Finite Group Databasebeta

← #6404020

Subgroups — #6404020

Order 512.

2300 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3273C211yesmaximal, characteristic
2#34320C212yesmaximal, complemented
3#23191C211yesmaximal, characteristic, complemented
4#23104C212yesmaximal, complemented
5#23035C212yesmaximal, complemented
6#22880C212yesmaximal, complemented
7#22879C212yesmaximal, complemented
8#22816C211yesmaximal, characteristic, complemented
9#22664C211yesmaximal, characteristic, complemented
10#22443C212yesmaximal, complemented
11#22427C212yesmaximal, complemented
12#22149C212yesmaximal, complemented
13#22042C212yesmaximal, complemented
14#22040C212yesmaximal, complemented
15C4×#495C211yesmaximal, characteristic, complemented
16#21540C212yesmaximal, complemented
17#21275C211yesmaximal, characteristic, complemented
18#21236C212yesmaximal, complemented
19C4×#436C211yesmaximal, characteristic, complemented
20C22×AGL(1,ℤ/8)C2212yes—
21C2×#546C2212yes—
22#3273C4116yescomplemented
23C2×#495C2211yescharacteristic
24C2×#468C2212yes—
25C2×#463C2212yes—
26C2×#452C2212yes—
27C2×#447C2212yes—
28C2×#440C2212yescomplemented
29C2×C4×Q16C2211yescharacteristic, complemented
30C2×C4×SD16C2212yescomplemented
31C2×C4×D8C2211yescharacteristic
32C2×C4×D8C2211yescharacteristic
33C2×#436C2211yescharacteristic
34C2×#436C2211yescharacteristic
35C2×#428C2212yescomplemented
36C2×#417C2212yes—
37C2×#418C2212yescomplemented
38C2×C4×M16C2212yescomplemented
39#2374—22no—
40#2367C2212yescomplemented
41#2363—22no—
42#2363C2212yes—
43#2360C2212yescomplemented
44#2358—22no—
45#2357C2212yescomplemented
46#2352C2212yes—
47#2342—22no—
48#2341C2212yes—
49D4×C22⋊C4C2212yescomplemented
50#2335—22no—
51#2333—22no—
52#2321—22no—
53C4×#124C2212yescomplemented
54C4×C22⋊Q8C2212yescomplemented
55C4×#121C2212yes—
56#2297C2212yes—
57#2293C2212yescomplemented
58C2×#390C2212yescomplemented
59#2273—22no—
60C42×D4C2211yescharacteristic
61#1983C2212yescomplemented
62#1973C2212yescomplemented
63#1973C2212yescomplemented
64#1972C2212yes—
65#1972C2212yes—
66#1970C2211yescharacteristic
67#1970C2212yes—
68#1970C2211yescharacteristic
69#1970C2211yescharacteristic
70#1969C2211yescharacteristic, complemented
71#1968C2212yescomplemented
72#1968C2212yescomplemented
73#1958C2212yescomplemented
74#1949C2212yescomplemented
75#1942C2211yescharacteristic, complemented
76#1942C2211yescharacteristic, complemented
77#1934C2212yescomplemented
78#1934C2212yescomplemented
79#1934C2212yescomplemented
80#1933C2212yescomplemented
81#1927C2212yescomplemented
82#1925C2212yescomplemented
83#1925C2212yescomplemented
84#1925C2212yescomplemented
85#1895C2212yes—
86#1894C2212yescomplemented
87#1880C2212yescomplemented
88#1880C2212yescomplemented
89#1879C2212yes—
90#1879C2212yes—
91#1879C2212yes—
92#1878C2212yescomplemented
93#1874C2212yes—
94#1873C2212yescomplemented
95#1864C2212yescomplemented
96#1863C2212yescomplemented
97#1854C2212yescomplemented
98#1852C2212yescomplemented
99#1846C2211yescharacteristic, complemented
100#1809C2212yescomplemented
101#1804C2212yescomplemented
102#1788C2212yes—
103#1786C2212yescomplemented
104#1776C2212yescomplemented
105C4×#107C2211yescharacteristic, complemented
106#1770C2211yescharacteristic, complemented
107#1770C2211yescharacteristic, complemented
108C4×C4⋊C8C2211yescharacteristic, complemented
109#1763C2212yescomplemented
110#1762C2212yescomplemented
111C4×#102C2212yescomplemented
112#1753C2212yescomplemented
113#1753C2212yescomplemented
114C4×C22⋊C8C2212yescomplemented
115C42×C8C2211yescharacteristic, complemented
116C22×#41C2312yes—
117C23×D4C2312yes—
118C2×AGL(1,ℤ/8)—44no—
119C2×AGL(1,ℤ/8)—44no—
120C2×AGL(1,ℤ/8)C2×C4116yescomplemented
121C22×Q16C2311yescharacteristic
122C22×SD16C2312yes—
123C22×SD16C2312yes—
124C22×D8C2311yescharacteristic
125C22×D8C2311yescharacteristic
126C22×D8C2312yes—
127C22×M16C2312yes—
128C22×M16C2312yes—
129#546—28no—
130#546C2×C4116yescomplemented
131C2×#124C2312yes—
132C2×#123—22no—
133C2×C22⋊Q8C2312yes—
134C2×#121—22no—
135C2×#121C2312yes—
136C2×#120—22no—
137C2×C4×Q8C2312yes—
138C2×C4×Q8C2312yes—
139C2×C4×D4—22no—
140C2×C4×D4D411yescharacteristic
141C2×C4×D4D411yescharacteristic
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×C4×D4C2312yes—
145C2×C4×D4C2311yescharacteristic
146C2×#117—22no—
147C2×#117C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C22⋊C4—22no—
150C22×C22⋊C4—22no—
151C22×C22⋊C4—22no—
152C22×C22⋊C4—22no—
153C22×C42C2312yes—
154#495C2×C418yescomplemented
155#468C2×C4116yescomplemented
156#463C2×C4116yescomplemented
157#452C2×C4116yescomplemented
158#447C2×C4116yescomplemented
159#440—44no—
160C4×Q16—42no—
161C4×SD16—44no—
162C4×D8—42no—
163C4×D8C2×C418yescomplemented
164#436—24no—
165#436C2×C418yescomplemented
166#428—44no—
167C2×#107C2311yescharacteristic
168C2×#107C2311yescharacteristic
169C2×#107C2311yescharacteristic
170C2×#107C2311yescharacteristic
171C2×#107C2312yes—
172C2×#107C2311yescharacteristic
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177#418—44no—
178#417—44no—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#102C2312yes—
185C2×#102C2312yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C4×M16—44no—
197C2×#97C2312yes—
198C2×#97C2312yes—
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2312yes—
204C2×C4×C8C2311yescharacteristic
205C2×C4×C8C2311yescharacteristic
206#391C2312yes—
207#391C2312yes—
208#390—22no—
209#390—22no—
210#390—22no—
211#390—22no—
212#390—22no—
213#390C2312yes—
214#390C2312yes—
215#390C2312yes—
216#390C2312yes—
217#390C2312yes—
218#390C2312yes—
219#389—22no—
220#389C2312yes—
221#389C2312yes—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#387—22no—
234#387—22no—
235#387—22no—
236#386—22no—
237#386—22no—
238#386—22no—
239#386—22no—
240#386—22no—
241#386—22no—
242#386—22no—
243#385—22no—
244#385—22no—
245#385—22no—
246#382C2312yes—
247#381—22no—
248#380—22no—
249#380C2312yes—
250#380C2312yes—
251#379—22no—
252C4×C4⋊C4—22no—
253C4×C4⋊C4D411yescharacteristic
254C4×C4⋊C4D411yescharacteristic
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C4×C4⋊C4C2311yescharacteristic
259C4×C22⋊C4—22no—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—22no—
263C4×C22⋊C4—22no—
264C4×C22⋊C4—22no—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268C4×C22⋊C4—22no—
269C4×C22⋊C4—22no—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272C4×C22⋊C4D412yes—
273C4×C22⋊C4D412yes—
274C4×C22⋊C4C2312yes—
275C43C2311yescharacteristic
276#340C2312yes—
277#340C2312yes—
278#340C2312yes—
279#340C2312yes—
280#340C2312yes—
281#340C2312yes—
282#340C2312yes—
283#336C2312yes—
284#336C2312yes—
285#336C2312yes—
286C25—22no—
287C2×#41—24no—
288C2×#41—42no—
289C2×#41—42no—
290C2×#41—42no—
291C2×#41—42no—
292C2×#41C22×C418yes—
293C22×Q8C2412yes—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—24no—
298C22×D4—42no—
299C22×D4—42no—
300C22×D4—42no—
301C22×D4—42no—
302C22×D4C22×C418yes—
303C22×D4C2×D411yescharacteristic
304C22×D4C2412yes—
305C22×D4C2412yes—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4C2×D412yes—
312C23×C4C2×D412yes—
313C23×C4C2412yes—
314AGL(1,ℤ/8)—432no—
315C2×Q16—41no—
316C2×Q16—41no—
317C2×Q16C22×C414yes—
318C2×SD16—24no—
319C2×SD16—24no—
320C2×SD16—42no—
321C2×SD16—42no—
322C2×SD16C22×C418yes—
323C2×SD16C22×C418yes—
324C2×D8—22no—
325C2×D8—22no—
326C2×D8—41no—
327C2×D8—42no—
328C2×D8—42no—
329C2×D8—41no—
330C2×D8C22×C414yes—
331C2×D8C22×C418yes—
332C2×D8C22×C414yes—
333C2×M16—24no—
334C2×M16—24no—
335C2×M16—24no—
336C2×M16—24no—
337C2×M16—42no—
338C2×M16C22×C418yes—
339C22×C8C2412yes—
340C22×C8C2411yescharacteristic
341C22×C8C2412yes—
342C22×C8C2411yescharacteristic
343C22×C8C2411yescharacteristic
344C22×C8C2411yescharacteristic
345#124—24no—
346#124C22×C418yes—
347#123—216no—
348C22⋊Q8—24no—
349C22⋊Q8C22×C418yes—
350#121—24no—
351#121—216no—
352#121C22×C418yes—
353#120—216no—
354C4×Q8—42no—
355C4×Q8—42no—
356C4×Q8—42no—
357C4×Q8—42no—
358C4×D4—24no—
359C4×D4—42no—
360C4×D4—42no—
361C4×D4—42no—
362C4×D4—42no—
363C4×D4—42no—
364C4×D4—42no—
365C4×D4—84no—
366C4×D4C22×C418yes—
367C4×D4C22×C414yes—
368C4×D4#4114yes—
369#117—42no—
370#117—42no—
371#117—84no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—216no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—48no—
412C2×C22⋊C4—48no—
413C2×C22⋊C4—84no—
414C2×C22⋊C4C2×D412yes—
415C2×C22⋊C4C2×D412yes—
416C2×C22⋊C4C2×D412yes—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D412yes—
430C2×C42C2×D412yes—
431C2×C42C2411yescharacteristic
432C2×C42C2412yes—
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435#107—22no—
436#107—22no—
437#107—42no—
438#107—41no—
439#107—41no—
440#107C22×C414yes—
441#106—24no—
442#106—42no—
443C4⋊C8—22no—
444C4⋊C8C22×C414yes—
445#103—24no—
446#103—42no—
447#103—42no—
448#103—42no—
449#103C22×C418yes—
450#102—24no—
451#102—24no—
452#102—42no—
453#102—42no—
454#102—42no—
455#102—42no—
456#102—42no—
457#102—42no—
458#102C22×C418yes—
459#102C22×C418yes—
460C22⋊C8—24no—
461C22⋊C8C22×C418yes—
462#97—24no—
463#97—42no—
464C4×C8—22no—
465C4×C8—22no—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8—41no—
469C4×C8—42no—
470C4×C8C22×C414yes—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95C2×D412yes—
485#95C2×D412yes—
486#95C2×D412yes—
487C24—22no—
488C24—22no—
489C24—28no—
490C24—44no—
491C24—44no—
492C24—82no—
493C24—82no—
494C24—82no—
495C24—82no—
496C24C22×D412yes—
497#41—48no—
498#41—48no—
499#41—84no—
500#41—84no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8C23×C414yes—
507C2×D4—28no—
508C2×D4—28no—
509C2×D4—28no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—84no—
525C2×D4—84no—
526C2×D4—82no—
527C2×D4—82no—
528C2×D4—82no—
529C2×D4—82no—
530C2×D4—82no—
531C2×D4—82no—
532C2×D4C4×D414yes—
533C2×D4C23×C414yes—
534C2×D4C23×C414yes—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—82no—
557C22×C4—82no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—82no—
566C22×C4C23×C414yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D412yes—
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C2×#4114yes—
577C22×C4C2511yescharacteristic
578Q16—44no—
579SD16—216no—
580SD16—48no—
581D8—28no—
582D8—44no—
583D8—48no—
584M16—216no—
585M16—48no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—22no—
594C2×C8—21no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8C23×C412yes—
599C2×C8C23×C414yes—
600C2×C8C23×C412yes—
601C2×C8H(5,𝔽2)12yes—
602C2×C8H(5,𝔽2)12yes—
603C2×C8H(5,𝔽2)12yes—
604C4⋊C4—28no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—44no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4—82no—
620C4⋊C4—82no—
621C4⋊C4C4×D414yes—
622C4⋊C4C23×C414yes—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—28no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—24no—
629C22⋊C4—42no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—82no—
640C22⋊C4—82no—
641C22⋊C4—82no—
642C22⋊C4—82no—
643C22⋊C4—82no—
644C22⋊C4—82no—
645C22⋊C4—82no—
646C22⋊C4—82no—
647C22⋊C4C4×D418yes—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—22no—
655C42—21no—
656C42—22no—
657C42—42no—
658C42—42no—
659C42—41no—
660C42—82no—
661C42—82no—
662C42—82no—
663C42—82no—
664C42—82no—
665C42—82no—
666C42C23×C412yes—
667C42C2×#4112yes—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—416no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—88no—
690C23—88no—
691C23—164no—
692C23—164no—
693C23—164no—
694C23—164no—
695C23C2×C4×D414yes—
696C23C23×D411yescharacteristic
697Q8—24no—
698Q8—24no—
699Q8—42no—
700Q8—42no—
701D4—24no—
702D4—24no—
703D4—24no—
704D4—24no—
705D4—44no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—88no—
711D4—88no—
712D4—88no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—84no—
757C2×C4—84no—
758C2×C4—88no—
759C2×C4—88no—
760C2×C4—164no—
761C2×C4—164no—
762C2×C4—164no—
763C2×C4C2×C4×D412yes—
764C2×C4C2×C4×D412yes—
765C2×C4C2×C4×D414yes—
766C2×C4#57512yes—
767C2×C4#57512yes—
768C2×C4#57612yes—
769C2×C4C24×C411yescharacteristic
770C2×C4C22×#4111yescharacteristic
771C2×C4C2×H(5,𝔽2)11yescharacteristic
772C2×C4C2×H(5,𝔽2)11yescharacteristic
773C2×C4C2×H(5,𝔽2)11yescharacteristic
774C2×C4#58511yescharacteristic
775C8—24no—
776C8—22no—
777C8—22no—
778C8—41no—
779C8—42no—
780C8#51814yes—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—1616no—
803C22C22×C4×D411yescharacteristic
804C22#349611yescharacteristic
805C22#349811yescharacteristic
806C22C2×#57511yescharacteristic
807C22C2×#57511yescharacteristic
808C22C2×#57611yescharacteristic
809C22#358411yescharacteristic
810C4—24no—
811C4—22no—
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—44no—
817C4—44no—
818C4—42no—
819C4—42no—
820C4—41no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4C2×#51811yescharacteristic
826C4C4×H(5,𝔽2)11yescharacteristic
827C4#351411yescharacteristic
828C4#351911yescharacteristic
829C2—44no—
830C2—84no—
831C2—84no—
832C2#3431011yescharacteristic
833C2C4×#57511yescharacteristic
834C2C4×#57611yescharacteristic
835C2#6226111yescharacteristic
836C2#6226311yescharacteristic
837C2#6242611yescharacteristic
838C2#6242811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3273C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34320C2semidirect
3. #23191C2semidirect
4. #23104C2semidirect
5. #23035C2semidirect
6. #22880C2semidirect
7. #22879C2semidirect
8. #22816C2semidirect
9. #22664C2semidirect
10. #22443C2semidirect
11. #22427C2semidirect
12. #22149C2semidirect
13. #22042C2semidirect
14. #22040C2semidirect
15. C4×#495C2semidirect
16. #21540C2semidirect
17. #21275C2semidirect
18. #21236C2semidirect
19. C4×#436C2semidirect
22. #3273C4semidirect
28. C2×#440C22semidirect
29. C2×C4×Q16C22semidirect
30. C2×C4×SD16C22semidirect
35. C2×#428C22semidirect
37. C2×#418C22semidirect
38. C2×C4×M16C22semidirect
40. #2367C22semidirect
43. #2360C22semidirect
45. #2357C22semidirect
49. D4×C22⋊C4C22semidirect
53. C4×#124C22semidirect
54. C4×C22⋊Q8C22semidirect
57. #2293C22semidirect
58. C2×#390C22semidirect
61. #1983C22semidirect
62. #1973C22semidirect
63. #1973C22semidirect
70. #1969C22semidirect
71. #1968C22semidirect
72. #1968C22semidirect
73. #1958C22semidirect
74. #1949C22semidirect
75. #1942C22semidirect
76. #1942C22semidirect
77. #1934C22semidirect
78. #1934C22semidirect
79. #1934C22semidirect
80. #1933C22semidirect
81. #1927C22semidirect
82. #1925C22semidirect
83. #1925C22semidirect
84. #1925C22semidirect
86. #1894C22semidirect
87. #1880C22semidirect
88. #1880C22semidirect
92. #1878C22semidirect
94. #1873C22semidirect
95. #1864C22semidirect
96. #1863C22semidirect
97. #1854C22semidirect
98. #1852C22semidirect
99. #1846C22semidirect
100. #1809C22semidirect
101. #1804C22semidirect
103. #1786C22semidirect
104. #1776C22semidirect
105. C4×#107C22semidirect
106. #1770C22semidirect
107. #1770C22semidirect
108. C4×C4⋊C8C22semidirect
109. #1763C22semidirect
110. #1762C22semidirect
111. C4×#102C22semidirect
112. #1753C22semidirect
113. #1753C22semidirect
114. C4×C22⋊C8C22semidirect
115. C42×C8C22semidirect
120. C2×AGL(1,ℤ/8)C2×C4semidirect
130. #546C2×C4semidirect
154. #495C2×C4semidirect
155. #468C2×C4semidirect
156. #463C2×C4semidirect
157. #452C2×C4semidirect
158. #447C2×C4semidirect
163. C4×D8C2×C4semidirect
165. #436C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32732
#343202
#231912
#231042
#230352
#228802
#228792
#228162
#226642
#224432
#224272
#221492
#220422
#220402
C4×#4952
#215402
#212752
#212362
C4×#4362