Finite Group Databasebeta

← #636801

Subgroups — #636801

Order 512.

4301 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#126C211yesmaximal, characteristic, complemented
2C2×#2853C211yesmaximal, characteristic, complemented
3C2×#2413C211yesmaximal, characteristic, complemented
4C2×#2411C211yesmaximal, characteristic
5#16659C214yesmaximal, complemented
6#16658C214yesmaximal, complemented
7#15092C211yesmaximal, characteristic, complemented
8#15091C211yesmaximal, characteristic, complemented
9#14931C214yesmaximal, complemented
10#14930C214yesmaximal, complemented
11#14918C211yesmaximal, characteristic, complemented
12#14911C211yesmaximal, characteristic
13#14263C211yesmaximal, characteristic, complemented
14#14262C211yesmaximal, characteristic, complemented
15#14256C211yesmaximal, characteristic, complemented
16#14255C211yesmaximal, characteristic
17#13870C211yesmaximal, characteristic, complemented
18#13868C211yesmaximal, characteristic, complemented
19#13756C211yesmaximal, characteristic, complemented
20C22×#126—28no—
21C22×#126—28no—
22C22×#126—28no—
23C22×#126C2214yes—
24C22×#126C2214yes—
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C42C2211yescharacteristic
37#2853—28no—
38#2413—28no—
39#2411—28no—
40C2×#398C2212yescomplemented
41C2×#396C2212yes—
42C2×#396C2212yescomplemented
43C2×#394C2212yes—
44C2×#390C2212yes—
45C2×#389C2212yescomplemented
46C2×#388C2212yes—
47C2×#388C2212yescomplemented
48C2×#388C2212yescomplemented
49C2×#388C2212yescomplemented
50C2×#387C2212yescomplemented
51C2×#387C2212yescomplemented
52C2×#386C2211yescharacteristic
53C2×#386C2211yescharacteristic
54C2×#386C2211yescharacteristic
55C2×#386C2211yescharacteristic
56C2×#385C2211yescharacteristic
57C2×#385C2211yescharacteristic
58C2×#385C2211yescharacteristic
59C2×#385C2211yescharacteristic
60C2×#381C2211yescharacteristic
61C2×#381C2211yescharacteristic
62C2×#381C2211yescharacteristic
63C2×#381C2211yescharacteristic
64C2×#379C2211yescharacteristic
65C2×#379C2211yescharacteristic
66C2×#379C2211yescharacteristic
67#1444C2214yescomplemented
68#1444C2214yescomplemented
69#1442C2214yescomplemented
70#1442C2214yescomplemented
71#1441C2214yescomplemented
72#1441C2214yescomplemented
73#1441C2214yescomplemented
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yescomplemented
82#1439C2214yescomplemented
83#1438C2214yes—
84#1438C2214yes—
85#1437C2214yes—
86#1436C2214yescomplemented
87C4⋊#95C2214yescomplemented
88C22⋊#95C2211yescharacteristic
89C22⋊#95C2211yescharacteristic
90C22⋊#95C2211yescharacteristic
91C22⋊#95C2211yescharacteristic
92C22⋊#95C2211yescharacteristic
93C22⋊#95C2211yescharacteristic
94C22⋊#95C2211yescharacteristic
95C22⋊#95C2211yescharacteristic
96C4×#95C2214yescomplemented
97C26C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C23×D4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C2×#126—2128no—
107C2×#126—216no—
108C2×#126—216no—
109C2×#126—216no—
110C2×#126—216no—
111C2×#126—216no—
112C2×#126—216no—
113C2×#123—24no—
114C2×#123—24no—
115C2×#123—24no—
116C2×#123—24no—
117C2×#123—24no—
118C2×#123—42no—
119C2×#120—24no—
120C2×#120—24no—
121C2×#120—42no—
122C2×#117—24no—
123C2×#117—24no—
124C2×#117—24no—
125C2×#117—24no—
126C2×#117—42no—
127C2×#117—42no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—24no—
134C22×C4⋊C4—24no—
135C22×C4⋊C4—24no—
136C22×C4⋊C4D418yescomplemented
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C22⋊C4—24no—
151C22×C22⋊C4—24no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4—24no—
157C22×C22⋊C4—24no—
158C22×C22⋊C4D418yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2314yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2314yes—
182C22×C42—24no—
183C22×C42—24no—
184C22×C42D418yescomplemented
185C22×C42C2312yes—
186C22×C42C2312yes—
187C22×C42C2312yes—
188C22×C42C2312yes—
189#398—28no—
190#396—28no—
191#396—28no—
192#394—28no—
193#390—28no—
194#389—28no—
195#388—28no—
196#388—28no—
197#388—28no—
198#388—28no—
199#387—28no—
200#387—28no—
201#386—24no—
202#386—24no—
203#386—24no—
204#386—24no—
205#385—24no—
206#385—24no—
207#385—24no—
208#385—24no—
209#381—24no—
210#381—24no—
211#381—24no—
212#381—42no—
213#379—24no—
214#379—24no—
215#379—42no—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C25—22no—
239C25—22no—
240C25—22no—
241C25—22no—
242C25—22no—
243C25—22no—
244C25—44no—
245C25—44no—
246C25C2×D414yes—
247C25C2411yescharacteristic
248C25C2412yes—
249C25C2411yescharacteristic
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—42no—
260C22×D4—44no—
261C22×D4—44no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4—44no—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308#126—2128no—
309#126—2128no—
310#123—416no—
311#123—416no—
312#120—416no—
313#117—416no—
314#117—416no—
315C2×C4⋊C4—232no—
316C2×C4⋊C4—232no—
317C2×C4⋊C4—232no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4C2×D418yes—
352C2×C4⋊C4C2×D418yes—
353C2×C22⋊C4—232no—
354C2×C22⋊C4—232no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—232no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4C2×D418yes—
416C2×C22⋊C4C2×D418yes—
417C2×C22⋊C4#4114yes—
418C2×C22⋊C4#4114yes—
419C2×C42—232no—
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—42no—
429C2×C42—42no—
430C2×C42C2×D418yes—
431C2×C42C2×D418yes—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—28no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—44no—
449#95—44no—
450#95—44no—
451#95—44no—
452#95—44no—
453#95—44no—
454C24—24no—
455C24—24no—
456C24—28no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—24no—
464C24—24no—
465C24—24no—
466C24—24no—
467C24—28no—
468C24—28no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—24no—
477C24—24no—
478C24—48no—
479C24—48no—
480C24—48no—
481C24—48no—
482C24—48no—
483C24—48no—
484C24—44no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24—88no—
489C24—88no—
490C24—88no—
491C24—88no—
492C24C22×D414yes—
493C24C22×D412yes—
494C24C22×D412yes—
495C24C22×D412yes—
496C24C2×#4112yes—
497C24C2×#4112yes—
498C24H(5,𝔽2)12yes—
499C242−1+412yes—
500C24C2511yescharacteristic
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—88no—
511C2×D4—84no—
512C2×D4—88no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
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—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4#120116yes—
616C22×C4C22×D414yes—
617C22×C4C22×D414yes—
618C22×C4C22×D414yes—
619C22×C4C22×D414yes—
620C22×C4C22×D414yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4114yes—
629C4⋊C4—232no—
630C4⋊C4—232no—
631C4⋊C4—216no—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—84no—
642C22⋊C4—232no—
643C22⋊C4—232no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—216no—
647C22⋊C4—216no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—84no—
662C22⋊C4—88no—
663C22⋊C4—84no—
664C22⋊C4—88no—
665C42—216no—
666C42—216no—
667C42—48no—
668C42—48no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—28no—
676C23—28no—
677C23—28no—
678C23—28no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—416no—
687C23—416no—
688C23—42no—
689C23—42no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—416no—
694C23—42no—
695C23—42no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—42no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—816no—
723C23—816no—
724C23—816no—
725C23—816no—
726C23—816no—
727C23—816no—
728C23C2×#12014yes—
729C23#53214yes—
730C23#53714yes—
731C23#54614yes—
732C23#54614yes—
733C23#54714yes—
734C23#54714yes—
735C23C23×D411yescharacteristic
736C23C23×D411yescharacteristic
737C23C23×D411yescharacteristic
738C23C22×#4111yescharacteristic
739C23C22×#4111yescharacteristic
740C23C2×H(5,𝔽2)11yescharacteristic
741C23C2×2−1+411yescharacteristic
742C23#58514yes—
743C23#58514yes—
744D4—816no—
745D4—88no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—232no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—416no—
779C2×C4—416no—
780C2×C4—416no—
781C2×C4—416no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—416no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4C2×#12014yes—
837C2×C4C2×#12014yes—
838C22—24no—
839C22—28no—
840C22—24no—
841C22—28no—
842C22—28no—
843C22—28no—
844C22—28no—
845C22—28no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—832no—
854C22—84no—
855C22—84no—
856C22—84no—
857C22—84no—
858C22—81no—
859C22—82no—
860C22—81no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—81no—
867C22#243018yes—
868C22C22×#12011yescharacteristic
869C22C2×#53211yescharacteristic
870C22C2×#53711yescharacteristic
871C22#344912yes—
872C22#344912yes—
873C22#344912yes—
874C22#344912yes—
875C22C2×#54611yescharacteristic
876C22C2×#54611yescharacteristic
877C22C2×#54711yescharacteristic
878C22C2×#54711yescharacteristic
879C22#348512yes—
880C22#348712yes—
881C22#352114yes—
882C22#352114yes—
883C22#356014yes—
884C22#356414yes—
885C4—24no—
886C4—24no—
887C4—44no—
888C4—44no—
889C4—44no—
890C4—44no—
891C4—44no—
892C4—44no—
893C4—44no—
894C4—81no—
895C4—82no—
896C4—81no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—81no—
901C2—28no—
902C2—84no—
903C2—161no—
904C2#3463211yescharacteristic
905C2C2×#243011yescharacteristic
906C2#3514512yes—
907C2#3514911yescharacteristic
908C2#3753812yes—
909C2#3803012yes—
910C2#3803112yes—
911C2#3804612yes—
912C2#3804712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×#126C2semidirect
2. C2×#2853C2semidirect
3. C2×#2413C2semidirect
5. #16659C2semidirect
6. #16658C2semidirect
7. #15092C2semidirect
8. #15091C2semidirect
9. #14931C2semidirect
10. #14930C2semidirect
11. #14918C2semidirect
13. #14263C2semidirect
14. #14262C2semidirect
15. #14256C2semidirect
17. #13870C2semidirect
18. #13868C2semidirect
19. #13756C2semidirect
40. C2×#398C22semidirect
42. C2×#396C22semidirect
45. C2×#389C22semidirect
47. C2×#388C22semidirect
48. C2×#388C22semidirect
49. C2×#388C22semidirect
50. C2×#387C22semidirect
51. C2×#387C22semidirect
67. #1444C22semidirect
68. #1444C22semidirect
69. #1442C22semidirect
70. #1442C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
81. #1439C22semidirect
82. #1439C22semidirect
86. #1436C22semidirect
87. C4⋊#95C22semidirect
96. C4×#95C22semidirect
136. C22×C4⋊C4D4semidirect
184. C22×C42D4semidirect

Maximal subgroups

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

subgroupindex
C23×#1262
C2×#28532
C2×#24132
C2×#24112
#166592
#166582
#150922
#150912
#149312
#149302
#149182
#149112
#142632
#142622
#142562
#142552
#138702
#138682
#137562