Finite Group Databasebeta

← #6765297

Subgroups — #6765297

Order 512.

1663 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36211C211yesmaximal, characteristic
2#36134C211yesmaximal, characteristic, complemented
3#33170C211yesmaximal, characteristic, complemented
4#30710C214yesmaximal, complemented
5#30601C214yesmaximal, complemented
6#30220C211yesmaximal, characteristic, complemented
7#29807C211yesmaximal, characteristic, complemented
8#29176C211yesmaximal, characteristic, complemented
9#28438C211yesmaximal, characteristic, complemented
10#27908C211yesmaximal, characteristic, complemented
11#27892C211yesmaximal, characteristic, complemented
12#27069C214yesmaximal, complemented
13#26941C214yesmaximal, complemented
14#25598C211yesmaximal, characteristic, complemented
15#25598C211yesmaximal, characteristic, complemented
16#22220C211yesmaximal, characteristic, complemented
17#21864C211yesmaximal, characteristic, complemented
18#21400C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#492C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#485C2214yes—
26C2×#465C2214yes—
27C2×#461C2214yes—
28C2×#431C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30#2868C2211yescharacteristic
31#2859C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2856C2211yescharacteristic
35#2856C2211yescharacteristic
36#2552—21no—
37#2542C2212yes—
38#2538—21no—
39#2535—21no—
40#2513—21no—
41#2513C2212yes—
42#2490—21no—
43#2490—21no—
44#2441—21no—
45#2441—21no—
46#2429C2212yes—
47#2429C2212yes—
48#2423—21no—
49#2423—21no—
50#2420—21no—
51#2420C2212yes—
52#2414—21no—
53#2414C2212yes—
54#2365C2212yes—
55#2363—21no—
56#2363C2212yes—
57#2357—21no—
58#2354—21no—
59Q8×C4⋊C4—21no—
60C4×C4⋊Q8C2211yescharacteristic
61C4×#127C2211yescharacteristic
62#2285C2211yescharacteristic
63#2285C2211yescharacteristic
64C42×D4C2211yescharacteristic
65#2097C2214yes—
66#2088C2214yes—
67#2055C2214yes—
68#2043C2214yes—
69#2043C2214yes—
70#2036C2214yes—
71#2013C2214yes—
72#2000C2214yes—
73#2000C2214yes—
74#2000C2214yes—
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1968C2214yes—
79#1957C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1928C2214yes—
87#1925C2214yes—
88#1923C2212yes—
89#1920C2214yes—
90#1916C2212yes—
91#1892C2214yes—
92#1880C2214yes—
93#1880C2214yes—
94#1873C2214yes—
95#1869C2212yes—
96#1862C2214yes—
97#1850C2212yes—
98#1845C2211yescharacteristic
99#1844C2211yescharacteristic
100#1834C2211yescharacteristic
101#1805C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×#103C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C22×SD16C2314yes—
108C22×SD16C2314yes—
109C23×C8C2312yes—
110#533—24no—
111#533—24no—
112#533—42no—
113#533—42no—
114C2×C4⋊Q8C2311yescharacteristic
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2312yes—
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2311yescharacteristic
119C2×#127C2311yescharacteristic
120C2×#125—21no—
121C2×#125—21no—
122C2×#125—21no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8C2312yes—
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2312yes—
128C2×C22⋊Q8C2312yes—
129C2×#121—21no—
130C2×#121—21no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121C2312yes—
134C2×#121C2312yes—
135C2×C4×Q8—21no—
136C2×C4×Q8—21no—
137C2×C4×Q8—21no—
138C2×C4×Q8C2312yes—
139C2×C4×Q8C2312yes—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4D411yescharacteristic
143C2×C4×D4D411yescharacteristic
144C2×C4×D4C2312yes—
145C2×C4×D4C2311yescharacteristic
146C2×#117—21no—
147C2×#117—21no—
148C2×#117—21no—
149C2×#117C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#492—42no—
153#492—42no—
154#486—24no—
155#485—48no—
156#465—48no—
157#461—48no—
158#431—42no—
159C2×#107C2314yes—
160C2×#106C2314yes—
161C2×C4⋊C8C2312yes—
162C2×C4⋊C8C2312yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×C22⋊C8C2312yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C4×C8—42no—
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2312yes—
180#399—22no—
181#399—22no—
182#398—22no—
183#398—22no—
184#397—22no—
185#397—22no—
186#397—22no—
187#396—22no—
188#396—22no—
189#394—22no—
190#394—22no—
191#392—22no—
192#391—21no—
193#391C2312yes—
194#391C2312yes—
195#390—22no—
196#390—22no—
197#390—22no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390C2312yes—
205#390C2312yes—
206#390C2312yes—
207#389—22no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—22no—
216#389—22no—
217#389C2312yes—
218#389C2312yes—
219#389C2312yes—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#387—22no—
227#387—22no—
228#386—22no—
229#386—22no—
230#384—22no—
231#384—21no—
232#384—21no—
233#384—21no—
234#384—21no—
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#382—21no—
240#382—21no—
241#382C2312yes—
242#381—22no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380C2312yes—
251C4×C4⋊C4—22no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4D411yescharacteristic
257C4×C4⋊C4D411yescharacteristic
258C4×C4⋊C4C2312yes—
259C4×C4⋊C4C2312yes—
260C4×C4⋊C4C2311yescharacteristic
261C4×C22⋊C4—22no—
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4C2311yescharacteristic
267C4×C22⋊C4C2311yescharacteristic
268C43C2311yescharacteristic
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C22×Q8—21no—
279C22×Q8C2412yes—
280C22×Q8C2412yes—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4C2×D411yescharacteristic
286C22×D4C2412yes—
287C23×C4—22no—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C2×SD16—28no—
295C2×SD16—44no—
296C2×SD16—44no—
297C2×SD16—44no—
298C2×SD16—44no—
299C2×SD16—44no—
300C22×C8—24no—
301C22×C8—42no—
302C22×C8—42no—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—44no—
313C4⋊Q8—44no—
314C4⋊Q8#4114yes—
315#127—22no—
316#127—22no—
317#125—44no—
318#125—44no—
319#125—82no—
320C22⋊Q8—24no—
321C22⋊Q8—24no—
322C22⋊Q8—42no—
323C22⋊Q8—42no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328#121—44no—
329#121—44no—
330#121—44no—
331#121—82no—
332#121—82no—
333#121—82no—
334C4×Q8—24no—
335C4×Q8—24no—
336C4×Q8—42no—
337C4×Q8—42no—
338C4×Q8—44no—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—42no—
344C4×D4—44no—
345C4×D4—44no—
346C4×D4—82no—
347#117—44no—
348#117—44no—
349#117—44no—
350#117—82no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
401C2×C22⋊C4C2×D411yescharacteristic
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428#107—44no—
429#106—28no—
430C4⋊C8—24no—
431C4⋊C8—42no—
432#103—28no—
433#103—44no—
434#103—44no—
435#103—44no—
436#103—44no—
437#103—44no—
438#102—28no—
439#102—44no—
440C22⋊C8—24no—
441C22⋊C8—42no—
442C22⋊C8—42no—
443C4×C8—22no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—22no—
447C4×C8—42no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95C2×D411yescharacteristic
461#95C2×D411yescharacteristic
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466C24—22no—
467C24C22×D411yescharacteristic
468C24C22×D411yescharacteristic
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—24no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—24no—
486C2×D4—41no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—82no—
496C2×D4—82no—
497C2×D4—82no—
498C2×D4—82no—
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—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—44no—
526C22×C4—82no—
527C22×C4—82no—
528C22×C4#13714yes—
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
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×D411yescharacteristic
541C22×C4C2511yescharacteristic
542SD16—88no—
543SD16—88no—
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—48no—
556C2×C8H(5,𝔽2)14yes—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—41no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—44no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C4⋊C4C2×#4114yes—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—82no—
604C22⋊C4—82no—
605C22⋊C4—82no—
606C22⋊C4—82no—
607C22⋊C4—82no—
608C22⋊C4—82no—
609C22⋊C4—82no—
610C22⋊C4—82no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—22no—
624C42—21no—
625C42—22no—
626C42—44no—
627C42—44no—
628C42—44no—
629C42—82no—
630C42—82no—
631C42#13514yes—
632C42C2×#4112yes—
633C42H(5,𝔽2)12yes—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23C2×#13712yes—
655C23C23×D411yescharacteristic
656Q8—48no—
657Q8—44no—
658Q8—44no—
659Q8—44no—
660Q8—44no—
661D4—44no—
662D4—44no—
663D4—44no—
664D4—84no—
665D4—84no—
666D4—164no—
667D4—164no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—28no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—24no—
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—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
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—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—164no—
725C2×C4#54612yes—
726C2×C4#54612yes—
727C2×C4C2×#13512yes—
728C2×C4C2×#13512yes—
729C2×C4C2×#13512yes—
730C2×C4C2×#13712yes—
731C2×C4C2×#13712yes—
732C2×C4#57712yes—
733C2×C4#57712yes—
734C2×C4C22×#4111yescharacteristic
735C2×C4C2×H(5,𝔽2)12yes—
736C2×C4C2×H(5,𝔽2)11yescharacteristic
737C2×C4#58512yes—
738C8—24no—
739C8—42no—
740C8—42no—
741C8—42no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22#344911yescharacteristic
764C22C2×#54611yescharacteristic
765C22#349811yescharacteristic
766C22C22×#13511yescharacteristic
767C22C22×#13711yescharacteristic
768C22C2×#57711yescharacteristic
769C22C2×#57711yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—44no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4#330314yes—
788C4#332014yes—
789C4#351712yes—
790C4#354212yes—
791C2—42no—
792C2—81no—
793C2—162no—
794C2#3808911yescharacteristic
795C2#6094711yescharacteristic
796C2#6101211yescharacteristic
797C2C2×#330311yescharacteristic
798C2C2×#332011yescharacteristic
799C2#6241411yescharacteristic
800C2#6242211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36211C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36134C2semidirect
3. #33170C2semidirect
4. #30710C2semidirect
5. #30601C2semidirect
6. #30220C2semidirect
7. #29807C2semidirect
8. #29176C2semidirect
9. #28438C2semidirect
10. #27908C2semidirect
11. #27892C2semidirect
12. #27069C2semidirect
13. #26941C2semidirect
14. #25598C2semidirect
15. #25598C2semidirect
16. #22220C2semidirect
17. #21864C2semidirect
18. #21400C2semidirect
19. #21101C2semidirect

Maximal subgroups

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

subgroupindex
#362112
#361342
#331702
#307102
#306012
#302202
#298072
#291762
#284382
#279082
#278922
#270692
#269412
#255982
#222202
#218642
#214002
#211012