Finite Group Databasebeta

← #29681424

Subgroups — #29681424

Order 15616.

1766 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic
2C2×#16840244C211yesmaximal, characteristic
3C2×#16839757C211yesmaximal, characteristic
4C2×#103×D61C211yesmaximal, characteristic, complemented
5#21448402C211yesmaximal, characteristic, complemented
6#21446162C211yesmaximal, characteristic, complemented
7#21446160C211yesmaximal, characteristic, complemented
8#21446158C211yesmaximal, characteristic, complemented
9#21446156C211yesmaximal, characteristic, complemented
10#21446154C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446150C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1878C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C2×#14519809—24no—
19C2×#14519809—24no—
20C2×#14519809C418yescomplemented
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840244—24no—
27#16840244—24no—
28C2×Q8×Dic61C2211yescharacteristic
29C2×C4×D244—21no—
30C2×C4×D244C2211yescharacteristic
31C2×#14519739—21no—
32C2×#14519739C2211yescharacteristic
33C2×#14519735C2211yescharacteristic
34C2×#14519734—21no—
35C2×#14519734C2211yescharacteristic
36C2×C4⋊C4×D61—21no—
37C2×C4⋊C4×D61C2211yescharacteristic
38#16839757—24no—
39C2×#14519702C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519701C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43#103×D61—24no—
44C2×#14519699C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46#16839669C2211yescharacteristic
47#16839668C2211yescharacteristic
48#16839667C2211yescharacteristic
49#16839666—21no—
50#16839666—21no—
51#16839624—21no—
52#16839624—21no—
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839517C2211yescharacteristic
57#16839516C2211yescharacteristic
58#16839516C2211yescharacteristic
59C22×Q16×C61C2211yescharacteristic
60C2×C4×Q8×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C61×#391C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C61×#336C2211yescharacteristic
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226C2×C414yes—
70C2×#11758226D414yes—
71C2×#11758226D414yes—
72C22×Dic122—21no—
73C22×Dic122C2311yescharacteristic
74C2×Q8×D61—22no—
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61—22no—
78C2×Q8×D61—22no—
79C2×Q8×D61C2×C414yescomplemented
80C22×D244—21no—
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61C2311yescharacteristic
88#14519809—232no—
89C2×#11758202—22no—
90C2×#11758202—22no—
91C2×#11758202C2×C414yescomplemented
92C2×#11758190—22no—
93C2×#11758190—22no—
94C2×#11758190C2×C414yescomplemented
95C2×#11758201—22no—
96C2×#11758201—22no—
97C2×#11758201C2×C414yescomplemented
98C2×#11758189—22no—
99C2×#11758189—22no—
100C2×#11758189C2×C414yescomplemented
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—22no—
104C2×C8×D61—22no—
105C2×C8×D61—22no—
106Q8×Dic61—22no—
107Q8×Dic61—22no—
108C4×D244—28no—
109C4×D244—22no—
110C4×D244—22no—
111#14519739—28no—
112#14519739—22no—
113#14519739—22no—
114#14519735—22no—
115#14519735—22no—
116#14519734—28no—
117#14519734—22no—
118#14519734—22no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196D411yescharacteristic
124C2×#11758196D411yescharacteristic
125C4⋊C4×D61—28no—
126C4⋊C4×D61—22no—
127C4⋊C4×D61D414yes—
128C2×#11758198—21no—
129C2×#11758198—21no—
130C2×#11758198—21no—
131C2×#11758198D411yescharacteristic
132C2×#11758198D411yescharacteristic
133C2×C4×Dic61—21no—
134C2×C4×Dic61—21no—
135C2×C4×Dic61C2311yescharacteristic
136#14519702—22no—
137#14519701—22no—
138#14519701—22no—
139#14519700—22no—
140#14519699—22no—
141#14519697—22no—
142#14519684—21no—
143#14519684—21no—
144#14519684—21no—
145#14519684—21no—
146#14519684—21no—
147#14519684—21no—
148C22×Q8×C61C2311yescharacteristic
149C22×Q8×C61C2311yescharacteristic
150C2×Q16×C61—22no—
151C2×Q16×C61—22no—
152C2×Q16×C61C2×C414yescomplemented
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155C4×Q8×C61—22no—
156C4×Q8×C61—22no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C42×C61—21no—
161C2×C42×C61C2311yescharacteristic
162#103×C61—22no—
163#103×C61—22no—
164#95×C61—21no—
165#95×C61—21no—
166C23×D61—21no—
167C23×D61C2×D411yescharacteristic
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61C22×C412yes—
177C2×Q8×C61C22×C412yes—
178C2×Q8×C61C2×D412yes—
179C2×Q8×C61C2×D412yes—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193#11758226—28no—
194#11758226—28no—
195#11758226—28no—
196#11758226C22⋊C4116yes—
197Q8×D61—28no—
198Q8×D61—28no—
199Q8×D61—44no—
200Q8×D61—44no—
201C2×D244—24no—
202C2×D244—24no—
203C2×D244—24no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244C22×C412yes—
208C2×D244C2×D412yes—
209C2×D244C2×D412yes—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—24no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—24no—
216C2×C4×D61—24no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—81no—
220C2×C4×D61—81no—
221C2×C4×D61—81no—
222C2×C4×D61—81no—
223C2×C4×D61—81no—
224C2×C4×D61—81no—
225C2×C4×D61C22×C412yes—
226C2×C4×D61C2×D412yes—
227C2×C4×D61C2×D412yes—
228C2×C4×D61C2×D412yes—
229C2×C4×D61#4112yes—
230C2×C4×D61#4112yes—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—24no—
237C2×Dic122—42no—
238C2×Dic122—42no—
239C2×Dic122C22×C412yes—
240Q16×C61—28no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61C22×C412yes—
247C4⋊C4×C61—24no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C2×D412yes—
252C42×C61—24no—
253C42×C61—21no—
254C42×C61—21no—
255#11758202—28no—
256#11758201—28no—
257#11758198—24no—
258#11758198—24no—
259#11758198—22no—
260#11758198—22no—
261#11758198—42no—
262C4⋊Dic61—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61C2×D412yes—
267#11758196—22no—
268#11758196—24no—
269#11758196—22no—
270C4×Dic61—24no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61—42no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418C22×C412yes—
280#11758190—28no—
281#11758189—28no—
282C8×D61—44no—
283C23×C61C22×D411yescharacteristic
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61C4×D412yes—
296C22×D61#12012yes—
297C22×D61#12112yes—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—41no—
304Q8×C61—41no—
305Q8×C61C2×C22⋊C414yes—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61C23×C411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C2×#4111yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×Dic61—22no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—22no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61C4×D412yes—
346C2×Dic61#12012yes—
347C2×Dic61#12112yes—
348D244—216no—
349D244—22no—
350D244—22no—
351D244—22no—
352D244C2×C22⋊C414yes—
353C4×D61—216no—
354C4×D61—48no—
355C4×D61—84no—
356C4×D61—84no—
357C4×D61—84no—
358C4×D61C2×C22⋊C414yes—
359C4×D61C4×D414yes—
360C4×D61#12114yes—
361C4×D61#12314yes—
362Dic122—22no—
363Dic122—22no—
364Dic122—41no—
365Dic122—41no—
366Dic122—48no—
367C8×C61—22no—
368C8×C61—41no—
369#92418—22no—
370#92418—41no—
371#20931—611nomaximal, Sylow
372C22×C61C2×C4×D411yescharacteristic
373C22×C61C2×#12011yescharacteristic
374C22×C61C2×#12111yescharacteristic
375C22×C61#57711yescharacteristic
376C22×C61#57711yescharacteristic
377C22×C61#57811yescharacteristic
378C22×C61#57811yescharacteristic
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—24no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61#38614yes—
393C4×C61—24no—
394C4×C61—41no—
395C4×C61—42no—
396C4×C61—41no—
397C4×C61—42no—
398C4×C61—81no—
399C4×C61C22×C22⋊C411yescharacteristic
400C4×C61C2×C4×D411yescharacteristic
401C4×C61C2×#12111yescharacteristic
402C4×C61C2×#12311yescharacteristic
403Dic61—41no—
404Dic61—42no—
405Dic61—41no—
406Dic61—42no—
407Dic61—81no—
408Dic61#38614yes—
409C22×#137—611no—
410C2×#520—611no—
411C2×#416—611no—
412C22×#103—611no—
413#2310—611no—
414#1878—611no—
415#1878—611no—
416#1878—611no—
417#1878D6111yescharacteristic, complemented
418#1877—611no—
419#1877—611no—
420#1877—611no—
421#1877—611no—
422#1736—611no—
423#1729—611no—
424C2×C61C2×#38611yescharacteristic
425C2×C61#294711yescharacteristic
426C2×C61#294711yescharacteristic
427C2×C61#300911yescharacteristic
428C2×C61#301111yescharacteristic
429C2×C61#304611yescharacteristic
430C2×C61#304611yescharacteristic
431D61—24no—
432D61—44no—
433C22×#41—611no—
434C23×Q8—611no—
435C2×#137—618no—
436C2×#137—1224no—
437C2×#137—1224no—
438C22×Q16—611no—
439C22×Q16C2×D6111yescharacteristic
440C22×SD16—611no—
441C22×SD16—611no—
442C22×M16—611no—
443C23×C8—611no—
444#520—1224no—
445#520—1224no—
446C2×C4×Q8—611no—
447C2×C4×Q8C2×D6111yescharacteristic
448C2×C4×D4—611no—
449C2×C4×D4—611no—
450C2×C4×D4—1221no—
451C2×C4×D4—1221no—
452C2×#117—611no—
453C2×#117—611no—
454C2×#117—1221no—
455C22×C4⋊C4—611no—
456C22×C4⋊C4—1221no—
457#416—1224no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—1224no—
463C2×#103C2×D6111yescharacteristic
464C2×#103C2×D6111yescharacteristic
465C2×#102—611no—
466C2×#102—611no—
467#391—611no—
468#391—611no—
469#391—611no—
470#391—1221no—
471#391—1221no—
472#391C2×D6111yescharacteristic
473#381—1221no—
474#381—1221no—
475#340—611no—
476#340—611no—
477#340—611no—
478#340C2×D6111yescharacteristic
479#336—611no—
480#336—611no—
481#336—611no—
482#336C2×D6111yescharacteristic
483C61#2093111yescharacteristic, complemented, Sylow
484C2×#41—614no—
485C2×#41—614no—
486C2×#41—614no—
487C2×#41—1222no—
488C2×#41—1222no—
489C2×#41—1222no—
490C22×Q8—614no—
491C22×Q8—611no—
492C22×Q8—1221no—
493C22×Q8—1222no—
494C22×Q8—1222no—
495C22×Q8—1222no—
496C22×Q8—1222no—
497C22×Q8—1222no—
498C22×Q8C22×D6111yescharacteristic
499C22×Q8C22×D6111yescharacteristic
500C22×D4—611no—
501C22×D4—1221no—
502C23×C4—611no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4—1221no—
507C23×C4—1221no—
508#137—12232no—
509C2×Q16—22no—
510C2×Q16—22no—
511C2×Q16—614no—
512C2×Q16—1222no—
513C2×Q16—1222no—
514C2×Q16C4×D6114yescomplemented
515C2×SD16—614no—
516C2×SD16—614no—
517C2×SD16—1222no—
518C2×SD16—1222no—
519C2×SD16—1222no—
520C2×SD16—1222no—
521C2×M16—614no—
522C2×M16—1222no—
523C2×M16—1222no—
524C22×C8—611no—
525C22×C8—611no—
526C22×C8—1222no—
527C22×C8—1222no—
528C22×C8—1222no—
529C22×C8C22×D6111yescharacteristic
530C22×C8C22×D6111yescharacteristic
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—1222no—
534C4×Q8—1222no—
535C4×D4—1222no—
536C4×D4—1222no—
537C4×D4—1228no—
538C4×D4—1222no—
539C4×D4—1228no—
540C4×D4—1222no—
541#117—1222no—
542#117—1222no—
543#117—1228no—
544#117—1222no—
545#117—1222no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—614no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—1222no—
553C2×C4⋊C4—1228no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C4⋊C4C22×D6111yescharacteristic
558C2×C22⋊C4—611no—
559C2×C22⋊C4—611no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C42—21no—
564C2×C42—611no—
565C2×C42—1221no—
566C2×C42—1221no—
567C2×C42C22×D6111yescharacteristic
568#103—22no—
569#103—22no—
570#103—1222no—
571#103—1222no—
572#103—1222no—
573#103—1222no—
574#102—1222no—
575#102—1222no—
576#95—21no—
577#95—21no—
578#95—1221no—
579#95—1221no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583#95—1221no—
584C24—611no—
585C24—1221no—
586#41—6116no—
587#41—1228no—
588#41—1228no—
589#41—1228no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—612no—
599C2×Q8—1224no—
600C2×Q8—1228no—
601C2×Q8—1228no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—2442no—
608C2×Q8—2442no—
609C2×Q8—2444no—
610C2×Q8—2444no—
611C2×Q8C2×C4×D6112yes—
612C2×Q8C2×C4×D6112yes—
613C2×Q8D4×D6112yes—
614C2×Q8D4×D6112yes—
615C2×D4—612no—
616C2×D4—612no—
617C2×D4—612no—
618C2×D4—1224no—
619C2×D4—1224no—
620C2×D4—1224no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—611no—
629C22×C4—612no—
630C22×C4—612no—
631C22×C4—612no—
632C22×C4—612no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—1224no—
638C22×C4—1224no—
639C22×C4—1224no—
640C22×C4—1224no—
641C22×C4—1224no—
642C22×C4—1224no—
643C22×C4—1224no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—4881no—
648C22×C4—4881no—
649C22×C4—4881no—
650C22×C4—4881no—
651C22×C4—4881no—
652C22×C4—4881no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4D4×D6111yescharacteristic
656C22×C4D4×D6111yescharacteristic
657C22×C4C23×D6111yescharacteristic
658Q16—28no—
659Q16—1228no—
660SD16—1228no—
661SD16—1228no—
662M16—1228no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—612no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—2444no—
675C2×C8C2×C4×D6112yes—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—612no—
681C4⋊C4—1222no—
682C4⋊C4—1224no—
683C4⋊C4—1222no—
684C4⋊C4—1224no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4D4×D6112yes—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4—2442no—
694C42—24no—
695C42—21no—
696C42—21no—
697C42—1224no—
698C42—1221no—
699C42—1221no—
700C42—2442no—
701C23—612no—
702C23—612no—
703C23—612no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23C2×D4×D6111yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723Q8—1222no—
724Q8—1222no—
725Q8—2448no—
726Q8—2441no—
727Q8—2441no—
728Q8C22⋊C4×D6114yes—
729D4—614no—
730D4—12216no—
731D4—1222no—
732D4—1222no—
733D4—1222no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—612no—
753C2×C4—612no—
754C2×C4—612no—
755C2×C4—614no—
756C2×C4—614no—
757C2×C4—614no—
758C2×C4—614no—
759C2×C4—12216no—
760C2×C4—1222no—
761C2×C4—1221no—
762C2×C4—1222no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—4884no—
769C2×C4—4884no—
770C2×C4—4884no—
771C2×C4—2448no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4C22×C4×D6111yescharacteristic
780C2×C4C2×D4×D6111yescharacteristic
781C2×C4C2×D4×D6111yescharacteristic
782C2×C4C2×D4×D6111yescharacteristic
783C2×C4#41×D6111yescharacteristic
784C2×C4#41×D6111yescharacteristic
785C8—22no—
786C8—41no—
787C8—1222no—
788C8—2441no—
789C22—614no—
790C22—1222no—
791C22—1222no—
792C22—1222no—
793C22—1222no—
794C22—1222no—
795C22—1222no—
796C22—1224no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22C4×D4×D6111yescharacteristic
804C22#120×D6111yescharacteristic
805C22#121×D6111yescharacteristic
806C22#1684056911yescharacteristic
807C22#1684057111yescharacteristic
808C22#1684057511yescharacteristic
809C22#1684057811yescharacteristic
810C4—24no—
811C4—41no—
812C4—42no—
813C4—41no—
814C4—42no—
815C4—81no—
816C4—614no—
817C4—4881no—
818C4—2441no—
819C4—2442no—
820C4—2441no—
821C4—2442no—
822C4C2×C22⋊C4×D6111yescharacteristic
823C4C4×D4×D6111yescharacteristic
824C4#121×D6111yescharacteristic
825C4#123×D6111yescharacteristic
826C2—1224no—
827C2—2444no—
828C2#386×D6111yescharacteristic
829C2#2145465711yescharacteristic
830C2#2145466111yescharacteristic
831C2#2145509311yescharacteristic
832C2#2145510911yescharacteristic
833C2#2145536611yescharacteristic
834C2#2145537211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1878C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenter#1878D61
hypocenterC61#20931
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
4. C2×#103×D61C2semidirect
5. #21448402C2semidirect
6. #21446162C2semidirect
7. #21446160C2semidirect
8. #21446158C2semidirect
9. #21446156C2semidirect
10. #21446154C2semidirect
11. #21446152C2semidirect
12. #21446150C2semidirect
13. #21445537C2semidirect
14. #21445514C2semidirect
15. C61×#1878C2semidirect
20. C2×#14519809C4semidirect
79. C2×Q8×D61C2×C4semidirect
91. C2×#11758202C2×C4semidirect
94. C2×#11758190C2×C4semidirect
97. C2×#11758201C2×C4semidirect
100. C2×#11758189C2×C4semidirect
152. C2×Q16×C61C2×C4semidirect
417. #1878D61semidirect
483. C61#20931semidirect
514. C2×Q16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145198092
C2×#168402442
C2×#168397572
C2×#103×D612
#214484022
#214461622
#214461602
#214461582
#214461562
#214461542
#214461522
#214461502
#214455372
#214455142
C61×#18782
#2093161