Finite Group Databasebeta

← #6480599

Subgroups — #6480599

Order 512.

1762 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35291C211yesmaximal, characteristic, complemented
2#35285C211yesmaximal, characteristic
3#33286C211yesmaximal, characteristic, complemented
4#33277C211yesmaximal, characteristic, complemented
5#33252C211yesmaximal, characteristic, complemented
6#33239C211yesmaximal, characteristic, complemented
7#30353C214yesmaximal, complemented
8#29569C214yesmaximal, complemented
9#28655C211yesmaximal, characteristic, complemented
10#28654C211yesmaximal, characteristic, complemented
11#28614C211yesmaximal, characteristic, complemented
12#28614C211yesmaximal, characteristic, complemented
13#25904C211yesmaximal, characteristic, complemented
14#25855C211yesmaximal, characteristic
15#25812C211yesmaximal, characteristic, complemented
16#25717C211yesmaximal, characteristic
17#24516C214yesmaximal, complemented
18#22052C214yesmaximal, complemented
19C4×#433C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C2×#500C2211yescharacteristic, complemented
23C2×#498C2211yescharacteristic, complemented
24C2×#492C2211yescharacteristic
25C2×#492C2211yescharacteristic
26C2×#487C2211yescharacteristic, complemented
27C2×#487C2211yescharacteristic, complemented
28C2×#486C2211yescharacteristic
29C2×#486C2211yescharacteristic
30C2×#450C2214yes—
31C2×#433C2212yes—
32#2862C2211yescharacteristic, complemented
33#2859C2211yescharacteristic, complemented
34#2858C2211yescharacteristic
35#2858C2211yescharacteristic
36#2858C2211yescharacteristic
37#2858C2211yescharacteristic
38#2857C2211yescharacteristic
39#2857C2211yescharacteristic
40#2645C2212yescomplemented
41#2641C2212yes—
42#2641C2212yes—
43#2625C2212yes—
44#2548—21no—
45#2548—21no—
46#2548—21no—
47#2548—21no—
48#2514—21no—
49#2509—21no—
50#2508—21no—
51#2495—21no—
52#2494—21no—
53#2489—21no—
54#2453—21no—
55#2435—21no—
56#2435—21no—
57#2435—21no—
58#2435—21no—
59#2421—21no—
60#2323C2212yes—
61#2320C2212yescomplemented
62#2309C2212yes—
63#2309C2212yes—
64C4×C4⋊Q8C2211yescharacteristic, complemented
65C4×C4⋊Q8C2211yescharacteristic, complemented
66C4×#117C2211yescharacteristic
67#2067C2214yescomplemented
68#2065C2214yescomplemented
69#2059C2214yescomplemented
70#2055C2214yescomplemented
71#2055C2214yescomplemented
72#2041C2214yes—
73#2026C2214yescomplemented
74#2014C2214yes—
75#1990C2211yescharacteristic, complemented
76#1990C2211yescharacteristic, complemented
77#1990C2211yescharacteristic, complemented
78#1990C2211yescharacteristic, complemented
79#1973C2214yescomplemented
80#1973C2214yescomplemented
81#1968C2214yescomplemented
82#1968C2214yescomplemented
83#1957C2211yescharacteristic
84#1957C2211yescharacteristic
85#1957C2211yescharacteristic
86#1957C2211yescharacteristic
87#1936C2214yescomplemented
88#1936C2214yescomplemented
89#1934C2214yescomplemented
90#1934C2214yescomplemented
91#1926C2214yescomplemented
92#1925C2214yescomplemented
93#1880C2214yescomplemented
94#1880C2214yescomplemented
95#1873C2214yes—
96#1854C2214yes—
97#1786C2214yes—
98#1768C2212yescomplemented
99C4×C4⋊C8C2211yescharacteristic, complemented
100C4×C4⋊C8C2211yescharacteristic, complemented
101#1750C2212yes—
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104#1746C2212yescomplemented
105C4×#97C2211yescharacteristic, complemented
106C42×C8C2211yescharacteristic, complemented
107C23×D4—21no—
108C23×D4—21no—
109C23×D4C2312yes—
110C22×SD16C2314yes—
111C22×SD16C2314yes—
112#533—42no—
113#533—42no—
114C2×C4⋊Q8C2311yescharacteristic
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×#127—21no—
119C2×#127—21no—
120C2×#127—42no—
121C2×#127—42no—
122C2×#127C2311yescharacteristic
123C2×#127C2311yescharacteristic
124C2×#127C2312yes—
125C2×#125—21no—
126C2×#125C2312yes—
127C2×#124—21no—
128C2×#124—21no—
129C2×#124—21no—
130C2×#124—21no—
131C2×#124—21no—
132C2×#124—21no—
133C2×#124—21no—
134C2×#124—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8C2312yes—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8C2312yes—
143C2×#117C2312yes—
144C2×#117C2311yescharacteristic
145C2×#117C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#500—42no—
148#498—42no—
149#492—42no—
150#492—42no—
151#487—42no—
152#487—42no—
153#486—42no—
154#486—42no—
155#450—216no—
156#433—28no—
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×C22⋊C8C2312yes—
170C2×C22⋊C8C2312yes—
171C2×#97C2312yes—
172C2×#97C2312yes—
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2312yes—
178C2×C4×C8C2312yes—
179#401—22no—
180#400—22no—
181#400—22no—
182#400—22no—
183#400—22no—
184#398—22no—
185#397—22no—
186#397—22no—
187#394—22no—
188#394—22no—
189#394—22no—
190#394—22no—
191#394—22no—
192#394—22no—
193#394—22no—
194#394—22no—
195#391—21no—
196#391—21no—
197#391—21no—
198#391—21no—
199#391C2312yes—
200#391C2312yes—
201#391C2312yes—
202#391C2312yes—
203#390—22no—
204#390—22no—
205#390—22no—
206#390—22no—
207#390—21no—
208#390—21no—
209#390—21no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390C2312yes—
216#390C2312yes—
217#390C2312yes—
218#390C2312yes—
219#390C2312yes—
220#390C2312yes—
221#390C2312yes—
222#390C2312yes—
223#389—22no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#388—22no—
237#388—22no—
238#387—22no—
239#387—22no—
240#387—22no—
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#383—22no—
244#382—21no—
245#382—21no—
246#382—21no—
247#382—22no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380C2312yes—
252#379—22no—
253#379—22no—
254#379—22no—
255#379—22no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4D411yescharacteristic
260C4×C4⋊C4D411yescharacteristic
261C4×C4⋊C4D411yescharacteristic
262C4×C4⋊C4D411yescharacteristic
263C4×C4⋊C4C2312yes—
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268#376C2311yescharacteristic
269#376C2311yescharacteristic
270C43C2311yescharacteristic
271C43C2311yescharacteristic
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280C25—22no—
281C22×Q8—21no—
282C22×Q8—21no—
283C22×Q8—21no—
284C22×Q8C2412yes—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—28no—
293C22×D4—42no—
294C22×D4—42no—
295C22×D4—44no—
296C22×D4—44no—
297C22×D4—44no—
298C22×D4—82no—
299C22×D4—82no—
300C22×D4—82no—
301C22×D4—82no—
302C22×D4C2412yes—
303C22×D4C2412yes—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2411yescharacteristic
307C2×SD16—28no—
308C2×SD16—28no—
309C2×SD16—44no—
310C2×SD16—44no—
311C2×SD16—44no—
312C2×SD16—44no—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325#127—22no—
326#127—22no—
327#127—22no—
328#127—22no—
329#127—42no—
330#127—42no—
331#127—44no—
332#127—44no—
333#125—42no—
334#125—42no—
335#125—82no—
336#124—82no—
337#124—82no—
338#124—82no—
339#124—82no—
340#124—82no—
341#124—82no—
342#124—82no—
343#124—82no—
344C22⋊Q8—28no—
345C22⋊Q8—44no—
346C22⋊Q8—44no—
347C22⋊Q8—82no—
348C4×Q8—44no—
349C4×Q8—44no—
350C4×Q8—44no—
351C4×Q8—82no—
352#117—24no—
353#117—42no—
354#117—42no—
355#117—42no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
374C2×C4⋊C4C2×D411yescharacteristic
375C2×C4⋊C4C2×D411yescharacteristic
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
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⋊C4—22no—
401C2×C22⋊C4C2×D411yescharacteristic
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426#107—44no—
427#106—44no—
428C4⋊C8—24no—
429C4⋊C8—24no—
430#103—44no—
431#103—44no—
432#102—28no—
433#102—28no—
434#102—44no—
435#102—44no—
436#102—44no—
437#102—44no—
438C22⋊C8—24no—
439C22⋊C8#4118yes—
440#97—24no—
441#97—42no—
442C4×C8—24no—
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#95—22no—
461#95—22no—
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470C24—22no—
471C24—22no—
472C24—44no—
473C24—44no—
474C24—44no—
475C24—82no—
476C24—82no—
477C24—82no—
478C24—82no—
479C24C22×D411yescharacteristic
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—24no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—88no—
519C2×D4—88no—
520C2×D4—82no—
521C2×D4—82no—
522C2×D4—82no—
523C2×D4—82no—
524C2×D4—816no—
525C2×D4—816no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C2×#4114yes—
555C22×C4C2511yescharacteristic
556SD16—88no—
557SD16—88no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8C2×#4114yes—
569C2×C8C2×#4114yes—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—24no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—82no—
606C22⋊C4—82no—
607C22⋊C4—82no—
608C22⋊C4—82no—
609C22⋊C4—82no—
610C22⋊C4—82no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—82no—
614C22⋊C4—82no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C22⋊C4—82no—
621C22⋊C4—82no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—21no—
635C42—21no—
636C42—22no—
637C42—22no—
638C42—44no—
639C42—44no—
640C42—82no—
641C42H(5,𝔽2)12yes—
642C42H(5,𝔽2)12yes—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—88no—
664C23—88no—
665C23—88no—
666C23—164no—
667C23—164no—
668C23—164no—
669C23—164no—
670C23#53212yes—
671C23C23×D411yescharacteristic
672Q8—44no—
673Q8—44no—
674Q8—84no—
675Q8—84no—
676Q8—84no—
677D4—44no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—88no—
682D4—88no—
683D4—88no—
684D4—84no—
685D4—84no—
686D4—84no—
687D4—84no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4#53212yes—
743C2×C4#53512yes—
744C2×C4#53512yes—
745C2×C4#57612yes—
746C2×C4#57712yes—
747C2×C4#57712yes—
748C2×C4#57712yes—
749C2×C4C22×#4112yes—
750C2×C4C2×H(5,𝔽2)11yescharacteristic
751C2×C4C2×H(5,𝔽2)11yescharacteristic
752C2×C4#58512yes—
753C8—24no—
754C8—24no—
755C8—42no—
756C8—42no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—1616no—
779C22C2×#53211yescharacteristic
780C22C2×#53511yescharacteristic
781C22#344911yescharacteristic
782C22C2×#57611yescharacteristic
783C22C2×#57711yescharacteristic
784C22C2×#57711yescharacteristic
785C22C2×#57711yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4#322214yes—
804C4#322414yes—
805C4#351412yes—
806C4#351412yes—
807C2—42no—
808C2—162no—
809C2—162no—
810C2#3513111yescharacteristic
811C2#6071211yescharacteristic
812C2#6072211yescharacteristic
813C2C2×#322211yescharacteristic
814C2C2×#322411yescharacteristic
815C2#6100611yescharacteristic
816C2#6101211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#127C22
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. #35291C2semidirect
3. #33286C2semidirect
4. #33277C2semidirect
5. #33252C2semidirect
6. #33239C2semidirect
7. #30353C2semidirect
8. #29569C2semidirect
9. #28655C2semidirect
10. #28654C2semidirect
11. #28614C2semidirect
12. #28614C2semidirect
13. #25904C2semidirect
15. #25812C2semidirect
17. #24516C2semidirect
18. #22052C2semidirect
19. C4×#433C2semidirect
22. C2×#500C22semidirect
23. C2×#498C22semidirect
26. C2×#487C22semidirect
27. C2×#487C22semidirect
32. #2862C22semidirect
33. #2859C22semidirect
40. #2645C22semidirect
61. #2320C22semidirect
64. C4×C4⋊Q8C22semidirect
65. C4×C4⋊Q8C22semidirect
67. #2067C22semidirect
68. #2065C22semidirect
69. #2059C22semidirect
70. #2055C22semidirect
71. #2055C22semidirect
73. #2026C22semidirect
75. #1990C22semidirect
76. #1990C22semidirect
77. #1990C22semidirect
78. #1990C22semidirect
79. #1973C22semidirect
80. #1973C22semidirect
81. #1968C22semidirect
82. #1968C22semidirect
87. #1936C22semidirect
88. #1936C22semidirect
89. #1934C22semidirect
90. #1934C22semidirect
91. #1926C22semidirect
92. #1925C22semidirect
93. #1880C22semidirect
94. #1880C22semidirect
98. #1768C22semidirect
99. C4×C4⋊C8C22semidirect
100. C4×C4⋊C8C22semidirect
104. #1746C22semidirect
105. C4×#97C22semidirect
106. C42×C8C22semidirect

Maximal subgroups

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

subgroupindex
#352912
#352852
#332862
#332772
#332522
#332392
#303532
#295692
#286552
#286542
#286142
#259042
#258552
#258122
#257172
#245162
#220522
C4×#4332