Finite Group Databasebeta

← #6798455

Subgroups — #6798455

Order 512.

1732 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36180C211yesmaximal, characteristic, complemented
2#36149C211yesmaximal, characteristic
3#33293C211yesmaximal, characteristic, complemented
4#31376C214yesmaximal, complemented
5#31374C214yesmaximal, complemented
6#29878C211yesmaximal, characteristic, complemented
7#29877C211yesmaximal, characteristic, complemented
8#29139C211yesmaximal, characteristic, complemented
9#28688C211yesmaximal, characteristic, complemented
10#27961C211yesmaximal, characteristic, complemented
11#27960C211yesmaximal, characteristic, complemented
12#26124C214yesmaximal, complemented
13#25673C211yesmaximal, characteristic, complemented
14#25671C211yesmaximal, characteristic, complemented
15#24977C214yesmaximal, complemented
16#21859C211yesmaximal, characteristic, complemented
17#21859C211yesmaximal, characteristic, complemented
18#21646C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×#554—21no—
21C2×#532C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×#500C2211yescharacteristic
24C2×#498C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#431C2211yescharacteristic
27C2×#431C2211yescharacteristic
28#2868C2211yescharacteristic
29#2862C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2567—21no—
35#2552—21no—
36#2552C2212yes—
37#2535C2212yes—
38#2502—21no—
39#2502—21no—
40#2447—21no—
41#2447—21no—
42#2440—21no—
43#2440—21no—
44#2440C2212yes—
45#2440C2212yes—
46#2427—21no—
47#2427—21no—
48#2420C2212yes—
49#2420C2212yes—
50#2407—21no—
51#2407—21no—
52#2349C2212yes—
53D4×C4⋊C4—21no—
54D4×C4⋊C4C2212yes—
55#2339—21no—
56#2339—21no—
57C4×C4⋊Q8C2211yescharacteristic
58C4×#127C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C42×D4C2211yescharacteristic
62#2100C2214yes—
63#2099C2214yes—
64#2088C2214yes—
65#2087C2214yes—
66#2085C2214yes—
67#2077C2214yes—
68#2076C2214yes—
69#2034C2214yes—
70#2033C2214yes—
71#2023C2214yes—
72#1993C2214yes—
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1990C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1955C2212yes—
84#1949C2214yes—
85#1940C2212yes—
86#1936C2214yes—
87#1924C2212yes—
88#1924C2212yes—
89#1874C2214yes—
90#1874C2214yes—
91#1864C2214yes—
92#1862C2214yes—
93#1836C2214yes—
94#1834C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97#1824C2214yes—
98#1823C2214yes—
99#1802C2214yes—
100#1802C2214yes—
101#1802C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103#1762C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×#41—21no—
108C22×#41—21no—
109#554—48no—
110#532—24no—
111#532—24no—
112#532—42no—
113#532—42no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2312yes—
120C2×#127C2311yescharacteristic
121C2×#125—22no—
122C2×#124—21no—
123C2×#124—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8—22no—
130C2×#121—21no—
131C2×#121—21no—
132C2×#121C2312yes—
133C2×#121C2312yes—
134C2×C4×Q8—21no—
135C2×C4×D4—22no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4D411yescharacteristic
141C2×C4×D4D411yescharacteristic
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×C4×D4C2312yes—
145C2×C4×D4C2311yescharacteristic
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#500—42no—
155#498—42no—
156#486—24no—
157#431—42no—
158#431—42no—
159C2×#107C2314yes—
160C2×#106C2314yes—
161C2×C4⋊C8C2312yes—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2312yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×C22⋊C8C2312yes—
169C2×C22⋊C8C2312yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172C2×#97C2312yes—
173C2×#97C2312yes—
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178#398—22no—
179#398—22no—
180#398—22no—
181#398—22no—
182#397—22no—
183#397—22no—
184#397—22no—
185#395—22no—
186#395—22no—
187#394—22no—
188#394—22no—
189#392—22no—
190#391—21no—
191#391—21no—
192#391—21no—
193#391—21no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391—21no—
198#391—21no—
199#390—21no—
200#390—21no—
201#390C2312yes—
202#389—22no—
203#389—22no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389C2312yes—
210#389C2312yes—
211#389C2312yes—
212#389C2312yes—
213#389C2312yes—
214#386—22no—
215#386—22no—
216#386—22no—
217#386—22no—
218#385—22no—
219#385—22no—
220#385—22no—
221#385—22no—
222#385—22no—
223#385—22no—
224#384—21no—
225#384—21no—
226#384—21no—
227#384—21no—
228#384—21no—
229#384—21no—
230#384C2311yescharacteristic
231#384C2311yescharacteristic
232#384C2312yes—
233#384C2312yes—
234#384C2312yes—
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#382C2312yes—
238#382C2312yes—
239#381—22no—
240#381—22no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—22no—
246#380C2312yes—
247#380C2312yes—
248#380C2312yes—
249#380C2312yes—
250C4×C4⋊C4—21no—
251C4×C4⋊C4D411yescharacteristic
252C4×C4⋊C4D411yescharacteristic
253C4×C4⋊C4C2312yes—
254C4×C4⋊C4C2311yescharacteristic
255C4×C22⋊C4D411yescharacteristic
256C4×C22⋊C4D411yescharacteristic
257C4×C22⋊C4D411yescharacteristic
258C4×C22⋊C4D411yescharacteristic
259C4×C22⋊C4C2311yescharacteristic
260C4×C22⋊C4C2311yescharacteristic
261C2×#95—22no—
262C43C2311yescharacteristic
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276C2×#41—44no—
277C2×#41—44no—
278C2×#41—44no—
279C2×#41—44no—
280C2×#41—82no—
281C2×#41—82no—
282C22×Q8—21no—
283C22×Q8—21no—
284C22×Q8—21no—
285C22×Q8—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4C2×D411yescharacteristic
291C22×D4C2412yes—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
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—22no—
313C4⋊Q8—44no—
314C4⋊Q8—44no—
315C4⋊Q8—82no—
316#127—22no—
317#127#4114yes—
318#125—48no—
319#124—44no—
320#124—44no—
321C22⋊Q8—48no—
322C22⋊Q8—48no—
323C22⋊Q8—44no—
324C22⋊Q8—44no—
325C22⋊Q8—82no—
326C22⋊Q8—82no—
327#121—24no—
328#121—24no—
329#121—42no—
330#121—42no—
331#121—44no—
332#121—44no—
333C4×Q8—44no—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4—24no—
337C4×D4—24no—
338C4×D4—24no—
339C4×D4—28no—
340C4×D4—42no—
341C4×D4—42no—
342C4×D4—44no—
343C4×D4—44no—
344C4×D4—48no—
345C4×D4—82no—
346C4×D4—82no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
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—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—82no—
377C2×C4⋊C4—82no—
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
400C2×C22⋊C4C2×D411yescharacteristic
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×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423#107—44no—
424#106—44no—
425C4⋊C8—24no—
426C4⋊C8—42no—
427C4⋊C8—42no—
428#102—28no—
429#102—44no—
430#102—44no—
431#102—44no—
432C22⋊C8—42no—
433C22⋊C8—42no—
434C22⋊C8—42no—
435C22⋊C8—42no—
436#97—24no—
437#97—42no—
438C4×C8—22no—
439C4×C8—22no—
440C4×C8—22no—
441C4×C8—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
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#95C2×D411yescharacteristic
457#95C2×D411yescharacteristic
458#95C2×D411yescharacteristic
459#95C2×D411yescharacteristic
460#95C2×D411yescharacteristic
461#95C2×D411yescharacteristic
462C24—22no—
463C24C22×D411yescharacteristic
464C24C22×D411yescharacteristic
465#41—816no—
466#41—816no—
467C2×Q8—44no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—82no—
478C2×Q8—82no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—82no—
496C2×D4—82no—
497C2×D4C2×#4114yes—
498C22×C4—22no—
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—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
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—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—82no—
531C22×C4—82no—
532C22×C4—82no—
533C22×C4—82no—
534C22×C4—82no—
535C22×C4—82no—
536C22×C4—82no—
537C22×C4—82no—
538C22×C4AGL(1,ℤ/8)14yes—
539C22×C4#13714yes—
540C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—44no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—44no—
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—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
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—21no—
632C42—22no—
633C42—44no—
634C42C2×#4112yes—
635C42H(5,𝔽2)12yes—
636C422−1+414yes—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—24no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C2×AGL(1,ℤ/8)12yes—
657C23C2×#13712yes—
658C23C23×D411yescharacteristic
659Q8—84no—
660Q8—84no—
661Q8—84no—
662Q8—164no—
663D4—28no—
664D4—28no—
665D4—44no—
666D4—48no—
667D4—48no—
668D4—88no—
669D4—88no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—28no—
679C2×C4—28no—
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—44no—
703C2×C4—44no—
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—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—88no—
726C2×C4—88no—
727C2×C4—164no—
728C2×C4—164no—
729C2×C4—164no—
730C2×C4#53612yes—
731C2×C4#53612yes—
732C2×C4#54612yes—
733C2×C4#54612yes—
734C2×C4C2×AGL(1,ℤ/8)12yes—
735C2×C4C2×AGL(1,ℤ/8)12yes—
736C2×C4C2×#13712yes—
737C2×C4C2×#13712yes—
738C2×C4#57612yes—
739C2×C4#57712yes—
740C2×C4C22×#4111yescharacteristic
741C2×C4C2×H(5,𝔽2)11yescharacteristic
742C2×C4C2×2−1+412yes—
743C2×C4#58512yes—
744C8—42no—
745C8—42no—
746C8—42no—
747C8—42no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22C2×#53611yescharacteristic
770C22C2×#54611yescharacteristic
771C22#350011yescharacteristic
772C22C22×AGL(1,ℤ/8)11yescharacteristic
773C22C22×#13711yescharacteristic
774C22C2×#57611yescharacteristic
775C22C2×#57711yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4#330614yes—
794C4#331414yes—
795C4#351512yes—
796C4#354712yes—
797C2—42no—
798C2—42no—
799C2—84no—
800C2#3895511yescharacteristic
801C2#6086011yescharacteristic
802C2#6087711yescharacteristic
803C2C2×#330611yescharacteristic
804C2C2×#331411yescharacteristic
805C2#6253511yescharacteristic
806C2#6254011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36149C2
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
1. #36180C2semidirect
3. #33293C2semidirect
4. #31376C2semidirect
5. #31374C2semidirect
6. #29878C2semidirect
7. #29877C2semidirect
8. #29139C2semidirect
9. #28688C2semidirect
10. #27961C2semidirect
11. #27960C2semidirect
12. #26124C2semidirect
13. #25673C2semidirect
14. #25671C2semidirect
15. #24977C2semidirect
16. #21859C2semidirect
17. #21859C2semidirect
18. #21646C2semidirect
19. #21265C2semidirect

Maximal subgroups

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

subgroupindex
#361802
#361492
#332932
#313762
#313742
#298782
#298772
#291392
#286882
#279612
#279602
#261242
#256732
#256712
#249772
#218592
#216462
#212652