Finite Group Databasebeta

← #524469

Subgroups — #524469

Order 512.

5406 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#548C211yesmaximal, characteristic
2C2×#2354C211yesmaximal, characteristic, complemented
3C2×#2310C211yesmaximal, characteristic, complemented
4C2×#2297C211yesmaximal, characteristic, complemented
5C2×#2290C211yesmaximal, characteristic, complemented
6#14702C211yesmaximal, characteristic, complemented
7#14421C214yesmaximal, complemented
8#14363C214yesmaximal, complemented
9#14273C211yesmaximal, characteristic, complemented
10#14257C211yesmaximal, characteristic, complemented
11#14153C211yesmaximal, characteristic, complemented
12#14138C211yesmaximal, characteristic, complemented
13#14136C211yesmaximal, characteristic, complemented
14#14099C214yesmaximal, complemented
15#13937C211yesmaximal, characteristic, complemented
16#13926C211yesmaximal, characteristic, complemented
17#13922C211yesmaximal, characteristic, complemented
18#13886C214yesmaximal, complemented
19#13786C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C24×Q8C2211yescharacteristic
22C2×#548—28no—
23C2×#548—28no—
24C2×#548C4116yescomplemented
25C22×#124C2212yes—
26C22×#124C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2212yes—
29C22×#121C2212yes—
30C22×#121C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×D4C2212yes—
33C22×C4×D4C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C22×#117C2211yescharacteristic
37C23×C42C2211yescharacteristic
38#2354—28no—
39#2310—28no—
40#2297—28no—
41C2×#391C2214yes—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#390C2212yes—
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55#2290—28no—
56C2×#388C2212yes—
57C2×#388C2212yes—
58C2×#388C2212yes—
59C2×#387C2212yes—
60C2×#386C2212yes—
61C2×#386C2214yes—
62C2×#385C2212yes—
63C2×#384C2211yescharacteristic
64C2×#381C2214yes—
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×C4×C4⋊C4C2212yes—
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2214yes—
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×#376C2211yescharacteristic
74#1446C2214yes—
75#1441C2214yes—
76#1440C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2214yes—
82#1438C2214yes—
83#1438C2214yes—
84#1437C2214yes—
85#1437C2214yes—
86#1436C2214yes—
87#1436C2214yes—
88#1436C2214yes—
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2214yes—
93C4⋊#95C2211yescharacteristic
94#1434C2214yes—
95C22⋊#95C2214yes—
96C22⋊#95C2214yes—
97C22⋊#95C2214yes—
98C22×#41—24no—
99C22×#41—24no—
100C22×#41—24no—
101C22×#41—24no—
102C22×#41—42no—
103C22×#41—42no—
104C22×#41C2×C418yes—
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×C4C2311yescharacteristic
122C24×C4C2311yescharacteristic
123C24×C4C2312yes—
124#548—2128no—
125C2×#124—28no—
126C2×#124—28no—
127C2×#124—24no—
128C2×#124—24no—
129C2×#124C2×C4116yes—
130C2×#124C2×C418yescomplemented
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—28no—
134C2×C22⋊Q8—28no—
135C2×C22⋊Q8C2×C418yes—
136C2×C22⋊Q8C2×C4116yescomplemented
137C2×#121—28no—
138C2×#121—28no—
139C2×#121—24no—
140C2×#121—24no—
141C2×#121C2×C4116yes—
142C2×#121C2×C418yescomplemented
143C2×C4×Q8—24no—
144C2×C4×Q8—24no—
145C2×C4×Q8C2×C418yescomplemented
146C2×C4×D4—28no—
147C2×C4×D4—28no—
148C2×C4×D4C2×C418yes—
149C2×C4×D4C2×C4116yescomplemented
150C2×C4×D4D418yes—
151C2×C4×D4D418yes—
152C2×#117—24no—
153C2×#117—24no—
154C2×#117—24no—
155C2×#117—24no—
156C2×#117—24no—
157C2×#117—24no—
158C2×#117—42no—
159C2×#117—42no—
160C2×#117—42no—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
185C22×C22⋊C4C2314yes—
186C22×C22⋊C4C2314yes—
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C42—24no—
191C22×C42—24no—
192C22×C42—42no—
193C22×C42C2311yescharacteristic
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196C22×C42C2312yes—
197C22×C42C2312yes—
198C22×C42C2312yes—
199C22×C42C2312yes—
200C22×C42C2311yescharacteristic
201C22×C42C2312yes—
202C22×C42C2311yescharacteristic
203#391—24no—
204#391—24no—
205#391—24no—
206#391—24no—
207#391—24no—
208#391—216no—
209#391—42no—
210#391—42no—
211#391D418yescomplemented
212#390—28no—
213#390—24no—
214#390—24no—
215#390—42no—
216#390—42no—
217#388—28no—
218#388—28no—
219#388—28no—
220#387—28no—
221#386—28no—
222#386—216no—
223#385—28no—
224#384—24no—
225#381—216no—
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—216no—
234#376—24no—
235C2×#95C2314yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2314yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2314yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2314yes—
249C2×#95C2314yes—
250C2×#95C2314yes—
251C2×#95C2314yes—
252C2×#95C2314yes—
253C2×#95C2314yes—
254C2×#95C2314yes—
255C25C2412yes—
256C25C2411yescharacteristic
257C25C2411yescharacteristic
258C2×#41—232no—
259C2×#41—232no—
260C2×#41—416no—
261C2×#41—416no—
262C2×#41—416no—
263C2×#41—416no—
264C2×#41—416no—
265C22×Q8—232no—
266C22×Q8—232no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—24no—
270C22×Q8—24no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—24no—
274C22×Q8—22no—
275C22×Q8—24no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—42no—
282C22×Q8—42no—
283C22×Q8—416no—
284C22×Q8—416no—
285C22×Q8—416no—
286C22×Q8—416no—
287C22×Q8—416no—
288C22×Q8C22×C414yes—
289C22×Q8C22×C418yes—
290C22×Q8C22×C414yes—
291C22×Q8C2×D414yes—
292C22×Q8#4114yes—
293C22×D4—24no—
294C22×D4—24no—
295C22×D4—24no—
296C22×D4—24no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—24no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—42no—
306C22×D4—42no—
307C22×D4—44no—
308C22×D4—44no—
309C22×D4—42no—
310C22×D4—42no—
311C22×D4C22×C414yes—
312C22×D4C22×C418yes—
313C22×D4C22×C418yes—
314C22×D4C22×C414yes—
315C22×D4C2×D414yes—
316C22×D4C2×D414yes—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—24no—
326C23×C4—24no—
327C23×C4—24no—
328C23×C4—24no—
329C23×C4—24no—
330C23×C4—24no—
331C23×C4—24no—
332C23×C4—24no—
333C23×C4—24no—
334C23×C4—24no—
335C23×C4—24no—
336C23×C4—42no—
337C23×C4—42no—
338C23×C4—42no—
339C23×C4—42no—
340C23×C4—42no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4—42no—
344C23×C4C22×C418yes—
345C23×C4C22×C418yes—
346C23×C4C22×C414yes—
347C23×C4C22×C414yes—
348C23×C4C2×D414yes—
349C23×C4C2×D414yes—
350C23×C4C2×D414yes—
351C23×C4C2×D414yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2411yescharacteristic
363C23×C4C2411yescharacteristic
364C23×C4C2411yescharacteristic
365C23×C4C2411yescharacteristic
366C23×C4C2412yes—
367C23×C4C2411yescharacteristic
368#124—264no—
369#124—232no—
370C22⋊Q8—232no—
371C22⋊Q8—264no—
372#121—264no—
373#121—232no—
374C4×Q8—232no—
375C4×D4—264no—
376C4×D4C22⋊C4164yescomplemented
377#117—416no—
378#117—416no—
379#117—416no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4C22×C418yes—
408C2×C4⋊C4C22×C418yes—
409C2×C4⋊C4C22×C414yes—
410C2×C4⋊C4C22×C414yes—
411C2×C4⋊C4C2×D414yes—
412C2×C4⋊C4C2×D414yes—
413C2×C4⋊C4C2×D414yes—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—28no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—28no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—44no—
446C2×C22⋊C4—44no—
447C2×C22⋊C4—44no—
448C2×C22⋊C4—44no—
449C2×C22⋊C4—44no—
450C2×C22⋊C4—44no—
451C2×C22⋊C4—44no—
452C2×C22⋊C4—44no—
453C2×C22⋊C4C22×C418yes—
454C2×C22⋊C4C22×C418yes—
455C2×C22⋊C4C22×C418yes—
456C2×C22⋊C4C22×C418yes—
457C2×C22⋊C4C22×C414yes—
458C2×C22⋊C4C22×C414yes—
459C2×C22⋊C4C2×D414yes—
460C2×C22⋊C4C2×D414yes—
461C2×C22⋊C4C2×D414yes—
462C2×C22⋊C4C2×D414yes—
463C2×C42—22no—
464C2×C42—24no—
465C2×C42—24no—
466C2×C42—22no—
467C2×C42—24no—
468C2×C42—22no—
469C2×C42—24no—
470C2×C42—24no—
471C2×C42—24no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—24no—
475C2×C42—22no—
476C2×C42—24no—
477C2×C42—24no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—416no—
484C2×C42—42no—
485C2×C42—42no—
486C2×C42—42no—
487C2×C42—44no—
488C2×C42C22×C418yes—
489C2×C42C22×C414yes—
490C2×C42C2×D414yes—
491C2×C42C2×D414yes—
492C2×C42C2×D414yes—
493#95—24no—
494#95—24no—
495#95—24no—
496#95—28no—
497#95—24no—
498#95—24no—
499#95—24no—
500#95—24no—
501#95—24no—
502#95—28no—
503#95—28no—
504#95—28no—
505#95—28no—
506#95—44no—
507#95—44no—
508#95—44no—
509#95—44no—
510#95—44no—
511#95—44no—
512#95C2×D4116yes—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—24no—
538C24—24no—
539C24C23×C414yes—
540C24C23×C412yes—
541C24C23×C412yes—
542C24C22×D412yes—
543C24C22×D412yes—
544C24C22×D412yes—
545C24C22×D412yes—
546C24C2511yescharacteristic
547#41—4128no—
548C2×Q8—28no—
549C2×Q8—216no—
550C2×Q8—28no—
551C2×Q8—216no—
552C2×Q8—28no—
553C2×Q8—28no—
554C2×Q8—28no—
555C2×Q8—28no—
556C2×Q8—28no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—48no—
560C2×Q8—48no—
561C2×Q8—48no—
562C2×Q8—48no—
563C2×Q8—48no—
564C2×Q8—4128no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×Q8—44no—
568C2×Q8—44no—
569C2×Q8C4×D4116yes—
570C2×D4—216no—
571C2×D4—216no—
572C2×D4—28no—
573C2×D4—216no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—48no—
577C2×D4—416no—
578C2×D4—48no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—48no—
582C2×D4—48no—
583C2×D4—48no—
584C2×D4—48no—
585C2×D4—48no—
586C2×D4—416no—
587C2×D4—48no—
588C2×D4—48no—
589C2×D4—44no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4C2×C22⋊C4116yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—216no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—216no—
650C22×C4—216no—
651C22×C4—216no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
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—24no—
673C22×C4—24no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—22no—
680C22×C4—24no—
681C22×C4—48no—
682C22×C4—48no—
683C22×C4—48no—
684C22×C4—48no—
685C22×C4—48no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4—48no—
690C22×C4—48no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4—48no—
696C22×C4—48no—
697C22×C4—48no—
698C22×C4C2×C22⋊C4116yes—
699C22×C4C2×C22⋊C4116yes—
700C22×C4C23×C414yes—
701C22×C4C23×C414yes—
702C22×C4C23×C412yes—
703C22×C4C23×C412yes—
704C22×C4C23×C412yes—
705C22×C4C23×C412yes—
706C22×C4C23×C414yes—
707C22×C4C23×C412yes—
708C22×C4C22×D414yes—
709C22×C4C22×D414yes—
710C22×C4C22×D412yes—
711C22×C4C22×D412yes—
712C22×C4C22×D412yes—
713C22×C4C22×D412yes—
714C22×C4C22×D412yes—
715C22×C4C22×D412yes—
716C22×C4C22×D412yes—
717C22×C4C22×D412yes—
718C22×C4C22×D414yes—
719C22×C4C22×D412yes—
720C22×C4C22×D412yes—
721C22×C4C22×D412yes—
722C22×C4C2×#4114yes—
723C22×C4C2×#4112yes—
724C22×C4H(5,𝔽2)12yes—
725C22×C4H(5,𝔽2)12yes—
726C22×C42−1+414yes—
727C4⋊C4—216no—
728C4⋊C4—216no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—84no—
738C4⋊C4C2×C22⋊C4116yes—
739C22⋊C4—216no—
740C22⋊C4—216no—
741C22⋊C4—216no—
742C22⋊C4—216no—
743C22⋊C4—416no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—416no—
749C22⋊C4—48no—
750C22⋊C4—84no—
751C22⋊C4—84no—
752C22⋊C4—88no—
753C22⋊C4—88no—
754C22⋊C4C2×C22⋊C4116yes—
755C22⋊C4C2×C22⋊C4116yes—
756C42—216no—
757C42—28no—
758C42—48no—
759C42—48no—
760C42—48no—
761C42—48no—
762C42—44no—
763C42—44no—
764C42—44no—
765C42C2×C22⋊C4116yes—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—24no—
789C23—24no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—24no—
795C23—24no—
796C23—24no—
797C23—28no—
798C23—28no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—44no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—42no—
826C23—42no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23C22×C22⋊C414yes—
834C23C22×C22⋊C414yes—
835C23C24×C411yescharacteristic
836C23C23×D411yescharacteristic
837C23C23×D411yescharacteristic
838C23C23×D411yescharacteristic
839C23C22×#4111yescharacteristic
840C23C2×H(5,𝔽2)11yescharacteristic
841C23C2×H(5,𝔽2)11yescharacteristic
842C23C2×2−1+412yes—
843C23#58512yes—
844C23#58512yes—
845C23#58512yes—
846Q8—232no—
847Q8—432no—
848Q8—416no—
849D4—416no—
850D4—432no—
851D4—432no—
852D4—416no—
853C2×C4—24no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—232no—
880C2×C4—232no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—28no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—28no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—432no—
895C2×C4—432no—
896C2×C4—432no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—44no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—44no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—44no—
926C2×C4—42no—
927C2×C4—44no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—44no—
937C2×C4—42no—
938C2×C4—44no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—44no—
943C2×C4—44no—
944C2×C4C22×C22⋊C414yes—
945C2×C4C22×C22⋊C414yes—
946C2×C4C22×C22⋊C414yes—
947C2×C4C22×C22⋊C414yes—
948C2×C4C22×C22⋊C414yes—
949C2×C4C2×C4×D418yes—
950C2×C4C2×C4×D414yes—
951C2×C4#51814yes—
952C2×C4D4214yes—
953C2×C4D4214yes—
954C2×C4#54614yes—
955C2×C4#54614yes—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—24no—
961C22—24no—
962C22—44no—
963C22—44no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—48no—
980C22—44no—
981C22—48no—
982C22—44no—
983C22—84no—
984C22—82no—
985C22—82no—
986C22—84no—
987C22—82no—
988C22—82no—
989C22C23×C22⋊C411yescharacteristic
990C22C22×C4×D411yescharacteristic
991C22C2×#51811yescharacteristic
992C22#342812yes—
993C22C4×2−1+412yes—
994C22#344912yes—
995C22#344911yescharacteristic
996C22#344911yescharacteristic
997C22C2×D4211yescharacteristic
998C22C2×D4211yescharacteristic
999C22C2×#54611yescharacteristic
1000C22C2×#54611yescharacteristic
1001C22#348712yes—
1002C22#348912yes—
1003C22#348912yes—
1004C22#349911yescharacteristic
1005C22#350011yescharacteristic
1006C22#351812yes—
1007C22#352412yes—
1008C22#354012yes—
1009C22#354112yes—
1010C22#355412yes—
1011C22#356212yes—
1012C4—24no—
1013C4—24no—
1014C4—28no—
1015C4—24no—
1016C4—24no—
1017C4—44no—
1018C4—44no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—82no—
1023C4—82no—
1024C4—82no—
1025C4—82no—
1026C4—82no—
1027C4D4×C22⋊C418yes—
1028C2—44no—
1029C2—44no—
1030C2—84no—
1031C2#3404411yescharacteristic
1032C2C2×D4×C22⋊C411yescharacteristic
1033C2#3425911yescharacteristic
1034C2#3429312yes—
1035C2#3447412yes—
1036C2#3765912yes—
1037C2#3768011yescharacteristic
1038C2#3768311yescharacteristic
1039C2#3803512yes—
1040C2#3809111yescharacteristic
1041C2#3809511yescharacteristic
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×#2354C2semidirect
3. C2×#2310C2semidirect
4. C2×#2297C2semidirect
5. C2×#2290C2semidirect
6. #14702C2semidirect
7. #14421C2semidirect
8. #14363C2semidirect
9. #14273C2semidirect
10. #14257C2semidirect
11. #14153C2semidirect
12. #14138C2semidirect
13. #14136C2semidirect
14. #14099C2semidirect
15. #13937C2semidirect
16. #13926C2semidirect
17. #13922C2semidirect
18. #13886C2semidirect
19. #13786C2semidirect
24. C2×#548C4semidirect
111. C23×Q8C2×C4semidirect
130. C2×#124C2×C4semidirect
136. C2×C22⋊Q8C2×C4semidirect
142. C2×#121C2×C4semidirect
145. C2×C4×Q8C2×C4semidirect
149. C2×C4×D4C2×C4semidirect
211. #391D4semidirect
376. C4×D4C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5482
C2×#23542
C2×#23102
C2×#22972
C2×#22902
#147022
#144212
#143632
#142732
#142572
#141532
#141382
#141362
#140992
#139372
#139262
#139222
#138862
#137862