Finite Group Databasebeta

← #6459140

Subgroups — #6459140

Order 512.

1757 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35292C211yesmaximal, characteristic
2#34188C211yesmaximal, characteristic, complemented
3#27974C211yesmaximal, characteristic, complemented
4#27961C211yesmaximal, characteristic, complemented
5#27949C211yesmaximal, characteristic, complemented
6#27909C211yesmaximal, characteristic, complemented
7#27891C211yesmaximal, characteristic, complemented
8#27890C211yesmaximal, characteristic, complemented
9#27878C211yesmaximal, characteristic, complemented
10#27877C211yesmaximal, characteristic, complemented
11#27868C214yesmaximal, complemented
12#24562C214yesmaximal, complemented
13#23770C214yesmaximal, complemented
14#21586C214yesmaximal, complemented
15#21410C211yesmaximal, characteristic, complemented
16#21401C211yesmaximal, characteristic, complemented
17#20824C211yesmaximal, characteristic, complemented
18#20817C211yesmaximal, characteristic, complemented
19C4×#408C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C2×C4×#41C2211yescharacteristic
22C2×#480C2214yes—
23C2×#408C2212yes—
24C2×C4×M16C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2856C2211yescharacteristic
29#2856C2211yescharacteristic
30#2624C2212yes—
31#2615C2212yes—
32#2592—21no—
33#2580—21no—
34#2540—21no—
35#2535—21no—
36#2414—21no—
37#2414—21no—
38#2407—21no—
39#2407—21no—
40#2355—21no—
41#2355—21no—
42#2354—21no—
43#2354—21no—
44#2352—21no—
45#2352—21no—
46#2352—21no—
47#2352—21no—
48#2324C2212yes—
49#2324C2212yes—
50#2314C2212yes—
51#2314C2212yes—
52#2311C2212yes—
53#2285C2211yescharacteristic
54#2285C2211yescharacteristic
55#2285C2211yescharacteristic
56#2285C2211yescharacteristic
57#2285C2211yescharacteristic
58#2285C2211yescharacteristic
59C2×#384C2211yescharacteristic
60#2274C2212yes—
61#2100C2214yes—
62#2093C2214yes—
63#2085C2214yes—
64#2076C2214yes—
65#2075C2214yes—
66#2073C2214yes—
67#2034C2214yes—
68#2033C2214yes—
69#1990C2211yescharacteristic
70#1990C2211yescharacteristic
71#1990C2211yescharacteristic
72#1990C2211yescharacteristic
73#1957C2211yescharacteristic
74#1957C2211yescharacteristic
75#1957C2211yescharacteristic
76#1957C2211yescharacteristic
77#1926C2214yes—
78#1925C2214yes—
79#1921C2214yes—
80#1918C2214yes—
81#1895C2214yes—
82#1893C2214yes—
83#1875C2214yes—
84#1854C2214yes—
85#1845C2211yescharacteristic
86#1845C2211yescharacteristic
87#1845C2211yescharacteristic
88#1844C2211yescharacteristic
89#1834C2211yescharacteristic
90#1834C2211yescharacteristic
91#1834C2211yescharacteristic
92#1834C2211yescharacteristic
93#1824C2214yes—
94#1809C2214yes—
95#1808C2214yes—
96#1776C2214yes—
97C4×#107C2214yes—
98#1762C2214yes—
99C4×#102C2214yes—
100#1750C2212yes—
101#1750C2212yes—
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1729C2212yes—
107C22×#41—21no—
108C22×#41C2311yescharacteristic
109C22×M16C2312yes—
110C23×C8C2312yes—
111#532—24no—
112#532—24no—
113C2×C4⋊Q8C2311yescharacteristic
114C2×#127C2311yescharacteristic
115C2×#124—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×#121—21no—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121C2312yes—
124C2×#121C2312yes—
125C2×#121C2312yes—
126C4×#41—24no—
127C4×#41—24no—
128C2×C4×Q8D411yescharacteristic
129C2×C4×Q8D411yescharacteristic
130C2×C4×D4—21no—
131C2×C4×D4D411yescharacteristic
132C2×C4×D4D411yescharacteristic
133C2×C4×D4D411yescharacteristic
134C2×C4×D4D411yescharacteristic
135C2×C4×D4D411yescharacteristic
136C2×C4×D4D411yescharacteristic
137C2×C4×D4C2312yes—
138C2×#117—21no—
139C2×#117—21no—
140C2×#117—21no—
141C2×#117—21no—
142C2×#117—21no—
143C2×#117C2312yes—
144C2×#117C2311yescharacteristic
145C2×#117C2311yescharacteristic
146C2×#117C2311yescharacteristic
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#480—216no—
154C2×#107C2314yes—
155C2×#107C2314yes—
156C2×#107C2314yes—
157C2×#106C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162#408—28no—
163C2×C22⋊C8C2312yes—
164C2×C22⋊C8C2312yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C4×M16—24no—
168C2×#97C2312yes—
169C2×C4×C8—24no—
170C2×C4×C8C2311yescharacteristic
171C2×C4×C8C2311yescharacteristic
172C2×C4×C8C2311yescharacteristic
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2312yes—
175#399—22no—
176#397—22no—
177#394—22no—
178#394—22no—
179#393—22no—
180#392—22no—
181#392—22no—
182#392—22no—
183#391—22no—
184#391—21no—
185#391—21no—
186#390—22no—
187#390—22no—
188#390—22no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390—21no—
193#390C2312yes—
194#390C2312yes—
195#389—21no—
196#389—21no—
197#389C2312yes—
198#389C2312yes—
199#388—22no—
200#388—22no—
201#388—22no—
202#388—22no—
203#388—22no—
204#388—22no—
205#387—22no—
206#387—22no—
207#387—22no—
208#387—22no—
209#386—22no—
210#386—22no—
211#386—22no—
212#386—22no—
213#385—22no—
214#385—22no—
215#384—21no—
216#384—21no—
217#384C2312yes—
218#384C2311yescharacteristic
219#384C2311yescharacteristic
220#384C2311yescharacteristic
221#384C2311yescharacteristic
222#384C2311yescharacteristic
223#384C2311yescharacteristic
224#382—21no—
225#382—21no—
226#382—21no—
227#382—21no—
228#382—21no—
229#382C2312yes—
230#380—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380—21no—
235#380—21no—
236#380—21no—
237#380—21no—
238#380—21no—
239#380C2312yes—
240#380C2312yes—
241#380C2312yes—
242#380C2312yes—
243#380C2312yes—
244#380C2312yes—
245#380C2312yes—
246C4×C4⋊C4—22no—
247C4×C4⋊C4—22no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C4×C4⋊C4C2312yes—
259C4×C4⋊C4C2312yes—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#336C2312yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—24no—
277C2×#41—42no—
278C2×#41—44no—
279C2×#41—82no—
280C2×#41—82no—
281C22×Q8—21no—
282C22×Q8C2×D411yescharacteristic
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C2×D411yescharacteristic
289C22×D4C2×D411yescharacteristic
290C22×D4C2×D411yescharacteristic
291C22×D4C2412yes—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C2×M16—24no—
304C2×M16—24no—
305C2×M16—42no—
306C22×C8—24no—
307C22×C8—24no—
308C22×C8—42no—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315#127—22no—
316#127—22no—
317#124—44no—
318C22⋊Q8—82no—
319C22⋊Q8—82no—
320#121—24no—
321#121—24no—
322#121—28no—
323#121—44no—
324#121—44no—
325#121—82no—
326#121—82no—
327#121—82no—
328#121—82no—
329C4×Q8—24no—
330C4×Q8—24no—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4—24no—
337C4×D4—24no—
338C4×D4—24no—
339C4×D4—44no—
340#117—22no—
341#117—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117—44no—
347#117—82no—
348#117—82no—
349#117—82no—
350#117—82no—
351#117—82no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
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—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—82no—
372C2×C4⋊C4—82no—
373C2×C4⋊C4C2×D411yescharacteristic
374C2×C4⋊C4C2×D411yescharacteristic
375C2×C4⋊C4C2×D411yescharacteristic
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
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⋊C4—22no—
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42#4114yes—
425C2×C42#4114yes—
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430#107—28no—
431#107—28no—
432#107—44no—
433#106—44no—
434#102—28no—
435#102—28no—
436#102—44no—
437#102—44no—
438C22⋊C8—24no—
439C22⋊C8—24no—
440C22⋊C8—24no—
441C22⋊C8#4118yescomplemented
442#97—24no—
443C4×C8—22no—
444C4×C8—22no—
445C4×C8—24no—
446C4×C8—22no—
447C4×C8—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#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464C24—22no—
465C24C22×D411yescharacteristic
466C24C22×D411yescharacteristic
467C24C22×D411yescharacteristic
468#41—48no—
469#41—48no—
470#41—816no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—41no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—24no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—82no—
500C2×D4—82no—
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—21no—
510C22×C4—21no—
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—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
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—44no—
538C22×C4—44no—
539C22×C4—82no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4#12314yes—
544C22×C4#12314yes—
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×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4114yes—
559C22×C4C2511yescharacteristic
560M16—48no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—48no—
572C2×C8C2×#4114yes—
573C2×C8C2×#4114yes—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—42no—
589C4⋊C4—44no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—82no—
603C4⋊C4—82no—
604C4⋊C4—82no—
605C4⋊C4—82no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C22⋊C4—82no—
621C22⋊C4—82no—
622C22⋊C4—82no—
623C22⋊C4—82no—
624C22⋊C4—82no—
625C22⋊C4—82no—
626C22⋊C4—82no—
627C22⋊C4—82no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—44no—
637C42—82no—
638C42—82no—
639C42—82no—
640C42—82no—
641C42—82no—
642C42#12314yes—
643C42#12314yes—
644C42C2×#4112yes—
645C42C2×#4112yes—
646C42C2×#4112yes—
647C42C2×#4112yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23C2×#12312yes—
675C23#53212yes—
676C23C23×D411yescharacteristic
677Q8—44no—
678Q8—84no—
679D4—44no—
680D4—44no—
681D4—44no—
682D4—44no—
683D4—44no—
684D4—88no—
685D4—84no—
686D4—84no—
687D4—164no—
688D4—164no—
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—28no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
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—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
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—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—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—88no—
746C2×C4—164no—
747C2×C4C2×#12312yes—
748C2×C4C2×#12312yes—
749C2×C4C2×#12312yes—
750C2×C4C2×#12312yes—
751C2×C4C2×#12312yes—
752C2×C4#53212yes—
753C2×C4#57612yes—
754C2×C4#57612yes—
755C2×C4#57712yes—
756C2×C4#57812yes—
757C2×C4C22×#4111yescharacteristic
758C2×C4C22×#4111yescharacteristic
759C2×C4C22×#4112yes—
760C2×C4#58512yes—
761C8—24no—
762C8—24no—
763C8—42no—
764C8—42no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22C22×#12311yescharacteristic
794C22C2×#53211yescharacteristic
795C22#344911yescharacteristic
796C22C2×#57611yescharacteristic
797C22C2×#57611yescharacteristic
798C22C2×#57711yescharacteristic
799C22C2×#57811yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4#309614yes—
817C4#309814yes—
818C4#347512yes—
819C4#347512yes—
820C2—42no—
821C2—42no—
822C2—81no—
823C2—162no—
824C2#3481011yescharacteristic
825C2C2×#309611yescharacteristic
826C2C2×#309811yescharacteristic
827C2#6071411yescharacteristic
828C2#6072311yescharacteristic
829C2#6100611yescharacteristic
830C2#6101411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35292C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34188C2semidirect
3. #27974C2semidirect
4. #27961C2semidirect
5. #27949C2semidirect
6. #27909C2semidirect
7. #27891C2semidirect
8. #27890C2semidirect
9. #27878C2semidirect
10. #27877C2semidirect
11. #27868C2semidirect
12. #24562C2semidirect
13. #23770C2semidirect
14. #21586C2semidirect
15. #21410C2semidirect
16. #21401C2semidirect
17. #20824C2semidirect
18. #20817C2semidirect
19. C4×#408C2semidirect
441. C22⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#352922
#341882
#279742
#279612
#279492
#279092
#278912
#278902
#278782
#278772
#278682
#245622
#237702
#215862
#214102
#214012
#208242
#208172
C4×#4082