Finite Group Databasebeta

← #30552182

Subgroups — #30552182

Order 15616.

1780 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459114C211yesmaximal, characteristic
2#533×D61C211yesmaximal, characteristic, complemented
3#21457057C214yesmaximal, complemented
4#21457048C212yesmaximal, complemented
5#21457039C212yesmaximal, complemented
6#21457035C211yesmaximal, characteristic, complemented
7#21457033C211yesmaximal, characteristic, complemented
8#21457026C212yesmaximal, complemented
9#21457013C211yesmaximal, characteristic, complemented
10#21457004C212yesmaximal, complemented
11#21456340C212yesmaximal, complemented
12#21456163C212yesmaximal, complemented
13#21455731C214yesmaximal, complemented
14#21455608C212yesmaximal, complemented
15#21455600C212yesmaximal, complemented
16#432×D61C211yesmaximal, characteristic, complemented
17C61×#3235C211yesmaximal, characteristic, complemented
18#16840319C2211yescharacteristic
19#16840319C2211yescharacteristic
20#16840318C2212yes—
21#16840317C2211yescharacteristic
22#16840317C2211yescharacteristic
23#16840317C2211yescharacteristic
24#16840317C2211yescharacteristic
25#16840316—21no—
26#16840316—21no—
27#16840315C2212yes—
28#16840314—21no—
29#16840314—21no—
30#16840310C2211yescharacteristic
31#16840310C2211yescharacteristic
32C4⋊Q8×D61C2211yescharacteristic
33C4⋊Q8×D61C2211yescharacteristic
34#16840294—21no—
35#16840294C2212yes—
36#16840293—21no—
37#16840293C2212yes—
38#16840291—21no—
39#16840291—21no—
40#125×D61C2212yes—
41#16840272—21no—
42#16840272C2212yes—
43#16840269—21no—
44C22⋊Q8×D61—21no—
45C22⋊Q8×D61—21no—
46#41×Dic61—21no—
47C4×#11758224—21no—
48C4×#11758224C2212yes—
49C4×Q8×D61—21no—
50C4×Q8×D61—21no—
51#117×D61C2212yes—
52C2×C42×D61C2211yescharacteristic
53#16840172C2212yescomplemented
54#16840171C2212yescomplemented
55#16840170C2214yescomplemented
56#16840169C2214yescomplemented
57#16840168C2212yescomplemented
58#16840132C2212yescomplemented
59#16840131C2212yescomplemented
60#16840126C2212yescomplemented
61#16840120C2214yescomplemented
62#16840120C2214yescomplemented
63#16840104C2214yes—
64#16840103C2214yes—
65#16840099C2214yes—
66#16840094C2214yes—
67#16840083C2214yes—
68#16840079C2214yes—
69#16840074C2214yes—
70#16840072C2214yescomplemented
71#16840068C2214yescomplemented
72#16840064C2214yescomplemented
73#16840060C2214yescomplemented
74#16840058C2212yescomplemented
75#16840054C2212yescomplemented
76#16840052C2212yescomplemented
77#16840048C2212yescomplemented
78#16840044C2212yescomplemented
79#16840042C2212yescomplemented
80#16839819C2211yescharacteristic
81#16839818C2212yes—
82#16839817C2212yes—
83#16839816C2212yes—
84#16839799C2214yes—
85#16839797C2214yes—
86C4⋊C8×D61C2212yes—
87#16839755C2214yes—
88#16839755C2214yes—
89C22⋊C8×D61C2212yes—
90#97×D61C2212yes—
91C61×#533C2211yescharacteristic
92C61×#532C2211yescharacteristic
93C61×#501C2212yescomplemented
94C61×#490C2212yescomplemented
95C61×#482C2214yes—
96C61×#476C2212yescomplemented
97C61×#474C2212yescomplemented
98C61×#432C2211yescharacteristic
99C2×#11758224—21no—
100C2×#11758224C2312yes—
101C2×Q8×D61—21no—
102C2×Q8×D61—21no—
103C22×C4×D61D411yescharacteristic
104C22×C4×D61D411yescharacteristic
105C22×C4×D61C2311yescharacteristic
106C2×C8×D61C2314yes—
107#14519777C2311yescharacteristic
108#14519777C2311yescharacteristic
109#14519777C2311yescharacteristic
110#14519777C2311yescharacteristic
111#14519776—21no—
112#14519776—21no—
113#14519776C2312yes—
114#14519776C2312yes—
115#14519775—21no—
116#14519775—21no—
117#14519770—22no—
118#14519770—22no—
119#14519769—21no—
120#14519769C2312yes—
121#14519768—21no—
122#14519768C2312yes—
123#14519768C2312yes—
124#14519768C2312yes—
125#14519767—22no—
126#14519767—22no—
127#14519764—21no—
128#14519764C2312yes—
129#14519759—22no—
130#14519759—22no—
131#14519758—22no—
132#14519757—21no—
133#14519757—21no—
134#14519757—21no—
135#14519757C2312yes—
136#14519756—21no—
137#14519756—21no—
138#14519756—21no—
139#14519756C2312yes—
140#14519755—22no—
141#14519755—22no—
142#14519754—22no—
143#14519754—22no—
144#14519753—21no—
145#14519753—21no—
146#14519753—21no—
147#14519753—21no—
148#14519748—21no—
149#14519748—21no—
150#14519748—21no—
151#14519748C2312yes—
152#14519745—22no—
153Q8×Dic61—21no—
154Q8×Dic61—21no—
155Q8×Dic61—21no—
156Q8×Dic61—21no—
157C4×Dic122—21no—
158C4×Dic122—21no—
159C4×Dic122—21no—
160C4×Dic122—22no—
161C4×Dic122—22no—
162C4×Dic122C2312yes—
163#14519742—21no—
164#14519742—21no—
165#14519742—22no—
166#14519742—22no—
167#14519742—21no—
168#14519742C2312yes—
169D4×Dic61—22no—
170D4×Dic61—22no—
171D4×Dic61—21no—
172D4×Dic61—21no—
173D4×Dic61—21no—
174D4×Dic61C2312yes—
175C4×C22⋊D61—22no—
176C4×C22⋊D61—22no—
177#14519737—22no—
178#14519737—22no—
179#14519736—21no—
180#14519736—22no—
181#14519736C2312yes—
182#14519735—21no—
183#14519735C2312yes—
184#14519735C2312yes—
185#14519735C2312yes—
186#14519734—22no—
187#14519733—22no—
188#14519733—22no—
189#14519733—22no—
190C4⋊C4×D61—22no—
191C4⋊C4×D61—22no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61—21no—
194C4⋊C4×D61C2312yes—
195C4⋊C4×D61C2312yes—
196C22⋊C4×D61—22no—
197C2×C4×Dic61—22no—
198C2×C4×Dic61D411yescharacteristic
199C2×C4×Dic61D411yescharacteristic
200C2×C4×Dic61C2311yescharacteristic
201C42×D61—22no—
202C42×D61D411yescharacteristic
203C42×D61D411yescharacteristic
204C42×D61D411yescharacteristic
205C42×D61D411yescharacteristic
206C42×D61C2311yescharacteristic
207C42×D61C2311yescharacteristic
208C42×D61C2311yescharacteristic
209C42×D61C2311yescharacteristic
210#14519711C2314yes—
211#14519710C2314yes—
212#14519710C2314yes—
213#14519709C2314yes—
214#14519708C2314yes—
215#14519708C2314yes—
216C4⋊#92418C2312yes—
217#14519706C2314yes—
218#14519702C2314yes—
219#14519702C2314yes—
220#14519700C2314yes—
221#14519700C2314yes—
222#14519698C2314yes—
223#14519698C2314yes—
224C22⋊#92418C2312yes—
225#14519689C2314yes—
226#14519688C2312yes—
227#14519687C2314yes—
228C2×#41×C61—21no—
229C4⋊Q8×C61C2311yescharacteristic
230C4⋊Q8×C61C2311yescharacteristic
231C4⋊Q8×C61C2311yescharacteristic
232#127×C61C2311yescharacteristic
233#125×C61C2312yes—
234#124×C61—21no—
235C22⋊Q8×C61—21no—
236C22⋊Q8×C61—21no—
237#121×C61—21no—
238#121×C61C2312yes—
239C4×Q8×C61—21no—
240C4×Q8×C61—21no—
241C4×D4×C61—21no—
242C4×D4×C61C2312yes—
243#117×C61C2312yes—
244C2×C42×C61C2311yescharacteristic
245#107×C61C2314yes—
246#106×C61C2314yes—
247C4⋊C8×C61C2312yes—
248#102×C61C2314yes—
249#102×C61C2314yes—
250C22⋊C8×C61C2312yes—
251#97×C61C2312yes—
252C23×D61C2×D411yescharacteristic
253#41×C61—44no—
254C2×Q8×C61—21no—
255C2×Q8×C61—21no—
256C2×Q8×C61—21no—
257C2×D4×C61—22no—
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61C2412yes—
261C22×C4×C61—22no—
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2411yescharacteristic
265C2×C22⋊D61—22no—
266C2×C22⋊D61—22no—
267C22×Dic61—22no—
268C22×Dic61—22no—
269C22×Dic61C2×D411yescharacteristic
270C22×Dic61C2×D411yescharacteristic
271C22×Dic61C2×D411yescharacteristic
272Q8×D61—44no—
273Q8×D61—44no—
274#11758224—28no—
275#11758224—44no—
276C2×C4×D61—24no—
277C2×C4×D61—22no—
278C2×C4×D61—22no—
279C2×C4×D61—42no—
280C2×C4×D61—42no—
281C2×C4×D61C2×D411yescharacteristic
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61C2×D411yescharacteristic
284C2×C4×D61C2×D411yescharacteristic
285C2×C4×D61C2×D411yescharacteristic
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2411yescharacteristic
292C2×C4×D61C2411yescharacteristic
293C2×Dic122—21no—
294C2×Dic122—21no—
295C2×Dic122—21no—
296C2×Dic122—22no—
297C2×Dic122—22no—
298C2×Dic122C2412yes—
299C2×C8×C61C2414yes—
300C4⋊C4×C61—21no—
301C4⋊C4×C61—22no—
302C4⋊C4×C61—22no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61C2412yes—
306C4⋊C4×C61C2412yes—
307C4⋊C4×C61C2412yes—
308C22⋊C4×C61—22no—
309C22⋊C4×C61—22no—
310C22⋊C4×C61—22no—
311C42×C61—22no—
312C42×C61C2×D411yescharacteristic
313C42×C61C2×D411yescharacteristic
314C42×C61C2411yescharacteristic
315C42×C61C2411yescharacteristic
316C22⋊Dic61—22no—
317C22⋊Dic61—22no—
318C22⋊Dic61—22no—
319C22⋊Dic61—22no—
320C22⋊Dic61—22no—
321C22⋊Dic61—22no—
322#11758198—22no—
323#11758198—22no—
324#11758198—22no—
325#11758198—22no—
326C4⋊Dic61—21no—
327C4⋊Dic61—21no—
328C4⋊Dic61—21no—
329C4⋊Dic61—21no—
330C4⋊Dic61—21no—
331C4⋊Dic61—22no—
332C4⋊Dic61—22no—
333C4⋊Dic61—22no—
334C4⋊Dic61—22no—
335C4⋊Dic61C2412yes—
336C4⋊Dic61C2412yes—
337C4⋊Dic61C2412yes—
338#11758196—22no—
339#11758196—22no—
340#11758196—22no—
341#11758196—22no—
342#11758196—22no—
343#11758196—22no—
344#11758196—22no—
345#11758196—22no—
346#11758196—22no—
347#11758196—22no—
348#11758196—22no—
349#11758196—22no—
350C4×Dic61—22no—
351C4×Dic61—22no—
352C4×Dic61—22no—
353C4×Dic61—22no—
354C4×Dic61—22no—
355C4×Dic61—22no—
356C4×Dic61C2×D411yescharacteristic
357C4×Dic61C2×D411yescharacteristic
358C4×Dic61C2×D411yescharacteristic
359C4×Dic61C2×D411yescharacteristic
360C4×Dic61C2×D411yescharacteristic
361C4×Dic61C2×D411yescharacteristic
362C4×Dic61C2×D411yescharacteristic
363C4×Dic61C2×D411yescharacteristic
364C4×Dic61C2×D411yescharacteristic
365C4×Dic61C2×D411yescharacteristic
366C4×Dic61C2411yescharacteristic
367C4×Dic61C2411yescharacteristic
368C2×#92418C2414yes—
369C8×D61—28no—
370C23×C61—22no—
371C23×C61C22×D411yescharacteristic
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—41no—
375C22×D61C22×D411yescharacteristic
376C22×D61C22×D411yescharacteristic
377Q8×C61—42no—
378Q8×C61—42no—
379Q8×C61—42no—
380D4×C61—24no—
381D4×C61—42no—
382D4×C61—42no—
383D4×C61—44no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—41no—
390C2×C4×C61—44no—
391C2×C4×C61C22×D411yescharacteristic
392C2×C4×C61C22×D411yescharacteristic
393C2×C4×C61C22×D411yescharacteristic
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D411yescharacteristic
396C2×C4×C61C2511yescharacteristic
397C22⋊D61—44no—
398C22⋊D61—44no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—44no—
407C2×Dic61—44no—
408C2×Dic61C22×D411yescharacteristic
409C2×Dic61C22×D411yescharacteristic
410C2×Dic61C22×D411yescharacteristic
411C2×Dic61C22×D411yescharacteristic
412C2×Dic61C22×D411yescharacteristic
413C2×Dic61C22×D411yescharacteristic
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—44no—
426C4×D61—44no—
427C4×D612−1+414yes—
428Dic122—24no—
429Dic122—44no—
430Dic122—44no—
431Dic122—42no—
432Dic122—42no—
433Dic122—42no—
434C8×C61—24no—
435#92418—24no—
436#60854—611nomaximal, Sylow
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—42no—
441C22×C61—42no—
442C22×C61—42no—
443C22×C61C23×D411yescharacteristic
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—44no—
449C2×D61#53612yes—
450C2×D61#57512yes—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—42no—
456C4×C61—42no—
457C4×C61—42no—
458C4×C61#57512yes—
459C4×C61C2×2−1+412yes—
460Dic61—21no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
464Dic61—21no—
465Dic61—42no—
466Dic61—42no—
467Dic61—42no—
468Dic61—42no—
469Dic61#53612yes—
470#3444—611no—
471C2×#533—611no—
472#3240—614no—
473#3239—612no—
474#3238—612no—
475#3237—611no—
476#3237—611no—
477#3236—612no—
478#3235—611no—
479#3235D6111yescharacteristic, complemented
480#3234—612no—
481#3162—612no—
482#3135—612no—
483#3091—614no—
484#3076—612no—
485#3076—612no—
486C2×#432—611no—
487C2×C61—41no—
488C2×C61—82no—
489C2×C61C2×#53611yescharacteristic
490C2×C61C2×#57511yescharacteristic
491C2×C61C2×#57511yescharacteristic
492D61—22no—
493D61—22no—
494#533—611no—
495#533—611no—
496#533—611no—
497#533—612no—
498#533—612no—
499#533—611no—
500#533—611no—
501#533—611no—
502#533—1221no—
503#533—1221no—
504#533—1221no—
505#533—1221no—
506#533C2×D6111yescharacteristic
507#532—611no—
508#532—611no—
509#532C2×D6111yescharacteristic
510C2×C4⋊Q8—611no—
511C2×C4⋊Q8—611no—
512#529—612no—
513#529—612no—
514#529—1221no—
515#529—1221no—
516#529—1221no—
517#529—1221no—
518C2×#125—612no—
519#525—612no—
520#525—1221no—
521#525—1221no—
522C2×C22⋊Q8—1221no—
523C2×C22⋊Q8—1221no—
524C4×#41—612no—
525C4×#41—1221no—
526C4×#41—1221no—
527C2×C4×Q8—1221no—
528C2×C4×Q8—1221no—
529C2×#117—612no—
530C22×C42—611no—
531#501—612no—
532#501—612no—
533#501—614no—
534#501—614no—
535#501—612no—
536#501C2×D6112yescomplemented
537#491—612no—
538#491—612no—
539#490—612no—
540#490C2×D6112yescomplemented
541#489—614no—
542#489—614no—
543#485—614no—
544#485—614no—
545#484—614no—
546#483—614no—
547#482—614no—
548#482C2×D6114yes—
549#481—614no—
550#480—614no—
551#479—614no—
552#479—614no—
553#478—614no—
554#478—614no—
555#477—612no—
556#477—612no—
557#476—612no—
558#476C2×D6112yescomplemented
559#475—612no—
560#475—612no—
561#474—612no—
562#474C2×D6112yescomplemented
563#432—611no—
564#432—612no—
565#432—612no—
566#432—612no—
567#432C2×D6111yescharacteristic
568#427—614no—
569#427—614no—
570C2×C4⋊C8—612no—
571#416—614no—
572#416—614no—
573C2×C22⋊C8—612no—
574C2×#97—612no—
575C61#6085411yescharacteristic, complemented, Sylow
576C2×#41—21no—
577C2×#41—612no—
578C2×#41—1221no—
579C22×Q8—1221no—
580C22×Q8—1221no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C22×C8—614no—
585C4⋊Q8—612no—
586C4⋊Q8—612no—
587C4⋊Q8—611no—
588C4⋊Q8—611no—
589C4⋊Q8—611no—
590C4⋊Q8—611no—
591C4⋊Q8—1221no—
592C4⋊Q8—1221no—
593C4⋊Q8—1221no—
594C4⋊Q8—1221no—
595C4⋊Q8C22×D6111yescharacteristic
596C4⋊Q8C22×D6111yescharacteristic
597C4⋊Q8C22×D6111yescharacteristic
598#127C22×D6111yescharacteristic
599#126—1222no—
600#126—1222no—
601#125—612no—
602#125—612no—
603#125—612no—
604#125—612no—
605#125—1222no—
606#125—1222no—
607#125—1221no—
608#125—1221no—
609#125C22×D6112yes—
610#124—21no—
611#124—612no—
612#124—1221no—
613#123—1222no—
614#123—1222no—
615#123—1222no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8—612no—
619C22⋊Q8—612no—
620C22⋊Q8—1222no—
621C22⋊Q8—1222no—
622C22⋊Q8—1222no—
623C22⋊Q8—1222no—
624C22⋊Q8—1221no—
625C22⋊Q8—1221no—
626C22⋊Q8—1221no—
627C22⋊Q8—1221no—
628C22⋊Q8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8—1221no—
632C22⋊Q8—1221no—
633C22⋊Q8—1221no—
634#121—21no—
635#121—612no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121C22×D6112yes—
640#120—1222no—
641C4×Q8—21no—
642C4×Q8—21no—
643C4×Q8—612no—
644C4×Q8—612no—
645C4×Q8—1222no—
646C4×Q8—1222no—
647C4×Q8—1221no—
648C4×Q8—1221no—
649C4×Q8—1222no—
650C4×Q8—1222no—
651C4×Q8—1221no—
652C4×Q8—1221no—
653C4×Q8—1221no—
654C4×Q8—1221no—
655C4×Q8—1221no—
656C4×Q8—1221no—
657C4×Q8—1221no—
658C4×Q8—1221no—
659C4×D4—21no—
660C4×D4—612no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1222no—
665C4×D4—1222no—
666C4×D4—1222no—
667C4×D4—1222no—
668C4×D4—1222no—
669C4×D4—1222no—
670C4×D4C22×D6112yes—
671#117—612no—
672#117—612no—
673#117—612no—
674#117—612no—
675#117—1222no—
676#117—1222no—
677#117—1222no—
678#117—1222no—
679#117—1222no—
680#117—1221no—
681#117—1221no—
682#117C22×D6112yes—
683C2×C4⋊C4—612no—
684C2×C4⋊C4—612no—
685C2×C4⋊C4—1222no—
686C2×C4⋊C4—1222no—
687C2×C4⋊C4—1221no—
688C2×C4⋊C4—1221no—
689C2×C22⋊C4—1222no—
690C2×C42—611no—
691C2×C42—611no—
692C2×C42—611no—
693C2×C42—611no—
694C2×C42—611no—
695C2×C42—611no—
696C2×C42—611no—
697C2×C42—611no—
698C2×C42—611no—
699C2×C42—611no—
700C2×C42—611no—
701C2×C42—1222no—
702C2×C42—1222no—
703C2×C42C22×D6111yescharacteristic
704#107—614no—
705#107—614no—
706#107—614no—
707#107C22×D6114yes—
708#106—614no—
709#106—614no—
710#106—614no—
711#106C22×D6114yes—
712C4⋊C8—614no—
713C4⋊C8—612no—
714C4⋊C8C22×D6112yes—
715#103—614no—
716#103—614no—
717#103—614no—
718#103—614no—
719#102—614no—
720#102—614no—
721#102C22×D6114yes—
722#102C22×D6114yes—
723C22⋊C8—612no—
724C22⋊C8—614no—
725C22⋊C8C22×D6112yes—
726#97—614no—
727#97—612no—
728#97C22×D6112yes—
729C24—611no—
730#41—44no—
731#41—1228no—
732#41—2444no—
733C2×Q8—21no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—612no—
737C2×Q8—1222no—
738C2×Q8—1222no—
739C2×Q8—1221no—
740C2×Q8—1221no—
741C2×Q8—1221no—
742C2×Q8—2444no—
743C2×Q8—2444no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—1222no—
748C2×D4—1222no—
749C2×D4C23×D6112yes—
750C22×C4—22no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—1224no—
767C22×C4—1222no—
768C22×C4—1222no—
769C22×C4—1222no—
770C22×C4—1222no—
771C22×C4—2442no—
772C22×C4—2442no—
773C22×C4D4×D6111yescharacteristic
774C22×C4D4×D6111yescharacteristic
775C22×C4C23×D6111yescharacteristic
776C2×C8—614no—
777C2×C8—1228no—
778C2×C8C23×D6114yes—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—612no—
785C4⋊C4—612no—
786C4⋊C4—612no—
787C4⋊C4—1222no—
788C4⋊C4—1222no—
789C4⋊C4—1222no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C4⋊C4—1222no—
793C4⋊C4—1222no—
794C4⋊C4—1222no—
795C4⋊C4—1222no—
796C4⋊C4—1222no—
797C4⋊C4—1222no—
798C4⋊C4—1222no—
799C4⋊C4—1222no—
800C4⋊C4—1222no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1222no—
804C4⋊C4—1222no—
805C4⋊C4—1221no—
806C4⋊C4—1221no—
807C4⋊C4—1221no—
808C4⋊C4C23×D6112yes—
809C4⋊C4C23×D6112yes—
810C4⋊C4C23×D6112yes—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—22no—
814C22⋊C4—1222no—
815C22⋊C4—1222no—
816C22⋊C4—1222no—
817C22⋊C4—1222no—
818C22⋊C4—1222no—
819C22⋊C4—1222no—
820C22⋊C4—1222no—
821C22⋊C4—1222no—
822C22⋊C4—1222no—
823C22⋊C4—1222no—
824C42—22no—
825C42—611no—
826C42—611no—
827C42—611no—
828C42—611no—
829C42—611no—
830C42—611no—
831C42—611no—
832C42—611no—
833C42—611no—
834C42—611no—
835C42—611no—
836C42—611no—
837C42—1222no—
838C42—1222no—
839C42—1222no—
840C42—1222no—
841C42—1222no—
842C42—1222no—
843C42D4×D6111yescharacteristic
844C42D4×D6111yescharacteristic
845C42C23×D6111yescharacteristic
846C42C23×D6111yescharacteristic
847C23—22no—
848C23—611no—
849C23—611no—
850C23—1222no—
851C23—1222no—
852C23—2441no—
853C23C2×D4×D6111yescharacteristic
854Q8—42no—
855Q8—42no—
856Q8—42no—
857Q8—1224no—
858Q8—2442no—
859Q8—2442no—
860Q8—2444no—
861Q8—2444no—
862Q8—2442no—
863D4—24no—
864D4—42no—
865D4—42no—
866D4—44no—
867D4—2444no—
868D4—2444no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—41no—
875C2×C4—44no—
876C2×C4—611no—
877C2×C4—614no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2444no—
900C2×C4—2444no—
901C2×C4—2444no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2444no—
905C2×C4C2×D4×D6111yescharacteristic
906C2×C4C2×D4×D6111yescharacteristic
907C2×C4C2×D4×D6111yescharacteristic
908C2×C4C2×D4×D6111yescharacteristic
909C2×C4C2×D4×D6111yescharacteristic
910C2×C4C24×D6111yescharacteristic
911C8—24no—
912C8—1224no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—612no—
920C22—612no—
921C22—1221no—
922C22—1221no—
923C22—1221no—
924C22—1221no—
925C22—2444no—
926C22C22×D4×D6111yescharacteristic
927C4—21no—
928C4—21no—
929C4—21no—
930C4—21no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—612no—
935C4—1221no—
936C4—1221no—
937C4—1221no—
938C4—1221no—
939C4—1221no—
940C4—2442no—
941C4—2442no—
942C4—2442no—
943C4—2442no—
944C4#1684055812yes—
945C42−1+4×D6112yes—
946C2—41no—
947C2—82no—
948C2—1222no—
949C2—1222no—
950C2#536×D6111yescharacteristic
951C2#575×D6111yescharacteristic
952C2C2×#1684055811yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3235C2
socleC22×C61C23×D4
prime radical#21459114C2
hypercenter#3235D61
hypocenterC61#60854
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3235

Complements

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

NH ≅ G/Ntype
2. #533×D61C2semidirect
3. #21457057C2semidirect
4. #21457048C2semidirect
5. #21457039C2semidirect
6. #21457035C2semidirect
7. #21457033C2semidirect
8. #21457026C2semidirect
9. #21457013C2semidirect
10. #21457004C2semidirect
11. #21456340C2semidirect
12. #21456163C2semidirect
13. #21455731C2semidirect
14. #21455608C2semidirect
15. #21455600C2semidirect
16. #432×D61C2semidirect
17. C61×#3235C2semidirect
53. #16840172C22semidirect
54. #16840171C22semidirect
55. #16840170C22semidirect
56. #16840169C22semidirect
57. #16840168C22semidirect
58. #16840132C22semidirect
59. #16840131C22semidirect
60. #16840126C22semidirect
61. #16840120C22semidirect
62. #16840120C22semidirect
70. #16840072C22semidirect
71. #16840068C22semidirect
72. #16840064C22semidirect
73. #16840060C22semidirect
74. #16840058C22semidirect
75. #16840054C22semidirect
76. #16840052C22semidirect
77. #16840048C22semidirect
78. #16840044C22semidirect
79. #16840042C22semidirect
93. C61×#501C22semidirect
94. C61×#490C22semidirect
96. C61×#476C22semidirect
97. C61×#474C22semidirect
479. #3235D61semidirect
536. #501C2×D61semidirect
540. #490C2×D61semidirect
558. #476C2×D61semidirect
562. #474C2×D61semidirect
575. C61#60854semidirect

Maximal subgroups

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

subgroupindex
#214591142
#533×D612
#214570572
#214570482
#214570392
#214570352
#214570332
#214570262
#214570132
#214570042
#214563402
#214561632
#214557312
#214556082
#214556002
#432×D612
C61×#32352
#6085461