Finite Group Databasebeta

← #678424

Subgroups — #678424

Order 512.

3748 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2C2×#2859C211yesmaximal, characteristic, complemented
3C2×#2562C211yesmaximal, characteristic
4C2×#2565C211yesmaximal, characteristic, complemented
5#15847C214yesmaximal, complemented
6#15271C214yesmaximal
7#15236C211yesmaximal, characteristic, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#15182C211yesmaximal, characteristic, complemented
11#14931C214yesmaximal, complemented
12#14160C211yesmaximal, characteristic, complemented
13#14072C214yesmaximal, complemented
14#13881C211yesmaximal, characteristic, complemented
15#13880C211yesmaximal, characteristic, complemented
16#13879C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18C4×#391C211yesmaximal, characteristic, complemented
19C4×#390C211yesmaximal, characteristic
20C2×#552—28no—
21C2×#552—28no—
22C2×#552—28no—
23C22×#126C2212yes—
24C22×#125C2211yescharacteristic
25C22×#125C2212yes—
26C22×#125C2211yescharacteristic
27C22×#123C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C22×#117C2212yes—
34C23×C4⋊C4C2211yescharacteristic
35#2859—28no—
36#2565—28no—
37#2562—28no—
38C2×#400C2212yes—
39C2×#398C2214yes—
40C2×#394C2212yes—
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#390C2212yes—
46C2×#389C2214yes—
47C2×#389C2214yes—
48C2×#388C2212yes—
49C2×#388C2212yes—
50C2×#387C2214yes—
51C2×#385C2214yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C43C2211yescharacteristic
69#1444C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1440C2214yes—
77#1440C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1437C2212yes—
83#1437C2212yes—
84#1436C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87#1436C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2212yes—
95C22⋊#95C2214yes—
96C4×#95C2214yes—
97C23×Q8C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102#552—2128no—
103C2×#126—28no—
104C2×#126—28no—
105C2×#126—28no—
106C2×#125—28no—
107C2×#125—28no—
108C2×#125—28no—
109C2×#125—24no—
110C2×#125—24no—
111C2×#125—24no—
112C2×#125—24no—
113C2×#125—24no—
114C2×#125D418yes—
115C2×#123—28no—
116C2×#123—28no—
117C2×#123—28no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8—24no—
126C2×C4×Q8D418yes—
127C2×C4×D4—24no—
128C2×C4×D4—24no—
129C2×C4×D4D418yes—
130C2×#117—24no—
131C2×#117—24no—
132C2×#117—24no—
133C2×#117—28no—
134C2×#117—28no—
135C2×#117—28no—
136C22×C4⋊C4—24no—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—24no—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2314yes—
151C22×C4⋊C4C2314yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C42C2312yes—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2312yes—
176C22×C42C2312yes—
177C22×C42C2312yes—
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2312yes—
181C22×C42C2311yescharacteristic
182#400—28no—
183#398—216no—
184#394—28no—
185#391—24no—
186#391—24no—
187#391—24no—
188#391—24no—
189#390—28no—
190#389—216no—
191#389—216no—
192#388—28no—
193#388—28no—
194#387—216no—
195#385—216no—
196#384—24no—
197#384—24no—
198#384—24no—
199#382—24no—
200#382—24no—
201#382—24no—
202#380—24no—
203#380—24no—
204#380—24no—
205#380—24no—
206C4×C4⋊C4—24no—
207C4×C4⋊C4—24no—
208C4×C22⋊C4—24no—
209C4×C22⋊C4—24no—
210C4×C22⋊C4—24no—
211C4×C22⋊C4—24no—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C43—24no—
236C25C2411yescharacteristic
237C25C2411yescharacteristic
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8C2×D414yes—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—42no—
249C22×D4C2×D414yes—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—28no—
266C23×C4—44no—
267C23×C4C2×D414yes—
268C23×C4C2×D414yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286#126—264no—
287#125—264no—
288#125—232no—
289#125—416no—
290#123—264no—
291C22⋊Q8—232no—
292C22⋊Q8—232no—
293C4×Q8—232no—
294C4×D4—232no—
295#117—232no—
296#117—264no—
297C2×C4⋊C4—232no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4C2×D414yes—
352C2×C4⋊C4C2×D414yes—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4C2×D418yes—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2×D418yes—
357C2×C4⋊C4C2×D418yes—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4C2×D414yes—
391C2×C22⋊C4C2×D414yes—
392C2×C22⋊C4#4118yes—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—44no—
416C2×C42C2×D418yes—
417C2×C42C2×D414yes—
418C2×C42C2×D414yes—
419C2×C42C2×D414yes—
420C2×C42#4114yes—
421C2×C42#4114yes—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—28no—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—28no—
438#95—28no—
439#95—28no—
440#95—28no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—21no—
451C24—21no—
452C24—22no—
453C24—22no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24C22×D412yes—
465C24C22×D412yes—
466C24C2×#4114yes—
467C24C2511yescharacteristic
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—44no—
478C2×D4—48no—
479C2×D4—48no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—216no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
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—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—416no—
565C22×C4—416no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4C22×D412yes—
577C22×C4C22×D414yes—
578C22×C4C22×D412yes—
579C22×C4C22×D414yes—
580C22×C4C22×D414yes—
581C22×C4C22×D414yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4114yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C42−1+414yes—
598C22×C42−1+412yes—
599C22×C42−1+412yes—
600C4⋊C4—216no—
601C4⋊C4—216no—
602C4⋊C4—216no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—216no—
607C4⋊C4—28no—
608C4⋊C4—216no—
609C4⋊C4—216no—
610C4⋊C4—416no—
611C4⋊C4—48no—
612C4⋊C4—416no—
613C4⋊C4—416no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C22⋊C4—216no—
621C22⋊C4—216no—
622C22⋊C4—216no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—216no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C42—216no—
634C42—216no—
635C42—28no—
636C42—28no—
637C42—48no—
638C42—48no—
639C42—44no—
640C42—44no—
641C42—84no—
642C42#120116yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23#53214yes—
689C23C23×D411yescharacteristic
690C23C23×D411yescharacteristic
691C23C23×D411yescharacteristic
692C23C22×#4111yescharacteristic
693C23C22×#4111yescharacteristic
694C23C22×#4112yes—
695C23C2×2−1+411yescharacteristic
696C23C2×2−1+411yescharacteristic
697C23C2×2−1+412yes—
698C23#58512yes—
699C23#58512yes—
700Q8—416no—
701D4—416no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—28no—
736C2×C4—24no—
737C2×C4—432no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—416no—
768C2×C4—416no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4C2×#12014yes—
797C2×C4C2×#12014yes—
798C2×C4C2×#12014yes—
799C2×C4#53214yes—
800C2×C4#53614yes—
801C2×C4#54714yes—
802C2×C4#54714yes—
803C2×C4#54814yes—
804C2×C4#54814yes—
805C2×C4#55218yescomplemented
806C22—24no—
807C22—24no—
808C22—24no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—44no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22C22×#12011yescharacteristic
829C22C2×#53211yescharacteristic
830C22C2×#53211yescharacteristic
831C22C2×#53611yescharacteristic
832C22#344911yescharacteristic
833C22C2×#54711yescharacteristic
834C22C2×#54711yescharacteristic
835C22C2×#54811yescharacteristic
836C22C2×#54811yescharacteristic
837C22D4×#4112yes—
838C22D4×#4112yes—
839C22C2×#55212yes—
840C22#347512yes—
841C22#348912yes—
842C22#349712yes—
843C22#349911yescharacteristic
844C22#350011yescharacteristic
845C22#350712yes—
846C22#350912yes—
847C22#351212yes—
848C22#351512yes—
849C22#356312yes—
850C22#356512yes—
851C4—28no—
852C4—24no—
853C4—24no—
854C4—44no—
855C4—44no—
856C4—42no—
857C4—42no—
858C4—44no—
859C4—44no—
860C4—44no—
861C4—44no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4#243218yes—
868C2—44no—
869C2—82no—
870C2C2×#243211yescharacteristic
871C2#3473811yescharacteristic
872C2#3566011yescharacteristic
873C2#3618111yescharacteristic
874C2#3618411yescharacteristic
875C2#3627012yes—
876C2#3948411yescharacteristic
877C2#3948511yescharacteristic
878C2#3995512yes—
879C2#5913812yes—
880C2#5914012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2859C2semidirect
4. C2×#2565C2semidirect
5. #15847C2semidirect
7. #15236C2semidirect
8. #15236C2semidirect
9. #15182C2semidirect
10. #15182C2semidirect
11. #14931C2semidirect
12. #14160C2semidirect
13. #14072C2semidirect
14. #13881C2semidirect
15. #13880C2semidirect
16. #13879C2semidirect
17. #13879C2semidirect
18. C4×#391C2semidirect
805. C2×C4#552semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#28592
C2×#25622
C2×#25652
#158472
#152712
#152362
#151822
#149312
#141602
#140722
#138812
#138802
#138792
C4×#3912
C4×#3902