Finite Group Databasebeta

← #6393456

Subgroups — #6393456

Order 512.

3658 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2C22×#435C211yesmaximal, characteristic, complemented
3#34181C211yesmaximal, characteristic, complemented
4#22493C214yesmaximal, complemented
5#22491C214yesmaximal, complemented
6#22421C214yesmaximal, complemented
7#22419C214yesmaximal, complemented
8#21887C212yesmaximal, complemented
9#21763C212yesmaximal, complemented
10#21759C211yesmaximal, characteristic, complemented
11#21758C211yesmaximal, characteristic, complemented
12#21406C212yesmaximal, complemented
13#20971C212yesmaximal, complemented
14C2×#1893C211yesmaximal, characteristic, complemented
15C2×#1892C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic, complemented
17C24×C8C2211yescharacteristic
18#3505—28no—
19#3505C4116yescomplemented
20C2×#553—22no—
21C2×#553C2212yes—
22C2×#552C2212yes—
23C2×#551—22no—
24C2×#548C2212yes—
25C2×#546C2212yes—
26C2×#539—21no—
27C2×#538—21no—
28C2×#534—21no—
29C2×#529C2212yes—
30C2×#525C2212yes—
31C22×C22⋊Q8C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C2×#518—21no—
34C2×#518—21no—
35C22×C4×D4C2211yescharacteristic
36C2×#435—28no—
37C2×#435C2214yes—
38C2×#435C2214yescomplemented
39C22×C4⋊C8C2211yescharacteristic, complemented
40C2×#417C2214yescomplemented
41C22×#103C2212yescomplemented
42C22×#102C2212yescomplemented
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic, complemented
45C22×#97C2211yescharacteristic, complemented
46#2349—22no—
47#2349—22no—
48D4×C4⋊C4C2214yes—
49D4×C4⋊C4C2214yescomplemented
50#2316—21no—
51#2315—21no—
52#2315—21no—
53#2285C2212yescomplemented
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2212yescomplemented
57#1992C2214yescomplemented
58#1989C2214yescomplemented
59#1983C2214yescomplemented
60#1959C2214yescomplemented
61#1895C2214yescomplemented
62#1894C2214yescomplemented
63#1893C2212yes—
64#1893C2212yes—
65#1893C2212yes—
66#1893C2212yes—
67#1893C2214yescomplemented
68#1892C2212yescomplemented
69#1892C2212yescomplemented
70#1892C2212yescomplemented
71#1892C2214yescomplemented
72#1892C2212yescomplemented
73#1874C2214yescomplemented
74#1874C2214yescomplemented
75#1872C2214yescomplemented
76#1872C2214yescomplemented
77#1825C2214yescomplemented
78#1824C2212yescomplemented
79#1823C2212yescomplemented
80#1803C2214yescomplemented
81#1802C2214yescomplemented
82#1788C2214yescomplemented
83#1787C2212yescomplemented
84#1786C2212yescomplemented
85#1763C2214yescomplemented
86#1762C2214yescomplemented
87#1736C2214yescomplemented
88C2×#340C2212yescomplemented
89C2×#340C2212yescomplemented
90C22×#41C2312yes—
91C23×Q8C2311yescharacteristic
92C23×D4—21no—
93C23×D4D411yescharacteristic
94C23×D4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C22×M16—24no—
98C22×M16—44no—
99C22×M16C2314yes—
100C23×C8—24no—
101C23×C8—44no—
102C23×C8C2311yescharacteristic
103C23×C8C2312yes—
104C23×C8C2312yes—
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108#553—232no—
109#553—28no—
110#553C2×C4116yescomplemented
111#552—28no—
112#552C2×C4116yescomplemented
113#551—232no—
114#548—28no—
115#548C2×C4116yescomplemented
116#546—28no—
117#546C2×C4116yescomplemented
118#539—216no—
119#538—216no—
120#534—216no—
121#529—28no—
122#529C2×C4116yescomplemented
123C2×#126—22no—
124C2×#126—22no—
125C2×#126—22no—
126C2×#125—22no—
127C2×#125C2312yes—
128C2×#124—22no—
129C2×#124C2312yes—
130#525—28no—
131#525C2×C4116yescomplemented
132C2×#123—22no—
133C2×#123—22no—
134C2×#123—22no—
135C2×#123—22no—
136C2×#123—22no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—24no—
140C2×C22⋊Q8—22no—
141C2×C22⋊Q8C2×C418yescomplemented
142C2×C22⋊Q8C2312yes—
143C2×C22⋊Q8C2312yes—
144C2×C22⋊Q8C2312yes—
145C2×#121—22no—
146C2×#121—22no—
147C2×#121—21no—
148C2×#121—21no—
149C2×#121—24no—
150C2×#121—22no—
151C2×#121C2×C418yescomplemented
152C2×#121C2312yes—
153C2×#121C2312yes—
154C2×#121C2312yes—
155C2×#120—22no—
156C2×#120—22no—
157#518—216no—
158#518—48no—
159C2×C4×Q8C2312yes—
160C2×C4×D4—22no—
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C2×C4×D4—22no—
166C2×C4×D4—22no—
167C2×C4×D4C2×C418yes—
168C2×C4×D4D418yes—
169C2×C4×D4D412yes—
170C2×C4×D4D412yes—
171C2×C4×D4C2312yes—
172C2×C4×D4C2312yes—
173C2×C4×D4C2312yes—
174C2×#117—22no—
175C2×#117—22no—
176C2×#117—22no—
177C2×#117C2312yes—
178C22×C4⋊C4—21no—
179C22×C4⋊C4D411yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2314yes—
184C22×C4⋊C4C2312yes—
185C22×C22⋊C4—21no—
186C22×C22⋊C4—21no—
187C22×C22⋊C4—22no—
188C22×C22⋊C4—21no—
189C22×C22⋊C4—21no—
190C22×C22⋊C4—22no—
191C22×C22⋊C4D411yescharacteristic
192C22×C22⋊C4D411yescharacteristic
193C22×C42C2311yescharacteristic
194#435—216no—
195#435—216no—
196C2×C4⋊C8—24no—
197C2×C4⋊C8C2314yes—
198#417—48no—
199C2×#103—44no—
200C2×#103C2314yes—
201C2×#103C2314yes—
202C2×#103C2314yes—
203C2×#103C2314yes—
204C2×#102—44no—
205C2×#102C2314yes—
206C2×#102C2314yes—
207C2×#102C2314yes—
208C2×#102C2314yes—
209C2×C22⋊C8—24no—
210C2×C22⋊C8—24no—
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2314yes—
214C2×#97—24no—
215C2×#97C2314yes—
216#389—24no—
217#389—24no—
218#385—24no—
219#385—24no—
220#385—24no—
221#385—24no—
222#384C2314yes—
223#382—22no—
224#380—22no—
225#380—21no—
226#380—21no—
227#380—22no—
228#380—21no—
229#380—21no—
230#380—22no—
231#380C2312yes—
232#380C2312yes—
233#380C2314yes—
234#380C2312yes—
235#380C2312yes—
236C4×C4⋊C4—22no—
237C4×C4⋊C4C2314yes—
238C2×#95—21no—
239C2×#95—21no—
240C2×#95—22no—
241#340C2314yes—
242#340C2314yes—
243#340C2314yes—
244#340C2314yes—
245#340C2314yes—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249C25—21no—
250C25C2×D411yescharacteristic
251C25C2×D411yescharacteristic
252C2×#41—24no—
253C2×#41—44no—
254C2×#41—44no—
255C2×#41C22×C418yes—
256C22×Q8—21no—
257C22×Q8—22no—
258C22×Q8—42no—
259C22×Q8—42no—
260C22×Q8C22×C414yes—
261C22×Q8C2412yes—
262C22×D4—24no—
263C22×D4—24no—
264C22×D4—28no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—42no—
272C22×D4—42no—
273C22×D4—44no—
274C22×D4—44no—
275C22×D4C22⋊C418yes—
276C22×D4C22×C414yes—
277C22×D4C2×D412yes—
278C22×D4C2×D412yes—
279C22×D4C2412yes—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—24no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4C22×C414yes—
293C23×C4C22×C414yes—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D412yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C2×M16—28no—
308C2×M16—28no—
309C2×M16—44no—
310C2×M16—416no—
311C22×C8—22no—
312C22×C8—24no—
313C22×C8—22no—
314C22×C8—24no—
315C22×C8—24no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—24no—
319C22×C8—24no—
320C22×C8—42no—
321C22×C8—42no—
322C22×C8—42no—
323C22×C8—42no—
324C22×C8—42no—
325C22×C8—416no—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330#126—216no—
331#126—216no—
332#126—216no—
333#125—216no—
334#125—24no—
335#125C22×C418yes—
336#124—216no—
337#124—24no—
338#124C22×C418yes—
339#123—216no—
340#123—216no—
341#123—216no—
342#123—216no—
343#123—216no—
344C22⋊Q8—28no—
345C22⋊Q8—28no—
346C22⋊Q8—24no—
347C22⋊Q8—24no—
348C22⋊Q8—24no—
349C22⋊Q8—216no—
350C22⋊Q8C22×C418yes—
351C22⋊Q8C22×C418yes—
352C22⋊Q8C22×C418yes—
353#121—216no—
354#121—216no—
355#121—28no—
356#121—28no—
357#121—24no—
358#121—24no—
359#121—24no—
360#121—216no—
361#121C22×C418yes—
362#121C22×C418yes—
363#121C22×C418yes—
364#120—216no—
365#120—216no—
366C4×Q8—24no—
367C4×Q8C22×C418yes—
368C4×D4—216no—
369C4×D4—216no—
370C4×D4—216no—
371C4×D4—216no—
372C4×D4—216no—
373C4×D4—24no—
374C4×D4—416no—
375C4×D4—416no—
376C4×D4C22⋊C4116yes—
377C4×D4C22⋊C4116yes—
378C4×D4C22×C418yes—
379C4×D4C22×C418yes—
380C4×D4C22×C418yes—
381C4×D4C2×D418yes—
382C4×D4C2×D418yes—
383#117—24no—
384#117—216no—
385#117—216no—
386#117—48no—
387#117C22×C418yes—
388C2×C4⋊C4—28no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4C22⋊C418yes—
411C2×C4⋊C4C22×C414yes—
412C2×C4⋊C4C22×C414yes—
413C2×C4⋊C4C2×D412yes—
414C2×C4⋊C4C2×D412yes—
415C2×C4⋊C4C2414yes—
416C2×C4⋊C4C2414yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—216no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—48no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4C22⋊C418yes—
441C2×C22⋊C4C22⋊C418yes—
442C2×C22⋊C4C2×D412yes—
443C2×C22⋊C4C2×D412yes—
444C2×C22⋊C4C2×D412yes—
445C2×C22⋊C4C2×D412yes—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—24no—
449C2×C42C22×C414yes—
450C2×C42C2×D412yes—
451C2×C42C2×D414yes—
452C2×C42C2412yes—
453C4⋊C8—28no—
454#103—28no—
455#103—44no—
456#103—44no—
457#103—44no—
458#102—28no—
459#102—44no—
460#102—44no—
461#102—44no—
462C22⋊C8—28no—
463C22⋊C8—24no—
464C22⋊C8—24no—
465#97—28no—
466#95—22no—
467#95—22no—
468#95—24no—
469#95—22no—
470#95—22no—
471#95—24no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—24no—
476C24—42no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24—42no—
481C24—42no—
482C24—82no—
483C24—82no—
484C24C2×C22⋊C414yes—
485C24C2×C22⋊C414yes—
486C24AGL(1,ℤ/8)14yes—
487C24#13714yes—
488C24C22×D412yes—
489C24C22×D411yescharacteristic
490C24C22×D411yescharacteristic
491C24C22×D411yescharacteristic
492#41—416no—
493#41—84no—
494#41—84no—
495C2×Q8—24no—
496C2×Q8—22no—
497C2×Q8—24no—
498C2×Q8—24no—
499C2×Q8—48no—
500C2×Q8—82no—
501C2×Q8—82no—
502C2×Q8—82no—
503C2×Q8C23×C414yes—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—232no—
509C2×D4—28no—
510C2×D4—28no—
511C2×D4—28no—
512C2×D4—28no—
513C2×D4—24no—
514C2×D4—22no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—48no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—432no—
523C2×D4—82no—
524C2×D4—82no—
525C2×D4—82no—
526C2×D4—84no—
527C2×D4—84no—
528C2×D4C2×C22⋊C418yes—
529C2×D4C2×C22⋊C418yes—
530C2×D4C23×C414yes—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—42no—
558C22×C4—44no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—84no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—84no—
578C22×C4C2×C22⋊C414yes—
579C22×C4C2×C22⋊C414yes—
580C22×C4C2×C22⋊C414yes—
581C22×C4C2×C22⋊C414yes—
582C22×C4C2×C22⋊C414yes—
583C22×C4C2×C22⋊C414yes—
584C22×C4C2×C22⋊C418yes—
585C22×C4C23×C412yes—
586C22×C4C23×C412yes—
587C22×C4C23×C412yes—
588C22×C4C23×C414yes—
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D414yes—
598C22×C4C22×D412yes—
599C22×C4C2511yescharacteristic
600M16—416no—
601C2×C8—28no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—24no—
609C2×C8—22no—
610C2×C8—24no—
611C2×C8—48no—
612C2×C8—48no—
613C2×C8—44no—
614C2×C8—44no—
615C2×C8—44no—
616C2×C8H(5,𝔽2)14yes—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—48no—
632C4⋊C4—84no—
633C4⋊C4—84no—
634C4⋊C4—82no—
635C4⋊C4—82no—
636C4⋊C4C2×C22⋊C418yes—
637C4⋊C4C2×C22⋊C418yes—
638C4⋊C4C23×C414yes—
639C4⋊C4C23×C414yes—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—48no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4C2×C22⋊C418yes—
656C22⋊C4C2×C22⋊C418yes—
657C22⋊C4C2×C22⋊C418yes—
658C22⋊C4C2×C22⋊C418yes—
659C42—28no—
660C42—28no—
661C42—48no—
662C42C2×C22⋊C418yes—
663C42C23×C414yes—
664C42C22×D414yes—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—28no—
676C23—24no—
677C23—44no—
678C23—44no—
679C23—48no—
680C23—48no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—42no—
686C23—42no—
687C23—48no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—164no—
693C23—164no—
694C23#417116yescomplemented
695C23C22×C22⋊C414yes—
696C23C22×C22⋊C412yes—
697C23C22×C22⋊C412yes—
698C23C22×C22⋊C412yes—
699C23C2×AGL(1,ℤ/8)12yes—
700C23C2×AGL(1,ℤ/8)12yes—
701C23C2×AGL(1,ℤ/8)12yes—
702C23C2×#13712yes—
703C23C2×#13712yes—
704C23C2×#13712yes—
705C23C23×D411yescharacteristic
706Q8—28no—
707Q8—42no—
708Q8—42no—
709Q8—84no—
710D4—216no—
711D4—216no—
712D4—28no—
713D4—416no—
714D4—416no—
715D4—42no—
716D4—42no—
717D4—84no—
718D4—88no—
719D4—88no—
720C2×C4—24no—
721C2×C4—28no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—28no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—48no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—48no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—88no—
761C2×C4—88no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—164no—
765C2×C4—164no—
766C2×C4—168no—
767C2×C4C22×C22⋊C414yes—
768C2×C4C22×C22⋊C414yes—
769C2×C4C22×C22⋊C412yes—
770C2×C4C22×C22⋊C414yes—
771C2×C4C22×C22⋊C412yes—
772C2×C4C22×C22⋊C412yes—
773C2×C4C24×C411yescharacteristic
774C2×C4C23×D411yescharacteristic
775C2×C4C2×H(5,𝔽2)12yes—
776C2×C4#58512yes—
777C8—24no—
778C8—42no—
779C8—42no—
780C8—42no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—416no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—88no—
803C22—84no—
804C22—84no—
805C22—168no—
806C22C2×#41714yes—
807C22C2×#41714yes—
808C22C2×#41714yes—
809C22C23×C22⋊C411yescharacteristic
810C22#349612yes—
811C22C22×AGL(1,ℤ/8)11yescharacteristic
812C22C22×#13711yescharacteristic
813C22#358412yes—
814C4—24no—
815C4—24no—
816C4—22no—
817C4—24no—
818C4—22no—
819C4—22no—
820C4—44no—
821C4—44no—
822C4—44no—
823C4—84no—
824C4—84no—
825C4C4×H(5,𝔽2)12yes—
826C4#348411yescharacteristic
827C4#348511yescharacteristic
828C2—24no—
829C2—24no—
830C2—24no—
831C2—44no—
832C2—84no—
833C2#3425611yescharacteristic
834C2C22×#41711yescharacteristic
835C2#6008611yescharacteristic
836C2#6225312yes—
837C2#6225412yes—
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3505C2
LCSG ▷ C2×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. C22×#435C2semidirect
3. #34181C2semidirect
4. #22493C2semidirect
5. #22491C2semidirect
6. #22421C2semidirect
7. #22419C2semidirect
8. #21887C2semidirect
9. #21763C2semidirect
10. #21759C2semidirect
11. #21758C2semidirect
12. #21406C2semidirect
13. #20971C2semidirect
14. C2×#1893C2semidirect
15. C2×#1892C2semidirect
16. C23×M16C22semidirect
19. #3505C4semidirect
38. C2×#435C22semidirect
39. C22×C4⋊C8C22semidirect
40. C2×#417C22semidirect
41. C22×#103C22semidirect
42. C22×#102C22semidirect
44. C22×C22⋊C8C22semidirect
45. C22×#97C22semidirect
49. D4×C4⋊C4C22semidirect
53. #2285C22semidirect
56. C2×#380C22semidirect
57. #1992C22semidirect
58. #1989C22semidirect
59. #1983C22semidirect
60. #1959C22semidirect
61. #1895C22semidirect
62. #1894C22semidirect
67. #1893C22semidirect
68. #1892C22semidirect
69. #1892C22semidirect
70. #1892C22semidirect
71. #1892C22semidirect
72. #1892C22semidirect
73. #1874C22semidirect
74. #1874C22semidirect
75. #1872C22semidirect
76. #1872C22semidirect
77. #1825C22semidirect
78. #1824C22semidirect
79. #1823C22semidirect
80. #1803C22semidirect
81. #1802C22semidirect
82. #1788C22semidirect
83. #1787C22semidirect
84. #1786C22semidirect
85. #1763C22semidirect
86. #1762C22semidirect
87. #1736C22semidirect
88. C2×#340C22semidirect
89. C2×#340C22semidirect
110. #553C2×C4semidirect
112. #552C2×C4semidirect
115. #548C2×C4semidirect
117. #546C2×C4semidirect
122. #529C2×C4semidirect
131. #525C2×C4semidirect
141. C2×C22⋊Q8C2×C4semidirect
151. C2×#121C2×C4semidirect
694. C23#417semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
C22×#4352
#341812
#224932
#224912
#224212
#224192
#218872
#217632
#217592
#217582
#214062
#209712
C2×#18932
C2×#18922