Finite Group Databasebeta

← #6629604

Subgroups — #6629604

Order 512.

1847 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35313C211yesmaximal, characteristic
2C4×#519C211yesmaximal, characteristic
3#33093C212yesmaximal, complemented
4#33091C212yesmaximal, complemented
5#33091C212yesmaximal, complemented
6#33091C212yesmaximal, complemented
7#33085C212yesmaximal, complemented
8#33085C212yesmaximal, complemented
9#33085C212yesmaximal, complemented
10#33083C212yesmaximal, complemented
11#21066C211yesmaximal, characteristic
12#21064C211yesmaximal, characteristic
13#21061C211yesmaximal, characteristic
14#21036C211yesmaximal, characteristic
15#21035C211yesmaximal, characteristic
16#21032C211yesmaximal, characteristic
17#20935C211yesmaximal, characteristic
18#20935C211yesmaximal, characteristic
19C2×#1878C211yesmaximal, characteristic
20#20880C211yesmaximal, characteristic
21#20877C211yesmaximal, characteristic
22#20874C211yesmaximal, characteristic
23#20774C211yesmaximal, characteristic
24C23×Q16C2211yescharacteristic
25C2×#519C2211yescharacteristic
26C2×#519C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#428C2211yescharacteristic
30C2×#427C2211yescharacteristic
31C2×#419C2211yescharacteristic
32C2×#419C2211yescharacteristic
33C2×#419C2211yescharacteristic
34C2×#419C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37#2863C2212yes—
38#2863C2212yes—
39#2645C2212yes—
40#2645C2212yes—
41#2514—21no—
42#2514—21no—
43#2511—21no—
44#2511—21no—
45#2493—22no—
46#2493—22no—
47#2317C2211yescharacteristic
48#2316C2211yescharacteristic
49#2310C2211yescharacteristic
50#2310C2211yescharacteristic
51#2296C2211yescharacteristic
52C2×#391C2211yescharacteristic
53#2276—21no—
54#2276—21no—
55#2276C2212yes—
56#2276C2212yes—
57#2274—22no—
58#2274C2211yescharacteristic
59#2274C2211yescharacteristic
60C42×Q8—21no—
61C42×Q8—21no—
62C42×Q8C2212yes—
63C42×Q8C2212yes—
64C4×#117—22no—
65C4×#117C2211yescharacteristic
66C4×#117C2211yescharacteristic
67#1928C2212yes—
68#1928C2212yes—
69#1928C2212yes—
70#1928C2212yes—
71#1928C2212yes—
72#1928C2212yes—
73#1927C2212yes—
74#1927C2212yes—
75#1927C2212yes—
76#1927C2212yes—
77#1927C2212yes—
78#1927C2212yes—
79#1921C2211yescharacteristic
80#1921C2211yescharacteristic
81#1921C2212yes—
82#1921C2212yes—
83#1920C2211yescharacteristic
84#1920C2211yescharacteristic
85#1920C2212yes—
86#1920C2212yes—
87#1919C2211yescharacteristic
88#1919C2211yescharacteristic
89#1919C2212yes—
90#1919C2212yes—
91#1918C2211yescharacteristic
92#1918C2211yescharacteristic
93#1918C2212yes—
94#1918C2212yes—
95#1878C2212yes—
96#1878C2212yes—
97#1878C2212yes—
98#1878C2212yes—
99#1878C2212yes—
100#1878C2212yes—
101#1878C2212yes—
102#1878C2212yes—
103#1878C2212yes—
104#1878C2212yes—
105#1878C2212yes—
106#1878C2212yes—
107#1865C2212yes—
108#1865C2212yes—
109#1865C2212yes—
110#1865C2212yes—
111#1865C2212yes—
112#1865C2212yes—
113#1863C2212yes—
114#1863C2212yes—
115#1863C2212yes—
116#1863C2212yes—
117#1863C2212yes—
118#1863C2212yes—
119#1840C2212yes—
120#1840C2212yes—
121#1839C2212yes—
122#1839C2212yes—
123#1736C2211yescharacteristic
124#1736C2211yescharacteristic
125#1735C2211yescharacteristic
126#1735C2211yescharacteristic
127#1735C2211yescharacteristic
128C2×#340C2211yescharacteristic
129#1729C2211yescharacteristic
130#1729C2211yescharacteristic
131#1729C2211yescharacteristic
132#1729C2211yescharacteristic
133#1728C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C23×Q8C2311yescharacteristic
136C23×Q8C2311yescharacteristic
137C22×Q16—24no—
138C22×Q16—24no—
139C22×Q16—24no—
140C22×Q16C2312yes—
141C22×Q16C2312yes—
142C22×M16C2311yescharacteristic
143C22×M16C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C23×C8C2311yescharacteristic
146#519—24no—
147#519—24no—
148#519—24no—
149#519—24no—
150C2×C4×Q8—24no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—24no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2312yes—
162C2×C4×Q8C2312yes—
163C2×C4×Q8C2312yes—
164C2×#117—22no—
165C2×#117—22no—
166C2×#117C2311yescharacteristic
167C2×#117C2311yescharacteristic
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C22×C4⋊C4—21no—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C42—21no—
176C22×C42C2311yescharacteristic
177#428—24no—
178#428—24no—
179#427—24no—
180C2×#107C2311yescharacteristic
181C2×#107C2311yescharacteristic
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#106C2311yescharacteristic
185C2×#106C2311yescharacteristic
186C2×#106C2312yes—
187C2×#106C2312yes—
188#419—24no—
189#419—24no—
190#419—24no—
191#419—24no—
192C2×#103—24no—
193C2×#103—24no—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206#401—22no—
207#401—22no—
208#400—22no—
209#400—22no—
210#400—22no—
211#400—22no—
212#400—22no—
213#400—22no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391C2312yes—
221#391C2312yes—
222#391C2312yes—
223#391C2312yes—
224#391C2312yes—
225#391C2312yes—
226#389—21no—
227#389—21no—
228#389C2312yes—
229#389C2312yes—
230#389C2312yes—
231#389C2312yes—
232#389C2311yescharacteristic
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#387—22no—
237#387—22no—
238#387—22no—
239#387—22no—
240#387—22no—
241#387—22no—
242#385—21no—
243#385—21no—
244#385—22no—
245#384—21no—
246#383—22no—
247#383—22no—
248#382—21no—
249#381—22no—
250#381—22no—
251#380—22no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—22no—
259C4×C4⋊C4—22no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4—22no—
263C4×C4⋊C4—22no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4—22no—
266C4×C4⋊C4—22no—
267C4×C4⋊C4—22no—
268C4×C4⋊C4—22no—
269C4×C4⋊C4—22no—
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4D411yescharacteristic
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2311yescharacteristic
276C4×C4⋊C4C2311yescharacteristic
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2312yes—
282C4×C22⋊C4—21no—
283C4×C22⋊C4—21no—
284C4×C22⋊C4—22no—
285C4×C22⋊C4—22no—
286C4×C22⋊C4D412yes—
287C4×C22⋊C4D412yes—
288#376—21no—
289#376—22no—
290#376—22no—
291#376C2312yes—
292C2×#95—21no—
293C2×#95—21no—
294C43—22no—
295C43—22no—
296C43—21no—
297C43C2312yes—
298#340C2311yescharacteristic
299#340C2311yescharacteristic
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#336C2312yes—
317#336C2311yescharacteristic
318#336C2311yescharacteristic
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2312yes—
323#336C2312yes—
324#336C2312yes—
325#336C2312yes—
326#336C2312yes—
327#336C2312yes—
328#336C2311yescharacteristic
329#336C2311yescharacteristic
330C22×Q8—21no—
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8#4114yes—
342C22×Q8#4114yes—
343C22×Q8#4114yes—
344C22×Q8C2412yes—
345C22×Q8C2412yes—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4C2×D411yescharacteristic
351C23×C4C2×D411yescharacteristic
352C23×C4C2411yescharacteristic
353C2×Q16—24no—
354C2×Q16—24no—
355C2×Q16—24no—
356C2×Q16—24no—
357C2×Q16—24no—
358C2×Q16—24no—
359C2×Q16—416no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8C2411yescharacteristic
373C22×C8C2411yescharacteristic
374C22×C8C2411yescharacteristic
375C22×C8C2411yescharacteristic
376C22×C8C2412yes—
377C22×C8C2412yes—
378C4×Q8—28no—
379C4×Q8—28no—
380C4×Q8—28no—
381C4×Q8—28no—
382C4×Q8—28no—
383C4×Q8—28no—
384C4×Q8—24no—
385C4×Q8—24no—
386C4×Q8—24no—
387C4×Q8—24no—
388C4×Q8—24no—
389C4×Q8—24no—
390C4×Q8—24no—
391C4×Q8—24no—
392C4×Q8—24no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—24no—
396#117—216no—
397#117—216no—
398#117—22no—
399#117—22no—
400#117—22no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—22no—
406#117—22no—
407#117—22no—
408#117#4114yes—
409#117#4114yes—
410C2×C4⋊C4—28no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4#4114yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4C2×D412yes—
450C2×C22⋊C4C2×D412yes—
451C2×C42—28no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D412yes—
475C2×C42C2×D412yes—
476C2×C42C2×D412yes—
477C2×C42C2×D412yes—
478C2×C42C2412yes—
479C2×C42C2412yes—
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482#107—22no—
483#107—22no—
484#107—24no—
485#107—24no—
486#106—22no—
487#106—22no—
488#106—24no—
489#106—24no—
490#103—24no—
491#103—24no—
492#103—24no—
493#103—24no—
494#103—24no—
495#103—24no—
496#103—24no—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—24no—
501#103—24no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95C2×D412yes—
531#95C2×D412yes—
532#95C2×D412yes—
533#95C2×D412yes—
534C24C22×D411yescharacteristic
535C2×Q8—24no—
536C2×Q8—24no—
537C2×Q8—24no—
538C2×Q8—28no—
539C2×Q8—28no—
540C2×Q8—28no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—42no—
551C2×Q8—42no—
552C2×Q8—42no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8#126116yes—
558C2×Q8C2×#4114yes—
559C2×Q8C2×#4114yes—
560C2×Q8C2×#4114yes—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D412yes—
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D412yes—
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4C2511yescharacteristic
607Q16—48no—
608Q16—48no—
609M16—44no—
610M16—44no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—21no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—44no—
630C2×C8—44no—
631C4⋊C4—28no—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—82no—
661C4⋊C4—82no—
662C4⋊C4—81no—
663C4⋊C4—82no—
664C4⋊C4—82no—
665C4⋊C4—81no—
666C4⋊C4C2×#4112yes—
667C4⋊C4C2×#4114yes—
668C4⋊C4C2×#4112yes—
669C4⋊C4C2×#4112yes—
670C4⋊C4C2×#4112yes—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C42—28no—
678C42—28no—
679C42—28no—
680C42—28no—
681C42—28no—
682C42—28no—
683C42—22no—
684C42—22no—
685C42—24no—
686C42—24no—
687C42—24no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—42no—
697C42—42no—
698C42—42no—
699C42—42no—
700C42—42no—
701C42—42no—
702C42—42no—
703C42—82no—
704C42—82no—
705C42—81no—
706C42—82no—
707C42—82no—
708C42—81no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23#52512yes—
714C23#52512yes—
715C23#52512yes—
716C23C23×D411yescharacteristic
717Q8—216no—
718Q8—24no—
719Q8—24no—
720Q8—24no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—42no—
725Q8—84no—
726Q8C2×#12618yes—
727C2×C4—21no—
728C2×C4—216no—
729C2×C4—21no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—44no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—82no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4—162no—
792C2×C4#52512yes—
793C2×C4#52512yes—
794C2×C4#52512yes—
795C2×C4C2×#12614yes—
796C2×C4#52914yes—
797C2×C4#52914yes—
798C2×C4#52914yes—
799C2×C4#57812yes—
800C2×C4C22×#4111yescharacteristic
801C2×C4C22×#4111yescharacteristic
802C2×C4C22×#4111yescharacteristic
803C2×C4C22×#4111yescharacteristic
804C2×C4C22×#4111yescharacteristic
805C2×C4C22×#4111yescharacteristic
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C8—42no—
811C8—42no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22#285214yes—
819C22C2×#52511yescharacteristic
820C22C2×#52511yescharacteristic
821C22C2×#52511yescharacteristic
822C22C2×#57811yescharacteristic
823C22#358411yescharacteristic
824C22#358611yescharacteristic
825C22#358611yescharacteristic
826C4—28no—
827C4—22no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—41no—
833C4—41no—
834C4—44no—
835C4—41no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—82no—
841C4—81no—
842C4—81no—
843C4—81no—
844C4—81no—
845C4—82no—
846C4#285214yes—
847C4C22×#12611yescharacteristic
848C4C2×#52911yescharacteristic
849C4C2×#52911yescharacteristic
850C4C2×#52911yescharacteristic
851C2—24no—
852C2C2×#285211yescharacteristic
853C2#6057311yescharacteristic
854C2#6057711yescharacteristic
855C2#6058111yescharacteristic
856C2#6058311yescharacteristic
857C2#6059411yescharacteristic
858C2#6059511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×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. #33093C2semidirect
4. #33091C2semidirect
5. #33091C2semidirect
6. #33091C2semidirect
7. #33085C2semidirect
8. #33085C2semidirect
9. #33085C2semidirect
10. #33083C2semidirect

Maximal subgroups

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

subgroupindex
#353132
C4×#5192
#330932
#330912
#330852
#330832
#210662
#210642
#210612
#210362
#210352
#210322
#209352
C2×#18782
#208802
#208772
#208742
#207742