Finite Group Databasebeta

← #6396463

Subgroups — #6396463

Order 512.

2066 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3206C211yesmaximal, characteristic
2#34226C211yesmaximal, characteristic
3#34216C211yesmaximal, characteristic, complemented
4#23112C214yesmaximal, complemented
5#23012C214yesmaximal, complemented
6#22885C214yesmaximal, complemented
7#22865C214yesmaximal, complemented
8#22268C211yesmaximal, characteristic, complemented
9#22268C211yesmaximal, characteristic, complemented
10#22221C211yesmaximal, characteristic, complemented
11#22218C211yesmaximal, characteristic, complemented
12#21984C211yesmaximal, characteristic, complemented
13#21692C211yesmaximal, characteristic, complemented
14C4×#492C211yesmaximal, characteristic, complemented
15#21647C211yesmaximal, characteristic, complemented
16C4×#487C211yesmaximal, characteristic, complemented
17#21410C211yesmaximal, characteristic
18#21202C211yesmaximal, characteristic, complemented
19#20472C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22#3206C4116yescomplemented
23C2×#492C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#461C2214yes—
28C2×#448C2214yes—
29C2×#440C2214yes—
30C2×C4×SD16C2214yes—
31C2×#431C2211yescharacteristic
32C2×#419C2214yes—
33C2×C4×M16C2211yescharacteristic
34#2369—21no—
35#2369—21no—
36#2367—21no—
37#2367—21no—
38#2365C2212yes—
39#2365C2212yes—
40#2363C2212yes—
41#2363C2212yes—
42#2357C2212yes—
43#2349C2212yes—
44#2345—21no—
45#2345—21no—
46#2341—21no—
47Q8×C22⋊C4C2212yes—
48Q8×C22⋊C4C2212yes—
49#2339—21no—
50#2331—21no—
51#2331—21no—
52#2324—21no—
53#2324—21no—
54#2319—21no—
55#2316—21no—
56C4×C4⋊Q8C2211yescharacteristic
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×C4⋊Q8C2211yescharacteristic
62C4×#127C2211yescharacteristic
63C4×#127C2211yescharacteristic
64#2285C2211yescharacteristic
65#2285C2211yescharacteristic
66#2275—21no—
67#2274—21no—
68C4×#117C2211yescharacteristic
69#1990C2211yescharacteristic
70#1990C2211yescharacteristic
71#1973C2214yes—
72#1968C2214yes—
73#1960C2214yes—
74#1957C2211yescharacteristic
75#1957C2211yescharacteristic
76#1956C2211yescharacteristic
77#1956C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1949C2214yes—
81#1935C2214yes—
82#1933C2214yes—
83#1928C2214yes—
84#1927C2214yes—
85#1895C2214yes—
86#1880C2214yes—
87#1880C2214yes—
88#1877C2214yes—
89#1877C2214yes—
90#1865C2214yes—
91#1863C2214yes—
92#1854C2214yes—
93#1845C2211yescharacteristic
94#1844C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97#1771C2212yes—
98#1771C2212yes—
99#1763C2214yes—
100#1762C2214yes—
101C4×#103C2214yes—
102#1753C2212yes—
103#1753C2212yes—
104#1744C2211yescharacteristic
105#1744C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C42×C8C2211yescharacteristic
108C22×#41—21no—
109C23×Q8C2312yes—
110C22×SD16C2314yes—
111C22×SD16C2314yes—
112C22×M16C2312yes—
113#532—24no—
114#532C2×C418yes—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8C2×C418yescomplemented
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2312yes—
122C2×C4⋊Q8C2311yescharacteristic
123C2×#127C2311yescharacteristic
124C2×#124—21no—
125C2×#121—21no—
126C2×#121C2312yes—
127C2×C4×Q8—21no—
128C2×C4×Q8—21no—
129C2×C4×Q8C2312yes—
130C2×C4×Q8C2312yes—
131C2×C4×Q8C2312yes—
132C2×C4×Q8C2312yes—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4C2312yes—
139C2×C4×D4C2312yes—
140C2×C4×D4C2312yes—
141C2×#117—21no—
142C2×#117D411yescharacteristic
143C2×#117D411yescharacteristic
144C2×#117C2312yes—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C42C2311yescharacteristic
148#492C2×C418yes—
149#492C2×C418yes—
150#487C2×C418yescomplemented
151#487C2×C418yescomplemented
152#461C2×C4132yescomplemented
153#448C2×C4132yescomplemented
154#440—48no—
155C4×SD16—48no—
156#431C2×C418yescomplemented
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8C2312yes—
160#419—48no—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×C22⋊C8C2312yes—
170C4×M16—24no—
171C2×#97C2312yes—
172C2×#97C2312yes—
173C2×#97C2312yes—
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2312yes—
177C2×C4×C8C2312yes—
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180#391—21no—
181#391—21no—
182#391—22no—
183#391—22no—
184#391—22no—
185#391—22no—
186#391C2312yes—
187#391C2312yes—
188#391C2312yes—
189#391C2312yes—
190#390—22no—
191#390—22no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390—21no—
196#390C2312yes—
197#390C2312yes—
198#389—22no—
199#389—22no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389C2312yes—
211#389C2312yes—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#387—22no—
217#387—22no—
218#387—22no—
219#387—22no—
220#386—22no—
221#386—22no—
222#385—22no—
223#385—22no—
224#384C2311yescharacteristic
225#384C2311yescharacteristic
226#384C2311yescharacteristic
227#384C2311yescharacteristic
228#382—21no—
229#382C2312yes—
230#381—22no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380—22no—
235#380—22no—
236#380—22no—
237#380C2312yes—
238C4×C4⋊C4—22no—
239C4×C4⋊C4—22no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4D411yescharacteristic
254C4×C4⋊C4D411yescharacteristic
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C4×C4⋊C4C2311yescharacteristic
259C4×C4⋊C4C2311yescharacteristic
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—22no—
263C4×C22⋊C4—22no—
264C4×C22⋊C4—22no—
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4C2311yescharacteristic
268C4×C22⋊C4C2311yescharacteristic
269#376D411yescharacteristic
270#376D411yescharacteristic
271C2×#95—22no—
272C43C2311yescharacteristic
273C43C2311yescharacteristic
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#336C2312yes—
279#336C2312yes—
280#336C2312yes—
281#336C2312yes—
282C2×#41—28no—
283C2×#41—82no—
284C2×#41—82no—
285C22×Q8—21no—
286C22×Q8—22no—
287C22×Q8—24no—
288C22×Q8—44no—
289C22×Q8—44no—
290C22×Q8C22×C418yes—
291C22×Q8C2412yes—
292C22×Q8C2412yes—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4C2412yes—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C2×SD16—44no—
305C2×SD16—44no—
306C2×SD16—44no—
307C2×SD16—44no—
308C2×SD16C22×C4116yes—
309C2×SD16C22×C4116yes—
310C2×M16—24no—
311C2×M16—24no—
312C2×M16—42no—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C4⋊Q8—28no—
318C4⋊Q8—28no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—24no—
322C4⋊Q8—22no—
323C4⋊Q8C22×C418yes—
324C4⋊Q8C22×C414yes—
325C4⋊Q8C22×C414yes—
326C4⋊Q8C22×C414yes—
327#127—22no—
328#127C22×C414yes—
329#124—28no—
330#121—28no—
331#121—24no—
332#121C22×C418yes—
333C4×Q8—44no—
334C4×Q8—44no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×Q8—82no—
338C4×Q8—82no—
339C4×D4—28no—
340C4×D4—24no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—44no—
344C4×D4—44no—
345C4×D4—82no—
346C4×D4—82no—
347C4×D4C22×C418yes—
348#117—24no—
349#117—42no—
350#117—44no—
351#117—44no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
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—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
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×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⋊C4C2×D411yescharacteristic
395C2×C22⋊C4C2×D411yescharacteristic
396C2×C22⋊C4C2×D411yescharacteristic
397C2×C22⋊C4C2×D411yescharacteristic
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42C22×C414yes—
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42#4114yes—
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424#107—44no—
425#106—44no—
426C4⋊C8C22×C418yes—
427#103—28no—
428#103—28no—
429#103—44no—
430#103—44no—
431#103C22×C4116yes—
432#103C22×C4116yes—
433#102—28no—
434#102—44no—
435C22⋊C8C22×C418yes—
436#97—24no—
437#97—24no—
438#97—42no—
439C4×C8—24no—
440C4×C8—22no—
441C4×C8—22no—
442C4×C8—42no—
443C4×C8C22×C414yes—
444C4×C8C22×C414yes—
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#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95C2×D411yescharacteristic
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469C24—22no—
470C24C22×D411yescharacteristic
471#41—816no—
472C2×Q8—24no—
473C2×Q8—28no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—24no—
479C2×Q8—24no—
480C2×Q8—416no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—82no—
484C2×Q8—82no—
485C2×Q8—88no—
486C2×Q8C23×C414yes—
487C2×Q8C23×C414yes—
488C2×D4—28no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—82no—
499C2×D4—82no—
500C2×D4C23×C414yes—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—82no—
519C22×C4—82no—
520C22×C4—82no—
521C22×C4—82no—
522C22×C4—82no—
523C22×C4—82no—
524C22×C4—82no—
525C22×C4—82no—
526C22×C4C4×D414yes—
527C22×C4C4×D414yes—
528C22×C4C23×C412yes—
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C2×#4112yes—
543C22×C4C2511yescharacteristic
544SD16—416no—
545SD16—416no—
546M16—48no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8C23×C414yes—
557C2×C8C23×C414yes—
558C2×C8H(5,𝔽2)14yes—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—82no—
584C4⋊C4—82no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4C23×C414yes—
590C22⋊C4—28no—
591C22⋊C4—28no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—82no—
600C22⋊C4—82no—
601C22⋊C4—82no—
602C22⋊C4—82no—
603C22⋊C4—82no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—44no—
616C42—82no—
617C42—82no—
618C42—82no—
619C42—82no—
620C42—82no—
621C42—82no—
622C42—82no—
623C42C4×D414yes—
624C42C4×D414yes—
625C42#13714yes—
626C42C23×C412yes—
627C42C23×C412yes—
628C42C2×#4112yes—
629C42C2×#4112yes—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—24no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23C2×C4×D412yes—
644C23C23×D411yescharacteristic
645Q8—28no—
646Q8—28no—
647Q8—48no—
648Q8—44no—
649Q8—44no—
650Q8—88no—
651D4—28no—
652D4—48no—
653D4—48no—
654D4—44no—
655D4—88no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—24no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
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—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—88no—
710C2×C4—88no—
711C2×C4—164no—
712C2×C4—164no—
713C2×C4C2×C4×D412yes—
714C2×C4C2×C4×D412yes—
715C2×C4C2×C4×D412yes—
716C2×C4C2×C4×D412yes—
717C2×C4C2×C4×D412yes—
718C2×C4C2×#13712yes—
719C2×C4C2×#13712yes—
720C2×C4C2×#13712yes—
721C2×C4#57512yes—
722C2×C4#57712yes—
723C2×C4#57712yes—
724C2×C4C24×C411yescharacteristic
725C2×C4C22×#4111yescharacteristic
726C2×C4C2×H(5,𝔽2)12yes—
727C2×C4#58512yes—
728C8—24no—
729C8—24no—
730C8—24no—
731C8—42no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22C22×C4×D411yescharacteristic
747C22#349811yescharacteristic
748C22#350011yescharacteristic
749C22C22×#13711yescharacteristic
750C22C2×#57511yescharacteristic
751C22C2×#57711yescharacteristic
752C22C2×#57711yescharacteristic
753C4—22no—
754C4—22no—
755C4—22no—
756C4—22no—
757C4—22no—
758C4—44no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—44no—
766C4—44no—
767C4—82no—
768C4—82no—
769C4—82no—
770C4—82no—
771C4C4×#13714yes—
772C4#294914yes—
773C4C4×H(5,𝔽2)12yes—
774C4#349412yes—
775C2—42no—
776C2—84no—
777C2#3427511yescharacteristic
778C2C2×C4×#13711yescharacteristic
779C2C2×#294911yescharacteristic
780C2#6242211yescharacteristic
781C2#6242711yescharacteristic
782C2#6254011yescharacteristic
783C2#6254311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C2×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
3. #34216C2semidirect
4. #23112C2semidirect
5. #23012C2semidirect
6. #22885C2semidirect
7. #22865C2semidirect
8. #22268C2semidirect
9. #22268C2semidirect
10. #22221C2semidirect
11. #22218C2semidirect
12. #21984C2semidirect
13. #21692C2semidirect
14. C4×#492C2semidirect
15. #21647C2semidirect
16. C4×#487C2semidirect
18. #21202C2semidirect
19. #20472C2semidirect
22. #3206C4semidirect
118. C2×C4⋊Q8C2×C4semidirect
150. #487C2×C4semidirect
151. #487C2×C4semidirect
152. #461C2×C4semidirect
153. #448C2×C4semidirect
156. #431C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32062
#342262
#342162
#231122
#230122
#228852
#228652
#222682
#222212
#222182
#219842
#216922
C4×#4922
#216472
C4×#4872
#214102
#212022
#204722