Finite Group Databasebeta

← #30547625

Subgroups — #30547625

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459222C211yesmaximal, characteristic, complemented
2C2×#16840234C211yesmaximal, characteristic
3#21455649C214yesmaximal, complemented
4#21455647C214yesmaximal, complemented
5#21455645C214yesmaximal, complemented
6#21455643C214yesmaximal, complemented
7#21455618C211yesmaximal, characteristic, complemented
8#21455616C211yesmaximal, characteristic, complemented
9#21455615C212yesmaximal, complemented
10#21455613C212yesmaximal, complemented
11#21455612C211yesmaximal, characteristic, complemented
12#21454406C212yesmaximal, complemented
13#21454381C211yesmaximal, characteristic, complemented
14#418×D61C212yesmaximal
15C61×#3077C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C2×M16×D61C2212yes—
18#16840392C2212yescomplemented
19#16840392C2212yescomplemented
20#16840391—21no—
21#16840391—21no—
22#16840389C2212yescomplemented
23#16840389C2212yescomplemented
24#16840387—21no—
25#16840387—21no—
26#16840319C2211yescharacteristic, complemented
27#16840316—22no—
28#16840316—22no—
29#16840315C2212yescomplemented
30#16840234—22no—
31#16840234—22no—
32#16840234C2214yes—
33#16840234C2214yes—
34C2×C4×D244C2211yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×#14519737—21no—
39C2×#14519735C2211yescharacteristic
40C2×#14519734C2211yescharacteristic
41#117×D61C2212yes—
42C22×#11758198—21no—
43C2×C22⋊C4×D61—21no—
44#16840065C2214yescomplemented
45#16840064C2214yescomplemented
46#16840063C2214yescomplemented
47#16840062C2214yescomplemented
48#16840061C2214yescomplemented
49#16840060C2214yescomplemented
50#16840059C2214yescomplemented
51#16840053C2212yescomplemented
52#16840052C2212yescomplemented
53#16840051C2214yescomplemented
54#16840050C2214yescomplemented
55#16840049C2212yescomplemented
56#16840043C2212yescomplemented
57#16840042C2212yescomplemented
58#16840041C2214yescomplemented
59#16840040C2214yescomplemented
60#16840039C2212yescomplemented
61#16839805C2212yescomplemented
62#16839804C2212yescomplemented
63#16839803C2214yescomplemented
64#16839802C2212yescomplemented
65#16839801C2214yescomplemented
66#16839799C2214yescomplemented
67#16839797C2214yescomplemented
68#16839787C2214yescomplemented
69#16839787C2214yescomplemented
70#16839786C2211yescharacteristic, complemented
71#16839785C2212yescomplemented
72#16839768C2212yes—
73#16839767C2212yes—
74#16839766C2212yes—
75#16839765C2214yes—
76#16839765C2214yes—
77#102×D61C2214yes—
78#102×D61C2214yes—
79C61×#533C2211yescharacteristic, complemented
80C2×C4×D4×C61C2211yescharacteristic
81C61×#478C2214yescomplemented
82C61×#476C2212yescomplemented
83C61×#474C2212yescomplemented
84C61×#428C2212yescomplemented
85C61×#423C2211yescharacteristic, complemented
86C61×#418C2212yes—
87C24×D61—21no—
88C22×D244C2311yescharacteristic
89C22×C22⋊D61—21no—
90C2×D4×D61—22no—
91C2×D4×D61—24no—
92C2×D4×D61Q818yescomplemented
93C2×D4×D61C2314yes—
94C23×Dic61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98C2×#11758194C2312yes—
99C2×#11758189C2314yes—
100M16×D61—28no—
101C2×C8×D61C2314yes—
102#14519777C2311yescharacteristic, complemented
103#14519777C2311yescharacteristic, complemented
104#14519776—22no—
105#14519776—22no—
106#14519776C2312yescomplemented
107#14519776C2312yescomplemented
108#14519775—22no—
109#14519775—22no—
110#14519769C2312yescomplemented
111#14519768C2312yescomplemented
112#14519768C2312yescomplemented
113#14519767—22no—
114#14519767—22no—
115#14519767—22no—
116#14519767—22no—
117#14519757—22no—
118#14519757—22no—
119#14519756—21no—
120#14519756—21no—
121#14519755—22no—
122#14519755—22no—
123#14519755—22no—
124#14519755—22no—
125#14519754—22no—
126#14519754—22no—
127#14519753—22no—
128#14519753—22no—
129C4×Dic122—21no—
130C4×Dic122—21no—
131C4×Dic122—22no—
132C4×Dic122—22no—
133C4×D244—21no—
134C4×D244—21no—
135C4×D244C2312yes—
136C4×D244C2312yes—
137D4×Dic61—22no—
138D4×Dic61C2314yes—
139#14519739—22no—
140#14519739C2314yes—
141C4×C22⋊D61—24no—
142C4×C22⋊D61—24no—
143#14519737—24no—
144#14519737—24no—
145#14519736C2312yes—
146#14519735—22no—
147#14519735C2312yes—
148#14519735C2312yes—
149#14519735C2314yes—
150#14519734—22no—
151#14519734D412yes—
152#14519734D412yes—
153#14519734C2312yes—
154#14519734C2312yes—
155#14519733—22no—
156C2×C4⋊Dic61C2311yescharacteristic
157C2×#11758196D411yescharacteristic
158C2×#11758196D411yescharacteristic
159C4⋊C4×D61C2312yes—
160C4⋊C4×D61C2312yes—
161C2×C22⋊Dic61—21no—
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—24no—
166C2×#11758198—24no—
167C2×#11758198D411yescharacteristic
168C2×#11758198D411yescharacteristic
169C22⋊C4×D61—22no—
170C22⋊C4×D61—24no—
171C22⋊C4×D61—24no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61C2311yescharacteristic
174C42×D61—22no—
175#14519711C2314yescomplemented
176#14519710C2314yescomplemented
177#14519710C2314yescomplemented
178#14519709C2314yescomplemented
179#14519708C2314yescomplemented
180#14519708C2314yescomplemented
181C4⋊#92418C2312yescomplemented
182C4⋊#92418C2312yescomplemented
183#14519706C2314yescomplemented
184#14519706C2314yescomplemented
185#14519699C2314yes—
186#14519699C2314yes—
187#14519698C2314yes—
188#14519698C2314yes—
189#14519697C2314yes—
190#14519697C2314yes—
191C22×D4×C61C2311yescharacteristic
192C23×C4×C61—21no—
193C2×M16×C61C2312yes—
194C4⋊Q8×C61C2311yescharacteristic, complemented
195C4⋊Q8×C61C2311yescharacteristic, complemented
196#125×C61C2312yescomplemented
197C22⋊Q8×C61—21no—
198C22⋊Q8×C61—21no—
199C4×Q8×C61—21no—
200C4×Q8×C61—21no—
201C4×D4×C61—21no—
202C4×D4×C61—21no—
203C4×D4×C61C2312yes—
204C4×D4×C61C2312yes—
205#117×C61C2312yes—
206C2×C4⋊C4×C61C2311yescharacteristic
207C2×C22⋊C4×C61—21no—
208C2×C42×C61C2311yescharacteristic
209#107×C61C2314yescomplemented
210#106×C61C2314yescomplemented
211C4⋊C8×C61C2312yescomplemented
212C4⋊C8×C61C2312yescomplemented
213#102×C61C2314yes—
214#102×C61C2314yes—
215C24×C61—21no—
216C23×D61—21no—
217C23×D61—28no—
218C23×D61—24no—
219C23×D61—82no—
220C23×D61—82no—
221C23×D61C2×D411yescharacteristic
222C2×Q8×C61—21no—
223C2×Q8×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—22no—
226C2×D4×C61C2×Q814yes—
227C2×D4×C61C2412yes—
228C22×C4×C61—21no—
229C22×C4×C61—22no—
230C22×C4×C61—22no—
231C22×C4×C61—82no—
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C2×C22⋊D61—28no—
236C2×C22⋊D61—24no—
237C22×Dic61—21no—
238C22×Dic61—24no—
239C22×Dic61—82no—
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243D4×D61—216no—
244D4×D61—28no—
245D4×D61C2×Q8116yes—
246C2×D244—21no—
247C2×D244—22no—
248C2×D244C2×Q814yes—
249C2×D244C2412yes—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×C4×D61—22no—
253C2×C4×D61—22no—
254C2×C4×D61—24no—
255C2×C4×D61—82no—
256C2×C4×D61—82no—
257C2×C4×D61C2×D412yes—
258C2×C4×D61C2×Q814yes—
259C2×C4×D61#4114yes—
260C2×C4×D61C2412yes—
261C2×Dic122—21no—
262C2×Dic122—21no—
263C2×Dic122—22no—
264C2×Dic122—22no—
265M16×C61—24no—
266C2×C8×C61C2414yes—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—22no—
269C4⋊C4×C61—22no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61C2412yes—
273C4⋊C4×C61C2412yes—
274C4⋊C4×C61C2412yes—
275C22⋊C4×C61—22no—
276C22⋊C4×C61—22no—
277C22⋊C4×C61—22no—
278C42×C61—22no—
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2411yescharacteristic
282C42×C61C2411yescharacteristic
283C22⋊Dic61—22no—
284C22⋊Dic61—24no—
285#11758198—24no—
286#11758198—22no—
287#11758198—22no—
288#11758198—22no—
289#11758198—22no—
290#11758198—24no—
291#11758198C2×D412yes—
292#11758198C2×D412yes—
293#11758198C2×D412yes—
294#11758198C2×D412yes—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61—22no—
299C4⋊Dic61—22no—
300C4⋊Dic61C2412yes—
301C4⋊Dic61C2412yes—
302C4⋊Dic61C2412yes—
303#11758196—22no—
304#11758196—22no—
305#11758196—22no—
306#11758196—22no—
307#11758196—22no—
308#11758196—22no—
309#11758196—22no—
310#11758196—22no—
311#11758196C2×D412yes—
312#11758196C2×D412yes—
313#11758196C2×D412yes—
314#11758196C2×D412yes—
315C4×Dic61—22no—
316C4×Dic61—22no—
317C4×Dic61—22no—
318C4×Dic61—24no—
319C4×Dic61C2×D412yes—
320C4×Dic61C2412yes—
321#11758194—24no—
322C2×#92418C2414yes—
323#11758189—28no—
324C8×D61—28no—
325C23×C61—24no—
326C23×C61—22no—
327C23×C61—42no—
328C23×C61—42no—
329C23×C61C22×D411yescharacteristic
330C22×D61—24no—
331C22×D61—22no—
332C22×D61—216no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—84no—
338C22×D61—84no—
339C22×D61—816no—
340C22×D61C22⋊Q814yes—
341C22×D61C22×D412yes—
342Q8×C61—81no—
343Q8×C61—81no—
344D4×C61—24no—
345D4×C61—22no—
346D4×C61C22×Q814yes—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—42no—
353C2×C4×C61—82no—
354C2×C4×C61—82no—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×Q812yes—
361C2×C4×C61C2×#4112yes—
362C2×C4×C61C2511yescharacteristic
363C22⋊D61—216no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—42no—
370C2×Dic61—84no—
371C2×Dic61C22⋊Q814yes—
372C2×Dic61C22×D412yes—
373C2×Dic61C22×D412yes—
374C2×Dic61C22×D412yes—
375D244—24no—
376D244—22no—
377D244C22×Q814yes—
378C4×D61—84no—
379C4×D61—82no—
380C4×D61—82no—
381C4×D61—82no—
382C4×D61—82no—
383C4×D61C22⋊Q818yes—
384C4×D61C22×Q814yes—
385C4×D61C2×#4114yes—
386Dic122—82no—
387Dic122—82no—
388Dic122—81no—
389Dic122—81no—
390C8×C61—24no—
391#92418—24no—
392#60490—611nomaximal, Sylow
393C22×C61—21no—
394C22×C61—21no—
395C22×C61—24no—
396C22×C61—48no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61C2×C22⋊Q812yes—
400C22×C61C23×D411yescharacteristic
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—24no—
404C2×D61—44no—
405C2×D61—48no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—816no—
409C2×D61C2×C22⋊Q814yes—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—42no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61C2×C22⋊Q812yes—
418C4×C61C23×Q811yescharacteristic
419C4×C61C22×#4111yescharacteristic
420Dic61—22no—
421Dic61—22no—
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425Dic61C2×C22⋊Q814yes—
426#3458—611no—
427C2×#518—611no—
428#3081—614no—
429#3081—614no—
430#3081—614no—
431#3081—614no—
432#3077—612no—
433#3077—611no—
434#3077—612no—
435#3077—611no—
436#3077—611no—
437#3077D6111yescharacteristic, complemented
438#2911—612no—
439#2905—611no—
440C2×#418—612no—
441C2×C61—22no—
442C2×C61—44no—
443C2×C61C22×C22⋊Q811yescharacteristic
444C2×C61#358511yescharacteristic
445C2×C61#358511yescharacteristic
446D61—24no—
447D61—44no—
448C23×D4—611no—
449C22×M16—612no—
450#544—612no—
451#544—612no—
452#544—612no—
453#544—612no—
454#544—1221no—
455#544—1221no—
456#543—1221no—
457#543—1221no—
458#533—612no—
459#533—611no—
460#533—1222no—
461#533—1222no—
462#533C2×D6111yescharacteristic, complemented
463#518—614no—
464#518—614no—
465#518—1222no—
466#518—1222no—
467C2×C4×D4—611no—
468C2×C4×D4—611no—
469C2×C4×D4—611no—
470C2×C4×D4—1221no—
471C2×C4×D4—1221no—
472C2×C4×D4C2×D6111yescharacteristic
473C2×#117—611no—
474C2×#117—612no—
475C2×#117—611no—
476C22×C22⋊C4—1221no—
477C22×C22⋊C4—1221no—
478#478—614no—
479#478—614no—
480#478—614no—
481#478—614no—
482#478—614no—
483#478—614no—
484#478—614no—
485#478C2×D6114yescomplemented
486#476—612no—
487#476—612no—
488#476—614no—
489#476—612no—
490#476—614no—
491#476C2×D6112yescomplemented
492#474—612no—
493#474—612no—
494#474—614no—
495#474—612no—
496#474—614no—
497#474C2×D6112yescomplemented
498#428—612no—
499#428—612no—
500#428—612no—
501#428—614no—
502#428—614no—
503#428C2×D6112yescomplemented
504#427—614no—
505#427—614no—
506#424—614no—
507#424—614no—
508#423—612no—
509#423—611no—
510#423C2×D6111yescharacteristic, complemented
511#418—612no—
512#418—612no—
513#418—612no—
514#418—614no—
515#418—614no—
516#418C2×D6112yes—
517C2×#102—614no—
518C2×#102—614no—
519C61#6049011yescharacteristic, complemented, Sylow
520C25—1221no—
521C22×D4—618no—
522C22×D4—614no—
523C22×D4—611no—
524C22×D4—1222no—
525C22×D4—1224no—
526C22×D4—1221no—
527C22×D4C22×D6111yescharacteristic
528C23×C4—21no—
529C23×C4—611no—
530C23×C4—1221no—
531C23×C4—1221no—
532C23×C4—1221no—
533C2×M16—612no—
534C2×M16—614no—
535C2×M16—1228no—
536C2×M16C22×D6112yes—
537C22×C8—614no—
538C4⋊Q8—612no—
539C4⋊Q8—612no—
540C4⋊Q8—611no—
541C4⋊Q8—611no—
542C4⋊Q8—1222no—
543C4⋊Q8—1222no—
544C4⋊Q8—1222no—
545C4⋊Q8—1222no—
546C4⋊Q8C22×D6111yescharacteristic, complemented
547C4⋊Q8C22×D6111yescharacteristic, complemented
548#125—612no—
549#125—612no—
550#125—612no—
551#125—1222no—
552#125—1222no—
553#125—1222no—
554#125—1222no—
555#125C22×D6112yescomplemented
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—1222no—
559C22⋊Q8—1222no—
560C22⋊Q8—1222no—
561C22⋊Q8—1222no—
562C22⋊Q8—1222no—
563C22⋊Q8—1222no—
564C22⋊Q8—1222no—
565C22⋊Q8—1222no—
566C22⋊Q8—1222no—
567C22⋊Q8—1222no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—1222no—
573C4×Q8—1222no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—614no—
579C4×D4—614no—
580C4×D4—612no—
581C4×D4—612no—
582C4×D4—1222no—
583C4×D4—1222no—
584C4×D4—1224no—
585C4×D4—1224no—
586C4×D4—1224no—
587C4×D4—1224no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4C22×D6112yes—
591C4×D4C22×D6112yes—
592#117—612no—
593#117—612no—
594#117—612no—
595#117—612no—
596#117—612no—
597#117—614no—
598#117—612no—
599#117—612no—
600#117—1222no—
601#117—1222no—
602#117—1222no—
603#117C22×D6112yes—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—612no—
608C2×C4⋊C4—612no—
609C2×C4⋊C4C22×D6111yescharacteristic
610C2×C22⋊C4—21no—
611C2×C22⋊C4—611no—
612C2×C22⋊C4—611no—
613C2×C22⋊C4—1224no—
614C2×C22⋊C4—1224no—
615C2×C22⋊C4—1222no—
616C2×C22⋊C4—1224no—
617C2×C22⋊C4—1224no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C42—611no—
623C2×C42—1222no—
624C2×C42—1221no—
625C2×C42C22×D6111yescharacteristic
626#107—614no—
627#107—614no—
628#107—614no—
629#107C22×D6114yescomplemented
630#106—614no—
631#106—614no—
632#106—614no—
633#106C22×D6114yescomplemented
634C4⋊C8—614no—
635C4⋊C8—614no—
636C4⋊C8—612no—
637C4⋊C8—612no—
638C4⋊C8C22×D6112yescomplemented
639C4⋊C8C22×D6112yescomplemented
640#102—614no—
641#102—614no—
642#102—614no—
643#102—614no—
644#102—614no—
645#102—614no—
646#102C22×D6114yes—
647#102C22×D6114yes—
648C24—21no—
649C24—611no—
650C24—1224no—
651C24—1228no—
652C24—1221no—
653C24—4882no—
654C24—4882no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—1222no—
658C2×Q8—1222no—
659C2×Q8—1221no—
660C2×Q8—1221no—
661C2×D4—21no—
662C2×D4—22no—
663C2×D4—6116no—
664C2×D4—614no—
665C2×D4—612no—
666C2×D4—12216no—
667C2×D4—1228no—
668C2×D4—1224no—
669C2×D4—1228no—
670C2×D4—1221no—
671C2×D4—1222no—
672C2×D4Q8×D6114yes—
673C2×D4C23×D6112yes—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—82no—
678C22×C4—611no—
679C22×C4—612no—
680C22×C4—614no—
681C22×C4—614no—
682C22×C4—612no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—1224no—
686C22×C4—1222no—
687C22×C4—1222no—
688C22×C4—1224no—
689C22×C4—1221no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—4882no—
693C22×C4—4882no—
694C22×C4—4882no—
695C22×C4D4×D6111yescharacteristic
696C22×C4D4×D6111yescharacteristic
697C22×C4C23×D6111yescharacteristic
698M16—24no—
699M16—1228no—
700M16—1224no—
701C2×C8—614no—
702C2×C8—1228no—
703C2×C8C23×D6114yes—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—612no—
710C4⋊C4—612no—
711C4⋊C4—612no—
712C4⋊C4—612no—
713C4⋊C4—612no—
714C4⋊C4—612no—
715C4⋊C4—612no—
716C4⋊C4—1222no—
717C4⋊C4—1222no—
718C4⋊C4—1222no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4—1222no—
724C4⋊C4—1221no—
725C4⋊C4—1222no—
726C4⋊C4—1222no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4C23×D6112yes—
730C4⋊C4C23×D6112yes—
731C4⋊C4C23×D6112yes—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—612no—
736C22⋊C4—612no—
737C22⋊C4—612no—
738C22⋊C4—612no—
739C22⋊C4—1224no—
740C22⋊C4—1224no—
741C22⋊C4—1222no—
742C22⋊C4—1222no—
743C22⋊C4—1224no—
744C22⋊C4—1222no—
745C22⋊C4—1222no—
746C22⋊C4—1222no—
747C42—22no—
748C42—612no—
749C42—612no—
750C42—1224no—
751C42—1222no—
752C42—1222no—
753C42—1222no—
754C42D4×D6111yescharacteristic
755C42D4×D6111yescharacteristic
756C42C23×D6111yescharacteristic
757C42C23×D6111yescharacteristic
758C23—24no—
759C23—22no—
760C23—42no—
761C23—42no—
762C23—612no—
763C23—614no—
764C23—12216no—
765C23—1224no—
766C23—1222no—
767C23—4884no—
768C23—4884no—
769C23—48816no—
770C23—2441no—
771C23—2441no—
772C23—2442no—
773C23—2442no—
774C23C2×D4×D6111yescharacteristic
775Q8—81no—
776Q8—81no—
777Q8—4881no—
778Q8—4881no—
779Q8—4882no—
780Q8—4882no—
781D4—24no—
782D4—22no—
783D4—614no—
784D4—12216no—
785D4—1224no—
786D4—1222no—
787D4C2×Q8×D6114yes—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—82no—
795C2×C4—82no—
796C2×C4—614no—
797C2×C4—612no—
798C2×C4—618no—
799C2×C4—614no—
800C2×C4—614no—
801C2×C4—612no—
802C2×C4—612no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—4882no—
807C2×C4—4882no—
808C2×C4—4884no—
809C2×C4—4882no—
810C2×C4—4882no—
811C2×C4—4884no—
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×C4C2×Q8×D6112yes—
821C2×C4#41×D6112yes—
822C2×C4C24×D6111yescharacteristic
823C8—24no—
824C8—1224no—
825C22—21no—
826C22—21no—
827C22—24no—
828C22—48no—
829C22—42no—
830C22—42no—
831C22—614no—
832C22—1222no—
833C22—1222no—
834C22—1224no—
835C22—48816no—
836C22—2444no—
837C22—2448no—
838C22—2442no—
839C22—2442no—
840C22C22⋊Q8×D6112yes—
841C22C22×D4×D6111yescharacteristic
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—614no—
850C4—1222no—
851C4—1222no—
852C4—2442no—
853C4—2442no—
854C4—2442no—
855C4C22⋊Q8×D6112yes—
856C4C22×Q8×D6111yescharacteristic
857C4C2×#41×D6111yescharacteristic
858C2—22no—
859C2—44no—
860C2—1224no—
861C2—2444no—
862C2C2×C22⋊Q8×D6111yescharacteristic
863C2#2146059511yescharacteristic
864C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3077C2
socleC22×C61C23×D4
prime radicalC22×D4×D61C22
hypercenter#3077D61
hypocenterC61#60490
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. #21459222C2semidirect
3. #21455649C2semidirect
4. #21455647C2semidirect
5. #21455645C2semidirect
6. #21455643C2semidirect
7. #21455618C2semidirect
8. #21455616C2semidirect
9. #21455615C2semidirect
10. #21455613C2semidirect
11. #21455612C2semidirect
12. #21454406C2semidirect
13. #21454381C2semidirect
15. C61×#3077C2semidirect
18. #16840392C22semidirect
19. #16840392C22semidirect
22. #16840389C22semidirect
23. #16840389C22semidirect
26. #16840319C22semidirect
29. #16840315C22semidirect
44. #16840065C22semidirect
45. #16840064C22semidirect
46. #16840063C22semidirect
47. #16840062C22semidirect
48. #16840061C22semidirect
49. #16840060C22semidirect
50. #16840059C22semidirect
51. #16840053C22semidirect
52. #16840052C22semidirect
53. #16840051C22semidirect
54. #16840050C22semidirect
55. #16840049C22semidirect
56. #16840043C22semidirect
57. #16840042C22semidirect
58. #16840041C22semidirect
59. #16840040C22semidirect
60. #16840039C22semidirect
61. #16839805C22semidirect
62. #16839804C22semidirect
63. #16839803C22semidirect
64. #16839802C22semidirect
65. #16839801C22semidirect
66. #16839799C22semidirect
67. #16839797C22semidirect
68. #16839787C22semidirect
69. #16839787C22semidirect
70. #16839786C22semidirect
71. #16839785C22semidirect
79. C61×#533C22semidirect
81. C61×#478C22semidirect
82. C61×#476C22semidirect
83. C61×#474C22semidirect
84. C61×#428C22semidirect
85. C61×#423C22semidirect
92. C2×D4×D61Q8semidirect
102. #14519777C23semidirect
103. #14519777C23semidirect
106. #14519776C23semidirect
107. #14519776C23semidirect
110. #14519769C23semidirect
111. #14519768C23semidirect
112. #14519768C23semidirect
175. #14519711C23semidirect
176. #14519710C23semidirect
177. #14519710C23semidirect
178. #14519709C23semidirect
179. #14519708C23semidirect
180. #14519708C23semidirect
181. C4⋊#92418C23semidirect
182. C4⋊#92418C23semidirect
183. #14519706C23semidirect
184. #14519706C23semidirect
194. C4⋊Q8×C61C23semidirect
195. C4⋊Q8×C61C23semidirect
196. #125×C61C23semidirect
209. #107×C61C23semidirect
210. #106×C61C23semidirect
211. C4⋊C8×C61C23semidirect
212. C4⋊C8×C61C23semidirect
437. #3077D61semidirect
462. #533C2×D61semidirect
485. #478C2×D61semidirect
491. #476C2×D61semidirect
497. #474C2×D61semidirect
503. #428C2×D61semidirect
510. #423C2×D61semidirect
519. C61#60490semidirect
546. C4⋊Q8C22×D61semidirect
547. C4⋊Q8C22×D61semidirect
555. #125C22×D61semidirect
629. #107C22×D61semidirect
633. #106C22×D61semidirect
638. C4⋊C8C22×D61semidirect
639. C4⋊C8C22×D61semidirect

Maximal subgroups

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

subgroupindex
#214592222
C2×#168402342
#214556492
#214556472
#214556452
#214556432
#214556182
#214556162
#214556152
#214556132
#214556122
#214544062
#214543812
#418×D612
C61×#30772
#6049061