Finite Group Databasebeta

← C2×#27252 #6440652

Subgroups — C2×#27252 #6440652

Order 512.

2934 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#477C211yesmaximal, characteristic, complemented
2C22×#452C211yesmaximal, characteristic
3C2×#2492C211yesmaximal, characteristic, complemented
4C2×#2341C211yesmaximal, characteristic
5#27252C2116yesmaximal, direct product factor
6C2×#2075C211yesmaximal, characteristic, complemented
7C2×#2055C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2023C211yesmaximal, characteristic, complemented
10C2×#1973C211yesmaximal, characteristic, complemented
11C2×#1925C211yesmaximal, characteristic, complemented
12C2×#1924C211yesmaximal, characteristic, complemented
13C2×#1878C211yesmaximal, characteristic, complemented
14C2×#1878C211yesmaximal, characteristic, complemented
15C2×#1788C211yesmaximal, characteristic
16C2×#1763C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C2×#477—28no—
25C2×#477C2218yescomplemented
26C2×#452—28no—
27C2×#452C2218yes—
28C22×#107C2211yescharacteristic
29C22×#107C2211yescharacteristic
30C22×C4⋊C8C2211yescharacteristic
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41C22×#97C2211yescharacteristic
42#2492—24no—
43#2492C2218yescomplemented
44C2×#400—21no—
45C2×#393—21no—
46#2341—24no—
47#2341C2218yes—
48C2×#391—21no—
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#390—21no—
52C2×#390—21no—
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#388—21no—
56C2×#380—21no—
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4—21no—
61C2×C4×C22⋊C4C2211yescharacteristic
62#2075C2218yescomplemented
63#2055C2218yescomplemented
64#2036C2218yescomplemented
65#2023C2218yescomplemented
66#1973C2218yescomplemented
67#1925C2218yescomplemented
68#1924C2218yescomplemented
69#1878C2218yescomplemented
70#1878C2218yescomplemented
71#1788C2218yes—
72#1763C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C22×#41—24no—
80C22×#41—24no—
81C22×#41—22no—
82C22×#41—24no—
83C22×#41—24no—
84C22×#41—42no—
85C22×#41—42no—
86C22×#41C2314yes—
87C23×Q8—21no—
88C23×Q8C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×D4—21no—
91C23×D4C2311yescharacteristic
92C24×C4—21no—
93C24×C4C2311yescharacteristic
94C22×Q16—24no—
95C22×Q16—24no—
96C22×Q16—24no—
97C22×Q16C2314yes—
98C22×SD16—24no—
99C22×SD16—24no—
100C22×SD16—42no—
101C22×SD16C2314yes—
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—22no—
108C2×C4⋊Q8—42no—
109C2×C4⋊Q8C2314yes—
110C2×C22⋊Q8—22no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8C2314yes—
114C2×C4×Q8—22no—
115C2×C4×Q8—22no—
116C2×C4×Q8—24no—
117C2×C4×Q8—24no—
118C2×C4×Q8—42no—
119C2×C4×Q8—42no—
120C2×C4×Q8C2314yes—
121C2×C4×Q8C2314yes—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4D411yescharacteristic
139C22×C22⋊C4D411yescharacteristic
140C22×C42—21no—
141C22×C42—21no—
142C22×C42—21no—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145#477—232no—
146#452—232no—
147C2×#107—24no—
148C2×#107—24no—
149C2×#107C2314yes—
150C2×#107C2314yes—
151C2×C4⋊C8—24no—
152C2×C4⋊C8C2314yes—
153C2×#103—24no—
154C2×#103—24no—
155C2×#103—42no—
156C2×#103—42no—
157C2×#103D418yes—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#102—24no—
164C2×#102—24no—
165C2×#102—42no—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×C22⋊C8—24no—
170C2×C22⋊C8—42no—
171C2×C22⋊C8C2314yes—
172C2×C22⋊C8C2314yes—
173C2×#97—42no—
174C2×#97C2314yes—
175#400—28no—
176#393—28no—
177#391—22no—
178#391—22no—
179#391—28no—
180#391C2314yes—
181#391C2314yes—
182#390—28no—
183#390—28no—
184#390—22no—
185#390—22no—
186#390C2314yes—
187#390C2314yes—
188#388—28no—
189#380—22no—
190#380—22no—
191#380—28no—
192#380C2314yes—
193#380C2314yes—
194C4×C4⋊C4—22no—
195C4×C4⋊C4C2314yes—
196C4×C22⋊C4—28no—
197C4×C22⋊C4D414yes—
198C4×C22⋊C4C2314yes—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95D411yescharacteristic
207C2×#95D411yescharacteristic
208#340C2314yes—
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#336C2314yes—
213#336C2314yes—
214C25—21no—
215C25C2×D411yescharacteristic
216C2×#41—216no—
217C2×#41—28no—
218C2×#41—28no—
219C2×#41—28no—
220C2×#41—28no—
221C2×#41—44no—
222C2×#41—44no—
223C2×#41—48no—
224C2×#41—48no—
225C2×#41—416no—
226C2×#41—416no—
227C2×#41—416no—
228C2×#41—416no—
229C22×Q8—21no—
230C22×Q8—21no—
231C22×Q8—24no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—44no—
242C22×Q8—44no—
243C22×Q8—82no—
244C22×Q8C2×D414yes—
245C22×Q8#4114yes—
246C22×Q8#4114yes—
247C22×Q8C2412yes—
248C22×Q8C2412yes—
249C22×D4—28no—
250C22×D4—24no—
251C22×D4—22no—
252C22×D4—21no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4#4114yes—
260C22×D4C2412yes—
261C23×C4—21no—
262C23×C4—28no—
263C23×C4—21no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4C2×D412yes—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C2×Q16—28no—
287C2×Q16—28no—
288C2×Q16—28no—
289C2×Q16—416no—
290C2×SD16—28no—
291C2×SD16—28no—
292C2×SD16—44no—
293C2×SD16—416no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8C2×D414yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C4⋊Q8—28no—
311C4⋊Q8—44no—
312C4⋊Q8—48no—
313C22⋊Q8—28no—
314C22⋊Q8—44no—
315C22⋊Q8—48no—
316C4×Q8—28no—
317C4×Q8—28no—
318C4×Q8—44no—
319C4×Q8—44no—
320C4×Q8—48no—
321C4×Q8—48no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2×D414yes—
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—24no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—82no—
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—22no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—44no—
376C2×C42—44no—
377C2×C42—82no—
378C2×C42C2×D412yes—
379C2×C42C2×D412yes—
380C2×C42C2412yes—
381C2×C42C2412yes—
382#107—28no—
383#107—28no—
384C4⋊C8—28no—
385#103—28no—
386#103—28no—
387#103—44no—
388#103—44no—
389#103C2×D4116yes—
390#102—28no—
391#102—28no—
392#102—44no—
393C22⋊C8—28no—
394C22⋊C8—44no—
395#97—44no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95C2×D414yes—
404#95C2×D414yes—
405C24—22no—
406C24—24no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24C22×D412yes—
421C24C22×D411yescharacteristic
422#41—416no—
423#41—416no—
424#41—416no—
425#41—464no—
426#41—416no—
427C2×Q8—24no—
428C2×Q8—28no—
429C2×Q8—24no—
430C2×Q8—24no—
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—48no—
443C2×Q8—48no—
444C2×Q8—42no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—84no—
452C2×Q8—816no—
453C2×Q8#124116yes—
454C2×Q8C22×D414yes—
455C2×Q8C2×#4114yes—
456C2×Q8C2×#4114yes—
457C2×D4—216no—
458C2×D4—24no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—432no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4C2×#4114yes—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—216no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
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—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
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—48no—
510C22×C4—48no—
511C22×C4—432no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
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×C4—42no—
532C22×C4—42no—
533C22×C4#13714yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D412yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4112yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C4C2511yescharacteristic
547Q16—416no—
548SD16—416no—
549C2×C8—28no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—44no—
562C2×C8—44no—
563C2×C8—44no—
564C2×C8C22×D414yes—
565C4⋊C4—24no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4C22×D414yes—
584C22⋊C4—28no—
585C22⋊C4—44no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—84no—
590C22⋊C4—84no—
591C22⋊C4—84no—
592C22⋊C4—84no—
593C42—24no—
594C42—24no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—48no—
600C42—48no—
601C42—84no—
602C23—22no—
603C23—24no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—44no—
611C23—44no—
612C23—48no—
613C23—44no—
614C23—48no—
615C23—42no—
616C23—42no—
617C23—48no—
618C23—44no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23—84no—
630C23#52512yes—
631C23D4212yes—
632C23#54612yes—
633C23C2×#13712yes—
634C23#57512yes—
635C23#57612yes—
636C23#57812yes—
637C23C23×D411yescharacteristic
638Q8—24no—
639Q8—24no—
640Q8—24no—
641Q8—216no—
642Q8—42no—
643Q8—42no—
644Q8—42no—
645Q8—42no—
646Q8—816no—
647Q8—84no—
648Q8C2×#12418yes—
649D4—24no—
650D4—24no—
651D4—432no—
652D4—42no—
653D4—42no—
654D4—48no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—216no—
660C2×C4—28no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—432no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—48no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
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—84no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4—84no—
707C2×C4—84no—
708C2×C4#52512yes—
709C2×C4C2×#12414yes—
710C2×C4#53814yes—
711C2×C4D4212yes—
712C2×C4#54614yes—
713C2×C4#54612yes—
714C2×C4#55114yes—
715C2×C4C2×#13714yes—
716C2×C4C23×D411yescharacteristic
717C2×C4C22×#4111yescharacteristic
718C2×C4C22×#4111yescharacteristic
719C2×C4C22×#4111yescharacteristic
720C2×C4C2×H(5,𝔽2)11yescharacteristic
721C2×C4C2×H(5,𝔽2)11yescharacteristic
722C8—24no—
723C8—42no—
724C8—42no—
725C8—42no—
726C22—44no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—42no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—82no—
737C22—82no—
738C22—88no—
739C22—816no—
740C22—82no—
741C22—82no—
742C22#247214yes—
743C22#311614yes—
744C22#312414yes—
745C22#326814yes—
746C22#327014yes—
747C22#331314yes—
748C22#333314yes—
749C22C2×#52511yescharacteristic
750C22C2×D4211yescharacteristic
751C22C2×#54611yescharacteristic
752C22C22×#13711yescharacteristic
753C22C2×#57511yescharacteristic
754C22C2×#57611yescharacteristic
755C22C2×#57811yescharacteristic
756C4—28no—
757C4—24no—
758C4—42no—
759C4—42no—
760C4—44no—
761C4—42no—
762C4—42no—
763C4—82no—
764C4—82no—
765C4—82no—
766C4—82no—
767C4—82no—
768C4#247214yes—
769C4C22×#12411yescharacteristic
770C4C2×#53811yescharacteristic
771C4C2×#54611yescharacteristic
772C4C2×#55111yescharacteristic
773C2—82no—
774C2—84no—
775C2#2725218yesdirect product factor
776C2C2×#247211yescharacteristic
777C2C2×#311611yescharacteristic
778C2C2×#312411yescharacteristic
779C2C2×#326811yescharacteristic
780C2C2×#327011yescharacteristic
781C2C2×#331311yescharacteristic
782C2C2×#333311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×#41C22
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. C22×#477C2semidirect
3. C2×#2492C2semidirect
5. #27252C2direct (N × H)
6. C2×#2075C2semidirect
7. C2×#2055C2semidirect
8. C2×#2036C2semidirect
9. C2×#2023C2semidirect
10. C2×#1973C2semidirect
11. C2×#1925C2semidirect
12. C2×#1924C2semidirect
13. C2×#1878C2semidirect
14. C2×#1878C2semidirect
16. C2×#1763C2semidirect
25. C2×#477C22semidirect
43. #2492C22semidirect
62. #2075C22semidirect
63. #2055C22semidirect
64. #2036C22semidirect
65. #2023C22semidirect
66. #1973C22semidirect
67. #1925C22semidirect
68. #1924C22semidirect
69. #1878C22semidirect
70. #1878C22semidirect
72. #1763C22semidirect
775. C2#27252direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4772
C22×#4522
C2×#24922
C2×#23412
#272522
C2×#20752
C2×#20552
C2×#20362
C2×#20232
C2×#19732
C2×#19252
C2×#19242
C2×#18782
C2×#17882
C2×#17632