Finite Group Databasebeta

← #6475713

Subgroups — #6475713

Order 512.

2056 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#33209C211yesmaximal, characteristic, complemented
4#33170C211yesmaximal, characteristic, complemented
5#33043C211yesmaximal, characteristic, complemented
6#33042C211yesmaximal, characteristic, complemented
7#29735C214yesmaximal, complemented
8#29467C214yesmaximal, complemented
9#29465C214yesmaximal, complemented
10#27892C211yesmaximal, characteristic, complemented
11#27891C211yesmaximal, characteristic, complemented
12#27876C211yesmaximal, characteristic, complemented
13#27875C211yesmaximal, characteristic, complemented
14#25674C211yesmaximal, characteristic, complemented
15#25673C211yesmaximal, characteristic, complemented
16#25598C211yesmaximal, characteristic, complemented
17#25597C211yesmaximal, characteristic, complemented
18#22185C214yesmaximal, complemented
19C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#525—21no—
23C23×C42C2211yescharacteristic
24C2×#500C2211yescharacteristic, complemented
25C2×#492C2211yescharacteristic, complemented
26C2×#487C2211yescharacteristic, complemented
27C2×#486C2211yescharacteristic, complemented
28C2×#465C2214yes—
29C22×C22⋊C8C2212yes—
30C22×C4×C8C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2856C2211yescharacteristic
39#2856C2211yescharacteristic
40#2855—21no—
41#2855C2212yes—
42#2854—21no—
43#2854C2212yes—
44#2851—21no—
45#2851—21no—
46#2850—21no—
47#2850—21no—
48#2848—21no—
49#2848C2212yes—
50#2847—21no—
51#2847C2212yes—
52C4×C22⋊Q8—21no—
53C4×C22⋊Q8—21no—
54C4×C22⋊Q8C2212yes—
55C4×C22⋊Q8C2212yes—
56C4×#121—21no—
57C4×#121—21no—
58C4×#121C2212yes—
59C4×#121C2212yes—
60#2297—21no—
61#2296—21no—
62#2285C2211yescharacteristic
63#2285C2211yescharacteristic
64#2280—21no—
65#2077C2214yes—
66#2077C2214yes—
67#2036C2214yes—
68#2036C2214yes—
69#2033C2214yes—
70#2033C2214yes—
71#2000C2214yes—
72#2000C2214yes—
73#1990C2211yescharacteristic, complemented
74#1990C2211yescharacteristic, complemented
75#1990C2211yescharacteristic, complemented
76#1990C2211yescharacteristic, complemented
77#1968C2214yescomplemented
78#1957C2211yescharacteristic, complemented
79#1957C2211yescharacteristic, complemented
80#1956C2211yescharacteristic, complemented
81#1956C2211yescharacteristic, complemented
82#1942C2214yescomplemented
83#1934C2214yescomplemented
84#1933C2214yescomplemented
85#1928C2214yescomplemented
86#1925C2214yescomplemented
87#1920C2214yescomplemented
88#1919C2214yescomplemented
89#1893C2214yes—
90#1892C2214yes—
91#1880C2214yescomplemented
92#1877C2214yescomplemented
93#1863C2214yescomplemented
94#1862C2214yescomplemented
95#1845C2211yescharacteristic, complemented
96#1844C2211yescharacteristic, complemented
97#1834C2211yescharacteristic, complemented
98#1834C2211yescharacteristic, complemented
99#1808C2214yes—
100C4×C22⋊C8C2212yes—
101C4×C22⋊C8C2212yes—
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C2×#336C2212yes—
107C22×#41—21no—
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111C22×SD16C2314yes—
112C23×C8C2312yes—
113C23×C8C2312yes—
114#533—42no—
115#533—42no—
116#532—42no—
117#532—42no—
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#125—21no—
123C2×#124—21no—
124#525—48no—
125C2×#123—22no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121C2312yes—
140C2×#121C2312yes—
141C2×#121C2312yes—
142C2×#120—22no—
143C2×C4×Q8—21no—
144C2×C4×Q8C2312yes—
145C2×C4×D4—22no—
146C2×C4×D4—22no—
147C2×C4×D4—21no—
148C2×C4×D4C2312yes—
149C2×#117—21no—
150C2×#117—21no—
151C2×#117—21no—
152C22×C42—42no—
153C22×C42—42no—
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#500—42no—
167#492—42no—
168#487—42no—
169#486—42no—
170#465—216no—
171C2×#107C2314yes—
172C2×#107C2314yes—
173C2×#106C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×C22⋊C8—28no—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×C4×C8—42no—
186C2×C4×C8—42no—
187C2×C4×C8C2311yescharacteristic
188C2×C4×C8C2311yescharacteristic
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2311yescharacteristic
191C2×C4×C8C2312yes—
192C2×C4×C8C2312yes—
193#391—21no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391C2312yes—
198#391C2312yes—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390C2312yes—
204#390C2312yes—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389C2312yes—
214#389C2312yes—
215#389C2312yes—
216#389C2312yes—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#387—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#386—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#385—22no—
232#385—22no—
233#385—22no—
234#385—22no—
235#385—22no—
236#385—22no—
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#382—21no—
242#382—21no—
243#381—22no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—21no—
254#380C2312yes—
255#380C2312yes—
256#380C2312yes—
257#380C2312yes—
258#380C2312yes—
259#380C2312yes—
260#379—22no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4—22no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4C2312yes—
266C4×C4⋊C4C2312yes—
267C4×C22⋊C4—22no—
268C4×C22⋊C4—22no—
269C4×C22⋊C4—22no—
270C4×C22⋊C4—22no—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280#336C2312yes—
281C25C2×D411yescharacteristic
282C2×#41—44no—
283C2×#41—44no—
284C2×#41—44no—
285C22×Q8—21no—
286C22×Q8—21no—
287C22×Q8C2412yes—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C2412yes—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—22no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—41no—
304C23×C4—41no—
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C2×SD16—28no—
324C2×SD16—44no—
325C2×SD16—44no—
326C22×C8—24no—
327C22×C8—42no—
328C22×C8—42no—
329C22×C8—42no—
330C22×C8—42no—
331C22×C8#4118yescomplemented
332C22×C8C2412yes—
333C22×C8C2412yes—
334C22×C8C2412yes—
335C22×C8C2412yes—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342#127—22no—
343#127—22no—
344#125—44no—
345#124—44no—
346#123—48no—
347C22⋊Q8—28no—
348C22⋊Q8—44no—
349C22⋊Q8—42no—
350C22⋊Q8—42no—
351C22⋊Q8—44no—
352C22⋊Q8—44no—
353C22⋊Q8—44no—
354C22⋊Q8—44no—
355C22⋊Q8—44no—
356#121—28no—
357#121—44no—
358#121—42no—
359#121—42no—
360#121—44no—
361#121—44no—
362#121—44no—
363#121—44no—
364#121—44no—
365#120—48no—
366C4×Q8—42no—
367C4×Q8—42no—
368C4×Q8—44no—
369C4×D4—42no—
370C4×D4—42no—
371C4×D4—44no—
372C4×D4—48no—
373C4×D4—48no—
374#117—44no—
375#117—44no—
376#117—44no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
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—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—42no—
435C2×C42—41no—
436C2×C42—41no—
437C2×C42—41no—
438C2×C42—41no—
439C2×C42—41no—
440C2×C42—41no—
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457#107—44no—
458#107—44no—
459#106—28no—
460#103—28no—
461#103—44no—
462#103—44no—
463#102—28no—
464#102—44no—
465#102—44no—
466C22⋊C8—24no—
467C22⋊C8—24no—
468C22⋊C8—24no—
469C22⋊C8—24no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8—22no—
474C4×C8—42no—
475C4×C8—42no—
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#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—41no—
499C24—41no—
500C24C22×D411yescharacteristic
501C24C22×D411yescharacteristic
502C24C22×D411yescharacteristic
503#41—816no—
504C2×Q8—24no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—24no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×D4—24no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—24no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—416no—
593C22×C4—416no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4#13514yes—
600C22×C4#13514yes—
601C22×C4AGL(1,ℤ/8)14yes—
602C22×C4#13714yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C2×#4114yes—
615C22×C4C2511yescharacteristic
616SD16—88no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—48no—
628C2×C8—48no—
629C2×C8C2×#4114yes—
630C2×C8C2×#4114yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—44no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—44no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—42no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—41no—
693C42—41no—
694C42—44no—
695C42—44no—
696C42—44no—
697C42H(5,𝔽2)12yes—
698C42H(5,𝔽2)12yes—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—28no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23#53212yes—
730C23C2×#13512yes—
731C23C2×#13512yes—
732C23C2×AGL(1,ℤ/8)12yes—
733C23C2×#13712yes—
734C23C23×D411yescharacteristic
735Q8—44no—
736Q8—44no—
737Q8—84no—
738Q8—84no—
739D4—44no—
740D4—44no—
741D4—88no—
742D4—88no—
743D4—88no—
744D4—84no—
745D4—84no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—88no—
811C2×C4#53212yes—
812C2×C4#53412yes—
813C2×C4#53412yes—
814C2×C4C2×#13512yes—
815C2×C4C2×#13512yes—
816C2×C4C2×#13512yes—
817C2×C4C2×#13512yes—
818C2×C4C2×AGL(1,ℤ/8)12yes—
819C2×C4C2×AGL(1,ℤ/8)12yes—
820C2×C4C2×#13712yes—
821C2×C4C2×#13712yes—
822C2×C4C22×#4112yes—
823C2×C4C2×H(5,𝔽2)11yescharacteristic
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4#58512yes—
826C8—24no—
827C8—24no—
828C8—42no—
829C8—42no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—416no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22#318214yes—
859C22C2×#53211yescharacteristic
860C22C2×#53411yescharacteristic
861C22#344911yescharacteristic
862C22C22×#13511yescharacteristic
863C22C22×#13511yescharacteristic
864C22C22×AGL(1,ℤ/8)11yescharacteristic
865C22C22×#13711yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4#318814yes—
883C4#319014yes—
884C4#350512yes—
885C4#350612yes—
886C2—24no—
887C2—42no—
888C2—42no—
889C2—162no—
890C2#3503211yescharacteristic
891C2#6067311yescharacteristic
892C2C2×#318211yescharacteristic
893C2C2×#318811yescharacteristic
894C2C2×#319011yescharacteristic
895C2#6094611yescharacteristic
896C2#6094711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36625C2semidirect
3. #33209C2semidirect
4. #33170C2semidirect
5. #33043C2semidirect
6. #33042C2semidirect
7. #29735C2semidirect
8. #29467C2semidirect
9. #29465C2semidirect
10. #27892C2semidirect
11. #27891C2semidirect
12. #27876C2semidirect
13. #27875C2semidirect
14. #25674C2semidirect
15. #25673C2semidirect
16. #25598C2semidirect
17. #25597C2semidirect
18. #22185C2semidirect
19. C2×C4×C22⋊C8C2semidirect
24. C2×#500C22semidirect
25. C2×#492C22semidirect
26. C2×#487C22semidirect
27. C2×#486C22semidirect
73. #1990C22semidirect
74. #1990C22semidirect
75. #1990C22semidirect
76. #1990C22semidirect
77. #1968C22semidirect
78. #1957C22semidirect
79. #1957C22semidirect
80. #1956C22semidirect
81. #1956C22semidirect
82. #1942C22semidirect
83. #1934C22semidirect
84. #1933C22semidirect
85. #1928C22semidirect
86. #1925C22semidirect
87. #1920C22semidirect
88. #1919C22semidirect
91. #1880C22semidirect
92. #1877C22semidirect
93. #1863C22semidirect
94. #1862C22semidirect
95. #1845C22semidirect
96. #1844C22semidirect
97. #1834C22semidirect
98. #1834C22semidirect
331. C22×C8#41semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#332092
#331702
#330432
#330422
#297352
#294672
#294652
#278922
#278912
#278762
#278752
#256742
#256732
#255982
#255972
#221852
C2×C4×C22⋊C82