Finite Group Databasebeta

← #6444010

Subgroups — #6444010

Order 512.

2336 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3093C212yesmaximal, complemented
2#34935C211yesmaximal, characteristic
3C2×#2354C211yesmaximal, characteristic, complemented
4#25025C214yesmaximal, complemented
5#25023C214yesmaximal, complemented
6#25017C212yesmaximal, complemented
7#25015C212yesmaximal, complemented
8#25013C212yesmaximal, complemented
9#25011C212yesmaximal, complemented
10#23642C212yesmaximal, complemented
11#23482C212yesmaximal, complemented
12#21190C211yesmaximal, characteristic, complemented
13#21170C211yesmaximal, characteristic, complemented
14#20845C212yesmaximal, complemented
15#20800C211yesmaximal, characteristic, complemented
16#20648C211yesmaximal, characteristic, complemented
17C4×#417C211yesmaximal, characteristic, complemented
18C2×#525C2212yes—
19C2×C4×#41C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×#117C2212yes—
22#3093—216no—
23C2×#485C2214yescomplemented
24C2×#485C2214yescomplemented
25C2×#482C2214yescomplemented
26C2×#482C2214yescomplemented
27C2×#428C2212yes—
28C2×#428C2212yes—
29C2×#428C2212yes—
30C2×#423C2211yescharacteristic
31C2×#417C2212yes—
32C2×#417C2211yescharacteristic
33C2×#417C2211yescharacteristic
34C2×#407C2212yes—
35C2×#407C2212yes—
36C2×C4×M16C2211yescharacteristic
37#2538C2211yescharacteristic
38#2538C2211yescharacteristic
39#2537C2211yescharacteristic
40#2537C2211yescharacteristic
41#2536C2212yes—
42#2535C2212yes—
43#2534—22no—
44#2486—21no—
45#2408—21no—
46#2392—22no—
47#2354—22no—
48#2354—21no—
49#2354—21no—
50#2354C2212yes—
51#2354C2212yes—
52#2354C2214yes—
53C4×#121—21no—
54C4×#121—21no—
55C2×#390—21no—
56C2×#388—22no—
57#2285C2211yescharacteristic
58C2×#384C2211yescharacteristic
59#2280C2212yes—
60C2×#380C2212yes—
61C2×C4×C4⋊C4—21no—
62C2×C4×C4⋊C4C2211yescharacteristic
63#2077C2214yescomplemented
64#2077C2214yescomplemented
65#2076C2214yescomplemented
66#2075C2214yescomplemented
67#2036C2214yescomplemented
68#2035C2214yescomplemented
69#2034C2214yescomplemented
70#2033C2214yescomplemented
71#1955C2214yes—
72#1954C2212yes—
73#1954C2212yes—
74#1949C2214yescomplemented
75#1948C2212yescomplemented
76#1947C2212yescomplemented
77#1854C2214yescomplemented
78#1854C2214yescomplemented
79#1854C2214yescomplemented
80#1854C2214yescomplemented
81#1847C2214yescomplemented
82#1845C2212yescomplemented
83#1844C2212yescomplemented
84#1803C2212yescomplemented
85#1803C2212yescomplemented
86#1802C2212yescomplemented
87#1802C2212yescomplemented
88#1763C2212yescomplemented
89#1762C2212yescomplemented
90C4×#103C2212yescomplemented
91C4×#102C2212yescomplemented
92#1736C2211yescharacteristic
93#1736C2212yes—
94#1736C2212yes—
95#1736C2211yescharacteristic
96C22×#41C2311yescharacteristic
97C23×D4D411yescharacteristic
98C24×C4C2312yes—
99C22×M16C2312yes—
100C22×M16C2311yescharacteristic
101C22×M16C2311yescharacteristic
102#525—28no—
103#525—44no—
104C2×#123—22no—
105C2×C22⋊Q8C2312yes—
106C2×C22⋊Q8C2312yes—
107C2×#121—21no—
108C2×#121—21no—
109C2×#121C2312yes—
110C2×#121C2312yes—
111C2×#120—22no—
112C4×#41—24no—
113C4×#41—24no—
114C2×C4×Q8C2311yescharacteristic
115C2×C4×Q8C2311yescharacteristic
116C2×C4×D4—22no—
117C2×C4×D4—22no—
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4—24no—
121C2×C4×D4—24no—
122C2×C4×D4D412yes—
123C2×C4×D4D411yescharacteristic
124C2×C4×D4D411yescharacteristic
125C2×C4×D4C2311yescharacteristic
126C2×C4×D4C2311yescharacteristic
127C2×C4×D4C2311yescharacteristic
128C2×C4×D4C2311yescharacteristic
129C2×C4×D4C2312yes—
130C2×#117—22no—
131C2×#117—22no—
132C2×#117—21no—
133C2×#117—28no—
134C2×#117—44no—
135C2×#117C2312yes—
136C2×#117C2311yescharacteristic
137C2×#117C2314yes—
138C2×#117C2314yes—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4D411yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C22⋊C4—22no—
146C22×C22⋊C4—22no—
147C22×C22⋊C4D412yes—
148C22×C42—22no—
149C22×C42—21no—
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152#485—216no—
153#485—216no—
154#482—216no—
155#482—216no—
156#428—28no—
157#428—28no—
158#428—44no—
159C2×#107C2314yes—
160C2×#107C2314yes—
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×#106C2314yes—
164C2×#106C2314yes—
165#423—24no—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168#417—28no—
169#417—24no—
170#417D418yescomplemented
171C2×#103C2314yes—
172C2×#103C2312yes—
173C2×#103C2312yes—
174C2×#102C2314yes—
175C2×#102C2312yes—
176C2×#102C2312yes—
177#407—28no—
178#407—28no—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2314yes—
181C2×C22⋊C8C2314yes—
182C2×C22⋊C8C2314yes—
183C4×M16—24no—
184C2×#97C2312yes—
185C2×C4×C8C2312yes—
186#398—22no—
187#397—22no—
188#396—22no—
189#396—22no—
190#394—22no—
191#394—22no—
192#394—22no—
193#392—22no—
194#390—22no—
195#390—22no—
196#390—24no—
197#390—21no—
198#390—21no—
199#389—21no—
200#389—21no—
201#388—24no—
202#388—24no—
203#388—24no—
204#388—24no—
205#388—22no—
206#388—22no—
207#386—22no—
208#386—22no—
209#384—21no—
210#384—21no—
211#384C2312yes—
212#384C2312yes—
213#384C2311yescharacteristic
214#384C2311yescharacteristic
215#382C2312yes—
216#381—22no—
217#380—22no—
218#380—22no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380C2312yes—
224#380C2314yes—
225#380C2312yes—
226#380C2314yes—
227#380C2312yes—
228#380C2312yes—
229#379—22no—
230C4×C4⋊C4—22no—
231C4×C4⋊C4—22no—
232C4×C4⋊C4—24no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C2×#95—22no—
242C2×#95—21no—
243#340C2314yes—
244#340C2314yes—
245#340C2312yes—
246#340C2314yes—
247#340C2312yes—
248#340C2314yes—
249#340C2312yes—
250#340C2312yes—
251C25C2×D412yes—
252C2×#41—22no—
253C2×#41—22no—
254C2×#41—22no—
255C2×#41—22no—
256C2×#41—22no—
257C2×#41C2×D414yes—
258C22×Q8C2411yescharacteristic
259C22×D4—21no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—24no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4C2×D411yescharacteristic
266C22×D4C2×D411yescharacteristic
267C22×D4C2×D412yes—
268C22×D4C2411yescharacteristic
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—21no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4C2×D412yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—24no—
294C2×M16—24no—
295C2×M16—24no—
296C2×M16C2×D414yes—
297C2×M16#4114yes—
298C22×C8C2414yes—
299C22×C8C2412yes—
300C22×C8C2412yes—
301#123—48no—
302C22⋊Q8—24no—
303C22⋊Q8—24no—
304C22⋊Q8—42no—
305C22⋊Q8—42no—
306#121—24no—
307#121—24no—
308#121—42no—
309#121—42no—
310#121—44no—
311#121—44no—
312#120—48no—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×D4—24no—
318C4×D4—24no—
319C4×D4—28no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—24no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—24no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—48no—
331C4×D4—48no—
332C4×D4—44no—
333C4×D4—44no—
334#117—24no—
335#117—22no—
336#117—22no—
337#117—24no—
338#117—28no—
339#117—28no—
340#117—44no—
341#117—44no—
342#117—48no—
343#117—48no—
344#117—44no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—82no—
368C2×C4⋊C4C2×D411yescharacteristic
369C2×C4⋊C4C2×D411yescharacteristic
370C2×C4⋊C4C2×D412yes—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4C2414yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2411yescharacteristic
375C2×C4⋊C4C2411yescharacteristic
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—48no—
397C2×C22⋊C4—84no—
398C2×C22⋊C4C2×D412yes—
399C2×C22⋊C4C2×D412yes—
400C2×C22⋊C4C2×D412yes—
401C2×C22⋊C4C2×D412yes—
402C2×C42—21no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—48no—
411C2×C42—44no—
412C2×C42—44no—
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42#4114yes—
416C2×C42#4114yes—
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419#107—28no—
420#107—28no—
421#107—44no—
422#106—28no—
423#106—28no—
424#106—44no—
425C4⋊C8—24no—
426C4⋊C8—24no—
427#103—28no—
428#103—24no—
429#103C2×D418yescomplemented
430#102—28no—
431#102—24no—
432#102C2×D418yescomplemented
433C22⋊C8—28no—
434C22⋊C8—28no—
435C22⋊C8—28no—
436C22⋊C8—28no—
437#97—24no—
438C4×C8—24no—
439#95—24no—
440#95—24no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449C24—24no—
450C24—21no—
451C24—24no—
452C24—24no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24C22×D412yes—
458C24C22×D412yes—
459C24C22×D411yescharacteristic
460#41—28no—
461#41—28no—
462#41—44no—
463#41—44no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8C22×D412yes—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—416no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—82no—
493C2×D4—82no—
494C2×D4C22×D412yes—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
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—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—42no—
537C22×C4—48no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4#12314yes—
551C22×C4#12314yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D412yes—
560C22×C4C2×#4112yes—
561C22×C4C2×#4112yes—
562C22×C4C2×#4112yes—
563C22×C4H(5,𝔽2)12yes—
564C22×C42−1+412yes—
565C22×C4C2511yescharacteristic
566M16—28no—
567M16—28no—
568M16—48no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—24no—
576C2×C8C22×D414yes—
577C2×C8C2×#4114yes—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—44no—
601C4⋊C4—42no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—81no—
606C4⋊C4—81no—
607C4⋊C4—82no—
608C4⋊C4—82no—
609C4⋊C4C22×D414yes—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—24no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—82no—
627C22⋊C4—82no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C42—48no—
631C42—48no—
632C42—44no—
633C42—42no—
634C42—42no—
635C42—42no—
636C42—44no—
637C42—44no—
638C42#12314yes—
639C42#12314yes—
640C42C2×#4112yes—
641C42C2×#4112yes—
642C42C2×#4112yes—
643C42C2×#4112yes—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—48no—
664C23—48no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—48no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23C2×#12312yes—
677C23D4212yes—
678C23#54712yes—
679C23C23×D411yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—41no—
683Q8—41no—
684D4—22no—
685D4—22no—
686D4—48no—
687D4—48no—
688D4—44no—
689D4—44no—
690D4—41no—
691D4—41no—
692D4—88no—
693D4—88no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—44no—
710C2×C4—48no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—48no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—48no—
719C2×C4—48no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4—88no—
748C2×C4—84no—
749C2×C4C2×#12312yes—
750C2×C4C2×#12312yes—
751C2×C4C2×#12312yes—
752C2×C4C2×#12312yes—
753C2×C4C2×#12312yes—
754C2×C4#53214yes—
755C2×C4#54214yes—
756C2×C4D4212yes—
757C2×C4#54712yes—
758C2×C4#54714yes—
759C2×C4#55314yes—
760C2×C4#57512yes—
761C2×C4#57512yes—
762C2×C4C23×D411yescharacteristic
763C2×C4C22×#4111yescharacteristic
764C2×C4C22×#4111yescharacteristic
765C2×C4C22×#4111yescharacteristic
766C2×C4C2×H(5,𝔽2)11yescharacteristic
767C2×C4C2×2−1+411yescharacteristic
768C8—24no—
769C8—24no—
770C8—44no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—816no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22#242214yes—
800C22C22×#12311yescharacteristic
801C22C2×D4211yescharacteristic
802C22C2×#54711yescharacteristic
803C22C2×#57511yescharacteristic
804C22C2×#57511yescharacteristic
805C22#358511yescharacteristic
806C22#358611yescharacteristic
807C4—22no—
808C4—22no—
809C4—22no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—44no—
814C4—82no—
815C4—81no—
816C4—81no—
817C4—82no—
818C4—84no—
819C4—82no—
820C4#242214yes—
821C4#309314yescomplemented
822C4C2×#53211yescharacteristic
823C4C2×#54211yescharacteristic
824C4C2×#54711yescharacteristic
825C4C2×#55311yescharacteristic
826C2—24no—
827C2—82no—
828C2—82no—
829C2—82no—
830C2C2×#242211yescharacteristic
831C2C2×#309311yescharacteristic
832C2#6051711yescharacteristic
833C2#6106711yescharacteristic
834C2#6107011yescharacteristic
835C2#6125611yescharacteristic
836C2#6125711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34935C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3093C2semidirect
3. C2×#2354C2semidirect
4. #25025C2semidirect
5. #25023C2semidirect
6. #25017C2semidirect
7. #25015C2semidirect
8. #25013C2semidirect
9. #25011C2semidirect
10. #23642C2semidirect
11. #23482C2semidirect
12. #21190C2semidirect
13. #21170C2semidirect
14. #20845C2semidirect
15. #20800C2semidirect
16. #20648C2semidirect
17. C4×#417C2semidirect
23. C2×#485C22semidirect
24. C2×#485C22semidirect
25. C2×#482C22semidirect
26. C2×#482C22semidirect
63. #2077C22semidirect
64. #2077C22semidirect
65. #2076C22semidirect
66. #2075C22semidirect
67. #2036C22semidirect
68. #2035C22semidirect
69. #2034C22semidirect
70. #2033C22semidirect
74. #1949C22semidirect
75. #1948C22semidirect
76. #1947C22semidirect
77. #1854C22semidirect
78. #1854C22semidirect
79. #1854C22semidirect
80. #1854C22semidirect
81. #1847C22semidirect
82. #1845C22semidirect
83. #1844C22semidirect
84. #1803C22semidirect
85. #1803C22semidirect
86. #1802C22semidirect
87. #1802C22semidirect
88. #1763C22semidirect
89. #1762C22semidirect
90. C4×#103C22semidirect
91. C4×#102C22semidirect
170. #417D4semidirect
429. #103C2×D4semidirect
432. #102C2×D4semidirect
821. C4#3093semidirect

Maximal subgroups

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

subgroupindex
C2×#30932
#349352
C2×#23542
#250252
#250232
#250172
#250152
#250132
#250112
#236422
#234822
#211902
#211702
#208452
#208002
#206482
C4×#4172