Finite Group Databasebeta

← D61×#3093 #30547796

Subgroups — D61×#3093 #30547796

Order 15616.

2346 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2C2×#117×D61C211yesmaximal, characteristic, complemented
3#21455753C212yesmaximal, complemented
4#21455752C211yesmaximal, characteristic, complemented
5#21455751C214yesmaximal, complemented
6#21455750C211yesmaximal, characteristic, complemented
7#21455749C212yesmaximal, complemented
8#21455748C211yesmaximal, characteristic, complemented
9#21455747C214yesmaximal, complemented
10#485×D61C214yesmaximal, complemented
11#482×D61C214yesmaximal, complemented
12#428×D61C212yesmaximal, complemented
13#417×D61C212yesmaximal, complemented
14#407×D61C211yesmaximal, characteristic, complemented
15C61×#3093C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C2×M16×D61C2212yes—
19#16840275C2212yes—
20#16840274C2211yescharacteristic
21#16840273C2211yescharacteristic
22#16840272C2212yes—
23#16840271—22no—
24#16840270—21no—
25#16840269C2211yescharacteristic
26#16840268—21no—
27#123×D61—21no—
28C22⋊Q8×D61C2212yes—
29#121×D61C2212yes—
30#120×D61—21no—
31C4×D4×D61—22no—
32C2×#14519736C2211yescharacteristic, complemented
33C2×#14519735C2212yescomplemented
34C2×#14519734—21no—
35C2×#14519733—21no—
36#117×D61—22no—
37#117×D61—22no—
38#117×D61C2214yes—
39#117×D61C2211yescharacteristic
40#117×D61C2214yescomplemented
41C2×C4⋊C4×D61C2212yes—
42C2×C22⋊C4×D61—21no—
43C2×C42×D61—21no—
44#16840106C2214yescomplemented
45#16840105C2214yescomplemented
46#16840104C2214yescomplemented
47#16840103C2214yescomplemented
48#16840102C2214yescomplemented
49#16840101C2214yescomplemented
50#16840100C2214yescomplemented
51#16840089C2214yescomplemented
52#16840088C2214yescomplemented
53#16840087C2214yescomplemented
54#16840086C2214yescomplemented
55#16840085C2214yescomplemented
56#16840084C2214yescomplemented
57#16840083C2214yescomplemented
58#16839805C2212yescomplemented
59#16839804C2212yescomplemented
60#16839803C2214yescomplemented
61#16839802C2212yescomplemented
62#16839801C2214yescomplemented
63#107×D61C2214yescomplemented
64#106×D61C2214yescomplemented
65#16839764C2212yescomplemented
66#16839763C2212yescomplemented
67#16839762C2214yescomplemented
68#16839761C2212yescomplemented
69#16839760C2214yescomplemented
70#103×D61C2214yescomplemented
71#102×D61C2214yescomplemented
72#16839726C2211yescharacteristic, complemented
73#16839725C2212yescomplemented
74#16839724C2214yescomplemented
75C22⋊C8×D61C2214yes—
76C61×#525C2211yescharacteristic
77C2×#117×C61C2211yescharacteristic, complemented
78C61×#485C2214yescomplemented
79C61×#482C2214yescomplemented
80C61×#428C2212yescomplemented
81C61×#417C2212yescomplemented
82C61×#407C2211yescharacteristic, complemented
83C24×D61D411yescharacteristic
84C2×#11758226C2311yescharacteristic
85C2×#11758222—21no—
86C2×#11758222C2311yescharacteristic
87C2×#11758224—21no—
88C2×#11758224C2311yescharacteristic
89#41×D61—28no—
90C2×Q8×D61C2311yescharacteristic
91C2×D4×D61—22no—
92C2×D4×D61—21no—
93C2×D4×D61C2311yescharacteristic
94C23×Dic61D411yescharacteristic
95C22×C4×D61—28no—
96C22×C4×D61—22no—
97C22×C4×D61—21no—
98C22×C4×D61D411yescharacteristic
99C22×C4×D61D412yes—
100C22×C4×D61D412yes—
101C22×C4×D61D411yescharacteristic
102C22×C4×D61C2312yes—
103C22×C4×D61C2312yes—
104C22×C4×D61C2311yescharacteristic
105C22×C4×D61C2311yescharacteristic
106C2×#11758194C2312yes—
107C2×#11758189C2314yes—
108M16×D61—28no—
109C2×C8×D61C2314yes—
110#14519762—22no—
111#14519761—21no—
112#14519760—21no—
113#14519759—22no—
114#14519758—21no—
115#14519757C2312yes—
116#14519756C2312yes—
117#14519755—22no—
118#14519754—22no—
119#14519753C2312yes—
120#14519752C2312yes—
121#14519751C2312yes—
122#14519750—22no—
123#14519749—22no—
124#14519748C2312yes—
125#14519747—21no—
126#14519747—22no—
127#14519746—21no—
128#14519745—21no—
129#14519745—22no—
130C4×D244—22no—
131D4×Dic61—22no—
132#14519739—22no—
133C4×C22⋊D61—22no—
134C4×C22⋊D61—22no—
135#14519737—22no—
136#14519737—22no—
137#14519736—22no—
138#14519736C2314yes—
139#14519736C2311yescharacteristic
140#14519735—22no—
141#14519735—22no—
142#14519735C2314yes—
143#14519735C2314yes—
144#14519735C2312yes—
145#14519734—24no—
146#14519734—24no—
147#14519734—21no—
148#14519733—24no—
149#14519733—24no—
150#14519733—21no—
151C2×C4⋊Dic61C2312yes—
152C2×#11758196—22no—
153C4⋊C4×D61—22no—
154C4⋊C4×D61—22no—
155C4⋊C4×D61—22no—
156C4⋊C4×D61C2314yes—
157C4⋊C4×D61C2314yes—
158C4⋊C4×D61C2312yes—
159C2×C22⋊Dic61—21no—
160C2×#11758198—22no—
161C22⋊C4×D61—24no—
162C22⋊C4×D61—24no—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—22no—
165C22⋊C4×D61—22no—
166C2×C4×Dic61—21no—
167C2×C4×Dic61—22no—
168C42×D61—24no—
169C42×D61—24no—
170C42×D61—21no—
171#14519711C2314yescomplemented
172#14519710C2314yescomplemented
173#14519710C2314yescomplemented
174#14519709C2314yescomplemented
175#14519708C2314yescomplemented
176#14519708C2314yescomplemented
177#14519702C2314yescomplemented
178#14519701C2314yescomplemented
179#14519700C2314yescomplemented
180#14519699C2314yescomplemented
181#14519698C2314yescomplemented
182#14519697C2314yescomplemented
183C22⋊#92418C2314yes—
184#14519689C2314yes—
185#14519689C2314yes—
186C2×#41×C61C2311yescharacteristic
187C23×C4×C61C2311yescharacteristic
188C2×M16×C61C2312yes—
189#123×C61—21no—
190C22⋊Q8×C61C2312yes—
191#121×C61C2312yes—
192#120×C61—21no—
193C4×D4×C61—22no—
194#117×C61—22no—
195#117×C61C2314yes—
196#117×C61C2311yescharacteristic
197C2×C4⋊C4×C61C2312yes—
198C2×C22⋊C4×C61—21no—
199C2×C42×C61—21no—
200#107×C61C2314yescomplemented
201#106×C61C2314yescomplemented
202#103×C61C2314yescomplemented
203#102×C61C2314yescomplemented
204C22⋊C8×C61C2314yes—
205C24×C61C2×D411yescharacteristic
206C23×D61—24no—
207C23×D61—21no—
208C23×D61—44no—
209C23×D61C2×D412yes—
210C23×D61C2×D411yescharacteristic
211C23×D61C2×D412yes—
212C23×D61C2×D411yescharacteristic
213#41×C61—24no—
214C2×Q8×C61C2411yescharacteristic
215C2×D4×C61—21no—
216C2×D4×C61—22no—
217C2×D4×C61C2411yescharacteristic
218C22×C4×C61—24no—
219C22×C4×C61—22no—
220C22×C4×C61—21no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D412yes—
223C22×C4×C61C2412yes—
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—21no—
226C2×C22⋊D61—22no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—22no—
229C2×C22⋊D61—21no—
230C22×Dic61—24no—
231C22×Dic61—22no—
232C22×Dic61—21no—
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D412yes—
235C22×Dic61C2×D412yes—
236C22×Dic61C2×D411yescharacteristic
237#11758226—24no—
238Q8×D61—24no—
239#11758224—24no—
240#11758224—44no—
241D4×D61—24no—
242D4×D61—48no—
243D4×D61—44no—
244#11758222—24no—
245#11758222—44no—
246C2×D244—21no—
247C2×D244—22no—
248C2×D244C2411yescharacteristic
249C2×C4×D61—24no—
250C2×C4×D61—24no—
251C2×C4×D61—24no—
252C2×C4×D61—28no—
253C2×C4×D61—28no—
254C2×C4×D61—28no—
255C2×C4×D61—28no—
256C2×C4×D61—21no—
257C2×C4×D61—24no—
258C2×C4×D61—24no—
259C2×C4×D61—22no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—48no—
263C2×C4×D61—44no—
264C2×C4×D61C2×D412yes—
265C2×C4×D61C2×D412yes—
266C2×C4×D61C2×D412yes—
267C2×C4×D61C2×D412yes—
268C2×C4×D61C2×D412yes—
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61#4118yes—
272C2×C4×D61C2412yes—
273C2×C4×D61C2411yescharacteristic
274C2×C4×D61C2411yescharacteristic
275C2×Dic122—21no—
276C2×Dic122C2411yescharacteristic
277M16×C61—24no—
278C2×C8×C61C2414yes—
279C4⋊C4×C61—22no—
280C4⋊C4×C61—22no—
281C4⋊C4×C61C2414yes—
282C4⋊C4×C61C2412yes—
283C22⋊C4×C61—24no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—22no—
286C22⋊C4×C61—22no—
287C42×C61—24no—
288C42×C61—21no—
289C22⋊Dic61—24no—
290C22⋊Dic61—21no—
291C22⋊Dic61—22no—
292C22⋊Dic61—22no—
293#11758198—24no—
294#11758198—24no—
295#11758198—22no—
296#11758198—22no—
297#11758198—22no—
298#11758198—22no—
299#11758198—22no—
300C4⋊Dic61—22no—
301C4⋊Dic61—22no—
302C4⋊Dic61C2414yes—
303C4⋊Dic61C2412yes—
304#11758196—22no—
305#11758196—24no—
306#11758196—24no—
307#11758196—22no—
308#11758196—22no—
309C4×Dic61—24no—
310C4×Dic61—21no—
311C4×Dic61—24no—
312C4×Dic61—24no—
313C4×Dic61—22no—
314#11758194—24no—
315C2×#92418C2414yes—
316#11758189—28no—
317C8×D61—28no—
318C23×C61—22no—
319C23×C61—21no—
320C23×C61—42no—
321C23×C61C22×D412yes—
322C23×C61C22×D411yescharacteristic
323C22×D61—24no—
324C22×D61—22no—
325C22×D61—24no—
326C22×D61—24no—
327C22×D61—24no—
328C22×D61—24no—
329C22×D61—21no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—416no—
334C22×D61—42no—
335C22×D61—44no—
336C22×D61#12314yes—
337C22×D61C22×D412yes—
338C22×D61C22×D411yescharacteristic
339C22×D61C22×D411yescharacteristic
340Q8×C61—22no—
341D4×C61—22no—
342D4×C61—44no—
343D4×C61—42no—
344C2×C4×C61—22no—
345C2×C4×C61—24no—
346C2×C4×C61—24no—
347C2×C4×C61—24no—
348C2×C4×C61—22no—
349C2×C4×C61—21no—
350C2×C4×C61—44no—
351C2×C4×C61—42no—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C2×#4114yes—
355C2×C4×C61C2511yescharacteristic
356C22⋊D61—44no—
357C22⋊D61—44no—
358C22⋊D61—42no—
359C22⋊D61—42no—
360C22⋊D61—42no—
361C2×Dic61—22no—
362C2×Dic61—24no—
363C2×Dic61—24no—
364C2×Dic61—24no—
365C2×Dic61—22no—
366C2×Dic61—21no—
367C2×Dic61—44no—
368C2×Dic61—42no—
369C2×Dic61#12314yes—
370C2×Dic61C22×D412yes—
371C2×Dic61C22×D411yescharacteristic
372C2×Dic61C22×D411yescharacteristic
373D244—22no—
374D244—44no—
375D244—42no—
376C4×D61—24no—
377C4×D61—24no—
378C4×D61—24no—
379C4×D61—24no—
380C4×D61—24no—
381C4×D61—24no—
382C4×D61—48no—
383C4×D61—42no—
384C4×D61—48no—
385C4×D61—44no—
386C4×D61—42no—
387C4×D61—42no—
388C4×D61#12314yes—
389C4×D61#12314yes—
390C4×D61C2×#4114yes—
391C4×D61C2×#4114yes—
392Dic122—22no—
393Dic122—42no—
394C8×C61—24no—
395#92418—24no—
396C2×#3093—611nomaximal, Sylow
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—44no—
402C22×C61—41no—
403C22×C61—42no—
404C22×C61C2×#12312yes—
405C22×C61C23×D411yescharacteristic
406C2×D61—22no—
407C2×D61—28no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—48no—
412C2×D61—44no—
413C2×D61—48no—
414C2×D61—41no—
415C2×D61—42no—
416C2×D61—84no—
417C2×D61C2×#12312yes—
418C2×D61C2×#12312yes—
419C2×D61#57514yes—
420C4×C61—22no—
421C4×C61—41no—
422C4×C61—44no—
423C4×C61—42no—
424C4×C61C2×#12312yes—
425C4×C61C22×#4112yes—
426Dic61—22no—
427Dic61—41no—
428Dic61—44no—
429Dic61—42no—
430Dic61C2×#12312yes—
431Dic61C2×#12312yes—
432C2×#525—611no—
433C22×#117—611no—
434#3093—614no—
435#3093—614no—
436#3093—612no—
437#3093—612no—
438#3093—611no—
439#3093—611no—
440#3093—611no—
441#3093D6111yescharacteristic, direct product factor
442C2×#485—614no—
443C2×#482—614no—
444C2×#428—612no—
445C2×#417—612no—
446C2×#407—611no—
447C2×C61—22no—
448C2×C61—42no—
449C2×C61—81no—
450C2×C61C22×#12311yescharacteristic
451C2×C61C2×#57512yes—
452D61—22no—
453D61—42no—
454D61—81no—
455D61#309314yesdirect product factor
456C22×#41—611no—
457C24×C4—611no—
458C22×M16—612no—
459#525—611no—
460#525—611no—
461#525—612no—
462#525—612no—
463#525—611no—
464#525—1222no—
465#525—1221no—
466#525—1221no—
467#525C2×D6111yescharacteristic
468C2×#123—1221no—
469C2×C22⋊Q8—612no—
470C2×#121—612no—
471C2×#120—1221no—
472C2×C4×D4—1222no—
473C2×#117—611no—
474C2×#117—614no—
475C2×#117—614no—
476C2×#117—611no—
477C2×#117—612no—
478C2×#117—1221no—
479C2×#117—1221no—
480C2×#117—1222no—
481C2×#117—1222no—
482C2×#117C2×D6111yescharacteristic, complemented
483C22×C4⋊C4—612no—
484C22×C22⋊C4—1221no—
485C22×C42—1221no—
486#485—614no—
487#485—614no—
488#485—614no—
489#485—614no—
490#485—614no—
491#485—614no—
492#485—614no—
493#485C2×D6114yescomplemented
494#482—614no—
495#482—614no—
496#482—614no—
497#482—614no—
498#482—614no—
499#482—614no—
500#482—614no—
501#482C2×D6114yescomplemented
502#428—612no—
503#428—612no—
504#428—612no—
505#428—614no—
506#428—614no—
507#428C2×D6112yescomplemented
508C2×#107—614no—
509C2×#106—614no—
510#417—612no—
511#417—612no—
512#417—612no—
513#417—614no—
514#417—614no—
515#417C2×D6112yescomplemented
516C2×#103—614no—
517C2×#102—614no—
518#407—611no—
519#407—612no—
520#407—614no—
521#407C2×D6111yescharacteristic, complemented
522C2×C22⋊C8—614no—
523C61C2×#309311yescharacteristic, complemented, Sylow
524C25—611no—
525C2×#41—611no—
526C2×#41—611no—
527C2×#41—611no—
528C2×#41—1221no—
529C2×#41—1221no—
530C2×#41—1228no—
531C2×#41C22×D6111yescharacteristic
532C22×Q8—611no—
533C22×D4—611no—
534C22×D4—1222no—
535C22×D4—1221no—
536C23×C4—611no—
537C23×C4—611no—
538C23×C4—612no—
539C23×C4—611no—
540C23×C4—612no—
541C23×C4—611no—
542C23×C4—612no—
543C23×C4—612no—
544C23×C4—611no—
545C23×C4—1228no—
546C23×C4—1221no—
547C23×C4—1222no—
548C23×C4C22×D6111yescharacteristic
549C2×M16—612no—
550C2×M16—614no—
551C2×M16—1228no—
552C2×M16C22×D6112yes—
553C22×C8—614no—
554#123—21no—
555#123—1222no—
556#123—1221no—
557#123—1222no—
558#123—1221no—
559#123—1221no—
560C22⋊Q8—612no—
561C22⋊Q8—612no—
562C22⋊Q8—612no—
563C22⋊Q8—1222no—
564C22⋊Q8—1222no—
565C22⋊Q8C22×D6112yes—
566#121—612no—
567#121—612no—
568#121—612no—
569#121—1222no—
570#121—1222no—
571#121C22×D6112yes—
572#120—21no—
573#120—1221no—
574#120—1222no—
575#120—1222no—
576#120—1221no—
577#120—1221no—
578C4×D4—22no—
579C4×D4—1222no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4—1222no—
583C4×D4—1222no—
584C4×D4—1222no—
585C4×D4—1222no—
586#117—22no—
587#117—614no—
588#117—611no—
589#117—614no—
590#117—614no—
591#117—612no—
592#117—1224no—
593#117—1224no—
594#117—1221no—
595#117—1224no—
596#117—1224no—
597#117—1221no—
598#117—1222no—
599#117—1222no—
600#117—1222no—
601#117C22×D6114yes—
602#117C22×D6111yescharacteristic
603C2×C4⋊C4—612no—
604C2×C4⋊C4—614no—
605C2×C4⋊C4—614no—
606C2×C4⋊C4—612no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4C22×D6112yes—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—1222no—
614C2×C22⋊C4—1224no—
615C2×C22⋊C4—1224no—
616C2×C22⋊C4—1221no—
617C2×C22⋊C4—1222no—
618C2×C22⋊C4—1222no—
619C2×C22⋊C4—1221no—
620C2×C42—21no—
621C2×C42—1224no—
622C2×C42—1224no—
623C2×C42—1221no—
624C2×C42—1222no—
625C2×C42—1221no—
626#107—614no—
627#107—614no—
628#107—614no—
629#107C22×D6114yescomplemented
630#106—614no—
631#106—614no—
632#106—614no—
633#106C22×D6114yescomplemented
634#103—614no—
635#103—614no—
636#103—614no—
637#103C22×D6114yescomplemented
638#102—614no—
639#102—614no—
640#102—614no—
641#102C22×D6114yescomplemented
642C22⋊C8—614no—
643C22⋊C8—614no—
644C22⋊C8—614no—
645C22⋊C8C22×D6114yes—
646C24—611no—
647C24—612no—
648C24—612no—
649C24—611no—
650C24—1224no—
651C24—1221no—
652C24—2444no—
653C24D4×D6111yescharacteristic
654#41—24no—
655#41—1224no—
656#41—1224no—
657#41—1224no—
658#41—2444no—
659#41—2444no—
660C2×Q8—611no—
661C2×Q8—1221no—
662C2×Q8—1224no—
663C2×Q8C23×D6111yescharacteristic
664C2×D4—22no—
665C2×D4—21no—
666C2×D4—611no—
667C2×D4—1222no—
668C2×D4—1221no—
669C2×D4—1224no—
670C2×D4—1221no—
671C2×D4—1222no—
672C2×D4—1221no—
673C2×D4—1222no—
674C2×D4—1221no—
675C2×D4—2444no—
676C2×D4—2448no—
677C2×D4C23×D6111yescharacteristic
678C22×C4—24no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—618no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—612no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—612no—
695C22×C4—612no—
696C22×C4—1224no—
697C22×C4—1228no—
698C22×C4—1228no—
699C22×C4—1228no—
700C22×C4—1228no—
701C22×C4—1221no—
702C22×C4—1224no—
703C22×C4—1224no—
704C22×C4—1224no—
705C22×C4—1222no—
706C22×C4—1221no—
707C22×C4—1224no—
708C22×C4—1221no—
709C22×C4—1224no—
710C22×C4—1222no—
711C22×C4—1221no—
712C22×C4—2444no—
713C22×C4—2448no—
714C22×C4D4×D6111yescharacteristic
715C22×C4D4×D6112yes—
716C22×C4C23×D6112yes—
717C22×C4C23×D6111yescharacteristic
718M16—24no—
719M16—1228no—
720M16—1224no—
721C2×C8—614no—
722C2×C8—1228no—
723C2×C8C23×D6114yes—
724C4⋊C4—22no—
725C4⋊C4—22no—
726C4⋊C4—614no—
727C4⋊C4—612no—
728C4⋊C4—1224no—
729C4⋊C4—1224no—
730C4⋊C4—1222no—
731C4⋊C4—1222no—
732C4⋊C4—1222no—
733C4⋊C4—1222no—
734C4⋊C4—1222no—
735C4⋊C4C23×D6114yes—
736C4⋊C4C23×D6112yes—
737C22⋊C4—24no—
738C22⋊C4—21no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—1222no—
742C22⋊C4—1224no—
743C22⋊C4—1224no—
744C22⋊C4—1222no—
745C22⋊C4—1222no—
746C22⋊C4—1222no—
747C22⋊C4—1222no—
748C22⋊C4—1224no—
749C22⋊C4—1221no—
750C22⋊C4—1222no—
751C22⋊C4—1222no—
752C42—24no—
753C42—21no—
754C42—1224no—
755C42—1224no—
756C42—1222no—
757C42—1224no—
758C42—1221no—
759C23—22no—
760C23—21no—
761C23—42no—
762C23—611no—
763C23—614no—
764C23—611no—
765C23—612no—
766C23—1224no—
767C23—1224no—
768C23—1224no—
769C23—1224no—
770C23—1224no—
771C23—1222no—
772C23—1221no—
773C23—2442no—
774C23—2442no—
775C23—2442no—
776C23—2442no—
777C23—2444no—
778C23—24416no—
779C23C2×D4×D6112yes—
780C23C2×D4×D6111yescharacteristic
781Q8—22no—
782Q8—1222no—
783Q8—2442no—
784D4—22no—
785D4—44no—
786D4—42no—
787D4—1222no—
788D4—2442no—
789D4—2444no—
790D4—2442no—
791D4—2444no—
792D4—2442no—
793D4—2444no—
794D4—2442no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—614no—
804C2×C4—611no—
805C2×C4—611no—
806C2×C4—614no—
807C2×C4—614no—
808C2×C4—614no—
809C2×C4—614no—
810C2×C4—612no—
811C2×C4—1224no—
812C2×C4—1224no—
813C2×C4—1224no—
814C2×C4—1224no—
815C2×C4—1224no—
816C2×C4—1224no—
817C2×C4—1222no—
818C2×C4—1224no—
819C2×C4—1224no—
820C2×C4—1224no—
821C2×C4—1222no—
822C2×C4—1221no—
823C2×C4—2442no—
824C2×C4—2448no—
825C2×C4—2442no—
826C2×C4—2444no—
827C2×C4—2448no—
828C2×C4—2442no—
829C2×C4—2444no—
830C2×C4—2442no—
831C2×C4C2×D4×D6112yes—
832C2×C4C2×D4×D6111yescharacteristic
833C2×C4#41×D6114yes—
834C2×C4C24×D6111yescharacteristic
835C8—24no—
836C8—1224no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—44no—
842C22—42no—
843C22—41no—
844C22—614no—
845C22—612no—
846C22—612no—
847C22—1228no—
848C22—1222no—
849C22—1222no—
850C22—1222no—
851C22—1222no—
852C22—4884no—
853C22—2444no—
854C22—2448no—
855C22—2448no—
856C22—2442no—
857C22—2441no—
858C22#123×D6112yes—
859C22C22×D4×D6111yescharacteristic
860C4—22no—
861C4—44no—
862C4—42no—
863C4—41no—
864C4—612no—
865C4—612no—
866C4—1222no—
867C4—2444no—
868C4—2442no—
869C4—2441no—
870C4#123×D6112yes—
871C4C2×#41×D6112yes—
872C2—22no—
873C2—42no—
874C2—81no—
875C2—614no—
876C2—1222no—
877C2—4881no—
878C2—2442no—
879C2C2×#123×D6111yescharacteristic
880C2#575×D6112yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3093C2
socleC22×C61C23×D4
prime radical#525×D61C2
hypercenter#3093D61
hypocenterC61C2×#3093
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3093

Complements

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

NH ≅ G/Ntype
2. C2×#117×D61C2semidirect
3. #21455753C2semidirect
4. #21455752C2semidirect
5. #21455751C2semidirect
6. #21455750C2semidirect
7. #21455749C2semidirect
8. #21455748C2semidirect
9. #21455747C2semidirect
10. #485×D61C2semidirect
11. #482×D61C2semidirect
12. #428×D61C2semidirect
13. #417×D61C2semidirect
14. #407×D61C2semidirect
15. C61×#3093C2semidirect
32. C2×#14519736C22semidirect
33. C2×#14519735C22semidirect
40. #117×D61C22semidirect
44. #16840106C22semidirect
45. #16840105C22semidirect
46. #16840104C22semidirect
47. #16840103C22semidirect
48. #16840102C22semidirect
49. #16840101C22semidirect
50. #16840100C22semidirect
51. #16840089C22semidirect
52. #16840088C22semidirect
53. #16840087C22semidirect
54. #16840086C22semidirect
55. #16840085C22semidirect
56. #16840084C22semidirect
57. #16840083C22semidirect
58. #16839805C22semidirect
59. #16839804C22semidirect
60. #16839803C22semidirect
61. #16839802C22semidirect
62. #16839801C22semidirect
63. #107×D61C22semidirect
64. #106×D61C22semidirect
65. #16839764C22semidirect
66. #16839763C22semidirect
67. #16839762C22semidirect
68. #16839761C22semidirect
69. #16839760C22semidirect
70. #103×D61C22semidirect
71. #102×D61C22semidirect
72. #16839726C22semidirect
73. #16839725C22semidirect
74. #16839724C22semidirect
77. C2×#117×C61C22semidirect
78. C61×#485C22semidirect
79. C61×#482C22semidirect
80. C61×#428C22semidirect
81. C61×#417C22semidirect
82. C61×#407C22semidirect
171. #14519711C23semidirect
172. #14519710C23semidirect
173. #14519710C23semidirect
174. #14519709C23semidirect
175. #14519708C23semidirect
176. #14519708C23semidirect
177. #14519702C23semidirect
178. #14519701C23semidirect
179. #14519700C23semidirect
180. #14519699C23semidirect
181. #14519698C23semidirect
182. #14519697C23semidirect
200. #107×C61C23semidirect
201. #106×C61C23semidirect
202. #103×C61C23semidirect
203. #102×C61C23semidirect
441. #3093D61direct (N × H)
455. D61#3093direct (N × H)
482. C2×#117C2×D61semidirect
493. #485C2×D61semidirect
501. #482C2×D61semidirect
507. #428C2×D61semidirect
515. #417C2×D61semidirect
521. #407C2×D61semidirect
523. C61C2×#3093semidirect
629. #107C22×D61semidirect
633. #106C22×D61semidirect
637. #103C22×D61semidirect
641. #102C22×D61semidirect

Maximal subgroups

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

subgroupindex
#525×D612
C2×#117×D612
#214557532
#214557522
#214557512
#214557502
#214557492
#214557482
#214557472
#485×D612
#482×D612
#428×D612
#417×D612
#407×D612
C61×#30932
C2×#309361