Finite Group Databasebeta

← #6496028

Subgroups — #6496028

Order 512.

3452 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic
2C2×#3239C212yesmaximal, complemented
3C2×#2857C211yesmaximal, characteristic, complemented
4#32954C212yesmaximal, complemented
5#32953C212yesmaximal, complemented
6#29689C214yesmaximal, complemented
7#25864C212yesmaximal, complemented
8#25819C212yesmaximal, complemented
9#25678C214yesmaximal, complemented
10#24067C214yesmaximal, complemented
11#24006C212yesmaximal, complemented
12#24005C212yesmaximal
13#21867C212yesmaximal, complemented
14#20715C211yesmaximal, characteristic, complemented
15C22×C4⋊Q8C2211yescharacteristic, complemented
16C2×#529—21no—
17C2×#529—21no—
18C2×#529—21no—
19C2×#529—21no—
20C2×#529—216no—
21C2×#529C2212yes—
22C2×#529C2212yes—
23C2×#529C2212yes—
24C2×#529C2212yes—
25C22×#126—21no—
26C22×#125C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×#123—21no—
29C22×C22⋊Q8—21no—
30C22×C22⋊Q8C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4—21no—
34C22×C4×D4C2211yescharacteristic
35C22×#117—21no—
36C23×C42C2211yescharacteristic
37#3239—216no—
38C2×#501C2214yescomplemented
39C2×#489C2214yescomplemented
40C2×#484C2214yescomplemented
41C2×#481C2214yes—
42C2×#475C2214yescomplemented
43C2×#474C2214yescomplemented
44C2×#432C2212yescomplemented
45#2857—21no—
46#2857—21no—
47#2857—21no—
48#2857—21no—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yescomplemented
52#2857C2212yescomplemented
53C2×#391—21no—
54C2×#389—21no—
55C2×#389C2212yescomplemented
56C2×#384C2211yescharacteristic, complemented
57C2×#380—21no—
58C2×#380C2212yes—
59#2059C2218yescomplemented
60#2042C2218yescomplemented
61#2036C2218yescomplemented
62#2034C2218yes—
63#1992C2214yescomplemented
64#1959C2214yescomplemented
65#1874C2214yes—
66#1872C2214yescomplemented
67#1865C2218yescomplemented
68#1862C2218yescomplemented
69#1853C2214yes—
70#1852C2214yes—
71#1817C2212yescomplemented
72#1803C2214yescomplemented
73#1802C2214yescomplemented
74#1797C2212yes—
75#1797C2212yescomplemented
76#1787C2214yes—
77#1786C2214yes—
78#1779C2212yes—
79#1749C2212yes—
80#1749C2212yescomplemented
81C23×Q8—21no—
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C24×C4—21no—
86C24×C4D411yescharacteristic
87C24×C4D411yescharacteristic
88C24×C4C2311yescharacteristic
89C2×C4⋊Q8—21no—
90C2×C4⋊Q8—21no—
91C2×C4⋊Q8—28no—
92C2×C4⋊Q8C2312yes—
93C2×C4⋊Q8C2312yes—
94#529—216no—
95#529—216no—
96#529—216no—
97#529—216no—
98#529—28no—
99#529—28no—
100#529—28no—
101#529—28no—
102#529—28no—
103#529—28no—
104#529—28no—
105#529D4116yes—
106C2×#126—216no—
107C2×#126—22no—
108C2×#126—22no—
109C2×#126—22no—
110C2×#126—22no—
111C2×#125—28no—
112C2×#125—21no—
113C2×#125—21no—
114C2×#125C2312yes—
115C2×#125C2312yes—
116C2×#124—28no—
117C2×#124—21no—
118C2×#124—21no—
119C2×#124C2312yes—
120C2×#124C2312yes—
121C2×#123—216no—
122C2×#123—22no—
123C2×#123—22no—
124C2×#123—22no—
125C2×#123—22no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—28no—
129C2×C22⋊Q8—22no—
130C2×C22⋊Q8—22no—
131C2×C22⋊Q8—22no—
132C2×C22⋊Q8—22no—
133C2×C22⋊Q8—48no—
134C2×C22⋊Q8C2312yes—
135C2×C22⋊Q8C2312yes—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—28no—
139C2×#121C2312yes—
140C2×#121C2312yes—
141C2×C4×Q8—28no—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8C2312yes—
145C2×C4×Q8C2312yes—
146C2×C4×D4—216no—
147C2×C4×D4—22no—
148C2×C4×D4—22no—
149C2×C4×D4—22no—
150C2×C4×D4—22no—
151C2×C4×D4—28no—
152C2×C4×D4—21no—
153C2×C4×D4—21no—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×#117—216no—
157C2×#117—22no—
158C2×#117—22no—
159C2×#117—22no—
160C2×#117—22no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—22no—
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C22⋊C4—21no—
174C22×C22⋊C4—21no—
175C22×C22⋊C4—21no—
176C22×C22⋊C4—21no—
177C22×C22⋊C4—21no—
178C22×C22⋊C4—22no—
179C22×C42—21no—
180C22×C42—28no—
181C22×C42D411yescharacteristic
182C22×C42D411yescharacteristic
183C22×C42D411yescharacteristic
184C22×C42D411yescharacteristic
185C22×C42D411yescharacteristic
186C22×C42D411yescharacteristic
187C22×C42C2311yescharacteristic
188C22×C42C2311yescharacteristic
189C22×C42C2311yescharacteristic
190C22×C42C2311yescharacteristic
191C22×C42C2311yescharacteristic
192C22×C42C2311yescharacteristic
193#501—216no—
194#489—216no—
195#484—216no—
196#481—216no—
197#475—216no—
198#474—216no—
199#432—28no—
200C2×#107C2318yes—
201C2×#106C2318yes—
202C2×C4⋊C8C2314yes—
203C2×#103C2318yes—
204C2×#103C2318yes—
205C2×#102C2318yes—
206C2×#102C2318yes—
207C2×C22⋊C8C2314yes—
208C2×C22⋊C8C2314yes—
209C2×C22⋊C8C2314yes—
210C2×#97C2314yes—
211#391—22no—
212#391—22no—
213#391—22no—
214#391—22no—
215#389—22no—
216#389—22no—
217#389—22no—
218#389—22no—
219#389—22no—
220#389—22no—
221#389C2314yes—
222#389C2314yes—
223#384—21no—
224#384—21no—
225#384C2312yes—
226#384C2312yes—
227#380—22no—
228#380—22no—
229#380—22no—
230#380—22no—
231#380—22no—
232#380—22no—
233#380C2314yes—
234#380C2314yes—
235C2×#95—22no—
236C2×#95—22no—
237#340C2318yes—
238#340C2318yes—
239#336C2314yes—
240#336C2314yes—
241C25—21no—
242C25C2×D411yescharacteristic
243C22×Q8—24no—
244C22×Q8—21no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—24no—
248C22×Q8—42no—
249C22×Q8—44no—
250C22×Q8—44no—
251C22×Q8—44no—
252C22×Q8C2412yes—
253C22×D4—28no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—24no—
257C22×D4—21no—
258C22×D4—24no—
259C22×D4—42no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4C2412yes—
263C23×C4—28no—
264C23×C4—24no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C22×C8C2418yes—
301C4⋊Q8—28no—
302C4⋊Q8—28no—
303C4⋊Q8—44no—
304C4⋊Q8—44no—
305#126—216no—
306#126—216no—
307#126—216no—
308#126—216no—
309#125—28no—
310#125—28no—
311#125—24no—
312#125—24no—
313#125—24no—
314#125C2×D418yes—
315#124—28no—
316#124—28no—
317#124—24no—
318#124—24no—
319#124—24no—
320#124C2×D418yes—
321#123—216no—
322#123—216no—
323#123—216no—
324#123—216no—
325C22⋊Q8—28no—
326C22⋊Q8—28no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329C22⋊Q8—24no—
330C22⋊Q8—48no—
331C22⋊Q8—48no—
332C22⋊Q8—48no—
333C22⋊Q8—48no—
334C22⋊Q8C2×D418yes—
335#121—28no—
336#121—28no—
337#121—24no—
338#121—24no—
339#121—24no—
340#121C2×D418yes—
341C4×Q8—28no—
342C4×Q8—28no—
343C4×Q8—24no—
344C4×Q8—24no—
345C4×Q8—24no—
346C4×Q8C2×D418yes—
347C4×D4—216no—
348C4×D4—216no—
349C4×D4—28no—
350C4×D4—28no—
351C4×D4—216no—
352C4×D4—24no—
353C4×D4—216no—
354C4×D4—24no—
355C4×D4—24no—
356C4×D4C2×D418yes—
357#117—216no—
358#117—216no—
359#117—216no—
360#117—216no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—48no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4C2414yes—
394C2×C4⋊C4C2414yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
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—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—48no—
415C2×C42—28no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D418yes—
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446#107—216no—
447#106—216no—
448C4⋊C8—28no—
449#103—216no—
450#103—48no—
451#102—216no—
452#102—48no—
453C22⋊C8—28no—
454C22⋊C8—28no—
455C22⋊C8—44no—
456#97—28no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—24no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—24no—
466C24—22no—
467C24—41no—
468C24—41no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24#13714yes—
476C24C22×D411yescharacteristic
477C24C22×D411yescharacteristic
478C24C22×D411yescharacteristic
479C2×Q8—24no—
480C2×Q8—22no—
481C2×Q8—24no—
482C2×Q8—24no—
483C2×Q8—416no—
484C2×Q8—42no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—42no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—816no—
493C2×Q8C22×D414yes—
494C2×D4—28no—
495C2×D4—24no—
496C2×D4—28no—
497C2×D4—22no—
498C2×D4—24no—
499C2×D4—24no—
500C2×D4—416no—
501C2×D4—42no—
502C2×D4—432no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—42no—
508C2×D4C22×D414yes—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—28no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
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—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—28no—
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—24no—
557C22×C4—24no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—416no—
569C22×C4—416no—
570C22×C4—416no—
571C22×C4—44no—
572C22×C4—432no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4#12014yes—
589C22×C4#12014yes—
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×D414yes—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C42−1+414yes—
604C22×C4C2511yescharacteristic
605C2×C8—28no—
606C2×C8—28no—
607C2×C8—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—24no—
611C4⋊C4—28no—
612C4⋊C4—24no—
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—48no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—48no—
632C4⋊C4C22×D414yes—
633C4⋊C4C22×D414yes—
634C22⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C42—28no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—28no—
658C42—22no—
659C42—22no—
660C42#12014yes—
661C42#12014yes—
662C42C22×D414yes—
663C42C22×D414yes—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—28no—
676C23—28no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—24no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—48no—
687C23—48no—
688C23—48no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23C2×#12012yes—
700C23#53612yes—
701C23C2×AGL(1,ℤ/8)12yes—
702C23C2×#13712yes—
703C23C2×#13712yes—
704C23C2×#13712yes—
705C23#57512yes—
706C23C23×D411yescharacteristic
707Q8—28no—
708Q8—48no—
709Q8—44no—
710Q8—88no—
711Q8—88no—
712D4—28no—
713D4—48no—
714D4—416no—
715D4—416no—
716D4—44no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—28no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—28no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—416no—
760C2×C4—48no—
761C2×C4—48no—
762C2×C4—48no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—416no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—88no—
780C2×C4—88no—
781C2×C4C2×#12012yes—
782C2×C4C2×#12012yes—
783C2×C4C2×#12012yes—
784C2×C4C2×#12012yes—
785C2×C4C2×#12012yes—
786C2×C4#53612yes—
787C2×C4C2×AGL(1,ℤ/8)12yes—
788C2×C4C2×AGL(1,ℤ/8)12yes—
789C2×C4#57512yes—
790C2×C4C23×D412yes—
791C2×C4C2×2−1+412yes—
792C2×C4#58512yes—
793C8—48no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—416no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—816no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22#300714yes—
823C22#323914yescomplemented
824C22C22×#12011yescharacteristic
825C22C2×#53611yescharacteristic
826C22#344911yescharacteristic
827C22C22×AGL(1,ℤ/8)11yescharacteristic
828C22C22×#13711yescharacteristic
829C22C2×#57511yescharacteristic
830C22C2×#57511yescharacteristic
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—22no—
836C4—22no—
837C4—41no—
838C4—44no—
839C4—41no—
840C4—41no—
841C4—44no—
842C4—41no—
843C4—44no—
844C4—84no—
845C4—84no—
846C4#300614yes—
847C4#348914yes—
848C2—24no—
849C2—24no—
850C2—42no—
851C2—84no—
852C2#3530511yescharacteristic
853C2C2×#300611yescharacteristic
854C2C2×#300711yescharacteristic
855C2C2×#323911yescharacteristic
856C2#6086611yescharacteristic
857C2#6094911yescharacteristic
858C2#6096011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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
2. C2×#3239C2semidirect
3. C2×#2857C2semidirect
4. #32954C2semidirect
5. #32953C2semidirect
6. #29689C2semidirect
7. #25864C2semidirect
8. #25819C2semidirect
9. #25678C2semidirect
10. #24067C2semidirect
11. #24006C2semidirect
13. #21867C2semidirect
14. #20715C2semidirect
15. C22×C4⋊Q8C22semidirect
38. C2×#501C22semidirect
39. C2×#489C22semidirect
40. C2×#484C22semidirect
42. C2×#475C22semidirect
43. C2×#474C22semidirect
44. C2×#432C22semidirect
51. #2857C22semidirect
52. #2857C22semidirect
55. C2×#389C22semidirect
56. C2×#384C22semidirect
59. #2059C22semidirect
60. #2042C22semidirect
61. #2036C22semidirect
63. #1992C22semidirect
64. #1959C22semidirect
66. #1872C22semidirect
67. #1865C22semidirect
68. #1862C22semidirect
71. #1817C22semidirect
72. #1803C22semidirect
73. #1802C22semidirect
75. #1797C22semidirect
80. #1749C22semidirect
823. C22#3239semidirect

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#32392
C2×#28572
#329542
#329532
#296892
#258642
#258192
#256782
#240672
#240062
#240052
#218672
#207152