Finite Group Databasebeta

← C2×#31294 #7504307

Subgroups — C2×#31294 #7504307

Order 512.

2992 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2495C211yesmaximal, characteristic, complemented
2C2×#2435C211yesmaximal, characteristic
3#31294C2116yesmaximal, direct product factor
4C2×#2092C211yesmaximal, characteristic, complemented
5C2×#2067C211yesmaximal, characteristic, complemented
6C2×#2042C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#1983C211yesmaximal, characteristic, complemented
11C2×#1958C211yesmaximal, characteristic, complemented
12C2×#1934C211yesmaximal, characteristic, complemented
13C2×#1926C211yesmaximal, characteristic, complemented
14C2×#1923C211yesmaximal, characteristic, complemented
15C2×#1786C211yesmaximal, characteristic
16C2×#1786C211yesmaximal, characteristic
17C24×D4C2211yescharacteristic
18C22×#124C2211yescharacteristic
19C22×#124C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#107C2211yescharacteristic, complemented
22C22×#106C2211yescharacteristic, complemented
23C22×C4⋊C8C2211yescharacteristic, complemented
24C22×#103C2211yescharacteristic, complemented
25C22×#103C2211yescharacteristic, complemented
26C22×#103C2211yescharacteristic, complemented
27C22×#103C2211yescharacteristic, complemented
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic
37C22×C22⋊C8C2211yescharacteristic
38C22×C4×C8C2211yescharacteristic, complemented
39#2495—24no—
40#2495C2218yescomplemented
41#2435—24no—
42#2435C2218yes—
43C2×#400—21no—
44C2×#397—21no—
45C2×#394—21no—
46C2×#394—21no—
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2211yescharacteristic, complemented
50C2×#389C2211yescharacteristic, complemented
51C2×#388—21no—
52C2×#383—21no—
53C2×#382C2211yescharacteristic, complemented
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#379—21no—
57C2×#379—21no—
58C2×C4×C4⋊C4C2211yescharacteristic, complemented
59C2×C4×C22⋊C4C2211yescharacteristic
60#2092C2218yescomplemented
61#2067C2218yescomplemented
62#2042C2218yescomplemented
63#2042C2218yescomplemented
64#2036C2218yescomplemented
65#2035C2218yescomplemented
66#1983C2218yescomplemented
67#1958C2218yescomplemented
68#1934C2218yescomplemented
69#1926C2218yescomplemented
70#1923C2218yescomplemented
71#1786C2218yes—
72#1786C2218yes—
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#336C2211yescharacteristic, complemented
76C2×#336C2211yescharacteristic, complemented
77C26—21no—
78C23×Q8C2311yescharacteristic
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—21no—
82C23×D4—22no—
83C23×D4—42no—
84C23×D4—42no—
85C23×D4—42no—
86C23×D4—42no—
87C23×D4C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2314yes—
90C24×C4C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C2×#124—24no—
96C2×#124—24no—
97C2×#124—22no—
98C2×#124—22no—
99C2×#124—42no—
100C2×#124—42no—
101C2×#124C2314yes—
102C2×#124C2314yes—
103C2×C22⋊Q8—22no—
104C2×C22⋊Q8—42no—
105C2×C22⋊Q8—42no—
106C2×C22⋊Q8C2314yes—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C22⋊C4—21no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4D411yescharacteristic
127C22×C22⋊C4D411yescharacteristic
128C22×C42—21no—
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131C2×#107—42no—
132C2×#107C2314yescomplemented
133C2×#106—42no—
134C2×#106C2314yescomplemented
135C2×C4⋊C8—42no—
136C2×C4⋊C8C2314yescomplemented
137C2×#103—42no—
138C2×#103—42no—
139C2×#103—42no—
140C2×#103—42no—
141C2×#103C2314yescomplemented
142C2×#103C2314yescomplemented
143C2×#103C2314yescomplemented
144C2×#103C2314yescomplemented
145C2×#102—24no—
146C2×#102—24no—
147C2×#102—42no—
148C2×#102—42no—
149C2×#102—42no—
150C2×#102—42no—
151C2×#102—42no—
152C2×#102—42no—
153C2×#102C2314yes—
154C2×#102C2314yes—
155C2×#102C2314yes—
156C2×#102C2314yes—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×C22⋊C8—42no—
162C2×C22⋊C8—42no—
163C2×C22⋊C8C2314yes—
164C2×C22⋊C8C2314yes—
165C2×C4×C8—42no—
166C2×C4×C8C2314yescomplemented
167#400—28no—
168#397—28no—
169#394—28no—
170#394—28no—
171#390—22no—
172#390—22no—
173#390C2314yes—
174#390C2314yes—
175#389—22no—
176#389—22no—
177#389C2314yescomplemented
178#389C2314yescomplemented
179#388—28no—
180#383—28no—
181#382—22no—
182#382C2314yescomplemented
183#380—22no—
184#380—22no—
185#380C2314yes—
186#380C2314yes—
187#379—28no—
188#379—28no—
189C4×C4⋊C4—22no—
190C4×C4⋊C4C2314yescomplemented
191C4×C22⋊C4D414yes—
192C4×C22⋊C4C2314yes—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95D411yescharacteristic
201C2×#95D411yescharacteristic
202#340C2314yescomplemented
203#340C2314yescomplemented
204#336C2314yescomplemented
205#336C2314yescomplemented
206C25—21no—
207C25—21no—
208C25—24no—
209C25—44no—
210C25—44no—
211C25—44no—
212C25—44no—
213C25—44no—
214C25—82no—
215C25—82no—
216C25C2×D411yescharacteristic
217C22×Q8—21no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8C2412yes—
225C22×D4—28no—
226C22×D4—28no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—48no—
245C22×D4—48no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—48no—
250C22×D4—416no—
251C22×D4—416no—
252C22×D4—416no—
253C22×D4—416no—
254C22×D4#4114yes—
255C22×D4#4114yes—
256C22×D4C2412yes—
257C22×D4C2412yes—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4C2×D412yes—
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8C2412yes—
291C22×C8C2412yes—
292C22×C8C2412yes—
293C22×C8C2412yes—
294#124—28no—
295#124—28no—
296#124—44no—
297#124—44no—
298#124—48no—
299#124—48no—
300C22⋊Q8—44no—
301C22⋊Q8—44no—
302C22⋊Q8—48no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—82no—
323C2×C4⋊C4—82no—
324C2×C4⋊C4C2412yes—
325C2×C4⋊C4C2412yes—
326C2×C4⋊C4C2412yes—
327C2×C4⋊C4C2412yes—
328C2×C4⋊C4C2412yes—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—82no—
349C2×C22⋊C4—82no—
350C2×C22⋊C4—82no—
351C2×C22⋊C4—82no—
352C2×C22⋊C4—82no—
353C2×C22⋊C4C2×D414yes—
354C2×C22⋊C4C2×D414yes—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—44no—
361C2×C42C2×D412yes—
362C2×C42C2×D412yes—
363C2×C42C2412yes—
364C2×C42C2412yes—
365#107—44no—
366#106—44no—
367C4⋊C8—44no—
368#103—44no—
369#103—44no—
370#103—44no—
371#103—44no—
372#102—28no—
373#102—28no—
374#102—44no—
375#102—44no—
376#102—44no—
377#102—44no—
378#102—44no—
379#102—44no—
380C22⋊C8—44no—
381C22⋊C8—44no—
382C4×C8—44no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95C2×D414yes—
391#95C2×D414yes—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—24no—
400C24—22no—
401C24—22no—
402C24—48no—
403C24—48no—
404C24—48no—
405C24—48no—
406C24—432no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—48no—
420C24—84no—
421C24—84no—
422C24—816no—
423C24—816no—
424C24—816no—
425C24—816no—
426C24—816no—
427C24—816no—
428C24#13514yes—
429C24C22×D412yes—
430C24C22×D411yescharacteristic
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—42no—
438C2×Q8—42no—
439C2×Q8—42no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—28no—
449C2×D4—28no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—416no—
464C2×D4—416no—
465C2×D4—416no—
466C2×D4—432no—
467C2×D4—464no—
468C2×D4—416no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4C2×#4114yes—
478C2×D4C2×#4114yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D411yescharacteristic
537C22×C4C2×#4112yes—
538C22×C4C2×#4112yes—
539C22×C4H(5,𝔽2)12yes—
540C22×C4H(5,𝔽2)12yes—
541C22×C4H(5,𝔽2)12yes—
542C22×C4H(5,𝔽2)12yes—
543C22×C4C2511yescharacteristic
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—44no—
557C2×C8—44no—
558C2×C8—44no—
559C2×C8—44no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—48no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—84no—
577C4⋊C4—84no—
578C22⋊C4—28no—
579C22⋊C4—44no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—84no—
587C22⋊C4—84no—
588C22⋊C4—84no—
589C22⋊C4—84no—
590C22⋊C4—84no—
591C42—24no—
592C42—24no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—48no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—28no—
602C23—28no—
603C23—28no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—432no—
614C23—42no—
615C23—42no—
616C23—48no—
617C23—48no—
618C23—42no—
619C23—42no—
620C23—48no—
621C23—48no—
622C23—48no—
623C23—42no—
624C23—42no—
625C23—48no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—816no—
633C23—816no—
634C23—816no—
635C23—816no—
636C23—816no—
637C23—8128no—
638C23—816no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23#53512yes—
648C23#54612yes—
649C23#54612yes—
650C23C2×#13514yes—
651C23C2×#13512yes—
652C23#57512yes—
653C23#57612yes—
654C23#57712yes—
655C23C23×D411yescharacteristic
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—84no—
661D4—24no—
662D4—24no—
663D4—24no—
664D4—24no—
665D4—432no—
666D4—42no—
667D4—42no—
668D4—48no—
669D4—48no—
670D4—42no—
671D4—42no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—48no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4#53512yes—
722C2×C4#53814yes—
723C2×C4#53814yes—
724C2×C4#54612yes—
725C2×C4#54612yes—
726C2×C4#55114yes—
727C2×C4#56014yes—
728C2×C4C22×#4111yescharacteristic
729C2×C4C22×#4111yescharacteristic
730C2×C4C2×H(5,𝔽2)11yescharacteristic
731C2×C4C2×H(5,𝔽2)11yescharacteristic
732C2×C4C2×H(5,𝔽2)11yescharacteristic
733C2×C4C2×H(5,𝔽2)11yescharacteristic
734C8—42no—
735C8—42no—
736C8—42no—
737C8—42no—
738C22—24no—
739C22—24no—
740C22—24no—
741C22—416no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—864no—
753C22—816no—
754C22—816no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22#268514yes—
764C22#321114yes—
765C22#322414yes—
766C22#329614yes—
767C22#329714yes—
768C22#331914yes—
769C22#332314yes—
770C22C2×#53511yescharacteristic
771C22C2×#54611yescharacteristic
772C22C2×#54611yescharacteristic
773C22C22×#13511yescharacteristic
774C22C2×#57511yescharacteristic
775C22C2×#57611yescharacteristic
776C22C2×#57711yescharacteristic
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4#268514yes—
789C4C2×#53811yescharacteristic
790C4C2×#53811yescharacteristic
791C4C2×#55111yescharacteristic
792C4C2×#56011yescharacteristic
793C2—44no—
794C2—84no—
795C2—84no—
796C2#3129418yesdirect product factor
797C2C2×#268511yescharacteristic
798C2C2×#321111yescharacteristic
799C2C2×#322411yescharacteristic
800C2C2×#329611yescharacteristic
801C2C2×#329711yescharacteristic
802C2C2×#331911yescharacteristic
803C2C2×#332311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24×D4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2495C2semidirect
3. #31294C2direct (N × H)
4. C2×#2092C2semidirect
5. C2×#2067C2semidirect
6. C2×#2042C2semidirect
7. C2×#2042C2semidirect
8. C2×#2036C2semidirect
9. C2×#2035C2semidirect
10. C2×#1983C2semidirect
11. C2×#1958C2semidirect
12. C2×#1934C2semidirect
13. C2×#1926C2semidirect
14. C2×#1923C2semidirect
21. C22×#107C22semidirect
22. C22×#106C22semidirect
23. C22×C4⋊C8C22semidirect
24. C22×#103C22semidirect
25. C22×#103C22semidirect
26. C22×#103C22semidirect
27. C22×#103C22semidirect
38. C22×C4×C8C22semidirect
40. #2495C22semidirect
49. C2×#389C22semidirect
50. C2×#389C22semidirect
53. C2×#382C22semidirect
58. C2×C4×C4⋊C4C22semidirect
60. #2092C22semidirect
61. #2067C22semidirect
62. #2042C22semidirect
63. #2042C22semidirect
64. #2036C22semidirect
65. #2035C22semidirect
66. #1983C22semidirect
67. #1958C22semidirect
68. #1934C22semidirect
69. #1926C22semidirect
70. #1923C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#336C22semidirect
76. C2×#336C22semidirect
132. C2×#107C23semidirect
134. C2×#106C23semidirect
136. C2×C4⋊C8C23semidirect
141. C2×#103C23semidirect
142. C2×#103C23semidirect
143. C2×#103C23semidirect
144. C2×#103C23semidirect
166. C2×C4×C8C23semidirect
177. #389C23semidirect
178. #389C23semidirect
182. #382C23semidirect
190. C4×C4⋊C4C23semidirect
202. #340C23semidirect
203. #340C23semidirect
204. #336C23semidirect
205. #336C23semidirect
796. C2#31294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24952
C2×#24352
#312942
C2×#20922
C2×#20672
C2×#20422
C2×#20362
C2×#20352
C2×#19832
C2×#19582
C2×#19342
C2×#19262
C2×#19232
C2×#17862