Finite Group Databasebeta

← #7631501

Subgroups — #7631501

Order 512.

9996 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#550C211yesmaximal, characteristic, complemented
2C2×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3#36410C218yesmaximal, complemented
4#36101C218yesmaximal, complemented
5#35741C218yesmaximal, complemented
6#35704C218yesmaximal, complemented
7#35554C212yesmaximal, complemented
8#35527C212yesmaximal, complemented
9#35355C218yesmaximal, complemented
10#35272C212yesmaximal, complemented
11#35076C214yesmaximal, complemented
12#34952C212yesmaximal, complemented
13#34736C214yesmaximal, complemented
14#34265C214yesmaximal, complemented
15#34186C211yesmaximal, characteristic, complemented
16C22×H(5,𝔽2)C2211yescharacteristic
17C23×#41C2212yescomplemented
18C2×#550—216no—
19C2×#550C2218yescomplemented
20C2×#550C2218yescomplemented
21C2×#535C2214yes—
22C22×#127C2212yes—
23C22×#127C2211yescharacteristic, complemented
24C2×#525C2218yescomplemented
25C22×#121C2212yescomplemented
26C22×#121C2214yescomplemented
27C4×H(5,𝔽2)—216no—
28C2×#520C2212yes—
29C2×#520C2214yescomplemented
30C2×#518C2214yes—
31C2×#518C2211yescharacteristic
32C2×#518C2214yescomplemented
33C2×C4×#41C2212yes—
34C2×C4×#41C2214yescomplemented
35C22×C4×Q8C2211yescharacteristic, complemented
36C22×C4×D4C2214yes—
37C22×C4×D4C2211yescharacteristic
38C22×C4×D4C2214yescomplemented
39C22×C4×D4C2212yescomplemented
40#2856C2218yescomplemented
41#2854C2218yescomplemented
42#2847C2218yescomplemented
43#2635C22116yescomplemented
44#2619C2218yescomplemented
45#2591C2218yescomplemented
46#2582C2214yescomplemented
47#2581C2214yescomplemented
48#2580C2214yescomplemented
49#2579C2218yescomplemented
50#2548C2214yescomplemented
51#2548C2214yescomplemented
52#2541C2214yescomplemented
53#2541C2214yescomplemented
54#2539C2218yescomplemented
55#2538C2214yescomplemented
56#2487C2214yescomplemented
57#2476C22132yescomplemented
58#2464C22132yescomplemented
59#2456C22132yescomplemented
60#2445C22116yescomplemented
61#2445C22116yescomplemented
62#2433C22116yescomplemented
63#2431C22116yescomplemented
64#2424C22132yescomplemented
65#2414C22116yescomplemented
66#2409C2214yescomplemented
67#2408C2218yescomplemented
68#2408C2218yescomplemented
69#2407C22116yescomplemented
70#2406C2218yescomplemented
71#2405C2218yescomplemented
72#2405C2218yescomplemented
73#2404C2218yescomplemented
74#2403C2218yes—
75#2403C2218yes—
76#2396C2218yescomplemented
77#2388C22116yescomplemented
78#2367C22116yescomplemented
79#2366C22116yescomplemented
80#2363C22116yescomplemented
81#2361C22116yescomplemented
82#2357C2218yescomplemented
83#2354C2218yescomplemented
84#2321C22116yescomplemented
85#2312C2214yescomplemented
86#2309C2212yes—
87#2309C2214yescomplemented
88C4×C22⋊Q8C2218yescomplemented
89C4×#120C22116yescomplemented
90#2297C2214yes—
91#2297C2218yescomplemented
92#2296C2214yescomplemented
93#2285C2212yescomplemented
94#2280C2214yescomplemented
95#2274C2212yescomplemented
96C2×H(5,𝔽2)—216no—
97C2×H(5,𝔽2)—28no—
98C22×#41—216no—
99C22×#41—416no—
100C22×#41C2314yes—
101C22×#41C2318yes—
102C22×#41C2312yes—
103C22×#41C2318yes—
104C23×Q8C2311yescharacteristic
105C23×D4C2312yes—
106C23×D4C2314yes—
107C23×D4C2314yes—
108C23×D4C2311yescharacteristic
109C23×D4C2314yes—
110C23×D4C2312yes—
111C23×D4C2314yes—
112C23×D4C2312yes—
113C24×C4C2314yes—
114C24×C4C2314yes—
115C24×C4C2312yes—
116#550—264no—
117#550—264no—
118#535—232no—
119C2×#127—216no—
120C2×#127—28no—
121C2×#127C2314yes—
122C2×#127C2314yes—
123C2×#127C2318yes—
124C2×#127C23116yes—
125C2×#124C2318yes—
126#525—432no—
127C2×#123C23116yes—
128C2×#123C23116yes—
129C2×C22⋊Q8C2318yes—
130C2×#121—216no—
131C2×#121—232no—
132C2×#121C2318yes—
133C2×#121C2318yes—
134C2×#121C23116yes—
135C2×#121C23132yes—
136C2×#121C23116yes—
137C2×#121C23116yes—
138C2×#120C23116yes—
139C2×#120C23116yes—
140C2×#120C23116yes—
141#520—232no—
142#520—216no—
143#518—28no—
144#518—232no—
145#518—232no—
146C4×#41—232no—
147C4×#41—216no—
148C2×C4×Q8—28no—
149C2×C4×Q8C2314yes—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2312yes—
152C2×C4×Q8C2314yes—
153C2×C4×Q8C2314yes—
154C2×C4×D4—232no—
155C2×C4×D4—232no—
156C2×C4×D4—216no—
157C2×C4×D4D4116yescomplemented
158C2×C4×D4C2318yes—
159C2×C4×D4C2314yes—
160C2×C4×D4C2312yes—
161C2×C4×D4C23116yes—
162C2×C4×D4C2314yes—
163C2×C4×D4C2318yes—
164C2×C4×D4C2314yes—
165C2×C4×D4C2318yes—
166C2×C4×D4C2312yes—
167C2×C4×D4C2314yes—
168C2×C4×D4C2318yes—
169C2×C4×D4C2314yes—
170C2×C4×D4C2318yes—
171C2×C4×D4C23132yes—
172C2×C4×D4C2314yes—
173C2×C4×D4C2314yes—
174C2×#117C2314yes—
175C2×#117C2312yes—
176C2×#117C2314yes—
177C2×#117C2314yes—
178C2×#117C2318yes—
179C2×#117C2318yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2314yes—
182C22×C4⋊C4C2314yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C22⋊C4C2314yes—
186C22×C22⋊C4C2314yes—
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C2318yes—
189C22×C22⋊C4C2312yes—
190C22×C42C2314yes—
191C22×C42C2314yes—
192C22×C42C2312yes—
193C22×C42C2311yescharacteristic
194#400C2318yes—
195#399C2318yes—
196#398C23116yes—
197#396C23116yes—
198#395C2318yes—
199#394C23116yes—
200#394C23116yes—
201#394C23132yes—
202#394C23132yes—
203#393C2318yes—
204#392C23116yes—
205#392C23116yes—
206#392C23132yes—
207#392C23132yes—
208#391C2318yes—
209#391C2318yes—
210#390C23116yes—
211#390C23116yes—
212#390C2318yes—
213#390C2318yes—
214#390C23132yes—
215#390C2318yes—
216#390C23116yes—
217#390C23116yes—
218#389C2318yes—
219#389C2318yes—
220#389C2318yes—
221#388C23132yes—
222#388C23132yes—
223#388C23132yes—
224#387C23116yes—
225#386C2318yes—
226#386C23132yes—
227#386C2318yes—
228#386C23116yes—
229#386C23116yes—
230#386C23132yes—
231#386C23116yes—
232#386C23116yes—
233#385C2318yes—
234#385C23116yes—
235#385C2318yes—
236#385C23132yes—
237#384C2314yes—
238#382C2314yes—
239#381C2318yes—
240#380C2314yes—
241#380C2318yes—
242#380C2318yes—
243#380C2314yes—
244#379C2318yes—
245#379C23116yes—
246C4×C4⋊C4C2314yes—
247C4×C4⋊C4C23116yes—
248C4×C4⋊C4C2314yes—
249C4×C4⋊C4C23116yes—
250C4×C22⋊C4C2318yes—
251C4×C22⋊C4C2318yes—
252C4×C22⋊C4C23116yes—
253C4×C22⋊C4C23132yes—
254C25C2414yes—
255C25C2414yes—
256C25C2412yes—
257H(5,𝔽2)—2128no—
258C2×#41—216no—
259C2×#41—232no—
260C2×#41—216no—
261C2×#41—28no—
262C2×#41—232no—
263C2×#41—232no—
264C2×#41—28no—
265C2×#41—216no—
266C2×#41—416no—
267C2×#41—432no—
268C2×#41—4128no—
269C2×#41#41116yescomplemented
270C22×Q8—28no—
271C22×Q8—24no—
272C22×Q8C2412yes—
273C22×Q8C2412yes—
274C22×Q8C2412yes—
275C22×D4—216no—
276C22×D4—216no—
277C22×D4—232no—
278C22×D4—216no—
279C22×D4—216no—
280C22×D4—216no—
281C22×D4—28no—
282C22×D4—28no—
283C22×D4—28no—
284C22×D4—28no—
285C22×D4—216no—
286C22×D4—216no—
287C22×D4—416no—
288C22×D4—48no—
289C22×D4—88no—
290C22×D4—84no—
291C22×D4C2×D418yes—
292C22×D4C2418yes—
293C22×D4C2418yes—
294C22×D4C2414yes—
295C22×D4C24116yes—
296C22×D4C2414yes—
297C22×D4C2414yes—
298C22×D4C2412yes—
299C22×D4C24132yes—
300C22×D4C24116yes—
301C22×D4C2418yes—
302C22×D4C2414yes—
303C23×C4—216no—
304C23×C4—216no—
305C23×C4—48no—
306C23×C4—416no—
307C23×C4—416no—
308C23×C4C2×D4116yes—
309C23×C4C2414yes—
310C23×C4C2412yes—
311C23×C4C2414yes—
312C23×C4C24116yes—
313C23×C4C2411yescharacteristic
314C23×C4C2414yes—
315C23×C4C2414yes—
316C23×C4C2412yes—
317C23×C4C2414yes—
318C23×C4C2414yes—
319C23×C4C2418yes—
320C23×C4C2414yes—
321C23×C4C2412yes—
322C23×C4C2411yescharacteristic
323C23×C4C2414yes—
324C23×C4C2411yescharacteristic
325#127—264no—
326#127—232no—
327#127—216no—
328#127—216no—
329#124—232no—
330#123—432no—
331#123—816no—
332C22⋊Q8—232no—
333#121—232no—
334#121—232no—
335#121—264no—
336#121—2128no—
337#121—432no—
338#121—816no—
339#120—264no—
340#120—432no—
341#120—816no—
342C4×Q8—216no—
343C4×Q8—216no—
344C4×Q8—216no—
345C4×Q8—28no—
346C4×Q8—28no—
347C4×D4—216no—
348C4×D4—216no—
349C4×D4—232no—
350C4×D4—216no—
351C4×D4—232no—
352C4×D4—232no—
353C4×D4—216no—
354C4×D4—216no—
355C4×D4—264no—
356C4×D4—232no—
357C4×D4—232no—
358C4×D4—28no—
359C4×D4—28no—
360C4×D4—464no—
361C4×D4C2×D4132yes—
362C4×D4C2×D4132yes—
363#117—28no—
364#117—216no—
365#117—216no—
366#117—232no—
367#117—216no—
368#117—416no—
369C2×C4⋊C4—216no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—216no—
373C2×C4⋊C4C2×D418yes—
374C2×C4⋊C4C2418yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2414yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2418yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2414yes—
382C2×C4⋊C4C2418yes—
383C2×C4⋊C4C2418yes—
384C2×C4⋊C4C24116yes—
385C2×C4⋊C4C2418yes—
386C2×C4⋊C4C24116yes—
387C2×C4⋊C4C2414yes—
388C2×C22⋊C4—216no—
389C2×C22⋊C4—216no—
390C2×C22⋊C4—216no—
391C2×C22⋊C4—232no—
392C2×C22⋊C4C2×D4116yes—
393C2×C22⋊C4C2414yes—
394C2×C22⋊C4C2418yes—
395C2×C22⋊C4C2414yes—
396C2×C22⋊C4C2414yes—
397C2×C22⋊C4C2418yes—
398C2×C22⋊C4C24116yes—
399C2×C22⋊C4C2418yes—
400C2×C22⋊C4C24116yes—
401C2×C22⋊C4C24132yes—
402C2×C22⋊C4C24116yes—
403C2×C22⋊C4C24132yes—
404C2×C22⋊C4C24116yes—
405C2×C22⋊C4C24116yes—
406C2×C22⋊C4C24132yes—
407C2×C22⋊C4C2418yes—
408C2×C42—28no—
409C2×C42—216no—
410C2×C42—216no—
411C2×C42C2×D418yes—
412C2×C42C2418yes—
413C2×C42C2414yes—
414C2×C42C2414yes—
415C2×C42C2418yes—
416C2×C42C2414yes—
417C2×C42C2418yes—
418C2×C42C24116yes—
419C2×C42C2412yes—
420C2×C42C2412yes—
421#95C24116yes—
422#95C2418yes—
423#95C24116yes—
424#95C24116yes—
425#95C24116yes—
426#95C2418yes—
427#95C24116yes—
428C24—28no—
429C24—216no—
430C24—28no—
431C24—28no—
432C24—216no—
433C24—44no—
434C24—48no—
435C24—44no—
436C24—48no—
437C24—48no—
438C24—48no—
439C24C22×D418yes—
440C24C2518yes—
441C24C2514yes—
442C24C2514yes—
443C24C2511yescharacteristic
444#41—2128no—
445#41—264no—
446#41—4128no—
447#41—4128no—
448C2×Q8—232no—
449C2×Q8—24no—
450C2×Q8—24no—
451C2×Q8—24no—
452C2×Q8—24no—
453C2×Q8—28no—
454C2×Q8—24no—
455C2×Q8C2×#4118yescomplemented
456C2×Q8H(5,𝔽2)18yescomplemented
457C2×D4—2128no—
458C2×D4—2128no—
459C2×D4—216no—
460C2×D4—28no—
461C2×D4—216no—
462C2×D4—28no—
463C2×D4—232no—
464C2×D4—232no—
465C2×D4—264no—
466C2×D4—232no—
467C2×D4—24no—
468C2×D4—216no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—216no—
472C2×D4—216no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—24no—
476C2×D4—216no—
477C2×D4—216no—
478C2×D4—232no—
479C2×D4—216no—
480C2×D4—416no—
481C2×D4—48no—
482C2×D4—464no—
483C2×D4—432no—
484C2×D4—432no—
485C2×D4—432no—
486C2×D4—416no—
487C2×D4—416no—
488C2×D4—416no—
489C2×D4—432no—
490C2×D4—816no—
491C2×D4—832no—
492C2×D4C22×D4116yes—
493C2×D4C2×#41116yes—
494C2×D4C2×#4118yescomplemented
495C22×C4—28no—
496C22×C4—24no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—28no—
500C22×C4—216no—
501C22×C4—28no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—232no—
508C22×C4—232no—
509C22×C4—216no—
510C22×C4—28no—
511C22×C4—216no—
512C22×C4—432no—
513C22×C4—44no—
514C22×C4—48no—
515C22×C4—416no—
516C22×C4—42no—
517C22×C4—44no—
518C22×C4—416no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—464no—
523C22×C4—832no—
524C22×C4C22×D4116yes—
525C22×C4C22×D414yes—
526C22×C4C22×D414yes—
527C22×C4C22×D418yes—
528C22×C4C22×D4116yes—
529C22×C4C22×D414yes—
530C22×C4C2×#4118yes—
531C22×C4C2×#41116yescomplemented
532C22×C4C25116yes—
533C22×C4C2514yes—
534C22×C4C2514yes—
535C22×C4C2514yes—
536C22×C4C2511yescharacteristic
537C22×C4C2514yes—
538C22×C4C2512yes—
539C22×C4C2514yes—
540C22×C4C2514yes—
541C22×C4C2512yes—
542C22×C4C2511yescharacteristic
543C4⋊C4—216no—
544C4⋊C4—28no—
545C4⋊C4—24no—
546C4⋊C4—216no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—28no—
550C4⋊C4—24no—
551C4⋊C4—216no—
552C4⋊C4—216no—
553C4⋊C4—232no—
554C4⋊C4—48no—
555C4⋊C4—416no—
556C4⋊C4C22×D4116yes—
557C22⋊C4—216no—
558C22⋊C4—28no—
559C22⋊C4—216no—
560C22⋊C4—216no—
561C22⋊C4—28no—
562C22⋊C4—28no—
563C22⋊C4—232no—
564C22⋊C4—264no—
565C22⋊C4—232no—
566C22⋊C4—416no—
567C22⋊C4—432no—
568C22⋊C4—416no—
569C22⋊C4—416no—
570C22⋊C4—432no—
571C22⋊C4C22×D4132yes—
572C42—28no—
573C42—216no—
574C42—28no—
575C42—28no—
576C42—216no—
577C42—216no—
578C42—416no—
579C42C22×D418yes—
580C42C22×D418yes—
581C23—22no—
582C23—22no—
583C23—232no—
584C23—24no—
585C23—28no—
586C23—24no—
587C23—28no—
588C23—28no—
589C23—28no—
590C23—28no—
591C23—216no—
592C23—28no—
593C23—216no—
594C23—216no—
595C23—216no—
596C23—48no—
597C23—48no—
598C23—416no—
599C23—416no—
600C23—416no—
601C23—88no—
602C23—816no—
603C23—832no—
604C23—832no—
605C23—88no—
606C23C23×D418yes—
607C23C23×D412yes—
608C23C22×#4118yes—
609C23C22×#4114yes—
610C23C2611yescharacteristic
611Q8—216no—
612Q8—216no—
613Q8—216no—
614D4—264no—
615D4—232no—
616D4—232no—
617D4—216no—
618D4—464no—
619D4—416no—
620D4—432no—
621D4—416no—
622D4—816no—
623D4—864no—
624D4—832no—
625C2×C4—216no—
626C2×C4—232no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—28no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—232no—
635C2×C4—28no—
636C2×C4—232no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—216no—
641C2×C4—216no—
642C2×C4—28no—
643C2×C4—216no—
644C2×C4—28no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—48no—
648C2×C4—416no—
649C2×C4—44no—
650C2×C4—464no—
651C2×C4—48no—
652C2×C4—416no—
653C2×C4—88no—
654C2×C4—816no—
655C2×C4—88no—
656C2×C4—88no—
657C2×C4#525116yescomplemented
658C2×C4C23×D414yes—
659C2×C4C23×D418yes—
660C2×C4C23×D412yes—
661C2×C4C23×D414yes—
662C2×C4C23×D412yes—
663C2×C4C22×#4118yes—
664C2×C4C22×#4114yes—
665C2×C4C22×#4114yes—
666C2×C4C2×H(5,𝔽2)18yes—
667C2×C4C2×H(5,𝔽2)14yes—
668C22—28no—
669C22—22no—
670C22—22no—
671C22—216no—
672C22—28no—
673C22—28no—
674C22—28no—
675C22—28no—
676C22—48no—
677C22—416no—
678C22—44no—
679C22—44no—
680C22—432no—
681C22—48no—
682C22—48no—
683C22—48no—
684C22—816no—
685C22—832no—
686C22—832no—
687C22C2×#52514yes—
688C22C24×D411yescharacteristic
689C22C23×#4112yes—
690C22C22×H(5,𝔽2)12yes—
691C22H(7,𝔽2)12yes—
692C4—28no—
693C4—22no—
694C4—28no—
695C4—24no—
696C4—28no—
697C4—416no—
698C4—44no—
699C4—44no—
700C4—44no—
701C4C2×#52518yes—
702C4#348414yes—
703C2—24no—
704C2—48no—
705C2—48no—
706C2—88no—
707C2C22×#52511yescharacteristic
708C2C2×#348411yescharacteristic
709C2#6285211yescharacteristic
710C2#6298614yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#550C2semidirect
2. C2×C4×H(5,𝔽2)C2semidirect
3. #36410C2semidirect
4. #36101C2semidirect
5. #35741C2semidirect
6. #35704C2semidirect
7. #35554C2semidirect
8. #35527C2semidirect
9. #35355C2semidirect
10. #35272C2semidirect
11. #35076C2semidirect
12. #34952C2semidirect
13. #34736C2semidirect
14. #34265C2semidirect
15. #34186C2semidirect
17. C23×#41C22semidirect
19. C2×#550C22semidirect
20. C2×#550C22semidirect
23. C22×#127C22semidirect
24. C2×#525C22semidirect
25. C22×#121C22semidirect
26. C22×#121C22semidirect
29. C2×#520C22semidirect
32. C2×#518C22semidirect
34. C2×C4×#41C22semidirect
35. C22×C4×Q8C22semidirect
38. C22×C4×D4C22semidirect
39. C22×C4×D4C22semidirect
40. #2856C22semidirect
41. #2854C22semidirect
42. #2847C22semidirect
43. #2635C22semidirect
44. #2619C22semidirect
45. #2591C22semidirect
46. #2582C22semidirect
47. #2581C22semidirect
48. #2580C22semidirect
49. #2579C22semidirect
50. #2548C22semidirect
51. #2548C22semidirect
52. #2541C22semidirect
53. #2541C22semidirect
54. #2539C22semidirect
55. #2538C22semidirect
56. #2487C22semidirect
57. #2476C22semidirect
58. #2464C22semidirect
59. #2456C22semidirect
60. #2445C22semidirect
61. #2445C22semidirect
62. #2433C22semidirect
63. #2431C22semidirect
64. #2424C22semidirect
65. #2414C22semidirect
66. #2409C22semidirect
67. #2408C22semidirect
68. #2408C22semidirect
69. #2407C22semidirect
70. #2406C22semidirect
71. #2405C22semidirect
72. #2405C22semidirect
73. #2404C22semidirect
76. #2396C22semidirect
77. #2388C22semidirect
78. #2367C22semidirect
79. #2366C22semidirect
80. #2363C22semidirect
81. #2361C22semidirect
82. #2357C22semidirect
83. #2354C22semidirect
84. #2321C22semidirect
85. #2312C22semidirect
87. #2309C22semidirect
88. C4×C22⋊Q8C22semidirect
89. C4×#120C22semidirect
91. #2297C22semidirect
92. #2296C22semidirect
93. #2285C22semidirect
94. #2280C22semidirect
95. #2274C22semidirect
157. C2×C4×D4D4semidirect
269. C2×#41#41semidirect
455. C2×Q8C2×#41semidirect
456. C2×Q8H(5,𝔽2)semidirect
494. C2×D4C2×#41semidirect
531. C22×C4C2×#41semidirect
657. C2×C4#525semidirect

Maximal subgroups

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

subgroupindex
C22×#5502
C2×C4×H(5,𝔽2)2
#364102
#361012
#357412
#357042
#355542
#355272
#353552
#352722
#350762
#349522
#347362
#342652
#341862