Finite Group Databasebeta

← #719735

Subgroups — #719735

Order 512.

3226 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2547C211yesmaximal, characteristic
2C2×#2546C211yesmaximal, characteristic, complemented
3C2×#2546C211yesmaximal, characteristic, complemented
4C2×#2545C211yesmaximal, characteristic
5C2×#2658C211yesmaximal, characteristic
6C2×#2367C211yesmaximal, characteristic
7#16469C214yesmaximal, complemented
8#15351C214yesmaximal, complemented
9#15294C214yesmaximal, complemented
10#15243C211yesmaximal, characteristic
11#15217C211yesmaximal, characteristic
12#15190C211yesmaximal, characteristic, complemented
13#15180C211yesmaximal, characteristic, complemented
14#14771C214yesmaximal, complemented
15#14155C211yesmaximal, characteristic, complemented
16#14027C211yesmaximal, characteristic
17#14024C211yesmaximal, characteristic, complemented
18#13848C211yesmaximal, characteristic, complemented
19#13786C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33#2658—28no—
34#2547—28no—
35#2546—28no—
36#2546—28no—
37#2545—28no—
38C2×#399C2214yes—
39C2×#399C2214yes—
40C2×#398C2212yes—
41C2×#398C2214yes—
42C2×#398C2212yes—
43C2×#397C2214yes—
44C2×#396C2214yes—
45#2367—28no—
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389C2214yes—
59C2×#389C2212yes—
60C2×#389C2212yes—
61C2×#388C2214yes—
62C2×#388C2212yes—
63C2×#388C2212yes—
64C2×#385C2212yes—
65C2×#380C2214yes—
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2212yes—
72C2×#376C2211yescharacteristic
73#1445C2214yes—
74#1444C2212yes—
75#1444C2214yes—
76#1444C2214yes—
77#1442C2212yes—
78#1442C2214yes—
79#1441C2212yes—
80#1441C2212yes—
81#1441C2214yes—
82#1441C2214yes—
83#1440C2214yes—
84#1440C2214yes—
85#1439C2214yes—
86#1439C2214yes—
87#1439C2214yes—
88#1436C2214yes—
89#1436C2214yes—
90C4⋊#95C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93#1434C2214yes—
94C22⋊#95C2214yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C23×Q8C2311yescharacteristic
101C23×D4C2311yescharacteristic
102C24×C4C2312yes—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8—42no—
119C2×C4⋊Q8—42no—
120C2×C4⋊Q8—42no—
121C2×#124—24no—
122C2×#124—24no—
123C2×#124—24no—
124C2×#124—24no—
125C2×#124—24no—
126C2×#124—24no—
127C2×#124—24no—
128C2×#124—24no—
129C2×#124—42no—
130C2×#124—42no—
131C2×#124—42no—
132C2×#124D418yes—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8—42no—
139C2×C4×D4—24no—
140C2×C4×D4—24no—
141C2×C4×D4—42no—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2314yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2314yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2312yes—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2312yes—
179C22×C42C2311yescharacteristic
180#399—216no—
181#399—216no—
182#398—216no—
183#398—28no—
184#398—28no—
185#397—216no—
186#396—216no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—24no—
191#391—24no—
192#391—24no—
193#391—24no—
194#391—42no—
195#391—42no—
196#391D418yes—
197#390—24no—
198#390—24no—
199#389—28no—
200#389—28no—
201#389—216no—
202#388—28no—
203#388—216no—
204#388—28no—
205#385—28no—
206#380—216no—
207C4×C4⋊C4—24no—
208C4×C4⋊C4—24no—
209C4×C4⋊C4—24no—
210C4×C4⋊C4—24no—
211C4×C4⋊C4D418yes—
212C4×C22⋊C4—28no—
213#376—24no—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2311yescharacteristic
240C2×#95C2311yescharacteristic
241C25C2412yes—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8C2×D414yes—
269C22×Q8C2×D414yes—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4C2×D414yes—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—28no—
280C23×C4—42no—
281C23×C4—44no—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C4⋊Q8—416no—
301C4⋊Q8—416no—
302C4⋊Q8—416no—
303C4⋊Q8—416no—
304C4⋊Q8—416no—
305C4⋊Q8—416no—
306#124—232no—
307#124—416no—
308#124—416no—
309#124—416no—
310C4×Q8—416no—
311C4×Q8—416no—
312C4×D4—416no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
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—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4C2×D414yes—
366C2×C4⋊C4C2×D414yes—
367C2×C4⋊C4C2×D414yes—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4C2×D418yes—
392C2×C22⋊C4C2×D418yes—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—42no—
414C2×C42—44no—
415C2×C42C2×D414yes—
416C2×C42C2×D414yes—
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—24no—
429#95—28no—
430#95—24no—
431#95—28no—
432#95—28no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—28no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—44no—
442#95—42no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95C2×D414yes—
447#95C2×D414yes—
448#95C2×D4116yes—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24C22×D414yes—
460C24C2511yescharacteristic
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—28no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
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—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—48no—
580C22×C4—416no—
581C22×C4—48no—
582C22×C4—84no—
583C22×C4—88no—
584C22×C4C22×D414yes—
585C22×C4C22×D412yes—
586C22×C4C22×D414yes—
587C22×C4C22×D412yes—
588C22×C4C22×D414yes—
589C22×C4C22×D414yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C2×#4114yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C4H(5,𝔽2)12yes—
606C22×C42−1+414yes—
607C22×C42−1+414yes—
608C22×C42−1+414yes—
609C4⋊C4—216no—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—416no—
620C4⋊C4—48no—
621C4⋊C4—416no—
622C4⋊C4—416no—
623C4⋊C4—48no—
624C4⋊C4—44no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—44no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—48no—
631C22⋊C4—416no—
632C22⋊C4—416no—
633C22⋊C4—416no—
634C22⋊C4—416no—
635C22⋊C4—48no—
636C22⋊C4—84no—
637C42—28no—
638C42—28no—
639C42—28no—
640C42—28no—
641C42—48no—
642C42—48no—
643C42—44no—
644C42—44no—
645C42—84no—
646C42#121116yes—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—28no—
651C23—28no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—44no—
659C23—44no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23C23×D411yescharacteristic
671C23C23×D411yescharacteristic
672C23C23×D411yescharacteristic
673C23C22×#4111yescharacteristic
674C23C22×#4111yescharacteristic
675C23C2×H(5,𝔽2)11yescharacteristic
676C23C2×H(5,𝔽2)11yescharacteristic
677C23C2×2−1+412yes—
678C23C2×2−1+412yes—
679C23C2×2−1+412yes—
680C23#58512yes—
681Q8—416no—
682Q8—416no—
683Q8—88no—
684Q8—88no—
685D4—416no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—816no—
784C2×C4C2×#12114yes—
785C2×C4C2×#12114yes—
786C2×C4C2×#12114yes—
787C2×C4#53214yes—
788C2×C4#53614yes—
789C2×C4#53614yes—
790C2×C4#54014yes—
791C2×C4D4214yes—
792C2×C4D4214yes—
793C2×C4#54614yes—
794C2×C4#55014yes—
795C22—48no—
796C22—44no—
797C22—48no—
798C22—44no—
799C22—44no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—84no—
805C22—84no—
806C22C22×#12111yescharacteristic
807C22C2×#53211yescharacteristic
808C22C2×#53611yescharacteristic
809C22C2×#53611yescharacteristic
810C22C2×#54011yescharacteristic
811C22C2×D4211yescharacteristic
812C22C2×D4211yescharacteristic
813C22C2×#54611yescharacteristic
814C22C2×#55011yescharacteristic
815C22#348612yes—
816C22#348912yes—
817C22#348912yes—
818C22#349912yes—
819C22#349911yescharacteristic
820C22#350011yescharacteristic
821C22#350712yes—
822C22#350712yes—
823C22#350912yes—
824C22#350912yes—
825C22#355212yes—
826C22#355212yes—
827C22#355412yes—
828C22#356112yes—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—24no—
833C4—44no—
834C4—44no—
835C4—42no—
836C4—42no—
837C4—44no—
838C4—44no—
839C4—44no—
840C4—44no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4#242818yes—
847C2—84no—
848C2C2×#242811yescharacteristic
849C2#3531611yescharacteristic
850C2#3562111yescharacteristic
851C2#3593812yes—
852C2#3767511yescharacteristic
853C2#3767611yescharacteristic
854C2#3974411yescharacteristic
855C2#3974611yescharacteristic
856C2#4270212yes—
857C2#4514412yes—
858C2#4533212yes—
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×#2546C2semidirect
3. C2×#2546C2semidirect
7. #16469C2semidirect
8. #15351C2semidirect
9. #15294C2semidirect
12. #15190C2semidirect
13. #15180C2semidirect
14. #14771C2semidirect
15. #14155C2semidirect
17. #14024C2semidirect
18. #13848C2semidirect
19. #13786C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25472
C2×#25462
C2×#25452
C2×#26582
C2×#23672
#164692
#153512
#152942
#152432
#152172
#151902
#151802
#147712
#141552
#140272
#140242
#138482
#137862