Finite Group Databasebeta

← #6456167

Subgroups — #6456167

Order 512.

1780 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34976C211yesmaximal, characteristic
2#34127C211yesmaximal, characteristic, complemented
3#25061C211yesmaximal, characteristic, complemented
4#25059C211yesmaximal, characteristic, complemented
5#25014C211yesmaximal, characteristic, complemented
6#25012C211yesmaximal, characteristic, complemented
7#24997C211yesmaximal, characteristic, complemented
8#24991C211yesmaximal, characteristic, complemented
9#24971C211yesmaximal, characteristic, complemented
10#24965C211yesmaximal, characteristic, complemented
11#24938C212yesmaximal, complemented
12#24936C212yesmaximal, complemented
13#24868C212yesmaximal, complemented
14#24862C212yesmaximal, complemented
15#23759C212yesmaximal, complemented
16#23758C212yesmaximal, complemented
17C4×#481C212yesmaximal, complemented
18C4×#483C212yesmaximal, complemented
19#21373C211yesmaximal, characteristic, complemented
20#21362C211yesmaximal, characteristic, complemented
21#20816C211yesmaximal, characteristic, complemented
22#20737C211yesmaximal, characteristic, complemented
23C4×#416C211yesmaximal, characteristic, complemented
24C2×C4×#41C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C2×#481C2212yes—
27C2×#483C2212yes—
28C2×#431C2211yescharacteristic
29C2×#416C2211yescharacteristic
30C2×#416C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2609—22no—
33#2582C2211yescharacteristic
34#2538C2211yescharacteristic
35#2538C2211yescharacteristic
36#2537C2211yescharacteristic
37#2485—21no—
38#2485C2212yes—
39#2407—21no—
40#2407C2212yes—
41#2392—22no—
42#2355C2211yescharacteristic
43#2355C2211yescharacteristic
44#2352C2212yes—
45#2352C2212yes—
46D4×C4⋊C4C2211yescharacteristic
47D4×C4⋊C4C2211yescharacteristic
48#2347—21no—
49#2343—22no—
50#2339—21no—
51C4×C22⋊Q8—21no—
52C4×C22⋊Q8C2212yes—
53C4×#121—21no—
54C4×#121C2212yes—
55#2295—21no—
56#2290—22no—
57#2285C2211yescharacteristic
58#2285C2211yescharacteristic
59#2283C2212yes—
60C42×D4—21no—
61C4×#117C2211yescharacteristic
62C2×C4×C4⋊C4C2212yes—
63#2101C2212yes—
64#2101C2212yes—
65#2097C2212yes—
66#2092C2212yes—
67#2085C2212yes—
68#2085C2212yes—
69#2077C2212yes—
70#2077C2212yes—
71#2076C2212yes—
72#2075C2212yes—
73#2074C2212yes—
74#2073C2212yes—
75#2036C2212yes—
76#2035C2212yes—
77#2034C2212yes—
78#2033C2212yes—
79#1984C2211yescharacteristic
80#1984C2211yescharacteristic
81#1954C2211yescharacteristic
82#1954C2211yescharacteristic
83#1948C2211yescharacteristic
84#1948C2211yescharacteristic
85#1947C2211yescharacteristic
86#1947C2211yescharacteristic
87#1927C2212yes—
88#1927C2212yes—
89#1926C2212yes—
90#1926C2212yes—
91#1920C2212yes—
92#1920C2212yes—
93#1919C2212yes—
94#1919C2212yes—
95#1874C2212yes—
96#1872C2212yes—
97#1869C2212yes—
98#1869C2212yes—
99#1854C2212yes—
100#1854C2212yes—
101#1853C2212yes—
102#1853C2212yes—
103#1844C2211yescharacteristic
104#1844C2211yescharacteristic
105#1834C2211yescharacteristic
106#1834C2211yescharacteristic
107#1825C2212yes—
108#1824C2212yes—
109#1823C2212yes—
110#1807C2212yes—
111#1807C2212yes—
112#1803C2211yescharacteristic
113#1803C2211yescharacteristic
114#1802C2211yescharacteristic
115#1802C2211yescharacteristic
116#1788C2212yes—
117C4×#107C2212yes—
118C4×#106C2212yes—
119C4×#106C2212yes—
120C4×#106C2212yes—
121C4×#103C2212yes—
122C4×#103C2211yescharacteristic
123C4×#103C2211yescharacteristic
124C4×#103C2211yescharacteristic
125C4×#103C2211yescharacteristic
126C4×#102C2212yes—
127C4×#102C2211yescharacteristic
128C4×#102C2211yescharacteristic
129C4×#102C2211yescharacteristic
130C4×#102C2211yescharacteristic
131C4×C22⋊C8C2212yes—
132C4×C22⋊C8C2212yes—
133#1735C2211yescharacteristic
134#1735C2211yescharacteristic
135C22×#41D411yescharacteristic
136C22×#41C2311yescharacteristic
137C23×C8C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8C2312yes—
141C2×#121—21no—
142C2×#121C2312yes—
143C4×#41—24no—
144C4×#41—24no—
145C4×#41—24no—
146C4×#41—24no—
147C2×C4×Q8D411yescharacteristic
148C2×C4×Q8C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×Q8C2311yescharacteristic
151C2×C4×D4—21no—
152C2×C4×D4—21no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4—22no—
156C2×C4×D4D412yes—
157C2×C4×D4D411yescharacteristic
158C2×C4×D4C2311yescharacteristic
159C2×C4×D4C2311yescharacteristic
160C2×C4×D4C2311yescharacteristic
161C2×C4×D4C2312yes—
162C2×#117—21no—
163C2×#117—21no—
164C2×#117—21no—
165C2×#117D412yes—
166C2×#117D411yescharacteristic
167C2×#117C2311yescharacteristic
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C42—22no—
173C22×C42—21no—
174C22×C42C2312yes—
175C22×C42C2311yescharacteristic
176#483—28no—
177#481—28no—
178#431—24no—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#106C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2311yescharacteristic
189#416—24no—
190#416—24no—
191C2×#103C2312yes—
192C2×#103C2311yescharacteristic
193C2×#103C2311yescharacteristic
194C2×#103C2311yescharacteristic
195C2×#103C2312yes—
196C2×#103C2311yescharacteristic
197C2×#102C2312yes—
198C2×#102C2311yescharacteristic
199C2×#102C2311yescharacteristic
200C2×#102C2311yescharacteristic
201C2×#102C2312yes—
202C2×#102C2311yescharacteristic
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2312yes—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C4×C8—24no—
209C2×C4×C8C2311yescharacteristic
210C2×C4×C8C2311yescharacteristic
211C2×C4×C8C2311yescharacteristic
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2312yes—
214#398—22no—
215#397—22no—
216#396—22no—
217#396—22no—
218#394—22no—
219#394—22no—
220#394—22no—
221#392—22no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391C2312yes—
226#390—21no—
227#390C2312yes—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389C2312yes—
233#389C2312yes—
234#388—22no—
235#388—22no—
236#388—22no—
237#388—22no—
238#387—22no—
239#387—22no—
240#387—22no—
241#387—22no—
242#387—22no—
243#387—22no—
244#386—22no—
245#386—22no—
246#386—22no—
247#386—22no—
248#385—22no—
249#385—22no—
250#385—22no—
251#385—22no—
252#384C2311yescharacteristic
253#384C2311yescharacteristic
254#384C2311yescharacteristic
255#384C2311yescharacteristic
256#383—22no—
257#382—21no—
258#382—21no—
259#382C2312yes—
260#382C2312yes—
261#381—22no—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380C2312yes—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270#380C2312yes—
271#380C2312yes—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—22no—
275C4×C4⋊C4—22no—
276C4×C4⋊C4—22no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2312yes—
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2311yescharacteristic
284C4×C4⋊C4C2312yes—
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2312yes—
287C4×C22⋊C4—21no—
288C4×C22⋊C4—22no—
289C4×C22⋊C4—21no—
290C4×C22⋊C4—22no—
291C4×C22⋊C4—22no—
292C4×C22⋊C4—22no—
293C4×C22⋊C4—22no—
294#376—21no—
295#376—22no—
296C2×#95—22no—
297C43—21no—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322C2×#41—24no—
323C2×#41—24no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—42no—
329C2×#41—41no—
330C2×#41—41no—
331C22×Q8C2×D411yescharacteristic
332C22×Q8C2411yescharacteristic
333C22×D4—21no—
334C22×D4—22no—
335C22×D4C2×D412yes—
336C22×D4C2×D411yescharacteristic
337C22×D4C2411yescharacteristic
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4C2×D412yes—
344C23×C4C2×D412yes—
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2412yes—
348C23×C4C2411yescharacteristic
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—41no—
354C22×C8—41no—
355C22×C8C2411yescharacteristic
356C22×C8C2411yescharacteristic
357C22×C8C2412yes—
358C22×C8C2412yes—
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22⋊Q8—24no—
362C22⋊Q8—42no—
363C22⋊Q8—44no—
364#121—24no—
365#121—42no—
366#121—44no—
367C4×Q8—24no—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373C4×Q8—22no—
374C4×D4—28no—
375C4×D4—24no—
376C4×D4—24no—
377C4×D4—24no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—44no—
385C4×D4—44no—
386C4×D4—44no—
387C4×D4—44no—
388C4×D4—84no—
389#117—24no—
390#117—28no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—41no—
396#117—41no—
397#117—44no—
398#117—82no—
399#117—82no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4C2×D411yescharacteristic
420C2×C4⋊C4C2×D412yes—
421C2×C4⋊C4C2×D411yescharacteristic
422C2×C4⋊C4C2×D412yes—
423C2×C4⋊C4C2412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2411yescharacteristic
426C2×C4⋊C4C2411yescharacteristic
427C2×C4⋊C4C2411yescharacteristic
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4C2×D412yes—
449C2×C22⋊C4C2×D412yes—
450C2×C22⋊C4C2×D412yes—
451C2×C42—24no—
452C2×C42—24no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—44no—
467C2×C42—84no—
468C2×C42C2×D412yes—
469C2×C42C2×D412yes—
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42#4114yes—
473C2×C42#4114yes—
474C2×C42C2412yes—
475C2×C42C2411yescharacteristic
476C2×C42C2411yescharacteristic
477#107—42no—
478#107—42no—
479#106—24no—
480#106—24no—
481#106—24no—
482#106—24no—
483#106—42no—
484#106—42no—
485C4⋊C8—22no—
486C4⋊C8—22no—
487#103—22no—
488#103—24no—
489#103—22no—
490#103—22no—
491#103—42no—
492#103#4114yescomplemented
493#102—22no—
494#102—24no—
495#102—22no—
496#102—22no—
497#102—42no—
498#102#4114yescomplemented
499C22⋊C8—24no—
500C22⋊C8—24no—
501C22⋊C8—24no—
502C22⋊C8—42no—
503C22⋊C8—42no—
504C4×C8—22no—
505C4×C8—22no—
506C4×C8—22no—
507C4×C8—22no—
508C4×C8—24no—
509#95—21no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—22no—
517#95—22no—
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#95—22no—
531C24—21no—
532C24C22×D411yescharacteristic
533C24C22×D412yes—
534#41—28no—
535#41—416no—
536#41—44no—
537#41—44no—
538#41—44no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8C2×#4112yes—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—82no—
564C2×D4#13514yes—
565C2×D4C2×#4112yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4#12314yes—
613C22×C4#12314yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2511yescharacteristic
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—44no—
642C2×C8—44no—
643C2×C8C2×#4112yes—
644C2×C8C2×#4112yes—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—82no—
682C4⋊C4C2×#4112yes—
683C4⋊C4C2×#4112yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—42no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C42—24no—
703C42—24no—
704C42—22no—
705C42—22no—
706C42—42no—
707C42—42no—
708C42—42no—
709C42—42no—
710C42—42no—
711C42—42no—
712C42—42no—
713C42—42no—
714C42—42no—
715C42—44no—
716C42—44no—
717C42—82no—
718C42—82no—
719C42#12314yes—
720C42#12314yes—
721C42C2×#4112yes—
722C42C2×#4112yes—
723C42C2×#4112yes—
724C42C2×#4112yes—
725C23—22no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23C2×#12312yes—
745C23C2×#13514yes—
746C23C23×D411yescharacteristic
747Q8—22no—
748Q8—22no—
749Q8—44no—
750Q8—41no—
751Q8—41no—
752D4—28no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—41no—
758D4—41no—
759D4—88no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—48no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—48no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—88no—
822C2×C4—88no—
823C2×C4—84no—
824C2×C4—84no—
825C2×C4C2×#12312yes—
826C2×C4C2×#12312yes—
827C2×C4C2×#12312yes—
828C2×C4C2×#12312yes—
829C2×C4C2×#12312yes—
830C2×C4C2×#13512yes—
831C2×C4#57512yes—
832C2×C4#57712yes—
833C2×C4#57712yes—
834C2×C4C22×#4111yescharacteristic
835C2×C4C22×#4111yescharacteristic
836C2×C4C22×#4111yescharacteristic
837C2×C4C22×#4111yescharacteristic
838C2×C4#58511yescharacteristic
839C2×C4#58511yescharacteristic
840C8—22no—
841C8—22no—
842C8—42no—
843C8—42no—
844C8—41no—
845C8—41no—
846C22—22no—
847C22—24no—
848C22—22no—
849C22—22no—
850C22—24no—
851C22—24no—
852C22—42no—
853C22—41no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—42no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22C22×#12311yescharacteristic
868C22D4×#4111yescharacteristic
869C22D4×#4111yescharacteristic
870C22C22×#13511yescharacteristic
871C22C2×#57511yescharacteristic
872C22C2×#57711yescharacteristic
873C22C2×#57711yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—82no—
884C4—81no—
885C4—82no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4—82no—
891C4#309114yes—
892C4#309914yes—
893C4#344411yescharacteristic
894C4#345511yescharacteristic
895C4#347511yescharacteristic
896C4#347511yescharacteristic
897C2—42no—
898C2—44no—
899C2—82no—
900C2#3474211yescharacteristic
901C2C2×#309111yescharacteristic
902C2C2×#309911yescharacteristic
903C2#6143211yescharacteristic
904C2#6143211yescharacteristic
905C2#6144811yescharacteristic
906C2#6145011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#34976C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34127C2semidirect
3. #25061C2semidirect
4. #25059C2semidirect
5. #25014C2semidirect
6. #25012C2semidirect
7. #24997C2semidirect
8. #24991C2semidirect
9. #24971C2semidirect
10. #24965C2semidirect
11. #24938C2semidirect
12. #24936C2semidirect
13. #24868C2semidirect
14. #24862C2semidirect
15. #23759C2semidirect
16. #23758C2semidirect
17. C4×#481C2semidirect
18. C4×#483C2semidirect
19. #21373C2semidirect
20. #21362C2semidirect
21. #20816C2semidirect
22. #20737C2semidirect
23. C4×#416C2semidirect
492. #103#41semidirect
498. #102#41semidirect

Maximal subgroups

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

subgroupindex
#349762
#341272
#250612
#250592
#250142
#250122
#249972
#249912
#249712
#249652
#249382
#249362
#248682
#248622
#237592
#237582
C4×#4812
C4×#4832
#213732
#213622
#208162
#207372
C4×#4162