Finite Group Databasebeta

← #520574

Subgroups — #520574

Order 512.

3526 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2353C212yesmaximal
2C2×C42×D4C211yesmaximal, characteristic
3#14688C211yesmaximal, characteristic, complemented
4#14686C211yesmaximal, characteristic, complemented
5#14685C211yesmaximal, characteristic, complemented
6#13966C212yesmaximal, complemented
7#13964C212yesmaximal, complemented
8#13960C212yesmaximal
9#13953C212yesmaximal, complemented
10#13949C212yesmaximal, complemented
11#13948C212yesmaximal, complemented
12#13884C212yesmaximal, complemented
13#13876C212yesmaximal, complemented
14#13872C212yesmaximal
15#13802C212yesmaximal, complemented
16C22⋊C4×C4⋊C4C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18#13755C211yesmaximal, characteristic, complemented
19C2×C4⋊#95C211yesmaximal, characteristic, complemented
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C23×C4⋊C4C2212yes—
24C23×C42C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2353—216no—
27C2×#388C2214yes—
28C2×#387C2214yes—
29C2×#386C2214yes—
30C2×#384C2212yes—
31C2×#383C2212yes—
32C2×#381C2212yes—
33C2×#380C2212yes—
34C2×#380C2212yes—
35C2×#380C2212yes—
36C2×#380C2212yes—
37C2×#380C2212yes—
38C42×D4C4116yescomplemented
39C2×C4×C4⋊C4C2212yes—
40C2×C4×C4⋊C4C2212yes—
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2212yes—
45C2×C4×C22⋊C4C2214yes—
46C2×C4×C22⋊C4C2211yescharacteristic
47C2×C4×C22⋊C4C2211yescharacteristic
48C2×C4×C22⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2211yescharacteristic
52C2×#376C2212yes—
53C22×#95C2212yes—
54C22×#95C2212yes—
55C2×C43C2211yescharacteristic
56#1442C2214yes—
57#1442C2214yes—
58#1441C2214yes—
59#1441C2214yes—
60#1439C2214yes—
61#1439C2214yes—
62#1436C2214yes—
63#1436C2214yes—
64#1436C2214yes—
65#1436C2214yes—
66C4⋊#95C2212yes—
67C4⋊#95C2212yes—
68C4⋊#95C2212yes—
69C4⋊#95C2212yes—
70C4⋊#95C2212yes—
71C4⋊#95C2211yescharacteristic
72C4⋊#95C2211yescharacteristic
73C4⋊#95C2211yescharacteristic
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2211yescharacteristic
79#1434C2212yes—
80#1434C2212yes—
81#1434C2212yes—
82#1434C2212yes—
83#1434C2212yes—
84#1434C2212yes—
85#1434C2212yes—
86#1434C2212yes—
87C22⋊#95C2214yes—
88C22⋊#95C2212yes—
89C22⋊#95C2212yes—
90C22⋊#95C2214yes—
91C4×#95C2212yes—
92C4×#95C2212yes—
93C23×D4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2314yes—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C2×C4×D4—24no—
102C2×C4×D4—24no—
103C2×C4×D4—24no—
104C2×C4×D4—24no—
105C2×C4×D4C2×C418yes—
106C2×C4×D4C2×C418yes—
107C2×C4×D4C2×C418yes—
108C2×C4×D4D418yes—
109C2×C4×D4Q818yes—
110C22×C4⋊C4—28no—
111C22×C4⋊C4—28no—
112C22×C4⋊C4—44no—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2311yescharacteristic
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2311yescharacteristic
132C22×C42—44no—
133C22×C42—44no—
134C22×C42C2×C418yes—
135C22×C42C2×C418yescomplemented
136C22×C42C2314yes—
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2314yes—
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#388—216no—
152#387—216no—
153#386—216no—
154#384—44no—
155#383—28no—
156#381—28no—
157#380—28no—
158#380—28no—
159#380—28no—
160#380—28no—
161#380—44no—
162C4×C4⋊C4—28no—
163C4×C4⋊C4—44no—
164C4×C4⋊C4C2×C418yescomplemented
165C4×C4⋊C4C2×C418yescomplemented
166C4×C4⋊C4C2×C418yescomplemented
167C4×C22⋊C4—28no—
168C4×C22⋊C4—216no—
169C4×C22⋊C4C2×C418yes—
170C4×C22⋊C4C2×C418yes—
171C4×C22⋊C4C2×C418yes—
172C4×C22⋊C4C2×C418yescomplemented
173C4×C22⋊C4C2×C418yescomplemented
174C4×C22⋊C4C2×C418yescomplemented
175#376—28no—
176C2×#95—28no—
177C2×#95—28no—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207C43C2×C418yescomplemented
208C25C2411yescharacteristic
209C25C2411yescharacteristic
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4C22×C414yes—
215C22×D4C2×D414yes—
216C22×D4C2×Q814yes—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—28no—
226C23×C4—28no—
227C23×C4—28no—
228C23×C4—28no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—44no—
238C23×C4—44no—
239C23×C4—44no—
240C23×C4C22×C414yes—
241C23×C4C22×C414yes—
242C23×C4C22×C414yes—
243C23×C4C22×C414yes—
244C23×C4C22×C414yes—
245C23×C4C22×C414yes—
246C23×C4C2×D414yes—
247C23×C4C2×D414yes—
248C23×C4C2×Q814yes—
249C23×C4C2×Q814yes—
250C23×C4#4114yes—
251C23×C4#4114yes—
252C23×C4#4114yes—
253C23×C4#4114yes—
254C23×C4C2414yes—
255C23×C4C2414yes—
256C23×C4C2414yes—
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2414yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C4×D4—232no—
272C4×D4—232no—
273C4×D4C4⋊C4164yescomplemented
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—432no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4C22×C414yes—
300C2×C4⋊C4C22×C414yes—
301C2×C4⋊C4C22×C414yes—
302C2×C4⋊C4C2×D414yes—
303C2×C4⋊C4C2×Q814yes—
304C2×C4⋊C4#4118yes—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4C22×C414yes—
323C2×C22⋊C4C22×C414yes—
324C2×C22⋊C4C22×C414yes—
325C2×C22⋊C4C22×C414yes—
326C2×C22⋊C4C22×C414yes—
327C2×C22⋊C4C22×C414yes—
328C2×C22⋊C4C2×D414yes—
329C2×C22⋊C4C2×D414yes—
330C2×C22⋊C4C2×Q814yes—
331C2×C22⋊C4C2×Q814yes—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—28no—
341C2×C42—28no—
342C2×C42—28no—
343C2×C42—416no—
344C2×C42—416no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42—42no—
348C2×C42—42no—
349C2×C42—42no—
350C2×C42—42no—
351C2×C42—44no—
352C2×C42—44no—
353C2×C42—44no—
354C2×C42C22×C414yes—
355C2×C42C22×C414yes—
356C2×C42C22×C414yes—
357C2×C42C22×C414yes—
358C2×C42C22×C414yes—
359C2×C42C22×C414yes—
360C2×C42C22×C414yes—
361C2×C42C22×C414yes—
362C2×C42C22×C414yes—
363C2×C42C22×C414yes—
364C2×C42C22×C414yes—
365C2×C42C22×C414yes—
366C2×C42C22×C414yes—
367C2×C42C2×D414yes—
368C2×C42C2×Q814yes—
369#95—24no—
370#95—24no—
371#95—28no—
372#95—24no—
373#95—28no—
374#95—24no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—24no—
379#95—28no—
380#95—24no—
381#95—28no—
382#95—28no—
383#95—24no—
384#95—24no—
385#95—28no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95C22×C414yes—
393#95C22×C414yes—
394#95C22×C414yes—
395#95C22×C414yes—
396#95C22×C414yes—
397#95C22×C414yes—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24C23×C412yes—
411C24C23×C412yes—
412C24C22×D412yes—
413C24C22×D412yes—
414C24C22×Q812yes—
415C24C22×Q812yes—
416C24C2×#4112yes—
417C24C2×#4112yes—
418C24C2×#4112yes—
419C24C2×#4112yes—
420C24C2511yescharacteristic
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—28no—
427C2×D4C2×C4⋊C4116yes—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—216no—
449C22×C4—216no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—416no—
514C22×C4—416no—
515C22×C4—416no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—416no—
519C22×C4—88no—
520C22×C4—88no—
521C22×C4—88no—
522C22×C4C2×C4⋊C4116yes—
523C22×C4C2×C4⋊C4116yescomplemented
524C22×C4#117116yes—
525C22×C4#117116yes—
526C22×C4C23×C412yes—
527C22×C4C23×C412yes—
528C22×C4C23×C412yes—
529C22×C4C23×C412yes—
530C22×C4C23×C412yes—
531C22×C4C23×C412yes—
532C22×C4C23×C412yes—
533C22×C4C23×C412yes—
534C22×C4C23×C412yes—
535C22×C4C23×C412yes—
536C22×C4C23×C412yes—
537C22×C4C23×C412yes—
538C22×C4C23×C412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×Q812yes—
545C22×C4C22×Q812yes—
546C22×C4C22×Q812yes—
547C22×C4C22×Q812yes—
548C22×C4C22×Q812yes—
549C22×C4C2×#4118yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4114yes—
559C22×C4H(5,𝔽2)14yes—
560C4⋊C4—28no—
561C4⋊C4—28no—
562C4⋊C4—216no—
563C4⋊C4—416no—
564C4⋊C4—48no—
565C4⋊C4—48no—
566C4⋊C4—48no—
567C4⋊C4—88no—
568C4⋊C4—88no—
569C4⋊C4C2×C4⋊C4116yescomplemented
570C22⋊C4—28no—
571C22⋊C4—28no—
572C22⋊C4—28no—
573C22⋊C4—28no—
574C22⋊C4—416no—
575C22⋊C4—416no—
576C22⋊C4—88no—
577C22⋊C4C2×C4⋊C4116yes—
578C22⋊C4C2×C4⋊C4116yescomplemented
579C42—28no—
580C42—28no—
581C42—28no—
582C42—28no—
583C42—28no—
584C42—28no—
585C42—44no—
586C42—44no—
587C42—44no—
588C42—44no—
589C42—44no—
590C42—44no—
591C42—416no—
592C42—88no—
593C42C2×C4⋊C4116yescomplemented
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23C22×C4⋊C414yes—
633C23C22×C4⋊C414yes—
634C23C2×#11714yes—
635C23C2×#11714yes—
636C23#53214yes—
637C23#53214yes—
638C23#53314yes—
639C23#53314yes—
640C23C24×C411yescharacteristic
641C23C23×D411yescharacteristic
642C23C23×Q811yescharacteristic
643C23C22×#4111yescharacteristic
644C23C22×#4111yescharacteristic
645C23C22×#4111yescharacteristic
646C23C22×#4111yescharacteristic
647C23C22×#4112yes—
648C23C2×H(5,𝔽2)12yes—
649C23#58512yes—
650C23#58512yes—
651D4—232no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—232no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—416no—
704C2×C4—416no—
705C2×C4—416no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—416no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—832no—
741C2×C4C22×C4⋊C414yes—
742C2×C4C22×C4⋊C414yes—
743C2×C4C22×C4⋊C414yes—
744C2×C4C22×C4⋊C414yes—
745C2×C4C22×C4⋊C414yes—
746C2×C4C2×#11714yes—
747C2×C4C2×#11714yes—
748C2×C4C2×#11714yes—
749C2×C4C2×#11714yes—
750C2×C4C4×#4114yes—
751C2×C4#51814yes—
752C2×C4#55118yes—
753C2×C4#55318yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—28no—
761C22—28no—
762C22—28no—
763C22—28no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22#228518yes—
776C22C23×C4⋊C411yescharacteristic
777C22C22×#11711yescharacteristic
778C22C22×#11711yescharacteristic
779C22C2×C4×#4111yescharacteristic
780C22C2×#51811yescharacteristic
781C22#342811yescharacteristic
782C22#342811yescharacteristic
783C22C2×#53211yescharacteristic
784C22C2×#53211yescharacteristic
785C22C2×#53311yescharacteristic
786C22C2×#53311yescharacteristic
787C22D4×#4112yes—
788C22C2×#55112yes—
789C22C2×#55312yes—
790C22#347512yes—
791C22Q8×#4112yes—
792C22#348012yes—
793C22#349612yes—
794C22#350112yes—
795C22#350512yes—
796C22#350512yes—
797C22#351012yes—
798C22#351212yes—
799C4—24no—
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—48no—
812C4—84no—
813C4—84no—
814C4—84no—
815C4#235318yescomplemented
816C2—28no—
817C2—44no—
818C2C2×#228511yescharacteristic
819C2C4⋊C4×#4111yescharacteristic
820C2C2×#235311yescharacteristic
821C2#3412111yescharacteristic
822C2#3418111yescharacteristic
823C2#3418511yescharacteristic
824C2#3418911yescharacteristic
825C2#3626212yes—
826C2#3626312yes—
827C2#3627712yes—
828C2#3627812yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #14688C2semidirect
4. #14686C2semidirect
5. #14685C2semidirect
6. #13966C2semidirect
7. #13964C2semidirect
9. #13953C2semidirect
10. #13949C2semidirect
11. #13948C2semidirect
12. #13884C2semidirect
13. #13876C2semidirect
15. #13802C2semidirect
16. C22⋊C4×C4⋊C4C2semidirect
17. C4×#380C2semidirect
18. #13755C2semidirect
19. C2×C4⋊#95C2semidirect
38. C42×D4C4semidirect
135. C22×C42C2×C4semidirect
164. C4×C4⋊C4C2×C4semidirect
165. C4×C4⋊C4C2×C4semidirect
166. C4×C4⋊C4C2×C4semidirect
172. C4×C22⋊C4C2×C4semidirect
173. C4×C22⋊C4C2×C4semidirect
174. C4×C22⋊C4C2×C4semidirect
207. C43C2×C4semidirect
273. C4×D4C4⋊C4semidirect
523. C22×C4C2×C4⋊C4semidirect
569. C4⋊C4C2×C4⋊C4semidirect
578. C22⋊C4C2×C4⋊C4semidirect
593. C42C2×C4⋊C4semidirect
815. C4#2353semidirect

Maximal subgroups

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

subgroupindex
C2×#23532
C2×C42×D42
#146882
#146862
#146852
#139662
#139642
#139602
#139532
#139492
#139482
#138842
#138762
#138722
#138022
C22⋊C4×C4⋊C42
C4×#3802
#137552
C2×C4⋊#952