Finite Group Databasebeta

← #6627183

Subgroups — #6627183

Order 512.

3335 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C2×#3361C212yesmaximal, complemented
3#36580C211yesmaximal, characteristic, complemented
4#32908C212yesmaximal, complemented
5#32902C211yesmaximal, characteristic
6#25938C214yesmaximal, complemented
7#25930C212yesmaximal, complemented
8#25907C212yesmaximal, complemented
9#25903C211yesmaximal, characteristic, complemented
10#24335C214yesmaximal, complemented
11#24331C212yesmaximal, complemented
12#24305C212yesmaximal, complemented
13#24302C211yesmaximal, characteristic, complemented
14#22519C212yesmaximal, complemented
15Q8×C22⋊C8C211yesmaximal, characteristic, complemented
16C4×#450C211yesmaximal, characteristic, complemented
17C4×#447C212yesmaximal, complemented
18C2×#559C2211yescharacteristic, complemented
19C2×#554—216no—
20C2×#554—21no—
21C2×#554—21no—
22C2×#554—22no—
23C2×#554C2212yes—
24C2×#554C2214yes—
25C2×#554C2212yes—
26C22×C4⋊Q8C2211yescharacteristic
27C22×#125C2212yes—
28C22×C22⋊Q8—21no—
29C22×C22⋊Q8—22no—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2212yes—
33C23×C4⋊C4—21no—
34#3361—216no—
35C2×#488C2214yescomplemented
36C2×#486C2212yescomplemented
37C2×#477C2212yescomplemented
38C2×#478C2214yescomplemented
39C2×#463C2214yes—
40C2×#459C2212yes—
41C2×#450C2211yescharacteristic
42C2×#447C2212yes—
43C2×C8×Q8C2212yescomplemented
44C2×C4×SD16C2212yes—
45C2×C4×D8C2214yes—
46#2856C2211yescharacteristic
47#2850C2212yes—
48#2592C2212yescomplemented
49#2582C2211yescharacteristic, complemented
50#2580C2212yescomplemented
51#2548C2211yescharacteristic, complemented
52#2458—22no—
53#2448—21no—
54#2443—22no—
55#2436—21no—
56#2367—21no—
57#2361—21no—
58#2355C2211yescharacteristic, complemented
59C4×C22⋊Q8C2211yescharacteristic
60C4×#121C2212yes—
61#2059C2214yescomplemented
62#2057C2212yescomplemented
63#2026C2214yescomplemented
64#2025C2214yescomplemented
65#2025C2214yescomplemented
66#2024C2212yescomplemented
67#2023C2214yescomplemented
68#1991C2214yescomplemented
69#1990C2212yescomplemented
70#1989C2214yescomplemented
71#1987C2212yescomplemented
72#1984C2212yescomplemented
73#1984C2214yescomplemented
74#1879C2214yes—
75#1879C2214yes—
76#1879C2214yes—
77#1877C2214yes—
78#1877C2212yes—
79#1874C2212yes—
80#1874C2212yes—
81#1874C2212yes—
82#1872C2211yescharacteristic
83#1872C2212yes—
84#1864C2212yes—
85#1862C2214yes—
86#1853C2211yescharacteristic
87#1852C2212yes—
88#1804C2214yes—
89#1802C2212yes—
90#1797C2211yescharacteristic
91#1797C2212yes—
92#1786C2211yescharacteristic
93C4×#102C2212yes—
94C4×#102C2214yes—
95C4×C22⋊C8C2211yescharacteristic
96C4×C22⋊C8C2212yes—
97C23×Q8—21no—
98C23×Q8D411yescharacteristic
99C23×D4C2311yescharacteristic
100C24×C4—21no—
101C24×C4—22no—
102C22×SD16C2312yes—
103C22×D8C2314yes—
104#559—28no—
105#554—216no—
106#554—232no—
107#554—216no—
108#554—28no—
109#554—216no—
110#554—28no—
111#554—216no—
112#554—28no—
113#554D4116yescomplemented
114C2×C4⋊Q8—28no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2312yes—
119C2×#127C2311yescharacteristic
120C2×#125—216no—
121C2×#125—22no—
122C2×#125—22no—
123C2×#125C2314yes—
124C2×#125C2314yes—
125C2×#124—21no—
126C2×#124—21no—
127C2×#124C2312yes—
128C2×#123—22no—
129C2×C22⋊Q8—232no—
130C2×C22⋊Q8—216no—
131C2×C22⋊Q8—22no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—22no—
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8—24no—
137C2×C22⋊Q8—24no—
138C2×C22⋊Q8C2311yescharacteristic
139C2×#121—21no—
140C2×#121—21no—
141C2×#121C2312yes—
142C2×C4×Q8—28no—
143C2×C4×Q8D411yescharacteristic
144C2×C4×Q8D411yescharacteristic
145C2×C4×Q8D412yes—
146C2×C4×Q8C2311yescharacteristic
147C2×C4×Q8C2312yes—
148C2×C4×Q8C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×D4—216no—
151C2×C4×D4—28no—
152C2×C4×D4—22no—
153C2×C4×D4—21no—
154C2×C4×D4—22no—
155C2×C4×D4—22no—
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×C4×D4C2312yes—
159C2×C4×D4C2314yes—
160C2×C4×D4C2312yes—
161C2×C4×D4C2312yes—
162C2×C4×D4C2314yes—
163C22×C4⋊C4—216no—
164C22×C4⋊C4—22no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—22no—
167C22×C4⋊C4—24no—
168C22×C4⋊C4—22no—
169C22×C4⋊C4—22no—
170C22×C4⋊C4D411yescharacteristic
171C22×C4⋊C4D412yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C22⋊C4—21no—
175C22×C22⋊C4—22no—
176C22×C42C2312yes—
177C22×C42C2311yescharacteristic
178#488—216no—
179#486—28no—
180#478—216no—
181#477—28no—
182#463—216no—
183#459—28no—
184#450—24no—
185#447—28no—
186C8×Q8—28no—
187C4×SD16—28no—
188C4×D8—216no—
189C2×#107C2314yes—
190C2×#106C2312yes—
191C2×C4⋊C8C2314yes—
192C2×C4⋊C8C2312yes—
193C2×#103C2314yes—
194C2×#103C2312yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×#102C2312yes—
199C2×#102C2314yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×C22⋊C8C2312yes—
203C2×C22⋊C8C2311yescharacteristic
204C2×C22⋊C8C2311yescharacteristic
205C2×C4×C8C2312yes—
206C2×C4×C8C2314yes—
207#399—22no—
208#398—22no—
209#397—22no—
210#394—22no—
211#393—22no—
212#393—22no—
213#391—21no—
214#391—21no—
215#391C2312yes—
216#391C2311yescharacteristic
217#390—21no—
218#390—21no—
219#390—21no—
220#390C2312yes—
221#390C2312yes—
222#390C2312yes—
223#389—21no—
224#389C2311yescharacteristic
225#389C2312yes—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#387—22no—
232#387—21no—
233#386—22no—
234#386—22no—
235#386—22no—
236#385—21no—
237#385—22no—
238#385—22no—
239#384C2311yescharacteristic
240#382C2312yes—
241#380C2311yescharacteristic
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2311yescharacteristic
246C4×C22⋊C4—21no—
247C4×C22⋊C4—22no—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2312yes—
253#340C2314yes—
254#340C2312yes—
255#336C2312yes—
256#336C2314yes—
257#336C2314yes—
258#336C2312yes—
259C25—21no—
260C22×Q8—28no—
261C22×Q8—24no—
262C22×Q8—24no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—42no—
266C22×Q8—82no—
267C22×Q8—82no—
268C22×Q8C2×D411yescharacteristic
269C22×Q8C2×D412yes—
270C22×Q8C2×D411yescharacteristic
271C22×Q8C2411yescharacteristic
272C22×D4—24no—
273C22×D4—24no—
274C22×D4—22no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—22no—
279C22×D4#4114yes—
280C22×D4C2412yes—
281C22×D4C2412yes—
282C23×C4—28no—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4—216no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—22no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—84no—
294C23×C4—84no—
295C23×C4C2×D412yes—
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D412yes—
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C2×SD16—24no—
301C2×SD16—24no—
302C2×SD16—24no—
303C2×D8—28no—
304C2×D8—28no—
305C2×D8—28no—
306C22×C8C2414yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C4⋊Q8—28no—
310C4⋊Q8—28no—
311C4⋊Q8—28no—
312C4⋊Q8—24no—
313C4⋊Q8C2×D418yes—
314#127—24no—
315#125—216no—
316#125—216no—
317#125—28no—
318#125—28no—
319#125—28no—
320#125C2×D4116yes—
321#124—28no—
322#124—44no—
323#124—44no—
324#123—48no—
325C22⋊Q8—216no—
326C22⋊Q8—232no—
327C22⋊Q8—232no—
328C22⋊Q8—232no—
329C22⋊Q8—232no—
330C22⋊Q8—216no—
331C22⋊Q8—232no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334#121—24no—
335#121—24no—
336#121—44no—
337#121—82no—
338C4×Q8—24no—
339C4×Q8—28no—
340C4×Q8—24no—
341C4×Q8—24no—
342C4×Q8—28no—
343C4×Q8—24no—
344C4×Q8C2×D418yes—
345C4×D4—216no—
346C4×D4—216no—
347C4×D4—28no—
348C4×D4—28no—
349C4×D4—28no—
350C4×D4—24no—
351C4×D4—28no—
352C4×D4—24no—
353C4×D4—28no—
354C4×D4—24no—
355C4×D4—28no—
356C4×D4—44no—
357C4×D4—84no—
358C4×D4C2×D4116yes—
359C4×D4C2×D418yes—
360C2×C4⋊C4—216no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—216no—
363C2×C4⋊C4—232no—
364C2×C4⋊C4—216no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—216no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4C2×D412yes—
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D412yes—
387C2×C4⋊C4C2×D412yes—
388C2×C4⋊C4C2×D412yes—
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D412yes—
391C2×C4⋊C4C2411yescharacteristic
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2414yes—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—216no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C42—28no—
416C2×C42—24no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—22no—
420C2×C42C2×D412yes—
421C2×C42C2×D412yes—
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2412yes—
425C2×C42C2411yescharacteristic
426C2×C42C2412yes—
427C2×C42C2411yescharacteristic
428#107—28no—
429#106—24no—
430C4⋊C8—24no—
431C4⋊C8—28no—
432#103—24no—
433#103—28no—
434#102—24no—
435#102—28no—
436#102—24no—
437#102—24no—
438#102—28no—
439#102—28no—
440#102—28no—
441C22⋊C8—24no—
442C22⋊C8—22no—
443C22⋊C8—22no—
444C4×C8—28no—
445C4×C8—24no—
446#95—21no—
447#95—21no—
448#95—22no—
449#95—21no—
450#95—22no—
451#95—21no—
452#95—21no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457C24—24no—
458C24—24no—
459C24—24no—
460C24—22no—
461C24—22no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24C22×D411yescharacteristic
467C2×Q8—28no—
468C2×Q8—24no—
469C2×Q8—22no—
470C2×Q8—28no—
471C2×Q8—22no—
472C2×Q8—24no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—22no—
480C2×Q8—42no—
481C2×Q8—416no—
482C2×Q8—82no—
483C2×Q8—82no—
484C2×Q8—82no—
485C2×Q8—82no—
486C2×Q8—816no—
487C2×Q8#12014yes—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—216no—
491C2×D4—216no—
492C2×D4—24no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—24no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4C22×D414yes—
510C2×D4C2×#4114yes—
511C2×D42−1+414yes—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—216no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—28no—
529C22×C4—216no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—41no—
538C22×C4—44no—
539C22×C4—432no—
540C22×C4—42no—
541C22×C4—44no—
542C22×C4—42no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—84no—
549C22×C4—84no—
550C22×C4—84no—
551C22×C4—84no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—832no—
555C22×C4#13514yes—
556C22×C4C22×D412yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C2×#4112yes—
566C22×C42−1+412yes—
567C22×C4C2511yescharacteristic
568SD16—48no—
569D8—416no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—24no—
578C2×C8—22no—
579C4⋊C4—216no—
580C4⋊C4—28no—
581C4⋊C4—24no—
582C4⋊C4—28no—
583C4⋊C4—216no—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—216no—
587C4⋊C4—28no—
588C4⋊C4—216no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—81no—
604C4⋊C4—82no—
605C4⋊C4—81no—
606C4⋊C4#12014yes—
607C4⋊C4#12018yes—
608C4⋊C4C22×D414yes—
609C4⋊C4C22×D418yes—
610C22⋊C4—216no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—216no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—82no—
624C22⋊C4—82no—
625C22⋊C4—82no—
626C42—24no—
627C42—24no—
628C42—22no—
629C42—22no—
630C42—24no—
631C42—22no—
632C42—42no—
633C42—42no—
634C42—82no—
635C42C22×D418yes—
636C42C22×D414yes—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—216no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—48no—
646C23—48no—
647C23—48no—
648C23—48no—
649C23—48no—
650C23—42no—
651C23—48no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23#54812yes—
663C23C2×#13512yes—
664C23#57612yes—
665C23C23×D411yescharacteristic
666Q8—28no—
667Q8—48no—
668Q8—44no—
669Q8—42no—
670Q8—42no—
671Q8—88no—
672Q8—88no—
673D4—216no—
674D4—24no—
675D4—24no—
676D4—24no—
677D4—44no—
678D4—44no—
679D4—88no—
680D4—84no—
681D4—162no—
682D4#54818yes—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—48no—
708C2×C4—48no—
709C2×C4—44no—
710C2×C4—416no—
711C2×C4—48no—
712C2×C4—416no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—416no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—816no—
734C2×C4—816no—
735C2×C4—164no—
736C2×C4C2×#12014yes—
737C2×C4C2×#12012yes—
738C2×C4C2×#12014yes—
739C2×C4C2×#12012yes—
740C2×C4#54812yes—
741C2×C4C2×#13512yes—
742C2×C4C2×#13512yes—
743C2×C4#57512yes—
744C2×C4C23×D412yes—
745C2×C4C22×#4111yescharacteristic
746C2×C4C2×2−1+412yes—
747C2×C4C2×2−1+411yescharacteristic
748C8—44no—
749C8—42no—
750C8—42no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—28no—
758C22—432no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22#336114yescomplemented
773C22C22×#12011yescharacteristic
774C22C2×#54811yescharacteristic
775C22#348611yescharacteristic
776C22C22×#13511yescharacteristic
777C22C2×#57511yescharacteristic
778C22C2×#57611yescharacteristic
779C22#358511yescharacteristic
780C4—22no—
781C4—24no—
782C4—24no—
783C4—22no—
784C4—22no—
785C4—42no—
786C4—44no—
787C4—42no—
788C4—41no—
789C4—48no—
790C4—82no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4#300214yes—
796C4C2×#54812yes—
797C4#348612yes—
798C2—24no—
799C2—48no—
800C2—162no—
801C2#3657511yescharacteristic
802C2C2×#300211yescharacteristic
803C2#6037211yescharacteristic
804C2C2×#336111yescharacteristic
805C2#6131811yescharacteristic
806C2#6181911yescharacteristic
807C2#6183511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#32902C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#554C2semidirect
2. C2×#3361C2semidirect
3. #36580C2semidirect
4. #32908C2semidirect
6. #25938C2semidirect
7. #25930C2semidirect
8. #25907C2semidirect
9. #25903C2semidirect
10. #24335C2semidirect
11. #24331C2semidirect
12. #24305C2semidirect
13. #24302C2semidirect
14. #22519C2semidirect
15. Q8×C22⋊C8C2semidirect
16. C4×#450C2semidirect
17. C4×#447C2semidirect
18. C2×#559C22semidirect
35. C2×#488C22semidirect
36. C2×#486C22semidirect
37. C2×#477C22semidirect
38. C2×#478C22semidirect
43. C2×C8×Q8C22semidirect
48. #2592C22semidirect
49. #2582C22semidirect
50. #2580C22semidirect
51. #2548C22semidirect
58. #2355C22semidirect
61. #2059C22semidirect
62. #2057C22semidirect
63. #2026C22semidirect
64. #2025C22semidirect
65. #2025C22semidirect
66. #2024C22semidirect
67. #2023C22semidirect
68. #1991C22semidirect
69. #1990C22semidirect
70. #1989C22semidirect
71. #1987C22semidirect
72. #1984C22semidirect
73. #1984C22semidirect
113. #554D4semidirect
772. C22#3361semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#33612
#365802
#329082
#329022
#259382
#259302
#259072
#259032
#243352
#243312
#243052
#243022
#225192
Q8×C22⋊C82
C4×#4502
C4×#4472