614no—
512#484—612no—
513#483—612no—
514#483—612no—
515#480—612no—
516#478—614no—
517#470—614no—
518#468—614no—
519#467—614no—
520#465—614no—
521#463—614no—
522#462—614no—
523#461—614no—
524#452—614no—
525#452—614no—
526#452—614no—
527#451—612no—
528#451—612no—
529#451—612no—
530#450—612no—
531#450—612no—
532#449—614no—
533#449—614no—
534#448—612no—
535#448—612no—
536#447—612no—
537#442—614no—
538#440—614no—
539#435—614no—
540#435—614no—
541#432—612no—
542#417—612no—
543#417—612no—
544#416—614no—
545#407—611no—
546#407—611no—
547C2×C22⋊C8—612no—
548C61#6157511yescharacteristic, complemented, Sylow
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—22no—
552C2×#41—44no—
553C2×#41—44no—
554C2×#41—612no—
555C2×#41C22×D6112yes—
556C2×#41C22×D6114yes—
557C2×#41C22×D6112yes—
558C22×Q8—611no—
559C22×Q8C22×D6111yescharacteristic
560C22×Q8C22×D6111yescharacteristic
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—611no—
564C22×D4—1221no—
565C22×D4C22⋊D6111yescharacteristic
566C22×D4C22×D6111yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C22×D6111yescharacteristic
571C23×C4C22×D6111yescharacteristic
572#137—2444no—
573AGL(1,ℤ/8)—2444no—
574#135—2448no—
575C2×Q16—614no—
576C2×Q16—614no—
577C2×SD16—614no—
578C2×SD16—614no—
579C2×SD16—614no—
580C2×D8—614no—
581C2×M16—612no—
582C2×M16—612no—
583C22×C8—614no—
584C4⋊Q8—22no—
585C4⋊Q8C22×D6114yes—
586#126—1222no—
587#126—1222no—
588#126—1222no—
589#125—612no—
590#125—1222no—
591#124—612no—
592#124—1222no—
593#123—24no—
594#123—24no—
595#123—24no—
596#123—24no—
597#123—1222no—
598#123—1222no—
599#123—1222no—
600#123—1222no—
601#123—1222no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—22no—
605C22⋊Q8—612no—
606C22⋊Q8—612no—
607C22⋊Q8—612no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1222no—
611C22⋊Q8C22×D6112yes—
612C22⋊Q8C22×D6112yes—
613C22⋊Q8C22×D6114yes—
614#121—24no—
615#121—24no—
616#121—612no—
617#121—612no—
618#121—612no—
619#121—1222no—
620#121—1222no—
621#121—1221no—
622#121—1221no—
623#121—1222no—
624#120—1222no—
625#120—1222no—
626C4×Q8—612no—
627C4×D4—22no—
628C4×D4—612no—
629C4×D4—1222no—
630C4×D4—1222no—
631C4×D4—1222no—
632C4×D4—1222no—
633C4×D4—1222no—
634C4×D4C22⋊D6112yes—
635C4×D4C22⋊D6112yes—
636C4×D4C22×D6114yes—
637C4×D4C22×D6112yes—
638C4×D4C22×D6112yes—
639#117—612no—
640#117—1222no—
641#117—1222no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—24no—
647C2×C4⋊C4—24no—
648C2×C4⋊C4—611no—
649C2×C4⋊C4—611no—
650C2×C4⋊C4—1221no—
651C2×C4⋊C4C22⋊D6111yescharacteristic
652C2×C4⋊C4C22×D6111yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1222no—
659C2×C22⋊C4C22⋊D6111yescharacteristic
660C2×C22⋊C4C22⋊D6111yescharacteristic
661C2×C42C22×D6111yescharacteristic
662#107—614no—
663#106—614no—
664C4⋊C8—614no—
665#103—614no—
666#103—614no—
667#103—614no—
668#103—614no—
669#103—614no—
670#102—614no—
671#102—614no—
672#102—614no—
673C22⋊C8—612no—
674C22⋊C8—612no—
675C22⋊C8—614no—
676C22⋊C8—612no—
677C22⋊C8—612no—
678#97—614no—
679C24—21no—
680C24—1221no—
681C24C2×C22⋊D6111yescharacteristic
682C24C2×C22⋊D6111yescharacteristic
683#41—28no—
684#41—24no—
685#41—24no—
686#41—44no—
687#41—42no—
688#41—42no—
689#41—44no—
690#41—44no—
691#41—48no—
692#41—2444no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—612no—
698C2×Q8—1221no—
699C2×Q8—2442no—
700C2×Q8C23×D6112yes—
701C2×Q8C23×D6112yes—
702C2×D4—24no—
703C2×D4—22no—
704C2×D4—24no—
705C2×D4—22no—
706C2×D4—21no—
707C2×D4—42no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—612no—
711C2×D4—1222no—
712C2×D4—1222no—
713C2×D4—1222no—
714C2×D4—1222no—
715C2×D4—1221no—
716C2×D4—2442no—
717C2×D4—2444no—
718C2×D4C2×C22⋊D6112yes—
719C2×D4C2×C22⋊D6112yes—
720C2×D4C23×D6112yes—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1222no—
737C22×C4—1222no—
738C22×C4C2×C22⋊D6111yescharacteristic
739C22×C4C2×C22⋊D6111yescharacteristic
740C22×C4C2×C22⋊D6111yescharacteristic
741C22×C4C2×C22⋊D6111yescharacteristic
742C22×C4C2×C22⋊D6111yescharacteristic
743C22×C4C2×C22⋊D6111yescharacteristic
744C22×C4C2×C22⋊D6112yes—
745C22×C4C23×D6111yescharacteristic
746C22×C4C23×D6111yescharacteristic
747C22×C4C23×D6111yescharacteristic
748C22×C4C23×D6112yes—
749Q16—2444no—
750Q16—2444no—
751SD16—1228no—
752SD16—2444no—
753SD16—2444no—
754D8—1228no—
755M16—2442no—
756M16—2442no—
757C2×C8—614no—
758C2×C8—614no—
759C2×C8—2444no—
760C4⋊C4—24no—
761C4⋊C4—24no—
762C4⋊C4—22no—
763C4⋊C4—22no—
764C4⋊C4—24no—
765C4⋊C4—21no—
766C4⋊C4—612no—
767C4⋊C4—612no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1222no—
771C4⋊C4—1222no—
772C4⋊C4—1222no—
773C4⋊C4—1222no—
774C4⋊C4—1222no—
775C4⋊C4—1222no—
776C4⋊C4C2×C22⋊D6112yes—
777C4⋊C4C2×C22⋊D6112yes—
778C4⋊C4C23×D6112yes—
779C22⋊C4—22no—
780C22⋊C4—24no—
781C22⋊C4—22no—
782C22⋊C4—24no—
783C22⋊C4—1222no—
784C22⋊C4—1222no—
785C22⋊C4—1222no—
786C22⋊C4—1222no—
787C22⋊C4—1222no—
788C22⋊C4—1222no—
789C22⋊C4—1222no—
790C22⋊C4—1222no—
791C22⋊C4—1222no—
792C22⋊C4—1222no—
793C22⋊C4C2×C22⋊D6112yes—
794C22⋊C4C2×C22⋊D6112yes—
795C22⋊C4C2×C22⋊D6112yes—
796C22⋊C4C2×C22⋊D6112yes—
797C42—1222no—
798C42—1222no—
799C42C2×C22⋊D6112yes—
800C42C23×D6112yes—
801C23—24no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—42no—
810C23—42no—
811C23—1222no—
812C23—4881no—
813C23—4881no—
814C23—2442no—
815C23C22×C22⋊D6111yescharacteristic
816C23C22×C22⋊D6112yes—
817C23C22×C22⋊D6111yescharacteristic
818C23C22×C22⋊D6111yescharacteristic
819Q8—22no—
820Q8—24no—
821Q8—22no—
822Q8—42no—
823Q8—42no—
824Q8—1224no—
825Q8—4881no—
826D4—24no—
827D4—22no—
828D4—42no—
829D4—42no—
830D4—44no—
831D4—48no—
832D4—44no—
833D4—1224no—
834D4—4881no—
835D4—4882no—
836D4—4882no—
837D4—2444no—
838D4—2444no—
839D4#1451982214yes—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—48no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—48no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—4882no—
865C2×C4—4882no—
866C2×C4—4881no—
867C2×C4—4881no—
868C2×C4—2442no—
869C2×C4C22×C22⋊D6112yes—
870C2×C4C22×C22⋊D6112yes—
871C2×C4C22×C22⋊D6111yescharacteristic
872C2×C4C22×C22⋊D6112yes—
873C2×C4C22×C22⋊D6111yescharacteristic
874C2×C4C22×C22⋊D6111yescharacteristic
875C2×C4C24×D6111yescharacteristic
876C8—1224no—
877C8—1224no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—22no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—21no—
889C22—24no—
890C22—48no—
891C22—42no—
892C22—42no—
893C22—82no—
894C22—82no—
895C22—9762no—
896C22—2442no—
897C22—2442no—
898C22—2442no—
899C22#1684056012yes—
900C22C23×C22⋊D6111yescharacteristic
901C4—22no—
902C4—22no—
903C4—22no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—2442no—
911C4—2442no—
912C4—2442no—
913C4C2×#1451982212yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—42no—
918C2—44no—
919C2—4882no—
920C2#2145945411yescharacteristic
921C2C2×#1684056011yescharacteristic
922C2#2146060611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#547C2
socleC22×C61C23×D4
hypercenterC2×#547D61
hypocenterC61#61575
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #21459658C2semidirect
2. #21457915C2semidirect
3. #21457795C2semidirect
4. #21457370C2semidirect
5. #21457345C2semidirect
6. #21456846C2semidirect
7. #21456640C2semidirect
8. #21456621C2semidirect
9. #21456600C2semidirect
10. #21455957C2semidirect
11. #21455079C2semidirect
12. #21455071C2semidirect
13. #21455037C2semidirect
14. #21454848C2semidirect
15. C2×C61×#547C2semidirect
16. C2×#14519807C22semidirect
17. C2×#14519802C22semidirect
18. C2×#14519797C22semidirect
20. #16840458C22semidirect
21. #16840452C22semidirect
23. #16840421C22semidirect
24. #16840408C22semidirect
33. #16840154C22semidirect
34. #16840130C22semidirect
35. #16840100C22semidirect
36. #16840095C22semidirect
37. #16840092C22semidirect
38. #16840090C22semidirect
40. #16840062C22semidirect
41. #16840018C22semidirect
42. #16840010C22semidirect
43. #16840001C22semidirect
44. #16839993C22semidirect
45. #16839977C22semidirect
46. #16839969C22semidirect
47. #16839964C22semidirect
48. #16839924C22semidirect
49. #16839924C22semidirect
50. #16839922C22semidirect
51. #16839918C22semidirect
52. #16839918C22semidirect
53. #16839917C22semidirect
54. #16839913C22semidirect
55. #16839912C22semidirect
56. #16839907C22semidirect
57. #16839907C22semidirect
61. #16839872C22semidirect
62. #16839862C22semidirect
63. #16839834C22semidirect
64. #16839834C22semidirect
65. #16839819C22semidirect
66. #16839763C22semidirect
67. #16839763C22semidirect
68. #16839758C22semidirect
71. C2×C22⋊#92418C22semidirect
73. C22×#41×C61C22semidirect
77. C61×#547C22semidirect
78. C2×C4⋊Q8×C61C22semidirect
82. C2×C22⋊Q8×C61C22semidirect
85. C2×C4×D4×C61C22semidirect
454. C2×#547D61semidirect
478. C22×#41C2×D61semidirect
490. #547C2×D61semidirect
495. C2×C4⋊Q8C2×D61semidirect
502. C2×C22⋊Q8C2×D61semidirect
507. C2×C4×D4C2×D61semidirect
548. C61#61575semidirect

Maximal subgroups

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

subgroupindex
#214596582
#214579152
#214577952
#214573702
#214573452
#214568462
#214566402
#214566212
#214566002
#214559572
#214550792
#214550712
#214550372
#214548482
C2×C61×#5472
#6157561