Finite Group Databasebeta

← #29696489

Subgroups — #29696489

Order 15616.

1262 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459377C211yesmaximal, characteristic
2C4×D4×Dic61C211yesmaximal, characteristic, complemented
3#21446795C211yesmaximal, characteristic, complemented
4#21446763C211yesmaximal, characteristic, complemented
5#21446260C212yesmaximal, complemented
6#21446121C212yesmaximal, complemented
7#21445916C212yesmaximal, complemented
8#21445836C211yesmaximal, characteristic, complemented
9C4×#14519703C211yesmaximal, characteristic, complemented
10C2×#16839523C212yesmaximal, complemented
11D4×M16×C61C211yesmaximal, characteristic, complemented
12#16840482C411yescharacteristic, complemented
13#16840477C411yescharacteristic, complemented
14#16840469C411yescharacteristic, complemented
15#16840458C412yescomplemented
16#16840452C412yescomplemented
17#16840447—21no—
18#16840438—22no—
19#16840416C411yescharacteristic, complemented
20#16840406—21no—
21#16840319C2211yescharacteristic
22#16840294—21no—
23#16840292—22no—
24#16840273C2212yes—
25C4×#11758222C2211yescharacteristic
26C4×#11758224—21no—
27C2×D4×Dic61—21no—
28C2×#14519736C2212yes—
29C22×C4×Dic61C2212yes—
30C2×#14519703C2211yescharacteristic
31C2×#14519703C2211yescharacteristic
32C2×#14519703C2212yes—
33C4⋊C4×Dic61—21no—
34C4×C4⋊Dic61C2211yescharacteristic
35C22⋊C4×Dic61—22no—
36C4×C22⋊Dic61C2212yes—
37C42×Dic61C2211yescharacteristic
38#16839523C2211yescharacteristic
39#16839523C2212yes—
40#16839523C2212yes—
41#16839523C2212yes—
42#16839523C2212yes—
43#16839523C2212yes—
44#16839523C2211yescharacteristic
45C22×M16×C61C2212yes—
46C2×C4×D4×C61C2211yescharacteristic
47C61×#436—21no—
48C61×#435—22no—
49C8×D4×C61—21no—
50C61×#423C2211yescharacteristic
51C61×#407C2212yes—
52C4×M16×C61C2211yescharacteristic
53C2×#11758222C2311yescharacteristic
54C2×#11758224—21no—
55C23×Dic61—22no—
56#14519777C2×C411yescharacteristic, complemented
57#14519777C2×C411yescharacteristic, complemented
58#14519772—22no—
59#14519770—22no—
60#14519770—22no—
61#14519769C2×C412yescomplemented
62#14519768—21no—
63#14519767—22no—
64#14519764—21no—
65#14519763—22no—
66#14519761—22no—
67#14519760—22no—
68#14519759—22no—
69#14519758—22no—
70#14519757—21no—
71#14519756—21no—
72#14519756—21no—
73#14519756C2×C412yescomplemented
74#14519756C2×C412yescomplemented
75#14519754—22no—
76#14519751C2×C412yescomplemented
77#14519751C2×C412yescomplemented
78#14519749—22no—
79#14519748—21no—
80#14519746—22no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×Dic122C2×C411yescharacteristic, complemented
84C4×Dic122C2×C411yescharacteristic, complemented
85#14519742—21no—
86C4×D244C2×C411yescharacteristic, complemented
87C4×D244C2×C411yescharacteristic, complemented
88D4×Dic61—28no—
89D4×Dic61—21no—
90C4×C22⋊D61—22no—
91C4×C22⋊D61—21no—
92C4×C22⋊D61—21no—
93C4×C22⋊D61—22no—
94#14519737—22no—
95#14519736—22no—
96#14519736—22no—
97#14519736C2×C412yescomplemented
98#14519736C2×C412yescomplemented
99#14519736C2311yescharacteristic
100#14519736C2312yes—
101#14519735—21no—
102#14519734—21no—
103#14519733—22no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61C2×C412yescomplemented
106C2×C4⋊Dic61C2×C412yescomplemented
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—24no—
112C2×C4×Dic61—22no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—42no—
115C2×C4×Dic61C2312yes—
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C42×D61—21no—
119#14519703—22no—
120#14519703—22no—
121#14519703—42no—
122#14519684—22no—
123#14519684—21no—
124C22×D4×C61D411yescharacteristic
125C23×C4×C61C2312yes—
126C2×M16×C61—22no—
127C2×M16×C61—24no—
128C2×M16×C61—42no—
129C2×M16×C61C2312yes—
130C2×M16×C61C2311yescharacteristic
131C2×M16×C61C2311yescharacteristic
132C22×C8×C61—22no—
133C4×D4×C61C2×C412yes—
134C4×D4×C61C2×C411yescharacteristic
135C4×D4×C61C2×C411yescharacteristic
136C4×D4×C61D411yescharacteristic
137C4×D4×C61D412yes—
138C4×D4×C61D411yescharacteristic
139C2×C4⋊C4×C61D411yescharacteristic
140C2×C22⋊C4×C61D412yes—
141C2×C42×C61C2311yescharacteristic
142C4⋊C8×C61—21no—
143C4⋊C8×C61—21no—
144C22⋊C8×C61—22no—
145C22⋊C8×C61—22no—
146#97×C61—21no—
147C4×C8×C61—21no—
148C24×C61C2×D412yes—
149C2×D4×C61—24no—
150C2×D4×C61C22⋊C411yescharacteristic
151C2×D4×C61C22⋊C412yes—
152C2×D4×C61C22⋊C411yescharacteristic
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2411yescharacteristic
165C2×C22⋊D61—22no—
166C2×C22⋊D61—21no—
167C2×C22⋊D61—22no—
168C22×Dic61—21no—
169C22×Dic61—28no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61—44no—
175C22×Dic61—44no—
176#11758224—44no—
177#11758222—21no—
178#11758222—21no—
179#11758222—21no—
180#11758222—21no—
181C2×D244C22×C411yescharacteristic
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122C22×C411yescharacteristic
188M16×C61—21no—
189M16×C61—22no—
190M16×C61—21no—
191M16×C61—22no—
192M16×C61—21no—
193M16×C61—44no—
194M16×C61#4112yescomplemented
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—22no—
198C2×C8×C61—44no—
199C4⋊C4×C61C22⋊C411yescharacteristic
200C4⋊C4×C61C22⋊C411yescharacteristic
201C4⋊C4×C61C22⋊C412yes—
202C22⋊C4×C61C22⋊C412yes—
203C22⋊C4×C61C22⋊C412yes—
204C22⋊C4×C61C22⋊C412yes—
205C22⋊C4×C61C22⋊C412yes—
206C42×C61C22×C411yescharacteristic
207C42×C61C22×C411yescharacteristic
208C42×C61C2×D411yescharacteristic
209C42×C61C2×D411yescharacteristic
210C22⋊Dic61—28no—
211C22⋊Dic61—22no—
212C22⋊Dic61—22no—
213C22⋊Dic61—22no—
214C22⋊Dic61—22no—
215C22⋊Dic61—21no—
216C22⋊Dic61—22no—
217#11758198—21no—
218#11758198—21no—
219#11758198—22no—
220#11758198—22no—
221C4⋊Dic61—24no—
222C4⋊Dic61—22no—
223C4⋊Dic61—22no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61C22×C411yescharacteristic
227C4⋊Dic61C22×C411yescharacteristic
228C4⋊Dic61C22×C412yes—
229C4⋊Dic61C22×C412yes—
230#11758196—22no—
231#11758196—22no—
232#11758196—21no—
233#11758196—21no—
234#11758196—22no—
235#11758196—22no—
236C4×Dic61—24no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—22no—
240C4×Dic61—22no—
241C4×Dic61—21no—
242C4×Dic61—22no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—22no—
246C4×Dic61—22no—
247C4×Dic61—21no—
248C4×Dic61—44no—
249C4×Dic61—42no—
250C4×Dic61#4112yescomplemented
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—24no—
254C23×C61—42no—
255C23×C61C2×C22⋊C412yes—
256C23×C61C2×C22⋊C412yes—
257C23×C61C22×D411yescharacteristic
258C22×D61—21no—
259D4×C61—24no—
260D4×C61—22no—
261D4×C61#10414yescomplemented
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—41no—
274C2×C4×C61C2×C22⋊C412yes—
275C2×C4×C61C2×C22⋊C411yescharacteristic
276C2×C4×C61C2×C22⋊C411yescharacteristic
277C2×C4×C61C2×C22⋊C412yes—
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61C2×C22⋊C411yescharacteristic
280C2×C4×C61C23×C411yescharacteristic
281C2×C4×C61C22×D411yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61H(5,𝔽2)11yescharacteristic
285C2×C4×C612−1+411yescharacteristic
286C22⋊D61—41no—
287C22⋊D61—41no—
288C22⋊D61—44no—
289C22⋊D61—82no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—24no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—416no—
301C2×Dic61—41no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—41no—
305C2×Dic61—44no—
306C2×Dic61—82no—
307D244—21no—
308D244—21no—
309C4×D61—41no—
310C4×D61—41no—
311C4×D61—42no—
312C4×D61—81no—
313Dic122—21no—
314Dic122—21no—
315Dic122—42no—
316Dic122—81no—
317C8×C61—22no—
318C8×C61—42no—
319C8×C61—41no—
320#22505—611nomaximal, Sylow
321C22×C61—22no—
322C22×C61—21no—
323C22×C61—21no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—44no—
329C22×C61—44no—
330C22×C61C2×#10414yes—
331C22×C61C22×C22⋊C411yescharacteristic
332C22×C61#54611yescharacteristic
333C22×C61#54711yescharacteristic
334C2×D61—41no—
335C2×D61—41no—
336C2×D61—41no—
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—21no—
340C4×C61—21no—
341C4×C61—21no—
342C4×C61C2×#10412yes—
343C4×C61C4×#4111yescharacteristic
344C4×C61#52011yescharacteristic
345C4×C61#54611yescharacteristic
346C4×C61#54711yescharacteristic
347Dic61—24no—
348Dic61—42no—
349Dic61—44no—
350Dic61—41no—
351Dic61—42no—
352Dic61—41no—
353Dic61—42no—
354Dic61—41no—
355#3475—611no—
356D4×M16D6111yescharacteristic, complemented
357C42×D4—611no—
358#1994—611no—
359#1986—611no—
360#1896—612no—
361#1871—612no—
362#1826—612no—
363#1806—611no—
364C4×#104—611no—
365C2×#339—612no—
366C2×C61—21no—
367C2×C61—21no—
368C2×C61—24no—
369C2×C61—42no—
370C2×C61#233911yescharacteristic
371C2×C61C22×#10411yescharacteristic
372C2×C61#290111yescharacteristic
373D61—81no—
374C22×M16C2×D6112yes—
375#556—611no—
376#555—611no—
377#554—611no—
378#553—612no—
379#552—612no—
380#552—1221no—
381#551—1222no—
382#547—611no—
383#546—1221no—
384#533—611no—
385#529—1222no—
386#529—1221no—
387#525—612no—
388C4×#41—611no—
389C4×#41—1221no—
390C2×C4×D4—1221no—
391C2×C4×D4C2×D6111yescharacteristic
392C2×#117—612no—
393C22×C42—612no—
394#436—21no—
395#435—22no—
396C8×D4—21no—
397#423C2×D6111yescharacteristic
398C2×#104—611no—
399C2×#104—611no—
400C2×#104—612no—
401#407C2×D6112yes—
402C4×M16C2×D6111yescharacteristic
403C4×C4⋊C4—611no—
404C4×C4⋊C4—1221no—
405C4×C22⋊C4—612no—
406C4×C22⋊C4—1222no—
407C43—611no—
408#339—612no—
409#339—611no—
410#339—612no—
411#339—612no—
412#339—612no—
413#339—612no—
414#339—611no—
415C61#2250511yescharacteristic, complemented, Sylow
416C2×#41—611no—
417C2×#41—1221no—
418C22×D4D24411yescharacteristic
419C23×C4—1222no—
420C23×C4C22×D6112yes—
421C2×M16—22no—
422C2×M16—24no—
423C2×M16—42no—
424C2×M16C22×D6112yes—
425C2×M16C22×D6111yescharacteristic
426C2×M16C22×D6111yescharacteristic
427C22×C8—22no—
428C4⋊Q8—611no—
429C4⋊Q8—611no—
430#126—1222no—
431#126—1222no—
432#126—1222no—
433#125—612no—
434#125—1222no—
435#125—1221no—
436#124—1221no—
437#124—1222no—
438#123—1222no—
439#123—1222no—
440#123—1222no—
441#123—1222no—
442C22⋊Q8—612no—
443C22⋊Q8—612no—
444C22⋊Q8—1221no—
445C22⋊Q8—1221no—
446C22⋊Q8—1221no—
447C22⋊Q8—1222no—
448#121—612no—
449#121—612no—
450#121—1222no—
451#121—1221no—
452#120—1222no—
453C4×Q8—611no—
454C4×Q8—611no—
455C4×Q8—1221no—
456C4×Q8—1221no—
457C4×Q8—1221no—
458C4×D4—611no—
459C4×D4—611no—
460C4×D4—1228no—
461C4×D4—1221no—
462C4×D4—1221no—
463C4×D4—1221no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4—1222no—
467C4×D4C4×D6111yescharacteristic
468C4×D4C4×D6112yes—
469C4×D4C4×D6111yescharacteristic
470C4×D4C22⋊D6111yescharacteristic
471C4×D4C22⋊D6112yes—
472C4×D4C22⋊D6111yescharacteristic
473#117—612no—
474#117—612no—
475#117—611no—
476#117—612no—
477#117—1222no—
478#117—1222no—
479#117—1221no—
480#117—1222no—
481#117—1221no—
482C2×C4⋊C4—612no—
483C2×C4⋊C4—612no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4D24411yescharacteristic
486C2×C22⋊C4—1222no—
487C2×C22⋊C4—1222no—
488C2×C22⋊C4D24412yes—
489C2×C42—611no—
490C2×C42—611no—
491C2×C42—612no—
492C2×C42—1224no—
493C2×C42—1221no—
494C2×C42—1222no—
495C2×C42—1221no—
496C2×C42—1221no—
497C2×C42—1222no—
498C2×C42—2442no—
499C2×C42C22×D6111yescharacteristic
500C4⋊C8—21no—
501C4⋊C8—21no—
502#104—1222no—
503#104—1222no—
504#104—2442no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507#97—21no—
508C4×C8—21no—
509#95—1222no—
510#95—1221no—
511C24C2×D24412yes—
512#41—1221no—
513#41—1221no—
514#41—1221no—
515#41—1221no—
516#41—2444no—
517C2×Q8—611no—
518C2×Q8—1221no—
519C2×Q8—1221no—
520C2×D4—24no—
521C2×D4—611no—
522C2×D4—1222no—
523C2×D4—1221no—
524C2×D4—1222no—
525C2×D4#1175819812yes—
526C2×D4#1175819811yescharacteristic
527C2×D4#1175819811yescharacteristic
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—1221no—
533C22×C4—1222no—
534C22×C4—1228no—
535C22×C4—1221no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—2444no—
542C22×C4—2444no—
543C22×C4C2×C4×D6112yes—
544C22×C4C2×C4×D6112yes—
545C22×C4C2×D24412yes—
546C22×C4C2×D24411yescharacteristic
547C22×C4C2×D24411yescharacteristic
548C22×C4C2×C22⋊D6112yes—
549C22×C4C2×C22⋊D6112yes—
550C22×C4C23×D6111yescharacteristic
551M16—21no—
552M16—21no—
553M16—22no—
554M16—22no—
555M16—21no—
556M16—44no—
557M16#1175822412yescomplemented
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—22no—
561C2×C8—44no—
562C4⋊C4—611no—
563C4⋊C4—611no—
564C4⋊C4—612no—
565C4⋊C4—612no—
566C4⋊C4—1224no—
567C4⋊C4—1222no—
568C4⋊C4—1222no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—1222no—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1222no—
575C4⋊C4—1221no—
576C4⋊C4—1221no—
577C4⋊C4#1175819811yescharacteristic
578C4⋊C4#1175819811yescharacteristic
579C4⋊C4#1175819812yes—
580C22⋊C4—1228no—
581C22⋊C4—1221no—
582C22⋊C4—1222no—
583C22⋊C4—1222no—
584C22⋊C4—1222no—
585C22⋊C4—1222no—
586C22⋊C4—1222no—
587C22⋊C4—1221no—
588C22⋊C4—1221no—
589C22⋊C4—1222no—
590C22⋊C4—1222no—
591C22⋊C4#1175819812yes—
592C22⋊C4#1175819812yes—
593C22⋊C4#1175819812yes—
594C22⋊C4#1175819812yes—
595C42—612no—
596C42—1224no—
597C42—1221no—
598C42—1222no—
599C42—1221no—
600C42—1222no—
601C42—1222no—
602C42—1221no—
603C42—1221no—
604C42—1222no—
605C42—1221no—
606C42—1222no—
607C42—1221no—
608C42—2444no—
609C42—2442no—
610C42C2×C4×D6111yescharacteristic
611C42C2×C4×D6111yescharacteristic
612C42C2×C22⋊D6111yescharacteristic
613C42C2×C22⋊D6111yescharacteristic
614C23—24no—
615C23—22no—
616C23—22no—
617C23—42no—
618C23—1221no—
619C23C2×#1175819812yes—
620C23C2×#1175819812yes—
621C23C22×D24411yescharacteristic
622Q8—1221no—
623Q8—1221no—
624Q8—4881no—
625Q8—2442no—
626D4—24no—
627D4—22no—
628D4—1221no—
629D4—1221no—
630D4—4882no—
631D4—2444no—
632D4—2441no—
633D4—2441no—
634D4#1451970314yescomplemented
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—41no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1224no—
652C2×C4—1221no—
653C2×C4—1221no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1221no—
657C2×C4—4881no—
658C2×C4—4882no—
659C2×C4—24416no—
660C2×C4—2441no—
661C2×C4—2442no—
662C2×C4—2444no—
663C2×C4—2442no—
664C2×C4—2441no—
665C2×C4—2442no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4C2×#1175819812yes—
669C2×C4C2×#1175819811yescharacteristic
670C2×C4C2×#1175819811yescharacteristic
671C2×C4C2×#1175819811yescharacteristic
672C2×C4C2×#1175819812yes—
673C2×C4C2×#1175819811yescharacteristic
674C2×C4C22×C4×D6111yescharacteristic
675C2×C4C22×C22⋊D6111yescharacteristic
676C2×C4#41×D6111yescharacteristic
677C2×C4C2×#1175822411yescharacteristic
678C2×C4#1451982211yescharacteristic
679C2×C4#1451982411yescharacteristic
680C8—22no—
681C8—42no—
682C8—41no—
683C22—21no—
684C22—21no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—44no—
691C22—44no—
692C22—2441no—
693C22—2441no—
694C22—2441no—
695C22C2×#1451970314yes—
696C22C22×#1175819811yescharacteristic
697C22#1684040711yescharacteristic
698C22#1684041611yescharacteristic
699C4—21no—
700C4—21no—
701C4—21no—
702C4—22no—
703C4—22no—
704C4—1224no—
705C4—2442no—
706C4—2444no—
707C4—2441no—
708C4—2442no—
709C4—2441no—
710C4—2442no—
711C4—2441no—
712C4C2×#1451970312yes—
713C4C4×#1175822411yescharacteristic
714C4#1684024111yescharacteristic
715C4#1684040611yescharacteristic
716C4#1684041111yescharacteristic
717C2—21no—
718C2—21no—
719C2—24no—
720C2—42no—
721C2—4881no—
722C2#2144864411yescharacteristic
723C2C22×#1451970311yescharacteristic
724C2#2145436411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×M16×C61C2
socleC22×C61C22×C22⋊C4
prime radical#21459377C2
cosocleC22×C4×C61C24
hypercenterD4×M16D61
hypocenterC61#22505
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. C4×D4×Dic61C2semidirect
3. #21446795C2semidirect
4. #21446763C2semidirect
5. #21446260C2semidirect
6. #21446121C2semidirect
7. #21445916C2semidirect
8. #21445836C2semidirect
9. C4×#14519703C2semidirect
10. C2×#16839523C2semidirect
11. D4×M16×C61C2semidirect
12. #16840482C4semidirect
13. #16840477C4semidirect
14. #16840469C4semidirect
15. #16840458C4semidirect
16. #16840452C4semidirect
19. #16840416C4semidirect
56. #14519777C2×C4semidirect
57. #14519777C2×C4semidirect
61. #14519769C2×C4semidirect
73. #14519756C2×C4semidirect
74. #14519756C2×C4semidirect
76. #14519751C2×C4semidirect
77. #14519751C2×C4semidirect
83. C4×Dic122C2×C4semidirect
84. C4×Dic122C2×C4semidirect
86. C4×D244C2×C4semidirect
87. C4×D244C2×C4semidirect
97. #14519736C2×C4semidirect
98. #14519736C2×C4semidirect
105. C2×C4⋊Dic61C2×C4semidirect
106. C2×C4⋊Dic61C2×C4semidirect
194. M16×C61#41semidirect
250. C4×Dic61#41semidirect
261. D4×C61#104semidirect
356. D4×M16D61semidirect
415. C61#22505semidirect
557. M16#11758224semidirect
634. D4#14519703semidirect

Maximal subgroups

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

subgroupindex
#214593772
C4×D4×Dic612
#214467952
#214467632
#214462602
#214461212
#214459162
#214458362
C4×#145197032
C2×#168395232
D4×M16×C612
#2250561