Finite Group Databasebeta

← #6686439

Subgroups — #6686439

Order 512.

1778 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3231C211yesmaximal, characteristic, complemented
2C2×#3185C211yesmaximal, characteristic, complemented
3#36151C211yesmaximal, characteristic
4#36134C211yesmaximal, characteristic
5#33212C211yesmaximal, characteristic, complemented
6#30686C214yesmaximal, complemented
7#30586C214yesmaximal
8#30279C211yesmaximal, characteristic, complemented
9#29845C211yesmaximal, characteristic, complemented
10#28687C211yesmaximal, characteristic, complemented
11#28616C211yesmaximal, characteristic, complemented
12#26577C214yesmaximal, complemented
13#26395C214yesmaximal, complemented
14#25812C211yesmaximal, characteristic, complemented
15#25674C211yesmaximal, characteristic, complemented
16#25672C211yesmaximal, characteristic, complemented
17#25600C211yesmaximal, characteristic, complemented
18#22218C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#533C2211yescharacteristic
24#3231—28no—
25#3185—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#498C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#494C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#485C2214yes—
36C2×#479C2214yes—
37C2×#470C2214yes—
38C2×#441C2214yes—
39C2×#431C2211yescharacteristic
40C2×C4×M16C2211yescharacteristic
41#2868C2211yescharacteristic
42#2862C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2552—21no—
48#2542—21no—
49#2538C2212yes—
50#2536—21no—
51#2489—21no—
52#2489C2212yes—
53#2453—21no—
54#2453C2212yes—
55#2441—21no—
56#2441—21no—
57#2429—21no—
58#2429—21no—
59#2423C2212yes—
60#2423C2212yes—
61#2421—21no—
62#2421—21no—
63#2415—21no—
64#2415C2212yes—
65#2365—21no—
66#2362—21no—
67#2362C2212yes—
68#2354—21no—
69#2351—21no—
70Q8×C4⋊C4C2212yes—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2095C2214yes—
75#2095C2214yes—
76#2084C2214yes—
77#2066C2214yes—
78#2059C2214yes—
79#2056C2214yes—
80#2036C2214yes—
81#2035C2214yes—
82#2035C2214yes—
83#2001C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1956C2211yescharacteristic
89#1956C2211yescharacteristic
90#1948C2214yes—
91#1944C2214yes—
92#1927C2214yes—
93#1924C2212yes—
94#1917C2212yes—
95#1878C2214yes—
96#1878C2214yes—
97#1870C2212yes—
98#1865C2214yes—
99#1865C2214yes—
100#1863C2214yes—
101#1854C2214yes—
102#1851C2212yes—
103#1844C2211yescharacteristic
104#1809C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×Q16C2314yes—
110C22×M16C2312yes—
111#533—24no—
112#533—24no—
113#533—24no—
114#533—24no—
115#533—42no—
116#533—42no—
117#533—42no—
118#533—42no—
119C2×C4⋊Q8—21no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×#125—21no—
128C2×#125—21no—
129C2×#125—21no—
130C2×#125C2312yes—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8C2312yes—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2312yes—
152C2×C4×Q8C2312yes—
153C2×C4×D4D411yescharacteristic
154C2×C4×D4D411yescharacteristic
155C2×C4×D4C2311yescharacteristic
156C2×#117—21no—
157C2×#117—21no—
158C2×#117—21no—
159C2×#117C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#500—24no—
163#500—42no—
164#498—24no—
165#498—24no—
166#494—24no—
167#487—24no—
168#487—24no—
169#487—42no—
170#487D418yescomplemented
171#485—216no—
172#479—216no—
173#470—216no—
174#441—216no—
175#431—24no—
176C2×#107C2314yes—
177C2×#107C2314yes—
178C2×#106C2314yes—
179C2×#106C2314yes—
180C2×#106C2314yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C4×M16—24no—
193C2×#97C2312yes—
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198#400—22no—
199#400—22no—
200#399—22no—
201#399—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#397—22no—
206#397—22no—
207#396—22no—
208#396—22no—
209#394—22no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391C2312yes—
217#391C2312yes—
218#391C2312yes—
219#391C2312yes—
220#390—22no—
221#389—22no—
222#389—22no—
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#389—22no—
233#389—22no—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#384—22no—
249#384—21no—
250#384—21no—
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#384C2312yes—
254#384C2312yes—
255#382—21no—
256#382—21no—
257#382—22no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266C4×C4⋊C4—22no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—22no—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8C2412yes—
296C22×Q8C2412yes—
297C22×D4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C2×Q16—28no—
305C2×Q16—28no—
306C2×Q16—44no—
307C2×M16—24no—
308C2×M16—24no—
309C2×M16—42no—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—44no—
325C4⋊Q8—82no—
326C4⋊Q8C2×D414yes—
327C4⋊Q8C2×D414yes—
328#125—24no—
329#125—42no—
330#125—44no—
331#125—44no—
332#125—44no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—44no—
337C22⋊Q8—42no—
338C22⋊Q8—42no—
339C22⋊Q8—42no—
340C22⋊Q8—44no—
341C22⋊Q8—44no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345C22⋊Q8—44no—
346C22⋊Q8—82no—
347C22⋊Q8—82no—
348C4×Q8—24no—
349C4×Q8—24no—
350C4×Q8—24no—
351C4×Q8—44no—
352C4×Q8—42no—
353C4×Q8—42no—
354C4×Q8—42no—
355C4×Q8—44no—
356C4×Q8—44no—
357C4×Q8—44no—
358C4×Q8—44no—
359C4×Q8—44no—
360C4×Q8—44no—
361C4×D4—24no—
362C4×D4—42no—
363C4×D4—42no—
364#117—24no—
365#117—42no—
366#117—44no—
367#117—44no—
368#117—44no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2×D411yescharacteristic
401C2×C4⋊C4C2×D411yescharacteristic
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
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×C22⋊C4—22no—
416C2×C22⋊C4C2×D411yescharacteristic
417C2×C22⋊C4C2×D411yescharacteristic
418C2×C22⋊C4C2×D411yescharacteristic
419C2×C22⋊C4C2×D411yescharacteristic
420C2×C22⋊C4C2×D411yescharacteristic
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445#107—28no—
446#107—44no—
447#106—28no—
448#106—28no—
449#106—44no—
450C4⋊C8—24no—
451C4⋊C8—24no—
452#103—28no—
453#103—28no—
454#103—44no—
455#103—44no—
456#103—44no—
457#103C2×D4116yes—
458C22⋊C8—24no—
459C22⋊C8—24no—
460C22⋊C8—42no—
461#97—24no—
462C4×C8—22no—
463C4×C8—22no—
464C4×C8—22no—
465C4×C8C2×D414yes—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95C2×D411yescharacteristic
483#95C2×D411yescharacteristic
484#95C2×D411yescharacteristic
485#95C2×D411yescharacteristic
486#95C2×D411yescharacteristic
487#95C2×D411yescharacteristic
488C24C22×D411yescharacteristic
489C24C22×D411yescharacteristic
490C2×Q8—24no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—24no—
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—24no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8C22×D414yes—
510C2×D4—22no—
511C2×D4—41no—
512C2×D4—41no—
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—21no—
530C22×C4—21no—
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×C4C2511yescharacteristic
554Q16—416no—
555M16—48no—
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—
565C2×C8—22no—
566C2×C8C22×D414yes—
567C2×C82−1+414yes—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—82no—
607C4⋊C4—82no—
608C4⋊C4—82no—
609C4⋊C4—82no—
610C4⋊C4C22×D414yes—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—41no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—82no—
624C22⋊C4—82no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—22no—
637C42—22no—
638C42—44no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42—44no—
643C42—44no—
644C42#13714yes—
645C42C22×D412yes—
646C42H(5,𝔽2)12yes—
647C23—21no—
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—
661C23C23×D411yescharacteristic
662Q8—28no—
663Q8—48no—
664Q8—44no—
665Q8—44no—
666Q8—44no—
667Q8—84no—
668Q8—84no—
669Q8—84no—
670D4—44no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—24no—
685C2×C4—24no—
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—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
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—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4D4212yes—
732C2×C4D4212yes—
733C2×C4C2×#13712yes—
734C2×C4C2×#13712yes—
735C2×C4C2×#13712yes—
736C2×C4#57512yes—
737C2×C4#57712yes—
738C2×C4#57812yes—
739C2×C4C23×D411yescharacteristic
740C2×C4C2×H(5,𝔽2)11yescharacteristic
741C2×C4C2×2−1+412yes—
742C2×C4#58512yes—
743C8—24no—
744C8—24no—
745C8—42no—
746C8—42no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22#344911yescharacteristic
762C22C2×D4211yescharacteristic
763C22#349911yescharacteristic
764C22C22×#13711yescharacteristic
765C22C2×#57511yescharacteristic
766C22C2×#57711yescharacteristic
767C22C2×#57811yescharacteristic
768C4—22no—
769C4—22no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—44no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—44no—
780C4—82no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4#327114yes—
787C4#327614yes—
788C4#348912yes—
789C4#355412yes—
790C2—81no—
791C2—81no—
792C2#3768011yescharacteristic
793C2#6096611yescharacteristic
794C2#6100811yescharacteristic
795C2C2×#327111yescharacteristic
796C2C2×#327611yescharacteristic
797C2#6247811yescharacteristic
798C2#6248211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
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. C2×#3231C2semidirect
2. C2×#3185C2semidirect
5. #33212C2semidirect
6. #30686C2semidirect
8. #30279C2semidirect
9. #29845C2semidirect
10. #28687C2semidirect
11. #28616C2semidirect
12. #26577C2semidirect
13. #26395C2semidirect
14. #25812C2semidirect
15. #25674C2semidirect
16. #25672C2semidirect
17. #25600C2semidirect
18. #22218C2semidirect
170. #487D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32312
C2×#31852
#361512
#361342
#332122
#306862
#305862
#302792
#298452
#286872
#286162
#265772
#263952
#258122
#256742
#256722
#256002
#222182
#211022