Finite Group Databasebeta

← #29679704

Subgroups — #29679704

Order 15616.

1330 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840527C211yesmaximal, characteristic
2C2×#16839809C211yesmaximal, characteristic, complemented
3C2×#16839803C211yesmaximal, characteristic, complemented
4#21454335C211yesmaximal, characteristic
5#417×D61C211yesmaximal, characteristic
6#21445884C211yesmaximal, characteristic, complemented
7#21445882C211yesmaximal, characteristic, complemented
8#21445881C211yesmaximal, characteristic, complemented
9#21445878C211yesmaximal, characteristic, complemented
10#21445877C211yesmaximal, characteristic, complemented
11#21445876C211yesmaximal, characteristic, complemented
12#21445875C211yesmaximal, characteristic, complemented
13#21445556C211yesmaximal, characteristic, complemented
14#343×D61C211yesmaximal, characteristic, complemented
15C61×#1816C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17#16840527—24no—
18#16840527C418yescomplemented
19C2×#14519785—21no—
20C2×#14519785C2211yescharacteristic
21C2×#14519784C2211yescharacteristic
22C2×#14519783—21no—
23C2×#14519783C2211yescharacteristic
24C22×#11758189—21no—
25C22×#11758189C2211yescharacteristic
26C2×M16×D61—21no—
27C2×M16×D61C2211yescharacteristic
28C2×M16×D61C2211yescharacteristic
29C2×M16×D61C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839809—24no—
33C2×#14519713C2211yescharacteristic, complemented
34C2×#14519712C2211yescharacteristic, complemented
35C2×#14519712C2211yescharacteristic, complemented
36#16839803—21no—
37#16839803—21no—
38#16839803—21no—
39#16839803—21no—
40C2×#14519710C2211yescharacteristic, complemented
41C2×#14519709C2211yescharacteristic, complemented
42C2×#14519708C2211yescharacteristic, complemented
43#16839769—21no—
44#16839765—21no—
45#16839764C2211yescharacteristic
46#16839764C2211yescharacteristic
47#16839763C2211yescharacteristic
48#16839763C2211yescharacteristic
49#16839762—21no—
50#16839761C2211yescharacteristic
51#16839761C2211yescharacteristic
52#16839760—21no—
53#16839757—21no—
54#16839755—21no—
55#103×D61—21no—
56#102×D61—21no—
57#16839531C2211yescharacteristic, complemented
58#16839531C2211yescharacteristic, complemented
59#16839530C2211yescharacteristic, complemented
60#16839530C2211yescharacteristic, complemented
61#16839530C2211yescharacteristic, complemented
62#16839530C2211yescharacteristic, complemented
63C2×#131×C61C2211yescharacteristic
64C2×#108×C61C2211yescharacteristic, complemented
65C2×#107×C61C2211yescharacteristic, complemented
66C61×#417C2211yescharacteristic
67C61×#417C2211yescharacteristic
68C61×#343C2211yescharacteristic, complemented
69C61×#343C2211yescharacteristic, complemented
70C2×#11758226D411yescharacteristic
71C2×#11758222—21no—
72C2×#11758222C2311yescharacteristic
73C2×#11758224—21no—
74C2×#11758224D411yescharacteristic
75#41×D61—22no—
76#41×D61—22no—
77#41×D61C2×C414yes—
78#41×D61Q814yes—
79C2×Q8×D61D411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61D411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85#14519785—22no—
86#14519785—28no—
87#14519785C2×C414yescomplemented
88#14519784—22no—
89#14519784C2×C414yescomplemented
90#14519783—22no—
91#14519783—28no—
92#14519783C2×C414yescomplemented
93C2×#11758194—21no—
94C2×#11758194C2311yescharacteristic
95C2×#11758194C2311yescharacteristic
96C2×#11758194C2311yescharacteristic
97C2×#11758189—21no—
98C2×#11758189—21no—
99C2×#11758189—21no—
100C2×#11758189—28no—
101C2×#11758189—21no—
102C2×#11758189—21no—
103C2×#11758189C2×C414yes—
104C2×#11758189D411yescharacteristic
105C2×#11758189D411yescharacteristic
106C2×#11758189D411yescharacteristic
107C2×#11758189D411yescharacteristic
108C2×#11758189D414yes—
109M16×D61—22no—
110M16×D61—28no—
111M16×D61—22no—
112M16×D61—22no—
113M16×D61—22no—
114M16×D61—22no—
115M16×D61C2×C414yes—
116C22×#92418—21no—
117C22×#92418C2311yescharacteristic
118C2×C8×D61—21no—
119C2×C8×D61—21no—
120C2×C8×D61—21no—
121C2×C8×D61—21no—
122C2×C8×D61—21no—
123#14519735—21no—
124#14519735—21no—
125#14519735—21no—
126#14519735—21no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61—21no—
134C2×#11758198—21no—
135C2×C4×Dic61—21no—
136#14519713—22no—
137#14519712—22no—
138#14519712—22no—
139#14519710—21no—
140#14519710—21no—
141#14519709—21no—
142#14519709—21no—
143#14519708—21no—
144#14519708—21no—
145#14519702—21no—
146#14519702—21no—
147#14519701—21no—
148#14519701—21no—
149#14519700—21no—
150#14519700—21no—
151#14519699—21no—
152#14519699—21no—
153#14519698—21no—
154#14519698—21no—
155#14519697—21no—
156#14519697—21no—
157C2×#41×C61C2311yescharacteristic
158#131×C61—22no—
159#131×C61C2×C414yescomplemented
160C2×M16×C61—21no—
161C2×M16×C61C2311yescharacteristic
162C2×M16×C61C2311yescharacteristic
163C2×M16×C61C2311yescharacteristic
164C22×C8×C61—21no—
165C22×C8×C61C2311yescharacteristic
166C2×C4⋊C4×C61C2311yescharacteristic
167C2×C4⋊C4×C61C2311yescharacteristic
168#108×C61—22no—
169#107×C61—21no—
170#107×C61—21no—
171#103×C61—21no—
172#103×C61—21no—
173#102×C61—21no—
174#102×C61—21no—
175C23×D61—21no—
176C23×D61#4111yescharacteristic
177#41×C61—21no—
178#41×C61—21no—
179#41×C61C22×C412yes—
180#41×C61C2×Q812yes—
181C2×Q8×C61C2×D411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C2×D411yescharacteristic
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61#4111yescharacteristic
195#11758226—22no—
196#11758226C4⋊C414yes—
197Q8×D61—22no—
198Q8×D61C4⋊C414yes—
199#11758224—24no—
200#11758224—24no—
201#11758224—22no—
202#11758224C4⋊C414yes—
203D4×D61—24no—
204D4×D61—24no—
205D4×D61—22no—
206D4×D61C4⋊C414yes—
207#11758222—21no—
208#11758222—21no—
209#11758222—24no—
210#11758222—24no—
211#11758222C22×C412yes—
212#11758222C2×Q812yes—
213C2×D244—21no—
214C2×D244C2×D411yescharacteristic
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—24no—
219C2×C4×D61—24no—
220C2×C4×D61—41no—
221C2×C4×D61—41no—
222C2×C4×D61—82no—
223C2×C4×D61C22×C412yes—
224C2×C4×D61C2×D412yes—
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×Q812yes—
230C2×C4×D61#4112yes—
231C2×Dic122—21no—
232C2×Dic122C2×D411yescharacteristic
233M16×C61—21no—
234M16×C61—24no—
235M16×C61—21no—
236M16×C61—21no—
237M16×C61—21no—
238M16×C61—21no—
239M16×C61C22×C412yes—
240C2×C8×C61—21no—
241C2×C8×C61—24no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61C22×C412yes—
245C2×C8×C61C2×D411yescharacteristic
246C2×C8×C61C2×D411yescharacteristic
247C2×C8×C61C2×D412yes—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252#11758198—41no—
253#11758198—41no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258#11758196—41no—
259#11758196—41no—
260C4×Dic61—41no—
261C4×Dic61—41no—
262#11758194—21no—
263#11758194—24no—
264#11758194—21no—
265#11758194—21no—
266#11758194—21no—
267#11758194—21no—
268#11758194C22×C412yes—
269C2×#92418—21no—
270C2×#92418—24no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418C22×C412yes—
274C2×#92418C2×D411yescharacteristic
275C2×#92418C2×D411yescharacteristic
276C2×#92418C2×D412yes—
277#11758189—24no—
278#11758189—24no—
279#11758189—24no—
280#11758189—42no—
281#11758189—42no—
282#11758189C22⋊C414yes—
283#11758189C22⋊C414yes—
284#11758189C22⋊C414yes—
285#11758189C22⋊C414yes—
286C8×D61—24no—
287C8×D61—24no—
288C8×D61—24no—
289C8×D61—42no—
290C8×D61—42no—
291C23×C61—21no—
292C23×C61C2×#4111yescharacteristic
293C22×D61—21no—
294C22×D61—24no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—81no—
298C22×D61—81no—
299C22×D61#11712yes—
300C22×D61#12111yescharacteristic
301C22×D61#12111yescharacteristic
302C22×D61C22⋊Q812yes—
303Q8×C61—21no—
304Q8×C61C2×C4⋊C412yes—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—21no—
308D4×C61C2×C4⋊C412yes—
309C2×C4×C61—21no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—81no—
315C2×C4×C61—81no—
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×Q811yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C22⋊D61—22no—
323C22⋊D61—22no—
324C22⋊D61—24no—
325C22⋊D61—24no—
326C2×Dic61—21no—
327C2×Dic61—24no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—81no—
331C2×Dic61—81no—
332C2×Dic61#11712yes—
333C2×Dic61#12111yescharacteristic
334C2×Dic61#12111yescharacteristic
335C2×Dic61C22⋊Q812yes—
336D244—24no—
337D244—21no—
338D244C2×C4⋊C412yes—
339C4×D61—24no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—24no—
343C4×D61—82no—
344C4×D61—82no—
345C4×D61C2×C22⋊C412yes—
346C4×D61C2×C22⋊C412yes—
347C4×D61C2×C4⋊C412yes—
348C4×D61C2×C4⋊C412yes—
349C4×D61#12112yes—
350C4×D61#12112yes—
351C4×D61C22⋊Q812yes—
352C4×D61C22⋊Q812yes—
353Dic122—21no—
354Dic122—24no—
355Dic122C2×C4⋊C412yes—
356C8×C61—22no—
357C8×C61—41no—
358C8×C61—41no—
359C8×C61C2×C22⋊C412yes—
360C8×C61C2×C22⋊C412yes—
361#92418—22no—
362#92418—41no—
363#92418—41no—
364#92418C2×C22⋊C412yes—
365#92418C2×C22⋊C412yes—
366#20679—611nomaximal, Sylow
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—22no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61C2×#11711yescharacteristic
373C22×C61C2×#12111yescharacteristic
374C22×C61C2×C22⋊Q811yescharacteristic
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—22no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—84no—
385C2×D61#38012yes—
386C2×D61#38012yes—
387C4×C61—22no—
388C4×C61—81no—
389C4×C61—81no—
390C4×C61C22×C22⋊C411yescharacteristic
391C4×C61C22×C4⋊C411yescharacteristic
392C4×C61C2×#12111yescharacteristic
393C4×C61C2×C22⋊Q811yescharacteristic
394Dic61—22no—
395Dic61—81no—
396Dic61—81no—
397Dic61#38012yes—
398Dic61#38012yes—
399C2×#568—611no—
400C2×#430—611no—
401C2×#428—611no—
402#2896—611no—
403C2×#417—611no—
404#1816—611no—
405#1816—611no—
406#1816—611no—
407#1816D6111yescharacteristic, complemented
408#1815—611no—
409#1815—611no—
410#1815—611no—
411#1815—611no—
412#1742—611no—
413C2×#343—611no—
414C2×C61—21no—
415C2×C61—21no—
416C2×C61—42no—
417C2×C61C2×#38011yescharacteristic
418C2×C61#306811yescharacteristic
419C2×C61#306911yescharacteristic
420D61—22no—
421D61—22no—
422D61—42no—
423C22×#41—611no—
424#568—618no—
425#568—1224no—
426C2×#131—611no—
427C2×#131—611no—
428C2×#131—611no—
429C2×#131—1221no—
430C2×#131—1221no—
431C2×#131C2×D6111yescharacteristic
432C22×M16—611no—
433C22×M16—611no—
434C22×M16—611no—
435C22×M16—611no—
436C22×M16—1221no—
437C22×M16—1221no—
438C2×#117—611no—
439C22×C4⋊C4—611no—
440#430—1224no—
441C2×#108—611no—
442C2×#108—611no—
443C2×#108—611no—
444C2×#108C2×D6111yescharacteristic, complemented
445#428—1221no—
446#428—1221no—
447#428—1221no—
448#428—1221no—
449C2×#107—611no—
450C2×#107C2×D6111yescharacteristic, complemented
451C2×#106—611no—
452C2×#106—611no—
453#419—1221no—
454#418—1221no—
455#417—611no—
456#417—611no—
457#417—611no—
458#417—611no—
459#417—611no—
460#417—611no—
461#417—1221no—
462#417—1221no—
463#417C2×D6111yescharacteristic
464#417C2×D6111yescharacteristic
465#416—1221no—
466#416—1221no—
467C2×#103—1221no—
468C2×#102—1221no—
469#343—611no—
470#343—611no—
471#343—611no—
472#343—611no—
473#343—611no—
474#343—611no—
475#343C2×D6111yescharacteristic, complemented
476#343C2×D6111yescharacteristic, complemented
477C61#2067911yescharacteristic, complemented, Sylow
478C2×#41—614no—
479C2×#41—614no—
480C2×#41—611no—
481C2×#41—611no—
482C2×#41—611no—
483C2×#41—1221no—
484C2×#41—1221no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41C22×D6111yescharacteristic
488C22×Q8—611no—
489C22×D4—611no—
490C22×D4—1221no—
491C23×C4—611no—
492C23×C4—1221no—
493C23×C4—1221no—
494#131—22no—
495#131—614no—
496#131—614no—
497#131—614no—
498#131—1228no—
499#131—1222no—
500#131—1222no—
501#131—1228no—
502#131—1222no—
503#131C4×D6114yescomplemented
504C2×M16—21no—
505C2×M16—614no—
506C2×M16—611no—
507C2×M16—611no—
508C2×M16—611no—
509C2×M16—611no—
510C2×M16—614no—
511C2×M16—611no—
512C2×M16—614no—
513C2×M16—611no—
514C2×M16—611no—
515C2×M16—1221no—
516C2×M16—1228no—
517C2×M16—1221no—
518C2×M16—1221no—
519C2×M16—1221no—
520C2×M16—1221no—
521C2×M16—1228no—
522C2×M16—1222no—
523C2×M16—1221no—
524C2×M16—1222no—
525C2×M16—1222no—
526C2×M16—1222no—
527C2×M16—1222no—
528C2×M16C22×D6111yescharacteristic
529C2×M16C22×D6111yescharacteristic
530C2×M16C22×D6111yescharacteristic
531C22×C8—21no—
532C22×C8—611no—
533C22×C8—1221no—
534C22×C8—1221no—
535C22×C8—1221no—
536C22×C8—1221no—
537C22×C8—1221no—
538C22×C8—1221no—
539C22×C8C22×D6111yescharacteristic
540#117—1221no—
541#117—1221no—
542#117—1221no—
543#117—1221no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4C22×D6111yescharacteristic
552C2×C4⋊C4C22×D6111yescharacteristic
553C2×C22⋊C4—1221no—
554C2×C42—1221no—
555#108—22no—
556#108—1222no—
557#108—1222no—
558#108—1222no—
559#107—21no—
560#107—21no—
561#107—1221no—
562#107—1221no—
563#106—1221no—
564#106—1221no—
565#106—1221no—
566#106—1221no—
567#103—21no—
568#103—21no—
569#103—1221no—
570#103—1221no—
571#103—1221no—
572#103—1221no—
573#103—1221no—
574#103—1221no—
575#102—21no—
576#102—21no—
577#102—1221no—
578#102—1221no—
579#102—1221no—
580#102—1221no—
581#102—1221no—
582#102—1221no—
583C24—611no—
584C24—1221no—
585#41—21no—
586#41—21no—
587#41—614no—
588#41—614no—
589#41—612no—
590#41—612no—
591#41—1224no—
592#41—1224no—
593#41—1224no—
594#41—1224no—
595#41—1222no—
596#41—1222no—
597#41—1221no—
598#41—1221no—
599#41C2×C4×D6112yes—
600#41Q8×D6112yes—
601C2×Q8—614no—
602C2×Q8—611no—
603C2×Q8—1221no—
604C2×Q8—1222no—
605C2×Q8D4×D6111yescharacteristic
606C2×D4—21no—
607C2×D4—614no—
608C2×D4—611no—
609C2×D4—1221no—
610C2×D4—1222no—
611C2×D4—1221no—
612C2×D4—1224no—
613C2×D4—1224no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4D4×D6111yescharacteristic
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—611no—
621C22×C4—612no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—1224no—
630C22×C4—1221no—
631C22×C4—1224no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—4882no—
638C22×C4—2441no—
639C22×C4—2441no—
640C22×C4C23×D6111yescharacteristic
641M16—21no—
642M16—24no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—21no—
647M16—614no—
648M16—614no—
649M16—614no—
650M16—614no—
651M16—612no—
652M16—1224no—
653M16—1224no—
654M16—1224no—
655M16—1221no—
656M16—1224no—
657M16—1221no—
658M16—1221no—
659M16—1221no—
660M16—1221no—
661M16—2442no—
662M16—2442no—
663M16C2×C4×D6112yes—
664C2×C8—21no—
665C2×C8—24no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—612no—
669C2×C8—611no—
670C2×C8—611no—
671C2×C8—612no—
672C2×C8—1224no—
673C2×C8—1224no—
674C2×C8—1224no—
675C2×C8—1221no—
676C2×C8—1224no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—2442no—
680C2×C8—2442no—
681C2×C8C2×C4×D6112yes—
682C2×C8D4×D6111yescharacteristic
683C2×C8D4×D6111yescharacteristic
684C2×C8D4×D6112yes—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—2441no—
694C4⋊C4—2441no—
695C22⋊C4—2441no—
696C22⋊C4—2441no—
697C42—2441no—
698C42—2441no—
699C23—21no—
700C23—611no—
701C23—611no—
702C23—612no—
703C23—612no—
704C23—1224no—
705C23—1221no—
706C23—4881no—
707C23—4881no—
708C23—2441no—
709C23—2441no—
710C23#41×D6111yescharacteristic
711Q8—21no—
712Q8—612no—
713Q8—1224no—
714Q8—1221no—
715Q8C4⋊C4×D6112yes—
716D4—22no—
717D4—22no—
718D4—21no—
719D4—612no—
720D4—1224no—
721D4—1224no—
722D4—1224no—
723D4—1222no—
724D4—1222no—
725D4—1221no—
726D4C4⋊C4×D6112yes—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—612no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—612no—
738C2×C4—612no—
739C2×C4—612no—
740C2×C4—612no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—612no—
744C2×C4—612no—
745C2×C4—612no—
746C2×C4—1224no—
747C2×C4—1224no—
748C2×C4—1224no—
749C2×C4—1221no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—4882no—
753C2×C4—4882no—
754C2×C4—4881no—
755C2×C4—4881no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4C22×C4×D6111yescharacteristic
759C2×C4C2×D4×D6111yescharacteristic
760C2×C4C2×D4×D6111yescharacteristic
761C2×C4C2×D4×D6111yescharacteristic
762C2×C4C2×Q8×D6111yescharacteristic
763C2×C4#41×D6111yescharacteristic
764C8—22no—
765C8—41no—
766C8—41no—
767C8—612no—
768C8—612no—
769C8—1222no—
770C8—2441no—
771C8—2441no—
772C8C22⋊C4×D6112yes—
773C8C22⋊C4×D6112yes—
774C22—21no—
775C22—21no—
776C22—22no—
777C22—41no—
778C22—41no—
779C22—612no—
780C22—612no—
781C22—1221no—
782C22—1221no—
783C22—1221no—
784C22—1221no—
785C22—1222no—
786C22—4884no—
787C22—2442no—
788C22—2442no—
789C22—2441no—
790C22—2441no—
791C22#117×D6111yescharacteristic
792C22#121×D6111yescharacteristic
793C22C22⋊Q8×D6111yescharacteristic
794C4—22no—
795C4—81no—
796C4—81no—
797C4—612no—
798C4—612no—
799C4—1222no—
800C4—4881no—
801C4—4881no—
802C4C2×C22⋊C4×D6111yescharacteristic
803C4C2×C4⋊C4×D6111yescharacteristic
804C4#121×D6111yescharacteristic
805C4C22⋊Q8×D6111yescharacteristic
806C2—21no—
807C2—21no—
808C2—42no—
809C2—1222no—
810C2—1222no—
811C2—2442no—
812C2#380×D6111yescharacteristic
813C2#2145554511yescharacteristic
814C2#2145555411yescharacteristic
subgroupG/H
centerC22#121×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1816C2
socleC22×C61C2×#121
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1816D61
hypocenterC61#20679
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1816

Complements

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

NH ≅ G/Ntype
2. C2×#16839809C2semidirect
3. C2×#16839803C2semidirect
6. #21445884C2semidirect
7. #21445882C2semidirect
8. #21445881C2semidirect
9. #21445878C2semidirect
10. #21445877C2semidirect
11. #21445876C2semidirect
12. #21445875C2semidirect
13. #21445556C2semidirect
14. #343×D61C2semidirect
15. C61×#1816C2semidirect
18. #16840527C4semidirect
33. C2×#14519713C22semidirect
34. C2×#14519712C22semidirect
35. C2×#14519712C22semidirect
40. C2×#14519710C22semidirect
41. C2×#14519709C22semidirect
42. C2×#14519708C22semidirect
57. #16839531C22semidirect
58. #16839531C22semidirect
59. #16839530C22semidirect
60. #16839530C22semidirect
61. #16839530C22semidirect
62. #16839530C22semidirect
64. C2×#108×C61C22semidirect
65. C2×#107×C61C22semidirect
68. C61×#343C22semidirect
69. C61×#343C22semidirect
87. #14519785C2×C4semidirect
89. #14519784C2×C4semidirect
92. #14519783C2×C4semidirect
159. #131×C61C2×C4semidirect
407. #1816D61semidirect
444. C2×#108C2×D61semidirect
450. C2×#107C2×D61semidirect
475. #343C2×D61semidirect
476. #343C2×D61semidirect
477. C61#20679semidirect
503. #131C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405272
C2×#168398092
C2×#168398032
#214543352
#417×D612
#214458842
#214458822
#214458812
#214458782
#214458772
#214458762
#214458752
#214455562
#343×D612
C61×#18162
#2067961