Finite Group Databasebeta

← #519265

Subgroups — #519265

Order 512.

5970 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#548C211yesmaximal, characteristic
2C2×#2352C211yesmaximal, characteristic, complemented
3C2×#2297C211yesmaximal, characteristic, complemented
4C22×#391C211yesmaximal, characteristic, complemented
5C2×C42×D4C211yesmaximal, characteristic, complemented
6#14708C211yesmaximal, characteristic, complemented
7#14702C211yesmaximal, characteristic, complemented
8#14698C211yesmaximal, characteristic, complemented
9#14153C211yesmaximal, characteristic, complemented
10#14138C211yesmaximal, characteristic, complemented
11#14137C211yesmaximal, characteristic, complemented
12#14099C214yesmaximal, complemented
13#14098C214yesmaximal, complemented
14#14023C214yesmaximal, complemented
15#13942C211yesmaximal, characteristic, complemented
16#13937C211yesmaximal, characteristic, complemented
17#13922C211yesmaximal, characteristic, complemented
18#13813C214yesmaximal, complemented
19C4×#391C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C24×Q8C2211yescharacteristic
22C2×#548—28no—
23C2×#548—28no—
24C2×#548C4116yescomplemented
25C22×#124C2212yes—
26C22×#124C2211yescharacteristic
27C22×C22⋊Q8C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×#121C2212yes—
30C22×#121C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×D4C2212yes—
33C22×C4×D4C2212yes—
34C22×C4×D4C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37C23×C42C2211yescharacteristic
38C23×C42C2211yescharacteristic
39#2352—28no—
40#2297—28no—
41C2×#391—28no—
42C2×#391C2214yes—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#388C2212yes—
56C2×#387C2212yes—
57C2×#386C2214yes—
58C2×#386C2214yes—
59C2×#386C2212yes—
60C2×#386C2214yes—
61C2×#382C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C42×D4—28no—
65C2×C4×C4⋊C4C2212yes—
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2212yes—
69C2×C4×C22⋊C4C2214yes—
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2212yes—
73C2×C4×C22⋊C4C2212yes—
74C22×#95C2214yes—
75C2×C43C2211yescharacteristic
76#1446C2214yes—
77#1441C2214yes—
78#1440C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2214yes—
82#1437C2214yes—
83#1437C2214yes—
84#1437C2214yes—
85#1437C2214yes—
86#1436C2214yes—
87#1436C2214yes—
88#1436C2214yes—
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93#1434C2214yes—
94C22⋊#95C2214yes—
95C22⋊#95C2214yes—
96C22⋊#95C2214yes—
97C4×#95C2214yes—
98C22×#41—24no—
99C22×#41—24no—
100C22×#41—24no—
101C22×#41—24no—
102C22×#41—42no—
103C22×#41—42no—
104C22×#41C2×C418yescomplemented
105C23×Q8—24no—
106C23×Q8—24no—
107C23×Q8—24no—
108C23×Q8—24no—
109C23×Q8—42no—
110C23×Q8—42no—
111C23×Q8C2×C418yescomplemented
112C23×Q8C2311yescharacteristic
113C23×Q8C2312yes—
114C23×Q8C2311yescharacteristic
115C23×D4C2311yescharacteristic
116C23×D4C2312yes—
117C23×D4C2312yes—
118C23×D4C2311yescharacteristic
119C24×C4C2312yes—
120C24×C4C2312yes—
121C24×C4C2312yes—
122C24×C4C2312yes—
123C24×C4C2312yes—
124C24×C4C2311yescharacteristic
125C24×C4C2311yescharacteristic
126#548—2128no—
127C2×#124—28no—
128C2×#124—28no—
129C2×#124—24no—
130C2×#124—24no—
131C2×#124C2×C4116yescomplemented
132C2×#124C2×C418yescomplemented
133C2×C22⋊Q8—24no—
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—28no—
136C2×C22⋊Q8—28no—
137C2×C22⋊Q8C2×C418yescomplemented
138C2×C22⋊Q8C2×C4116yescomplemented
139C2×#121—28no—
140C2×#121—28no—
141C2×#121—24no—
142C2×#121—24no—
143C2×#121C2×C4116yes—
144C2×#121C2×C418yescomplemented
145C2×C4×Q8—24no—
146C2×C4×Q8—24no—
147C2×C4×Q8C2×C418yescomplemented
148C2×C4×D4—28no—
149C2×C4×D4—28no—
150C2×C4×D4—28no—
151C2×C4×D4—28no—
152C2×C4×D4—28no—
153C2×C4×D4C2×C418yes—
154C2×C4×D4C2×C4116yescomplemented
155C2×C4×D4D418yes—
156C2×C4×D4D418yes—
157C2×#117—24no—
158C2×#117—24no—
159C2×#117—42no—
160C22×C4⋊C4—24no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—42no—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2314yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2314yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2314yes—
185C22×C22⋊C4C2314yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C42—24no—
189C22×C42—24no—
190C22×C42—24no—
191C22×C42—24no—
192C22×C42—42no—
193C22×C42—42no—
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196C22×C42C2312yes—
197C22×C42C2311yescharacteristic
198C22×C42C2312yes—
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2312yes—
203C22×C42C2311yescharacteristic
204C22×C42C2312yes—
205C22×C42C2311yescharacteristic
206#391—24no—
207#391—24no—
208#391—24no—
209#391—24no—
210#391—24no—
211#391—216no—
212#391—42no—
213#391—42no—
214#391D418yescomplemented
215#390—24no—
216#390—24no—
217#390—42no—
218#390—42no—
219#388—28no—
220#387—28no—
221#386—28no—
222#386—216no—
223#386—216no—
224#386—216no—
225#382—24no—
226#380—24no—
227#380—24no—
228C4×C4⋊C4—28no—
229C4×C4⋊C4—24no—
230C4×C4⋊C4—24no—
231C4×C22⋊C4—24no—
232C4×C22⋊C4—24no—
233C4×C22⋊C4—28no—
234C4×C22⋊C4—28no—
235C4×C22⋊C4—28no—
236C4×C22⋊C4—216no—
237C2×#95—216no—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2314yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2314yes—
244C2×#95C2314yes—
245C2×#95C2314yes—
246C2×#95C2314yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2314yes—
250C2×#95C2312yes—
251C2×#95C2314yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2314yes—
256C2×#95C2314yes—
257C2×#95C2314yes—
258C43—24no—
259C25C2412yes—
260C25C2411yescharacteristic
261C25C2411yescharacteristic
262C2×#41—232no—
263C2×#41—232no—
264C2×#41—416no—
265C2×#41—416no—
266C2×#41—416no—
267C2×#41—416no—
268C2×#41—416no—
269C22×Q8—232no—
270C22×Q8—232no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—24no—
274C22×Q8—24no—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—24no—
278C22×Q8—22no—
279C22×Q8—24no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8—22no—
285C22×Q8—42no—
286C22×Q8—42no—
287C22×Q8—416no—
288C22×Q8—416no—
289C22×Q8—416no—
290C22×Q8—416no—
291C22×Q8—416no—
292C22×Q8C22×C414yes—
293C22×Q8C22×C418yes—
294C22×Q8C22×C414yes—
295C22×Q8C2×D414yes—
296C22×Q8#4114yes—
297C22×D4—24no—
298C22×D4—24no—
299C22×D4—24no—
300C22×D4—24no—
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—28no—
304C22×D4—28no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—24no—
308C22×D4—22no—
309C22×D4—24no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—42no—
314C22×D4—42no—
315C22×D4C22×C418yes—
316C22×D4C22×C414yes—
317C22×D4C22×C418yes—
318C22×D4C22×C414yes—
319C22×D4C2×D414yes—
320C22×D4C2×D414yes—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—24no—
330C23×C4—24no—
331C23×C4—24no—
332C23×C4—24no—
333C23×C4—24no—
334C23×C4—24no—
335C23×C4—24no—
336C23×C4—24no—
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—24no—
340C23×C4—24no—
341C23×C4—24no—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—24no—
345C23×C4—28no—
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—42no—
350C23×C4—42no—
351C23×C4—42no—
352C23×C4—42no—
353C23×C4—42no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4—42no—
357C23×C4—42no—
358C23×C4—44no—
359C23×C4C22×C418yes—
360C23×C4C22×C418yes—
361C23×C4C22×C414yes—
362C23×C4C22×C414yes—
363C23×C4C2×D414yes—
364C23×C4C2×D414yes—
365C23×C4C2×D414yes—
366C23×C4C2×D414yes—
367C23×C4#4118yescomplemented
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2411yescharacteristic
384#124—264no—
385#124—232no—
386C22⋊Q8—232no—
387C22⋊Q8—264no—
388#121—264no—
389#121—232no—
390C4×Q8—232no—
391C4×D4—264no—
392C4×D4—264no—
393C4×D4C22⋊C4164yescomplemented
394#117—416no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—416no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4C22×C418yes—
420C2×C4⋊C4C22×C418yes—
421C2×C4⋊C4C22×C414yes—
422C2×C4⋊C4C22×C414yes—
423C2×C4⋊C4C2×D414yes—
424C2×C4⋊C4C2×D414yes—
425C2×C4⋊C4C2×D414yes—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—28no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—28no—
444C2×C22⋊C4—28no—
445C2×C22⋊C4—28no—
446C2×C22⋊C4—28no—
447C2×C22⋊C4—28no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—28no—
450C2×C22⋊C4—28no—
451C2×C22⋊C4—44no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—44no—
454C2×C22⋊C4—44no—
455C2×C22⋊C4—44no—
456C2×C22⋊C4—44no—
457C2×C22⋊C4—44no—
458C2×C22⋊C4C22×C418yes—
459C2×C22⋊C4C22×C418yes—
460C2×C22⋊C4C22×C418yes—
461C2×C22⋊C4C22×C418yes—
462C2×C22⋊C4C22×C414yes—
463C2×C22⋊C4C22×C414yes—
464C2×C22⋊C4C2×D414yes—
465C2×C22⋊C4C2×D414yes—
466C2×C22⋊C4C2×D414yes—
467C2×C22⋊C4C2×D414yes—
468C2×C22⋊C4#4118yescomplemented
469C2×C42—24no—
470C2×C42—24no—
471C2×C42—24no—
472C2×C42—22no—
473C2×C42—24no—
474C2×C42—24no—
475C2×C42—22no—
476C2×C42—24no—
477C2×C42—24no—
478C2×C42—24no—
479C2×C42—22no—
480C2×C42—24no—
481C2×C42—24no—
482C2×C42—24no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—24no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—24no—
493C2×C42—24no—
494C2×C42—416no—
495C2×C42—416no—
496C2×C42—42no—
497C2×C42—42no—
498C2×C42—42no—
499C2×C42—42no—
500C2×C42—44no—
501C2×C42C22×C418yes—
502C2×C42C22×C414yes—
503C2×C42C2×D414yes—
504C2×C42C2×D414yes—
505C2×C42C2×D414yes—
506#95—28no—
507#95—28no—
508#95—28no—
509#95—24no—
510#95—24no—
511#95—24no—
512#95—24no—
513#95—24no—
514#95—28no—
515#95—24no—
516#95—24no—
517#95—24no—
518#95—28no—
519#95—28no—
520#95—28no—
521#95—28no—
522#95—28no—
523#95—44no—
524#95—44no—
525#95C2×D4116yes—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—22no—
531C24—22no—
532C24—21no—
533C24—22no—
534C24—22no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—24no—
544C24—24no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—24no—
549C24—24no—
550C24C23×C414yes—
551C24C23×C412yes—
552C24C23×C412yes—
553C24C22×D412yes—
554C24C22×D412yes—
555C24C22×D412yes—
556C24C22×D412yes—
557C24C2×#4114yes—
558C24C2×#4114yes—
559C24C2511yescharacteristic
560#41—4128no—
561C2×Q8—28no—
562C2×Q8—216no—
563C2×Q8—28no—
564C2×Q8—216no—
565C2×Q8—28no—
566C2×Q8—28no—
567C2×Q8—28no—
568C2×Q8—28no—
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—28no—
572C2×Q8—48no—
573C2×Q8—48no—
574C2×Q8—48no—
575C2×Q8—48no—
576C2×Q8—48no—
577C2×Q8—4128no—
578C2×Q8—44no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8C4×D4116yescomplemented
583C2×D4—216no—
584C2×D4—216no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—216no—
588C2×D4—216no—
589C2×D4—232no—
590C2×D4—28no—
591C2×D4—216no—
592C2×D4—28no—
593C2×D4—28no—
594C2×D4—48no—
595C2×D4—48no—
596C2×D4—48no—
597C2×D4—48no—
598C2×D4—48no—
599C2×D4—416no—
600C2×D4—48no—
601C2×D4—48no—
602C2×D4—44no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4C2×C22⋊C4116yes—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—28no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—28no—
637C22×C4—28no—
638C22×C4—28no—
639C22×C4—216no—
640C22×C4—216no—
641C22×C4—216no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—24no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—216no—
675C22×C4—216no—
676C22×C4—216no—
677C22×C4—216no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4—48no—
696C22×C4—48no—
697C22×C4—48no—
698C22×C4—48no—
699C22×C4—48no—
700C22×C4—48no—
701C22×C4—48no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—48no—
708C22×C4—48no—
709C22×C4—48no—
710C22×C4—48no—
711C22×C4—48no—
712C22×C4—48no—
713C22×C4—48no—
714C22×C4—416no—
715C22×C4—48no—
716C22×C4—48no—
717C22×C4—84no—
718C22×C4—88no—
719C22×C4C2×C22⋊C4116yes—
720C22×C4C2×C22⋊C4116yes—
721C22×C4C23×C414yes—
722C22×C4C23×C414yes—
723C22×C4C23×C412yes—
724C22×C4C23×C412yes—
725C22×C4C23×C412yes—
726C22×C4C23×C412yes—
727C22×C4C23×C414yes—
728C22×C4C23×C412yes—
729C22×C4C22×D414yes—
730C22×C4C22×D412yes—
731C22×C4C22×D412yes—
732C22×C4C22×D412yes—
733C22×C4C22×D412yes—
734C22×C4C22×D412yes—
735C22×C4C22×D412yes—
736C22×C4C22×D412yes—
737C22×C4C22×D412yes—
738C22×C4C22×D414yes—
739C22×C4C22×D414yes—
740C22×C4C22×D412yes—
741C22×C4C22×D412yes—
742C22×C4C22×D412yes—
743C22×C4C2×#4114yes—
744C22×C4C2×#4114yes—
745C22×C4C2×#4114yes—
746C22×C4C2×#4114yes—
747C22×C4C2×#4114yes—
748C22×C4C2×#4112yes—
749C22×C4H(5,𝔽2)12yes—
750C22×C4H(5,𝔽2)12yes—
751C22×C42−1+414yes—
752C4⋊C4—216no—
753C4⋊C4—216no—
754C4⋊C4—216no—
755C4⋊C4—28no—
756C4⋊C4—28no—
757C4⋊C4—48no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4C2×C22⋊C4116yes—
762C22⋊C4—216no—
763C22⋊C4—216no—
764C22⋊C4—216no—
765C22⋊C4—216no—
766C22⋊C4—216no—
767C22⋊C4—216no—
768C22⋊C4—416no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—416no—
772C22⋊C4—88no—
773C22⋊C4—88no—
774C22⋊C4—84no—
775C22⋊C4C2×C22⋊C4116yes—
776C22⋊C4C2×C22⋊C4116yes—
777C42—216no—
778C42—216no—
779C42—28no—
780C42—48no—
781C42—48no—
782C42—48no—
783C42—48no—
784C42—44no—
785C42—44no—
786C42—44no—
787C42—84no—
788C42C2×C22⋊C4116yes—
789C23—22no—
790C23—22no—
791C23—24no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—22no—
802C23—22no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—22no—
808C23—24no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—24no—
819C23—22no—
820C23—22no—
821C23—24no—
822C23—24no—
823C23—28no—
824C23—24no—
825C23—28no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—44no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—42no—
847C23—42no—
848C23—44no—
849C23—44no—
850C23—44no—
851C23—44no—
852C23C22×C22⋊C414yes—
853C23C22×C22⋊C414yes—
854C23C4×#4118yes—
855C23#52518yes—
856C23#53214yes—
857C23#53214yes—
858C23C24×C411yescharacteristic
859C23C23×D411yescharacteristic
860C23C23×D411yescharacteristic
861C23C23×D411yescharacteristic
862C23C22×#4111yescharacteristic
863C23C22×#4112yes—
864C23C22×#4112yes—
865C23C2×H(5,𝔽2)11yescharacteristic
866C23C2×H(5,𝔽2)11yescharacteristic
867C23C2×2−1+412yes—
868C23#58512yes—
869Q8—232no—
870Q8—432no—
871Q8—416no—
872D4—232no—
873D4—432no—
874D4—432no—
875D4—416no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—24no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—232no—
909C2×C4—232no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—28no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—28no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—432no—
927C2×C4—432no—
928C2×C4—432no—
929C2×C4—432no—
930C2×C4—44no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—44no—
959C2×C4—44no—
960C2×C4—44no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—44no—
965C2×C4—44no—
966C2×C4—44no—
967C2×C4—816no—
968C2×C4C22×C22⋊C414yes—
969C2×C4C22×C22⋊C414yes—
970C2×C4C22×C22⋊C414yes—
971C2×C4C22×C22⋊C414yes—
972C2×C4C22×C22⋊C414yes—
973C2×C4C2×C4×D418yes—
974C2×C4C2×C4×D414yes—
975C2×C4#51814yes—
976C2×C4D4214yes—
977C2×C4D4214yes—
978C2×C4#54614yes—
979C2×C4#54614yes—
980C2×C4#54818yescomplemented
981C22—28no—
982C22—28no—
983C22—28no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—24no—
989C22—28no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—44no—
995C22—44no—
996C22—44no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22—42no—
1001C22—44no—
1002C22—48no—
1003C22—44no—
1004C22—48no—
1005C22—44no—
1006C22—44no—
1007C22—84no—
1008C22—84no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22—82no—
1013C22#229718yescomplemented
1014C22C23×C22⋊C411yescharacteristic
1015C22C22×C4×D411yescharacteristic
1016C22C2×C4×#4112yes—
1017C22C2×#51811yescharacteristic
1018C22C4×2−1+412yes—
1019C22C2×#52512yes—
1020C22C2×#53211yescharacteristic
1021C22C2×#53211yescharacteristic
1022C22C2×D4211yescharacteristic
1023C22C2×D4211yescharacteristic
1024C22C2×#54611yescharacteristic
1025C22C2×#54611yescharacteristic
1026C22C2×#54812yes—
1027C22D4×#4112yes—
1028C22#348012yes—
1029C22#348212yes—
1030C22#348912yes—
1031C22#349911yescharacteristic
1032C22#350011yescharacteristic
1033C22#350512yes—
1034C22#351112yes—
1035C22#351412yes—
1036C22#352012yes—
1037C4—28no—
1038C4—24no—
1039C4—24no—
1040C4—28no—
1041C4—24no—
1042C4—24no—
1043C4—44no—
1044C4—44no—
1045C4—44no—
1046C4—44no—
1047C4—44no—
1048C4—44no—
1049C4—82no—
1050C4—82no—
1051C4—82no—
1052C4D4×C22⋊C418yes—
1053C2—28no—
1054C2—44no—
1055C2—84no—
1056C2C2×#229711yescharacteristic
1057C2C2×D4×C22⋊C411yescharacteristic
1058C2C4×#54812yes—
1059C2#3425911yescharacteristic
1060C2#3432712yes—
1061C2#3609712yes—
1062C2#3612211yescharacteristic
1063C2#3612411yescharacteristic
1064C2#3637412yes—
1065C2#3637611yescharacteristic
1066C2#3639611yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#548C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2352C2semidirect
3. C2×#2297C2semidirect
4. C22×#391C2semidirect
5. C2×C42×D4C2semidirect
6. #14708C2semidirect
7. #14702C2semidirect
8. #14698C2semidirect
9. #14153C2semidirect
10. #14138C2semidirect
11. #14137C2semidirect
12. #14099C2semidirect
13. #14098C2semidirect
14. #14023C2semidirect
15. #13942C2semidirect
16. #13937C2semidirect
17. #13922C2semidirect
18. #13813C2semidirect
19. C4×#391C2semidirect
24. C2×#548C4semidirect
104. C22×#41C2×C4semidirect
111. C23×Q8C2×C4semidirect
131. C2×#124C2×C4semidirect
132. C2×#124C2×C4semidirect
137. C2×C22⋊Q8C2×C4semidirect
138. C2×C22⋊Q8C2×C4semidirect
144. C2×#121C2×C4semidirect
147. C2×C4×Q8C2×C4semidirect
154. C2×C4×D4C2×C4semidirect
214. #391D4semidirect
367. C23×C4#41semidirect
393. C4×D4C22⋊C4semidirect
468. C2×C22⋊C4#41semidirect
582. C2×Q8C4×D4semidirect
980. C2×C4#548semidirect
1013. C22#2297semidirect

Maximal subgroups

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

subgroupindex
C22×#5482
C2×#23522
C2×#22972
C22×#3912
C2×C42×D42
#147082
#147022
#146982
#141532
#141382
#141372
#140992
#140982
#140232
#139422
#139372
#139222
#138132
C4×#3912