Finite Group Databasebeta

← #6400598

Subgroups — #6400598

Order 512.

1941 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3358C211yesmaximal, characteristic
2#34487C211yesmaximal, characteristic, complemented
3#34330C211yesmaximal, characteristic, complemented
4#23220C211yesmaximal, characteristic, complemented
5#23215C212yesmaximal, complemented
6#23108C212yesmaximal, complemented
7#23093C211yesmaximal, characteristic, complemented
8#23079C212yesmaximal, complemented
9#23060C211yesmaximal, characteristic, complemented
10#22813C211yesmaximal, characteristic, complemented
11#22810C212yesmaximal, complemented
12#22725C211yesmaximal, characteristic, complemented
13#22545C211yesmaximal, characteristic, complemented
14#22523C211yesmaximal, characteristic, complemented
15#22230C212yesmaximal, complemented
16#22219C211yesmaximal, characteristic, complemented
17#22158C212yesmaximal, complemented
18#22145C211yesmaximal, characteristic, complemented
19#21624C212yesmaximal, complemented
20C4×#474C211yesmaximal, characteristic, complemented
21#21134C212yesmaximal, complemented
22#21118C211yesmaximal, characteristic, complemented
23#20571C211yesmaximal, characteristic, complemented
24C2×#550C2211yescharacteristic
25C2×D4×Q8C2211yescharacteristic
26#3358C4116yescomplemented
27C2×#486C2212yes—
28C2×#486C2211yescharacteristic
29C2×#474C2211yescharacteristic
30C2×#474C2212yes—
31C2×#459C2211yescharacteristic
32C2×#459C2212yes—
33C2×#446C2211yescharacteristic
34C2×C8×Q8C2211yescharacteristic
35C2×C4×D8C2212yes—
36C2×C4×D8C2211yescharacteristic
37#2378—22no—
38#2369C2212yes—
39#2366C2211yescharacteristic
40#2366C2212yes—
41#2365C2211yescharacteristic
42#2364—22no—
43#2363—21no—
44#2362—21no—
45#2357C2212yes—
46#2357C2212yes—
47#2355C2211yescharacteristic
48#2355C2211yescharacteristic
49#2354C2211yescharacteristic
50#2354C2211yescharacteristic
51Q8×C22⋊C4—21no—
52#2339—21no—
53#2333—22no—
54#2332—22no—
55#2331C2212yes—
56#2328C2212yes—
57#2323—21no—
58#2319C2212yes—
59#2310—21no—
60C4×C4⋊Q8C2211yescharacteristic
61C4×#127C2211yescharacteristic
62C4×#121—21no—
63#2297—21no—
64#2295C2211yescharacteristic
65#2293C2211yescharacteristic
66#2275C2212yes—
67C42×D4C2211yescharacteristic
68#1993C2212yes—
69#1990C2211yescharacteristic
70#1988C2211yescharacteristic
71#1987C2212yes—
72#1982C2211yescharacteristic
73#1982C2212yes—
74#1972C2212yes—
75#1970C2212yes—
76#1970C2212yes—
77#1961C2212yes—
78#1957C2211yescharacteristic
79#1949C2212yes—
80#1949C2212yes—
81#1947C2211yescharacteristic
82#1947C2211yescharacteristic
83#1936C2212yes—
84#1934C2212yes—
85#1934C2212yes—
86#1926C2211yescharacteristic
87#1926C2212yes—
88#1926C2212yes—
89#1926C2212yes—
90#1926C2212yes—
91#1926C2212yes—
92#1926C2211yescharacteristic
93#1925C2212yes—
94#1925C2212yes—
95#1921C2211yescharacteristic
96#1921C2211yescharacteristic
97#1918C2212yes—
98#1918C2212yes—
99#1879C2212yes—
100#1879C2211yescharacteristic
101#1879C2211yescharacteristic
102#1879C2212yes—
103#1864C2212yes—
104#1864C2211yescharacteristic
105#1864C2211yescharacteristic
106#1864C2212yes—
107#1864C2212yes—
108#1862C2212yes—
109#1862C2212yes—
110#1846C2212yes—
111#1844C2211yescharacteristic
112#1804C2212yes—
113#1804C2212yes—
114#1802C2211yescharacteristic
115#1802C2211yescharacteristic
116#1776C2212yes—
117C4×#107C2212yes—
118C4×#107C2212yes—
119C4×#106C2211yescharacteristic
120C4×#106C2212yes—
121#1771C2212yes—
122#1770C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124C8×C4⋊C4C2212yes—
125#1768C2212yes—
126C4×C4⋊C8C2211yescharacteristic
127#1762C2212yes—
128#1762C2212yes—
129#1762C2212yes—
130C4×#102C2211yescharacteristic
131C4×#102C2212yes—
132C4×#102C2211yescharacteristic
133C4×#102C2212yes—
134#1746C2212yes—
135#1744C2211yescharacteristic
136C22×#41—21no—
137C23×Q8—21no—
138C22×D8C2312yes—
139C22×D8C2311yescharacteristic
140#550—24no—
141#550C2×C418yes—
142D4×Q8—24no—
143D4×Q8C2×C418yescomplemented
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2312yes—
146C2×#127C2311yescharacteristic
147C2×#127C2312yes—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—22no—
150C2×#121—22no—
151C2×#121—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8C2311yescharacteristic
155C2×C4×D4—21no—
156C2×C4×D4—22no—
157C2×C4×D4—21no—
158C2×C4×D4—21no—
159C2×C4×D4C2311yescharacteristic
160C2×C4×D4C2312yes—
161C2×C4×D4C2311yescharacteristic
162C2×C4×D4C2311yescharacteristic
163C2×C4×D4C2312yes—
164C2×C4×D4C2312yes—
165C2×C4×D4C2312yes—
166C2×C4×D4C2311yescharacteristic
167C2×#117—21no—
168C2×#117—21no—
169C2×#117—21no—
170C22×C42—21no—
171#486C2×C4116yescomplemented
172#486C2×C418yescomplemented
173#474C2×C418yescomplemented
174#474C2×C4116yescomplemented
175#459C2×C418yescomplemented
176#459C2×C4116yescomplemented
177#446—24no—
178C8×Q8C2×C418yescomplemented
179C4×D8C2×C4116yescomplemented
180C4×D8C2×C418yescomplemented
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2311yescharacteristic
185C2×#106C2311yescharacteristic
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2311yescharacteristic
189C2×C4⋊C8C2311yescharacteristic
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2312yes—
193C2×#102C2311yescharacteristic
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×#102C2311yescharacteristic
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2311yescharacteristic
200C2×#102C2312yes—
201C2×#102C2311yescharacteristic
202C2×#102C2312yes—
203C2×#102C2311yescharacteristic
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2311yescharacteristic
209C2×#97C2312yes—
210C2×#97C2312yes—
211C2×C4×C8C2311yescharacteristic
212C2×C4×C8C2312yes—
213C2×C4×C8C2312yes—
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2312yes—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—22no—
221#391—22no—
222#391—22no—
223#391—22no—
224#391D411yescharacteristic
225#391D411yescharacteristic
226#390—22no—
227#390—21no—
228#390—21no—
229#390—21no—
230#390C2312yes—
231#390C2311yescharacteristic
232#390C2312yes—
233#390C2312yes—
234#390C2312yes—
235#390C2311yescharacteristic
236#389—22no—
237#389—21no—
238#389D411yescharacteristic
239#389D411yescharacteristic
240#389C2312yes—
241#389C2312yes—
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—21no—
249#388—21no—
250#388—22no—
251#388—22no—
252#388—22no—
253#388—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387D412yes—
260#387D412yes—
261#386—22no—
262#386—22no—
263#386—22no—
264#386—22no—
265#386—22no—
266#386—22no—
267#386—22no—
268#384C2311yescharacteristic
269#384C2311yescharacteristic
270#382C2312yes—
271#382C2312yes—
272#381—22no—
273#381—22no—
274#381—22no—
275#380—21no—
276#380—21no—
277#380—22no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—22no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2312yes—
284C4×C4⋊C4C2312yes—
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2311yescharacteristic
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2312yes—
294C4×C22⋊C4—21no—
295C4×C22⋊C4—21no—
296C4×C22⋊C4—21no—
297C4×C22⋊C4—21no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—22no—
303#376C2312yes—
304C2×#95—22no—
305C43C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#336C2312yes—
321#336C2311yescharacteristic
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2312yes—
325#336C2312yes—
326#336C2311yescharacteristic
327C2×#41—28no—
328C2×#41—82no—
329C2×#41—82no—
330C22×Q8—28no—
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—82no—
334C22×Q8—82no—
335C22×Q8C2×D411yescharacteristic
336C22×D4—21no—
337C22×D4—22no—
338C22×D4—21no—
339C22×D4—22no—
340C22×D4C2411yescharacteristic
341C22×D4C2412yes—
342C22×D4C2411yescharacteristic
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—21no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—21no—
351C2×D8—42no—
352C2×D8—41no—
353C2×D8—41no—
354C2×D8—42no—
355C2×D8C22×C418yes—
356C2×D8C22×C414yes—
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8—24no—
365C4⋊Q8C22×C414yes—
366C4⋊Q8C22×C418yes—
367#127—22no—
368#127—24no—
369#127C22×C414yes—
370#127C22×C418yes—
371C22⋊Q8—28no—
372C22⋊Q8—216no—
373#121—28no—
374#121—216no—
375C4×Q8—82no—
376C4×Q8—82no—
377C4×Q8C22×C414yes—
378C4×Q8#4114yes—
379C4×D4—22no—
380C4×D4—24no—
381C4×D4—22no—
382C4×D4—24no—
383C4×D4—22no—
384C4×D4—24no—
385C4×D4—41no—
386C4×D4—42no—
387C4×D4—41no—
388C4×D4—42no—
389C4×D4—42no—
390C4×D4—41no—
391C4×D4—82no—
392C4×D4—82no—
393C4×D4—82no—
394C4×D4—84no—
395C4×D4C22×C414yes—
396C4×D4C22×C418yes—
397C4×D4C22×C414yes—
398C4×D4C22×C418yes—
399#117—82no—
400#117—82no—
401#117—82no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4C2×D411yescharacteristic
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D412yes—
415C2×C4⋊C4C2×D412yes—
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2×D412yes—
418C2×C4⋊C4C2411yescharacteristic
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2411yescharacteristic
421C2×C4⋊C4C2411yescharacteristic
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2411yescharacteristic
424C2×C4⋊C4C2411yescharacteristic
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2411yescharacteristic
427C2×C22⋊C4—22no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—22no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—22no—
457C2×C42—82no—
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2412yes—
465C2×C42C2411yescharacteristic
466C2×C42C2412yes—
467#107—42no—
468#107—42no—
469#107C22×C418yes—
470#107C22×C414yes—
471#106—22no—
472#106—42no—
473#106—41no—
474#106—42no—
475C4⋊C8—22no—
476C4⋊C8—24no—
477C4⋊C8C22×C414yes—
478C4⋊C8C22×C418yes—
479#102—22no—
480#102—41no—
481#102—42no—
482#102—42no—
483#102—42no—
484#102—42no—
485#102—42no—
486#102—42no—
487#102—41no—
488#102—41no—
489#102C22×C414yes—
490#102C22×C414yes—
491#102C22×C418yes—
492#102C22×C418yes—
493#102C22×C418yes—
494#102C22×C418yes—
495#97—24no—
496#97—42no—
497C4×C8—22no—
498C4×C8—42no—
499C4×C8—42no—
500C4×C8C22×C414yes—
501C4×C8C22×C418yes—
502#95—21no—
503#95—22no—
504#95—22no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—22no—
509#95—22no—
510#95—21no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—21no—
520#95C2×D412yes—
521#95C2×D412yes—
522#95C2×D412yes—
523#95C2×D412yes—
524#95C2×D412yes—
525#95C2×D412yes—
526#95C2×D412yes—
527C24—21no—
528C24—22no—
529C24—21no—
530#41—816no—
531C2×Q8—24no—
532C2×Q8—28no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—42no—
536C2×Q8—42no—
537C2×Q8—82no—
538C2×Q8—82no—
539C2×Q8—816no—
540C2×Q8C4×D414yes—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—82no—
568C2×D4C23×C412yes—
569C2×D4C23×C414yes—
570C2×D4C23×C412yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—42no—
585C22×C4—44no—
586C22×C4—42no—
587C22×C4—44no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4C22×D412yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D412yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C2511yescharacteristic
615D8—48no—
616D8—44no—
617C2×C8—21no—
618C2×C8—22no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—22no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—22no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8C23×C412yes—
633C2×C8C23×C414yes—
634C2×C8C23×C412yes—
635C4⋊C4—28no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—81no—
658C4⋊C4—81no—
659C4⋊C4—81no—
660C4⋊C4—81no—
661C4⋊C4—82no—
662C4⋊C4—82no—
663C4⋊C4C4×D418yes—
664C4⋊C4C4×D414yes—
665C4⋊C4C23×C412yes—
666C4⋊C4C23×C414yes—
667C4⋊C4C23×C412yes—
668C4⋊C42−1+412yes—
669C22⋊C4—24no—
670C22⋊C4—28no—
671C22⋊C4—24no—
672C22⋊C4—28no—
673C22⋊C4—42no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—44no—
679C22⋊C4—81no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—21no—
693C42—22no—
694C42—21no—
695C42—22no—
696C42—21no—
697C42—21no—
698C42—41no—
699C42—42no—
700C42—42no—
701C42—82no—
702C42—81no—
703C42—81no—
704C42—82no—
705C42—82no—
706C42—82no—
707C42—82no—
708C42—82no—
709C42C23×C414yes—
710C42C23×C412yes—
711C42C2×#4112yes—
712C42C2×#4114yes—
713C23—22no—
714C23—22no—
715C23—24no—
716C23—41no—
717C23—42no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—41no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23C23×D411yescharacteristic
735Q8—28no—
736Q8—48no—
737Q8—88no—
738D4—22no—
739D4—22no—
740D4—24no—
741D4—22no—
742D4—22no—
743D4—24no—
744D4—48no—
745D4—41no—
746D4—41no—
747D4—42no—
748D4—41no—
749D4—41no—
750D4—42no—
751D4—84no—
752D4—88no—
753D4—88no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—48no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—88no—
807C2×C4—88no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4—164no—
811C2×C4—164no—
812C2×C4C2×C4×D412yes—
813C2×C4C2×C4×D414yes—
814C2×C4C2×C4×D414yes—
815C2×C4C2×C4×D412yes—
816C2×C4#57612yes—
817C2×C4#57612yes—
818C2×C4#57712yes—
819C2×C4C24×C411yescharacteristic
820C2×C4C22×#4111yescharacteristic
821C2×C4C2×2−1+411yescharacteristic
822C2×C4#58511yescharacteristic
823C2×C4#58511yescharacteristic
824C2×C4#58511yescharacteristic
825C8—24no—
826C8—22no—
827C8—22no—
828C8—41no—
829C8—41no—
830C8—42no—
831C22—42no—
832C22—42no—
833C22—44no—
834C22—44no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—44no—
840C22—81no—
841C22—82no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—82no—
846C22—82no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—82no—
851C22—81no—
852C22C22×C4×D411yescharacteristic
853C22#348711yescharacteristic
854C22#348911yescharacteristic
855C22C2×#57611yescharacteristic
856C22C2×#57611yescharacteristic
857C22C2×#57711yescharacteristic
858C22#358411yescharacteristic
859C4—24no—
860C4—22no—
861C4—24no—
862C4—22no—
863C4—42no—
864C4—42no—
865C4—44no—
866C4—41no—
867C4—42no—
868C4—41no—
869C4—41no—
870C4—42no—
871C4—42no—
872C4—81no—
873C4—82no—
874C4—81no—
875C4—81no—
876C4—82no—
877C4#294814yes—
878C4#342811yescharacteristic
879C4C4×2−1+411yescharacteristic
880C4#351811yescharacteristic
881C4#352411yescharacteristic
882C2—82no—
883C2—82no—
884C2—84no—
885C2#3429311yescharacteristic
886C2C2×#294811yescharacteristic
887C2C4×#57711yescharacteristic
888C2#6192611yescharacteristic
889C2#6193711yescharacteristic
890C2#6219911yescharacteristic
891C2#6222211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3358C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34487C2semidirect
3. #34330C2semidirect
4. #23220C2semidirect
5. #23215C2semidirect
6. #23108C2semidirect
7. #23093C2semidirect
8. #23079C2semidirect
9. #23060C2semidirect
10. #22813C2semidirect
11. #22810C2semidirect
12. #22725C2semidirect
13. #22545C2semidirect
14. #22523C2semidirect
15. #22230C2semidirect
16. #22219C2semidirect
17. #22158C2semidirect
18. #22145C2semidirect
19. #21624C2semidirect
20. C4×#474C2semidirect
21. #21134C2semidirect
22. #21118C2semidirect
23. #20571C2semidirect
26. #3358C4semidirect
143. D4×Q8C2×C4semidirect
171. #486C2×C4semidirect
172. #486C2×C4semidirect
173. #474C2×C4semidirect
174. #474C2×C4semidirect
175. #459C2×C4semidirect
176. #459C2×C4semidirect
178. C8×Q8C2×C4semidirect
179. C4×D8C2×C4semidirect
180. C4×D8C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33582
#344872
#343302
#232202
#232152
#231082
#230932
#230792
#230602
#228132
#228102
#227252
#225452
#225232
#222302
#222192
#221582
#221452
#216242
C4×#4742
#211342
#211182
#205712