Finite Group Databasebeta

← #6765469

Subgroups — #6765469

Order 512.

2080 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36211C211yesmaximal, characteristic, complemented
2#36121C211yesmaximal, characteristic, complemented
3#33171C211yesmaximal, characteristic, complemented
4#30919C214yesmaximal, complemented
5#30400C214yesmaximal, complemented
6#30204C211yesmaximal, characteristic, complemented
7#29843C211yesmaximal, characteristic, complemented
8#28615C211yesmaximal, characteristic, complemented
9#28514C211yesmaximal, characteristic, complemented
10#27890C211yesmaximal, characteristic, complemented
11#27878C211yesmaximal, characteristic, complemented
12#27229C214yesmaximal, complemented
13#27199C214yesmaximal, complemented
14#25721C211yesmaximal, characteristic, complemented
15#25599C211yesmaximal, characteristic, complemented
16#22269C211yesmaximal, characteristic, complemented
17#21803C211yesmaximal, characteristic, complemented
18#21401C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#546—21no—
21C2×#532C2211yescharacteristic
22C22×#127C2211yescharacteristic
23C2×#493C2211yescharacteristic
24C2×#493C2211yescharacteristic
25C2×#486C2211yescharacteristic, complemented
26C2×#478C2214yescomplemented
27C2×#466C2214yescomplemented
28C2×#447C2214yes—
29C2×#431C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic, complemented
31#2859C2211yescharacteristic, complemented
32#2858C2211yescharacteristic
33#2857C2211yescharacteristic
34#2856C2211yescharacteristic
35#2856C2211yescharacteristic
36#2856C2211yescharacteristic, complemented
37#2544—21no—
38#2535C2212yes—
39#2513—21no—
40#2513—21no—
41#2490C2212yes—
42#2490C2212yescomplemented
43#2445—21no—
44#2445C2212yes—
45#2435—21no—
46#2431—21no—
47#2428—21no—
48#2428C2212yes—
49#2420—21no—
50#2420—21no—
51#2414—21no—
52#2414—21no—
53#2408—21no—
54#2408C2212yes—
55#2363—21no—
56#2363—21no—
57#2357C2212yescomplemented
58D4×C22⋊C4—21no—
59D4×C22⋊C4C2212yes—
60C4×#127C2211yescharacteristic
61C4×#127C2211yescharacteristic, complemented
62#2285C2211yescharacteristic
63#2285C2211yescharacteristic, complemented
64C42×D4C2211yescharacteristic
65#2092C2214yescomplemented
66#2076C2214yes—
67#2073C2214yescomplemented
68#2065C2214yescomplemented
69#2054C2214yescomplemented
70#2034C2214yes—
71#2034C2214yescomplemented
72#2025C2214yescomplemented
73#2011C2214yes—
74#1999C2214yescomplemented
75#1990C2211yescharacteristic, complemented
76#1990C2211yescharacteristic, complemented
77#1990C2211yescharacteristic, complemented
78#1982C2214yes—
79#1970C2214yescomplemented
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1957C2211yescharacteristic
84#1957C2211yescharacteristic
85#1957C2211yescharacteristic
86#1957C2211yescharacteristic, complemented
87#1926C2214yescomplemented
88#1923C2212yes—
89#1921C2214yescomplemented
90#1916C2212yescomplemented
91#1893C2214yescomplemented
92#1879C2214yescomplemented
93#1879C2214yescomplemented
94#1879C2214yescomplemented
95#1879C2214yescomplemented
96#1869C2212yes—
97#1850C2212yescomplemented
98#1845C2211yescharacteristic, complemented
99#1844C2211yescharacteristic, complemented
100#1834C2211yescharacteristic, complemented
101#1786C2214yes—
102C4×C4⋊C8C2211yescharacteristic, complemented
103C4×#102C2214yescomplemented
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic, complemented
106#1744C2211yescharacteristic, complemented
107C22×#41—21no—
108C23×D4—21no—
109C23×D4—21no—
110C23×D4C2312yes—
111C22×D8C2314yes—
112C22×D8C2314yes—
113C23×C8C2312yes—
114#546—48no—
115#532—24no—
116#532—42no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×#127—24no—
119C2×#127—21no—
120C2×#127—21no—
121C2×#127—42no—
122C2×#127C2311yescharacteristic
123C2×#127C2311yescharacteristic
124C2×#127C2312yes—
125C2×#127C2311yescharacteristic
126C2×#125C2312yes—
127C2×#124—21no—
128C2×#124—21no—
129C2×#124—21no—
130C2×#123—22no—
131C2×C22⋊Q8—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—22no—
140C2×#121C2312yes—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×#121C2312yes—
144C2×#120—22no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4D411yescharacteristic
151C2×C4×D4D411yescharacteristic
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2311yescharacteristic
156C2×#117—21no—
157C2×#117—21no—
158C22×C22⋊C4—22no—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#493—24no—
162#493—42no—
163#486—42no—
164#478—48no—
165#466—48no—
166#447—48no—
167#431—42no—
168C2×#107C2314yes—
169C2×#106C2314yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×C4×C8—42no—
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2311yescharacteristic
188C2×C4×C8C2312yes—
189#397—22no—
190#397—22no—
191#397—22no—
192#394—22no—
193#394—22no—
194#394—22no—
195#394—22no—
196#394—22no—
197#394—22no—
198#392—22no—
199#392—22no—
200#392—22no—
201#391—21no—
202#390—22no—
203#390—22no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390—21no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390—21no—
216#390C2312yes—
217#390C2312yes—
218#390C2312yes—
219#390C2312yes—
220#390C2312yes—
221#390C2312yes—
222#390C2312yes—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389C2312yes—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#386—22no—
238#386—22no—
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#382—21no—
244#382—21no—
245#382C2312yes—
246#381—22no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380C2312yes—
251#380C2312yes—
252#380C2312yes—
253#379—22no—
254#379—22no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4D411yescharacteristic
258C4×C4⋊C4D411yescharacteristic
259C4×C4⋊C4C2312yes—
260C4×C4⋊C4C2312yes—
261C4×C4⋊C4C2311yescharacteristic
262C4×C22⋊C4—22no—
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4C2311yescharacteristic
268C4×C22⋊C4C2311yescharacteristic
269C43C2311yescharacteristic
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279C25—22no—
280C2×#41—44no—
281C2×#41—44no—
282C2×#41—82no—
283C22×Q8—21no—
284C22×D4—24no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—42no—
299C22×D4—44no—
300C22×D4—44no—
301C22×D4—44no—
302C22×D4—44no—
303C22×D4—44no—
304C22×D4—44no—
305C22×D4—82no—
306C22×D4—82no—
307C22×D4C2×D411yescharacteristic
308C22×D4C2412yes—
309C22×D4C2412yes—
310C22×D4C2412yes—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C2×D8—28no—
321C2×D8—28no—
322C2×D8—44no—
323C2×D8—44no—
324C2×D8—44no—
325C2×D8—44no—
326C22×C8—24no—
327C22×C8—42no—
328C22×C8—42no—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C22×C8C2412yes—
332C22×C8C2412yes—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335#127—24no—
336#127—22no—
337#127—22no—
338#127—22no—
339#127—22no—
340#127—22no—
341#127—42no—
342#127—44no—
343#127—44no—
344#127#4114yes—
345#125—44no—
346#124—44no—
347#124—44no—
348#124—82no—
349#123—48no—
350C22⋊Q8—44no—
351#121—24no—
352#121—48no—
353#121—42no—
354#121—44no—
355#121—44no—
356#121—44no—
357#121—44no—
358#121—44no—
359#121—44no—
360#121—44no—
361#121—82no—
362#121—82no—
363#121—82no—
364#120—48no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—44no—
369C4×D4—42no—
370C4×D4—42no—
371C4×D4—44no—
372C4×D4—44no—
373C4×D4—44no—
374C4×D4—82no—
375C4×D4—82no—
376C4×D4—82no—
377#117—82no—
378#117—82no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2×D411yescharacteristic
393C2×C4⋊C4C2×D411yescharacteristic
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
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—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×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—48no—
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449#107—28no—
450#106—44no—
451C4⋊C8—24no—
452C4⋊C8—42no—
453#102—28no—
454#102—44no—
455#102—44no—
456#102—44no—
457#102—44no—
458#102—44no—
459#102—44no—
460#102—44no—
461C22⋊C8—24no—
462C22⋊C8—42no—
463C22⋊C8—42no—
464C4×C8—22no—
465C4×C8—22no—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8—42no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95C2×D411yescharacteristic
478#95C2×D411yescharacteristic
479#95C2×D411yescharacteristic
480#95C2×D411yescharacteristic
481#95C2×D411yescharacteristic
482#95C2×D411yescharacteristic
483C24—22no—
484C24—22no—
485C24—22no—
486C24—44no—
487C24—44no—
488C24—44no—
489C24—44no—
490C24—82no—
491C24—82no—
492C24—82no—
493C24C22×D411yescharacteristic
494C24C22×D411yescharacteristic
495#41—816no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—24no—
502C2×D4—24no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—24no—
506C2×D4—22no—
507C2×D4—24no—
508C2×D4—22no—
509C2×D4—24no—
510C2×D4—22no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—41no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—44no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—816no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4—82no—
546C2×D4—88no—
547C2×D4—88no—
548C2×D4—816no—
549C2×D4—82no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4C2×#4114yes—
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—22no—
570C22×C4—21no—
571C22×C4—21no—
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—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4#13514yes—
590C22×C4AGL(1,ℤ/8)14yes—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C2511yescharacteristic
604D8—88no—
605D8—88no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—48no—
618C2×C8H(5,𝔽2)14yes—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—22no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—41no—
628C4⋊C4—44no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—82no—
639C4⋊C4—82no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—41no—
645C22⋊C4—41no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—82no—
657C22⋊C4—82no—
658C22⋊C4—82no—
659C22⋊C4—82no—
660C22⋊C4—82no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C22⋊C4—82no—
665C22⋊C4—82no—
666C22⋊C4—82no—
667C22⋊C4—82no—
668C22⋊C4—82no—
669C22⋊C4—82no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—22no—
682C42—21no—
683C42—22no—
684C42—82no—
685C42—82no—
686C42C2×#4112yes—
687C42H(5,𝔽2)12yes—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—24no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—88no—
722C23—88no—
723C23—88no—
724C23—88no—
725C23—164no—
726C23—164no—
727C23—164no—
728C23C2×#13512yes—
729C23C2×AGL(1,ℤ/8)12yes—
730C23C23×D411yescharacteristic
731Q8—84no—
732D4—28no—
733D4—44no—
734D4—44no—
735D4—44no—
736D4—44no—
737D4—44no—
738D4—44no—
739D4—48no—
740D4—48no—
741D4—88no—
742D4—88no—
743D4—88no—
744D4—88no—
745D4—84no—
746D4—84no—
747D4—84no—
748D4—84no—
749D4—164no—
750D4—164no—
751D4—164no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
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—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—44no—
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—88no—
804C2×C4—164no—
805C2×C4—164no—
806C2×C4#54612yes—
807C2×C4#54612yes—
808C2×C4C2×#13512yes—
809C2×C4C2×#13512yes—
810C2×C4C2×AGL(1,ℤ/8)12yes—
811C2×C4C2×AGL(1,ℤ/8)12yes—
812C2×C4#57612yes—
813C2×C4#57612yes—
814C2×C4C22×#4111yescharacteristic
815C2×C4C2×H(5,𝔽2)12yes—
816C2×C4C2×H(5,𝔽2)11yescharacteristic
817C2×C4#58512yes—
818C8—24no—
819C8—42no—
820C8—42no—
821C8—42no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—1616no—
858C22#344911yescharacteristic
859C22C2×#54611yescharacteristic
860C22#349811yescharacteristic
861C22C22×#13511yescharacteristic
862C22C22×AGL(1,ℤ/8)11yescharacteristic
863C22C2×#57611yescharacteristic
864C22C2×#57611yescharacteristic
865C4—22no—
866C4—22no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4#329714yes—
881C4#331814yes—
882C4#351412yes—
883C4#354212yes—
884C2—42no—
885C2—42no—
886C2—84no—
887C2—162no—
888C2—162no—
889C2#3809011yescharacteristic
890C2#6094611yescharacteristic
891C2#6101111yescharacteristic
892C2C2×#329711yescharacteristic
893C2C2×#331811yescharacteristic
894C2#6241711yescharacteristic
895C2#6242311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×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
1. #36211C2semidirect
2. #36121C2semidirect
3. #33171C2semidirect
4. #30919C2semidirect
5. #30400C2semidirect
6. #30204C2semidirect
7. #29843C2semidirect
8. #28615C2semidirect
9. #28514C2semidirect
10. #27890C2semidirect
11. #27878C2semidirect
12. #27229C2semidirect
13. #27199C2semidirect
14. #25721C2semidirect
15. #25599C2semidirect
16. #22269C2semidirect
17. #21803C2semidirect
18. #21401C2semidirect
19. #21101C2semidirect
25. C2×#486C22semidirect
26. C2×#478C22semidirect
27. C2×#466C22semidirect
30. C22×C4×C8C22semidirect
31. #2859C22semidirect
36. #2856C22semidirect
42. #2490C22semidirect
57. #2357C22semidirect
61. C4×#127C22semidirect
63. #2285C22semidirect
65. #2092C22semidirect
67. #2073C22semidirect
68. #2065C22semidirect
69. #2054C22semidirect
71. #2034C22semidirect
72. #2025C22semidirect
74. #1999C22semidirect
75. #1990C22semidirect
76. #1990C22semidirect
77. #1990C22semidirect
79. #1970C22semidirect
86. #1957C22semidirect
87. #1926C22semidirect
89. #1921C22semidirect
90. #1916C22semidirect
91. #1893C22semidirect
92. #1879C22semidirect
93. #1879C22semidirect
94. #1879C22semidirect
95. #1879C22semidirect
97. #1850C22semidirect
98. #1845C22semidirect
99. #1844C22semidirect
100. #1834C22semidirect
102. C4×C4⋊C8C22semidirect
103. C4×#102C22semidirect
105. C4×C22⋊C8C22semidirect
106. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#362112
#361212
#331712
#309192
#304002
#302042
#298432
#286152
#285142
#278902
#278782
#272292
#271992
#257212
#255992
#222692
#218032
#214012
#211012