Finite Group Databasebeta

← #6404377

Subgroups — #6404377

Order 512.

1924 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3358C211yesmaximal, characteristic
2#34494C211yesmaximal, characteristic, complemented
3#34487C211yesmaximal, characteristic, complemented
4#23216C211yesmaximal, characteristic, complemented
5#23215C212yesmaximal, complemented
6#23108C212yesmaximal, complemented
7#23099C211yesmaximal, characteristic, complemented
8#22979C212yesmaximal, complemented
9#22968C211yesmaximal, characteristic, complemented
10#22772C212yesmaximal, complemented
11#22766C211yesmaximal, characteristic, complemented
12#22741C211yesmaximal, characteristic, complemented
13#22545C211yesmaximal, characteristic, complemented
14#22523C211yesmaximal, characteristic, complemented
15#22158C212yesmaximal, complemented
16#22151C211yesmaximal, characteristic, complemented
17#22127C212yesmaximal, complemented
18#22116C211yesmaximal, characteristic, complemented
19#21644C212yesmaximal, complemented
20C4×#486C211yesmaximal, characteristic, complemented
21#21284C212yesmaximal, complemented
22#21275C211yesmaximal, characteristic, complemented
23#20516C211yesmaximal, characteristic, complemented
24C2×#550C2211yescharacteristic
25C2×D4×Q8C2211yescharacteristic
26#3358C4116yescomplemented
27C2×#486C2211yescharacteristic
28C2×#486C2212yes—
29C2×#474C2211yescharacteristic
30C2×#474C2212yes—
31C2×#459C2211yescharacteristic
32C2×#459C2212yes—
33C2×#446C2211yescharacteristic
34C2×C8×Q8C2211yescharacteristic
35C2×C4×D8C2211yescharacteristic
36C2×C4×D8C2212yes—
37#2378—22no—
38#2377—22no—
39#2369C2212yes—
40#2366C2211yescharacteristic
41#2366C2212yes—
42#2365C2211yescharacteristic
43#2362—21no—
44#2361—21no—
45#2357C2212yes—
46#2355C2211yescharacteristic
47#2355C2211yescharacteristic
48#2354C2211yescharacteristic
49#2349C2212yes—
50D4×C4⋊C4C2211yescharacteristic
51Q8×C22⋊C4—21no—
52#2339—21no—
53#2332—22no—
54#2331C2212yes—
55#2328C2212yes—
56#2325—22no—
57#2324—21no—
58#2323—21no—
59#2319C2212yes—
60#2319C2212yes—
61#2311—21no—
62#2310—21no—
63C4×C4⋊Q8C2211yescharacteristic
64C4×#127C2211yescharacteristic
65#2295C2211yescharacteristic
66#2293C2211yescharacteristic
67#2293C2211yescharacteristic
68#1993C2212yes—
69#1990C2211yescharacteristic
70#1988C2211yescharacteristic
71#1987C2212yes—
72#1982C2211yescharacteristic
73#1982C2212yes—
74#1972C2212yes—
75#1972C2212yes—
76#1970C2211yescharacteristic
77#1970C2211yescharacteristic
78#1961C2212yes—
79#1957C2211yescharacteristic
80#1949C2212yes—
81#1949C2212yes—
82#1948C2211yescharacteristic
83#1948C2211yescharacteristic
84#1943C2212yes—
85#1943C2212yes—
86#1942C2211yescharacteristic
87#1942C2211yescharacteristic
88#1936C2212yes—
89#1936C2212yes—
90#1934C2211yescharacteristic
91#1934C2211yescharacteristic
92#1934C2211yescharacteristic
93#1934C2211yescharacteristic
94#1934C2212yes—
95#1934C2212yes—
96#1934C2212yes—
97#1934C2212yes—
98#1926C2212yes—
99#1926C2212yes—
100#1925C2212yes—
101#1921C2212yes—
102#1921C2212yes—
103#1918C2212yes—
104#1879C2212yes—
105#1879C2212yes—
106#1879C2212yes—
107#1864C2212yes—
108#1864C2212yes—
109#1862C2212yes—
110#1835C2212yes—
111#1834C2211yescharacteristic
112#1804C2212yes—
113#1804C2212yes—
114#1802C2211yescharacteristic
115#1802C2211yescharacteristic
116C4×#107C2211yescharacteristic
117C4×#106C2212yes—
118#1771C2212yes—
119#1770C2211yescharacteristic
120C8×C4⋊C4C2212yes—
121C8×C4⋊C4C2211yescharacteristic
122#1768C2212yes—
123#1767C2211yescharacteristic
124#1762C2212yes—
125#1762C2212yes—
126#1762C2212yes—
127#1762C2212yes—
128C4×#102C2211yescharacteristic
129C4×#102C2211yescharacteristic
130C4×#102C2212yes—
131C4×#102C2212yes—
132C4×#102C2212yes—
133C4×#102C2212yes—
134#1726C2212yes—
135C42×C8C2211yescharacteristic
136C22×#41—21no—
137C23×Q8—21no—
138C22×D8C2311yescharacteristic
139C22×D8C2312yes—
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—21no—
151C2×#121—22no—
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×D4C2311yescharacteristic
161C2×C4×D4C2312yes—
162C2×C4×D4C2312yes—
163C2×C4×D4C2312yes—
164C2×C4×D4C2312yes—
165C2×C4×D4C2312yes—
166C2×#117—21no—
167C2×#117—21no—
168C2×#117—21no—
169C22×C4⋊C4—21no—
170#486C2×C418yescomplemented
171#486C2×C4116yescomplemented
172#474C2×C418yescomplemented
173#474C2×C4116yescomplemented
174#459C2×C418yescomplemented
175#459C2×C4116yescomplemented
176#446—24no—
177C8×Q8C2×C418yescomplemented
178C4×D8C2×C418yescomplemented
179C4×D8C2×C4116yescomplemented
180C2×#107C2311yescharacteristic
181C2×#107C2311yescharacteristic
182C2×#107C2311yescharacteristic
183C2×#107C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2311yescharacteristic
189C2×C4⋊C8C2312yes—
190C2×#102C2312yes—
191C2×#102C2311yescharacteristic
192C2×#102C2311yescharacteristic
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×#102C2311yescharacteristic
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2311yescharacteristic
200C2×#102C2312yes—
201C2×#102C2311yescharacteristic
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2311yescharacteristic
206C2×#97C2312yes—
207C2×#97C2312yes—
208C2×#97C2312yes—
209C2×C4×C8C2311yescharacteristic
210C2×C4×C8C2311yescharacteristic
211C2×C4×C8C2311yescharacteristic
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2312yes—
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2312yes—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—22no—
222#391—22no—
223#391—22no—
224#391—22no—
225#391D411yescharacteristic
226#391D411yescharacteristic
227#390—21no—
228#390—22no—
229#390—21no—
230#390—21no—
231#390C2312yes—
232#390C2311yescharacteristic
233#390C2312yes—
234#390C2312yes—
235#390C2311yescharacteristic
236#390C2311yescharacteristic
237#390C2311yescharacteristic
238#389—22no—
239#389—21no—
240#389D411yescharacteristic
241#389D411yescharacteristic
242#389C2312yes—
243#389C2311yescharacteristic
244#389C2312yes—
245#389C2312yes—
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#388—22no—
250#388—22no—
251#388—21no—
252#388—21no—
253#388—21no—
254#388—21no—
255#388—22no—
256#388—22no—
257#388—22no—
258#388—22no—
259#388—22no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#387D412yes—
266#387D412yes—
267#386—22no—
268#386—22no—
269#386—22no—
270#386—22no—
271#386—22no—
272#386—22no—
273#386—22no—
274#385—22no—
275#385—22no—
276#385—22no—
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#382C2312yes—
280#382C2312yes—
281#381—22no—
282#381—22no—
283#381—22no—
284#380—21no—
285#380—21no—
286#380—22no—
287#380—22no—
288#380—22no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—22no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2311yescharacteristic
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2312yes—
302C4×C22⋊C4—21no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—22no—
305#376C2312yes—
306C2×#95—22no—
307C43C2311yescharacteristic
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#340C2312yes—
324#336C2312yes—
325#336C2312yes—
326#336C2312yes—
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—22no—
348C23×C4—22no—
349C23×C4—22no—
350C2×D8—41no—
351C2×D8—41no—
352C2×D8—42no—
353C2×D8—42no—
354C2×D8C22×C414yes—
355C2×D8C22×C418yes—
356C22×C8C2411yescharacteristic
357C22×C8C2412yes—
358C22×C8C2411yescharacteristic
359C22×C8C2412yes—
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C4⋊Q8—22no—
363C4⋊Q8—24no—
364C4⋊Q8C22×C414yes—
365C4⋊Q8C22×C418yes—
366#127—22no—
367#127—24no—
368#127C22×C414yes—
369#127C22×C418yes—
370C22⋊Q8—28no—
371C22⋊Q8—216no—
372#121—28no—
373#121—216no—
374C4×Q8—82no—
375C4×Q8—82no—
376C4×Q8C22×C414yes—
377C4×Q8#4114yes—
378C4×D4—22no—
379C4×D4—24no—
380C4×D4—22no—
381C4×D4—24no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—42no—
385C4×D4—42no—
386C4×D4—42no—
387C4×D4—42no—
388C4×D4—82no—
389C4×D4—82no—
390C4×D4—82no—
391C4×D4—84no—
392C4×D4C22×C414yes—
393C4×D4C22×C418yes—
394C4×D4C22×C414yes—
395C4×D4C22×C418yes—
396#117—82no—
397#117—82no—
398#117—82no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
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—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—82no—
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2×D412yes—
416C2×C4⋊C4C2×D412yes—
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2×D412yes—
419C2×C4⋊C4C2411yescharacteristic
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2411yescharacteristic
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2411yescharacteristic
424C2×C4⋊C4C2411yescharacteristic
425C2×C4⋊C4C2411yescharacteristic
426C2×C4⋊C4C2411yescharacteristic
427C2×C4⋊C4C2412yes—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2412yes—
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2412yes—
465#107—41no—
466#107—41no—
467#107C22×C414yes—
468#107C22×C418yes—
469#106—42no—
470#106—42no—
471C4⋊C8—22no—
472C4⋊C8—24no—
473C4⋊C8C22×C414yes—
474C4⋊C8C22×C418yes—
475#102—24no—
476#102—22no—
477#102—22no—
478#102—42no—
479#102—41no—
480#102—42no—
481#102—42no—
482#102—42no—
483#102—42no—
484#102—41no—
485#102C22×C414yes—
486#102C22×C418yes—
487#102C22×C414yes—
488#102C22×C418yes—
489#102C22×C418yes—
490#102C22×C418yes—
491#97—24no—
492#97—42no—
493#97—42no—
494C4×C8—22no—
495C4×C8—22no—
496C4×C8—41no—
497C4×C8—41no—
498C4×C8—42no—
499C4×C8—41no—
500C4×C8C22×C414yes—
501C4×C8C22×C418yes—
502#95—21no—
503#95—22no—
504#95—22no—
505#95—21no—
506#95—21no—
507#95—22no—
508#95—21no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—21no—
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—21no—
529C24—22no—
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—22no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—21no—
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—22no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—44no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4C22×D412yes—
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×C4C2511yescharacteristic
612D8—44no—
613D8—48no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—21no—
623C2×C8—22no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8C23×C412yes—
629C2×C8C23×C412yes—
630C2×C8C23×C414yes—
631C2×C82−1+412yes—
632C4⋊C4—28no—
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—24no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—81no—
656C4⋊C4—82no—
657C4⋊C4—81no—
658C4⋊C4—81no—
659C4⋊C4—81no—
660C4⋊C4—81no—
661C4⋊C4—81no—
662C4⋊C4—82no—
663C4⋊C4—82no—
664C4⋊C4C4×D418yes—
665C4⋊C4C4×D414yes—
666C4⋊C4C23×C412yes—
667C4⋊C4C23×C414yes—
668C4⋊C4C23×C412yes—
669C22⋊C4—24no—
670C22⋊C4—28no—
671C22⋊C4—24no—
672C22⋊C4—28no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C22⋊C4—82no—
678C22⋊C4—81no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—22no—
698C42—22no—
699C42—41no—
700C42—42no—
701C42—42no—
702C42—82no—
703C42—82no—
704C42—82no—
705C42—82no—
706C42—82no—
707C42C23×C414yes—
708C42C23×C412yes—
709C42C2×#4112yes—
710C42C2×#4114yes—
711C23—22no—
712C23—22no—
713C23—24no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—42no—
732C23C23×D411yescharacteristic
733Q8—28no—
734Q8—48no—
735Q8—88no—
736D4—22no—
737D4—22no—
738D4—24no—
739D4—22no—
740D4—22no—
741D4—24no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4—42no—
746D4—41no—
747D4—41no—
748D4—42no—
749D4—84no—
750D4—88no—
751D4—88no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—48no—
785C2×C4—48no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—88no—
805C2×C4—88no—
806C2×C4—164no—
807C2×C4—164no—
808C2×C4—164no—
809C2×C4C2×C4×D412yes—
810C2×C4C2×C4×D414yes—
811C2×C4C2×C4×D414yes—
812C2×C4C2×C4×D412yes—
813C2×C4#57612yes—
814C2×C4#57612yes—
815C2×C4#57712yes—
816C2×C4C24×C411yescharacteristic
817C2×C4C22×#4111yescharacteristic
818C2×C4C2×2−1+411yescharacteristic
819C2×C4#58511yescharacteristic
820C2×C4#58511yescharacteristic
821C2×C4#58511yescharacteristic
822C8—22no—
823C8—24no—
824C8—22no—
825C8—22no—
826C8—41no—
827C8—42no—
828C22—42no—
829C22—42no—
830C22—44no—
831C22—42no—
832C22—42no—
833C22—44no—
834C22—42no—
835C22—44no—
836C22—42no—
837C22—81no—
838C22—82no—
839C22—81no—
840C22—82no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—82no—
846C22—81no—
847C22—81no—
848C22—82no—
849C22C22×C4×D411yescharacteristic
850C22#349711yescharacteristic
851C22#350011yescharacteristic
852C22C2×#57611yescharacteristic
853C22C2×#57611yescharacteristic
854C22C2×#57711yescharacteristic
855C22#358411yescharacteristic
856C4—24no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—42no—
861C4—42no—
862C4—44no—
863C4—42no—
864C4—41no—
865C4—42no—
866C4—41no—
867C4—41no—
868C4—82no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—81no—
873C4—82no—
874C4#294814yes—
875C4#342811yescharacteristic
876C4C4×2−1+411yescharacteristic
877C4#351611yescharacteristic
878C4#352411yescharacteristic
879C2—82no—
880C2—82no—
881C2—84no—
882C2#3431211yescharacteristic
883C2C2×#294811yescharacteristic
884C2C4×#57711yescharacteristic
885C2#6238111yescharacteristic
886C2#6238411yescharacteristic
887C2#6255011yescharacteristic
888C2#6256111yescharacteristic
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. #34494C2semidirect
3. #34487C2semidirect
4. #23216C2semidirect
5. #23215C2semidirect
6. #23108C2semidirect
7. #23099C2semidirect
8. #22979C2semidirect
9. #22968C2semidirect
10. #22772C2semidirect
11. #22766C2semidirect
12. #22741C2semidirect
13. #22545C2semidirect
14. #22523C2semidirect
15. #22158C2semidirect
16. #22151C2semidirect
17. #22127C2semidirect
18. #22116C2semidirect
19. #21644C2semidirect
20. C4×#486C2semidirect
21. #21284C2semidirect
22. #21275C2semidirect
23. #20516C2semidirect
26. #3358C4semidirect
143. D4×Q8C2×C4semidirect
170. #486C2×C4semidirect
171. #486C2×C4semidirect
172. #474C2×C4semidirect
173. #474C2×C4semidirect
174. #459C2×C4semidirect
175. #459C2×C4semidirect
177. C8×Q8C2×C4semidirect
178. C4×D8C2×C4semidirect
179. 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
#344942
#344872
#232162
#232152
#231082
#230992
#229792
#229682
#227722
#227662
#227412
#225452
#225232
#221582
#221512
#221272
#221162
#216442
C4×#4862
#212842
#212752
#205162