Finite Group Databasebeta

← #6459062

Subgroups — #6459062

Order 512.

2015 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36621C211yesmaximal, characteristic
2C2×#2285C211yesmaximal, characteristic, complemented
3#27978C211yesmaximal, characteristic, complemented
4#27966C211yesmaximal, characteristic, complemented
5#27953C211yesmaximal, characteristic, complemented
6#27914C211yesmaximal, characteristic, complemented
7#27894C212yesmaximal, complemented
8#27880C212yesmaximal, complemented
9#27858C212yesmaximal, complemented
10#27857C212yesmaximal, complemented
11#24551C212yesmaximal, complemented
12#24550C212yesmaximal
13#23762C212yesmaximal, complemented
14#23760C212yesmaximal, complemented
15#21579C212yesmaximal, complemented
16#21578C212yesmaximal, complemented
17#21406C212yesmaximal, complemented
18#20823C212yesmaximal, complemented
19C2×#1749C211yesmaximal, characteristic, complemented
20C2×#529C2211yescharacteristic
21C22×#117—21no—
22C23×C42C2211yescharacteristic
23C2×#483C2212yes—
24C2×#480C2212yes—
25C22×C22⋊C8C2212yes—
26C22×#97C2212yes—
27#2855C2211yescharacteristic
28#2854C2211yescharacteristic
29#2853—21no—
30#2852—21no—
31#2852—21no—
32#2851C2211yescharacteristic
33#2851C2211yescharacteristic
34#2850C2211yescharacteristic
35#2850C2211yescharacteristic
36#2849—21no—
37#2848C2211yescharacteristic
38#2847C2211yescharacteristic
39C4×C22⋊Q8C2211yescharacteristic
40C4×C22⋊Q8C2211yescharacteristic
41C4×#123—21no—
42C4×#121C2211yescharacteristic
43C4×#121C2211yescharacteristic
44C4×#120—21no—
45#2290—21no—
46#2290—21no—
47#2285—21no—
48#2285—21no—
49#2285—21no—
50#2285—21no—
51#2285C2212yes—
52#2285C2212yes—
53#2285C2212yes—
54#2285C2212yes—
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57#2283C2211yescharacteristic
58C2×#382—21no—
59C2×#380—21no—
60C2×#380C2212yes—
61C2×C4×C4⋊C4—21no—
62C2×C4×C4⋊C4C2212yes—
63#2100C2212yescomplemented
64#2100C2212yescomplemented
65#2095C2212yescomplemented
66#2094C2212yescomplemented
67#2084C2212yescomplemented
68#2083C2212yescomplemented
69#2077C2214yes—
70#2075C2214yes—
71#2072C2212yescomplemented
72#2071C2212yescomplemented
73#2035C2214yes—
74#2033C2214yes—
75#1992C2212yescomplemented
76#1992C2212yescomplemented
77#1959C2212yescomplemented
78#1959C2212yescomplemented
79#1928C2214yescomplemented
80#1926C2214yescomplemented
81#1921C2214yescomplemented
82#1919C2214yescomplemented
83#1893C2214yes—
84#1892C2214yes—
85#1874C2212yes—
86#1872C2212yes—
87#1853C2212yes—
88#1852C2212yes—
89#1847C2212yescomplemented
90#1847C2212yescomplemented
91#1836C2212yescomplemented
92#1836C2212yescomplemented
93#1823C2212yes—
94#1823C2212yes—
95#1808C2214yes—
96#1807C2214yes—
97#1776C2214yescomplemented
98#1776C2214yescomplemented
99#1763C2214yescomplemented
100#1762C2214yescomplemented
101#1749C2211yescharacteristic
102#1749C2211yescharacteristic
103#1749C2212yes—
104#1749C2212yes—
105#1749C2212yes—
106C2×#336C2212yes—
107C24×C4D411yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4C2311yescharacteristic
110C23×C8C2314yes—
111#529—28no—
112C2×#126—21no—
113C2×#125C2311yescharacteristic
114C2×#124C2311yescharacteristic
115C2×#123—21no—
116C2×#123—21no—
117C2×C22⋊Q8C2311yescharacteristic
118C2×C22⋊Q8C2311yescharacteristic
119C2×C22⋊Q8C2311yescharacteristic
120C2×#121C2311yescharacteristic
121C2×#121C2311yescharacteristic
122C2×#121C2311yescharacteristic
123C2×#120—21no—
124C2×C4×Q8C2311yescharacteristic
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4C2311yescharacteristic
129C2×#117—22no—
130C2×#117—22no—
131C2×#117—22no—
132C2×#117—22no—
133C2×#117—21no—
134C2×#117—48no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4—22no—
142C22×C42—28no—
143C22×C42—22no—
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#483—28no—
157#480—28no—
158C2×#107C2314yes—
159C2×#107C2314yes—
160C2×#106C2314yes—
161C2×#106C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×C22⋊C8—28no—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2312yes—
169C2×C22⋊C8C2312yes—
170C2×#97—28no—
171C2×#97C2312yes—
172C2×#97C2312yes—
173C2×#97C2314yes—
174#391C2311yescharacteristic
175#391C2311yescharacteristic
176#390C2311yescharacteristic
177#390C2311yescharacteristic
178#389C2311yescharacteristic
179#389C2311yescharacteristic
180#389C2311yescharacteristic
181#389C2311yescharacteristic
182#388—21no—
183#388—21no—
184#388—21no—
185#388—21no—
186#388—21no—
187#388—21no—
188#388—21no—
189#388—21no—
190#387—21no—
191#387—21no—
192#387—21no—
193#387—21no—
194#387—21no—
195#387—21no—
196#387—21no—
197#387—21no—
198#386—21no—
199#386—21no—
200#386—21no—
201#386—21no—
202#386—21no—
203#386—21no—
204#386—21no—
205#386—21no—
206#386—21no—
207#386—21no—
208#385—21no—
209#385—21no—
210#385—21no—
211#385—21no—
212#385—21no—
213#385—21no—
214#385—21no—
215#385—21no—
216#385—21no—
217#385—21no—
218#384—21no—
219#384—21no—
220#384—21no—
221#384—21no—
222#384C2312yes—
223#384C2312yes—
224#384C2312yes—
225#384C2312yes—
226#383—21no—
227#382—22no—
228#382—22no—
229#382—22no—
230#382—22no—
231#382C2311yescharacteristic
232#382C2311yescharacteristic
233#381—21no—
234#381—21no—
235#380—22no—
236#380—22no—
237#380—22no—
238#380—22no—
239#380—22no—
240#380—22no—
241#380C2311yescharacteristic
242#380C2314yes—
243#380C2311yescharacteristic
244#380C2311yescharacteristic
245#380C2314yes—
246#380C2311yescharacteristic
247#380C2311yescharacteristic
248#380C2311yescharacteristic
249#379—21no—
250C4×C4⋊C4—22no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4—22no—
253C4×C4⋊C4—22no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4—22no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4C2314yes—
259C4×C4⋊C4C2314yes—
260C4×C4⋊C4C2311yescharacteristic
261C4×C4⋊C4C2311yescharacteristic
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267#376—21no—
268C2×#95—22no—
269C2×#95—22no—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#336C2312yes—
279#336C2312yes—
280#336C2314yes—
281C25C2×D411yescharacteristic
282C22×Q8C2411yescharacteristic
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4C2411yescharacteristic
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—21no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C22×C8—28no—
318C22×C8—28no—
319C22×C8—44no—
320C22×C8C2414yes—
321C22×C8C2414yes—
322#126—44no—
323#125—24no—
324#124—24no—
325#123—44no—
326#123—44no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329C22⋊Q8—42no—
330#121—24no—
331#121—24no—
332#121—42no—
333#120—44no—
334C4×Q8—24no—
335C4×D4—24no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4—44no—
339#117—48no—
340#117—48no—
341#117—48no—
342#117—48no—
343#117—44no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
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—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4C2414yes—
372C2×C4⋊C4C2414yes—
373C2×C4⋊C4C2411yescharacteristic
374C2×C4⋊C4C2411yescharacteristic
375C2×C4⋊C4C2411yescharacteristic
376C2×C4⋊C4C2411yescharacteristic
377C2×C4⋊C4C2411yescharacteristic
378C2×C4⋊C4C2411yescharacteristic
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—48no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—48no—
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
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×C42#4118yes—
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435#107—28no—
436#107—44no—
437#106—28no—
438#106—44no—
439#103—28no—
440#103—44no—
441#102—28no—
442#102—44no—
443C22⋊C8—24no—
444C22⋊C8—28no—
445C22⋊C8#4118yes—
446#97—28no—
447#97—24no—
448#97—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—21no—
478C24—41no—
479C24—41no—
480C24AGL(1,ℤ/8)14yes—
481C24C22×D411yescharacteristic
482C24C22×D411yescharacteristic
483C24C22×D411yescharacteristic
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C22×C4—232no—
500C22×C4—22no—
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—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—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—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—416no—
559C22×C4—416no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—42no—
569C22×C4#12314yes—
570C22×C4#12314yes—
571C22×C4#13714yes—
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C2×#4114yes—
584C22×C4C2×#4114yes—
585C22×C4C2511yescharacteristic
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—24no—
589C2×C8—24no—
590C2×C8—24no—
591C2×C8—416no—
592C2×C8C2×#4118yes—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—44no—
622C4⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—48no—
657C42—48no—
658C42—42no—
659C42—42no—
660C42—42no—
661C42#12314yes—
662C42#12314yes—
663C42C2×#4114yes—
664C42C2×#4114yes—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—28no—
674C23—21no—
675C23—28no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23C2×#12312yes—
694C23#53212yes—
695C23C2×AGL(1,ℤ/8)12yes—
696C23C2×AGL(1,ℤ/8)12yes—
697C23C2×AGL(1,ℤ/8)12yes—
698C23C2×#13712yes—
699C23#57512yes—
700C23C23×D411yescharacteristic
701Q8—44no—
702D4—44no—
703D4—84no—
704D4—84no—
705D4—84no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—44no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—84no—
776C2×C4—88no—
777C2×C4—88no—
778C2×C4C2×#12312yes—
779C2×C4C2×#12312yes—
780C2×C4C2×#12312yes—
781C2×C4C2×#12312yes—
782C2×C4C2×#12312yes—
783C2×C4#53212yes—
784C2×C4C2×#13712yes—
785C2×C4C2×#13712yes—
786C2×C4#57512yes—
787C2×C4C22×#4112yes—
788C2×C4C22×#4112yes—
789C2×C4#58512yes—
790C8—28no—
791C8—44no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—416no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22#309214yes—
820C22#318014yes—
821C22C22×#12311yescharacteristic
822C22C2×#53211yescharacteristic
823C22#344911yescharacteristic
824C22C22×AGL(1,ℤ/8)11yescharacteristic
825C22C22×#13711yescharacteristic
826C22C2×#57511yescharacteristic
827C22C2×#57511yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—22no—
836C4—22no—
837C4—41no—
838C4—41no—
839C4—84no—
840C4—81no—
841C4—81no—
842C4—84no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4#347514yes—
849C2—24no—
850C2—24no—
851C2—42no—
852C2—161no—
853C2#3481011yescharacteristic
854C2C2×#309211yescharacteristic
855C2#6051111yescharacteristic
856C2C2×#318011yescharacteristic
857C2#6070111yescharacteristic
858C2#6095811yescharacteristic
859C2#6096311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2847C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2285C2semidirect
3. #27978C2semidirect
4. #27966C2semidirect
5. #27953C2semidirect
6. #27914C2semidirect
7. #27894C2semidirect
8. #27880C2semidirect
9. #27858C2semidirect
10. #27857C2semidirect
11. #24551C2semidirect
13. #23762C2semidirect
14. #23760C2semidirect
15. #21579C2semidirect
16. #21578C2semidirect
17. #21406C2semidirect
18. #20823C2semidirect
19. C2×#1749C2semidirect
63. #2100C22semidirect
64. #2100C22semidirect
65. #2095C22semidirect
66. #2094C22semidirect
67. #2084C22semidirect
68. #2083C22semidirect
71. #2072C22semidirect
72. #2071C22semidirect
75. #1992C22semidirect
76. #1992C22semidirect
77. #1959C22semidirect
78. #1959C22semidirect
79. #1928C22semidirect
80. #1926C22semidirect
81. #1921C22semidirect
82. #1919C22semidirect
89. #1847C22semidirect
90. #1847C22semidirect
91. #1836C22semidirect
92. #1836C22semidirect
97. #1776C22semidirect
98. #1776C22semidirect
99. #1763C22semidirect
100. #1762C22semidirect

Maximal subgroups

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

subgroupindex
#366212
C2×#22852
#279782
#279662
#279532
#279142
#278942
#278802
#278582
#278572
#245512
#245502
#237622
#237602
#215792
#215782
#214062
#208232
C2×#17492