Finite Group Databasebeta

← #6345225

Subgroups — #6345225

Order 512.

1833 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60946C211yesmaximal, characteristic
2#60204C211yesmaximal, characteristic, complemented
3C2×#2931C211yesmaximal, characteristic, complemented
4#17976C212yesmaximal, complemented
5#17975C212yesmaximal, complemented
6#17962C212yesmaximal, complemented
7#17960C212yesmaximal, complemented
8#17940C214yesmaximal, complemented
9#17938C214yesmaximal, complemented
10#17917C214yesmaximal, complemented
11#17914C214yesmaximal, complemented
12#17817C211yesmaximal, characteristic, complemented
13#17504C211yesmaximal, characteristic, complemented
14#17500C211yesmaximal, characteristic, complemented
15C2×#1451C211yesmaximal, characteristic, complemented
16C22×#131—21no—
17#3444C2211yescharacteristic
18C2×#532C2211yescharacteristic
19#3247C414yes—
20#3230C411yescharacteristic
21#3228C412yes—
22#3227C411yescharacteristic
23#3208C411yescharacteristic
24#3207C412yes—
25#3205C411yescharacteristic
26#3188C414yes—
27#3169C2212yes—
28#3167C2212yes—
29#3106C2214yes—
30#3105C2214yes—
31#2966—21no—
32#2966—21no—
33#2966C2212yes—
34#2966C2212yes—
35#2965—21no—
36#2965C2212yescomplemented
37C8×#41—21no—
38C8×#41C2212yescomplemented
39#2960C2211yescharacteristic, complemented
40#2960C2211yescharacteristic, complemented
41#2931—21no—
42#2931—21no—
43#2931—21no—
44#2931—21no—
45#2931C2212yes—
46#2931C2212yes—
47#2931C2212yes—
48#2931C2212yes—
49#2931C2211yescharacteristic, complemented
50#2931C2211yescharacteristic, complemented
51#2929—21no—
52#2929—21no—
53C2×#436—21no—
54C2×#436C2212yes—
55C2×C8×D4—21no—
56C2×C8×D4C2212yes—
57#2922—21no—
58#2920C2211yescharacteristic
59C2×#431C2211yescharacteristic
60C2×#423C2211yescharacteristic
61C2×#408—21no—
62C4×#131—21no—
63C2×C4×M16C2211yescharacteristic
64C22×C4×C8C2211yescharacteristic
65#1594C2218yescomplemented
66#1592C2218yescomplemented
67#1583C2218yescomplemented
68#1582C2218yescomplemented
69#1581C2218yescomplemented
70#1581C2218yescomplemented
71#1580C2218yescomplemented
72SD16⋊C8C2218yescomplemented
73#1574C2214yescomplemented
74#1573C2214yes—
75#1567C2212yescomplemented
76#1566C2212yescomplemented
77#1493C2212yescomplemented
78#1492C2212yes—
79#1492C2212yes—
80#1492C2212yescomplemented
81#1490C2214yes—
82#1489C2214yescomplemented
83#1484C2214yes—
84#1483C2214yes—
85#1451C2212yes—
86#1451C2212yes—
87#1451C2212yescomplemented
88#1451C2212yescomplemented
89C2×#322C2212yescomplemented
90C2×#322C2212yescomplemented
91C22×#41—21no—
92C2×#131—21no—
93C2×#131—21no—
94C2×#131—22no—
95C2×#131—22no—
96C2×#131—22no—
97C2×#131—22no—
98C2×#131—48no—
99C22×M16—21no—
100C22×M16—21no—
101C22×M16—22no—
102C23×C8—22no—
103C23×C8D411yescharacteristic
104C23×C8D411yescharacteristic
105#533C2×C411yescharacteristic
106#533C2×C411yescharacteristic
107#533C2311yescharacteristic
108#532—21no—
109#532—21no—
110#532—21no—
111#532—21no—
112#532C2×C411yescharacteristic
113#532C2×C412yes—
114#532C2×C412yes—
115#532C2×C411yescharacteristic
116#532C2312yes—
117#532C2312yes—
118#532C2311yescharacteristic
119C2×C4⋊Q8C2×C411yescharacteristic
120C2×#127C2×C411yescharacteristic
121#529—21no—
122#529—21no—
123#529—21no—
124#529—21no—
125#529C2×C412yes—
126#529C2312yes—
127C2×#124—21no—
128#525—21no—
129#525—21no—
130#525C2×C412yes—
131C2×#121—21no—
132C2×#121C2×C412yes—
133C4×#41—21no—
134C4×#41—21no—
135C4×#41C2312yes—
136C2×C4×D4—21no—
137C2×C4×D4C2312yes—
138C22×C42C2311yescharacteristic
139#500C2×C412yes—
140#498C2×C412yes—
141#493C2×C412yes—
142#492C2×C412yes—
143#487C2×C412yes—
144#486C2×C412yes—
145#486C2×C412yes—
146#486C2×C412yes—
147#484C2×C414yes—
148#482C2×C418yes—
149#481C2×C414yes—
150#478C2×C418yes—
151#477C2×C414yes—
152#476C2×C414yes—
153#466C2×C418yes—
154#465C2×C418yes—
155#463C2×C418yes—
156#460C2×C414yes—
157#459C2×C414yes—
158#450C2×C414yes—
159#449C2×C418yes—
160#447C2×C414yes—
161#446—21no—
162#446—21no—
163#446C2312yes—
164#446C2312yes—
165C8×Q8—21no—
166C8×Q8—21no—
167C8×Q8C2312yes—
168C8×Q8C2312yes—
169C4×SD16C2318yes—
170C4×D8C2318yes—
171#436—22no—
172#436—22no—
173#436—22no—
174#436—22no—
175#436—22no—
176#436—22no—
177#436—21no—
178#436—21no—
179#436C2312yes—
180#436C2314yes—
181#436C2314yes—
182#436C2312yes—
183#435—22no—
184#435—22no—
185#435—22no—
186#435—22no—
187C8×D4—22no—
188C8×D4—22no—
189C8×D4—22no—
190C8×D4—22no—
191C8×D4—22no—
192C8×D4—22no—
193C8×D4—22no—
194C8×D4—22no—
195C8×D4—22no—
196C8×D4—22no—
197C8×D4—21no—
198C8×D4—21no—
199C8×D4C2314yes—
200C8×D4C2312yes—
201C8×D4C2312yes—
202C8×D4C2314yes—
203#433—22no—
204#433—22no—
205#432—21no—
206#432C2312yes—
207#431—21no—
208#431—22no—
209#431—22no—
210#431C2×C411yescharacteristic
211#431C2×C412yes—
212#431C2×C411yescharacteristic
213#431C2312yes—
214#431C2312yes—
215#431C2312yes—
216#424—21no—
217#424—21no—
218#423—21no—
219#423—21no—
220#423C2311yescharacteristic
221#423C2312yes—
222#423C2311yescharacteristic
223#423C2312yes—
224C2×C4⋊C8—21no—
225C2×C4⋊C8C2×C412yes—
226C2×C4⋊C8C2312yes—
227#408—22no—
228#408—22no—
229#408—22no—
230#408—22no—
231#408—21no—
232#408—21no—
233#407—21no—
234C2×C22⋊C8—22no—
235C2×C22⋊C8—22no—
236C2×C22⋊C8C2×C412yes—
237#405—21no—
238#405—21no—
239#405—22no—
240#405—22no—
241C4×M16—21no—
242C4×M16—21no—
243C4×M16—21no—
244C4×M16—22no—
245C4×M16C2312yes—
246C4×M16C2312yes—
247C2×#97—21no—
248C2×C4×C8—22no—
249C2×C4×C8D411yescharacteristic
250C2×C4×C8D411yescharacteristic
251C2×C4×C8D411yescharacteristic
252C2×C4×C8D411yescharacteristic
253C2×C4×C8D411yescharacteristic
254C2×C4×C8D411yescharacteristic
255C2×C4×C8C2312yes—
256C2×C4×C8C2312yes—
257C2×C4×C8C2311yescharacteristic
258C2×C4×C8C2311yescharacteristic
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263#335C2318yes—
264#334C2318yes—
265Q8⋊C8C2318yes—
266D4⋊C8C2318yes—
267D4⋊C8C2318yes—
268D4⋊C8C2318yes—
269#322C2314yes—
270#322C2314yes—
271#322C2314yes—
272#322C2314yes—
273C2×#41—21no—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—21no—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—44no—
280C2×#41—44no—
281C2×#41C22×C412yes—
282C22×Q8—21no—
283C22×D4—22no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4C22×C412yes—
287C23×C4—22no—
288C23×C4C22×C411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4#4111yescharacteristic
291C2×SD16C22×C418yes—
292C2×D8C22×C418yes—
293#131—44no—
294#131—48no—
295#131—48no—
296#131—48no—
297#131—44no—
298#131—48no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—21no—
302C2×M16—21no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—24no—
306C2×M16—24no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—48no—
310C2×M16—44no—
311C2×M16—44no—
312C22×C8—24no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—24no—
316C22×C8—24no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—42no—
320C22×C8—48no—
321C22×C8C22×C414yes—
322C22×C8C2×D411yescharacteristic
323C22×C8C2×D411yescharacteristic
324C22×C8C2×D411yescharacteristic
325C22×C8C2×D411yescharacteristic
326C22×C8C2×D411yescharacteristic
327C22×C8C2×D411yescharacteristic
328C22×C8C2×D411yescharacteristic
329C22×C8C2×D411yescharacteristic
330C22×C8C2×D411yescharacteristic
331C22×C8C2×D411yescharacteristic
332C22×C8C2×D411yescharacteristic
333C22×C8C2×D411yescharacteristic
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8C22×C411yescharacteristic
337C4⋊Q8C22×C412yes—
338C4⋊Q8C22×C412yes—
339C4⋊Q8C22×C411yescharacteristic
340C4⋊Q8C22×C411yescharacteristic
341#127—21no—
342#127—21no—
343#127C22×C412yes—
344#127C22×C412yes—
345#127C22×C411yescharacteristic
346#126—22no—
347#126—22no—
348#125—21no—
349#125—21no—
350#125C22×C412yes—
351#124—22no—
352#124—22no—
353#124—21no—
354#124—22no—
355#124—22no—
356#124—21no—
357#124C22×C412yes—
358#123—22no—
359#123—22no—
360#123—22no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8C22×C412yes—
366C22⋊Q8C22×C412yes—
367#121—22no—
368#121—22no—
369#121—22no—
370#121—22no—
371#121—21no—
372#121—21no—
373#121—21no—
374#121—22no—
375#121—22no—
376#121—21no—
377#121C22×C414yes—
378#121C22×C414yes—
379#121C22×C412yes—
380#121C22×C412yes—
381#120—22no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8C22×C412yes—
387C4×Q8C2412yes—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—21no—
403C4×D4—22no—
404C4×D4C22×C414yes—
405C4×D4C22×C412yes—
406C4×D4C2414yes—
407C4×D4C2412yes—
408#117—21no—
409#117—21no—
410#117—22no—
411#117—22no—
412#117—22no—
413#117C22×C412yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4C22×C412yes—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C42—22no—
419C2×C42C22×C411yescharacteristic
420C2×C42C22×C411yescharacteristic
421C2×C42C22×C411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42#4111yescharacteristic
426C2×C42#4111yescharacteristic
427C2×C42#4111yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431#107C22×C418yes—
432#106C22×C418yes—
433C4⋊C8—22no—
434C4⋊C8—22no—
435C4⋊C8—22no—
436C4⋊C8—22no—
437C4⋊C8—22no—
438C4⋊C8—22no—
439C4⋊C8—22no—
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8C22×C412yes—
443C4⋊C8C22×C412yes—
444C4⋊C8C22×C414yes—
445C4⋊C8C2412yes—
446C4⋊C8C2412yes—
447C4⋊C8C2414yes—
448#103C22×C418yes—
449#102C22×C418yes—
450#102C22×C418yes—
451#102C22×C418yes—
452C22⋊C8—22no—
453C22⋊C8—22no—
454C22⋊C8—24no—
455C22⋊C8—24no—
456C22⋊C8—24no—
457C22⋊C8—24no—
458C22⋊C8—22no—
459C22⋊C8—22no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462C22⋊C8C22×C412yes—
463C22⋊C8C22×C414yes—
464C22⋊C8C22×C412yes—
465#97—22no—
466#97—22no—
467#97—22no—
468#97—22no—
469#97—22no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8—22no—
474C4×C8C22×C412yes—
475C4×C8C22×C412yes—
476C4×C8C2×D411yescharacteristic
477C4×C8C2×D411yescharacteristic
478C4×C8C2×D411yescharacteristic
479C4×C8C2×D411yescharacteristic
480C4×C8C2×D411yescharacteristic
481C4×C8C2×D411yescharacteristic
482C4×C8C2×D411yescharacteristic
483C4×C8C2×D411yescharacteristic
484C4×C8C2×D411yescharacteristic
485C4×C8C2×D411yescharacteristic
486C4×C8C2×D411yescharacteristic
487C4×C8C2×D411yescharacteristic
488C4×C8C2414yes—
489C4×C8C2414yes—
490C4×C8C2411yescharacteristic
491C4×C8C2411yescharacteristic
492C4×C8C2411yescharacteristic
493C4×C8C2411yescharacteristic
494C24—22no—
495C24C4×D411yescharacteristic
496#41—44no—
497#41—44no—
498#41—48no—
499#41—48no—
500#41—44no—
501#41—44no—
502#41—42no—
503#41—42no—
504#41—44no—
505#41—44no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—44no—
511C2×Q8C23×C412yes—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—48no—
527C2×D4—44no—
528C2×D4C23×C412yes—
529C2×D4C23×C414yes—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—42no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4C4×D411yescharacteristic
543C22×C4C4×D411yescharacteristic
544C22×C4C4×D411yescharacteristic
545C22×C4C4×D411yescharacteristic
546C22×C4C4×D411yescharacteristic
547C22×C4C4×D411yescharacteristic
548C22×C4C4×D411yescharacteristic
549C22×C4C4×D411yescharacteristic
550C22×C4C4×D411yescharacteristic
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C2×#4111yescharacteristic
558C22×C4C2×#4111yescharacteristic
559C22×C4C2×#4111yescharacteristic
560SD16—48no—
561D8—48no—
562M16—48no—
563M16—44no—
564M16—44no—
565M16—44no—
566M16—44no—
567M16—44no—
568M16—42no—
569M16—42no—
570M16—48no—
571M16—44no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—24no—
582C2×C8—24no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—44no—
588C2×C8—48no—
589C2×C8—44no—
590C2×C8—44no—
591C2×C8—44no—
592C2×C8—48no—
593C2×C8—44no—
594C2×C8AGL(1,ℤ/8)14yes—
595C2×C8C23×C414yes—
596C2×C8C23×C414yes—
597C2×C8C22×D411yescharacteristic
598C2×C8C22×D411yescharacteristic
599C2×C8C22×D411yescharacteristic
600C2×C8C22×D411yescharacteristic
601C2×C8C22×D411yescharacteristic
602C2×C8C22×D411yescharacteristic
603C2×C8C22×D411yescharacteristic
604C2×C8C22×D411yescharacteristic
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4C23×C412yes—
619C4⋊C4C23×C412yes—
620C4⋊C4C23×C414yes—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42C4×D411yescharacteristic
638C42C4×D411yescharacteristic
639C42C4×D411yescharacteristic
640C42C4×D411yescharacteristic
641C42C4×D411yescharacteristic
642C42C4×D411yescharacteristic
643C42C23×C411yescharacteristic
644C42C23×C411yescharacteristic
645C42C23×C411yescharacteristic
646C42C22×D411yescharacteristic
647C42C22×D411yescharacteristic
648C42C22×D411yescharacteristic
649C42C2×#4111yescharacteristic
650C42C2×#4111yescharacteristic
651C42C2×#4111yescharacteristic
652C42C2511yescharacteristic
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—41no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23C2×C4×D411yescharacteristic
662C23C2×C4×D411yescharacteristic
663C23C2×C4×D411yescharacteristic
664Q8—24no—
665Q8—44no—
666Q8—44no—
667Q8—42no—
668Q8—42no—
669D4—24no—
670D4—28no—
671D4—44no—
672D4—44no—
673D4—48no—
674D4—44no—
675D4—48no—
676D4—44no—
677D4—44no—
678D4—44no—
679D4—42no—
680D4—44no—
681D4—44no—
682D4—42no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—48no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4#44414yes—
714C2×C4C2×C4×D411yescharacteristic
715C2×C4C2×C4×D411yescharacteristic
716C2×C4C2×C4×D411yescharacteristic
717C2×C4C2×C4×D411yescharacteristic
718C2×C4C2×C4×D411yescharacteristic
719C2×C4C2×C4×D411yescharacteristic
720C2×C4C2×C4×D411yescharacteristic
721C2×C4C2×C4×D411yescharacteristic
722C2×C4C2×C4×D411yescharacteristic
723C2×C4C2×AGL(1,ℤ/8)12yes—
724C2×C4#57512yes—
725C2×C4C24×C411yescharacteristic
726C2×C4C23×D411yescharacteristic
727C2×C4C22×#4111yescharacteristic
728C8—24no—
729C8—24no—
730C8—21no—
731C8—21no—
732C8—21no—
733C8—21no—
734C8—21no—
735C8—21no—
736C8—44no—
737C8—44no—
738C8—42no—
739C8—42no—
740C8C2×AGL(1,ℤ/8)12yes—
741C8C2×AGL(1,ℤ/8)12yes—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—44no—
750C22—42no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—44no—
755C22—42no—
756C22—88no—
757C22C4×AGL(1,ℤ/8)12yes—
758C22C2×#44412yes—
759C22C22×C4×D411yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—42no—
768C4—42no—
769C4—44no—
770C4—42no—
771C4C4×AGL(1,ℤ/8)12yes—
772C4C2×#44412yes—
773C4C2×#44412yes—
774C4#357312yes—
775C4C22×AGL(1,ℤ/8)11yescharacteristic
776C4C2×#57511yescharacteristic
777C2—22no—
778C2—22no—
779C2—41no—
780C2—82no—
781C2—84no—
782C2#6014011yescharacteristic
783C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
784C2C22×#44411yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60946C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4×C8 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60204C2semidirect
3. C2×#2931C2semidirect
4. #17976C2semidirect
5. #17975C2semidirect
6. #17962C2semidirect
7. #17960C2semidirect
8. #17940C2semidirect
9. #17938C2semidirect
10. #17917C2semidirect
11. #17914C2semidirect
12. #17817C2semidirect
13. #17504C2semidirect
14. #17500C2semidirect
15. C2×#1451C2semidirect
36. #2965C22semidirect
38. C8×#41C22semidirect
39. #2960C22semidirect
40. #2960C22semidirect
49. #2931C22semidirect
50. #2931C22semidirect
65. #1594C22semidirect
66. #1592C22semidirect
67. #1583C22semidirect
68. #1582C22semidirect
69. #1581C22semidirect
70. #1581C22semidirect
71. #1580C22semidirect
72. SD16⋊C8C22semidirect
73. #1574C22semidirect
75. #1567C22semidirect
76. #1566C22semidirect
77. #1493C22semidirect
80. #1492C22semidirect
82. #1489C22semidirect
87. #1451C22semidirect
88. #1451C22semidirect
89. C2×#322C22semidirect
90. C2×#322C22semidirect

Maximal subgroups

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

subgroupindex
#609462
#602042
C2×#29312
#179762
#179752
#179622
#179602
#179402
#179382
#179172
#179142
#178172
#175042
#175002
C2×#14512