Finite Group Databasebeta

← #29700428

Subgroups — #29700428

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×#16839903C211yesmaximal, characteristic
2C2×#16839861C211yesmaximal, characteristic, complemented
3C2×#16839770C211yesmaximal, characteristic, complemented
4#21448857C211yesmaximal, characteristic
5#21448651C211yesmaximal, characteristic, complemented
6#21446671C211yesmaximal, characteristic, complemented
7#21446507C211yesmaximal, characteristic, complemented
8#21446459C211yesmaximal, characteristic, complemented
9#21446255C211yesmaximal, characteristic
10#21446175C211yesmaximal, characteristic, complemented
11#21446154C211yesmaximal, characteristic, complemented
12#21446084C211yesmaximal, characteristic, complemented
13#21445638C211yesmaximal, characteristic, complemented
14#21445605C211yesmaximal, characteristic, complemented
15C61×#1854C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519742C2211yescharacteristic
22C2×#14519742C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24#16839903C418yescomplemented
25#16839861—24no—
26#16839770—24no—
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519687C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839667C2211yescharacteristic
38#16839667C2211yescharacteristic
39#16839666—21no—
40#16839666—21no—
41#16839663C2211yescharacteristic
42#16839662—21no—
43#16839658C2211yescharacteristic
44#16839653—21no—
45#16839638—21no—
46#16839620—21no—
47C4⋊C4×Dic61C2211yescharacteristic
48C22⋊C4×Dic61—21no—
49C4×#11758198—21no—
50C4×C22⋊Dic61C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C2×#107×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122—22no—
63C22×Dic122—22no—
64C22×Dic122—21no—
65C22×Dic122—22no—
66C22×Dic122—41no—
67C22×Dic122—41no—
68C22×Dic122C2×C414yescomplemented
69C22×Dic122C2311yescharacteristic
70C22×Dic122C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C2×#11758190—22no—
76C2×#11758190—22no—
77C2×#11758190—41no—
78C2×#11758190—41no—
79C2×#11758190C2×C414yes—
80C2×#11758190C2×C414yes—
81C2×#11758194—22no—
82C2×#11758194—22no—
83C2×#11758194—41no—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519751—22no—
87#14519751C2×C414yes—
88#14519742—22no—
89#14519742—22no—
90#14519742—41no—
91#14519742—41no—
92#14519739—22no—
93#14519739—41no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61D411yescharacteristic
99C2×C22⋊Dic61D411yescharacteristic
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61C2311yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109#14519702C2×C414yescomplemented
110#14519702C2×C414yescomplemented
111#14519700—22no—
112#14519700—22no—
113#14519700—22no—
114#14519700D414yescomplemented
115#14519697—22no—
116#14519697—41no—
117#14519687—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
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130#117×C61—22no—
131#117×C61—41no—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139#107×C61—22no—
140#106×C61—41no—
141C22⋊C8×C61C2×C414yescomplemented
142#95×C61—21no—
143C24×C61C2×D411yescharacteristic
144C23×D61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61#4112yes—
156C22×C4×C61C2411yescharacteristic
157C2×C22⋊D61—24no—
158C2×C22⋊D61—81no—
159C2×C22⋊D61—81no—
160C22×Dic61—21no—
161C22×Dic61—24no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—42no—
165C22×Dic61—42no—
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244C22×C412yes—
176C2×C4×D61—42no—
177C2×C4×D61—42no—
178C2×C4×D61—81no—
179C2×Dic122—21no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—28no—
187C2×Dic122—24no—
188C2×Dic122—21no—
189C2×Dic122—44no—
190C2×Dic122—44no—
191C2×Dic122—44no—
192C2×Dic122—42no—
193C2×Dic122—42no—
194C2×Dic122C22×C412yes—
195C2×Dic122C22×C412yes—
196C2×Dic122C2×D412yes—
197C2×Dic122#4112yes—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61C22×C412yes—
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—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61C2×D412yes—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C42×C61—42no—
215C22⋊Dic61—22no—
216C22⋊Dic61—41no—
217#11758198—24no—
218#11758198—42no—
219#11758198—42no—
220#11758198—81no—
221C4⋊Dic61—21no—
222C4⋊Dic61C22×C412yes—
223#11758196—42no—
224#11758196—42no—
225#11758196—81no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—42no—
231C4×Dic61—42no—
232C4×Dic61—81no—
233#11758194—44no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418C2×D412yes—
240#11758190—28no—
241#11758190—44no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61C4×D412yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—22no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61C4×D412yes—
276C2×C4×C61C23×C411yescharacteristic
277C2×C4×C61C22×D411yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C2×C4×C61H(5,𝔽2)11yescharacteristic
281C2×C4×C61H(5,𝔽2)11yescharacteristic
282C22⋊D61—84no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—21no—
286C2×Dic61—22no—
287C2×Dic61—21no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—48no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61#13712yes—
305D244—22no—
306D244—22no—
307D244—41no—
308D244—41no—
309C4×D61—84no—
310Dic122—22no—
311Dic122—22no—
312Dic122—22no—
313Dic122—22no—
314Dic122—22no—
315Dic122—48no—
316Dic122—41no—
317Dic122—41no—
318Dic122C4×D414yes—
319C8×C61—22no—
320C8×C61—22no—
321#92418—22no—
322#92418—41no—
323#22865—611nomaximal, Sylow
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61C2×C4×D411yescharacteristic
332C22×C61D4211yescharacteristic
333C22×C61#54611yescharacteristic
334C22×C61C2×#13711yescharacteristic
335C22×C61#57511yescharacteristic
336C22×C61#57711yescharacteristic
337C22×C61#57711yescharacteristic
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—81no—
342C2×D61—81no—
343C2×D61—81no—
344C2×D61—81no—
345C4×C61—22no—
346C4×C61—42no—
347C4×C61—81no—
348C4×C61—81no—
349C4×C61—81no—
350C4×C61C2×C4×D411yescharacteristic
351C4×C61#51811yescharacteristic
352C4×C61#54611yescharacteristic
353C4×C61#55111yescharacteristic
354Dic61—24no—
355Dic61—22no—
356Dic61—42no—
357Dic61—42no—
358Dic61—41no—
359Dic61—41no—
360Dic61—41no—
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#1865—611no—
373#1854D6111yescharacteristic, complemented
374C4×#103—611no—
375#1753—611no—
376C2×C61—42no—
377C2×C61#235811yescharacteristic
378C2×C61C4×#13711yescharacteristic
379C2×C61#294911yescharacteristic
380C2×C61#327511yescharacteristic
381C2×C61#327811yescharacteristic
382C2×C61#332011yescharacteristic
383C2×C61#332111yescharacteristic
384D61—82no—
385C23×Q8—611no—
386C22×SD16—611no—
387C22×SD16—611no—
388C22×M16—611no—
389C2×#121—611no—
390C2×C4×Q8—611no—
391C2×C4×Q8—611no—
392C2×C4×D4—611no—
393C2×#117C2×D6111yescharacteristic
394#448—618no—
395#440—1224no—
396C2×#107C2×D6111yescharacteristic
397C2×#106C2×D6111yescharacteristic
398#419—1224no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×C22⋊C8C2×D6111yescharacteristic
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#389—611no—
417#388—1221no—
418#386—1221no—
419#380—1221no—
420#380C2×D6111yescharacteristic
421C4×C4⋊C4—611no—
422C4×C22⋊C4—611no—
423C4×C22⋊C4—1221no—
424C4×C22⋊C4—1221no—
425#340—611no—
426#340—611no—
427#340C2×D6111yescharacteristic
428#340C2×D6111yescharacteristic
429#336—611no—
430#336—611no—
431C61#2286511yescharacteristic, complemented, Sylow
432C22×Q8—614no—
433C22×Q8—611no—
434C22×Q8—611no—
435C22×Q8—1222no—
436C22×Q8—1222no—
437C22×Q8—1221no—
438C22×Q8—1222no—
439C22×Q8—2441no—
440C22×Q8—2441no—
441C22×D4—611no—
442C22×D4—1221no—
443C23×C4—1221no—
444C23×C4—1221no—
445C23×C4C22×D6111yescharacteristic
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—1222no—
462C4×Q8—1222no—
463C4×Q8—2441no—
464C4×Q8—2441no—
465C4×D4—1222no—
466C4×D4—2441no—
467#117—22no—
468#117—41no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4C22×D6111yescharacteristic
474C2×C4⋊C4C22×D6111yescharacteristic
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C42—21no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491#107—22no—
492#106—41no—
493#103—614no—
494#103—614no—
495#103—614no—
496#103—1222no—
497#103—1222no—
498#103—1222no—
499#102—1222no—
500#102—2441no—
501C22⋊C8C4×D6114yescomplemented
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—1221no—
514C24D4×D6111yescharacteristic
515C2×Q8—612no—
516C2×Q8—612no—
517C2×Q8—612no—
518C2×Q8—612no—
519C2×Q8—1228no—
520C2×Q8—1221no—
521C2×Q8—1221no—
522C2×Q8—1221no—
523C2×Q8—1221no—
524C2×Q8—1224no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—2442no—
530C2×Q8—2442no—
531C2×Q8—2444no—
532C2×Q8—2444no—
533C2×Q8—2444no—
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—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1224no—
559C22×C4—4881no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4C2×C4×D6112yes—
565C22×C4D4×D6111yescharacteristic
566C22×C4#1175822612yes—
567C22×C4C23×D6111yescharacteristic
568SD16—1228no—
569SD16—2444no—
570M16—2444no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—612no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8C2×C4×D6112yes—
582C2×C8C2×C4×D6112yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—612no—
591C4⋊C4—1221no—
592C4⋊C4—4881no—
593C4⋊C4—2442no—
594C4⋊C4—2442no—
595C4⋊C4D4×D6112yes—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—1222no—
599C22⋊C4—1224no—
600C22⋊C4—4881no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C22⋊C4—2441no—
604C42—42no—
605C42—1221no—
606C42—1221no—
607C42—1221no—
608C42—1221no—
609C42—4881no—
610C42—2442no—
611C42—2442no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—1222no—
619C23—2441no—
620C23—2441no—
621C23—2441no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23#1451973912yes—
626C23C2×D4×D6111yescharacteristic
627Q8—614no—
628Q8—1222no—
629Q8—1222no—
630Q8—1222no—
631Q8—1222no—
632Q8—1222no—
633Q8—2448no—
634Q8—2441no—
635Q8—2441no—
636D4—1222no—
637D4—1222no—
638D4—4884no—
639D4—2441no—
640D4—2441no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
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—1222no—
661C2×C4—1221no—
662C2×C4—1222no—
663C2×C4—1221no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—4884no—
677C2×C4—2448no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4#1451973912yes—
683C2×C4C22×C4×D6111yescharacteristic
684C2×C4C2×D4×D6111yescharacteristic
685C2×C4#41×D6111yescharacteristic
686C2×C4C2×#1175822611yescharacteristic
687C2×C4#1451982211yescharacteristic
688C2×C4#1451982311yescharacteristic
689C8—22no—
690C8—22no—
691C8—1222no—
692C8—2441no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—4881no—
701C22—4881no—
702C22—4881no—
703C22—4881no—
704C22—2442no—
705C22—2442no—
706C22—2442no—
707C22C2×#1451973911yescharacteristic
708C22#1684039411yescharacteristic
709C22#1684040411yescharacteristic
710C22#137×D6111yescharacteristic
711C22#1684055811yescharacteristic
712C22#1684056911yescharacteristic
713C22#1684056911yescharacteristic
714C4—22no—
715C4—42no—
716C4—81no—
717C4—81no—
718C4—81no—
719C4—1222no—
720C4—1224no—
721C4—2441no—
722C4—2441no—
723C4—2442no—
724C4—2441no—
725C4—2442no—
726C4C4×D4×D6111yescharacteristic
727C4#1684023411yescharacteristic
728C4#1684040311yescharacteristic
729C4#1684043911yescharacteristic
730C2—42no—
731C2—4882no—
732C2#2144879511yescharacteristic
733C2#2145463711yescharacteristic
734C2#2145467711yescharacteristic
735C2#2145744811yescharacteristic
736C2#2145747811yescharacteristic
737C2#2145799311yescharacteristic
738C2#2145800811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1854C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenter#1854D61
hypocenterC61#22865
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#16839861C2semidirect
3. C2×#16839770C2semidirect
5. #21448651C2semidirect
6. #21446671C2semidirect
7. #21446507C2semidirect
8. #21446459C2semidirect
10. #21446175C2semidirect
11. #21446154C2semidirect
12. #21446084C2semidirect
13. #21445638C2semidirect
14. #21445605C2semidirect
15. C61×#1854C2semidirect
24. #16839903C4semidirect
68. C22×Dic122C2×C4semidirect
109. #14519702C2×C4semidirect
110. #14519702C2×C4semidirect
114. #14519700D4semidirect
141. C22⋊C8×C61C2×C4semidirect
373. #1854D61semidirect
431. C61#22865semidirect
501. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399032
C2×#168398612
C2×#168397702
#214488572
#214486512
#214466712
#214465072
#214464592
#214462552
#214461752
#214461542
#214460842
#214456382
#214456052
C61×#18542
#2286561