Finite Group Databasebeta

← #30547632

Subgroups — #30547632

Order 15616.

1962 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459222C211yesmaximal, characteristic
2C2×#16840238C211yesmaximal, characteristic
3#21455660C214yesmaximal, complemented
4#21455658C214yesmaximal, complemented
5#21455656C214yesmaximal, complemented
6#21455654C214yesmaximal, complemented
7#21455626C211yesmaximal, characteristic, complemented
8#21455624C211yesmaximal, characteristic, complemented
9#21455623C212yesmaximal, complemented
10#21455621C212yesmaximal, complemented
11#21455620C211yesmaximal, characteristic, complemented
12#21454406C212yesmaximal
13#21454381C211yesmaximal, characteristic
14#419×D61C212yesmaximal
15C61×#3078C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C2×M16×D61C2212yes—
18#16840392C2212yes—
19#16840392C2212yes—
20#16840391—21no—
21#16840391—21no—
22#16840389C2212yes—
23#16840389C2212yes—
24#16840387—21no—
25#16840387—21no—
26#16840319C2211yescharacteristic
27#16840316—22no—
28#16840316—22no—
29#16840315C2212yes—
30#16840238—22no—
31#16840238—22no—
32#16840238C2214yes—
33#16840238C2214yes—
34C2×Q8×Dic61C2211yescharacteristic
35C2×C4×Dic122—21no—
36C2×C4×Dic122C2211yescharacteristic
37C2×#14519742—21no—
38C2×#14519742C2211yescharacteristic
39C2×#14519735—21no—
40C2×#14519735C2211yescharacteristic
41C2×#14519734—21no—
42C2×#14519734C2211yescharacteristic
43#117×D61C2212yes—
44#16840072C2214yescomplemented
45#16840071C2214yescomplemented
46#16840070C2214yescomplemented
47#16840069C2214yescomplemented
48#16840068C2214yescomplemented
49#16840067C2214yescomplemented
50#16840066C2214yescomplemented
51#16840058C2212yescomplemented
52#16840057C2212yescomplemented
53#16840056C2214yescomplemented
54#16840055C2214yescomplemented
55#16840054C2212yescomplemented
56#16840048C2212yescomplemented
57#16840047C2212yescomplemented
58#16840046C2214yescomplemented
59#16840045C2214yescomplemented
60#16840044C2212yescomplemented
61#16839805C2212yes—
62#16839804C2212yes—
63#16839803C2214yes—
64#16839802C2212yes—
65#16839801C2214yes—
66#16839799C2214yes—
67#16839797C2214yes—
68#16839787C2214yes—
69#16839787C2214yes—
70#16839786C2211yescharacteristic
71#16839785C2212yes—
72#16839772C2212yes—
73#16839771C2212yes—
74#16839770C2212yes—
75#16839769C2214yes—
76#16839769C2214yes—
77#103×D61C2214yes—
78#103×D61C2214yes—
79C61×#533C2211yescharacteristic
80C2×C4×Q8×C61C2211yescharacteristic
81C61×#479C2214yescomplemented
82C61×#477C2212yescomplemented
83C61×#475C2212yescomplemented
84C61×#428C2212yes—
85C61×#423C2211yescharacteristic
86C61×#419C2212yes—
87C22×Dic122—21no—
88C22×Dic122C2311yescharacteristic
89C2×Q8×D61—22no—
90C2×Q8×D61—24no—
91C2×Q8×D61Q818yescomplemented
92C2×Q8×D61C2314yes—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C2×#11758194C2312yes—
96C2×#11758189C2314yes—
97M16×D61—28no—
98C2×C8×D61C2314yes—
99#14519777C2311yescharacteristic
100#14519777C2311yescharacteristic
101#14519776—22no—
102#14519776—22no—
103#14519776C2312yes—
104#14519776C2312yes—
105#14519775—22no—
106#14519775—22no—
107#14519769C2312yes—
108#14519768C2312yes—
109#14519768C2312yes—
110#14519767—22no—
111#14519767—22no—
112#14519767—22no—
113#14519767—22no—
114#14519757—22no—
115#14519757—22no—
116#14519756—21no—
117#14519756—21no—
118#14519755—22no—
119#14519755—22no—
120#14519755—22no—
121#14519755—22no—
122#14519754—22no—
123#14519754—22no—
124#14519753—22no—
125#14519753—22no—
126Q8×Dic61—22no—
127Q8×Dic61C2314yes—
128C4×Dic122—21no—
129C4×Dic122—21no—
130C4×Dic122—21no—
131C4×Dic122—21no—
132C4×Dic122—24no—
133C4×Dic122—24no—
134C4×Dic122—22no—
135C4×Dic122—22no—
136C4×Dic122C2312yes—
137C4×Dic122C2312yes—
138#14519742—24no—
139#14519742—24no—
140#14519742—22no—
141#14519742C2314yes—
142#14519736C2312yes—
143#14519735—22no—
144#14519735—24no—
145#14519735—24no—
146#14519735C2312yes—
147#14519735C2312yes—
148#14519735C2314yes—
149#14519734—22no—
150#14519734—24no—
151#14519734—24no—
152#14519734D412yes—
153#14519734D412yes—
154#14519734C2312yes—
155#14519734C2312yes—
156#14519733—22no—
157C2×C4⋊Dic61—21no—
158C2×C4⋊Dic61C2311yescharacteristic
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196D411yescharacteristic
162C2×#11758196D411yescharacteristic
163C4⋊C4×D61C2312yes—
164C4⋊C4×D61C2312yes—
165C2×#11758198—21no—
166C2×#11758198D411yescharacteristic
167C2×#11758198D411yescharacteristic
168C22⋊C4×D61—22no—
169C2×C4×Dic61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61C2311yescharacteristic
174C42×D61—22no—
175#14519711C2314yes—
176#14519710C2314yes—
177#14519710C2314yes—
178#14519709C2314yes—
179#14519708C2314yes—
180#14519708C2314yes—
181C4⋊#92418C2312yes—
182C4⋊#92418C2312yes—
183#14519706C2314yes—
184#14519706C2314yes—
185#14519702C2314yes—
186#14519702C2314yes—
187#14519701C2314yes—
188#14519701C2314yes—
189#14519700C2314yes—
190#14519700C2314yes—
191C22×Q8×C61C2311yescharacteristic
192C2×M16×C61C2312yes—
193C4⋊Q8×C61C2311yescharacteristic
194C4⋊Q8×C61C2311yescharacteristic
195#125×C61C2312yes—
196C22⋊Q8×C61—21no—
197C22⋊Q8×C61—21no—
198C4×Q8×C61—21no—
199C4×Q8×C61—21no—
200C4×Q8×C61—21no—
201C4×Q8×C61—21no—
202C4×Q8×C61C2312yes—
203C4×Q8×C61C2312yes—
204#117×C61C2312yes—
205C2×C4⋊C4×C61—21no—
206C2×C4⋊C4×C61C2311yescharacteristic
207C2×C42×C61—21no—
208C2×C42×C61C2311yescharacteristic
209#107×C61C2314yes—
210#106×C61C2314yes—
211C4⋊C8×C61C2312yes—
212C4⋊C8×C61C2312yes—
213#103×C61C2314yes—
214#103×C61C2314yes—
215C23×D61C2×D411yescharacteristic
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—22no—
220C2×Q8×C61C2×Q814yes—
221C2×Q8×C61C2412yes—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2411yescharacteristic
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232Q8×D61—216no—
233Q8×D61—28no—
234Q8×D61C2×Q8116yes—
235C2×C4×D61—28no—
236C2×C4×D61—24no—
237C2×C4×D61—22no—
238C2×C4×D61—22no—
239C2×C4×D61C2×D412yes—
240C2×C4×D61C2×Q814yes—
241C2×C4×D61#4114yes—
242C2×C4×D61C2412yes—
243C2×Dic122—21no—
244C2×Dic122—22no—
245C2×Dic122—28no—
246C2×Dic122—24no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—22no—
250C2×Dic122—22no—
251C2×Dic122C2×Q814yes—
252C2×Dic122C2412yes—
253M16×C61—24no—
254C2×C8×C61C2414yes—
255C4⋊C4×C61—22no—
256C4⋊C4×C61—22no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—22no—
259C4⋊C4×C61—22no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61C2412yes—
263C4⋊C4×C61C2412yes—
264C4⋊C4×C61C2412yes—
265C22⋊C4×C61—22no—
266C42×C61—22no—
267C42×C61—22no—
268C42×C61—22no—
269C42×C61C2×D411yescharacteristic
270C42×C61C2×D411yescharacteristic
271C42×C61C2411yescharacteristic
272C42×C61C2411yescharacteristic
273C22⋊Dic61—22no—
274#11758198—22no—
275#11758198—22no—
276#11758198—24no—
277#11758198C2×D412yes—
278#11758198C2×D412yes—
279#11758198C2×D412yes—
280#11758198C2×D412yes—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—24no—
285C4⋊Dic61—22no—
286C4⋊Dic61—22no—
287C4⋊Dic61C2412yes—
288C4⋊Dic61C2412yes—
289C4⋊Dic61C2412yes—
290#11758196—22no—
291#11758196—22no—
292#11758196—22no—
293#11758196—22no—
294#11758196—22no—
295#11758196—22no—
296#11758196—24no—
297#11758196—22no—
298#11758196—22no—
299#11758196—22no—
300#11758196—22no—
301#11758196C2×D412yes—
302#11758196C2×D412yes—
303#11758196C2×D412yes—
304#11758196C2×D412yes—
305C4×Dic61—22no—
306C4×Dic61—22no—
307C4×Dic61—22no—
308C4×Dic61—22no—
309C4×Dic61—22no—
310C4×Dic61—24no—
311C4×Dic61—24no—
312C4×Dic61—24no—
313C4×Dic61C2×D412yes—
314C4×Dic61C2412yes—
315#11758194—24no—
316C2×#92418C2414yes—
317#11758189—28no—
318C8×D61—28no—
319C23×C61C22×D411yescharacteristic
320C22×D61—41no—
321C22×D61—41no—
322C22×D61C22⋊Q814yes—
323C22×D61C22×D412yes—
324Q8×C61—24no—
325Q8×C61—22no—
326Q8×C61—81no—
327Q8×C61—81no—
328Q8×C61C22×Q814yes—
329C2×C4×C61—24no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—42no—
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×Q812yes—
343C2×C4×C61C2×#4112yes—
344C2×C4×C61C2511yescharacteristic
345C2×Dic61—24no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—42no—
353C2×Dic61C22⋊Q814yes—
354C2×Dic61C22×D412yes—
355C2×Dic61C22×D412yes—
356C2×Dic61C22×D412yes—
357C4×D61—216no—
358C4×D61—82no—
359C4×D61—82no—
360C4×D61C22⋊Q818yes—
361C4×D61C22×Q814yes—
362C4×D61C2×#4114yes—
363Dic122—24no—
364Dic122—22no—
365Dic122—216no—
366Dic122—82no—
367Dic122—82no—
368Dic122—81no—
369Dic122—81no—
370Dic122C22×Q814yes—
371C8×C61—24no—
372#92418—24no—
373#60491—611nomaximal, Sylow
374C22×C61—21no—
375C22×C61—21no—
376C22×C61C2×C22⋊Q812yes—
377C22×C61C23×D411yescharacteristic
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—44no—
381C2×D61C2×C22⋊Q814yes—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—24no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61C2×C22⋊Q812yes—
391C4×C61C23×Q811yescharacteristic
392C4×C61C22×#4111yescharacteristic
393Dic61—22no—
394Dic61—22no—
395Dic61—24no—
396Dic61—42no—
397Dic61—42no—
398Dic61—42no—
399Dic61C2×C22⋊Q814yes—
400#3458—611no—
401C2×#519—611no—
402#3082—614no—
403#3082—614no—
404#3082—614no—
405#3082—614no—
406#3078—612no—
407#3078—611no—
408#3078—612no—
409#3078—611no—
410#3078—611no—
411#3078D6111yescharacteristic, complemented
412#2911—612no—
413#2905—611no—
414C2×#419—612no—
415C2×C61—22no—
416C2×C61C22×C22⋊Q811yescharacteristic
417C2×C61#358611yescharacteristic
418C2×C61#358611yescharacteristic
419D61—24no—
420C23×Q8—611no—
421C22×M16—612no—
422#544—612no—
423#544—612no—
424#544—612no—
425#544—612no—
426#544—1221no—
427#544—1221no—
428#543—1221no—
429#543—1221no—
430#533—612no—
431#533—611no—
432#533—1222no—
433#533—1222no—
434#533C2×D6111yescharacteristic
435#519—614no—
436#519—614no—
437#519—1222no—
438#519—1222no—
439C2×C4×Q8—611no—
440C2×C4×Q8—611no—
441C2×C4×Q8—611no—
442C2×C4×Q8—1221no—
443C2×C4×Q8—1221no—
444C2×C4×Q8C2×D6111yescharacteristic
445C2×#117—611no—
446C2×#117—612no—
447C2×#117—611no—
448C2×#117—1221no—
449C2×#117—1221no—
450#479—614no—
451#479—614no—
452#479—614no—
453#479—614no—
454#479—614no—
455#479—614no—
456#479—614no—
457#479C2×D6114yescomplemented
458#477—612no—
459#477—612no—
460#477—614no—
461#477—612no—
462#477—614no—
463#477C2×D6112yescomplemented
464#475—612no—
465#475—612no—
466#475—614no—
467#475—612no—
468#475—614no—
469#475C2×D6112yescomplemented
470#428—612no—
471#428—612no—
472#428—612no—
473#428—614no—
474#428—614no—
475#428C2×D6112yes—
476#427—614no—
477#427—614no—
478#424—614no—
479#424—614no—
480#423—612no—
481#423—611no—
482#423C2×D6111yescharacteristic
483#419—612no—
484#419—612no—
485#419—612no—
486#419—614no—
487#419—614no—
488#419C2×D6112yes—
489C2×#103—614no—
490C2×#103—614no—
491C61#6049111yescharacteristic, complemented, Sylow
492C22×Q8—618no—
493C22×Q8—614no—
494C22×Q8—611no—
495C22×Q8—1221no—
496C22×Q8—1222no—
497C22×Q8—1224no—
498C22×Q8C22×D6111yescharacteristic
499C23×C4—611no—
500C23×C4—1221no—
501C2×M16—612no—
502C2×M16—614no—
503C2×M16—1228no—
504C2×M16C22×D6112yes—
505C22×C8—614no—
506C4⋊Q8—612no—
507C4⋊Q8—612no—
508C4⋊Q8—611no—
509C4⋊Q8—611no—
510C4⋊Q8—1222no—
511C4⋊Q8—1222no—
512C4⋊Q8—1222no—
513C4⋊Q8—1222no—
514C4⋊Q8C22×D6111yescharacteristic
515C4⋊Q8C22×D6111yescharacteristic
516#125—612no—
517#125—612no—
518#125—612no—
519#125—1222no—
520#125—1222no—
521#125—1222no—
522#125—1222no—
523#125C22×D6112yes—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—1222no—
527C22⋊Q8—1222no—
528C22⋊Q8—1222no—
529C22⋊Q8—1222no—
530C22⋊Q8—1222no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533C22⋊Q8—1222no—
534C22⋊Q8—1222no—
535C22⋊Q8—1222no—
536C22⋊Q8—1221no—
537C22⋊Q8—1221no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—614no—
543C4×Q8—614no—
544C4×Q8—612no—
545C4×Q8—612no—
546C4×Q8—1222no—
547C4×Q8—1222no—
548C4×Q8—1224no—
549C4×Q8—1224no—
550C4×Q8—1222no—
551C4×Q8—1222no—
552C4×Q8—1224no—
553C4×Q8—1224no—
554C4×Q8—1221no—
555C4×Q8—1221no—
556C4×Q8—1221no—
557C4×Q8—1221no—
558C4×Q8C22×D6112yes—
559C4×Q8C22×D6112yes—
560#117—612no—
561#117—612no—
562#117—612no—
563#117—612no—
564#117—612no—
565#117—614no—
566#117—612no—
567#117—612no—
568#117—1224no—
569#117—1224no—
570#117—1222no—
571#117—1222no—
572#117—1224no—
573#117—1224no—
574#117—1222no—
575#117C22×D6112yes—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—611no—
578C2×C4⋊C4—611no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—612no—
581C2×C4⋊C4—612no—
582C2×C4⋊C4—1221no—
583C2×C4⋊C4—1221no—
584C2×C4⋊C4—1221no—
585C2×C4⋊C4C22×D6111yescharacteristic
586C2×C22⋊C4—611no—
587C2×C22⋊C4—611no—
588C2×C22⋊C4—1222no—
589C2×C22⋊C4—1221no—
590C2×C42—21no—
591C2×C42—611no—
592C2×C42—1222no—
593C2×C42—1221no—
594C2×C42—1221no—
595C2×C42—1221no—
596C2×C42—1221no—
597C2×C42C22×D6111yescharacteristic
598#107—614no—
599#107—614no—
600#107—614no—
601#107C22×D6114yes—
602#106—614no—
603#106—614no—
604#106—614no—
605#106C22×D6114yes—
606C4⋊C8—614no—
607C4⋊C8—614no—
608C4⋊C8—612no—
609C4⋊C8—612no—
610C4⋊C8C22×D6112yes—
611C4⋊C8C22×D6112yes—
612#103—614no—
613#103—614no—
614#103—614no—
615#103—614no—
616#103—614no—
617#103—614no—
618#103C22×D6114yes—
619#103C22×D6114yes—
620C24—611no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—22no—
625C2×Q8—6116no—
626C2×Q8—614no—
627C2×Q8—612no—
628C2×Q8—1224no—
629C2×Q8—1228no—
630C2×Q8—1222no—
631C2×Q8—1222no—
632C2×Q8—12216no—
633C2×Q8—1228no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×Q8—1222no—
638C2×Q8Q8×D6114yes—
639C2×Q8C23×D6112yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—611no—
643C22×C4—612no—
644C22×C4—614no—
645C22×C4—614no—
646C22×C4—612no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—1224no—
650C22×C4—1228no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4D4×D6111yescharacteristic
656C22×C4D4×D6111yescharacteristic
657C22×C4C23×D6111yescharacteristic
658M16—24no—
659M16—1228no—
660M16—1224no—
661C2×C8—614no—
662C2×C8—1228no—
663C2×C8C23×D6114yes—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—612no—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—612no—
675C4⋊C4—612no—
676C4⋊C4—612no—
677C4⋊C4—612no—
678C4⋊C4—1222no—
679C4⋊C4—1222no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1222no—
683C4⋊C4—1222no—
684C4⋊C4—1222no—
685C4⋊C4—1222no—
686C4⋊C4—1222no—
687C4⋊C4—1222no—
688C4⋊C4—1221no—
689C4⋊C4—1222no—
690C4⋊C4—1222no—
691C4⋊C4—1222no—
692C4⋊C4—1222no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4C23×D6112yes—
696C4⋊C4C23×D6112yes—
697C4⋊C4C23×D6112yes—
698C22⋊C4—22no—
699C22⋊C4—612no—
700C22⋊C4—612no—
701C22⋊C4—612no—
702C22⋊C4—612no—
703C22⋊C4—1224no—
704C22⋊C4—1222no—
705C22⋊C4—1222no—
706C22⋊C4—1222no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—612no—
711C42—612no—
712C42—1224no—
713C42—1222no—
714C42—1222no—
715C42—1224no—
716C42—1224no—
717C42—1222no—
718C42—1222no—
719C42—1222no—
720C42D4×D6111yescharacteristic
721C42D4×D6111yescharacteristic
722C42C23×D6111yescharacteristic
723C42C23×D6111yescharacteristic
724C23—612no—
725C23—614no—
726C23—2441no—
727C23—2441no—
728C23C2×D4×D6111yescharacteristic
729Q8—24no—
730Q8—22no—
731Q8—81no—
732Q8—81no—
733Q8—614no—
734Q8—12216no—
735Q8—1224no—
736Q8—1222no—
737Q8—4881no—
738Q8—4881no—
739Q8—4882no—
740Q8—4882no—
741Q8C2×Q8×D6114yes—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—614no—
751C2×C4—612no—
752C2×C4—618no—
753C2×C4—614no—
754C2×C4—614no—
755C2×C4—612no—
756C2×C4—612no—
757C2×C4—12216no—
758C2×C4—1224no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—4882no—
764C2×C4—4882no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2442no—
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4C2×D4×D6111yescharacteristic
770C2×C4C2×D4×D6111yescharacteristic
771C2×C4C2×D4×D6111yescharacteristic
772C2×C4C2×D4×D6111yescharacteristic
773C2×C4C2×Q8×D6112yes—
774C2×C4#41×D6112yes—
775C2×C4C24×D6111yescharacteristic
776C8—24no—
777C8—1224no—
778C22—21no—
779C22—21no—
780C22—614no—
781C22—1222no—
782C22—1222no—
783C22—2444no—
784C22C22⋊Q8×D6112yes—
785C22C22×D4×D6111yescharacteristic
786C4—24no—
787C4—21no—
788C4—21no—
789C4—21no—
790C4—21no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—614no—
795C4—1224no—
796C4—1222no—
797C4—1222no—
798C4—2442no—
799C4—2442no—
800C4—2442no—
801C4C22⋊Q8×D6112yes—
802C4C22×Q8×D6111yescharacteristic
803C4C2×#41×D6111yescharacteristic
804C2—22no—
805C2—1224no—
806C2C2×C22⋊Q8×D6111yescharacteristic
807C2#2146060211yescharacteristic
808C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3078C2
socleC22×C61C23×D4
prime radicalC23×D61C2×D4
hypercenter#3078D61
hypocenterC61#60491
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #21455660C2semidirect
4. #21455658C2semidirect
5. #21455656C2semidirect
6. #21455654C2semidirect
7. #21455626C2semidirect
8. #21455624C2semidirect
9. #21455623C2semidirect
10. #21455621C2semidirect
11. #21455620C2semidirect
15. C61×#3078C2semidirect
44. #16840072C22semidirect
45. #16840071C22semidirect
46. #16840070C22semidirect
47. #16840069C22semidirect
48. #16840068C22semidirect
49. #16840067C22semidirect
50. #16840066C22semidirect
51. #16840058C22semidirect
52. #16840057C22semidirect
53. #16840056C22semidirect
54. #16840055C22semidirect
55. #16840054C22semidirect
56. #16840048C22semidirect
57. #16840047C22semidirect
58. #16840046C22semidirect
59. #16840045C22semidirect
60. #16840044C22semidirect
81. C61×#479C22semidirect
82. C61×#477C22semidirect
83. C61×#475C22semidirect
91. C2×Q8×D61Q8semidirect
411. #3078D61semidirect
457. #479C2×D61semidirect
463. #477C2×D61semidirect
469. #475C2×D61semidirect
491. C61#60491semidirect

Maximal subgroups

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

subgroupindex
#214592222
C2×#168402382
#214556602
#214556582
#214556562
#214556542
#214556262
#214556242
#214556232
#214556212
#214556202
#214544062
#214543812
#419×D612
C61×#30782
#6049161