Finite Group Databasebeta

← #29700433

Subgroups — #29700433

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839902C211yesmaximal, characteristic
2C2×#16839860C211yesmaximal, characteristic, complemented
3C2×#16839769C211yesmaximal, characteristic, complemented
4#21448856C211yesmaximal, characteristic
5Q8×#11758198C211yesmaximal, characteristic, complemented
6#21446671C211yesmaximal, characteristic, complemented
7#21446508C211yesmaximal, characteristic, complemented
8#21446458C211yesmaximal, characteristic, complemented
9#21446256C211yesmaximal, characteristic
10#21446172C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446017C211yesmaximal, characteristic, complemented
13#103×Dic61C211yesmaximal, characteristic, complemented
14#21445601C211yesmaximal, characteristic, complemented
15C61×#1865C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×Q8×Dic61C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×#14519735C2211yescharacteristic
24#16839902C418yescomplemented
25#16839860—24no—
26C2×#14519710C2211yescharacteristic
27#16839769—24no—
28C2×#14519702C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519688C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839668—21no—
38#16839668C2211yescharacteristic
39#16839667—21no—
40#16839667C2211yescharacteristic
41#16839663—21no—
42#16839663C2211yescharacteristic
43#16839652—21no—
44#16839640—21no—
45#16839619—21no—
46#16839619C2211yescharacteristic
47C4⋊C4×Dic61C2211yescharacteristic
48C4×#11758198—21no—
49C4×#11758198C2211yescharacteristic
50#16839609—21no—
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C2×#106×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C22×Dic122—21no—
63C22×Dic122C2311yescharacteristic
64C2×Q8×D61—22no—
65C2×Q8×D61—22no—
66C2×Q8×D61—22no—
67C2×Q8×D61—41no—
68C2×Q8×D61—41no—
69C2×Q8×D61C2×C414yescomplemented
70C22×D244—21no—
71C22×D244C2311yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61C2311yescharacteristic
75C2×#11758190—41no—
76C2×#11758190—41no—
77C2×#11758190C2×C414yes—
78C2×#11758201—22no—
79C2×#11758201—22no—
80C2×#11758201C2×C414yes—
81C2×#11758189—22no—
82C2×#11758189—22no—
83C2×#11758189—41no—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519752—22no—
87#14519752C2×C414yes—
88Q8×Dic61—22no—
89Q8×Dic61—41no—
90C4×D244—22no—
91C4×D244—41no—
92#14519735—22no—
93#14519735—41no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198D411yescharacteristic
104C2×#11758198D411yescharacteristic
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61C2311yescharacteristic
109#14519710—22no—
110#14519702—22no—
111#14519701D414yescomplemented
112#14519700—22no—
113#14519700C2×C414yescomplemented
114#14519699—41no—
115#14519697—22no—
116#14519689C2×C414yescomplemented
117#14519688—22no—
118C8×Dic61—41no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684D411yescharacteristic
126#14519684D411yescharacteristic
127C22×Q8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C4×Q8×C61—22no—
131C4×Q8×C61—41no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C42×C61—21no—
138C2×C42×C61C2311yescharacteristic
139#106×C61—41no—
140#103×C61—22no—
141#103×C61C2×C414yescomplemented
142#95×C61—21no—
143C23×D61—21no—
144C23×D61C2×D411yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61C22×C412yes—
149C2×Q8×C61C2×D412yes—
150C2×Q8×C61#4112yes—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2411yescharacteristic
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164Q8×D61—28no—
165Q8×D61—44no—
166Q8×D61—44no—
167Q8×D61—44no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—24no—
174C2×D244—81no—
175C2×D244—81no—
176C2×D244C22×C412yes—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—24no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×C4×D61—81no—
187C2×C4×D61C22×C412yes—
188C2×C4×D61#4112yes—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—24no—
195C2×Dic122—42no—
196C2×Dic122—42no—
197C2×Dic122C22×C412yes—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61C22×C412yes—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61—81no—
211C4⋊C4×C61C22×C412yes—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—42no—
215#11758201—28no—
216#11758198—24no—
217#11758198—22no—
218#11758198—41no—
219#11758198—42no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—81no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—42no—
228C4⋊Dic61C2×D412yes—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—42no—
232C4×Dic61—42no—
233C4×Dic61—81no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418C22×C412yes—
239C2×#92418C2×D412yes—
240#11758190—44no—
241#11758189—44no—
242C23×C61C22×D411yescharacteristic
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—22no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61C4×D412yes—
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61—22no—
260Q8×C61C4×D414yes—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61C23×C411yescharacteristic
280C2×C4×C61C22×D411yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61H(5,𝔽2)11yescharacteristic
284C2×C4×C61H(5,𝔽2)11yescharacteristic
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61C4×D412yes—
302C2×Dic61#13712yes—
303D244—22no—
304D244—22no—
305D244—41no—
306D244—41no—
307D244—84no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—48no—
313C4×D61—84no—
314Dic122—22no—
315Dic122—22no—
316Dic122—48no—
317Dic122—41no—
318Dic122—41no—
319C8×C61—22no—
320C8×C61—41no—
321#92418—22no—
322#92418—22no—
323#22865—611nomaximal, Sylow
324C22×C61C2×C4×D411yescharacteristic
325C22×C61D4211yescharacteristic
326C22×C61#54611yescharacteristic
327C22×C61C2×#13711yescharacteristic
328C22×C61#57511yescharacteristic
329C22×C61#57711yescharacteristic
330C22×C61#57711yescharacteristic
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61—41no—
335C2×D61—41no—
336C2×D61—41no—
337C2×D61—41no—
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—81no—
342C2×D61—81no—
343C2×D61—81no—
344C2×D61—81no—
345C4×C61—24no—
346C4×C61—42no—
347C4×C61—41no—
348C4×C61—41no—
349C4×C61—81no—
350C4×C61—81no—
351C4×C61C2×C4×D411yescharacteristic
352C4×C61#51811yescharacteristic
353C4×C61#54611yescharacteristic
354C4×C61#55111yescharacteristic
355Dic61—22no—
356Dic61—22no—
357Dic61—42no—
358Dic61—42no—
359Dic61—41no—
360Dic61—81no—
361C2×#448—611no—
362C2×#440—611no—
363C2×#419—611no—
364#2363—611no—
365Q8×C22⋊C4—611no—
366#1968—611no—
367#1935—611no—
368#1928—611no—
369#1895—611no—
370#1880—611no—
371#1877—611no—
372#1865D6111yescharacteristic, complemented
373#1854—611no—
374C4×#103—611no—
375#1753—611no—
376C2×C61#235811yescharacteristic
377C2×C61C4×#13711yescharacteristic
378C2×C61#294911yescharacteristic
379C2×C61#327511yescharacteristic
380C2×C61#327811yescharacteristic
381C2×C61#332011yescharacteristic
382C2×C61#332111yescharacteristic
383D61—42no—
384D61—82no—
385C23×Q8—611no—
386C22×SD16—611no—
387C22×SD16—611no—
388C22×M16—611no—
389C2×#121—611no—
390C2×C4×Q8—611no—
391C2×C4×Q8C2×D6111yescharacteristic
392C2×C4×D4—611no—
393C2×#117—611no—
394#448—618no—
395#440—1224no—
396C2×#107—611no—
397C2×#106C2×D6111yescharacteristic
398#419—1224no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103C2×D6111yescharacteristic
404C2×#103C2×D6111yescharacteristic
405C2×#102—611no—
406C2×#102—611no—
407C2×C22⋊C8—611no—
408C2×#97—611no—
409C2×C4×C8—611no—
410#391—611no—
411#391—611no—
412#391—1221no—
413#391—1221no—
414#390—611no—
415#390—1221no—
416#389C2×D6111yescharacteristic
417#388—1221no—
418#386—1221no—
419#380—611no—
420#380—1221no—
421C4×C4⋊C4—611no—
422C4×C22⋊C4—611no—
423C4×C22⋊C4—1221no—
424C4×C22⋊C4—1221no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340C2×D6111yescharacteristic
429#336—611no—
430#336C2×D6111yescharacteristic
431C61#2286511yescharacteristic, complemented, Sylow
432C22×Q8—614no—
433C22×Q8—611no—
434C22×Q8—1221no—
435C22×Q8—1222no—
436C22×Q8—1222no—
437C22×Q8—1222no—
438C22×Q8—2441no—
439C22×Q8—2441no—
440C22×Q8C22×D6111yescharacteristic
441C22×D4—611no—
442C22×D4—1221no—
443C23×C4—611no—
444C23×C4—1221no—
445C23×C4—1221no—
446C2×SD16—614no—
447C2×SD16—614no—
448C2×SD16—1222no—
449C2×SD16—1222no—
450C2×SD16—2441no—
451C2×SD16—2441no—
452C2×M16—1222no—
453C2×M16—1222no—
454C2×M16—2441no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8C22×D6111yescharacteristic
458C22×C8C22×D6111yescharacteristic
459#121—614no—
460#121—1222no—
461C4×Q8—22no—
462C4×Q8—41no—
463C4×Q8—1222no—
464C4×Q8—2441no—
465C4×D4—1222no—
466C4×D4—2441no—
467#117—1222no—
468#117—2441no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4C22×D6111yescharacteristic
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C42—21no—
486C2×C42—611no—
487C2×C42—1221no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42C22×D6111yescharacteristic
491#107—1222no—
492#106—41no—
493#103—22no—
494#103—614no—
495#103—614no—
496#103—1222no—
497#103—1222no—
498#103C4×D6114yescomplemented
499#102—1222no—
500#102—2441no—
501C22⋊C8—614no—
502#97—1222no—
503C4×C8—2441no—
504#95—21no—
505#95—611no—
506#95—611no—
507#95—1221no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513C24—611no—
514C24—1221no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—612no—
519C2×Q8—1224no—
520C2×Q8—1221no—
521C2×Q8—1228no—
522C2×Q8—1221no—
523C2×Q8—1221no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—2442no—
527C2×Q8—2442no—
528C2×Q8—2444no—
529C2×Q8—2444no—
530C2×Q8—2444no—
531C2×Q8C2×C4×D6112yes—
532C2×Q8D4×D6112yes—
533C2×Q8#1175822612yes—
534C2×D4—612no—
535C2×D4—1224no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—4881no—
542C2×D4—4881no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—611no—
552C22×C4—1224no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—4881no—
561C22×C4—2442no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4D4×D6111yescharacteristic
566C22×C4D4×D6111yescharacteristic
567C22×C4C23×D6111yescharacteristic
568SD16—1228no—
569SD16—2444no—
570M16—2444no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—612no—
577C2×C8—612no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8C2×C4×D6112yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—81no—
590C4⋊C4—612no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—2442no—
595C4⋊C4C2×C4×D6112yes—
596C22⋊C4—1222no—
597C22⋊C4—1224no—
598C22⋊C4—4881no—
599C22⋊C4—2441no—
600C22⋊C4—2442no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C22⋊C4—2442no—
604C42—21no—
605C42—21no—
606C42—42no—
607C42—1221no—
608C42—1221no—
609C42—4881no—
610C42—2442no—
611C42—2442no—
612C23—612no—
613C23—1221no—
614C23—1221no—
615C23—1221no—
616C23—1221no—
617C23—1221no—
618C23—1221no—
619C23—1222no—
620C23—2441no—
621C23—2441no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23—2441no—
626C23C2×D4×D6111yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—1222no—
631Q8—1222no—
632Q8—2448no—
633Q8—2441no—
634Q8—2441no—
635Q8#1451973914yes—
636D4—1222no—
637D4—1222no—
638D4—4884no—
639D4—2441no—
640D4—2441no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1222no—
673C2×C4—1221no—
674C2×C4—4884no—
675C2×C4—2448no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4C22×C4×D6111yescharacteristic
684C2×C4C2×D4×D6111yescharacteristic
685C2×C4#41×D6111yescharacteristic
686C2×C4C2×#1175822611yescharacteristic
687C2×C4#1451982211yescharacteristic
688C2×C4#1451982311yescharacteristic
689C8—22no—
690C8—41no—
691C8—1222no—
692C8—1222no—
693C22—1222no—
694C22—1222no—
695C22—1222no—
696C22—4881no—
697C22—4881no—
698C22—4881no—
699C22—4881no—
700C22—2442no—
701C22—2442no—
702C22—2442no—
703C22—2441no—
704C22—2441no—
705C22—2441no—
706C22—2441no—
707C22C4×D4×D6111yescharacteristic
708C22#1684039411yescharacteristic
709C22#1684040311yescharacteristic
710C22#137×D6111yescharacteristic
711C22#1684056111yescharacteristic
712C22#1684056811yescharacteristic
713C22#1684056911yescharacteristic
714C4—24no—
715C4—41no—
716C4—41no—
717C4—42no—
718C4—81no—
719C4—81no—
720C4—1222no—
721C4—1222no—
722C4—4881no—
723C4—2442no—
724C4—2441no—
725C4—2442no—
726C4C2×#1451973911yescharacteristic
727C4#1684023411yescharacteristic
728C4#1684040411yescharacteristic
729C4#1684043911yescharacteristic
730C2—4882no—
731C2—2442no—
732C2#2144879511yescharacteristic
733C2#2145463511yescharacteristic
734C2#2145467311yescharacteristic
735C2#2145744311yescharacteristic
736C2#2145748311yescharacteristic
737C2#2145798711yescharacteristic
738C2#2145800211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1865C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
cosocleC22×C4×C61C24
hypercenter#1865D61
hypocenterC61#22865
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
2. C2×#16839860C2semidirect
3. C2×#16839769C2semidirect
5. Q8×#11758198C2semidirect
6. #21446671C2semidirect
7. #21446508C2semidirect
8. #21446458C2semidirect
10. #21446172C2semidirect
11. #21446152C2semidirect
12. #21446017C2semidirect
13. #103×Dic61C2semidirect
14. #21445601C2semidirect
15. C61×#1865C2semidirect
24. #16839902C4semidirect
69. C2×Q8×D61C2×C4semidirect
111. #14519701D4semidirect
113. #14519700C2×C4semidirect
116. #14519689C2×C4semidirect
141. #103×C61C2×C4semidirect
372. #1865D61semidirect
431. C61#22865semidirect
498. #103C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399022
C2×#168398602
C2×#168397692
#214488562
Q8×#117581982
#214466712
#214465082
#214464582
#214462562
#214461722
#214461522
#214460172
#103×Dic612
#214456012
C61×#18652
#2286561