Finite Group Databasebeta

← #6484762

Subgroups — #6484762

Order 512.

1830 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3231C211yesmaximal, characteristic, complemented
2C2×#3228C211yesmaximal, characteristic
3#35298C211yesmaximal, characteristic
4#34214C211yesmaximal, characteristic, complemented
5#33115C214yesmaximal, complemented
6#29769C214yesmaximal, complemented
7#28750C211yesmaximal, characteristic, complemented
8#28750C211yesmaximal, characteristic, complemented
9#28689C211yesmaximal, characteristic, complemented
10#28687C211yesmaximal, characteristic, complemented
11#28656C211yesmaximal, characteristic, complemented
12#28655C211yesmaximal, characteristic, complemented
13#28654C211yesmaximal, characteristic, complemented
14#28653C211yesmaximal, characteristic, complemented
15#28293C214yesmaximal, complemented
16#28215C214yesmaximal, complemented
17#21860C211yesmaximal, characteristic, complemented
18#21859C211yesmaximal, characteristic
19#20809C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23#3231—28no—
24#3228—28no—
25C2×#500C2211yescharacteristic
26C2×#500C2211yescharacteristic
27C2×#498C2211yescharacteristic
28C2×#498C2211yescharacteristic
29C2×#487C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#486C2211yescharacteristic
32C2×#486C2211yescharacteristic
33C2×#485C2214yes—
34C2×#482C2214yes—
35C2×#479C2214yes—
36C2×#478C2214yes—
37C2×#431C2211yescharacteristic
38C2×#431C2211yescharacteristic
39#2868C2211yescharacteristic
40#2862C2211yescharacteristic
41#2858C2211yescharacteristic
42#2858C2211yescharacteristic
43#2620C2212yes—
44#2620C2212yes—
45#2566—21no—
46#2566—21no—
47#2545—21no—
48#2545—21no—
49#2500—21no—
50#2500—21no—
51#2432—21no—
52#2432—21no—
53#2360—21no—
54#2360—21no—
55#2360—21no—
56#2360—21no—
57#2355—21no—
58#2355—21no—
59Q8×C4⋊C4—21no—
60Q8×C4⋊C4—21no—
61#2330C2212yes—
62#2330C2212yes—
63#2326C2212yes—
64#2326C2212yes—
65#2317C2212yes—
66C4×C4⋊Q8C2211yescharacteristic
67C4×C4⋊Q8C2211yescharacteristic
68C4×C4⋊Q8C2211yescharacteristic
69C4×C4⋊Q8C2211yescharacteristic
70C2×#384C2211yescharacteristic
71#2274C2212yes—
72C4×#117C2211yescharacteristic
73#2084C2214yes—
74#2083C2214yes—
75#2068C2214yes—
76#2067C2214yes—
77#2066C2214yes—
78#2065C2214yes—
79#2042C2214yes—
80#2042C2214yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1983C2214yes—
86#1983C2214yes—
87#1957C2211yescharacteristic
88#1957C2211yescharacteristic
89#1956C2211yescharacteristic
90#1956C2211yescharacteristic
91#1948C2214yes—
92#1947C2214yes—
93#1928C2214yes—
94#1927C2214yes—
95#1926C2214yes—
96#1925C2214yes—
97#1874C2214yes—
98#1872C2214yes—
99#1843C2212yes—
100#1832C2212yes—
101#1803C2214yes—
102#1802C2214yes—
103#1798C2212yes—
104#1798C2212yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C4⋊C8C2211yescharacteristic
107C4×C4⋊C8C2211yescharacteristic
108C4×C4⋊C8C2211yescharacteristic
109C22×#41—21no—
110#533—24no—
111#533—24no—
112#533—24no—
113#533D418yes—
114#532—24no—
115#532—24no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×#127C2311yescharacteristic
124C2×#125—21no—
125C2×#125C2312yes—
126C2×#124—21no—
127C2×#124—21no—
128C2×#124—21no—
129C2×#124C2312yes—
130C2×#124C2312yes—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8C2312yes—
135C2×#121—21no—
136C2×#121C2312yes—
137C2×C4×Q8—21no—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8C2312yes—
145C2×C4×D4—21no—
146C2×C4×D4C2312yes—
147C2×#117—21no—
148C2×#117C2312yes—
149C2×#117C2311yescharacteristic
150C2×#117C2311yescharacteristic
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4C2312yes—
154C22×C42C2311yescharacteristic
155#500—24no—
156#500—24no—
157#498—24no—
158#498—24no—
159#487—24no—
160#487—24no—
161#486—24no—
162#486—24no—
163#485—216no—
164#482—216no—
165#479—216no—
166#478—216no—
167#431—24no—
168#431—24no—
169C2×#107C2314yes—
170C2×#107C2314yes—
171C2×#106C2314yes—
172C2×#106C2314yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2311yescharacteristic
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193#396—22no—
194#396—22no—
195#396—22no—
196#396—22no—
197#394—22no—
198#394—22no—
199#394—22no—
200#394—22no—
201#391—21no—
202#391—21no—
203#391—21no—
204#391—21no—
205#391—21no—
206#391—21no—
207#391C2312yes—
208#391C2312yes—
209#390—21no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390C2312yes—
216#390C2312yes—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—22no—
222#389—22no—
223#389—22no—
224#389—22no—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#387—22no—
234#387—22no—
235#387—22no—
236#387—22no—
237#385—22no—
238#385—22no—
239#385—22no—
240#385—22no—
241#385—22no—
242#385—22no—
243#384—22no—
244#384—21no—
245#384—21no—
246#384—21no—
247#384—21no—
248#384C2311yescharacteristic
249#384C2311yescharacteristic
250#384C2312yes—
251#384C2312yes—
252#384C2312yes—
253#382—22no—
254#382—21no—
255#382—21no—
256C4×C4⋊C4—22no—
257C4×C4⋊C4—22no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4D411yescharacteristic
263C4×C4⋊C4D411yescharacteristic
264C4×C4⋊C4D411yescharacteristic
265C4×C4⋊C4D411yescharacteristic
266C4×C4⋊C4C2312yes—
267C4×C4⋊C4C2312yes—
268C4×C4⋊C4C2312yes—
269C4×C4⋊C4C2312yes—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272C4×C22⋊C4D411yescharacteristic
273C4×C22⋊C4D411yescharacteristic
274C4×C22⋊C4D411yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276#376C2311yescharacteristic
277#376C2311yescharacteristic
278C43C2311yescharacteristic
279C43C2311yescharacteristic
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#336C2312yes—
285#336C2312yes—
286#336C2312yes—
287#336C2312yes—
288C2×#41—44no—
289C2×#41—82no—
290C2×#41—82no—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8C2412yes—
296C22×D4—22no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4C2412yes—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2411yescharacteristic
305C22×C8C2412yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—82no—
318C4⋊Q8—82no—
319C4⋊Q8C2×D414yes—
320C4⋊Q8C2×D414yes—
321#127—22no—
322#127—22no—
323#125—24no—
324#125—44no—
325#125C2×D418yes—
326#124—28no—
327#124—44no—
328#124—44no—
329#124—82no—
330#124—82no—
331C22⋊Q8—28no—
332C22⋊Q8—28no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—44no—
336#121—24no—
337#121—24no—
338#121—44no—
339C4×Q8—28no—
340C4×Q8—28no—
341C4×Q8—24no—
342C4×Q8—24no—
343C4×Q8—44no—
344C4×Q8—82no—
345C4×Q8—82no—
346C4×Q8—82no—
347C4×Q8—82no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—44no—
351#117—24no—
352#117—24no—
353#117—42no—
354#117—44no—
355#117C2×D418yes—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—82no—
383C2×C4⋊C4—82no—
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D414yes—
427C2×C42#4114yes—
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434#107—28no—
435#107—28no—
436#106—28no—
437#106—28no—
438C4⋊C8—24no—
439C4⋊C8—24no—
440C4⋊C8—24no—
441C4⋊C8—24no—
442C4⋊C8—42no—
443C4⋊C8—42no—
444#103—28no—
445#103—28no—
446#103—44no—
447#103—44no—
448#102—28no—
449#102—28no—
450#102—44no—
451#102—44no—
452C22⋊C8—24no—
453C22⋊C8—24no—
454C4×C8—22no—
455C4×C8—22no—
456C4×C8—22no—
457C4×C8—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472#95C2×D411yescharacteristic
473#95C2×D411yescharacteristic
474#95C2×D411yescharacteristic
475#95C2×D411yescharacteristic
476#95C2×D411yescharacteristic
477#95C2×D411yescharacteristic
478C24—22no—
479C24C22×D411yescharacteristic
480#41—816no—
481C2×Q8—24no—
482C2×Q8—24no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—24no—
486C2×Q8—24no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—44no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—82no—
509C2×D4—82no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—82no—
526C22×C4—82no—
527C22×C4—82no—
528C22×C4—82no—
529C22×C4#12114yes—
530C22×C4#12114yes—
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D412yes—
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C2×#4112yes—
546C22×C4C2511yescharacteristic
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—22no—
557C2×C8—22no—
558C2×C8—22no—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—44no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C4⋊C4—82no—
592C4⋊C4—82no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C4⋊C4—82no—
596C4⋊C4C22×D414yes—
597C4⋊C4C22×D414yes—
598C22⋊C4—28no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—82no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—82no—
614C42—28no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—44no—
627C42—82no—
628C42—82no—
629C42—82no—
630C42—82no—
631C42#12114yes—
632C42#12114yes—
633C42C22×D412yes—
634C42C22×D412yes—
635C42C2×#4112yes—
636C42C2×#4112yes—
637C422−1+414yes—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23C2×#12112yes—
652C23C23×D411yescharacteristic
653Q8—48no—
654Q8—48no—
655Q8—44no—
656Q8—44no—
657Q8—84no—
658Q8—84no—
659D4—44no—
660D4—44no—
661D4—88no—
662D4—84no—
663D4—84no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
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—42no—
716C2×C4—42no—
717C2×C4—88no—
718C2×C4—164no—
719C2×C4C2×#12112yes—
720C2×C4C2×#12112yes—
721C2×C4C2×#12112yes—
722C2×C4C2×#12112yes—
723C2×C4C2×#12112yes—
724C2×C4#53612yes—
725C2×C4#53612yes—
726C2×C4#57612yes—
727C2×C4#57712yes—
728C2×C4#57712yes—
729C2×C4#57812yes—
730C2×C4C23×D411yescharacteristic
731C2×C4C22×#4111yescharacteristic
732C2×C4C2×2−1+412yes—
733C2×C4#58512yes—
734C8—42no—
735C8—42no—
736C8—42no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22C22×#12111yescharacteristic
753C22C2×#53611yescharacteristic
754C22#344911yescharacteristic
755C22C2×#57611yescharacteristic
756C22C2×#57711yescharacteristic
757C22C2×#57711yescharacteristic
758C22C2×#57811yescharacteristic
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—44no—
765C4—44no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4—82no—
776C4—82no—
777C4#304514yes—
778C4#304614yes—
779C4#349712yes—
780C4#350712yes—
781C2—42no—
782C2—162no—
783C2#3517811yescharacteristic
784C2C2×#304511yescharacteristic
785C2C2×#304611yescharacteristic
786C2#6088011yescharacteristic
787C2#6088111yescharacteristic
788C2#6100611yescharacteristic
789C2#6100811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3231C2semidirect
4. #34214C2semidirect
5. #33115C2semidirect
6. #29769C2semidirect
7. #28750C2semidirect
8. #28750C2semidirect
9. #28689C2semidirect
10. #28687C2semidirect
11. #28656C2semidirect
12. #28655C2semidirect
13. #28654C2semidirect
14. #28653C2semidirect
15. #28293C2semidirect
16. #28215C2semidirect
17. #21860C2semidirect
19. #20809C2semidirect

Maximal subgroups

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

subgroupindex
C2×#32312
C2×#32282
#352982
#342142
#331152
#297692
#287502
#286892
#286872
#286562
#286552
#286542
#286532
#282932
#282152
#218602
#218592
#208092