Finite Group Databasebeta

← #6404581

Subgroups — #6404581

Order 512.

1963 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3392C211yesmaximal, characteristic
2#34494C211yesmaximal, characteristic
3#34488C211yesmaximal, characteristic, complemented
4#23190C211yesmaximal, characteristic, complemented
5#23190C212yesmaximal, complemented
6#23012C212yesmaximal, complemented
7#23010C212yesmaximal, complemented
8#22997C211yesmaximal, characteristic, complemented
9#22996C211yesmaximal, characteristic, complemented
10#22727C211yesmaximal, characteristic, complemented
11#22673C212yesmaximal, complemented
12#22671C211yesmaximal, characteristic, complemented
13#22547C211yesmaximal, characteristic, complemented
14#22545C211yesmaximal, characteristic
15#22162C212yesmaximal, complemented
16#22160C212yesmaximal, complemented
17#22147C211yesmaximal, characteristic, complemented
18#22146C211yesmaximal, characteristic, complemented
19#21695C212yesmaximal, complemented
20#21692C211yesmaximal, characteristic, complemented
21#21285C212yesmaximal, complemented
22#21279C211yesmaximal, characteristic, complemented
23#20521C211yesmaximal, characteristic, complemented
24C2×#557C2211yescharacteristic
25C2×#550C2211yescharacteristic
26#3392C4116yescomplemented
27C2×#492C2211yescharacteristic
28C2×#492C2212yes—
29C2×#460C2211yescharacteristic
30C2×#460C2212yes—
31C2×#461C2211yescharacteristic
32C2×#461C2212yes—
33C2×#446C2211yescharacteristic
34C2×C8×Q8C2211yescharacteristic
35C2×#440C2212yes—
36C2×#440C2212yes—
37C2×#440C2212yes—
38C2×#440C2212yes—
39C2×C4×SD16C2212yes—
40C2×C4×SD16C2212yes—
41C2×C4×SD16C2211yescharacteristic
42C2×C4×SD16C2212yes—
43#2382—22no—
44#2377—22no—
45#2370—21no—
46#2366C2211yescharacteristic
47#2366C2212yes—
48#2365C2211yescharacteristic
49#2365C2212yes—
50#2361—21no—
51#2355—21no—
52#2355C2211yescharacteristic
53#2355C2211yescharacteristic
54#2351C2212yes—
55Q8×C4⋊C4C2211yescharacteristic
56#2349C2212yes—
57D4×C4⋊C4C2211yescharacteristic
58#2339—21no—
59#2336—22no—
60#2330—21no—
61#2328C2212yes—
62#2327C2212yes—
63#2325—22no—
64#2324—21no—
65#2320—21no—
66#2320C2212yes—
67#2319C2212yes—
68#2311—21no—
69C4×C4⋊Q8C2211yescharacteristic
70C4×#127C2211yescharacteristic
71#2295C2211yescharacteristic
72#2295C2211yescharacteristic
73#2293C2211yescharacteristic
74#1982C2211yescharacteristic
75#1982C2212yes—
76#1981C2211yescharacteristic
77#1981C2212yes—
78#1973C2211yescharacteristic
79#1973C2211yescharacteristic
80#1973C2212yes—
81#1973C2212yes—
82#1973C2212yes—
83#1968C2212yes—
84#1968C2212yes—
85#1961C2212yes—
86#1960C2212yes—
87#1957C2211yescharacteristic
88#1956C2211yescharacteristic
89#1949C2212yes—
90#1949C2212yes—
91#1948C2211yescharacteristic
92#1948C2211yescharacteristic
93#1944C2211yescharacteristic
94#1944C2211yescharacteristic
95#1944C2212yes—
96#1936C2211yescharacteristic
97#1936C2211yescharacteristic
98#1935C2211yescharacteristic
99#1935C2211yescharacteristic
100#1934C2212yes—
101#1934C2212yes—
102#1933C2212yes—
103#1933C2212yes—
104#1880C2212yes—
105#1880C2212yes—
106#1880C2212yes—
107#1877C2212yes—
108#1877C2212yes—
109#1877C2212yes—
110#1865C2212yes—
111#1865C2212yes—
112#1864C2212yes—
113#1864C2212yes—
114#1863C2212yes—
115#1862C2212yes—
116#1846C2212yes—
117#1845C2211yescharacteristic
118#1805C2212yes—
119#1804C2212yes—
120#1803C2211yescharacteristic
121#1802C2211yescharacteristic
122C4×#107C2211yescharacteristic
123C4×#107C2212yes—
124#1771C2212yes—
125#1770C2211yescharacteristic
126#1770C2212yes—
127C8×C4⋊C4C2211yescharacteristic
128#1768C2212yes—
129C4×C4⋊C8C2211yescharacteristic
130#1763C2212yes—
131#1762C2212yes—
132C4×#103C2211yescharacteristic
133C4×#102C2211yescharacteristic
134#1726C2212yes—
135C4×#97C2211yescharacteristic
136C22×#41—21no—
137C22×SD16C2312yes—
138C22×SD16C2311yescharacteristic
139C22×SD16C2312yes—
140C22×SD16C2312yes—
141C22×SD16C2312yes—
142#557—24no—
143#557C2×C418yescomplemented
144#550—24no—
145#550C2×C418yes—
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2312yes—
148C2×#127C2311yescharacteristic
149C2×#127C2312yes—
150C2×#125—21no—
151C2×#125—22no—
152C2×#121—21no—
153C2×#121—22no—
154C2×C4×Q8—21no—
155C2×C4×Q8C2311yescharacteristic
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2312yes—
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2311yescharacteristic
161C2×C4×D4—21no—
162C2×C4×D4—22no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2312yes—
167C2×C4×D4C2312yes—
168C2×C4×D4C2312yes—
169C2×C4×D4C2312yes—
170C2×#117—21no—
171C22×C4⋊C4—21no—
172#492C2×C418yescomplemented
173#492C2×C4116yescomplemented
174#461C2×C418yescomplemented
175#461C2×C4116yescomplemented
176#460C2×C418yescomplemented
177#460C2×C4116yescomplemented
178#446—24no—
179C8×Q8C2×C418yescomplemented
180#440—44no—
181#440—44no—
182#440—44no—
183#440—44no—
184C4×SD16—44no—
185C4×SD16—44no—
186C4×SD16C2×C418yescomplemented
187C4×SD16C2×C4116yescomplemented
188C2×#107C2312yes—
189C2×#107C2311yescharacteristic
190C2×#107C2311yescharacteristic
191C2×#107C2312yes—
192C2×#106C2312yes—
193C2×#106C2312yes—
194C2×#106C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2311yescharacteristic
198C2×C4⋊C8C2312yes—
199C2×#103C2311yescharacteristic
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2311yescharacteristic
206C2×#103C2311yescharacteristic
207C2×#103C2312yes—
208C2×#102C2311yescharacteristic
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2311yescharacteristic
215C2×#102C2311yescharacteristic
216C2×#102C2312yes—
217C2×#97C2311yescharacteristic
218C2×#97C2311yescharacteristic
219C2×#97C2312yes—
220C2×#97C2312yes—
221C2×#97C2311yescharacteristic
222C2×#97C2311yescharacteristic
223C2×C4×C8C2312yes—
224C2×C4×C8C2311yescharacteristic
225C2×C4×C8C2312yes—
226C2×C4×C8C2311yescharacteristic
227C2×C4×C8C2312yes—
228#391—21no—
229#391—21no—
230#391D411yescharacteristic
231#391D411yescharacteristic
232#391C2312yes—
233#391C2312yes—
234#391C2311yescharacteristic
235#391C2311yescharacteristic
236#390—21no—
237#390—22no—
238#390—21no—
239#390—21no—
240#390C2312yes—
241#390C2312yes—
242#390C2311yescharacteristic
243#390C2311yescharacteristic
244#389—21no—
245#389—22no—
246#389—22no—
247#389—22no—
248#389—21no—
249#389—21no—
250#389—22no—
251#389D411yescharacteristic
252#389D411yescharacteristic
253#389C2311yescharacteristic
254#389C2312yes—
255#389C2311yescharacteristic
256#389C2312yes—
257#389C2311yescharacteristic
258#389C2311yescharacteristic
259#388—21no—
260#388—21no—
261#388—22no—
262#388—22no—
263#387—22no—
264#387—22no—
265#387—21no—
266#387—21no—
267#387—22no—
268#387—22no—
269#387—22no—
270#387—22no—
271#387—22no—
272#387—22no—
273#387—22no—
274#387—22no—
275#387—22no—
276#387D412yes—
277#387D412yes—
278#386—22no—
279#386—22no—
280#386—22no—
281#386—22no—
282#386—22no—
283#386—22no—
284#386—22no—
285#385—22no—
286#385—22no—
287#385—22no—
288#384—21no—
289#384C2311yescharacteristic
290#384C2311yescharacteristic
291#383—22no—
292#382—22no—
293#382—22no—
294#382C2312yes—
295#382C2312yes—
296#381—22no—
297#380—21no—
298#380—22no—
299#380—22no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4—22no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4—21no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4—22no—
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2312yes—
315C4×C22⋊C4—21no—
316#376—21no—
317#376C2312yes—
318C2×#95—22no—
319C43C2311yescharacteristic
320#340C2312yes—
321#340C2312yes—
322#340C2311yescharacteristic
323#340C2311yescharacteristic
324#340C2312yes—
325#340C2311yescharacteristic
326#340C2312yes—
327#340C2311yescharacteristic
328#340C2311yescharacteristic
329#340C2311yescharacteristic
330#336C2312yes—
331#336C2312yes—
332#336C2312yes—
333C2×#41—28no—
334C2×#41—82no—
335C2×#41—82no—
336C22×Q8C2×D411yescharacteristic
337C22×Q8C2411yescharacteristic
338C22×Q8C2412yes—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4—22no—
343C22×D4C2411yescharacteristic
344C22×D4C2412yes—
345C23×C4—21no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C2×SD16—24no—
351C2×SD16—22no—
352C2×SD16—24no—
353C2×SD16—22no—
354C2×SD16—42no—
355C2×SD16—42no—
356C2×SD16—42no—
357C2×SD16—42no—
358C2×SD16—42no—
359C2×SD16—42no—
360C2×SD16C22×C418yes—
361C2×SD16C22×C414yes—
362C2×SD16C22×C418yes—
363C2×SD16C22×C418yes—
364C2×SD16C22×C418yes—
365C22×C8C2411yescharacteristic
366C22×C8C2412yes—
367C22×C8C2412yes—
368C22×C8C2411yescharacteristic
369C22×C8C2411yescharacteristic
370C22×C8C2411yescharacteristic
371C4⋊Q8—22no—
372C4⋊Q8—24no—
373C4⋊Q8C22×C414yes—
374C4⋊Q8C22×C418yes—
375#127—22no—
376#127—24no—
377#127C22×C414yes—
378#127C22×C418yes—
379#125—28no—
380#125—216no—
381#121—28no—
382#121—216no—
383C4×Q8—28no—
384C4×Q8—22no—
385C4×Q8—24no—
386C4×Q8—42no—
387C4×Q8—42no—
388C4×Q8—42no—
389C4×Q8—42no—
390C4×Q8—42no—
391C4×Q8—42no—
392C4×Q8C22×C414yes—
393C4×Q8C22×C418yes—
394C4×Q8C22×C414yes—
395C4×Q8#4114yes—
396C4×D4—22no—
397C4×D4—24no—
398C4×D4—42no—
399C4×D4—42no—
400C4×D4—42no—
401C4×D4—42no—
402C4×D4—42no—
403C4×D4—42no—
404C4×D4—82no—
405C4×D4—82no—
406C4×D4—82no—
407C4×D4—84no—
408C4×D4C22×C414yes—
409C4×D4C22×C418yes—
410#117—82no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—82no—
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C22⋊C4—22no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—21no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42C2×D411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2411yescharacteristic
472C2×C42C2412yes—
473C2×C42C2411yescharacteristic
474C2×C42C2411yescharacteristic
475C2×C42C2412yes—
476#107—24no—
477#107—22no—
478#107—22no—
479#107—42no—
480#106—42no—
481#106—42no—
482#106C22×C414yes—
483C4⋊C8—22no—
484C4⋊C8—24no—
485C4⋊C8C22×C414yes—
486C4⋊C8C22×C418yes—
487#103—22no—
488#103—24no—
489#103—42no—
490#103—41no—
491#103—42no—
492#103—42no—
493#103—42no—
494#103C22×C414yes—
495#103C22×C418yes—
496#102—22no—
497#102—24no—
498#102—42no—
499#102—41no—
500#102—42no—
501#102—42no—
502#102—42no—
503#102C22×C414yes—
504#102C22×C418yes—
505#97—22no—
506#97—22no—
507#97—24no—
508#97—22no—
509#97—24no—
510#97—41no—
511C4×C8—24no—
512C4×C8—22no—
513C4×C8—42no—
514C4×C8C22×C414yes—
515C4×C8C22×C418yes—
516#95—21no—
517#95—22no—
518#95—22no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—21no—
534#95—22no—
535#95—22no—
536#95—21no—
537#95—21no—
538#95C2×D412yes—
539#95C2×D412yes—
540#95C2×D412yes—
541#95C2×D412yes—
542#95C2×D412yes—
543#95C2×D412yes—
544#95C2×D412yes—
545C24—21no—
546C24—22no—
547#41—816no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—21no—
560C2×Q8C4×D414yes—
561C2×Q8C23×C412yes—
562C2×Q8C23×C414yes—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—82no—
581C2×D4—81no—
582C2×D4—82no—
583C2×D4—82no—
584C2×D4—82no—
585C2×D4C23×C412yes—
586C2×D4C23×C414yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D412yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C2511yescharacteristic
623SD16—216no—
624SD16—28no—
625SD16—48no—
626SD16—48no—
627SD16—48no—
628C2×C8—21no—
629C2×C8—22no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—22no—
636C2×C8—21no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8C23×C414yes—
641C2×C8C23×C412yes—
642C2×C8C23×C412yes—
643C2×C8H(5,𝔽2)12yes—
644C2×C8H(5,𝔽2)12yes—
645C2×C82−1+412yes—
646C4⋊C4—28no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—28no—
650C4⋊C4—24no—
651C4⋊C4—28no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—82no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4C4×D418yes—
684C4⋊C4C4×D414yes—
685C4⋊C4C23×C412yes—
686C4⋊C4C23×C412yes—
687C22⋊C4—24no—
688C22⋊C4—28no—
689C22⋊C4—42no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C42—28no—
701C42—24no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—21no—
706C42—21no—
707C42—22no—
708C42—21no—
709C42—21no—
710C42—41no—
711C42—41no—
712C42—42no—
713C42—42no—
714C42—82no—
715C42—82no—
716C42—82no—
717C42—82no—
718C42—82no—
719C42C23×C414yes—
720C42C23×C412yes—
721C42C2×#4112yes—
722C42C2×#4114yes—
723C23—22no—
724C23—24no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—42no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—41no—
737C23C23×D411yescharacteristic
738Q8—28no—
739Q8—22no—
740Q8—24no—
741Q8—22no—
742Q8—24no—
743Q8—41no—
744Q8—42no—
745Q8—41no—
746Q8—42no—
747D4—22no—
748D4—24no—
749D4—22no—
750D4—24no—
751D4—48no—
752D4—41no—
753D4—42no—
754D4—41no—
755D4—42no—
756D4—84no—
757D4—88no—
758D4—88no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—88no—
815C2×C4—164no—
816C2×C4—164no—
817C2×C4—164no—
818C2×C4C2×C4×D414yes—
819C2×C4C2×C4×D412yes—
820C2×C4C2×C4×D414yes—
821C2×C4C2×C4×D412yes—
822C2×C4#57712yes—
823C2×C4#57712yes—
824C2×C4C24×C411yescharacteristic
825C2×C4C22×#4111yescharacteristic
826C2×C4C2×H(5,𝔽2)11yescharacteristic
827C2×C4C2×H(5,𝔽2)11yescharacteristic
828C2×C4C2×2−1+411yescharacteristic
829C2×C4#58511yescharacteristic
830C8—24no—
831C8—22no—
832C8—22no—
833C8—41no—
834C8—42no—
835C8#52014yes—
836C22—42no—
837C22—44no—
838C22—42no—
839C22—44no—
840C22—42no—
841C22—44no—
842C22—81no—
843C22—82no—
844C22—82no—
845C22—81no—
846C22—81no—
847C22—82no—
848C22—81no—
849C22—82no—
850C22C22×C4×D411yescharacteristic
851C22#349711yescharacteristic
852C22#349811yescharacteristic
853C22C2×#57711yescharacteristic
854C22C2×#57711yescharacteristic
855C22#358511yescharacteristic
856C22#358611yescharacteristic
857C4—24no—
858C4—22no—
859C4—24no—
860C4—42no—
861C4—41no—
862C4—41no—
863C4—42no—
864C4—42no—
865C4—44no—
866C4—42no—
867C4—42no—
868C4—41no—
869C4—41no—
870C4—82no—
871C4—82no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4#294914yes—
877C4C2×#52011yescharacteristic
878C4C4×H(5,𝔽2)11yescharacteristic
879C4#351711yescharacteristic
880C4#352211yescharacteristic
881C2—82no—
882C2—84no—
883C2#3431311yescharacteristic
884C2C2×#294911yescharacteristic
885C2#6017411yescharacteristic
886C2#6240111yescharacteristic
887C2#6240211yescharacteristic
888C2#6246511yescharacteristic
889C2#6246611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#550C22
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
3. #34488C2semidirect
4. #23190C2semidirect
5. #23190C2semidirect
6. #23012C2semidirect
7. #23010C2semidirect
8. #22997C2semidirect
9. #22996C2semidirect
10. #22727C2semidirect
11. #22673C2semidirect
12. #22671C2semidirect
13. #22547C2semidirect
15. #22162C2semidirect
16. #22160C2semidirect
17. #22147C2semidirect
18. #22146C2semidirect
19. #21695C2semidirect
20. #21692C2semidirect
21. #21285C2semidirect
22. #21279C2semidirect
23. #20521C2semidirect
26. #3392C4semidirect
143. #557C2×C4semidirect
172. #492C2×C4semidirect
173. #492C2×C4semidirect
174. #461C2×C4semidirect
175. #461C2×C4semidirect
176. #460C2×C4semidirect
177. #460C2×C4semidirect
179. C8×Q8C2×C4semidirect
186. C4×SD16C2×C4semidirect
187. C4×SD16C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33922
#344942
#344882
#231902
#230122
#230102
#229972
#229962
#227272
#226732
#226712
#225472
#225452
#221622
#221602
#221472
#221462
#216952
#216922
#212852
#212792
#205212