Finite Group Databasebeta

← C2×#31388 #7504594

Subgroups — C2×#31388 #7504594

Order 512.

2346 conjugacy classes of subgroups.

The subgroup lattice has 763 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×#2417C211yesmaximal, characteristic
3#31388C2116yesmaximal, direct product factor
4C2×#2100C211yesmaximal, characteristic, complemented
5C2×#2076C211yesmaximal, characteristic, complemented
6C2×#2072C211yesmaximal, characteristic, complemented
7C2×#2036C211yesmaximal, characteristic, complemented
8C2×#2001C211yesmaximal, characteristic, complemented
9C2×#2001C211yesmaximal, characteristic, complemented
10C2×#1892C211yesmaximal, characteristic, complemented
11C2×#1892C211yesmaximal, characteristic, complemented
12C2×#1878C211yesmaximal, characteristic, complemented
13C2×#1872C211yesmaximal, characteristic, complemented
14C2×#1869C211yesmaximal, characteristic
15C2×#1863C211yesmaximal, characteristic, complemented
16C2×#1824C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C22×#107C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36#2538—24no—
37#2538C2218yes—
38#2417—24no—
39#2417C2218yes—
40C2×#398—21no—
41C2×#396—21no—
42C2×#396—21no—
43C2×#396—21no—
44C2×#391C2211yescharacteristic
45C2×#390—21no—
46C2×#389—21no—
47C2×#389C2211yescharacteristic
48C2×#386—21no—
49C2×#384C2211yescharacteristic
50C2×#380—21no—
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54#2100C2218yescomplemented
55#2076C2218yescomplemented
56#2072C2218yescomplemented
57#2036C2218yescomplemented
58#2001C2218yescomplemented
59#2001C2218yescomplemented
60#1892C2218yescomplemented
61#1892C2218yescomplemented
62#1878C2218yescomplemented
63#1872C2218yescomplemented
64#1869C2218yes—
65#1863C2218yescomplemented
66#1824C2218yescomplemented
67C2×#340C2211yescharacteristic
68C2×#340C2211yescharacteristic
69C2×#340C2211yescharacteristic
70C2×#340C2211yescharacteristic
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#336C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C23×Q8C2311yescharacteristic
78C23×Q8C2311yescharacteristic
79C23×D4D411yescharacteristic
80C24×C4—21no—
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C22×Q16—24no—
84C22×Q16—42no—
85C22×Q16—42no—
86C22×Q16C2314yes—
87C23×C8—42no—
88C23×C8—42no—
89C23×C8—42no—
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2314yes—
95C2×C22⋊Q8—22no—
96C2×C22⋊Q8—22no—
97C2×C22⋊Q8—22no—
98C2×C22⋊Q8—22no—
99C2×C22⋊Q8—24no—
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—42no—
103C2×C22⋊Q8—42no—
104C2×C22⋊Q8—42no—
105C2×C22⋊Q8—42no—
106C2×C22⋊Q8—42no—
107C2×C22⋊Q8C2314yes—
108C2×C22⋊Q8C2314yes—
109C2×C22⋊Q8C2314yes—
110C2×C22⋊Q8C2314yes—
111C2×C4×Q8—22no—
112C2×C4×Q8—42no—
113C2×C4×Q8—42no—
114C2×C4×Q8C2314yes—
115C2×C4×D4—42no—
116C2×C4×D4—42no—
117C2×C4×D4D414yes—
118C2×C4×D4C2314yes—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—22no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—42no—
131C22×C4⋊C4D411yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4D411yescharacteristic
147C22×C22⋊C4D411yescharacteristic
148C22×C42—21no—
149C22×C42C2311yescharacteristic
150C2×#107—42no—
151C2×#107C2314yes—
152C2×#103—24no—
153C2×#103—42no—
154C2×#103—42no—
155C2×#103—42no—
156C2×#103—42no—
157C2×#103—42no—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×C22⋊C8—42no—
165C2×C22⋊C8—42no—
166C2×C22⋊C8—42no—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169C2×C22⋊C8C2314yes—
170#398—28no—
171#396—28no—
172#396—28no—
173#396—28no—
174#391—22no—
175#391C2314yes—
176#390—28no—
177#389—28no—
178#389—22no—
179#389C2314yes—
180#386—28no—
181#384—22no—
182#384C2314yes—
183#380—22no—
184#380—22no—
185#380—22no—
186#380—28no—
187#380C2314yes—
188#380C2314yes—
189#380C2314yes—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196#340C2314yes—
197#340C2314yes—
198#340C2314yes—
199#340C2314yes—
200#340C2314yes—
201#340C2314yes—
202#340C2314yes—
203#340C2314yes—
204#336C2314yes—
205#336C2314yes—
206C25C2×D411yescharacteristic
207C25C2×D411yescharacteristic
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8#4114yes—
222C22×Q8C2412yes—
223C22×Q8C2412yes—
224C22×D4—42no—
225C22×D4—42no—
226C22×D4Q1618yescomplemented
227C22×D4C2×D414yes—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—24no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4—82no—
252C23×C4C2×D412yes—
253C23×C4C2×D412yes—
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C2×Q16—28no—
262C2×Q16—44no—
263C2×Q16—44no—
264C2×Q16—416no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—44no—
278C22×C8—44no—
279C22×C8—44no—
280C22×C8—416no—
281C22×C8C2412yes—
282C22×C8C2412yes—
283C22×C8C2412yes—
284C22×C8C2412yes—
285C22⋊Q8—28no—
286C22⋊Q8—28no—
287C22⋊Q8—28no—
288C22⋊Q8—44no—
289C22⋊Q8—44no—
290C22⋊Q8—44no—
291C22⋊Q8—44no—
292C22⋊Q8—44no—
293C22⋊Q8—48no—
294C22⋊Q8—48no—
295C22⋊Q8—48no—
296C22⋊Q8—48no—
297C4×Q8—44no—
298C4×Q8—44no—
299C4×Q8—48no—
300C4×D4—48no—
301C4×D4—44no—
302C4×D4—44no—
303C2×C4⋊C4—21no—
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—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—48no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—82no—
341C2×C4⋊C4—82no—
342C2×C4⋊C4C2×D414yes—
343C2×C4⋊C4#4114yes—
344C2×C4⋊C4C2412yes—
345C2×C4⋊C4C2412yes—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—82no—
364C2×C22⋊C4—82no—
365C2×C22⋊C4—82no—
366C2×C22⋊C4C2×D414yes—
367C2×C22⋊C4C2×D414yes—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—44no—
372C2×C42C2×D412yes—
373C2×C42C2412yes—
374#107—44no—
375#103—28no—
376#103—44no—
377#103—44no—
378#103—44no—
379#103—44no—
380#103—44no—
381C22⋊C8—44no—
382C22⋊C8—44no—
383C22⋊C8—44no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24C2×Q1614yes—
403C24C2×Q1614yes—
404C24C22×D412yes—
405C24C22×D412yes—
406C24C22×D411yescharacteristic
407C2×Q8—24no—
408C2×Q8—22no—
409C2×Q8—28no—
410C2×Q8—28no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—44no—
424C2×Q8—42no—
425C2×Q8—42no—
426C2×Q8—42no—
427C2×Q8—44no—
428C2×Q8—44no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8—44no—
432C2×Q8C2×#4114yes—
433C2×D4—44no—
434C2×D4—416no—
435C2×D4—44no—
436C2×D4C2×Q16116yescomplemented
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—48no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—48no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—84no—
509C22×C4—816no—
510C22×C4C2×Q1614yes—
511C22×C4C22×D412yes—
512C22×C4C22×D412yes—
513C22×C4C22×D412yes—
514C22×C4C22×D412yes—
515C22×C4C22×D411yescharacteristic
516C22×C4C2×#4112yes—
517C22×C4C2×#4112yes—
518C22×C4H(5,𝔽2)12yes—
519C22×C4H(5,𝔽2)12yes—
520C22×C4H(5,𝔽2)12yes—
521C22×C4H(5,𝔽2)12yes—
522C22×C4C2511yescharacteristic
523Q16—416no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—416no—
537C2×C8—44no—
538C2×C8—44no—
539C2×C8—44no—
540C2×C8—44no—
541C4⋊C4—24no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—44no—
554C4⋊C4—48no—
555C4⋊C4—48no—
556C4⋊C4—48no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—84no—
567C4⋊C4—84no—
568C4⋊C4C2×#4114yes—
569C22⋊C4—44no—
570C22⋊C4—44no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—84no—
576C22⋊C4—84no—
577C22⋊C4—84no—
578C42—24no—
579C42—22no—
580C42—22no—
581C42—48no—
582C23—28no—
583C23—28no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—28no—
591C23—28no—
592C23—28no—
593C23—28no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23#53412yes—
609C23#54612yes—
610C23#54612yes—
611C23C22×Q1614yes—
612C23C22×Q1614yes—
613C23C22×Q1612yes—
614C23#57512yes—
615C23#57712yes—
616C23#57712yes—
617C23C23×D411yescharacteristic
618Q8—24no—
619Q8—24no—
620Q8—42no—
621Q8—48no—
622Q8—42no—
623Q8—42no—
624Q8—42no—
625Q8—42no—
626Q8—42no—
627Q8—84no—
628D4—416no—
629C2×C4—28no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—42no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—48no—
647C2×C4—44no—
648C2×C4—42no—
649C2×C4—48no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—48no—
657C2×C4—48no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—816no—
681C2×C4—84no—
682C2×C4—84no—
683C2×C4—84no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4#53412yes—
688C2×C4#53814yes—
689C2×C4#54014yes—
690C2×C4#54612yes—
691C2×C4#54612yes—
692C2×C4#55314yes—
693C2×C4#56014yes—
694C2×C4C22×Q1614yes—
695C2×C4C22×#4111yescharacteristic
696C2×C4C22×#4111yescharacteristic
697C2×C4C2×H(5,𝔽2)11yescharacteristic
698C2×C4C2×H(5,𝔽2)11yescharacteristic
699C2×C4C2×H(5,𝔽2)11yescharacteristic
700C2×C4C2×H(5,𝔽2)11yescharacteristic
701C8—42no—
702C8—42no—
703C8—42no—
704C8—42no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—416no—
716C22—416no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22#268814yes—
722C22#318914yes—
723C22#320414yes—
724C22#329914yes—
725C22#329914yes—
726C22#331114yes—
727C22#331714yes—
728C22C2×#53411yescharacteristic
729C22C2×#54611yescharacteristic
730C22C2×#54611yescharacteristic
731C22C23×Q1611yescharacteristic
732C22C2×#57511yescharacteristic
733C22C2×#57711yescharacteristic
734C22C2×#57711yescharacteristic
735C4—24no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—44no—
740C4—44no—
741C4—82no—
742C4—82no—
743C4—82no—
744C4—82no—
745C4—82no—
746C4—82no—
747C4#268814yes—
748C4C2×#53811yescharacteristic
749C4C2×#54011yescharacteristic
750C4C2×#55311yescharacteristic
751C4C2×#56011yescharacteristic
752C2—44no—
753C2—44no—
754C2#3138818yesdirect product factor
755C2C2×#268811yescharacteristic
756C2C2×#318911yescharacteristic
757C2C2×#320411yescharacteristic
758C2C2×#329911yescharacteristic
759C2C2×#329911yescharacteristic
760C2C2×#331111yescharacteristic
761C2C2×#331711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #31388C2direct (N × H)
4. C2×#2100C2semidirect
5. C2×#2076C2semidirect
6. C2×#2072C2semidirect
7. C2×#2036C2semidirect
8. C2×#2001C2semidirect
9. C2×#2001C2semidirect
10. C2×#1892C2semidirect
11. C2×#1892C2semidirect
12. C2×#1878C2semidirect
13. C2×#1872C2semidirect
15. C2×#1863C2semidirect
16. C2×#1824C2semidirect
54. #2100C22semidirect
55. #2076C22semidirect
56. #2072C22semidirect
57. #2036C22semidirect
58. #2001C22semidirect
59. #2001C22semidirect
60. #1892C22semidirect
61. #1892C22semidirect
62. #1878C22semidirect
63. #1872C22semidirect
65. #1863C22semidirect
66. #1824C22semidirect
226. C22×D4Q16semidirect
436. C2×D4C2×Q16semidirect
754. C2#31388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#24172
#313882
C2×#21002
C2×#20762
C2×#20722
C2×#20362
C2×#20012
C2×#18922
C2×#18782
C2×#18722
C2×#18692
C2×#18632
C2×#18242