Finite Group Databasebeta

← C4×#16840008 #29686642

Subgroups — C4×#16840008 #29686642

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840008C211yesmaximal, characteristic
2C2×C4×#11758190C211yesmaximal, characteristic, complemented
3C4×#14519756C211yesmaximal, characteristic, complemented
4C4×#14519751C211yesmaximal, characteristic
5#21446700C211yesmaximal, characteristic, complemented
6#21446557C211yesmaximal, characteristic, complemented
7#21446516C211yesmaximal, characteristic, complemented
8#21446509C211yesmaximal, characteristic, complemented
9#21446257C211yesmaximal, characteristic
10#21446252C211yesmaximal, characteristic, complemented
11#21445852C211yesmaximal, characteristic, complemented
12C4×#14519711C211yesmaximal, characteristic, complemented
13C4×#14519702C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C2×C4×M16×C61C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×C22⋊D61—21no—
22#16840008C418yesdirect product factor
23C4×#11758190—24no—
24C2×#14519711C2211yescharacteristic
25C2×#14519711C2211yescharacteristic
26C2×#14519709C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33#16839668C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839653—21no—
38#16839646—21no—
39#16839641—21no—
40#16839635—21no—
41#16839622C2211yescharacteristic
42#16839622C2211yescharacteristic
43C4×#11758196—21no—
44C4×C4⋊Dic61C2211yescharacteristic
45C4×C4⋊Dic61C2211yescharacteristic
46C4×#11758198—21no—
47C4×C22⋊Dic61—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic
57C4×M16×C61—24no—
58C2×#97×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic
61C2×C4×C8×C61C2211yescharacteristic
62C22×Dic122C2311yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C4×D61—21no—
66C2×#11758190—22no—
67C2×#11758190—22no—
68C2×#11758190C2×C414yescomplemented
69#14519756—22no—
70#14519756C2×C414yescomplemented
71#14519751—22no—
72#14519751C2×C414yes—
73C4×Dic122—22no—
74C4×Dic122—22no—
75C4×D244—22no—
76C4×D244—22no—
77C4×C22⋊D61—44no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98#14519711—22no—
99#14519711C2×C414yescomplemented
100#14519709—22no—
101#14519702—22no—
102#14519702—22no—
103#14519702C2×C414yescomplemented
104#14519699—22no—
105#14519699—22no—
106#14519699C2×C414yescomplemented
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C23×C4×C61D411yescharacteristic
116C23×C4×C61D411yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C2×M16×C61—22no—
119C2×M16×C61—22no—
120C2×M16×C61—22no—
121C2×M16×C61—22no—
122C2×M16×C61—22no—
123C2×M16×C61C2×C414yescomplemented
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C42×C61—22no—
129C2×C42×C61—22no—
130C2×C42×C61D411yescharacteristic
131C2×C42×C61D411yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C2×C42×C61C2311yescharacteristic
134#97×C61—22no—
135#97×C61—22no—
136C4×C8×C61—22no—
137C4×C8×C61D414yescomplemented
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—41no—
149C22×C4×C61—41no—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61#4112yes—
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—24no—
159C2×C22⋊D61—42no—
160C2×C22⋊D61—42no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244C22×C412yes—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×Dic122—21no—
178C2×Dic122—21no—
179C2×Dic122—21no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122C22×C412yes—
183M16×C61—28no—
184M16×C61—28no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61C22×C412yes—
192C2×C8×C61C22×C412yes—
193C2×C8×C61C2×D412yes—
194C2×C8×C61C2×D412yes—
195C2×C8×C61#4112yes—
196C2×C8×C61#4112yes—
197C42×C61—22no—
198C42×C61—22no—
199C42×C61—21no—
200C42×C61—21no—
201C42×C61C2×D412yes—
202C42×C61#4112yes—
203C22⋊Dic61—24no—
204C22⋊Dic61—42no—
205C22⋊Dic61—42no—
206#11758198—24no—
207#11758198—42no—
208#11758198—42no—
209#11758198—42no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61C22×C412yes—
221C4⋊Dic61C22×C412yes—
222#11758196—24no—
223#11758196—42no—
224#11758196—42no—
225#11758196—42no—
226C4×Dic61—42no—
227C4×Dic61—42no—
228C4×Dic61—42no—
229#11758190—28no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61C4×D412yes—
237C23×C61C22×D411yescharacteristic
238C22×D61—22no—
239C22×D61—41no—
240C22×D61—41no—
241C22×D61—41no—
242C22×D61—41no—
243C22×D61—41no—
244C22×D61—41no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—44no—
260C2×C4×C61—44no—
261C2×C4×C61C4×D412yes—
262C2×C4×C61#12112yes—
263C2×C4×C61#12112yes—
264C2×C4×C61AGL(1,ℤ/8)12yes—
265C2×C4×C61#13712yes—
266C2×C4×C61C23×C411yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C2×#4111yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C22⋊D61—48no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294D244—22no—
295D244—22no—
296D244—41no—
297D244—41no—
298C4×D61—84no—
299Dic122—22no—
300Dic122—22no—
301Dic122—41no—
302Dic122—41no—
303C8×C61—22no—
304C8×C61—22no—
305C8×C61—22no—
306C8×C61C4×D414yescomplemented
307C4×#468—611nomaximal, Sylow
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61C2×C4×D411yescharacteristic
316C22×C61C2×#12111yescharacteristic
317C22×C61#53211yescharacteristic
318C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C61C2×#13711yescharacteristic
320C22×C61#57511yescharacteristic
321C22×C61#57511yescharacteristic
322C2×D61—42no—
323C2×D61—42no—
324C2×D61—42no—
325C2×D61—81no—
326C2×D61—81no—
327C2×D61—81no—
328C2×D61—81no—
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—41no—
332C4×C61—41no—
333C4×C61#46814yescomplemented
334C4×C61C2×C4×D411yescharacteristic
335C4×C61C4×#4111yescharacteristic
336C4×C61#52511yescharacteristic
337C4×C61#52911yescharacteristic
338Dic61—42no—
339Dic61—42no—
340Dic61—42no—
341Dic61—81no—
342Dic61—81no—
343Dic61—81no—
344Dic61—81no—
345C2×#468—611no—
346C2×C4×SD16—611no—
347C2×C4×M16D6111yescharacteristic, complemented
348C4×C22⋊Q8—611no—
349C4×#121—611no—
350#1973—611no—
351#1943—611no—
352#1936—611no—
353#1935—611no—
354#1895—611no—
355#1894—611no—
356#1809—611no—
357C4×#107—611no—
358C4×#103—611no—
359C4×#102—611no—
360C2×C61—42no—
361C2×C61C4×#12111yescharacteristic
362C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
363C2×C61C4×#13711yescharacteristic
364C2×C61C2×#46811yescharacteristic
365C2×C61#305411yescharacteristic
366C2×C61#317111yescharacteristic
367C2×C61#317211yescharacteristic
368D61—82no—
369C22×SD16—611no—
370C22×M16C2×D6111yescharacteristic
371C22×M16C2×D6111yescharacteristic
372C2×C22⋊Q8—611no—
373C2×#121—611no—
374C2×C4×Q8—611no—
375C2×C4×D4—611no—
376C2×C4×D4—1221no—
377C22×C42C2×D6111yescharacteristic
378#468—618no—
379C4×SD16—1224no—
380C2×#107—611no—
381C2×#107—611no—
382C2×#106—611no—
383C2×#103—611no—
384C2×#103—611no—
385C2×#103—611no—
386C2×#102—611no—
387C2×#102—611no—
388C2×#102—611no—
389C4×M16—24no—
390C2×#97C2×D6111yescharacteristic
391C2×#97C2×D6111yescharacteristic
392C2×C4×C8C2×D6111yescharacteristic
393C2×C4×C8C2×D6111yescharacteristic
394#391—611no—
395#390—611no—
396#389—611no—
397#389—611no—
398#388—1221no—
399#387—1221no—
400#386—1221no—
401#385—1221no—
402#380—611no—
403#380—611no—
404C4×C4⋊C4—611no—
405C4×C4⋊C4—611no—
406C4×C4⋊C4—1221no—
407C4×C22⋊C4—1221no—
408C4×C22⋊C4—1221no—
409#340—611no—
410#340—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415C61C4×#46811yescharacteristic, complemented, Sylow
416C22×Q8—611no—
417C22×D4—611no—
418C22×D4—1221no—
419C23×C4—1221no—
420C23×C4D24411yescharacteristic
421C23×C4D24411yescharacteristic
422C23×C4C22×D6111yescharacteristic
423C2×SD16—614no—
424C2×SD16—1222no—
425C2×SD16—1222no—
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—22no—
429C2×M16—22no—
430C2×M16—22no—
431C2×M16C4×D6114yescomplemented
432C22×C8C22×D6111yescharacteristic
433C22×C8C22×D6111yescharacteristic
434C22×C8C22×D6111yescharacteristic
435C22×C8C22×D6111yescharacteristic
436C22⋊Q8—614no—
437C22⋊Q8—1222no—
438#121—614no—
439#121—1222no—
440C4×Q8—1222no—
441C4×Q8—1222no—
442C4×D4—1222no—
443C4×D4—1222no—
444C4×D4—2444no—
445C2×C4⋊C4—611no—
446C2×C4⋊C4—611no—
447C2×C4⋊C4—611no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—1221no—
452C2×C4⋊C4—1221no—
453C2×C4⋊C4—1221no—
454C2×C4⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4—1221no—
459C2×C22⋊C4—1221no—
460C2×C22⋊C4—1221no—
461C2×C22⋊C4—1221no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—1221no—
465C2×C42—1221no—
466C2×C42—1221no—
467C2×C42D24411yescharacteristic
468C2×C42D24411yescharacteristic
469C2×C42C22×D6111yescharacteristic
470C2×C42C22×D6111yescharacteristic
471#107—614no—
472#107—1222no—
473#106—1222no—
474#103—614no—
475#103—1222no—
476#103—1222no—
477#102—614no—
478#102—1222no—
479#102—1222no—
480#97—22no—
481#97—22no—
482C4×C8—22no—
483C4×C8C22⋊D6114yescomplemented
484#95—1221no—
485#95—1221no—
486#95—1221no—
487#95—1221no—
488#95—1221no—
489#95—1221no—
490#95—1221no—
491#95—1221no—
492C24—1221no—
493C24C2×D24411yescharacteristic
494C2×Q8—612no—
495C2×Q8—1221no—
496C2×Q8—1221no—
497C2×Q8—1221no—
498C2×Q8—1221no—
499C2×Q8—1221no—
500C2×D4—612no—
501C2×D4—1224no—
502C2×D4—1221no—
503C2×D4—1221no—
504C2×D4—1221no—
505C2×D4—1221no—
506C2×D4—1221no—
507C2×D4—2442no—
508C2×D4—2442no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—2442no—
527C22×C4—2442no—
528C22×C4—2442no—
529C22×C4C2×C4×D6112yes—
530C22×C4C2×D24411yescharacteristic
531C22×C4C2×D24411yescharacteristic
532C22×C4C2×D24411yescharacteristic
533C22×C4C2×D24411yescharacteristic
534C22×C4C2×D24411yescharacteristic
535C22×C4#1175822212yes—
536C22×C4C23×D6111yescharacteristic
537SD16—1228no—
538M16—28no—
539M16—28no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8C2×C4×D6112yes—
547C2×C8C2×C4×D6112yes—
548C2×C8#1175822212yes—
549C2×C8#1175822212yes—
550C2×C8C2×C22⋊D6112yes—
551C2×C8C2×C22⋊D6112yes—
552C4⋊C4—612no—
553C4⋊C4—612no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—1224no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—2442no—
566C4⋊C4—2442no—
567C4⋊C4—2442no—
568C22⋊C4—1224no—
569C22⋊C4—1224no—
570C22⋊C4—2442no—
571C22⋊C4—2442no—
572C22⋊C4—2442no—
573C22⋊C4—2442no—
574C22⋊C4—2442no—
575C42—21no—
576C42—21no—
577C42—22no—
578C42—22no—
579C42—2442no—
580C42—2442no—
581C42—2442no—
582C42#1175822212yes—
583C42C2×C22⋊D6112yes—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—1222no—
591C23—2441no—
592C23—2441no—
593C23—2441no—
594C23—2441no—
595C23—2441no—
596C23—2441no—
597C23C4×D24412yes—
598C23C22×D24411yescharacteristic
599Q8—1222no—
600Q8—1222no—
601Q8—2441no—
602Q8—2441no—
603D4—1222no—
604D4—1222no—
605D4—2448no—
606D4—2441no—
607D4—2441no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—4884no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4C4×D24412yes—
647C2×C4#1451975112yes—
648C2×C4#1451975112yes—
649C2×C4#1451980512yes—
650C2×C4#1451981012yes—
651C2×C4C22×C4×D6111yescharacteristic
652C2×C4C22×C22⋊D6111yescharacteristic
653C2×C4C2×#1175822211yescharacteristic
654C2×C4C2×#1175822211yescharacteristic
655C2×C4C2×#1175822211yescharacteristic
656C2×C4C2×#1175822211yescharacteristic
657C8—22no—
658C8—22no—
659C8—22no—
660C8C4×C22⋊D6114yescomplemented
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—4881no—
669C22—4881no—
670C22—4881no—
671C22—4881no—
672C22—2442no—
673C22—2442no—
674C22—2442no—
675C22C2×C4×D24411yescharacteristic
676C22C2×#1451975111yescharacteristic
677C22#1684031211yescharacteristic
678C22C2×#1451980511yescharacteristic
679C22C2×#1451981011yescharacteristic
680C22#1684056211yescharacteristic
681C22#1684056211yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—4881no—
687C4—4881no—
688C4—4881no—
689C4—4881no—
690C4—2442no—
691C4—2442no—
692C4—2442no—
693C4#1684000814yesdirect product factor
694C4C2×C4×C22⋊D6111yescharacteristic
695C4C4×#1175822211yescharacteristic
696C4#1684027311yescharacteristic
697C4#1684029611yescharacteristic
698C2—42no—
699C2—4882no—
700C2C4×#1451975111yescharacteristic
701C2C4×#1451980511yescharacteristic
702C2C4×#1451981011yescharacteristic
703C2C2×#1684000811yescharacteristic
704C2#2145542811yescharacteristic
705C2#2145641411yescharacteristic
706C2#2145642511yescharacteristic
subgroupG/H
centerC22×C4C2×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×M16×C61C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenterC2×C4×M16D61
hypocenterC61C4×#468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758190C2semidirect
3. C4×#14519756C2semidirect
5. #21446700C2semidirect
6. #21446557C2semidirect
7. #21446516C2semidirect
8. #21446509C2semidirect
10. #21446252C2semidirect
11. #21445852C2semidirect
12. C4×#14519711C2semidirect
13. C4×#14519702C2semidirect
14. C4×#14519699C2semidirect
15. C2×C4×M16×C61C2semidirect
22. #16840008C4direct (N × H)
68. C2×#11758190C2×C4semidirect
70. #14519756C2×C4semidirect
99. #14519711C2×C4semidirect
103. #14519702C2×C4semidirect
106. #14519699C2×C4semidirect
123. C2×M16×C61C2×C4semidirect
137. C4×C8×C61D4semidirect
306. C8×C61C4×D4semidirect
333. C4×C61#468semidirect
347. C2×C4×M16D61semidirect
415. C61C4×#468semidirect
431. C2×M16C4×D61semidirect
483. C4×C8C22⋊D61semidirect
660. C8C4×C22⋊D61semidirect
693. C4#16840008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168400082
C2×C4×#117581902
C4×#145197562
C4×#145197512
#214467002
#214465572
#214465162
#214465092
#214462572
#214462522
#214458522
C4×#145197112
C4×#145197022
C4×#145196992
C2×C4×M16×C612
C4×#46861