Finite Group Databasebeta

← #10829209

Subgroups — #10829209

Order 768.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5541C211yesmaximal, characteristic
2C3×#2536C211yesmaximal, characteristic
3C2×#5022C211yesmaximal, characteristic, complemented
4C2×C4×#216C211yesmaximal, characteristic, complemented
5#71700C211yesmaximal, characteristic, complemented
6#71700C211yesmaximal, characteristic, complemented
7#71693C211yesmaximal, characteristic, complemented
8#71692C211yesmaximal, characteristic, complemented
9#71614C211yesmaximal, characteristic
10#69559C211yesmaximal, characteristic, complemented
11#69554C211yesmaximal, characteristic, complemented
12#69527C211yesmaximal, characteristic, complemented
13#69526C211yesmaximal, characteristic, complemented
14#69506C211yesmaximal, characteristic, complemented
15#69504C211yesmaximal, characteristic, complemented
16#24127—31nomaximal, Sylow
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C2×#935—21no—
23C2×#926C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27#5541—24no—
28#5541—24no—
29C2×#889—21no—
30C2×#879—21no—
31C2×#877—21no—
32C2×#870C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C3×#398—21no—
35C3×#394—21no—
36C3×#388—21no—
37C3×#388—21no—
38C3×#382C2211yescharacteristic
39C3×#380C2211yescharacteristic
40C3×#380C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46C2×#830C2211yescharacteristic
47C2×#830C2211yescharacteristic
48C4×#216—24no—
49#5022—24no—
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55C2×#807C2211yescharacteristic
56C2×C4⋊(C3⋊C8)C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#552—31no—
65C2×#479—31no—
66C2×C4×Q16—31no—
67#2536D311yescharacteristic
68#2036—31no—
69#2035—31no—
70#2001—31no—
71#2001—31no—
72#1991—31no—
73#1954—31no—
74#1873—31no—
75#1872—31no—
76#1854—31no—
77#1852—31no—
78#1805—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4D411yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×Dic3—21no—
84C22×Dic6C2311yescharacteristic
85C3×C22⋊Q8—22no—
86C3×C22⋊Q8—22no—
87C3×C22⋊Q8—41no—
88C3×C22⋊Q8—41no—
89C3×C4×Q8—22no—
90C3×C4×Q8—22no—
91C3×C4×D4—22no—
92C3×C4×D4—22no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4D411yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4D411yescharacteristic
105C2×C3×C22⋊C4D411yescharacteristic
106C2×C3×C42—21no—
107C2×C3×C42C2311yescharacteristic
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#216—22no—
112C2×#216—22no—
113C2×#216—22no—
114#935—28no—
115#926—22no—
116#926—22no—
117C2×C4⋊Dic3—21no—
118C2×C4⋊Dic3—22no—
119C2×C4⋊Dic3—22no—
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123#924—22no—
124#924—22no—
125#924—22no—
126#924—22no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3—21no—
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138#889—28no—
139#879—28no—
140#877—28no—
141#870—22no—
142#870D414yes—
143C4×Dic6—22no—
144C4×Dic6D414yes—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95—21no—
149#835—22no—
150#835—22no—
151#835—22no—
152#830—22no—
153#830—22no—
154#830—41no—
155#830—41no—
156#810—22no—
157#810—41no—
158#810—41no—
159#808—22no—
160#807—22no—
161#807—22no—
162C4⋊(C3⋊C8)—22no—
163C4×C3⋊C8—22no—
164C22×Q16—31no—
165#552—64no—
166#552—64no—
167C2×#126—61no—
168C2×#125—31no—
169C2×#125—61no—
170C2×#123—61no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×C4×Q8—31no—
176C2×C4×Q8C2×D311yescharacteristic
177C2×C4×D4C2×D311yescharacteristic
178C2×#117—31no—
179C2×#117—61no—
180C22×C4⋊C4—31no—
181#479—64no—
182C4×Q16—64no—
183C2×#107—31no—
184C2×#107—31no—
185C2×#106—31no—
186C2×C4⋊C8—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×C4×C8—31no—
198#398—21no—
199#394—21no—
200#388—21no—
201#388—21no—
202#382C2×D311yescharacteristic
203#380C2×D311yescharacteristic
204#380C2×D311yescharacteristic
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340—31no—
211C24×C3C2×D411yescharacteristic
212C24×C3C2×D411yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8#4112yes—
219C2×C3×D4—22no—
220C2×C3×D4—22no—
221C2×C3×D4—41no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C22×Dic3—24no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—42no—
249C22×Dic3—42no—
250C2×Dic6—21no—
251C2×Dic6—21no—
252C2×Dic6—21no—
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6C2×D412yes—
256C3×C4⋊C4—22no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—42no—
264C3×C4⋊C4—42no—
265C3×C4⋊C4—42no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—42no—
269C3×C22⋊C4—42no—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—42no—
272C3×C42—42no—
273C3×C42C2×D412yes—
274C3×C42C2×D412yes—
275#217—24no—
276#217—24no—
277#217—24no—
278#216—28no—
279C4⋊Dic3—24no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3—21no—
283C4⋊Dic3C2×D412yes—
284C4⋊Dic3C2×D412yes—
285C4⋊Dic3C2×D412yes—
286Dic3⋊C4—24no—
287Dic3⋊C4—24no—
288Dic3⋊C4—24no—
289Dic3⋊C4—24no—
290Dic3⋊C4—24no—
291C4×Dic3—24no—
292C4×Dic3—24no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8#4112yes—
305C22×Q8—31no—
306C22×Q8C22×D311yescharacteristic
307C22×D4#6711yescharacteristic
308C23×C4—61no—
309C23×C4C22×D311yescharacteristic
310C23×C4C22×D311yescharacteristic
311C2×Q16—62no—
312C2×Q16—62no—
313C2×Q16—62no—
314C22×C8—31no—
315C22×C8—31no—
316C22×C8—31no—
317C22×C8—31no—
318#126—68no—
319#125—34no—
320#125—68no—
321#125—62no—
322#123—68no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—41no—
326C22⋊Q8—41no—
327C22⋊Q8—62no—
328C22⋊Q8—62no—
329C22⋊Q8—62no—
330C22⋊Q8—62no—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8—34no—
334C4×Q8—62no—
335C4×D4—22no—
336C4×D4—22no—
337#117—68no—
338#117—62no—
339#117—62no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—62no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—61no—
349C2×C4⋊C4—61no—
350C2×C4⋊C4—61no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4#6711yescharacteristic
355C2×C4⋊C4C22×D311yescharacteristic
356C2×C4⋊C4C22×D311yescharacteristic
357C2×C4⋊C4C22×D311yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—61no—
363C2×C22⋊C4—61no—
364C2×C22⋊C4—61no—
365C2×C22⋊C4#6711yescharacteristic
366C2×C22⋊C4#6711yescharacteristic
367C2×C42—21no—
368C2×C42—61no—
369C2×C42—61no—
370C2×C42C22×D311yescharacteristic
371#107—62no—
372#107—62no—
373#106—62no—
374C4⋊C8—62no—
375#103—62no—
376#103—62no—
377#103—62no—
378#103—62no—
379#103—121no—
380#103—121no—
381C22⋊C8—62no—
382C22⋊C8—62no—
383C22⋊C8—121no—
384C22⋊C8—121no—
385C4×C8—62no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3#13512yes—
404C23×C3C22×D411yescharacteristic
405C3×Q8—22no—
406C3×Q8—22no—
407C3×Q8—41no—
408C3×Q8—41no—
409C3×D4—44no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4#12012yes—
441C2×C3×C4#12012yes—
442C2×C3×C4C22×D411yescharacteristic
443C2×C3×C4C22×D411yescharacteristic
444C2×C3×C4C2×#4111yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446C2×C3×C4H(5,𝔽2)11yescharacteristic
447C2×C3×C42−1+411yescharacteristic
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—48no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461Dic6—22no—
462Dic6—22no—
463Dic6—41no—
464Dic6—41no—
465C3⋊C8—22no—
466C3⋊C8—41no—
467C3⋊C8—41no—
468C3⋊C8—41no—
469C24C2×#6711yescharacteristic
470C24C2×#6711yescharacteristic
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—32no—
477C2×Q8—61no—
478C2×Q8—61no—
479C2×Q8—61no—
480C2×Q8—61no—
481C2×Q8—61no—
482C2×Q8#23712yes—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—41no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—64no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—122no—
508C22×C4—122no—
509C22×C4C2×#6711yescharacteristic
510C22×C4C2×#6711yescharacteristic
511C22×C4C2×#6711yescharacteristic
512C22×C4C2×#6711yescharacteristic
513C22×C4C23×D311yescharacteristic
514Q16—68no—
515C2×C8—32no—
516C2×C8—61no—
517C2×C8—61no—
518C2×C8—61no—
519C2×C8—61no—
520C2×C8—61no—
521C2×C8—61no—
522C2×C8—61no—
523C2×C8—61no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—32no—
535C4⋊C4—32no—
536C4⋊C4—32no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—64no—
541C4⋊C4—64no—
542C4⋊C4—64no—
543C4⋊C4—64no—
544C4⋊C4—64no—
545C4⋊C4—64no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—64no—
556C22⋊C4—64no—
557C22⋊C4—64no—
558C42—42no—
559C42—64no—
560C42—64no—
561C42D3×D412yes—
562C42D3×D412yes—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3C2×#12011yescharacteristic
578C22×C3#54611yescharacteristic
579C22×C3#54711yescharacteristic
580C22×C3C2×#13511yescharacteristic
581C22×C3#57511yescharacteristic
582C22×C3#57811yescharacteristic
583C22×C3#57811yescharacteristic
584C3×C4—22no—
585C3×C4—22no—
586C3×C4—41no—
587C3×C4—41no—
588C3×C4—42no—
589C3×C4—81no—
590C3×C4—81no—
591C3×C4—81no—
592C3×C4#52511yescharacteristic
593C3×C4#53711yescharacteristic
594C3×C4#54811yescharacteristic
595C3×C4#55011yescharacteristic
596Dic3—42no—
597Dic3—42no—
598Dic3—42no—
599Dic3—42no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23#95012yes—
614C23C22×#6711yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619Q8—62no—
620Q8—62no—
621Q8—121no—
622Q8—121no—
623D4—44no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—128no—
659C2×C4—121no—
660C2×C4—121no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4#93712yes—
668C2×C4#93712yes—
669C2×C4C2×D3×D411yescharacteristic
670C2×C4C2×D3×D411yescharacteristic
671C2×C4C2×#23711yescharacteristic
672C2×C4#100411yescharacteristic
673C2×C4D3×#4111yescharacteristic
674C2×C4#101011yescharacteristic
675C8—62no—
676C8—121no—
677C8—121no—
678C8—121no—
679C2×C3—42no—
680C2×C3—81no—
681C2×C3#240711yescharacteristic
682C2×C3#300211yescharacteristic
683C2×C3#301111yescharacteristic
684C2×C3#330011yescharacteristic
685C2×C3#332711yescharacteristic
686C2×C3#333611yescharacteristic
687C2×C3#335211yescharacteristic
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22C2×#93711yescharacteristic
703C22#580611yescharacteristic
704C22C2×#95011yescharacteristic
705C22#582211yescharacteristic
706C22#582411yescharacteristic
707C22#583811yescharacteristic
708C22#583811yescharacteristic
709C4—22no—
710C4—22no—
711C4—41no—
712C4—41no—
713C4—42no—
714C4—81no—
715C4—81no—
716C4—81no—
717C4—122no—
718C4—122no—
719C4—122no—
720C4—122no—
721C4#559811yescharacteristic
722C4#559911yescharacteristic
723C4#560611yescharacteristic
724C4#560811yescharacteristic
725C3#2412711yescharacteristic, complemented, Sylow
726C2—42no—
727C2—81no—
728C2#8270111yescharacteristic
729C2#8292611yescharacteristic
730C2#8341111yescharacteristic
731C2#8353411yescharacteristic
732C2#8354111yescharacteristic
733C2#8359011yescharacteristic
734C2#8359711yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2536C2
socleC23×C3C22×D4
prime radicalC22×C3×D4D4
hypercenter#2536D3
hypocenterC3#24127
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
3. C2×#5022C2semidirect
4. C2×C4×#216C2semidirect
5. #71700C2semidirect
6. #71700C2semidirect
7. #71693C2semidirect
8. #71692C2semidirect
10. #69559C2semidirect
11. #69554C2semidirect
12. #69527C2semidirect
13. #69526C2semidirect
14. #69506C2semidirect
15. #69504C2semidirect
725. C3#24127semidirect

Maximal subgroups

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

subgroupindex
C2×#55412
C3×#25362
C2×#50222
C2×C4×#2162
#717002
#716932
#716922
#716142
#695592
#695542
#695272
#695262
#695062
#695042
#241273