Finite Group Databasebeta

← #6595551

Subgroups — #6595551

Order 512.

3505 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C2×#3331C212yesmaximal, complemented
3#36100C211yesmaximal, characteristic
4#32982C212yesmaximal, complemented
5#32906C211yesmaximal, characteristic, complemented
6#25902C211yesmaximal, characteristic, complemented
7#25573C212yesmaximal, complemented
8#25561C214yesmaximal, complemented
9#24386C212yesmaximal, complemented
10#24299C211yesmaximal, characteristic, complemented
11#24118C212yesmaximal, complemented
12#23981C214yesmaximal, complemented
13#23922C212yesmaximal, complemented
14#22502C212yesmaximal, complemented
15#22401C211yesmaximal, characteristic, complemented
16C4×#448C211yesmaximal, characteristic, complemented
17#20909C212yesmaximal, complemented
18C2×#554—216no—
19C2×#554—21no—
20C2×#554—21no—
21C2×#554—22no—
22C2×#554C2212yes—
23C2×#554C2214yes—
24C2×#554C2212yes—
25C2×#547C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×#125—21no—
28C2×#525C2212yes—
29C22×C22⋊Q8—22no—
30C22×C22⋊Q8C2212yes—
31C22×C4×Q8C2211yescharacteristic
32C22×C4×D4—21no—
33C22×C4×D4C2211yescharacteristic
34C23×C4⋊C4C2212yes—
35#3331—216no—
36C2×#487C2212yescomplemented
37C2×#483C2214yescomplemented
38C2×#476C2212yescomplemented
39C2×#470C2214yescomplemented
40C2×#462C2212yescomplemented
41C2×#452C2214yescomplemented
42C2×#451C2212yes—
43C2×#448C2211yescharacteristic
44C2×C4×SD16C2212yescomplemented
45C2×#436C2212yes—
46C2×#417C2214yescomplemented
47C2×#407C2212yes—
48#2857C2211yescharacteristic
49#2848C2212yes—
50#2542C2211yescharacteristic
51#2537C2211yescharacteristic
52#2455—22no—
53#2422—21no—
54#2418—22no—
55#2415C2212yes—
56#2408—21no—
57#2407C2212yes—
58#2361—21no—
59#2354C2211yescharacteristic
60D4×C4⋊C4—21no—
61C4×#121C2211yescharacteristic
62#2058C2212yescomplemented
63#2035C2214yescomplemented
64#2024C2214yescomplemented
65#2023C2212yescomplemented
66#2001C2214yescomplemented
67#2001C2214yescomplemented
68#2000C2214yescomplemented
69#1990C2212yescomplemented
70#1987C2212yescomplemented
71#1954C2212yes—
72#1894C2214yescomplemented
73#1880C2212yescomplemented
74#1878C2214yescomplemented
75#1874C2212yes—
76#1874C2211yescharacteristic
77#1874C2214yescomplemented
78#1873C2214yescomplemented
79#1872C2212yes—
80#1872C2212yes—
81#1872C2212yes—
82#1872C2214yescomplemented
83#1872C2214yescomplemented
84#1870C2214yes—
85#1865C2212yescomplemented
86#1853C2212yes—
87#1853C2211yescharacteristic
88#1853C2214yescomplemented
89#1823C2214yescomplemented
90#1803C2212yescomplemented
91#1797C2211yescharacteristic
92#1787C2211yescharacteristic
93#1779C2212yes—
94C4×#103C2212yescomplemented
95C4×C22⋊C8C2211yescharacteristic
96#1736C2214yescomplemented
97C22×#41C2312yes—
98C23×Q8—21no—
99C23×Q8C2311yescharacteristic
100C23×D4D411yescharacteristic
101C24×C4—22no—
102C24×C4C2312yes—
103C22×Q16C2314yes—
104C22×SD16C2312yes—
105C22×M16C2314yes—
106#554—216no—
107#554—232no—
108#554—216no—
109#554—28no—
110#554—216no—
111#554—28no—
112#554—28no—
113#554—216no—
114#554D4116yescomplemented
115#547—28no—
116C2×C4⋊Q8—28no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2312yes—
121C2×C4⋊Q8C2312yes—
122C2×#125—216no—
123C2×#125—22no—
124C2×#125—24no—
125C2×#125—22no—
126#525—28no—
127#525—44no—
128C2×#123—22no—
129C2×#123—22no—
130C2×C22⋊Q8—232no—
131C2×C22⋊Q8—22no—
132C2×C22⋊Q8—22no—
133C2×C22⋊Q8—216no—
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8—24no—
137C2×C22⋊Q8—24no—
138C2×C22⋊Q8C2312yes—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2314yes—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2314yes—
143C2×C22⋊Q8C2312yes—
144C2×#121—21no—
145C2×#121—21no—
146C2×#121C2312yes—
147C2×#121C2311yescharacteristic
148C2×#120—22no—
149C2×C4×Q8—28no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8C2312yes—
153C2×C4×Q8C2312yes—
154C2×C4×D4—216no—
155C2×C4×D4—24no—
156C2×C4×D4—22no—
157C2×C4×D4—22no—
158C2×C4×D4—28no—
159C2×C4×D4—21no—
160C2×C4×D4—22no—
161C2×C4×D4—22no—
162C2×C4×D4D411yescharacteristic
163C2×C4×D4D411yescharacteristic
164C2×C4×D4D412yes—
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2312yes—
167C2×C4×D4C2311yescharacteristic
168C2×C4×D4C2311yescharacteristic
169C2×#117C2312yes—
170C22×C4⋊C4—22no—
171C22×C4⋊C4—22no—
172C22×C4⋊C4—22no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4—22no—
176C22×C4⋊C4—216no—
177C22×C4⋊C4—21no—
178C22×C4⋊C4D411yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2314yes—
182C22×C4⋊C4C2314yes—
183C22×C22⋊C4—22no—
184C22×C22⋊C4D412yes—
185C22×C42—21no—
186C22×C42C2311yescharacteristic
187#487—28no—
188#483—216no—
189#476—28no—
190#470—216no—
191#462—28no—
192#452—216no—
193#451—44no—
194#448—24no—
195C4×SD16—28no—
196#436—28no—
197C2×#106C2314yes—
198C2×#106C2312yes—
199C2×C4⋊C8C2312yes—
200#417—216no—
201C2×#103C2314yes—
202C2×#103C2314yes—
203C2×#103C2314yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2314yes—
207C2×#103C2312yes—
208C2×#102C2312yes—
209C2×#102C2314yes—
210#407—44no—
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2314yes—
213C2×C22⋊C8C2311yescharacteristic
214C2×C22⋊C8C2311yescharacteristic
215C2×C22⋊C8C2314yes—
216C2×C22⋊C8C2314yes—
217C2×C4×C8C2312yes—
218#399—22no—
219#397—22no—
220#394—22no—
221#394—22no—
222#394—22no—
223#392—22no—
224#391C2312yes—
225#390—21no—
226#390—21no—
227#390C2311yescharacteristic
228#389—22no—
229#389—21no—
230#389—21no—
231#389C2311yescharacteristic
232#388—22no—
233#388—22no—
234#388—21no—
235#386—21no—
236#386—22no—
237#385—22no—
238#385—22no—
239#385—22no—
240#385—22no—
241#384—21no—
242#384C2311yescharacteristic
243#380—21no—
244#380—21no—
245#380—21no—
246#380C2312yes—
247#380C2311yescharacteristic
248#380C2312yes—
249#379—22no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4C2311yescharacteristic
252C4×C22⋊C4—21no—
253#340C2314yes—
254#340C2314yes—
255#340C2312yes—
256#340C2314yes—
257#340C2314yes—
258#340C2312yes—
259#340C2314yes—
260#336C2312yes—
261#336C2312yes—
262C25C2×D412yes—
263C2×#41—24no—
264C2×#41—28no—
265C2×#41—42no—
266C2×#41—44no—
267C22×Q8—28no—
268C22×Q8—24no—
269C22×Q8—21no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—22no—
274C22×Q8—42no—
275C22×Q8—82no—
276C22×Q8—82no—
277C22×Q8C2412yes—
278C22×Q8C2412yes—
279C22×D4—24no—
280C22×D4—24no—
281C22×D4—21no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—24no—
285C22×D4C2×D412yes—
286C22×D4C2×D411yescharacteristic
287C22×D4C2×D411yescharacteristic
288C22×D4C2411yescharacteristic
289C23×C4—21no—
290C23×C4—22no—
291C23×C4—21no—
292C23×C4—216no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—28no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—21no—
299C23×C4—22no—
300C23×C4—44no—
301C23×C4—84no—
302C23×C4—84no—
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D412yes—
305C23×C4C2×D412yes—
306C23×C4C2×D412yes—
307C23×C4C2×D411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C2×Q16—28no—
312C2×Q16—44no—
313C2×Q16—44no—
314C2×SD16—24no—
315C2×SD16—24no—
316C2×SD16—42no—
317C2×M16—28no—
318C2×M16—44no—
319C2×M16—44no—
320C22×C8C2412yes—
321C22×C8C2414yes—
322C22×C8C2412yes—
323C4⋊Q8—28no—
324C4⋊Q8—28no—
325C4⋊Q8—28no—
326C4⋊Q8—24no—
327C4⋊Q8—24no—
328C4⋊Q8C2×D418yes—
329#125—232no—
330#125—216no—
331#125—216no—
332#123—48no—
333#123—48no—
334C22⋊Q8—216no—
335C22⋊Q8—232no—
336C22⋊Q8—232no—
337C22⋊Q8—216no—
338C22⋊Q8—232no—
339C22⋊Q8—28no—
340C22⋊Q8—28no—
341C22⋊Q8—28no—
342C22⋊Q8—232no—
343C22⋊Q8—28no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346C22⋊Q8—24no—
347C22⋊Q8—42no—
348C22⋊Q8—44no—
349C22⋊Q8C2×D4116yes—
350#121—22no—
351#121—24no—
352#121—42no—
353#121—44no—
354#121—44no—
355#121#4114yes—
356#120—48no—
357C4×Q8—28no—
358C4×Q8—28no—
359C4×Q8—24no—
360C4×Q8—24no—
361C4×Q8—24no—
362C4×Q8C2×D418yes—
363C4×D4—232no—
364C4×D4—216no—
365C4×D4—216no—
366C4×D4—24no—
367C4×D4—28no—
368C4×D4—24no—
369C4×D4—28no—
370C4×D4—24no—
371C4×D4—24no—
372C4×D4—48no—
373C4×D4—48no—
374C4×D4—44no—
375C4×D4C2×D418yes—
376#117—24no—
377#117—42no—
378C2×C4⋊C4—216no—
379C2×C4⋊C4—216no—
380C2×C4⋊C4—216no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—216no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—28no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—28no—
398C2×C4⋊C4—28no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2×D412yes—
412C2×C4⋊C4C2×D4116yes—
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2411yescharacteristic
416C2×C4⋊C4C2411yescharacteristic
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2414yes—
419C2×C4⋊C4C2411yescharacteristic
420C2×C22⋊C4—216no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4C2×D412yes—
438C2×C22⋊C4C2×D412yes—
439C2×C22⋊C4C2×D412yes—
440C2×C22⋊C4C2×D412yes—
441C2×C42—28no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—24no—
445C2×C42—22no—
446C2×C42—21no—
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451#106—24no—
452#106—28no—
453C4⋊C8—24no—
454#103—24no—
455#103—28no—
456#103—28no—
457#103—28no—
458#103—24no—
459#103—42no—
460#103—44no—
461#102—24no—
462#102—28no—
463C22⋊C8—28no—
464C22⋊C8—22no—
465C22⋊C8—22no—
466C22⋊C8—24no—
467C22⋊C8—44no—
468C22⋊C8—44no—
469C4×C8—24no—
470#95—21no—
471#95—21no—
472#95—22no—
473#95—21no—
474#95—22no—
475#95—22no—
476#95—22no—
477C24—24no—
478C24—24no—
479C24—24no—
480C24—24no—
481C24—24no—
482C24—21no—
483C24—42no—
484C24—42no—
485C24C22×D412yes—
486C24C22×D412yes—
487C24C22×D411yescharacteristic
488#41—416no—
489#41—88no—
490C2×Q8—24no—
491C2×Q8—28no—
492C2×Q8—28no—
493C2×Q8—22no—
494C2×Q8—24no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—24no—
502C2×Q8—48no—
503C2×Q8—48no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—82no—
507C2×Q8—82no—
508C2×Q8—82no—
509C2×Q8—82no—
510C2×Q8—816no—
511C2×Q8C22×D414yes—
512C2×D4—232no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—22no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—21no—
523C2×D4—22no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—82no—
531C2×D4—82no—
532C2×D4#12014yes—
533C2×D4#13714yes—
534C2×D4C2×#4112yes—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—28no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—216no—
553C22×C4—216no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—41no—
571C22×C4—416no—
572C22×C4—416no—
573C22×C4—44no—
574C22×C4—42no—
575C22×C4—44no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—82no—
585C22×C4—84no—
586C22×C4—84no—
587C22×C4—84no—
588C22×C4—84no—
589C22×C4—832no—
590C22×C4#13714yes—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D418yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C2×#4112yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4C2511yescharacteristic
602Q16—88no—
603SD16—48no—
604M16—88no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—24no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—24no—
611C2×C8—22no—
612C2×C8—24no—
613C2×C8—22no—
614C4⋊C4—24no—
615C4⋊C4—216no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—216no—
620C4⋊C4—216no—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—216no—
624C4⋊C4—24no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—44no—
634C4⋊C4—42no—
635C4⋊C4—44no—
636C4⋊C4—42no—
637C4⋊C4—44no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—81no—
641C4⋊C4—82no—
642C4⋊C4#12014yes—
643C4⋊C4C22×D414yes—
644C4⋊C4C22×D418yes—
645C4⋊C4C2×#4112yes—
646C22⋊C4—216no—
647C22⋊C4—216no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—42no—
658C22⋊C4—44no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—81no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C22⋊C4#12018yes—
665C42—28no—
666C42—28no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—44no—
671C42—42no—
672C42C22×D414yes—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—216no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—48no—
692C23—48no—
693C23—48no—
694C23—48no—
695C23—48no—
696C23—48no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23C2×#12014yes—
704C23#54612yes—
705C23C2×#13714yes—
706C23C2×#13712yes—
707C23#57712yes—
708C23C23×D411yescharacteristic
709Q8—24no—
710Q8—24no—
711Q8—48no—
712Q8—42no—
713Q8—42no—
714Q8—44no—
715Q8—44no—
716Q8—88no—
717Q8—88no—
718D4—216no—
719D4—24no—
720D4—28no—
721D4—28no—
722D4—48no—
723D4—42no—
724D4—88no—
725D4—88no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—24no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—24no—
738C2×C4—28no—
739C2×C4—21no—
740C2×C4—24no—
741C2×C4—21no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—28no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—48no—
750C2×C4—48no—
751C2×C4—48no—
752C2×C4—44no—
753C2×C4—48no—
754C2×C4—416no—
755C2×C4—48no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—41no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—88no—
779C2×C4—816no—
780C2×C4—816no—
781C2×C4—84no—
782C2×C4C2×#12012yes—
783C2×C4C2×#12014yes—
784C2×C4C2×#12012yes—
785C2×C4#54612yes—
786C2×C4C2×#13712yes—
787C2×C4C2×#13712yes—
788C2×C4C2×#13712yes—
789C2×C4C23×D412yes—
790C2×C4C22×#4111yescharacteristic
791C2×C4C2×H(5,𝔽2)11yescharacteristic
792C2×C4#58512yes—
793C8—42no—
794C8—42no—
795C8—44no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—432no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22#333114yescomplemented
825C22C22×#12011yescharacteristic
826C22C2×#54611yescharacteristic
827C22#348511yescharacteristic
828C22C22×#13711yescharacteristic
829C22C22×#13711yescharacteristic
830C22C2×#57711yescharacteristic
831C22#358511yescharacteristic
832C4—22no—
833C4—24no—
834C4—22no—
835C4—22no—
836C4—42no—
837C4—44no—
838C4—41no—
839C4—44no—
840C4—48no—
841C4—42no—
842C4—81no—
843C4—82no—
844C4—81no—
845C4—82no—
846C4#300414yes—
847C4D4×#4112yes—
848C4#348812yes—
849C2—24no—
850C2—44no—
851C2—44no—
852C2—82no—
853C2#3621211yescharacteristic
854C2C2×#300411yescharacteristic
855C2#6037311yescharacteristic
856C2C2×#333111yescharacteristic
857C2#6116211yescharacteristic
858C2#6171911yescharacteristic
859C2#6173511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36100C2
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
1. C22×#554C2semidirect
2. C2×#3331C2semidirect
4. #32982C2semidirect
5. #32906C2semidirect
6. #25902C2semidirect
7. #25573C2semidirect
8. #25561C2semidirect
9. #24386C2semidirect
10. #24299C2semidirect
11. #24118C2semidirect
12. #23981C2semidirect
13. #23922C2semidirect
14. #22502C2semidirect
15. #22401C2semidirect
16. C4×#448C2semidirect
17. #20909C2semidirect
36. C2×#487C22semidirect
37. C2×#483C22semidirect
38. C2×#476C22semidirect
39. C2×#470C22semidirect
40. C2×#462C22semidirect
41. C2×#452C22semidirect
44. C2×C4×SD16C22semidirect
46. C2×#417C22semidirect
62. #2058C22semidirect
63. #2035C22semidirect
64. #2024C22semidirect
65. #2023C22semidirect
66. #2001C22semidirect
67. #2001C22semidirect
68. #2000C22semidirect
69. #1990C22semidirect
70. #1987C22semidirect
72. #1894C22semidirect
73. #1880C22semidirect
74. #1878C22semidirect
77. #1874C22semidirect
78. #1873C22semidirect
82. #1872C22semidirect
83. #1872C22semidirect
85. #1865C22semidirect
88. #1853C22semidirect
89. #1823C22semidirect
90. #1803C22semidirect
94. C4×#103C22semidirect
96. #1736C22semidirect
114. #554D4semidirect
824. C22#3331semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#33312
#361002
#329822
#329062
#259022
#255732
#255612
#243862
#242992
#241182
#239812
#239222
#225022
#224012
C4×#4482
#209092