Finite Group Databasebeta

← #6499931

Subgroups — #6499931

Order 512.

3478 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2C2×#3196C212yesmaximal, complemented
3C2×#2417C211yesmaximal, characteristic, complemented
4#25562C214yesmaximal, complemented
5#25548C214yesmaximal, complemented
6#24452C214yesmaximal, complemented
7#24449C214yesmaximal, complemented
8#24067C212yesmaximal, complemented
9#24006C211yesmaximal, characteristic, complemented
10#24005C211yesmaximal, characteristic, complemented
11#23937C212yesmaximal, complemented
12#23921C211yesmaximal, characteristic, complemented
13#23919C211yesmaximal, characteristic, complemented
14#21742C211yesmaximal, characteristic, complemented
15#20909C212yesmaximal, complemented
16#3505—216no—
17C2×#553—22no—
18C2×#553C2212yes—
19C2×#552C2212yes—
20C2×#551—22no—
21C2×#548C2212yes—
22C2×#546C2212yes—
23C2×#539—21no—
24C2×#538—21no—
25C2×#534—21no—
26C2×#529C2212yes—
27C2×#525C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic, complemented
31C22×#121C2211yescharacteristic
32C2×#518—21no—
33C22×C4×D4C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic, complemented
35#3196—216no—
36C2×#484C2212yescomplemented
37C2×#481C2212yes—
38C2×#485C2214yescomplemented
39C2×#470C2214yescomplemented
40C2×#468C2214yescomplemented
41C2×#452C2214yescomplemented
42C2×#451C2212yescomplemented
43C2×#451C2212yescomplemented
44C2×#448C2212yes—
45C2×#450C2212yescomplemented
46C2×#417C2214yescomplemented
47C2×#407C2212yescomplemented
48#2417—22no—
49#2417—22no—
50#2417C2214yes—
51#2417C2214yescomplemented
52C2×#398—21no—
53C2×#396—21no—
54C2×#391C2211yescharacteristic, complemented
55C2×#389C2211yescharacteristic, complemented
56C2×#386—21no—
57C2×#380—21no—
58C2×#380C2211yescharacteristic
59#2059C2214yescomplemented
60#2042C2214yescomplemented
61#2036C2214yescomplemented
62#2034C2214yescomplemented
63#2026C2214yescomplemented
64#2015C2214yescomplemented
65#2001C2214yescomplemented
66#2000C2214yescomplemented
67#1878C2214yescomplemented
68#1877C2214yescomplemented
69#1874C2212yes—
70#1874C2212yes—
71#1874C2214yescomplemented
72#1872C2212yescomplemented
73#1872C2212yescomplemented
74#1872C2212yescomplemented
75#1872C2212yescomplemented
76#1872C2214yescomplemented
77#1870C2214yes—
78#1870C2214yescomplemented
79#1865C2214yescomplemented
80#1862C2214yescomplemented
81#1853C2212yescomplemented
82#1852C2212yescomplemented
83#1817C2212yescomplemented
84#1787C2212yescomplemented
85#1786C2212yescomplemented
86#1779C2211yescharacteristic
87#1779C2211yescharacteristic
88#1736C2214yescomplemented
89C22×#41C2312yes—
90C23×Q8C2311yescharacteristic
91C23×Q8C2311yescharacteristic
92C23×D4—21no—
93C23×D4D411yescharacteristic
94C23×D4C2311yescharacteristic
95C24×C4—21no—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C22×Q16C2314yes—
99C22×SD16C2314yes—
100C22×M16C2314yes—
101#553—232no—
102#553—28no—
103#553—28no—
104#552—28no—
105#552—28no—
106#551—232no—
107#548—28no—
108#548—28no—
109#546—28no—
110#546—28no—
111#539—216no—
112#538—216no—
113#534—216no—
114#529—28no—
115#529—28no—
116C2×#126—22no—
117C2×#126—22no—
118C2×#126—22no—
119C2×#125—22no—
120C2×#125C2312yes—
121C2×#124—22no—
122C2×#124C2312yes—
123#525—28no—
124#525D4116yes—
125C2×#123—22no—
126C2×#123—22no—
127C2×#123—22no—
128C2×#123—22no—
129C2×#123—22no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—28no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—22no—
136C2×C22⋊Q8—22no—
137C2×C22⋊Q8—28no—
138C2×C22⋊Q8—44no—
139C2×C22⋊Q8C2314yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
143C2×C22⋊Q8C2312yes—
144C2×C22⋊Q8C2312yes—
145C2×#121—22no—
146C2×#121—22no—
147C2×#121—21no—
148C2×#121—21no—
149C2×#121—28no—
150C2×#121—22no—
151C2×#121C2312yes—
152C2×#121C2312yes—
153C2×#121C2312yes—
154C2×#120—22no—
155C2×#120—22no—
156#518—216no—
157C2×C4×Q8C2312yes—
158C2×C4×D4—28no—
159C2×C4×D4—22no—
160C2×C4×D4—22no—
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4—22no—
164C2×C4×D4D412yes—
165C2×C4×D4D412yes—
166C2×C4×D4C2312yes—
167C2×C4×D4C2312yes—
168C2×C4×D4C2312yes—
169C2×#117—22no—
170C2×#117—22no—
171C2×#117C2312yes—
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4—21no—
176C22×C4⋊C4—22no—
177C22×C4⋊C4—21no—
178C22×C4⋊C4—44no—
179C22×C4⋊C4D411yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2314yes—
185C22×C4⋊C4C2311yescharacteristic
186C22×C22⋊C4—21no—
187C22×C22⋊C4—21no—
188C22×C22⋊C4—22no—
189C22×C22⋊C4—21no—
190C22×C22⋊C4—21no—
191C22×C22⋊C4—21no—
192C22×C22⋊C4D411yescharacteristic
193C22×C22⋊C4D411yescharacteristic
194C22×C42C2311yescharacteristic
195#485—216no—
196#484—28no—
197#481—28no—
198#470—216no—
199#468—216no—
200#452—216no—
201#451—28no—
202#451—44no—
203#450—44no—
204#448—28no—
205C2×#107C2314yes—
206C2×#106C2314yes—
207#417—48no—
208C2×#103C2314yes—
209C2×#103C2314yes—
210C2×#103C2314yes—
211C2×#103C2314yes—
212C2×#103C2314yes—
213C2×#102C2314yes—
214C2×#102C2314yes—
215C2×#102C2314yes—
216#407—28no—
217C2×C22⋊C8C2314yes—
218C2×C22⋊C8C2312yes—
219C2×C22⋊C8C2312yes—
220C2×C22⋊C8C2312yes—
221C2×C22⋊C8C2312yes—
222C2×C22⋊C8C2312yes—
223C2×C22⋊C8C2312yes—
224#398—24no—
225#398—24no—
226#396—24no—
227#396—24no—
228#391—22no—
229#391C2314yes—
230#389—22no—
231#389C2314yes—
232#386—24no—
233#386—24no—
234#380—21no—
235#380—21no—
236#380—24no—
237#380—24no—
238#380C2312yes—
239#380C2312yes—
240C2×#95—21no—
241C2×#95—21no—
242C2×#95—21no—
243C2×#95—21no—
244#340C2314yes—
245#340C2314yes—
246#340C2314yes—
247#340C2314yes—
248#336C2314yes—
249#336C2314yes—
250C25—21no—
251C25C2×D411yescharacteristic
252C25C2×D411yescharacteristic
253C2×#41—24no—
254C2×#41—44no—
255C2×#41—44no—
256C2×#41C2×D418yes—
257C22×Q8—24no—
258C22×Q8—21no—
259C22×Q8—21no—
260C22×Q8—24no—
261C22×Q8—42no—
262C22×Q8—42no—
263C22×Q8—42no—
264C22×Q8—42no—
265C22×Q8C2412yes—
266C22×Q8C2412yes—
267C22×D4—28no—
268C22×D4—24no—
269C22×D4—24no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—24no—
275C22×D4—21no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4—42no—
279C22×D4—44no—
280C22×D4—44no—
281C22×D4C2×D412yes—
282C22×D4C2×D412yes—
283C22×D4C2412yes—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—24no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—24no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—44no—
300C23×C4—44no—
301C23×C4—82no—
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D412yes—
309C23×C4C2×D418yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C2×Q16—28no—
315C2×Q16—44no—
316C2×Q16—44no—
317C2×SD16—28no—
318C2×SD16—44no—
319C2×SD16—44no—
320C2×M16—28no—
321C2×M16—44no—
322C2×M16—44no—
323C22×C8C2414yes—
324C22×C8C2414yes—
325#126—216no—
326#126—216no—
327#126—216no—
328#125—216no—
329#125—24no—
330#125—24no—
331#124—216no—
332#124—24no—
333#124—24no—
334#123—216no—
335#123—216no—
336#123—216no—
337#123—216no—
338#123—216no—
339C22⋊Q8—28no—
340C22⋊Q8—28no—
341C22⋊Q8—216no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346C22⋊Q8—28no—
347C22⋊Q8—28no—
348C22⋊Q8—24no—
349C22⋊Q8—24no—
350C22⋊Q8—42no—
351C22⋊Q8—42no—
352C22⋊Q8—44no—
353C22⋊Q8—44no—
354C22⋊Q8—48no—
355C22⋊Q8C2×D418yes—
356C22⋊Q8C2×D418yes—
357#121—28no—
358#121—28no—
359#121—216no—
360#121—216no—
361#121—216no—
362#121—24no—
363#121—24no—
364#121—24no—
365#121—24no—
366#121C2×D418yes—
367#121C2×D418yes—
368#120—216no—
369#120—216no—
370C4×Q8—24no—
371C4×Q8—24no—
372C4×D4—216no—
373C4×D4—216no—
374C4×D4—216no—
375C4×D4—24no—
376C4×D4—28no—
377C4×D4—28no—
378C4×D4—216no—
379C4×D4—216no—
380C4×D4—24no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—24no—
384C4×D4—24no—
385#117—216no—
386#117—216no—
387#117—24no—
388#117C2×D418yes—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—44no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—48no—
415C2×C4⋊C4—44no—
416C2×C4⋊C4—44no—
417C2×C4⋊C4—44no—
418C2×C4⋊C4—82no—
419C2×C4⋊C4C2×D412yes—
420C2×C4⋊C4C2×D412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—216no—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—44no—
447C2×C22⋊C4—44no—
448C2×C22⋊C4—82no—
449C2×C22⋊C4C2×D412yes—
450C2×C22⋊C4C2×D412yes—
451C2×C22⋊C4C2×D412yes—
452C2×C22⋊C4C2×D412yes—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—24no—
456C2×C42C2×D412yes—
457C2×C42C2412yes—
458#107—28no—
459#106—28no—
460#103—28no—
461#103—28no—
462#103—28no—
463#103—28no—
464#103—44no—
465#102—28no—
466#102—28no—
467#102—44no—
468C22⋊C8—24no—
469C22⋊C8—24no—
470C22⋊C8—28no—
471C22⋊C8—42no—
472C22⋊C8—42no—
473C22⋊C8—42no—
474C22⋊C8—42no—
475#95—22no—
476#95—22no—
477#95—24no—
478#95—24no—
479#95—24no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—24no—
485C24—22no—
486C24—41no—
487C24—41no—
488C24—41no—
489C24—41no—
490C24—41no—
491C24—41no—
492C24—41no—
493C24—41no—
494C24—42no—
495C24—42no—
496C24—81no—
497C24—81no—
498C24—81no—
499C24—81no—
500C24#12014yes—
501C24#13714yes—
502C24C22×D412yes—
503C24C22×D411yescharacteristic
504C24C22×D411yescharacteristic
505C24C22×D411yescharacteristic
506#41—416no—
507#41—88no—
508C2×Q8—24no—
509C2×Q8—22no—
510C2×Q8—24no—
511C2×Q8—24no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—24no—
515C2×Q8—24no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—81no—
520C2×Q8—81no—
521C2×Q8—88no—
522C2×Q8—88no—
523C2×Q8C22×D414yes—
524C2×D4—28no—
525C2×D4—24no—
526C2×D4—28no—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—28no—
532C2×D4—28no—
533C2×D4—22no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—416no—
539C2×D4—432no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—81no—
545C2×D4—81no—
546C2×D4—88no—
547C2×D4—82no—
548C2×D4—82no—
549C2×D4—82no—
550C2×D4—82no—
551C2×D4C22×D414yes—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—28no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—416no—
583C22×C4—42no—
584C22×C4—41no—
585C22×C4—42no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—48no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—48no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—88no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—84no—
618C22×C4—81no—
619C22×C4—81no—
620C22×C4—816no—
621C22×C4#12014yes—
622C22×C4#12018yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D412yes—
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D414yes—
630C22×C4C22×D414yes—
631C22×C4C22×D414yes—
632C22×C4C2511yescharacteristic
633Q16—88no—
634SD16—88no—
635M16—88no—
636C2×C8—24no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—24no—
641C2×C8—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—28no—
645C4⋊C4—24no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—28no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—48no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—48no—
664C4⋊C4—84no—
665C4⋊C4C22×D414yes—
666C4⋊C4C22×D414yes—
667C4⋊C4H(5,𝔽2)14yes—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—28no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—24no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—24no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—48no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C42—28no—
688C42—24no—
689C42—28no—
690C42—22no—
691C42—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—22no—
699C23—21no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—21no—
708C23—22no—
709C23—21no—
710C23—28no—
711C23—22no—
712C23—22no—
713C23—21no—
714C23—21no—
715C23—28no—
716C23—24no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—48no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—82no—
733C23—82no—
734C23—82no—
735C23—82no—
736C23—84no—
737C23—84no—
738C23—162no—
739C23—162no—
740C23—162no—
741C23—162no—
742C23C2×#12014yes—
743C23C2×#12012yes—
744C23C2×#13712yes—
745C23C2×#13712yes—
746C23C2×#13712yes—
747C23#57512yes—
748C23C23×D411yescharacteristic
749Q8—28no—
750Q8—44no—
751Q8—44no—
752Q8—44no—
753Q8—84no—
754Q8—84no—
755D4—28no—
756D4—48no—
757D4—48no—
758D4—416no—
759D4—416no—
760D4—44no—
761D4—88no—
762D4—88no—
763D4—84no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—24no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—44no—
788C2×C4—48no—
789C2×C4—48no—
790C2×C4—48no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
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—42no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—88no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—88no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4—816no—
820C2×C4—84no—
821C2×C4—84no—
822C2×C4—84no—
823C2×C4C2×#12014yes—
824C2×C4C2×#12012yes—
825C2×C4C23×D412yes—
826C2×C4C2×H(5,𝔽2)12yes—
827C2×C4#58512yes—
828C8—44no—
829C8—44no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—24no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—24no—
844C22—24no—
845C22—416no—
846C22—42no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—42no—
853C22—42no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—88no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—168no—
867C22#300714yes—
868C22C22×#12011yescharacteristic
869C22#348411yescharacteristic
870C22#348511yescharacteristic
871C22C22×#13711yescharacteristic
872C22C2×#57511yescharacteristic
873C22#358511yescharacteristic
874C22#358611yescharacteristic
875C4—24no—
876C4—22no—
877C4—41no—
878C4—41no—
879C4—44no—
880C4—44no—
881C4—42no—
882C4—44no—
883C4—42no—
884C4—44no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4#349614yes—
889C2—24no—
890C2—44no—
891C2—42no—
892C2—42no—
893C2—84no—
894C2#3534711yescharacteristic
895C2C2×#300711yescharacteristic
896C2#6037111yescharacteristic
897C2#6157411yescharacteristic
898C2#6158111yescharacteristic
899C2#6170911yescharacteristic
900C2#6171611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3505C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3196C2semidirect
3. C2×#2417C2semidirect
4. #25562C2semidirect
5. #25548C2semidirect
6. #24452C2semidirect
7. #24449C2semidirect
8. #24067C2semidirect
9. #24006C2semidirect
10. #24005C2semidirect
11. #23937C2semidirect
12. #23921C2semidirect
13. #23919C2semidirect
14. #21742C2semidirect
15. #20909C2semidirect
30. C22×C22⋊Q8C22semidirect
34. C23×C4⋊C4C22semidirect
36. C2×#484C22semidirect
38. C2×#485C22semidirect
39. C2×#470C22semidirect
40. C2×#468C22semidirect
41. C2×#452C22semidirect
42. C2×#451C22semidirect
43. C2×#451C22semidirect
45. C2×#450C22semidirect
46. C2×#417C22semidirect
47. C2×#407C22semidirect
51. #2417C22semidirect
54. C2×#391C22semidirect
55. C2×#389C22semidirect
59. #2059C22semidirect
60. #2042C22semidirect
61. #2036C22semidirect
62. #2034C22semidirect
63. #2026C22semidirect
64. #2015C22semidirect
65. #2001C22semidirect
66. #2000C22semidirect
67. #1878C22semidirect
68. #1877C22semidirect
71. #1874C22semidirect
72. #1872C22semidirect
73. #1872C22semidirect
74. #1872C22semidirect
75. #1872C22semidirect
76. #1872C22semidirect
78. #1870C22semidirect
79. #1865C22semidirect
80. #1862C22semidirect
81. #1853C22semidirect
82. #1852C22semidirect
83. #1817C22semidirect
84. #1787C22semidirect
85. #1786C22semidirect
88. #1736C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
C2×#31962
C2×#24172
#255622
#255482
#244522
#244492
#240672
#240062
#240052
#239372
#239212
#239192
#217422
#209092