Finite Group Databasebeta

← #6400111

Subgroups — #6400111

Order 512.

1909 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3329C211yesmaximal, characteristic
2#34487C211yesmaximal, characteristic, complemented
3#34321C211yesmaximal, characteristic
4#23217C211yesmaximal, characteristic, complemented
5#23100C211yesmaximal, characteristic, complemented
6#23069C211yesmaximal, characteristic, complemented
7#23034C212yesmaximal, complemented
8#22919C212yesmaximal, complemented
9#22875C212yesmaximal, complemented
10#22805C211yesmaximal, characteristic, complemented
11#22663C211yesmaximal, characteristic, complemented
12#22581C212yesmaximal, complemented
13#22489C211yesmaximal, characteristic
14D4×#103C211yesmaximal, characteristic, complemented
15#22218C211yesmaximal, characteristic, complemented
16#22200C212yesmaximal, complemented
17#22113C211yesmaximal, characteristic, complemented
18#22058C212yesmaximal, complemented
19#21591C212yesmaximal, complemented
20C4×#461C211yesmaximal, characteristic, complemented
21#21114C211yesmaximal, characteristic, complemented
22#21064C212yesmaximal, complemented
23#20562C211yesmaximal, characteristic, complemented
24C2×#555C2211yescharacteristic
25C2×D4×Q8C2211yescharacteristic
26#3329C4116yescomplemented
27C2×#487C2211yescharacteristic
28C2×#485C2212yes—
29C2×#477C2211yescharacteristic
30C2×#468C2212yes—
31C2×#461C2211yescharacteristic
32C2×#448C2212yes—
33C2×C4×SD16C2212yes—
34C2×C4×SD16C2211yescharacteristic
35C2×#436C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37C2×#428C2212yes—
38C2×#419C2212yes—
39C22×#103C2212yes—
40#2378—22no—
41#2369—21no—
42#2369C2211yescharacteristic
43#2367—22no—
44#2365C2211yescharacteristic
45#2363—21no—
46#2362C2212yes—
47#2361C2212yes—
48#2357—21no—
49#2355C2211yescharacteristic
50#2354C2211yescharacteristic
51#2354C2211yescharacteristic
52D4×C4⋊C4C2211yescharacteristic
53#2347—21no—
54#2347C2212yes—
55Q8×C22⋊C4C2212yes—
56#2337—22no—
57#2332—22no—
58#2331—21no—
59#2324C2212yes—
60#2323C2212yes—
61#2319—21no—
62#2310C2212yes—
63C4×C4⋊Q8C2211yescharacteristic
64C4×C4⋊Q8C2211yescharacteristic
65C4×#121—21no—
66#2296—21no—
67#2295C2211yescharacteristic
68#2293C2211yescharacteristic
69#2274C2212yes—
70C42×D4C2211yescharacteristic
71#1990C2211yescharacteristic
72#1987C2211yescharacteristic
73#1981C2211yescharacteristic
74#1973C2212yes—
75#1968C2212yes—
76#1956C2211yescharacteristic
77#1948C2211yescharacteristic
78#1947C2211yescharacteristic
79#1942C2212yes—
80#1935C2212yes—
81#1933C2212yes—
82#1933C2212yes—
83#1928C2212yes—
84#1928C2211yescharacteristic
85#1928C2212yes—
86#1928C2211yescharacteristic
87#1928C2212yes—
88#1927C2212yes—
89#1927C2212yes—
90#1927C2212yes—
91#1927C2212yes—
92#1927C2212yes—
93#1926C2212yes—
94#1921C2212yes—
95#1919C2211yescharacteristic
96#1919C2211yescharacteristic
97#1918C2212yes—
98#1893C2212yes—
99#1892C2212yes—
100#1880C2212yes—
101#1877C2211yescharacteristic
102#1877C2212yes—
103#1877C2211yescharacteristic
104#1875C2212yes—
105#1872C2212yes—
106#1865C2212yes—
107#1865C2212yes—
108#1863C2212yes—
109#1862C2211yescharacteristic
110#1862C2211yescharacteristic
111#1854C2212yes—
112#1853C2212yes—
113#1844C2211yescharacteristic
114#1825C2212yes—
115#1809C2212yes—
116#1803C2211yescharacteristic
117#1802C2211yescharacteristic
118#1787C2212yes—
119#1776C2212yes—
120C4×#107C2211yescharacteristic
121C4×#106C2212yes—
122#1770C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124C4×C4⋊C8C2211yescharacteristic
125#1763C2212yes—
126C4×#103C2211yescharacteristic
127C4×#103C2212yes—
128C4×#103C2212yes—
129C4×#102C2211yescharacteristic
130#1753C2212yes—
131C8×C22⋊C4C2212yes—
132#1750C2212yes—
133#1744C2211yescharacteristic
134#1735C2212yes—
135#1729C2212yes—
136C23×Q8C2312yes—
137C22×SD16C2311yescharacteristic
138C22×SD16C2312yes—
139C22×M16C2312yes—
140C23×C8C2312yes—
141#555—24no—
142#555C2×C418yes—
143D4×Q8—24no—
144D4×Q8C2×C418yescomplemented
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×#124—22no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8C2312yes—
151C2×#121—21no—
152C2×#121C2312yes—
153C2×C4×Q8—21no—
154C2×C4×Q8C2311yescharacteristic
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2312yes—
157C2×C4×D4—21no—
158C2×C4×D4—21no—
159C2×C4×D4—22no—
160C2×C4×D4C2311yescharacteristic
161C2×C4×D4C2311yescharacteristic
162C2×C4×D4C2311yescharacteristic
163C2×C4×D4C2311yescharacteristic
164C2×#117—21no—
165C2×#117—21no—
166C2×#117C2312yes—
167C2×#117C2312yes—
168C2×#117C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C42—21no—
171#487C2×C418yescomplemented
172#485C2×C4116yescomplemented
173#477C2×C418yescomplemented
174#468C2×C4116yescomplemented
175#461C2×C418yescomplemented
176#448C2×C4116yescomplemented
177C4×SD16—44no—
178C4×SD16C2×C418yescomplemented
179#436C2×C418yescomplemented
180C8×D4—24no—
181#428—44no—
182C2×#107C2311yescharacteristic
183C2×#107C2311yescharacteristic
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2311yescharacteristic
190C2×C4⋊C8C2311yescharacteristic
191C2×C4⋊C8C2311yescharacteristic
192#419C2×C4116yescomplemented
193C2×#103—44no—
194C2×#103C2311yescharacteristic
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2311yescharacteristic
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2311yescharacteristic
206C2×#102C2312yes—
207C2×#102C2311yescharacteristic
208C2×#102C2311yescharacteristic
209C2×#102C2311yescharacteristic
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×#97C2312yes—
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2312yes—
215C2×C4×C8C2312yes—
216C2×C4×C8C2311yescharacteristic
217#391—22no—
218#391—22no—
219#391—21no—
220#391—22no—
221#391—22no—
222#391—22no—
223#391C2312yes—
224#391C2311yescharacteristic
225#391C2312yes—
226#391C2312yes—
227#391C2311yescharacteristic
228#390—21no—
229#390—22no—
230#390D411yescharacteristic
231#390D411yescharacteristic
232#390C2312yes—
233#389—21no—
234#389—22no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389D411yescharacteristic
241#389D411yescharacteristic
242#389C2312yes—
243#389C2311yescharacteristic
244#389C2312yes—
245#389C2311yescharacteristic
246#388—22no—
247#388—22no—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—22no—
252#388—22no—
253#388—22no—
254#388—22no—
255#388—22no—
256#388D412yes—
257#388D412yes—
258#387—22no—
259#387—21no—
260#387—21no—
261#387—22no—
262#387—22no—
263#387—22no—
264#386—22no—
265#386—22no—
266#385—22no—
267#385—22no—
268#385—22no—
269#384C2311yescharacteristic
270#384C2311yescharacteristic
271#383—22no—
272#382—21no—
273#381—22no—
274#381—22no—
275#380—21no—
276#380—22no—
277#380C2312yes—
278#380C2312yes—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—22no—
283C4×C4⋊C4—22no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—22no—
290C4×C4⋊C4—22no—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2312yes—
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2311yescharacteristic
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—21no—
305C4×C22⋊C4—21no—
306C4×C22⋊C4C2312yes—
307#376—21no—
308C43C2311yescharacteristic
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2312yes—
321#340C2312yes—
322#340C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2312yes—
326#336C2311yescharacteristic
327#336C2311yescharacteristic
328#336C2312yes—
329#336C2312yes—
330C22×Q8—21no—
331C22×Q8—22no—
332C22×Q8—24no—
333C22×Q8—42no—
334C22×Q8—42no—
335C22×Q8—42no—
336C22×Q8—42no—
337C22×Q8C22×C418yes—
338C22×Q8C2412yes—
339C22×Q8C2411yescharacteristic
340C22×D4—22no—
341C22×D4C2×D411yescharacteristic
342C22×D4C2411yescharacteristic
343C23×C4—22no—
344C23×C4—21no—
345C23×C4—22no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4C2412yes—
349C2×SD16—41no—
350C2×SD16—42no—
351C2×SD16—41no—
352C2×SD16—42no—
353C2×SD16C22×C414yes—
354C2×SD16C22×C418yes—
355C2×M16—42no—
356C2×M16—42no—
357C2×M16C22×C418yes—
358C22×C8—24no—
359C22×C8—42no—
360C22×C8—42no—
361C22×C8C2411yescharacteristic
362C22×C8C2412yes—
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2412yes—
366C22×C8C2411yescharacteristic
367C4⋊Q8—28no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8C22×C414yes—
371C4⋊Q8C22×C414yes—
372#124—216no—
373C22⋊Q8—24no—
374C22⋊Q8—216no—
375C22⋊Q8C22×C418yes—
376#121—28no—
377#121—24no—
378#121C22×C418yes—
379C4×Q8—22no—
380C4×Q8—42no—
381C4×Q8—42no—
382C4×Q8—42no—
383C4×Q8—42no—
384C4×Q8—82no—
385C4×Q8C22×C414yes—
386C4×D4—28no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—41no—
390C4×D4—41no—
391C4×D4—41no—
392C4×D4—82no—
393C4×D4—84no—
394C4×D4C22×C414yes—
395C4×D4C22×C414yes—
396C4×D4#4114yes—
397#117—24no—
398#117—28no—
399#117—42no—
400#117—42no—
401#117—42no—
402#117—42no—
403#117—82no—
404#117C22×C418yes—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4C2×D411yescharacteristic
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2×D412yes—
426C2×C4⋊C4C2×D412yes—
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
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×C22⋊C4C2×D412yes—
452C2×C22⋊C4C2×D412yes—
453C2×C42—22no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—22no—
466C2×C42—82no—
467C2×C42C2×D411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2411yescharacteristic
472C2×C42C2412yes—
473C2×C42C2411yescharacteristic
474C2×C42C2411yescharacteristic
475#107—22no—
476#107—41no—
477#107—42no—
478#107C22×C418yes—
479#106—24no—
480#106—42no—
481#106—42no—
482#106C22×C414yes—
483C4⋊C8—22no—
484C4⋊C8C22×C414yes—
485#103—22no—
486#103—24no—
487#103—42no—
488#103—42no—
489#103—42no—
490#103—42no—
491#103—41no—
492#103C22×C414yes—
493#103C22×C418yes—
494#103C22×C418yes—
495#103C22×C418yes—
496#103C22×C418yes—
497#102—41no—
498#102—41no—
499#102—42no—
500#102C22×C414yes—
501C22⋊C8—24no—
502C22⋊C8C22×C418yes—
503#97—42no—
504C4×C8—22no—
505C4×C8—42no—
506C4×C8—42no—
507C4×C8C22×C414yes—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
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—21no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—21no—
532#95C2×D412yes—
533#95C2×D412yes—
534#95C2×D412yes—
535C24—21no—
536C24C22×D412yes—
537C2×Q8—28no—
538C2×Q8—24no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—48no—
550C2×Q8—48no—
551C2×Q8—81no—
552C2×Q8—81no—
553C2×Q8—82no—
554C2×Q8—82no—
555C2×Q8—84no—
556C2×Q8—84no—
557C2×Q8C23×C412yes—
558C2×Q8C23×C414yes—
559C2×D4—28no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—82no—
568C2×D4—82no—
569C2×D4C4×D414yes—
570C2×D4C23×C412yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4C23×C414yes—
602C22×C4C22×D412yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C2×#4114yes—
612C22×C4C2511yescharacteristic
613SD16—44no—
614SD16—48no—
615M16—48no—
616C2×C8—22no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—22no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—21no—
627C2×C8—22no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—84no—
632C2×C8C23×C412yes—
633C2×C8C23×C412yes—
634C2×C8C23×C414yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—28no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—44no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—44no—
662C4⋊C4—42no—
663C4⋊C4—81no—
664C4⋊C4—81no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—81no—
669C4⋊C4C4×D414yes—
670C4⋊C4C23×C412yes—
671C4⋊C4C23×C412yes—
672C4⋊C4C23×C414yes—
673C4⋊C4H(5,𝔽2)12yes—
674C22⋊C4—28no—
675C22⋊C4—28no—
676C22⋊C4—28no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4C4×D418yes—
690C42—28no—
691C42—24no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—21no—
696C42—22no—
697C42—22no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—41no—
702C42—42no—
703C42—42no—
704C42—82no—
705C42—81no—
706C42—81no—
707C42—82no—
708C42—82no—
709C42—82no—
710C42—82no—
711C42—82no—
712C42—82no—
713C42C23×C412yes—
714C42C2×#4112yes—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23C2×C4×D414yes—
729C23C23×D411yescharacteristic
730Q8—22no—
731Q8—24no—
732Q8—24no—
733Q8—22no—
734Q8—42no—
735Q8—41no—
736Q8—42no—
737Q8—41no—
738Q8—88no—
739Q8—84no—
740D4—22no—
741D4—22no—
742D4—28no—
743D4—41no—
744D4—41no—
745D4—88no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—48no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—84no—
806C2×C4—88no—
807C2×C4—84no—
808C2×C4—164no—
809C2×C4C2×C4×D414yes—
810C2×C4C2×C4×D412yes—
811C2×C4C2×C4×D412yes—
812C2×C4#57712yes—
813C2×C4#57712yes—
814C2×C4#57812yes—
815C2×C4C24×C411yescharacteristic
816C2×C4C22×#4111yescharacteristic
817C2×C4C2×H(5,𝔽2)11yescharacteristic
818C2×C4#58511yescharacteristic
819C2×C4#58511yescharacteristic
820C2×C4#58511yescharacteristic
821C8—22no—
822C8—22no—
823C8—24no—
824C8—42no—
825C8—41no—
826C8—41no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C22×C4×D411yescharacteristic
842C22#348511yescharacteristic
843C22#348811yescharacteristic
844C22C2×#57711yescharacteristic
845C22C2×#57711yescharacteristic
846C22C2×#57811yescharacteristic
847C22#358411yescharacteristic
848C4—22no—
849C4—22no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—44no—
854C4—42no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—44no—
862C4—81no—
863C4—81no—
864C4—81no—
865C4—82no—
866C4—82no—
867C4#294714yes—
868C4#342811yescharacteristic
869C4C4×H(5,𝔽2)11yescharacteristic
870C4#351411yescharacteristic
871C4#352111yescharacteristic
872C2—44no—
873C2—82no—
874C2#3429211yescharacteristic
875C2C2×#294711yescharacteristic
876C2C4×#57711yescharacteristic
877C2#6178511yescharacteristic
878C2#6178911yescharacteristic
879C2#6205211yescharacteristic
880C2#6207211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#555C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34487C2semidirect
4. #23217C2semidirect
5. #23100C2semidirect
6. #23069C2semidirect
7. #23034C2semidirect
8. #22919C2semidirect
9. #22875C2semidirect
10. #22805C2semidirect
11. #22663C2semidirect
12. #22581C2semidirect
14. D4×#103C2semidirect
15. #22218C2semidirect
16. #22200C2semidirect
17. #22113C2semidirect
18. #22058C2semidirect
19. #21591C2semidirect
20. C4×#461C2semidirect
21. #21114C2semidirect
22. #21064C2semidirect
23. #20562C2semidirect
26. #3329C4semidirect
144. D4×Q8C2×C4semidirect
171. #487C2×C4semidirect
172. #485C2×C4semidirect
173. #477C2×C4semidirect
174. #468C2×C4semidirect
175. #461C2×C4semidirect
176. #448C2×C4semidirect
178. C4×SD16C2×C4semidirect
179. #436C2×C4semidirect
192. #419C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33292
#344872
#343212
#232172
#231002
#230692
#230342
#229192
#228752
#228052
#226632
#225812
#224892
D4×#1032
#222182
#222002
#221132
#220582
#215912
C4×#4612
#211142
#210642
#205622