Finite Group Databasebeta

← #6467749

Subgroups — #6467749

Order 512.

2046 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3185C211yesmaximal, characteristic, complemented
2C2×#3182C211yesmaximal, characteristic
3#36639C211yesmaximal, characteristic
4C4×#533C211yesmaximal, characteristic, complemented
5#28750C211yesmaximal, characteristic, complemented
6#28719C211yesmaximal, characteristic, complemented
7#28688C211yesmaximal, characteristic, complemented
8#28656C211yesmaximal, characteristic, complemented
9#28654C211yesmaximal, characteristic, complemented
10#28616C211yesmaximal, characteristic, complemented
11#28614C211yesmaximal, characteristic, complemented
12#28582C214yesmaximal, complemented
13#28444C211yesmaximal, characteristic, complemented
14#24757C214yesmaximal, complemented
15#23687C214yesmaximal, complemented
16#21508C214yesmaximal, complemented
17#21410C211yesmaximal, characteristic
18#21409C211yesmaximal, characteristic, complemented
19C4×#423C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23#3185—28no—
24#3182—28no—
25C2×#500C2211yescharacteristic
26C2×#498C2211yescharacteristic
27C2×#494C2211yescharacteristic
28C2×#492C2211yescharacteristic
29C2×#487C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#486C2211yescharacteristic
33C2×#470C2214yes—
34C2×#468C2214yes—
35C2×#464C2214yes—
36C2×#441C2214yes—
37C2×#440C2214yes—
38C2×#423C2212yes—
39C2×C4×M16C2211yescharacteristic
40C2×C4×M16C2211yescharacteristic
41#2862C2211yescharacteristic
42#2862C2211yescharacteristic
43#2861—21no—
44#2861—21no—
45#2858C2211yescharacteristic
46#2858C2211yescharacteristic
47#2850—21no—
48#2850—21no—
49#2850C2212yes—
50#2850C2212yes—
51C4×C4⋊Q8C2211yescharacteristic
52C4×C4⋊Q8C2211yescharacteristic
53C4×C4⋊Q8C2211yescharacteristic
54C4×C4⋊Q8C2211yescharacteristic
55C4×#125—21no—
56C4×#125—21no—
57C4×#124—21no—
58C4×#124—21no—
59C4×#124C2212yes—
60C4×#124C2212yes—
61C4×C22⋊Q8—21no—
62C4×C22⋊Q8—21no—
63C4×C22⋊Q8C2212yes—
64C4×C22⋊Q8C2212yes—
65#2297—21no—
66#2297—21no—
67#2296—21no—
68#2295—21no—
69#2295C2212yes—
70#2285C2211yescharacteristic
71C42×Q8—21no—
72C42×Q8C2212yes—
73C4×#117—21no—
74C2×C43C2211yescharacteristic
75#2085C2214yes—
76#2074C2214yes—
77#2068C2214yes—
78#2065C2214yes—
79#2056C2214yes—
80#2055C2214yes—
81#2042C2214yes—
82#2015C2214yes—
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1983C2214yes—
88#1957C2211yescharacteristic
89#1957C2211yescharacteristic
90#1956C2211yescharacteristic
91#1956C2211yescharacteristic
92#1949C2214yes—
93#1928C2214yes—
94#1926C2214yes—
95#1895C2214yes—
96#1894C2214yes—
97#1880C2214yes—
98#1878C2214yes—
99#1805C2214yes—
100#1767C2212yes—
101#1767C2212yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×C4⋊C8C2211yescharacteristic
104C4×C4⋊C8C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106#1763C2214yes—
107#1762C2214yes—
108#1728C2212yes—
109C22×#41—21no—
110C22×Q16C2314yes—
111C22×SD16C2314yes—
112C22×M16C2312yes—
113C22×M16C2312yes—
114#533—24no—
115#533—24no—
116#533—24no—
117#533D418yes—
118#532—24no—
119#532—24no—
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×#127C2311yescharacteristic
126C2×#125—21no—
127C2×#125—21no—
128C2×#124—21no—
129C2×#124—21no—
130C2×#124—21no—
131C2×#124C2312yes—
132C2×#124C2312yes—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8C2312yes—
136C2×C22⋊Q8C2312yes—
137C2×#121—21no—
138C2×#121C2312yes—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8C2312yes—
144C2×C4×Q8C2312yes—
145C2×C4×Q8C2312yes—
146C2×C4×Q8C2312yes—
147C2×C4×D4—21no—
148C2×C4×D4C2312yes—
149C2×#117—21no—
150C2×#117—21no—
151C2×#117—21no—
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159#500—24no—
160#498—24no—
161#494—24no—
162#492—24no—
163#487—24no—
164#487—24no—
165#487—24no—
166#486—24no—
167#470—216no—
168#468—216no—
169#464—216no—
170#441—216no—
171#440—216no—
172C2×#107C2314yes—
173C2×#106C2314yes—
174#423—28no—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C4×M16—24no—
188C4×M16—24no—
189C2×#97C2312yes—
190C2×#97C2312yes—
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2311yescharacteristic
194C2×C4×C8C2311yescharacteristic
195#391—21no—
196#391—21no—
197#391—21no—
198#391—21no—
199#391—21no—
200#391—21no—
201#391—21no—
202#391—21no—
203#391C2312yes—
204#391C2312yes—
205#391C2312yes—
206#391C2312yes—
207#390—21no—
208#390—21no—
209#390—21no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390C2312yes—
214#390C2312yes—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389C2312yes—
222#389C2312yes—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#387—22no—
232#387—22no—
233#387—22no—
234#387—22no—
235#386—22no—
236#386—22no—
237#386—22no—
238#386—22no—
239#385—22no—
240#385—22no—
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#382—21no—
244#382—21no—
245#382—21no—
246#382C2312yes—
247#382C2312yes—
248#380—21no—
249#380C2312yes—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4—22no—
256C4×C4⋊C4—22no—
257C4×C4⋊C4—22no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4—22no—
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2312yes—
265C4×C4⋊C4C2312yes—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268C4×C22⋊C4—22no—
269C4×C22⋊C4—22no—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272#376—22no—
273C43—22no—
274C43D411yescharacteristic
275C43D411yescharacteristic
276C43D411yescharacteristic
277C43D411yescharacteristic
278C43C2311yescharacteristic
279C43C2311yescharacteristic
280C43C2311yescharacteristic
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290C2×#41—44no—
291C2×#41—44no—
292C2×#41—44no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8C2412yes—
297C22×Q8C2412yes—
298C22×D4—22no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4C2412yes—
302C23×C4—22no—
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2411yescharacteristic
310C2×Q16—28no—
311C2×Q16—28no—
312C2×Q16—44no—
313C2×SD16—28no—
314C2×SD16—28no—
315C2×SD16—44no—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—42no—
321C2×M16—42no—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8C2×D414yes—
335C4⋊Q8C2×D414yes—
336#127—22no—
337#127—22no—
338#125—28no—
339#125—44no—
340#124—28no—
341#124—44no—
342#124—44no—
343#124—44no—
344#124—44no—
345C22⋊Q8—28no—
346C22⋊Q8—24no—
347C22⋊Q8—24no—
348C22⋊Q8—24no—
349C22⋊Q8—44no—
350C22⋊Q8C2×D418yes—
351#121—24no—
352#121—24no—
353#121—44no—
354C4×Q8—28no—
355C4×Q8—24no—
356C4×Q8—24no—
357C4×Q8—24no—
358C4×Q8—28no—
359C4×Q8—44no—
360C4×Q8—44no—
361C4×Q8—44no—
362C4×Q8—44no—
363C4×Q8C2×D418yes—
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—44no—
367#117—28no—
368#117—44no—
369#117—44no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
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⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
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×C42C2×D411yescharacteristic
441C2×C42C2×D414yes—
442C2×C42C2×D411yescharacteristic
443C2×C42#4114yes—
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450#107—28no—
451#106—28no—
452C4⋊C8—24no—
453C4⋊C8—24no—
454C4⋊C8—24no—
455C4⋊C8#4118yescomplemented
456#103—28no—
457#103—28no—
458#103—28no—
459#103—28no—
460#103—44no—
461#102—28no—
462#102—28no—
463#102—44no—
464#97—24no—
465#97—24no—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8—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#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488C24—22no—
489C24C22×D411yescharacteristic
490#41—816no—
491C2×Q8—24no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—24no—
495C2×Q8—24no—
496C2×Q8—22no—
497C2×Q8—24no—
498C2×Q8—24no—
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×Q8C22×D414yes—
508C2×D4—22no—
509C2×D4—24no—
510C2×D4—22no—
511C2×D4—24no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
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—22no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4#12114yes—
550C22×C4#12114yes—
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D412yes—
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C2×#4112yes—
566C22×C4C2511yescharacteristic
567Q16—416no—
568SD16—416no—
569M16—48no—
570M16—48no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8C2×#4114yes—
582C2×C8C2×#4114yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—28no—
587C4⋊C4—28no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—44no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4C22×D414yes—
610C22⋊C4—28no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C42—28no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—44no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—44no—
652C42#12114yes—
653C42#12114yes—
654C42#13714yes—
655C42C22×D412yes—
656C42C22×D412yes—
657C42C2×#4112yes—
658C42C2×#4112yes—
659C42C2×#4114yes—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23C2×#12112yes—
674C23C23×D411yescharacteristic
675Q8—28no—
676Q8—44no—
677Q8—48no—
678Q8—44no—
679Q8—44no—
680Q8—84no—
681Q8—84no—
682D4—44no—
683D4—44no—
684D4—88no—
685D4—84no—
686D4—84no—
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—24no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—24no—
706C2×C4—24no—
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—21no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
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—88no—
743C2×C4C2×#12112yes—
744C2×C4C2×#12112yes—
745C2×C4C2×#12112yes—
746C2×C4C2×#12112yes—
747C2×C4C2×#12112yes—
748C2×C4#53212yes—
749C2×C4#53212yes—
750C2×C4C2×#13712yes—
751C2×C4C2×#13712yes—
752C2×C4C2×#13712yes—
753C2×C4#57512yes—
754C2×C4#57512yes—
755C2×C4#57512yes—
756C2×C4C23×D411yescharacteristic
757C2×C4C22×#4112yes—
758C2×C4C22×#4111yescharacteristic
759C2×C4#58512yes—
760C8—24no—
761C8—24no—
762C8—42no—
763C8—42no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22C22×#12111yescharacteristic
779C22C2×#53211yescharacteristic
780C22#344911yescharacteristic
781C22C22×#13711yescharacteristic
782C22C2×#57511yescharacteristic
783C22C2×#57511yescharacteristic
784C22C2×#57511yescharacteristic
785C4—22no—
786C4—22no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—44no—
797C4—44no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4#303714yes—
804C4#304014yes—
805C4D4×#4112yes—
806C4#348012yes—
807C2—42no—
808C2—162no—
809C2#3493711yescharacteristic
810C2C2×#303711yescharacteristic
811C2C2×#304011yescharacteristic
812C2#6069311yescharacteristic
813C2#6070111yescharacteristic
814C2#6096611yescharacteristic
815C2#6097211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3185C2semidirect
4. C4×#533C2semidirect
5. #28750C2semidirect
6. #28719C2semidirect
7. #28688C2semidirect
8. #28656C2semidirect
9. #28654C2semidirect
10. #28616C2semidirect
11. #28614C2semidirect
12. #28582C2semidirect
13. #28444C2semidirect
14. #24757C2semidirect
15. #23687C2semidirect
16. #21508C2semidirect
18. #21409C2semidirect
19. C4×#423C2semidirect
455. C4⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#31852
C2×#31822
#366392
C4×#5332
#287502
#287192
#286882
#286562
#286542
#286162
#286142
#285822
#284442
#247572
#236872
#215082
#214102
#214092
C4×#4232