Finite Group Databasebeta

← #29680888

Subgroups — #29680888

Order 15616.

1422 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#520×D61C211yesmaximal, characteristic
2#21454406C211yesmaximal, characteristic, complemented
3C2×#16839777C211yesmaximal, characteristic
4#21454335C211yesmaximal, characteristic
5#21448440C211yesmaximal, characteristic, complemented
6#21446055C211yesmaximal, characteristic, complemented
7#21446054C211yesmaximal, characteristic, complemented
8#21446053C211yesmaximal, characteristic, complemented
9#21446052C211yesmaximal, characteristic, complemented
10#21446044C211yesmaximal, characteristic, complemented
11#21446043C211yesmaximal, characteristic, complemented
12#21446042C211yesmaximal, characteristic, complemented
13#343×D61C211yesmaximal, characteristic, complemented
14#21445527C211yesmaximal, characteristic, complemented
15C61×#1859C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19#16840245C2211yescharacteristic
20#16840244—21no—
21#16840243—21no—
22#16840243C2211yescharacteristic
23#16840242—21no—
24#16840242C2211yescharacteristic
25#16840241—22no—
26#16840241—21no—
27C4×Q8×D61—21no—
28C4×D4×D61—21no—
29C4×D4×D61—22no—
30C2×#14519735C2211yescharacteristic
31C2×#14519734C2211yescharacteristic
32#117×D61—21no—
33#117×D61C2211yescharacteristic
34C2×C4⋊C4×D61—21no—
35C2×C4⋊C4×D61C2211yescharacteristic
36#16839805C2211yescharacteristic, complemented
37#16839804C2211yescharacteristic, complemented
38#16839803—21no—
39#16839802C2211yescharacteristic, complemented
40#16839801—21no—
41#16839799—21no—
42#16839797—21no—
43#16839777C418yescomplemented
44C2×#14519705C2211yescharacteristic
45C2×#14519704C2211yescharacteristic
46C2×#14519703C2211yescharacteristic
47#16839769—21no—
48#16839765—21no—
49#16839764C2211yescharacteristic
50#16839763C2211yescharacteristic
51#16839761C2211yescharacteristic
52#16839757—21no—
53#16839755—21no—
54#16839657—22no—
55#16839633—22no—
56#16839631C2211yescharacteristic, complemented
57#16839628C2211yescharacteristic, complemented
58#16839627C2211yescharacteristic, complemented
59#16839531C2211yescharacteristic, complemented
60#16839530C2211yescharacteristic, complemented
61#16839530C2211yescharacteristic, complemented
62#16839523C2211yescharacteristic, complemented
63#16839522C2211yescharacteristic, complemented
64#16839521C2211yescharacteristic, complemented
65C61×#520C2211yescharacteristic
66C61×#428C2211yescharacteristic, complemented
67C2×#104×C61C2211yescharacteristic
68C61×#417C2211yescharacteristic
69C61×#384C2211yescharacteristic, complemented
70C61×#343C2211yescharacteristic, complemented
71C61×#339C2211yescharacteristic, complemented
72C2×#11758226D411yescharacteristic
73C2×#11758222—21no—
74C2×#11758222C2311yescharacteristic
75C2×#11758224—21no—
76C2×#11758224D411yescharacteristic
77#41×D61—22no—
78#41×D61—22no—
79#41×D61C2×C414yes—
80#41×D61Q814yes—
81C2×Q8×D61D411yescharacteristic
82C2×D4×D61—21no—
83C2×D4×D61D411yescharacteristic
84C22×C4×D61—21no—
85C22×C4×D61—22no—
86C22×C4×D61D412yes—
87C22×C4×D61C2311yescharacteristic
88C2×#11758194C2311yescharacteristic
89C2×#11758194C2311yescharacteristic
90C2×#11758189—21no—
91C2×#11758189—21no—
92M16×D61—22no—
93M16×D61—22no—
94M16×D61—22no—
95M16×D61C2×C414yescomplemented
96C2×C8×D61—21no—
97C2×C8×D61—21no—
98Q8×Dic61—21no—
99C4×Dic122—22no—
100C4×Dic122—21no—
101#14519742—22no—
102#14519742—21no—
103C4×D244—22no—
104C4×D244—21no—
105D4×Dic61—21no—
106D4×Dic61—22no—
107#14519739—22no—
108#14519739—21no—
109C4×C22⋊D61—22no—
110C4×C22⋊D61—22no—
111C4×C22⋊D61—22no—
112#14519737—22no—
113#14519737—22no—
114#14519737—22no—
115#14519736—21no—
116#14519736C2311yescharacteristic
117#14519735—21no—
118#14519735—21no—
119#14519735—21no—
120#14519735—21no—
121#14519735—21no—
122#14519735—21no—
123#14519735D411yescharacteristic
124#14519735D411yescharacteristic
125#14519734—22no—
126#14519734—21no—
127#14519734—22no—
128#14519734C2×C414yescomplemented
129#14519733—22no—
130#14519733—21no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×#11758196—22no—
135C2×#11758196—21no—
136C2×#11758196—22no—
137C2×#11758196D412yes—
138C4⋊C4×D61—22no—
139C4⋊C4×D61—22no—
140C4⋊C4×D61—21no—
141C4⋊C4×D61—21no—
142C4⋊C4×D61—21no—
143C4⋊C4×D61—21no—
144C4⋊C4×D61—21no—
145C4⋊C4×D61—21no—
146C4⋊C4×D61D411yescharacteristic
147C4⋊C4×D61D411yescharacteristic
148C2×#11758198—21no—
149C2×#11758198—21no—
150C22⋊C4×D61—22no—
151C22⋊C4×D61—21no—
152C2×C4×Dic61—21no—
153C2×C4×Dic61C2311yescharacteristic
154C42×D61—22no—
155C42×D61—21no—
156#14519711—21no—
157#14519710—21no—
158#14519710—21no—
159#14519709—21no—
160#14519708—21no—
161#14519708—21no—
162#14519705C2×C414yescomplemented
163#14519704C2×C414yescomplemented
164#14519703C2×C414yescomplemented
165#14519702—21no—
166#14519701—21no—
167#14519700—21no—
168#14519699—21no—
169#14519698—21no—
170#14519697—21no—
171#14519684—22no—
172#14519684—22no—
173C2×#41×C61C2311yescharacteristic
174C2×M16×C61C2311yescharacteristic
175C2×M16×C61C2311yescharacteristic
176C4×Q8×C61—21no—
177C4×D4×C61—21no—
178C4×D4×C61—22no—
179#117×C61—21no—
180#117×C61C2311yescharacteristic
181C2×C4⋊C4×C61—21no—
182C2×C4⋊C4×C61—22no—
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C4⋊C4×C61C2311yescharacteristic
185C2×C42×C61C2311yescharacteristic
186#107×C61—21no—
187#106×C61—21no—
188#104×C61C2×C414yescomplemented
189#103×C61—21no—
190#102×C61—21no—
191C23×D61—21no—
192C23×D61C2×D411yescharacteristic
193#41×C61—21no—
194#41×C61—21no—
195#41×C61C22×C412yes—
196#41×C61C2×Q812yes—
197C2×Q8×C61C2×D411yescharacteristic
198C2×D4×C61—21no—
199C2×D4×C61C2×D411yescharacteristic
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—22no—
203C22×C4×C61—21no—
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—22no—
212C22×Dic61—21no—
213C22×Dic61C2×D412yes—
214C22×Dic61C2×D411yescharacteristic
215#11758226—22no—
216#11758226C4⋊C414yescomplemented
217Q8×D61—22no—
218Q8×D61C4⋊C414yescomplemented
219#11758224—24no—
220#11758224—24no—
221#11758224—22no—
222#11758224C4⋊C414yescomplemented
223D4×D61—24no—
224D4×D61—24no—
225D4×D61—22no—
226D4×D61C4⋊C414yescomplemented
227#11758222—21no—
228#11758222—21no—
229#11758222—24no—
230#11758222—24no—
231#11758222C22×C412yes—
232#11758222C2×Q812yes—
233C2×D244—21no—
234C2×D244C2×D411yescharacteristic
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—24no—
239C2×C4×D61—24no—
240C2×C4×D61—21no—
241C2×C4×D61—22no—
242C2×C4×D61—21no—
243C2×C4×D61—22no—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—84no—
247C2×C4×D61—82no—
248C2×C4×D61C22×C412yes—
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×Q812yes—
254C2×C4×D61#4112yes—
255C2×C4×D61#4112yes—
256C2×Dic122—21no—
257C2×Dic122C2×D411yescharacteristic
258M16×C61—21no—
259M16×C61—21no—
260M16×C61—21no—
261M16×C61C22×C412yescomplemented
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C4⋊C4×C61—22no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—82no—
270C4⋊C4×C61C2×D411yescharacteristic
271C4⋊C4×C61C2×D411yescharacteristic
272C22⋊C4×C61—22no—
273C22⋊C4×C61—21no—
274C42×C61—22no—
275C42×C61—21no—
276C42×C61—21no—
277C42×C61C22×C412yescomplemented
278C22⋊Dic61—22no—
279C22⋊Dic61—21no—
280#11758198—22no—
281#11758198—22no—
282#11758198—24no—
283#11758198—21no—
284#11758198—21no—
285#11758198—41no—
286#11758198—41no—
287C4⋊Dic61—22no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61C2×D411yescharacteristic
293C4⋊Dic61C2×D411yescharacteristic
294#11758196—22no—
295#11758196—22no—
296#11758196—24no—
297#11758196—22no—
298#11758196—21no—
299#11758196—22no—
300#11758196—21no—
301#11758196—82no—
302C4×Dic61—22no—
303C4×Dic61—22no—
304C4×Dic61—22no—
305C4×Dic61—21no—
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—41no—
310C4×Dic61—41no—
311C4×Dic61C22×C412yescomplemented
312#11758194—21no—
313#11758194—21no—
314#11758194—21no—
315#11758194C22×C412yescomplemented
316C2×#92418—21no—
317C2×#92418—21no—
318#11758189—24no—
319#11758189—42no—
320C8×D61—24no—
321C8×D61—42no—
322C23×C61—21no—
323C23×C61C22×D411yescharacteristic
324C22×D61—21no—
325C22×D61—24no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61C4×D412yes—
331C22×D61#12011yescharacteristic
332C22×D61#12011yescharacteristic
333C22×D61C22⋊Q812yes—
334Q8×C61—21no—
335Q8×C61C2×C4⋊C412yes—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—21no—
339D4×C61C2×C4⋊C412yes—
340C2×C4×C61—21no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—21no—
345C2×C4×C61—22no—
346C2×C4×C61—21no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—42no—
350C2×C4×C61—42no—
351C2×C4×C61—41no—
352C2×C4×C61—82no—
353C2×C4×C61C23×C411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×Q811yescharacteristic
357C2×C4×C61C2×#4111yescharacteristic
358C2×C4×C61C2×#4111yescharacteristic
359C22⋊D61—22no—
360C22⋊D61—22no—
361C22⋊D61—24no—
362C22⋊D61—24no—
363C2×Dic61—21no—
364C2×Dic61—24no—
365C2×Dic61—22no—
366C2×Dic61—21no—
367C2×Dic61—22no—
368C2×Dic61—21no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—41no—
374C2×Dic61—82no—
375C2×Dic61C4×D412yes—
376C2×Dic61#12011yescharacteristic
377C2×Dic61#12011yescharacteristic
378C2×Dic61C22⋊Q812yes—
379D244—24no—
380D244—21no—
381D244C2×C4⋊C412yes—
382C4×D61—24no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—24no—
386C4×D61—42no—
387C4×D61—44no—
388C4×D61—42no—
389C4×D61—82no—
390C4×D61—82no—
391C4×D61—82no—
392C4×D61C2×C4⋊C412yes—
393C4×D61C2×C4⋊C412yes—
394C4×D61C4×D412yes—
395C4×D61C4×D412yes—
396C4×D61C22⋊Q812yes—
397C4×D61C22⋊Q812yes—
398C4×D61#12312yes—
399C4×D61#12312yes—
400Dic122—21no—
401Dic122—24no—
402Dic122C2×C4⋊C412yes—
403C8×C61—22no—
404C8×C61—41no—
405#92418—22no—
406#92418—41no—
407#20864—611nomaximal, Sylow
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—22no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61C2×C4×D411yescharacteristic
414C22×C61C2×#12011yescharacteristic
415C22×C61C2×C22⋊Q811yescharacteristic
416C2×D61—21no—
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—22no—
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—48no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61#38512yes—
427C2×D61#38512yes—
428C4×C61—22no—
429C4×C61—42no—
430C4×C61—42no—
431C4×C61—41no—
432C4×C61—41no—
433C4×C61—81no—
434C4×C61C22×C4⋊C411yescharacteristic
435C4×C61C2×C4×D411yescharacteristic
436C4×C61C2×C22⋊Q811yescharacteristic
437C4×C61C2×#12311yescharacteristic
438Dic61—22no—
439Dic61—42no—
440Dic61—42no—
441Dic61—41no—
442Dic61—41no—
443Dic61—81no—
444Dic61#38512yes—
445Dic61#38512yes—
446C2×#520—611no—
447#2911—611no—
448C2×#421—611no—
449#2896—611no—
450#2317—611no—
451#1860—611no—
452#1860—611no—
453#1860—611no—
454#1860—611no—
455#1859—611no—
456#1859—611no—
457#1859—611no—
458#1859D6111yescharacteristic, complemented
459C2×#343—611no—
460#1733—611no—
461C2×C61—21no—
462C2×C61—21no—
463C2×C61—42no—
464C2×C61C2×#38511yescharacteristic
465C2×C61#301911yescharacteristic
466C2×C61#302011yescharacteristic
467D61—22no—
468D61—22no—
469D61—42no—
470C22×#41—611no—
471C22×M16—611no—
472C22×M16—611no—
473#520—611no—
474#520—611no—
475#520—611no—
476#520—1221no—
477#520—1222no—
478#520—1221no—
479#520—1221no—
480#520—1221no—
481#520C2×D6111yescharacteristic
482C2×C4×Q8—1221no—
483C2×C4×D4—1222no—
484C2×C4×D4—1221no—
485C2×#117—611no—
486C2×#117—611no—
487C2×#117—611no—
488C2×#117—1221no—
489C22×C4⋊C4—611no—
490C22×C4⋊C4—1221no—
491#428—611no—
492#428—611no—
493#428—611no—
494#428—1221no—
495#428—1221no—
496#428C2×D6111yescharacteristic, complemented
497#427—1221no—
498#427—1221no—
499#421—618no—
500C2×#104—611no—
501C2×#104—611no—
502C2×#104—611no—
503C2×#104C2×D6111yescharacteristic
504#419—1221no—
505#418—1221no—
506#417—611no—
507#417—611no—
508#417—611no—
509#417C2×D6111yescharacteristic
510#416—1221no—
511#416—1221no—
512#389—1222no—
513#385—1222no—
514#384—611no—
515#384C2×D6111yescharacteristic, complemented
516#382—611no—
517#382—611no—
518#343—611no—
519#343—611no—
520#343—611no—
521#343C2×D6111yescharacteristic, complemented
522#339—611no—
523#339—611no—
524#339—611no—
525#339C2×D6111yescharacteristic, complemented
526C61#2086411yescharacteristic, complemented, Sylow
527C2×#41—614no—
528C2×#41—614no—
529C2×#41—611no—
530C2×#41—611no—
531C2×#41—611no—
532C2×#41—1221no—
533C2×#41—1221no—
534C2×#41—1222no—
535C2×#41—1222no—
536C2×#41C22×D6111yescharacteristic
537C22×Q8—611no—
538C22×D4—611no—
539C22×D4—1221no—
540C23×C4—611no—
541C23×C4—612no—
542C23×C4—1221no—
543C23×C4—1222no—
544C2×M16—611no—
545C2×M16—614no—
546C2×M16—611no—
547C2×M16—1221no—
548C2×M16—1221no—
549C2×M16—1222no—
550C2×M16—1222no—
551C2×M16—1222no—
552C2×M16C22×D6111yescharacteristic
553C2×M16C22×D6111yescharacteristic
554C22×C8—1221no—
555C22×C8—1221no—
556C4×Q8—21no—
557C4×Q8—1221no—
558C4×Q8—1222no—
559C4×Q8—1221no—
560C4×Q8—1222no—
561C4×Q8—1221no—
562C4×D4—21no—
563C4×D4—22no—
564C4×D4—1221no—
565C4×D4—1222no—
566C4×D4—1222no—
567C4×D4—1222no—
568C4×D4—1222no—
569C4×D4—1221no—
570C4×D4—1222no—
571C4×D4—1222no—
572C4×D4—1222no—
573C4×D4—1222no—
574C4×D4—1221no—
575C4×D4—1222no—
576#117—21no—
577#117—614no—
578#117—611no—
579#117—611no—
580#117—611no—
581#117—1221no—
582#117—1222no—
583#117—1222no—
584#117—1221no—
585#117—1222no—
586#117—1221no—
587#117—1221no—
588#117—1221no—
589#117—1221no—
590#117—1221no—
591#117—1221no—
592#117—1221no—
593#117C22×D6111yescharacteristic
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—612no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4C22×D6111yescharacteristic
614C2×C4⋊C4C22×D6111yescharacteristic
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1222no—
617C2×C22⋊C4—1221no—
618C2×C22⋊C4—1221no—
619C2×C42—611no—
620C2×C42—1221no—
621C2×C42—1222no—
622C2×C42—1221no—
623C2×C42C22×D6111yescharacteristic
624#107—21no—
625#107—1221no—
626#107—1221no—
627#107—1221no—
628#106—21no—
629#106—1221no—
630#106—1221no—
631#106—1221no—
632#104—614no—
633#104—614no—
634#104—614no—
635#104C4×D6114yescomplemented
636#103—21no—
637#103—1221no—
638#103—1221no—
639#103—1221no—
640#102—21no—
641#102—1221no—
642#102—1221no—
643#102—1221no—
644#95—1222no—
645#95—1222no—
646C24—611no—
647C24—1221no—
648#41—21no—
649#41—21no—
650#41—614no—
651#41—614no—
652#41—612no—
653#41—612no—
654#41—1224no—
655#41—1224no—
656#41—1224no—
657#41—1224no—
658#41—1222no—
659#41—1222no—
660#41—1221no—
661#41—1221no—
662#41C2×C4×D6112yes—
663#41Q8×D6112yes—
664C2×Q8—614no—
665C2×Q8—611no—
666C2×Q8—1221no—
667C2×Q8—1222no—
668C2×Q8D4×D6111yescharacteristic
669C2×D4—21no—
670C2×D4—614no—
671C2×D4—611no—
672C2×D4—1221no—
673C2×D4—1222no—
674C2×D4—1221no—
675C2×D4—1224no—
676C2×D4—1224no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4D4×D6111yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—611no—
685C22×C4—612no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—612no—
691C22×C4—612no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—1221no—
695C22×C4—1224no—
696C22×C4—1224no—
697C22×C4—1221no—
698C22×C4—1222no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1222no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1222no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—4882no—
710C22×C4—4884no—
711C22×C4D4×D6112yes—
712C22×C4C23×D6111yescharacteristic
713M16—21no—
714M16—21no—
715M16—21no—
716M16—612no—
717M16—1224no—
718M16—1221no—
719M16—1221no—
720M16—1221no—
721M16—2442no—
722M16C2×C4×D6112yescomplemented
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—1224no—
726C2×C8—1221no—
727C2×C8—1221no—
728C2×C8—2442no—
729C4⋊C4—22no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—82no—
735C4⋊C4—611no—
736C4⋊C4—611no—
737C4⋊C4—1222no—
738C4⋊C4—1221no—
739C4⋊C4—1222no—
740C4⋊C4—1221no—
741C4⋊C4—1224no—
742C4⋊C4—1222no—
743C4⋊C4—1222no—
744C4⋊C4—1222no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—4882no—
750C4⋊C4D4×D6111yescharacteristic
751C4⋊C4D4×D6111yescharacteristic
752C22⋊C4—22no—
753C22⋊C4—21no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1224no—
757C22⋊C4—1222no—
758C22⋊C4—1222no—
759C22⋊C4—1222no—
760C22⋊C4—1221no—
761C22⋊C4—2441no—
762C22⋊C4—2441no—
763C42—22no—
764C42—21no—
765C42—21no—
766C42—612no—
767C42—1221no—
768C42—1221no—
769C42—1222no—
770C42—1222no—
771C42—1222no—
772C42—1221no—
773C42—1221no—
774C42—2441no—
775C42—2441no—
776C42C2×C4×D6112yescomplemented
777C23—21no—
778C23—611no—
779C23—611no—
780C23—612no—
781C23—612no—
782C23—1224no—
783C23—1221no—
784C23—2441no—
785C23—2441no—
786C23—2442no—
787C23—2442no—
788C23C2×D4×D6111yescharacteristic
789Q8—21no—
790Q8—612no—
791Q8—1224no—
792Q8—1221no—
793Q8C4⋊C4×D6112yes—
794D4—22no—
795D4—22no—
796D4—21no—
797D4—612no—
798D4—1224no—
799D4—1224no—
800D4—1224no—
801D4—1222no—
802D4—1222no—
803D4—1221no—
804D4C4⋊C4×D6112yes—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—82no—
818C2×C4—612no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—612no—
822C2×C4—612no—
823C2×C4—612no—
824C2×C4—612no—
825C2×C4—612no—
826C2×C4—612no—
827C2×C4—612no—
828C2×C4—612no—
829C2×C4—612no—
830C2×C4—1224no—
831C2×C4—1224no—
832C2×C4—1224no—
833C2×C4—1221no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1222no—
840C2×C4—4882no—
841C2×C4—4882no—
842C2×C4—4882no—
843C2×C4—4882no—
844C2×C4—2442no—
845C2×C4—2444no—
846C2×C4—2442no—
847C2×C4—2442no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2442no—
852C2×C4C22×C4×D6111yescharacteristic
853C2×C4C2×D4×D6111yescharacteristic
854C2×C4C2×D4×D6111yescharacteristic
855C2×C4C2×Q8×D6111yescharacteristic
856C2×C4#41×D6111yescharacteristic
857C2×C4#41×D6111yescharacteristic
858C8—22no—
859C8—41no—
860C8—1222no—
861C8—2441no—
862C22—21no—
863C22—21no—
864C22—22no—
865C22—41no—
866C22—41no—
867C22—612no—
868C22—612no—
869C22—1221no—
870C22—1221no—
871C22—1221no—
872C22—1221no—
873C22—1222no—
874C22—2442no—
875C22—2442no—
876C22—2448no—
877C22—2441no—
878C22—2441no—
879C22C4×D4×D6111yescharacteristic
880C22#120×D6111yescharacteristic
881C22C22⋊Q8×D6111yescharacteristic
882C4—22no—
883C4—42no—
884C4—42no—
885C4—41no—
886C4—41no—
887C4—81no—
888C4—612no—
889C4—612no—
890C4—1222no—
891C4—4881no—
892C4—2442no—
893C4—2441no—
894C4—2442no—
895C4—2441no—
896C4C2×C4⋊C4×D6111yescharacteristic
897C4C4×D4×D6111yescharacteristic
898C4C22⋊Q8×D6111yescharacteristic
899C4#123×D6111yescharacteristic
900C2—21no—
901C2—21no—
902C2—42no—
903C2—1222no—
904C2—1222no—
905C2—2442no—
906C2#385×D6111yescharacteristic
907C2#2145517311yescharacteristic
908C2#2145518411yescharacteristic
subgroupG/H
centerC22#120×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1859C2
socleC22×C61C2×#120
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1859D61
hypocenterC61#20864
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1859

Complements

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

NH ≅ G/Ntype
2. #21454406C2semidirect
5. #21448440C2semidirect
6. #21446055C2semidirect
7. #21446054C2semidirect
8. #21446053C2semidirect
9. #21446052C2semidirect
10. #21446044C2semidirect
11. #21446043C2semidirect
12. #21446042C2semidirect
13. #343×D61C2semidirect
14. #21445527C2semidirect
15. C61×#1859C2semidirect
36. #16839805C22semidirect
37. #16839804C22semidirect
39. #16839802C22semidirect
43. #16839777C4semidirect
56. #16839631C22semidirect
57. #16839628C22semidirect
58. #16839627C22semidirect
59. #16839531C22semidirect
60. #16839530C22semidirect
61. #16839530C22semidirect
62. #16839523C22semidirect
63. #16839522C22semidirect
64. #16839521C22semidirect
66. C61×#428C22semidirect
69. C61×#384C22semidirect
70. C61×#343C22semidirect
71. C61×#339C22semidirect
95. M16×D61C2×C4semidirect
128. #14519734C2×C4semidirect
162. #14519705C2×C4semidirect
163. #14519704C2×C4semidirect
164. #14519703C2×C4semidirect
188. #104×C61C2×C4semidirect
216. #11758226C4⋊C4semidirect
218. Q8×D61C4⋊C4semidirect
222. #11758224C4⋊C4semidirect
226. D4×D61C4⋊C4semidirect
261. M16×C61C22×C4semidirect
277. C42×C61C22×C4semidirect
311. C4×Dic61C22×C4semidirect
315. #11758194C22×C4semidirect
458. #1859D61semidirect
496. #428C2×D61semidirect
515. #384C2×D61semidirect
521. #343C2×D61semidirect
525. #339C2×D61semidirect
526. C61#20864semidirect
635. #104C4×D61semidirect
722. M16C2×C4×D61semidirect
776. C42C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
#520×D612
#214544062
C2×#168397772
#214543352
#214484402
#214460552
#214460542
#214460532
#214460522
#214460442
#214460432
#214460422
#343×D612
#214455272
C61×#18592
#2086461