Finite Group Databasebeta

← #6396461

Subgroups — #6396461

Order 512.

2038 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3210C211yesmaximal, characteristic
2#34226C211yesmaximal, characteristic
3#34214C211yesmaximal, characteristic, complemented
4#23111C214yesmaximal, complemented
5#23009C214yesmaximal, complemented
6#22879C214yesmaximal, complemented
7#22862C214yesmaximal, complemented
8#22270C211yesmaximal, characteristic, complemented
9#22268C211yesmaximal, characteristic, complemented
10#22221C211yesmaximal, characteristic, complemented
11#22220C211yesmaximal, characteristic, complemented
12#21982C211yesmaximal, characteristic, complemented
13#21692C211yesmaximal, characteristic, complemented
14C4×#494C211yesmaximal, characteristic, complemented
15#21647C211yesmaximal, characteristic, complemented
16C4×#486C211yesmaximal, characteristic, complemented
17#21409C211yesmaximal, characteristic, complemented
18#21200C211yesmaximal, characteristic
19#20472C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22#3210C4116yescomplemented
23C2×#494C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#464C2214yes—
28C2×#452C2214yes—
29C2×#440C2214yes—
30C2×C4×Q16C2214yes—
31C2×#431C2211yescharacteristic
32C2×#417C2214yes—
33C2×C4×M16C2211yescharacteristic
34#2367C2212yes—
35#2367C2212yes—
36#2363—21no—
37#2363—21no—
38#2360—21no—
39#2360—21no—
40#2360C2212yes—
41#2360C2212yes—
42#2357—21no—
43#2355—21no—
44#2355C2212yes—
45Q8×C4⋊C4—21no—
46Q8×C4⋊C4C2212yes—
47#2349—21no—
48#2341C2212yes—
49#2339C2212yes—
50#2330—21no—
51#2330—21no—
52#2324—21no—
53#2324—21no—
54#2319—21no—
55#2317—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
65C2×#384C2211yescharacteristic
66#2275—21no—
67#2274—21no—
68C4×#117C2211yescharacteristic
69#1990C2211yescharacteristic
70#1990C2211yescharacteristic
71#1973C2214yes—
72#1969C2214yes—
73#1959C2214yes—
74#1957C2211yescharacteristic
75#1957C2211yescharacteristic
76#1956C2211yescharacteristic
77#1956C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1947C2214yes—
81#1935C2214yes—
82#1934C2214yes—
83#1928C2214yes—
84#1925C2214yes—
85#1894C2214yes—
86#1880C2214yes—
87#1878C2214yes—
88#1878C2214yes—
89#1877C2214yes—
90#1863C2214yes—
91#1862C2214yes—
92#1852C2214yes—
93#1845C2211yescharacteristic
94#1845C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97#1771C2212yes—
98#1771C2212yes—
99#1763C2214yes—
100#1763C2214yes—
101C4×#102C2214yes—
102#1753C2212yes—
103#1753C2212yes—
104#1744C2211yescharacteristic
105#1744C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C42×C8C2211yescharacteristic
108C22×#41C2312yes—
109C22×Q16C2314yes—
110C22×SD16C2314yes—
111C22×M16C2312yes—
112#533—24no—
113#533C2×C418yescomplemented
114#532—24no—
115#532C2×C418yes—
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×#127C2311yescharacteristic
120C2×#125—21no—
121C2×#124C2312yes—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8C2312yes—
124C2×#121—21no—
125C2×#121—21no—
126C2×C4×Q8—21no—
127C2×C4×Q8—21no—
128C2×C4×Q8—21no—
129C2×C4×Q8C2312yes—
130C2×C4×Q8C2312yes—
131C2×C4×Q8C2312yes—
132C2×C4×Q8C2312yes—
133C2×C4×Q8C2312yes—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4C2312yes—
141C2×C4×D4C2312yes—
142C2×#117—21no—
143C2×#117—21no—
144C2×#117D411yescharacteristic
145C2×#117D411yescharacteristic
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4C2312yes—
149C22×C42C2311yescharacteristic
150#494C2×C418yescomplemented
151#492C2×C418yescomplemented
152#487C2×C418yescomplemented
153#486C2×C418yescomplemented
154#464C2×C4132yescomplemented
155#452C2×C4132yescomplemented
156#440—48no—
157C4×Q16—48no—
158#431C2×C418yescomplemented
159C2×#107C2314yes—
160C2×#107C2314yes—
161C2×C4⋊C8C2312yes—
162#417—48no—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×C22⋊C8C2312yes—
172C4×M16—24no—
173C2×#97C2312yes—
174C2×#97C2312yes—
175C2×#97C2312yes—
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2312yes—
179C2×C4×C8C2312yes—
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182#391—21no—
183#391—21no—
184#391C2312yes—
185#391C2312yes—
186#391C2312yes—
187#391C2312yes—
188#390—22no—
189#390—22no—
190#390—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390C2312yes—
195#390C2312yes—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—22no—
207#389—22no—
208#389—22no—
209#389—22no—
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#385—22no—
225#385—22no—
226#384—22no—
227#384—21no—
228#384—21no—
229#384C2311yescharacteristic
230#384C2311yescharacteristic
231#384C2311yescharacteristic
232#384C2311yescharacteristic
233#384C2312yes—
234#382—22no—
235#382—21no—
236#381—22no—
237#380—21no—
238#380—22no—
239#380C2312yes—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
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—24no—
283C2×#41—44no—
284C2×#41—44no—
285C2×#41C22×C418yes—
286C22×Q8—21no—
287C22×Q8C2412yes—
288C22×Q8C2412yes—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4C2412yes—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C2×Q16—44no—
301C2×Q16—44no—
302C2×Q16C22×C4116yes—
303C2×SD16—44no—
304C2×SD16—44no—
305C2×SD16C22×C4116yes—
306C2×M16—24no—
307C2×M16—24no—
308C2×M16—42no—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8C22×C414yes—
317C4⋊Q8C22×C414yes—
318C4⋊Q8C22×C414yes—
319#127—22no—
320#127C22×C414yes—
321#125—28no—
322#124—24no—
323#124C22×C418yes—
324C22⋊Q8—28no—
325C22⋊Q8—24no—
326C22⋊Q8C22×C418yes—
327#121—28no—
328#121—28no—
329C4×Q8—28no—
330C4×Q8—24no—
331C4×Q8—44no—
332C4×Q8—44no—
333C4×Q8—44no—
334C4×Q8—44no—
335C4×Q8—82no—
336C4×Q8—82no—
337C4×Q8C22×C418yes—
338C4×D4—28no—
339C4×D4—28no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—44no—
344C4×D4—82no—
345C4×D4—82no—
346#117—28no—
347#117—24no—
348#117—42no—
349#117—82no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
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—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—82no—
377C2×C4⋊C4C2×D411yescharacteristic
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×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⋊C4C2×D411yescharacteristic
397C2×C22⋊C4C2×D411yescharacteristic
398C2×C22⋊C4C2×D411yescharacteristic
399C2×C22⋊C4C2×D411yescharacteristic
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42C22×C414yes—
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×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42#4114yes—
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426#107—44no—
427#107—44no—
428C4⋊C8C22×C418yes—
429#103—28no—
430#103—28no—
431#103—44no—
432#103—44no—
433#103C22×C4116yes—
434#102—28no—
435#102—44no—
436#102C22×C4116yes—
437C22⋊C8C22×C418yes—
438#97—24no—
439#97—24no—
440#97—42no—
441C4×C8—24no—
442C4×C8—22no—
443C4×C8—22no—
444C4×C8—42no—
445C4×C8C22×C414yes—
446C4×C8C22×C414yes—
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—416no—
472#41—88no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—24no—
479C2×Q8—24no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8C23×C414yes—
483C2×Q8C23×C414yes—
484C2×D4—28no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—82no—
495C2×D4—82no—
496C2×D4C23×C414yes—
497C22×C4—22no—
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—28no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—82no—
515C22×C4—82no—
516C22×C4—82no—
517C22×C4—82no—
518C22×C4—82no—
519C22×C4—82no—
520C22×C4—82no—
521C22×C4—82no—
522C22×C4C4×D414yes—
523C22×C4C4×D414yes—
524C22×C4C23×C412yes—
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
539C22×C4C2511yescharacteristic
540Q16—416no—
541SD16—416no—
542M16—48no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8C23×C414yes—
553C2×C8C23×C414yes—
554C2×C8H(5,𝔽2)14yes—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—28no—
561C4⋊C4—28no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—44no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—82no—
581C4⋊C4—82no—
582C4⋊C4—82no—
583C4⋊C4—82no—
584C4⋊C4—82no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4C23×C414yes—
589C22⋊C4—28no—
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—82no—
599C22⋊C4—82no—
600C22⋊C4—82no—
601C22⋊C4—82no—
602C22⋊C4—82no—
603C42—28no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—82no—
616C42—82no—
617C42—82no—
618C42—82no—
619C42—82no—
620C42—82no—
621C42—82no—
622C42C4×D414yes—
623C42C4×D414yes—
624C42#13714yes—
625C42C23×C412yes—
626C42C23×C412yes—
627C42C2×#4112yes—
628C42C2×#4112yes—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—24no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23C2×C4×D412yes—
643C23C23×D411yescharacteristic
644Q8—28no—
645Q8—28no—
646Q8—48no—
647Q8—44no—
648Q8—44no—
649D4—28no—
650D4—48no—
651D4—48no—
652D4—44no—
653D4—88no—
654C2×C4—21no—
655C2×C4—21no—
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—24no—
665C2×C4—28no—
666C2×C4—28no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
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—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—42no—
690C2×C4—42no—
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—88no—
708C2×C4—164no—
709C2×C4—164no—
710C2×C4—164no—
711C2×C4C2×C4×D412yes—
712C2×C4C2×C4×D412yes—
713C2×C4C2×C4×D412yes—
714C2×C4C2×C4×D412yes—
715C2×C4C2×C4×D412yes—
716C2×C4C2×#13712yes—
717C2×C4C2×#13712yes—
718C2×C4C2×#13712yes—
719C2×C4#57512yes—
720C2×C4#57612yes—
721C2×C4#57812yes—
722C2×C4C24×C411yescharacteristic
723C2×C4C22×#4111yescharacteristic
724C2×C4C2×H(5,𝔽2)12yes—
725C2×C4#58512yes—
726C8—24no—
727C8—24no—
728C8—24no—
729C8—42no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22C22×C4×D411yescharacteristic
745C22#349811yescharacteristic
746C22#350011yescharacteristic
747C22C22×#13711yescharacteristic
748C22C2×#57511yescharacteristic
749C22C2×#57611yescharacteristic
750C22C2×#57811yescharacteristic
751C4—22no—
752C4—22no—
753C4—22no—
754C4—22no—
755C4—22no—
756C4—44no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—44no—
764C4—44no—
765C4—82no—
766C4—82no—
767C4—82no—
768C4—82no—
769C4C4×#13714yes—
770C4#295114yes—
771C4C4×H(5,𝔽2)12yes—
772C4#349412yes—
773C2—42no—
774C2—84no—
775C2#3427511yescharacteristic
776C2C2×C4×#13711yescharacteristic
777C2C2×#295111yescharacteristic
778C2#6242411yescharacteristic
779C2#6242611yescharacteristic
780C2#6253711yescharacteristic
781C2#6254511yescharacteristic
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. #34214C2semidirect
4. #23111C2semidirect
5. #23009C2semidirect
6. #22879C2semidirect
7. #22862C2semidirect
8. #22270C2semidirect
9. #22268C2semidirect
10. #22221C2semidirect
11. #22220C2semidirect
12. #21982C2semidirect
13. #21692C2semidirect
14. C4×#494C2semidirect
15. #21647C2semidirect
16. C4×#486C2semidirect
17. #21409C2semidirect
19. #20472C2semidirect
22. #3210C4semidirect
113. #533C2×C4semidirect
150. #494C2×C4semidirect
151. #492C2×C4semidirect
152. #487C2×C4semidirect
153. #486C2×C4semidirect
154. #464C2×C4semidirect
155. #452C2×C4semidirect
158. #431C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32102
#342262
#342142
#231112
#230092
#228792
#228622
#222702
#222682
#222212
#222202
#219822
#216922
C4×#4942
#216472
C4×#4862
#214092
#212002
#204722