Finite Group Databasebeta

← #30549346

Subgroups — #30549346

Order 15616.

2078 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840392C211yesmaximal, characteristic, complemented
2#21459146C211yesmaximal, characteristic
3#21456222C211yesmaximal, characteristic, complemented
4#21456217C212yesmaximal, complemented
5#21456213C211yesmaximal, characteristic, complemented
6#21456212C211yesmaximal, characteristic, complemented
7#21456210C212yesmaximal, complemented
8#21456185C214yesmaximal, complemented
9#21456183C214yesmaximal, complemented
10#21456174C214yesmaximal, complemented
11#21456172C214yesmaximal, complemented
12#21454335C212yesmaximal, complemented
13#417×D61C212yesmaximal, complemented
14#21454236C211yesmaximal, characteristic, complemented
15C61×#3142C211yesmaximal, characteristic, complemented
16C2×#41×D61C2212yes—
17C2×M16×D61C2212yes—
18#16840392—22no—
19#16840392—22no—
20#16840392C2214yescomplemented
21#16840392C2214yescomplemented
22#16840339—21no—
23#16840339—21no—
24#16840337C2212yes—
25#16840332C2212yes—
26#16840330C2212yes—
27#16840325C2212yes—
28#16840320—21no—
29#16840320—21no—
30#16840312C2211yescharacteristic
31#16840308C2212yes—
32C2×#14519777C2211yescharacteristic, complemented
33C2×#14519776—21no—
34C2×#14519776C2211yescharacteristic, complemented
35C2×#14519768C2211yescharacteristic, complemented
36C2×#14519767—21no—
37#16840271—22no—
38#16840271—22no—
39C2×#14519757—21no—
40C2×#14519755—21no—
41C2×#14519735C2211yescharacteristic
42C2×#14519734C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840132C2212yescomplemented
45#16840129C2214yescomplemented
46#16840128C2212yescomplemented
47#16840125C2214yescomplemented
48#16840123C2214yescomplemented
49#16840122C2214yescomplemented
50#16840121C2214yescomplemented
51#16840120C2214yescomplemented
52#16840119C2214yescomplemented
53#16840118C2214yescomplemented
54#16840115C2214yescomplemented
55#16840113C2212yescomplemented
56#16840112C2212yescomplemented
57#16840111C2214yescomplemented
58#16840109C2212yescomplemented
59#16840108C2212yescomplemented
60#16840107C2214yescomplemented
61#16839769C2214yescomplemented
62#16839765C2214yescomplemented
63#16839764C2212yescomplemented
64#16839764C2212yescomplemented
65#16839763C2212yescomplemented
66#16839763C2212yescomplemented
67#16839762C2214yes—
68#16839761C2212yescomplemented
69#16839761C2212yescomplemented
70#16839760C2214yes—
71#16839757C2214yes—
72#16839755C2214yes—
73#103×D61C2214yescomplemented
74#102×D61C2214yescomplemented
75#16839719C2214yescomplemented
76#16839716C2214yescomplemented
77C4×#11758194C2211yescharacteristic, complemented
78M16×Dic61C2212yescomplemented
79C61×#532C2211yescharacteristic
80C2×#125×C61C2211yescharacteristic, complemented
81C61×#491C2212yescomplemented
82C61×#490C2212yescomplemented
83C61×#488C2214yescomplemented
84C61×#417C2212yescomplemented
85C61×#417C2212yescomplemented
86C4×M16×C61C2211yescharacteristic, complemented
87C2×#11758226C2312yes—
88C2×#11758222—22no—
89C2×#11758222C2312yes—
90C2×#11758224—22no—
91C2×#11758224C2312yes—
92#41×D61—28no—
93#41×D61—28no—
94C22×Dic122—21no—
95C22×Dic122—21no—
96C2×Q8×D61C2312yes—
97C2×D4×D61—22no—
98C2×D4×D61C2312yes—
99C22×C4×D61—21no—
100C22×C4×D61—22no—
101C22×C4×D61C2311yescharacteristic
102C2×#11758194C2312yes—
103C2×#11758189C2314yes—
104M16×D61—28no—
105C2×C8×D61C2314yes—
106#14519777—21no—
107#14519777—21no—
108#14519777C2311yescharacteristic
109#14519777C2312yes—
110#14519777C2312yes—
111#14519776—24no—
112#14519776—24no—
113#14519776—22no—
114#14519776C2314yes—
115#14519775C2312yes—
116#14519774C2311yescharacteristic
117#14519773C2312yes—
118#14519768—22no—
119#14519768C2314yes—
120#14519767—24no—
121#14519767—24no—
122#14519766C2312yes—
123#14519765C2312yes—
124#14519764C2312yes—
125#14519762—22no—
126#14519762—22no—
127#14519759—22no—
128#14519759—22no—
129#14519757—24no—
130#14519757—24no—
131#14519755—24no—
132#14519755—24no—
133#14519755—22no—
134#14519755—22no—
135#14519754—22no—
136#14519754—22no—
137#14519751—21no—
138#14519751—21no—
139#14519750—22no—
140#14519750—22no—
141#14519749—22no—
142#14519749—22no—
143#14519749—22no—
144#14519749—22no—
145#14519747—22no—
146#14519747—22no—
147#14519745—22no—
148#14519745—22no—
149C4×D244—21no—
150C4×D244—21no—
151C4×C22⋊D61—22no—
152C4×C22⋊D61—22no—
153#14519735—22no—
154#14519735C2314yes—
155#14519734D412yes—
156#14519734D412yes—
157#14519734C2312yes—
158#14519734C2312yes—
159C2×C4⋊Dic61—21no—
160C2×C4⋊Dic61—21no—
161C2×C4⋊Dic61C2311yescharacteristic
162C2×C4⋊Dic61C2311yescharacteristic
163C2×#11758196—21no—
164C2×#11758196—21no—
165C2×#11758196—21no—
166C2×#11758196D411yescharacteristic
167C2×#11758196D411yescharacteristic
168C4⋊C4×D61—22no—
169C4⋊C4×D61C2314yes—
170C2×#11758198—21no—
171C2×#11758198D411yescharacteristic
172C2×#11758198D411yescharacteristic
173C2×C4×Dic61—21no—
174C2×C4×Dic61C2311yescharacteristic
175#14519702C2314yes—
176#14519702C2314yes—
177#14519701C2314yes—
178#14519701C2314yes—
179#14519700C2314yes—
180#14519700C2314yes—
181#14519699C2314yes—
182#14519699C2314yes—
183#14519698C2314yes—
184#14519698C2314yes—
185#14519697C2314yes—
186#14519697C2314yes—
187#14519688C2312yes—
188#14519687C2314yes—
189C4×#92418C2312yes—
190C8×Dic61C2314yes—
191C2×#41×C61C2312yes—
192C2×M16×C61C2312yes—
193C4⋊Q8×C61C2311yescharacteristic
194#127×C61C2311yescharacteristic
195#125×C61—21no—
196#125×C61—21no—
197#125×C61C2312yes—
198#125×C61C2312yes—
199#124×C61C2312yes—
200#121×C61—21no—
201#121×C61—21no—
202C4×D4×C61—21no—
203C4×D4×C61—21no—
204C2×C4⋊C4×C61—21no—
205C2×C4⋊C4×C61—21no—
206C2×C4⋊C4×C61C2311yescharacteristic
207C2×C4⋊C4×C61C2311yescharacteristic
208C2×C42×C61C2311yescharacteristic
209#103×C61C2314yes—
210#103×C61C2314yes—
211#102×C61C2314yes—
212#102×C61C2314yes—
213#97×C61C2312yes—
214C4×C8×C61C2312yes—
215C23×D61—22no—
216C23×D61C2×D411yescharacteristic
217#41×C61—24no—
218#41×C61—24no—
219C2×Q8×C61C2412yes—
220C2×D4×C61—22no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61C2412yes—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—22no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—22no—
231C2×C22⋊D61—22no—
232C2×C22⋊D61—22no—
233C2×C22⋊D61—22no—
234C2×C22⋊D61—22no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—22no—
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241#11758226—24no—
242#11758226—24no—
243Q8×D61—24no—
244Q8×D61—24no—
245#11758224—24no—
246#11758224—24no—
247#11758224—48no—
248D4×D61—24no—
249D4×D61—24no—
250D4×D61—48no—
251#11758222—24no—
252#11758222—24no—
253#11758222—48no—
254C2×D244—22no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244C2412yes—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—24no—
262C2×C4×D61—48no—
263C2×C4×D61—82no—
264C2×C4×D61C2×D412yes—
265C2×C4×D61#4118yes—
266C2×C4×D61C2412yes—
267C2×Dic122—22no—
268C2×Dic122—22no—
269C2×Dic122—22no—
270C2×Dic122—24no—
271C2×Dic122—82no—
272C2×Dic122—82no—
273C2×Dic122C2412yes—
274M16×C61—24no—
275C2×C8×C61C2414yes—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—22no—
278C4⋊C4×C61—22no—
279C4⋊C4×C61—22no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C2412yes—
285C4⋊C4×C61C2412yes—
286C22⋊C4×C61—22no—
287C22⋊C4×C61—22no—
288C42×C61C2×D411yescharacteristic
289C42×C61C2×D411yescharacteristic
290C42×C61C2411yescharacteristic
291C42×C61C2411yescharacteristic
292C22⋊Dic61—22no—
293C22⋊Dic61—22no—
294#11758198—24no—
295#11758198—22no—
296#11758198—22no—
297#11758198—22no—
298#11758198—22no—
299#11758198C2×D412yes—
300#11758198C2×D412yes—
301#11758198C2×D412yes—
302#11758198C2×D412yes—
303C4⋊Dic61—21no—
304C4⋊Dic61—22no—
305C4⋊Dic61—22no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61—24no—
310C4⋊Dic61C2412yes—
311C4⋊Dic61C2412yes—
312#11758196—24no—
313#11758196—24no—
314#11758196—24no—
315#11758196—22no—
316#11758196—22no—
317#11758196C2×D412yes—
318#11758196C2×D412yes—
319#11758196C2×D412yes—
320#11758196C2×D412yes—
321C4×Dic61—24no—
322C4×Dic61C2×D412yes—
323C4×Dic61C2412yes—
324#11758194—24no—
325C2×#92418C2414yes—
326#11758189—28no—
327C8×D61—28no—
328C23×C61—22no—
329C23×C61C22×D411yescharacteristic
330C22×D61—22no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—44no—
334C22×D61—82no—
335C22×D61—82no—
336C22×D61#12414yes—
337C22×D61C22×D412yes—
338Q8×C61—22no—
339Q8×C61—22no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—44no—
343D4×C61—81no—
344D4×C61—81no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—42no—
351C2×C4×C61—42no—
352C2×C4×C61—44no—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C2×#4114yes—
359C2×C4×C61C2511yescharacteristic
360C22⋊D61—44no—
361C22⋊D61—44no—
362C22⋊D61—44no—
363C22⋊D61—82no—
364C22⋊D61—82no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C2×Dic61—44no—
373C2×Dic61#12414yes—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376C2×Dic61C22×D412yes—
377D244—22no—
378D244—22no—
379D244—44no—
380D244—81no—
381D244—81no—
382C4×D61—44no—
383C4×D61—44no—
384C4×D61—44no—
385C4×D61—84no—
386C4×D61#12418yes—
387C4×D61C2×#4114yes—
388C4×D61C2×#4114yes—
389Dic122—22no—
390Dic122—22no—
391Dic122—44no—
392Dic122—84no—
393Dic122—82no—
394Dic122—82no—
395C8×C61—24no—
396#92418—24no—
397#60621—611nomaximal, Sylow
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61C2×#12412yes—
404C22×C61C23×D411yescharacteristic
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—44no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—88no—
412C2×D61C2×#12414yes—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61—42no—
420C4×C61C2×#12412yes—
421C4×C61C22×#4112yes—
422Dic61—22no—
423Dic61—22no—
424Dic61—42no—
425Dic61—42no—
426Dic61—42no—
427Dic61C2×#12414yes—
428C2×#544—611no—
429#3449—611no—
430#3142—612no—
431#3142—611no—
432#3142D6111yescharacteristic, complemented
433#3141—612no—
434#3141—611no—
435#3141—611no—
436#3137—614no—
437#3137—614no—
438#3136—614no—
439#3136—614no—
440#2896—612no—
441C2×#417—612no—
442#2873—611no—
443C2×C61—22no—
444C2×C61—82no—
445C2×C61C22×#12411yescharacteristic
446C2×C61#358511yescharacteristic
447C2×C61#358611yescharacteristic
448D61—24no—
449D61—82no—
450C22×#41—612no—
451C22×M16—612no—
452#544—614no—
453#544—614no—
454#544—1222no—
455#544—1222no—
456#537—1221no—
457#537—1221no—
458#536—612no—
459#536—612no—
460#535—612no—
461#535—612no—
462#534—1221no—
463#534—1221no—
464#532—612no—
465#532—611no—
466#532C2×D6111yescharacteristic
467C2×C4⋊Q8—611no—
468C2×C4⋊Q8—611no—
469C2×C4⋊Q8—1221no—
470C2×#125—611no—
471C2×#125—1221no—
472C2×#125C2×D6111yescharacteristic, complemented
473#525—1222no—
474#525—1222no—
475C2×C22⋊Q8—1221no—
476C2×C22⋊Q8—1221no—
477C2×#117—611no—
478C2×#117—611no—
479C22×C4⋊C4—611no—
480#491—612no—
481#491—614no—
482#491C2×D6112yescomplemented
483#490—612no—
484#490—614no—
485#490C2×D6112yescomplemented
486#489—614no—
487#489—614no—
488#489—614no—
489#489—614no—
490#488—614no—
491#488—614no—
492#488—614no—
493#488C2×D6114yescomplemented
494#487—612no—
495#487—614no—
496#487—612no—
497#486—612no—
498#486—614no—
499#486—612no—
500#419—614no—
501#418—614no—
502#417—612no—
503#417—612no—
504#417—612no—
505#417—612no—
506#417—612no—
507#417—612no—
508#417—614no—
509#417—614no—
510#417C2×D6112yescomplemented
511#417C2×D6112yescomplemented
512#416—614no—
513#416—614no—
514C2×#103—614no—
515C2×#102—614no—
516#405—614no—
517#405—614no—
518C4×M16—612no—
519C4×M16—611no—
520C4×M16C2×D6111yescharacteristic, complemented
521C61#6062111yescharacteristic, complemented, Sylow
522C2×#41—612no—
523C2×#41—612no—
524C2×#41—612no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1228no—
528C2×#41—1228no—
529C2×#41C22×D6112yes—
530C22×Q8—612no—
531C22×Q8—1221no—
532C22×Q8—1221no—
533C22×D4—612no—
534C22×D4—1222no—
535C23×C4—611no—
536C23×C4—1222no—
537C23×C4—1221no—
538C2×M16—612no—
539C2×M16—614no—
540C2×M16—1228no—
541C2×M16C22×D6112yes—
542C22×C8—614no—
543C4⋊Q8—614no—
544C4⋊Q8—612no—
545C4⋊Q8—612no—
546C4⋊Q8—612no—
547C4⋊Q8—611no—
548C4⋊Q8—1222no—
549C4⋊Q8—1224no—
550C4⋊Q8—1224no—
551C4⋊Q8—1221no—
552C4⋊Q8—1221no—
553C4⋊Q8C22×D6111yescharacteristic
554#127—612no—
555#127—611no—
556#127C22×D6111yescharacteristic
557#125—21no—
558#125—21no—
559#125—614no—
560#125—1222no—
561#125—1224no—
562#125—1224no—
563#125C22×D6112yes—
564#125C22×D6112yes—
565#124—612no—
566#124—612no—
567#124—612no—
568#124C22×D6112yes—
569#123—1222no—
570#123—1222no—
571#123—1222no—
572#123—1222no—
573C22⋊Q8—1222no—
574C22⋊Q8—1222no—
575C22⋊Q8—1224no—
576C22⋊Q8—1224no—
577C22⋊Q8—1224no—
578C22⋊Q8—1224no—
579C22⋊Q8—1222no—
580C22⋊Q8—1222no—
581#121—21no—
582#121—21no—
583#121—1222no—
584#121—1222no—
585#121—1222no—
586#121—1222no—
587#121—1222no—
588#121—1222no—
589#121—1221no—
590#121—1221no—
591#120—1222no—
592#120—1222no—
593#120—1222no—
594#120—1222no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—1222no—
598C4×D4—1222no—
599C4×D4—1221no—
600C4×D4—1221no—
601#117—612no—
602#117—612no—
603#117—612no—
604#117—612no—
605#117—614no—
606#117—1222no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—614no—
614C2×C4⋊C4—1222no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4—1221no—
620C2×C4⋊C4C22×D6111yescharacteristic
621C2×C4⋊C4C22×D6111yescharacteristic
622C2×C22⋊C4—611no—
623C2×C22⋊C4—611no—
624C2×C22⋊C4—1221no—
625C2×C42—611no—
626C2×C42—1221no—
627C2×C42C22×D6111yescharacteristic
628#103—614no—
629#103—614no—
630#103—614no—
631#103—614no—
632#103—614no—
633#103—614no—
634#103C22×D6114yes—
635#103C22×D6114yes—
636#102—614no—
637#102—614no—
638#102—614no—
639#102—614no—
640#102—614no—
641#102—614no—
642#102C22×D6114yes—
643#102C22×D6114yes—
644#97—614no—
645#97—612no—
646#97C22×D6112yes—
647C4×C8—614no—
648C4×C8—612no—
649C4×C8C22×D6112yes—
650C24—611no—
651C24—1222no—
652#41—24no—
653#41—24no—
654#41—1224no—
655#41—1224no—
656#41—1224no—
657#41—1224no—
658#41—1224no—
659#41—1224no—
660#41—2448no—
661#41—2448no—
662C2×Q8—612no—
663C2×Q8—1224no—
664C2×Q8—1222no—
665C2×Q8—1224no—
666C2×Q8—1224no—
667C2×Q8—1222no—
668C2×Q8—1222no—
669C2×Q8—4882no—
670C2×Q8—4882no—
671C2×Q8C23×D6112yes—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—612no—
676C2×D4—1222no—
677C2×D4—1224no—
678C2×D4—1224no—
679C2×D4—1222no—
680C2×D4—1222no—
681C2×D4—1222no—
682C2×D4—1222no—
683C2×D4—1222no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—2448no—
687C2×D4C23×D6112yes—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—611no—
692C22×C4—612no—
693C22×C4—618no—
694C22×C4—612no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—1222no—
698C22×C4—1224no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1222no—
704C22×C4—4882no—
705C22×C4—2448no—
706C22×C4D4×D6111yescharacteristic
707C22×C4D4×D6111yescharacteristic
708C22×C4C23×D6111yescharacteristic
709M16—24no—
710M16—1228no—
711M16—1224no—
712C2×C8—614no—
713C2×C8—1228no—
714C2×C8C23×D6114yes—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—612no—
724C4⋊C4—612no—
725C4⋊C4—612no—
726C4⋊C4—612no—
727C4⋊C4—612no—
728C4⋊C4—612no—
729C4⋊C4—1224no—
730C4⋊C4—1224no—
731C4⋊C4—1224no—
732C4⋊C4—1224no—
733C4⋊C4—1222no—
734C4⋊C4—1222no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1222no—
738C4⋊C4—1222no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4C23×D6112yes—
742C4⋊C4C23×D6112yes—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—612no—
746C22⋊C4—612no—
747C22⋊C4—612no—
748C22⋊C4—612no—
749C22⋊C4—1222no—
750C22⋊C4—1222no—
751C22⋊C4—1224no—
752C22⋊C4—1222no—
753C22⋊C4—1222no—
754C22⋊C4—1222no—
755C22⋊C4—1222no—
756C42—612no—
757C42—612no—
758C42—1224no—
759C42D4×D6111yescharacteristic
760C42D4×D6111yescharacteristic
761C42C23×D6111yescharacteristic
762C42C23×D6111yescharacteristic
763C23—22no—
764C23—612no—
765C23—614no—
766C23—1222no—
767C23—4882no—
768C23—4882no—
769C23—2441no—
770C23—2441no—
771C23—2444no—
772C23C2×D4×D6111yescharacteristic
773Q8—22no—
774Q8—22no—
775Q8—1222no—
776Q8—1222no—
777Q8—4882no—
778Q8—4882no—
779Q8—4884no—
780Q8—2444no—
781D4—22no—
782D4—22no—
783D4—44no—
784D4—81no—
785D4—81no—
786D4—1222no—
787D4—1222no—
788D4—4881no—
789D4—4881no—
790D4—4882no—
791D4—4882no—
792D4—2444no—
793D4—2444no—
794D4—2444no—
795D4—2444no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—614no—
805C2×C4—612no—
806C2×C4—618no—
807C2×C4—614no—
808C2×C4—614no—
809C2×C4—612no—
810C2×C4—612no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—4884no—
815C2×C4—2444no—
816C2×C4—2444no—
817C2×C4—2444no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2442no—
821C2×C4—2442no—
822C2×C4—2444no—
823C2×C4C2×D4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4C2×D4×D6111yescharacteristic
827C2×C4C2×D4×D6111yescharacteristic
828C2×C4#41×D6114yes—
829C2×C4C24×D6111yescharacteristic
830C8—24no—
831C8—1224no—
832C22—21no—
833C22—21no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—614no—
838C22—1222no—
839C22—1222no—
840C22—4888no—
841C22—2444no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22#124×D6112yes—
846C22C22×D4×D6111yescharacteristic
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—614no—
855C4—1222no—
856C4—1222no—
857C4—2442no—
858C4—2442no—
859C4—2442no—
860C4#124×D6112yes—
861C4C2×#41×D6112yes—
862C2—22no—
863C2—82no—
864C2—1224no—
865C2—4882no—
866C2C2×#124×D6111yescharacteristic
867C2#2146059611yescharacteristic
868C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3142C2
socleC22×C61C23×D4
prime radical#21459146C2
hypercenter#3142D61
hypocenterC61#60621
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. C2×#16840392C2semidirect
3. #21456222C2semidirect
4. #21456217C2semidirect
5. #21456213C2semidirect
6. #21456212C2semidirect
7. #21456210C2semidirect
8. #21456185C2semidirect
9. #21456183C2semidirect
10. #21456174C2semidirect
11. #21456172C2semidirect
12. #21454335C2semidirect
13. #417×D61C2semidirect
14. #21454236C2semidirect
15. C61×#3142C2semidirect
20. #16840392C22semidirect
21. #16840392C22semidirect
32. C2×#14519777C22semidirect
34. C2×#14519776C22semidirect
35. C2×#14519768C22semidirect
44. #16840132C22semidirect
45. #16840129C22semidirect
46. #16840128C22semidirect
47. #16840125C22semidirect
48. #16840123C22semidirect
49. #16840122C22semidirect
50. #16840121C22semidirect
51. #16840120C22semidirect
52. #16840119C22semidirect
53. #16840118C22semidirect
54. #16840115C22semidirect
55. #16840113C22semidirect
56. #16840112C22semidirect
57. #16840111C22semidirect
58. #16840109C22semidirect
59. #16840108C22semidirect
60. #16840107C22semidirect
61. #16839769C22semidirect
62. #16839765C22semidirect
63. #16839764C22semidirect
64. #16839764C22semidirect
65. #16839763C22semidirect
66. #16839763C22semidirect
68. #16839761C22semidirect
69. #16839761C22semidirect
73. #103×D61C22semidirect
74. #102×D61C22semidirect
75. #16839719C22semidirect
76. #16839716C22semidirect
77. C4×#11758194C22semidirect
78. M16×Dic61C22semidirect
80. C2×#125×C61C22semidirect
81. C61×#491C22semidirect
82. C61×#490C22semidirect
83. C61×#488C22semidirect
84. C61×#417C22semidirect
85. C61×#417C22semidirect
86. C4×M16×C61C22semidirect
432. #3142D61semidirect
472. C2×#125C2×D61semidirect
482. #491C2×D61semidirect
485. #490C2×D61semidirect
493. #488C2×D61semidirect
510. #417C2×D61semidirect
511. #417C2×D61semidirect
520. C4×M16C2×D61semidirect
521. C61#60621semidirect

Maximal subgroups

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

subgroupindex
C2×#168403922
#214591462
#214562222
#214562172
#214562132
#214562122
#214562102
#214561852
#214561832
#214561742
#214561722
#214543352
#417×D612
#214542362
C61×#31422
#6062161