Finite Group Databasebeta

← #6371707

Subgroups — #6371707

Order 512.

3194 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2905C211yesmaximal, characteristic, complemented
2C22×#421C211yesmaximal, characteristic
3C2×#2896C211yesmaximal, characteristic
4C2×#2879C211yesmaximal, characteristic
5C2×#2873C211yesmaximal, characteristic, complemented
6#21100C218yesmaximal, complemented
7#21099C218yesmaximal, complemented
8#21098C218yesmaximal, complemented
9C2×#1738C211yesmaximal, characteristic, complemented
10C2×#1733C211yesmaximal, characteristic, complemented
11C23×#41C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C23×M16C2211yescharacteristic
15C23×M16C2211yescharacteristic
16C22×#117C2211yescharacteristic
17C22×#117C2211yescharacteristic
18#2905—22no—
19#2905—22no—
20#2905C2214yescomplemented
21#2905C2214yescomplemented
22C2×#424—22no—
23C2×#424C2214yescomplemented
24C2×#423—22no—
25C2×#421—28no—
26C2×#421C2214yes—
27C2×#421C2214yes—
28C22×#104C2214yes—
29#2896C414yescomplemented
30#2896C414yescomplemented
31#2896C2214yes—
32#2896C2214yes—
33C2×#417C414yescomplemented
34C2×#419C412yescomplemented
35C2×#418C412yescomplemented
36C2×#416C2214yes—
37#2879—22no—
38#2879—22no—
39#2879C2214yes—
40#2879C2214yes—
41C2×#408—22no—
42C2×#408C2214yes—
43C2×#407—22no—
44#2873—28no—
45C2×#405C2214yescomplemented
46C2×#405C2214yescomplemented
47C2×C4×M16C2214yescomplemented
48#1938C22132yescomplemented
49#1937C22132yescomplemented
50#1738C2214yescomplemented
51#1738C2214yescomplemented
52C2×#341C2214yescomplemented
53#1733C2214yescomplemented
54#1733C2214yescomplemented
55C2×#339C2214yescomplemented
56C22×#41—21no—
57C22×#41—21no—
58C22×#41—21no—
59C22×#41—21no—
60C22×#41—21no—
61C22×#41—21no—
62C22×#41—24no—
63C22×#41—24no—
64C22×#41—24no—
65C22×#41—24no—
66C22×#41C2×C412yes—
67C22×#41C2×C412yes—
68C22×#41C2×C412yes—
69C22×#41C2312yes—
70C22×#41C2312yes—
71C22×#41C2312yes—
72C23×Q8C2×C411yescharacteristic
73C23×D4—21no—
74C23×D4C2×C411yescharacteristic
75C24×C4—21no—
76C24×C4C2311yescharacteristic
77C22×M16—24no—
78C22×M16—24no—
79C22×M16—24no—
80C22×M16—24no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—21no—
84C22×M16—21no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—24no—
88C22×M16—24no—
89C22×M16—24no—
90C22×M16—24no—
91C22×M16C2×C412yes—
92C22×M16C2×C412yes—
93C22×M16C2×C412yes—
94C22×M16C2×C412yes—
95C22×M16D412yes—
96C22×M16D412yes—
97C22×M16D412yes—
98C22×M16D412yes—
99C22×M16C2312yes—
100C22×M16C2312yes—
101C22×M16C2312yes—
102C22×M16C2312yes—
103C22×M16C2312yes—
104C22×M16C2312yes—
105C22×M16C2312yes—
106C22×M16C2312yes—
107C22×M16C2312yes—
108C22×M16C2312yes—
109C23×C8—21no—
110C23×C8—21no—
111C23×C8C2312yes—
112C23×C8C2312yes—
113C2×#117—21no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—24no—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117C2×C412yes—
123C2×#117C2×C412yes—
124C2×#117C2×C412yes—
125C2×#117D418yes—
126C2×#117C2312yes—
127C2×#117C2312yes—
128C2×#117C2312yes—
129C2×#117C2312yes—
130C2×#117C2312yes—
131C22×C4⋊C4—21no—
132C22×C4⋊C4C2×C412yes—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C42—21no—
136C22×C42C2312yes—
137#424—28no—
138#424—28no—
139#424—28no—
140#424C23116yescomplemented
141#423—28no—
142#423—28no—
143C2×C4⋊C8—28no—
144#421—216no—
145#421—216no—
146C2×#104—216no—
147C2×#104C23116yes—
148#419C2×C418yes—
149#419C2×C418yescomplemented
150#418C2×C418yes—
151#418C2×C418yescomplemented
152#417C2×C4116yes—
153#417C2×C4116yescomplemented
154#416C2×C4116yescomplemented
155#416C23116yes—
156C2×#103C2×C418yescomplemented
157C2×#102C2×C418yescomplemented
158#408—28no—
159#408—28no—
160#408—28no—
161#408C23116yes—
162#407—28no—
163#407—28no—
164C2×C22⋊C8—28no—
165#405—216no—
166#405—216no—
167C4×M16—216no—
168C2×#97C2318yescomplemented
169C2×C4×C8C2318yescomplemented
170#341C23116yescomplemented
171#339C23116yescomplemented
172C25—21no—
173C25#4111yescharacteristic
174C2×#41—22no—
175C2×#41—22no—
176C2×#41—22no—
177C2×#41—22no—
178C2×#41—22no—
179C2×#41—22no—
180C2×#41—22no—
181C2×#41—22no—
182C2×#41—22no—
183C2×#41—22no—
184C2×#41—22no—
185C2×#41—22no—
186C2×#41—28no—
187C2×#41—28no—
188C2×#41—28no—
189C2×#41—28no—
190C2×#41—28no—
191C2×#41—28no—
192C2×#41—24no—
193C2×#41—24no—
194C2×#41—24no—
195C2×#41—24no—
196C2×#41—24no—
197C2×#41—24no—
198C2×#41—24no—
199C2×#41—24no—
200C2×#41—24no—
201C2×#41—24no—
202C2×#41—24no—
203C2×#41—24no—
204C2×#41—44no—
205C2×#41—44no—
206C2×#41—44no—
207C2×#41—44no—
208C2×#41—44no—
209C2×#41—44no—
210C2×#41—44no—
211C2×#41—44no—
212C2×#41—44no—
213C2×#41—44no—
214C2×#41—44no—
215C2×#41—44no—
216C2×#41C22×C414yes—
217C2×#41C22×C414yes—
218C2×#41C22×C414yes—
219C2×#41C2414yes—
220C22×Q8—21no—
221C22×Q8—21no—
222C22×Q8—21no—
223C22×Q8—24no—
224C22×Q8—24no—
225C22×Q8C22×C412yes—
226C22×Q8C22×C412yes—
227C22×Q8C22×C412yes—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4C22×C412yes—
242C22×D4C22×C412yes—
243C22×D4C22×C412yes—
244C23×C4—21no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4C22×C411yescharacteristic
256C23×C4C22×C411yescharacteristic
257C23×C4C22×C411yescharacteristic
258C23×C4C22×C411yescharacteristic
259C23×C4C2×D414yes—
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4#4114yes—
265C23×C4#4114yes—
266C23×C4#4111yescharacteristic
267C23×C4#4111yescharacteristic
268C23×C4#4111yescharacteristic
269C23×C4#4114yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C2×M16—28no—
274C2×M16—28no—
275C2×M16—28no—
276C2×M16—28no—
277C2×M16—28no—
278C2×M16—28no—
279C2×M16—28no—
280C2×M16—28no—
281C2×M16—24no—
282C2×M16—24no—
283C2×M16—24no—
284C2×M16—24no—
285C2×M16—24no—
286C2×M16—24no—
287C2×M16—24no—
288C2×M16—24no—
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—24no—
296C2×M16—24no—
297C2×M16—24no—
298C2×M16—24no—
299C2×M16—24no—
300C2×M16—24no—
301C2×M16—24no—
302C2×M16—24no—
303C2×M16—24no—
304C2×M16—24no—
305C2×M16—24no—
306C2×M16—24no—
307C2×M16—44no—
308C2×M16—44no—
309C2×M16—44no—
310C2×M16—44no—
311C2×M16—44no—
312C2×M16—44no—
313C2×M16C22×C414yes—
314C2×M16C22×C414yes—
315C2×M16C22×C414yes—
316C2×M16C22×C414yes—
317C2×M16C2×D414yes—
318C2×M16C2×D414yes—
319C2×M16C2×D414yes—
320C2×M16C2×D414yes—
321C2×M16C2414yes—
322C2×M16C2414yes—
323C22×C8—24no—
324C22×C8—24no—
325C22×C8—24no—
326C22×C8—24no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—44no—
334C22×C8—44no—
335C22×C8C22×C414yes—
336C22×C8C22×C414yes—
337C22×C8C2×D414yes—
338C22×C8C2×D414yes—
339C22×C8C2414yes—
340C22×C8C2414yes—
341#117—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117—22no—
347#117—28no—
348#117—28no—
349#117—22no—
350#117—22no—
351#117—22no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117—24no—
356#117—24no—
357#117C22×C414yes—
358#117C22×C414yes—
359#117C22×C414yes—
360#117C2×D418yes—
361#117C2×D418yes—
362#117C2414yes—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4C22×C414yes—
370C2×C4⋊C4C22×C414yes—
371C2×C4⋊C4C22×C414yes—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42C2×D418yes—
390C2×C42C2414yes—
391C4⋊C8—232no—
392#104—232no—
393#103C22×C4132yes—
394#102C22×C4132yes—
395C22⋊C8—232no—
396#97—216no—
397C4×C8—216no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—44no—
402C24—82no—
403C24—84no—
404C24C4×D411yescharacteristic
405C24C4×D411yescharacteristic
406C24C4×D411yescharacteristic
407C24C4×D411yescharacteristic
408C24#12314yes—
409C24#12614yes—
410C24C2×#4111yescharacteristic
411C24C2×#4111yescharacteristic
412C24C2×#4111yescharacteristic
413#41—28no—
414#41—28no—
415#41—28no—
416#41—28no—
417#41—28no—
418#41—28no—
419#41—24no—
420#41—24no—
421#41—24no—
422#41—24no—
423#41—44no—
424#41—44no—
425#41—44no—
426#41—44no—
427#41—44no—
428#41—44no—
429#41—44no—
430#41—44no—
431#41—44no—
432#41—44no—
433#41—44no—
434#41—44no—
435#41—48no—
436#41—48no—
437#41—48no—
438#41—48no—
439#41—48no—
440#41—48no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—24no—
445C2×Q8—24no—
446C2×Q8—24no—
447C2×Q8—24no—
448C2×Q8—24no—
449C2×Q8—24no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8C23×C414yes—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4C23×C414yes—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—28no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4#11714yes—
505C22×C4#11714yes—
506C22×C4#11714yes—
507C22×C4#11714yes—
508C22×C4C4×D414yes—
509C22×C4C4×D414yes—
510C22×C4C4×D414yes—
511C22×C4C4×D414yes—
512C22×C4C4×D411yescharacteristic
513C22×C4C4×D411yescharacteristic
514C22×C4C4×D411yescharacteristic
515C22×C4C4×D411yescharacteristic
516C22×C4C4×D411yescharacteristic
517C22×C4C4×D411yescharacteristic
518C22×C4C4×D411yescharacteristic
519C22×C4C4×D411yescharacteristic
520C22×C4C4×D411yescharacteristic
521C22×C4C4×D411yescharacteristic
522C22×C4C4×D411yescharacteristic
523C22×C4C4×D411yescharacteristic
524C22×C4#12114yes—
525C22×C4#12114yes—
526C22×C4#12114yes—
527C22×C4#12114yes—
528C22×C4#12314yes—
529C22×C4#12314yes—
530C22×C4#12314yes—
531C22×C4#12414yes—
532C22×C4#12414yes—
533C22×C4#12414yes—
534C22×C4#12414yes—
535C22×C4#12614yes—
536C22×C4#12614yes—
537C22×C4#12614yes—
538C22×C4C23×C411yescharacteristic
539C22×C4C23×C411yescharacteristic
540C22×C4C23×C411yescharacteristic
541C22×C4C23×C411yescharacteristic
542C22×C4C23×C411yescharacteristic
543C22×C4C23×C411yescharacteristic
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4112yes—
559C22×C4C2×#4111yescharacteristic
560C22×C4C2×#4111yescharacteristic
561C22×C4C2×#4111yescharacteristic
562C22×C4C2×#4112yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4C2511yescharacteristic
566M16—28no—
567M16—28no—
568M16—28no—
569M16—28no—
570M16—28no—
571M16—28no—
572M16—28no—
573M16—28no—
574M16—24no—
575M16—24no—
576M16—24no—
577M16—24no—
578M16—44no—
579M16—44no—
580M16—44no—
581M16—44no—
582M16—44no—
583M16—44no—
584C2×C8—28no—
585C2×C8—28no—
586C2×C8—28no—
587C2×C8—28no—
588C2×C8—24no—
589C2×C8—24no—
590C2×C8—24no—
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—44no—
595C2×C8—44no—
596C2×C8—44no—
597C2×C8—44no—
598C2×C8—44no—
599C2×C8—44no—
600C2×C8C23×C418yes—
601C2×C8C22×D418yes—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4C23×C418yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—24no—
614C42—24no—
615C42—24no—
616C42—24no—
617C42—28no—
618C42—24no—
619C42—24no—
620C42C22×D418yes—
621C23—24no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—48no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—84no—
634C23—84no—
635C23—84no—
636C23—84no—
637C23—816no—
638C23#38814yes—
639C23#38814yes—
640C23#38814yes—
641C23#38814yes—
642C23C2×C4×D411yescharacteristic
643C23C2×C4×D411yescharacteristic
644C23C2×C4×D411yescharacteristic
645C23C2×C4×D411yescharacteristic
646C23C2×C4×D411yescharacteristic
647C23C2×C4×D411yescharacteristic
648C23C2×#12312yes—
649C23C2×#12312yes—
650C23C2×#12312yes—
651C23C2×#12612yes—
652C23C2×#12612yes—
653C23C2×#12612yes—
654C23C22×#4111yescharacteristic
655Q8—24no—
656Q8—24no—
657Q8—44no—
658Q8—44no—
659Q8—44no—
660D4—24no—
661D4—24no—
662D4—44no—
663D4—44no—
664D4—48no—
665D4—48no—
666D4—48no—
667D4—44no—
668D4—44no—
669D4—44no—
670C2×C4—28no—
671C2×C4—24no—
672C2×C4—28no—
673C2×C4—48no—
674C2×C4—48no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—48no—
681C2×C4—48no—
682C2×C4—48no—
683C2×C4—84no—
684C2×C4—84no—
685C2×C4—88no—
686C2×C4#38814yes—
687C2×C4#38814yes—
688C2×C4#38814yes—
689C2×C4#38814yes—
690C2×C4#38814yes—
691C2×C4#38814yes—
692C2×C4#38814yes—
693C2×C4#38814yes—
694C2×C4#38814yes—
695C2×C4#38814yes—
696C2×C4#38814yes—
697C2×C4#38814yes—
698C2×C4C2×#11712yes—
699C2×C4C2×#11712yes—
700C2×C4C2×#11712yes—
701C2×C4C2×#11712yes—
702C2×C4C2×#11712yes—
703C2×C4C2×#11712yes—
704C2×C4C2×C4×D412yes—
705C2×C4C2×C4×D412yes—
706C2×C4C2×C4×D412yes—
707C2×C4C2×C4×D412yes—
708C2×C4C2×C4×D412yes—
709C2×C4C2×C4×D412yes—
710C2×C4C2×C4×D411yescharacteristic
711C2×C4C2×C4×D411yescharacteristic
712C2×C4C2×C4×D411yescharacteristic
713C2×C4C2×C4×D411yescharacteristic
714C2×C4C2×C4×D411yescharacteristic
715C2×C4C2×C4×D411yescharacteristic
716C2×C4C2×#12112yes—
717C2×C4C2×#12112yes—
718C2×C4C2×#12112yes—
719C2×C4C2×#12112yes—
720C2×C4C2×#12112yes—
721C2×C4C2×#12112yes—
722C2×C4C2×#12312yes—
723C2×C4C2×#12312yes—
724C2×C4C2×#12312yes—
725C2×C4C2×#12412yes—
726C2×C4C2×#12412yes—
727C2×C4C2×#12412yes—
728C2×C4C2×#12412yes—
729C2×C4C2×#12412yes—
730C2×C4C2×#12412yes—
731C2×C4C2×#12612yes—
732C2×C4C2×#12612yes—
733C2×C4C2×#12612yes—
734C2×C4C24×C411yescharacteristic
735C2×C4C23×D411yescharacteristic
736C2×C4C23×D411yescharacteristic
737C2×C4C22×#4111yescharacteristic
738C2×C4C22×#4111yescharacteristic
739C2×C4C22×#4111yescharacteristic
740C8—28no—
741C8—28no—
742C8—44no—
743C8—44no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—42no—
752C22—44no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—48no—
762C22—44no—
763C22—88no—
764C22—88no—
765C22—88no—
766C22C2×#38812yes—
767C22C2×#38812yes—
768C22C2×#38812yes—
769C22C2×#38812yes—
770C22C2×#38812yes—
771C22C2×#38812yes—
772C22C22×C4×D411yescharacteristic
773C22C22×#12311yescharacteristic
774C22C22×#12611yescharacteristic
775C4—48no—
776C4—48no—
777C4—44no—
778C4C2×#38812yes—
779C4C2×#38812yes—
780C4C2×#38812yes—
781C4C2×#38812yes—
782C4C2×#38812yes—
783C4C2×#38812yes—
784C4C22×#11711yescharacteristic
785C4C22×C4×D411yescharacteristic
786C4C22×#12111yescharacteristic
787C4C22×#12411yescharacteristic
788C2—21no—
789C2—22no—
790C2—22no—
791C2—22no—
792C2—21no—
793C2—22no—
794C2—22no—
795C2—22no—
796C2—84no—
797C2C22×#38811yescharacteristic
798C2#6018212yes—
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×C4×D4
prime radicalC23×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C23×M16 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2905C2semidirect
5. C2×#2873C2semidirect
6. #21100C2semidirect
7. #21099C2semidirect
8. #21098C2semidirect
9. C2×#1738C2semidirect
10. C2×#1733C2semidirect
20. #2905C22semidirect
21. #2905C22semidirect
23. C2×#424C22semidirect
29. #2896C4semidirect
30. #2896C4semidirect
33. C2×#417C4semidirect
34. C2×#419C4semidirect
35. C2×#418C4semidirect
45. C2×#405C22semidirect
46. C2×#405C22semidirect
47. C2×C4×M16C22semidirect
48. #1938C22semidirect
49. #1937C22semidirect
50. #1738C22semidirect
51. #1738C22semidirect
52. C2×#341C22semidirect
53. #1733C22semidirect
54. #1733C22semidirect
55. C2×#339C22semidirect
140. #424C23semidirect
149. #419C2×C4semidirect
151. #418C2×C4semidirect
153. #417C2×C4semidirect
154. #416C2×C4semidirect
156. C2×#103C2×C4semidirect
157. C2×#102C2×C4semidirect
168. C2×#97C23semidirect
169. C2×C4×C8C23semidirect
170. #341C23semidirect
171. #339C23semidirect

Maximal subgroups

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

subgroupindex
C2×#29052
C22×#4212
C2×#28962
C2×#28792
C2×#28732
#211002
#210992
#210982
C2×#17382
C2×#17332