Finite Group Databasebeta

← #29681957

Subgroups — #29681957

Order 15616.

1686 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840558C211yesmaximal, characteristic
2C2×#16840527C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4#417×D61C211yesmaximal, characteristic, complemented
5C2×#16839743C211yesmaximal, characteristic, complemented
6#21446335C211yesmaximal, characteristic, complemented
7#21446334C211yesmaximal, characteristic, complemented
8#21446333C211yesmaximal, characteristic, complemented
9#21446332C211yesmaximal, characteristic, complemented
10#21446330C211yesmaximal, characteristic, complemented
11#21446329C211yesmaximal, characteristic, complemented
12#21446324C211yesmaximal, characteristic, complemented
13#343×D61C211yesmaximal, characteristic, complemented
14#21445544C211yesmaximal, characteristic, complemented
15C61×#1907C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C2×#41×D61C2211yescharacteristic
18#16840558—24no—
19#16840558C418yescomplemented
20C2×#14519810C2211yescharacteristic
21C2×#14519807C2211yescharacteristic
22C2×#14519806—21no—
23C2×#14519803C2211yescharacteristic
24C2×#14519801—21no—
25C2×#14519798—21no—
26C2×#14519796—21no—
27#16840527—24no—
28#16840527—24no—
29C2×#14519785—21no—
30C2×#14519785C2211yescharacteristic
31C2×#14519784C2211yescharacteristic
32C2×#14519783—21no—
33C2×#14519783C2211yescharacteristic
34C22×#11758189—21no—
35C22×#11758189C2211yescharacteristic
36C2×M16×D61—21no—
37C2×M16×D61C2211yescharacteristic
38C2×M16×D61C2211yescharacteristic
39C2×M16×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41#16839764C2211yescharacteristic
42#16839763C2211yescharacteristic
43#16839762—21no—
44#16839761C2211yescharacteristic
45#16839760—21no—
46#16839760—21no—
47#16839760—21no—
48#16839760—21no—
49#16839760—21no—
50C2×#14519702C2211yescharacteristic, complemented
51C2×#14519700C2211yescharacteristic, complemented
52#103×D61—21no—
53C2×#14519698C2211yescharacteristic, complemented
54#102×D61—21no—
55#16839743—24no—
56C2×#14519695C2211yescharacteristic, complemented
57C2×#14519695C2211yescharacteristic, complemented
58C2×#14519694C2211yescharacteristic, complemented
59#16839531C2211yescharacteristic, complemented
60#16839530C2211yescharacteristic, complemented
61#16839530C2211yescharacteristic, complemented
62#16839527C2211yescharacteristic, complemented
63#16839526C2211yescharacteristic, complemented
64#16839526C2211yescharacteristic, complemented
65C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
66C2×#131×C61C2211yescharacteristic
67C61×#417C2211yescharacteristic
68C2×#102×C61C2211yescharacteristic, complemented
69C2×#100×C61C2211yescharacteristic, complemented
70C61×#343C2211yescharacteristic, complemented
71C61×#341C2211yescharacteristic, complemented
72C2×#11758226D411yescharacteristic
73C2×#11758222—21no—
74C2×#11758222C2311yescharacteristic
75C2×#11758224—21no—
76C2×#11758224—21no—
77C2×#11758224—21no—
78C2×#11758224—21no—
79C2×#11758224—21no—
80C2×#11758224—22no—
81C2×#11758224—22no—
82C2×#11758224—22no—
83C2×#11758224C2×C414yes—
84C2×#11758224D411yescharacteristic
85#41×D61—22no—
86#41×D61—22no—
87#41×D61C2×C414yes—
88#41×D61D414yes—
89C22×Dic122C2311yescharacteristic
90C2×Q8×D61D411yescharacteristic
91C22×C22⋊D61—21no—
92C2×D4×D61—21no—
93C2×D4×D61D411yescharacteristic
94C23×Dic61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98#14519810—22no—
99#14519810C2×C414yescomplemented
100#14519807—22no—
101#14519807C2×C414yescomplemented
102#14519806—28no—
103#14519803—22no—
104#14519803C2×C414yescomplemented
105#14519801—28no—
106#14519798—28no—
107#14519796—28no—
108C2×Dic244—21no—
109C2×#11758202—21no—
110C2×#11758190—21no—
111C2×#11758200—21no—
112C2×#11758200—21no—
113C2×#11758199—21no—
114#14519785—28no—
115#14519785—22no—
116#14519785—22no—
117#14519784—22no—
118#14519784—22no—
119#14519783—28no—
120#14519783—22no—
121#14519783—22no—
122C2×#11758194—21no—
123C2×#11758194C2311yescharacteristic
124C2×#11758194C2311yescharacteristic
125C2×#11758194C2311yescharacteristic
126C2×#11758189—28no—
127C2×#11758189—21no—
128C2×#11758189—21no—
129C2×#11758189—22no—
130C2×#11758189—22no—
131C2×#11758189—21no—
132C2×#11758189—21no—
133C2×#11758189—21no—
134C2×#11758189D411yescharacteristic
135C2×#11758189D411yescharacteristic
136C2×#11758189D411yescharacteristic
137C2×#11758189D411yescharacteristic
138M16×D61—28no—
139M16×D61—22no—
140M16×D61—22no—
141M16×D61—22no—
142M16×D61—22no—
143M16×D61C2×C414yes—
144M16×D61D414yes—
145C22×#92418—21no—
146C22×#92418C2311yescharacteristic
147C2×C8×D61—21no—
148C2×C8×D61—21no—
149C2×C8×D61—21no—
150C2×C8×D61—21no—
151C2×C8×D61—21no—
152C2×C4⋊Dic61C2311yescharacteristic
153C2×#11758196—21no—
154C4⋊C4×D61—21no—
155C4⋊C4×D61—21no—
156C4⋊C4×D61—21no—
157C4⋊C4×D61—21no—
158#14519702—21no—
159#14519702—21no—
160#14519702—21no—
161#14519701—21no—
162#14519700—21no—
163#14519700—21no—
164#14519700—21no—
165#14519699—21no—
166#14519698—21no—
167#14519698—21no—
168#14519698—21no—
169#14519697—21no—
170#14519695—22no—
171#14519695—22no—
172#14519694—22no—
173C2×#41×C61C2311yescharacteristic
174C22×D4×C61C2311yescharacteristic
175AGL(1,ℤ/8)×C61—22no—
176AGL(1,ℤ/8)×C61C2×C414yescomplemented
177C2×SD16×C61—21no—
178C2×D8×C61—21no—
179#131×C61—22no—
180#131×C61—22no—
181C2×M16×C61—21no—
182C2×M16×C61C2311yescharacteristic
183C2×M16×C61C2311yescharacteristic
184C2×M16×C61C2311yescharacteristic
185C22×C8×C61—21no—
186C22×C8×C61C2311yescharacteristic
187C2×C4⋊C4×C61C2311yescharacteristic
188#103×C61—21no—
189#102×C61—21no—
190#102×C61—21no—
191#102×C61—21no—
192#100×C61—22no—
193C24×C61—21no—
194C23×D61—21no—
195C23×D61#4111yescharacteristic
196#41×C61—21no—
197#41×C61—21no—
198#41×C61C22×C412yes—
199#41×C61C2×D412yes—
200C2×Q8×C61C2×D411yescharacteristic
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61C22×C412yes—
208C2×D4×C61C2×D411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—24no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—41no—
217C2×C22⋊D61—41no—
218C2×C22⋊D61—42no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—24no—
222C22×Dic61—21no—
223C22×Dic61—41no—
224C22×Dic61—41no—
225C22×Dic61—42no—
226C22×Dic61#4111yescharacteristic
227#11758226—22no—
228#11758226C22⋊C414yes—
229Q8×D61—22no—
230Q8×D61C22⋊C414yes—
231#11758224—24no—
232#11758224—24no—
233#11758224—24no—
234#11758224—24no—
235#11758224—24no—
236#11758224—24no—
237#11758224—22no—
238#11758224—42no—
239#11758224—42no—
240#11758224—42no—
241#11758224—42no—
242#11758224C22⋊C414yes—
243D4×D61—24no—
244D4×D61—24no—
245D4×D61—22no—
246D4×D61C22⋊C414yes—
247#11758222—21no—
248#11758222—21no—
249#11758222—24no—
250#11758222—24no—
251#11758222C22×C412yes—
252#11758222C2×D412yes—
253C2×D244—21no—
254C2×D244C2×D411yescharacteristic
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—24no—
259C2×C4×D61—24no—
260C2×C4×D61—41no—
261C2×C4×D61—41no—
262C2×C4×D61—82no—
263C2×C4×D61C22×C412yes—
264C2×C4×D61C2×D412yes—
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D412yes—
270C2×C4×D61#4112yes—
271C2×Dic122—21no—
272C2×Dic122—21no—
273C2×Dic122—21no—
274C2×Dic122—21no—
275C2×Dic122—21no—
276C2×Dic122—21no—
277C2×Dic122C22×C412yes—
278C2×Dic122C2×D411yescharacteristic
279SD16×C61—24no—
280D8×C61—24no—
281M16×C61—24no—
282M16×C61—21no—
283M16×C61—21no—
284M16×C61—21no—
285M16×C61—21no—
286M16×C61C22×C412yes—
287M16×C61C2×D412yes—
288C2×C8×C61—24no—
289C2×C8×C61—21no—
290C2×C8×C61—21no—
291C2×C8×C61—21no—
292C2×C8×C61—21no—
293C2×C8×C61—21no—
294C2×C8×C61C2×D411yescharacteristic
295C2×C8×C61C2×D411yescharacteristic
296C4⋊C4×C61—21no—
297C4⋊C4×C61—21no—
298#11758202—24no—
299#11758200—24no—
300#11758200—24no—
301#11758199—24no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304#11758196—41no—
305#11758196—41no—
306#11758194—24no—
307#11758194—21no—
308#11758194—21no—
309#11758194—21no—
310#11758194—21no—
311#11758194C22×C412yes—
312#11758194C2×D412yes—
313C2×#92418—24no—
314C2×#92418—21no—
315C2×#92418—21no—
316C2×#92418—21no—
317C2×#92418—21no—
318C2×#92418—21no—
319C2×#92418C2×D411yescharacteristic
320C2×#92418C2×D411yescharacteristic
321Dic244—24no—
322#11758190—24no—
323#11758189—24no—
324#11758189—24no—
325#11758189—24no—
326#11758189—22no—
327#11758189—24no—
328#11758189—22no—
329#11758189—22no—
330#11758189—22no—
331#11758189—42no—
332C8×D61—24no—
333C8×D61—24no—
334C8×D61—24no—
335C8×D61—24no—
336C8×D61—42no—
337C23×C61—21no—
338C23×C61—22no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—81no—
342C23×C61—81no—
343C23×C61C2×#4111yescharacteristic
344C22×D61—21no—
345C22×D61—24no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—81no—
349C22×D61—81no—
350C22×D61C4×D412yes—
351C22×D61#12111yescharacteristic
352C22×D61#12111yescharacteristic
353C22×D61#12312yes—
354Q8×C61—21no—
355Q8×C61C2×C22⋊C412yes—
356D4×C61—22no—
357D4×C61—22no—
358D4×C61—22no—
359D4×C61—22no—
360D4×C61—21no—
361D4×C61—41no—
362D4×C61—41no—
363D4×C61C2×C22⋊C412yes—
364C2×C4×C61—21no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—41no—
368C2×C4×C61—81no—
369C2×C4×C61C23×C411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C2×#4111yescharacteristic
375C22⋊D61—22no—
376C22⋊D61—22no—
377C22⋊D61—24no—
378C22⋊D61—24no—
379C22⋊D61—44no—
380C22⋊D61—44no—
381C2×Dic61—21no—
382C2×Dic61—24no—
383C2×Dic61—22no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—44no—
387C2×Dic61—44no—
388C2×Dic61—41no—
389C2×Dic61—81no—
390C2×Dic61C4×D412yes—
391C2×Dic61#12111yescharacteristic
392C2×Dic61#12111yescharacteristic
393C2×Dic61#12312yes—
394D244—24no—
395D244—21no—
396D244C2×C22⋊C412yes—
397C4×D61—24no—
398C4×D61—22no—
399C4×D61—22no—
400C4×D61—24no—
401C4×D61—82no—
402C4×D61—82no—
403C4×D61C2×C22⋊C412yes—
404C4×D61C2×C22⋊C412yes—
405C4×D61C4×D412yes—
406C4×D61C4×D412yes—
407C4×D61#12012yes—
408C4×D61#12012yes—
409C4×D61#12112yes—
410C4×D61#12112yes—
411Dic122—21no—
412Dic122—24no—
413Dic122—22no—
414Dic122—22no—
415Dic122—41no—
416Dic122—41no—
417Dic122C2×C22⋊C412yes—
418C8×C61—22no—
419C8×C61—22no—
420C8×C61—21no—
421C8×C61—21no—
422C8×C61—41no—
423#92418—22no—
424#92418—22no—
425#92418—21no—
426#92418—21no—
427#92418—41no—
428#21004—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—22no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—42no—
435C22×C61—82no—
436C22×C61—82no—
437C22×C61—81no—
438C22×C61—81no—
439C22×C61C2×C4×D411yescharacteristic
440C22×C61C2×#12111yescharacteristic
441C22×C61C2×#12311yescharacteristic
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—22no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—84no—
452C2×D61#38612yes—
453C2×D61#38612yes—
454C4×C61—22no—
455C4×C61—81no—
456C4×C61C22×C22⋊C411yescharacteristic
457C4×C61C2×C4×D411yescharacteristic
458C4×C61C2×#12011yescharacteristic
459C4×C61C2×#12111yescharacteristic
460Dic61—22no—
461Dic61—42no—
462Dic61—81no—
463Dic61#38612yes—
464Dic61#38612yes—
465C2×#575—611no—
466C2×#568—611no—
467C2×#417—611no—
468C2×#417—611no—
469C2×#413—611no—
470#1908—611no—
471#1908—611no—
472#1908—611no—
473#1908—611no—
474#1907—611no—
475#1907—611no—
476#1907—611no—
477#1907D6111yescharacteristic, complemented
478C2×#343—611no—
479#1738—611no—
480C2×C61—21no—
481C2×C61—21no—
482C2×C61—42no—
483C2×C61—82no—
484C2×C61C2×#38611yescharacteristic
485C2×C61#306811yescharacteristic
486C2×C61#306911yescharacteristic
487D61—22no—
488D61—22no—
489D61—42no—
490C22×#41—611no—
491C22×#41—611no—
492#575—618no—
493#575—1224no—
494C2×#137—611no—
495C2×#137—611no—
496C2×#137—1221no—
497C2×AGL(1,ℤ/8)—611no—
498C2×AGL(1,ℤ/8)—1221no—
499C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
500C2×#135—1221no—
501C2×#135—1221no—
502#568—1224no—
503#568—1224no—
504C2×#131—611no—
505C2×#131—611no—
506C2×#131—611no—
507C2×#131—1221no—
508C2×#131—1221no—
509C2×#131C2×D6111yescharacteristic
510C22×M16—611no—
511C22×M16—611no—
512C22×M16—611no—
513C22×M16—611no—
514C22×M16—1221no—
515C22×M16—1221no—
516C22×C4⋊C4—611no—
517#417—611no—
518#417—611no—
519#417—611no—
520#417—1221no—
521#417—1221no—
522#417—1221no—
523#417—1221no—
524#417—1221no—
525#417—1221no—
526#417C2×D6111yescharacteristic
527C2×#103—611no—
528C2×#103—611no—
529C2×#103—1221no—
530C2×#102—611no—
531C2×#102—1221no—
532C2×#102C2×D6111yescharacteristic, complemented
533#413—1224no—
534C2×#101—611no—
535C2×#101—611no—
536C2×#100—611no—
537C2×#100C2×D6111yescharacteristic, complemented
538#343—611no—
539#343—611no—
540#343—611no—
541#343C2×D6111yescharacteristic, complemented
542#341—611no—
543#341—611no—
544#341—611no—
545#341C2×D6111yescharacteristic, complemented
546C61#2100411yescharacteristic, complemented, Sylow
547C2×#41—614no—
548C2×#41—614no—
549C2×#41—611no—
550C2×#41—614no—
551C2×#41—611no—
552C2×#41—611no—
553C2×#41—1221no—
554C2×#41—1221no—
555C2×#41—1222no—
556C2×#41—1222no—
557C2×#41—1222no—
558C2×#41—1221no—
559C2×#41—1221no—
560C2×#41—1222no—
561C2×#41—1222no—
562C2×#41—1221no—
563C2×#41—1221no—
564C2×#41C22×D6111yescharacteristic
565C22×Q8—611no—
566C22×Q8—611no—
567C22×D4—611no—
568C22×D4—1221no—
569C22×D4—1221no—
570C22×D4C22×D6111yescharacteristic
571C23×C4—611no—
572C23×C4—1221no—
573C23×C4—1221no—
574C23×C4—1221no—
575#137—614no—
576#137—614no—
577#137—1222no—
578#137—1228no—
579#137—1222no—
580AGL(1,ℤ/8)—22no—
581AGL(1,ℤ/8)—614no—
582AGL(1,ℤ/8)—1228no—
583AGL(1,ℤ/8)—1222no—
584AGL(1,ℤ/8)C4×D6114yescomplemented
585#135—1228no—
586#135—1228no—
587C2×Q16—1221no—
588C2×Q16—1221no—
589C2×SD16—21no—
590C2×SD16—1221no—
591C2×SD16—1221no—
592C2×SD16—1221no—
593C2×D8—21no—
594C2×D8—1221no—
595#131—22no—
596#131—22no—
597#131—1222no—
598#131—1222no—
599#131—1228no—
600#131—1222no—
601#131—1228no—
602#131—1222no—
603#131—1222no—
604#131—1222no—
605C2×M16—21no—
606C2×M16—611no—
607C2×M16—611no—
608C2×M16—611no—
609C2×M16—611no—
610C2×M16—611no—
611C2×M16—611no—
612C2×M16—614no—
613C2×M16—614no—
614C2×M16—611no—
615C2×M16—1221no—
616C2×M16—1221no—
617C2×M16—1222no—
618C2×M16—1222no—
619C2×M16—1221no—
620C2×M16—1228no—
621C2×M16—1221no—
622C2×M16—1221no—
623C2×M16—1222no—
624C2×M16—1222no—
625C2×M16—1228no—
626C2×M16—1221no—
627C2×M16—1222no—
628C2×M16—1222no—
629C2×M16C22×D6111yescharacteristic
630C2×M16C22×D6111yescharacteristic
631C2×M16C22×D6111yescharacteristic
632C22×C8—21no—
633C22×C8—611no—
634C22×C8—1221no—
635C22×C8—1221no—
636C22×C8—1221no—
637C22×C8—1221no—
638C22×C8—1221no—
639C22×C8—1221no—
640C22×C8C22×D6111yescharacteristic
641C2×C4⋊C4—611no—
642C2×C4⋊C4—1221no—
643C2×C4⋊C4—1221no—
644C2×C4⋊C4—1221no—
645C2×C4⋊C4—1221no—
646C2×C4⋊C4—1221no—
647C2×C4⋊C4C22×D6111yescharacteristic
648#103—21no—
649#103—1221no—
650#103—1221no—
651#103—1221no—
652#103—1221no—
653#103—1221no—
654#103—1221no—
655#103—1221no—
656#102—21no—
657#102—21no—
658#102—21no—
659#102—1221no—
660#102—1221no—
661#102—1221no—
662#102—1221no—
663#102—1221no—
664#101—1222no—
665#101—1222no—
666#100—22no—
667#100—1222no—
668C24—21no—
669C24—611no—
670C24—1221no—
671#41—21no—
672#41—21no—
673#41—614no—
674#41—614no—
675#41—612no—
676#41—612no—
677#41—1224no—
678#41—1224no—
679#41—1224no—
680#41—1224no—
681#41—1222no—
682#41—1222no—
683#41—1224no—
684#41—1224no—
685#41—1224no—
686#41—1224no—
687#41—1221no—
688#41—1221no—
689#41—2442no—
690#41—2442no—
691#41—2442no—
692#41—2442no—
693#41C2×C4×D6112yes—
694#41D4×D6112yes—
695C2×Q8—614no—
696C2×Q8—612no—
697C2×Q8—611no—
698C2×Q8—1221no—
699C2×Q8—1222no—
700C2×Q8—1221no—
701C2×Q8—1221no—
702C2×Q8—1221no—
703C2×Q8—1221no—
704C2×Q8—1221no—
705C2×Q8D4×D6111yescharacteristic
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—614no—
713C2×D4—611no—
714C2×D4—1221no—
715C2×D4—1222no—
716C2×D4—1221no—
717C2×D4—1224no—
718C2×D4—1224no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1224no—
722C2×D4—2441no—
723C2×D4—2441no—
724C2×D4—2442no—
725C2×D4C2×C4×D6112yes—
726C2×D4D4×D6111yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—611no—
730C22×C4—612no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—612no—
736C22×C4—612no—
737C22×C4—612no—
738C22×C4—1224no—
739C22×C4—1221no—
740C22×C4—1224no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1224no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—4882no—
748C22×C4—2441no—
749C22×C4—2441no—
750C22×C4—2441no—
751C22×C4—2441no—
752C22×C4—2442no—
753C22×C4C23×D6111yescharacteristic
754Q16—1224no—
755Q16—1224no—
756SD16—24no—
757SD16—1224no—
758SD16—1224no—
759SD16—1224no—
760D8—24no—
761D8—1224no—
762M16—24no—
763M16—21no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16—612no—
768M16—612no—
769M16—1222no—
770M16—1224no—
771M16—1222no—
772M16—1222no—
773M16—1222no—
774M16—1224no—
775M16—1224no—
776M16—1224no—
777M16—1224no—
778M16—1221no—
779M16—1221no—
780M16—1221no—
781M16—1221no—
782M16—2442no—
783M16C2×C4×D6112yes—
784M16D4×D6112yes—
785C2×C8—24no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—611no—
792C2×C8—611no—
793C2×C8—1224no—
794C2×C8—1224no—
795C2×C8—1224no—
796C2×C8—1224no—
797C2×C8—1224no—
798C2×C8—1221no—
799C2×C8—1221no—
800C2×C8—1221no—
801C2×C8—1221no—
802C2×C8—1221no—
803C2×C8—2442no—
804C2×C8D4×D6111yescharacteristic
805C2×C8D4×D6111yescharacteristic
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—2441no—
811C4⋊C4—2441no—
812C23—21no—
813C23—22no—
814C23—41no—
815C23—41no—
816C23—81no—
817C23—81no—
818C23—611no—
819C23—611no—
820C23—612no—
821C23—612no—
822C23—1224no—
823C23—1221no—
824C23—4881no—
825C23—4881no—
826C23—2441no—
827C23—2441no—
828C23#41×D6111yescharacteristic
829Q8—21no—
830Q8—612no—
831Q8—1224no—
832Q8—1221no—
833Q8—1222no—
834Q8—1222no—
835Q8—2441no—
836Q8—2441no—
837Q8C22⋊C4×D6112yes—
838D4—22no—
839D4—22no—
840D4—22no—
841D4—22no—
842D4—21no—
843D4—41no—
844D4—41no—
845D4—612no—
846D4—1224no—
847D4—1224no—
848D4—1224no—
849D4—1222no—
850D4—1222no—
851D4—1221no—
852D4—2444no—
853D4—2444no—
854D4C22⋊C4×D6112yes—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—41no—
859C2×C4—81no—
860C2×C4—612no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—612no—
864C2×C4—612no—
865C2×C4—612no—
866C2×C4—612no—
867C2×C4—612no—
868C2×C4—612no—
869C2×C4—612no—
870C2×C4—612no—
871C2×C4—612no—
872C2×C4—1224no—
873C2×C4—1224no—
874C2×C4—1224no—
875C2×C4—1221no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—4882no—
880C2×C4—4882no—
881C2×C4—4881no—
882C2×C4—2444no—
883C2×C4—2444no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4C22×C4×D6111yescharacteristic
888C2×C4C2×D4×D6111yescharacteristic
889C2×C4C2×D4×D6111yescharacteristic
890C2×C4C2×D4×D6111yescharacteristic
891C2×C4C2×D4×D6111yescharacteristic
892C2×C4#41×D6111yescharacteristic
893C8—22no—
894C8—21no—
895C8—22no—
896C8—21no—
897C8—41no—
898C8—1222no—
899C8—1221no—
900C8—1221no—
901C8—1222no—
902C8—2441no—
903C22—21no—
904C22—21no—
905C22—22no—
906C22—41no—
907C22—41no—
908C22—42no—
909C22—82no—
910C22—82no—
911C22—81no—
912C22—81no—
913C22—612no—
914C22—612no—
915C22—1221no—
916C22—1221no—
917C22—1221no—
918C22—1221no—
919C22—1222no—
920C22—4884no—
921C22—2442no—
922C22—2442no—
923C22—2441no—
924C22—2441no—
925C22C4×D4×D6111yescharacteristic
926C22#121×D6111yescharacteristic
927C22#123×D6111yescharacteristic
928C4—22no—
929C4—81no—
930C4—612no—
931C4—612no—
932C4—1222no—
933C4—4881no—
934C4—2442no—
935C4C2×C22⋊C4×D6111yescharacteristic
936C4C4×D4×D6111yescharacteristic
937C4#120×D6111yescharacteristic
938C4#121×D6111yescharacteristic
939C2—21no—
940C2—21no—
941C2—42no—
942C2—82no—
943C2—1222no—
944C2—1222no—
945C2—2442no—
946C2#386×D6111yescharacteristic
947C2#2145554511yescharacteristic
948C2#2145555111yescharacteristic
subgroupG/H
centerC22#121×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1907C2
socleC22×C61C2×#121
prime radicalC2×#16840558C2
cosocleC22×C4×C61C24
hypercenter#1907D61
hypocenterC61#21004
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1907

Complements

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

NH ≅ G/Ntype
2. C2×#16840527C2semidirect
3. C2×#16839760C2semidirect
4. #417×D61C2semidirect
5. C2×#16839743C2semidirect
6. #21446335C2semidirect
7. #21446334C2semidirect
8. #21446333C2semidirect
9. #21446332C2semidirect
10. #21446330C2semidirect
11. #21446329C2semidirect
12. #21446324C2semidirect
13. #343×D61C2semidirect
14. #21445544C2semidirect
15. C61×#1907C2semidirect
19. #16840558C4semidirect
50. C2×#14519702C22semidirect
51. C2×#14519700C22semidirect
53. C2×#14519698C22semidirect
56. C2×#14519695C22semidirect
57. C2×#14519695C22semidirect
58. C2×#14519694C22semidirect
59. #16839531C22semidirect
60. #16839530C22semidirect
61. #16839530C22semidirect
62. #16839527C22semidirect
63. #16839526C22semidirect
64. #16839526C22semidirect
68. C2×#102×C61C22semidirect
69. C2×#100×C61C22semidirect
70. C61×#343C22semidirect
71. C61×#341C22semidirect
99. #14519810C2×C4semidirect
101. #14519807C2×C4semidirect
104. #14519803C2×C4semidirect
176. AGL(1,ℤ/8)×C61C2×C4semidirect
477. #1907D61semidirect
532. C2×#102C2×D61semidirect
537. C2×#100C2×D61semidirect
541. #343C2×D61semidirect
545. #341C2×D61semidirect
546. C61#21004semidirect
584. AGL(1,ℤ/8)C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405582
C2×#168405272
C2×#168397602
#417×D612
C2×#168397432
#214463352
#214463342
#214463332
#214463322
#214463302
#214463292
#214463242
#343×D612
#214455442
C61×#19072
#2100461