Finite Group Databasebeta

← #6615869

Subgroups — #6615869

Order 512.

1751 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
1#36211C211yesmaximal, characteristic
2#36134C211yesmaximal, characteristic, complemented
3#33232C211yesmaximal, characteristic, complemented
4#33174C211yesmaximal, characteristic, complemented
5#33170C211yesmaximal, characteristic, complemented
6#29207C211yesmaximal, characteristic, complemented
7#28936C214yesmaximal, complemented
8#28918C214yesmaximal, complemented
9#28438C211yesmaximal, characteristic, complemented
10#27892C211yesmaximal, characteristic, complemented
11#27889C211yesmaximal, characteristic, complemented
12#25598C211yesmaximal, characteristic, complemented
13#25598C211yesmaximal, characteristic, complemented
14#25400C214yesmaximal, complemented
15#23112C214yesmaximal, complemented
16#21646C211yesmaximal, characteristic, complemented
17#21409C211yesmaximal, characteristic, complemented
18#21400C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#492C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#491C2214yes—
25C2×#486C2211yescharacteristic
26C2×#468C2214yes—
27C2×#465C2214yes—
28C2×#461C2214yes—
29C2×#435C2212yes—
30C2×C4×M16C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2868C2211yescharacteristic
33#2859C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2856C2211yescharacteristic
37#2856C2211yescharacteristic
38#2552—21no—
39#2542C2212yes—
40#2538—21no—
41#2535C2212yes—
42#2513—21no—
43#2513—21no—
44#2490C2212yes—
45#2490C2212yes—
46#2441—21no—
47#2441—21no—
48#2429C2212yes—
49#2429C2212yes—
50#2423—21no—
51#2423—21no—
52#2420—21no—
53#2420—21no—
54#2414—21no—
55#2414—21no—
56#2365C2212yes—
57#2363—21no—
58#2363—21no—
59#2357C2212yes—
60#2354—21no—
61Q8×C4⋊C4—21no—
62C4×C4⋊Q8C2211yescharacteristic
63C4×#127C2211yescharacteristic
64#2285C2211yescharacteristic
65#2285C2211yescharacteristic
66C42×D4C2211yescharacteristic
67#2059C2214yes—
68#2036C2214yes—
69#2035C2214yes—
70#2013C2214yes—
71#2000C2214yes—
72#2000C2214yes—
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1973C2214yes—
77#1968C2214yes—
78#1960C2214yes—
79#1957C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1949C2214yes—
87#1936C2214yes—
88#1928C2214yes—
89#1927C2214yes—
90#1894C2214yes—
91#1892C2214yes—
92#1880C2214yes—
93#1880C2214yes—
94#1845C2211yescharacteristic
95#1844C2211yescharacteristic
96#1834C2211yescharacteristic
97#1771C2212yes—
98C4×C4⋊C8C2211yescharacteristic
99#1763C2214yes—
100#1762C2214yes—
101C4×#103C2214yes—
102#1753C2212yes—
103#1752C2212yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×SD16C2314yes—
108C22×SD16C2314yes—
109C22×M16C2312yes—
110C23×C8C2312yes—
111#533—24no—
112#533—24no—
113#533—42no—
114#533—42no—
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2312yes—
119C2×C4⋊Q8C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#125—21no—
122C2×#125—21no—
123C2×#125C2312yes—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2312yes—
128C2×C22⋊Q8C2312yes—
129C2×C22⋊Q8C2312yes—
130C2×#121—21no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121C2312yes—
135C2×#121C2312yes—
136C2×C4×Q8—21no—
137C2×C4×Q8—21no—
138C2×C4×Q8—21no—
139C2×C4×Q8C2312yes—
140C2×C4×Q8C2312yes—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4D411yescharacteristic
144C2×C4×D4D411yescharacteristic
145C2×C4×D4C2312yes—
146C2×C4×D4C2311yescharacteristic
147C2×#117—21no—
148C2×#117—21no—
149C2×#117—21no—
150C2×#117—21no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#492—42no—
154#492—42no—
155#491—48no—
156#486—24no—
157#468—48no—
158#465—48no—
159#461—216no—
160#435—28no—
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×C4⋊C8C2312yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C4×M16—42no—
175C2×#97C2312yes—
176C2×#97C2312yes—
177C2×#97C2312yes—
178C2×C4×C8—42no—
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2312yes—
184#399—22no—
185#399—22no—
186#398—22no—
187#398—22no—
188#397—22no—
189#397—22no—
190#397—22no—
191#396—22no—
192#396—22no—
193#394—22no—
194#394—22no—
195#392—22no—
196#391—21no—
197#391C2312yes—
198#391C2312yes—
199#390—22no—
200#390—22no—
201#390—22no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390C2312yes—
209#390C2312yes—
210#390C2312yes—
211#389—22no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—22no—
222#389—22no—
223#389C2312yes—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#387—22no—
231#387—22no—
232#386—22no—
233#386—22no—
234#384—22no—
235#384—21no—
236#384—21no—
237#384—21no—
238#384—21no—
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#382—21no—
244#382—21no—
245#382C2312yes—
246#381—22no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380C2312yes—
254#380C2312yes—
255C4×C4⋊C4—22no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4D411yescharacteristic
260C4×C4⋊C4D411yescharacteristic
261C4×C4⋊C4C2312yes—
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2311yescharacteristic
265C4×C22⋊C4—22no—
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4D411yescharacteristic
269C4×C22⋊C4D411yescharacteristic
270C4×C22⋊C4C2311yescharacteristic
271C4×C22⋊C4C2311yescharacteristic
272C43C2311yescharacteristic
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280C22×Q8—21no—
281C22×Q8C2412yes—
282C22×Q8C2412yes—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4C2×D411yescharacteristic
288C22×D4C2412yes—
289C23×C4—22no—
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C2×SD16—28no—
297C2×SD16—28no—
298C2×SD16—44no—
299C2×SD16—44no—
300C2×SD16—44no—
301C2×SD16—44no—
302C2×M16—24no—
303C2×M16—24no—
304C2×M16—42no—
305C22×C8—24no—
306C22×C8—24no—
307C22×C8—42no—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—28no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—44no—
319C4⋊Q8#4114yes—
320#127—22no—
321#127—22no—
322#125—44no—
323#125—44no—
324#125—44no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—42no—
328C22⋊Q8—42no—
329C22⋊Q8—44no—
330C22⋊Q8—44no—
331C22⋊Q8—44no—
332C22⋊Q8—44no—
333#121—44no—
334#121—44no—
335#121—44no—
336#121—44no—
337#121—82no—
338#121—82no—
339C4×Q8—24no—
340C4×Q8—24no—
341C4×Q8—42no—
342C4×Q8—42no—
343C4×Q8—44no—
344C4×Q8—44no—
345C4×Q8—44no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—28no—
349C4×D4—42no—
350C4×D4—82no—
351C4×D4—82no—
352#117—44no—
353#117—44no—
354#117—82no—
355#117—82no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
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—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
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⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433#107—44no—
434#106—44no—
435C4⋊C8#4118yes—
436#103—28no—
437#103—28no—
438#103—28no—
439#103—28no—
440#103—44no—
441#103—44no—
442#102—28no—
443#102—28no—
444C22⋊C8—24no—
445C22⋊C8—24no—
446#97—24no—
447#97—24no—
448#97—42no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8—22no—
453C4×C8—42no—
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#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472C24—22no—
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—41no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—82no—
502C2×D4—82no—
503C2×D4—82no—
504C2×D4—82no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
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—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—44no—
532C22×C4—82no—
533C22×C4—82no—
534C22×C4#13714yes—
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C2511yescharacteristic
548SD16—88no—
549SD16—88no—
550M16—48no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—48no—
561C2×C8C2×#4114yes—
562C2×C8C2×#4114yes—
563C2×C8H(5,𝔽2)14yes—
564C4⋊C4—22no—
565C4⋊C4—24no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—41no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—82no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4C2×#4114yes—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—41no—
604C22⋊C4—41no—
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—
614C22⋊C4—82no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—22no—
632C42—21no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42—82no—
637C42—82no—
638C42C2×#4114yes—
639C42C2×#4112yes—
640C42H(5,𝔽2)12yes—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23C2×#13712yes—
662C23C23×D411yescharacteristic
663Q8—48no—
664Q8—44no—
665Q8—44no—
666Q8—44no—
667Q8—44no—
668D4—44no—
669D4—44no—
670D4—44no—
671D4—84no—
672D4—84no—
673D4—164no—
674D4—164no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—28no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—24no—
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—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
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—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—164no—
732C2×C4#53212yes—
733C2×C4#53212yes—
734C2×C4#54612yes—
735C2×C4#54612yes—
736C2×C4C2×#13712yes—
737C2×C4C2×#13712yes—
738C2×C4#57512yes—
739C2×C4#57712yes—
740C2×C4#57712yes—
741C2×C4C22×#4111yescharacteristic
742C2×C4C22×#4112yes—
743C2×C4C2×H(5,𝔽2)12yes—
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C8—24no—
746C8—24no—
747C8—24no—
748C8—42no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22C2×#53211yescharacteristic
771C22C2×#54611yescharacteristic
772C22#349811yescharacteristic
773C22C22×#13711yescharacteristic
774C22C2×#57511yescharacteristic
775C22C2×#57711yescharacteristic
776C22C2×#57711yescharacteristic
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—44no—
786C4—41no—
787C4—41no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4#330714yes—
795C4#332014yes—
796C4#348312yes—
797C4#351912yes—
798C2—42no—
799C2—81no—
800C2—162no—
801C2#3641211yescharacteristic
802C2#6070111yescharacteristic
803C2#6071211yescharacteristic
804C2C2×#332011yescharacteristic
805C2C2×#330711yescharacteristic
806C2#6242211yescharacteristic
807C2#6242711yescharacteristic
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. #33232C2semidirect
4. #33174C2semidirect
5. #33170C2semidirect
6. #29207C2semidirect
7. #28936C2semidirect
8. #28918C2semidirect
9. #28438C2semidirect
10. #27892C2semidirect
11. #27889C2semidirect
12. #25598C2semidirect
13. #25598C2semidirect
14. #25400C2semidirect
15. #23112C2semidirect
16. #21646C2semidirect
17. #21409C2semidirect
18. #21400C2semidirect
19. C4×#435C2semidirect

Maximal subgroups

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

subgroupindex
#362112
#361342
#332322
#331742
#331702
#292072
#289362
#289182
#284382
#278922
#278892
#255982
#254002
#231122
#216462
#214092
#214002
C4×#4352