Finite Group Databasebeta

← #4457658

Subgroups — #4457658

Order 512.

3688 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#542C211yesmaximal, characteristic
2C2×#2565C211yesmaximal, characteristic, complemented
3C2×#2566C211yesmaximal, characteristic, complemented
4C2×#2629C211yesmaximal, characteristic, complemented
5#16659C214yesmaximal, complemented
6#16505C214yesmaximal, complemented
7#16264C214yesmaximal, complemented
8#16257C214yesmaximal, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15230C211yesmaximal, characteristic, complemented
11#15226C211yesmaximal, characteristic, complemented
12#15226C211yesmaximal, characteristic, complemented
13#15219C211yesmaximal, characteristic
14#15182C211yesmaximal, characteristic, complemented
15#15143C211yesmaximal, characteristic, complemented
16#15130C211yesmaximal, characteristic
17#13926C211yesmaximal, characteristic, complemented
18#13906C211yesmaximal, characteristic, complemented
19#13852C211yesmaximal, characteristic, complemented
20C2×#542—28no—
21C2×#542—28no—
22C2×#542—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#126C2212yes—
25C22×#125C2211yescharacteristic
26C22×#124C2212yes—
27C22×#124C2211yescharacteristic
28C22×#123C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2212yes—
31C22×#121C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#2629—28no—
36#2566—28no—
37#2565—28no—
38C2×#398C2212yes—
39C2×#398C2212yes—
40C2×#398C2214yes—
41C2×#396C2214yes—
42C2×#396C2212yes—
43C2×#396C2212yes—
44C2×#395C2214yes—
45C2×#394C2214yes—
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#387C2214yes—
57C2×#385C2214yes—
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C2×#382C2211yescharacteristic
62C2×#382C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×#380C2214yes—
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2211yescharacteristic
70#1446C2214yes—
71#1444C2214yes—
72#1442C2214yes—
73#1441C2212yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2212yes—
77#1441C2214yes—
78#1440C2214yes—
79#1440C2214yes—
80#1440C2214yes—
81#1440C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2214yes—
88#1439C2214yes—
89#1438C2214yes—
90C4⋊#95C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2312yes—
99C23×D4C2311yescharacteristic
100C23×D4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103#542—2128no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×#126—28no—
108C2×#126—28no—
109C2×#126—28no—
110C2×#125—24no—
111C2×#125—24no—
112C2×#125—24no—
113C2×#124—24no—
114C2×#124—24no—
115C2×#124—28no—
116C2×#124—28no—
117C2×#124—24no—
118C2×#124—28no—
119C2×#123—28no—
120C2×#123—28no—
121C2×#123—28no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—28no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—28no—
126C2×C22⋊Q8—28no—
127C2×C22⋊Q8—24no—
128C2×#121—24no—
129C2×#121—24no—
130C2×#121—24no—
131C2×C4×Q8—24no—
132C2×C4×Q8—24no—
133C2×C4×Q8D418yes—
134C2×C4×D4—24no—
135C2×C4×D4—24no—
136C2×C4×D4D418yes—
137C2×#117—24no—
138C2×#117—24no—
139C2×#117D418yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2314yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2314yes—
172C22×C22⋊C4C2314yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2314yes—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2311yescharacteristic
181C22×C42C2312yes—
182C22×C42C2311yescharacteristic
183#398—216no—
184#398—28no—
185#398—28no—
186#396—216no—
187#396—28no—
188#396—28no—
189#395—48no—
190#394—48no—
191#391—24no—
192#391—24no—
193#391—42no—
194#391—42no—
195#390—24no—
196#390—24no—
197#390—42no—
198#390—42no—
199#389—24no—
200#389—24no—
201#387—216no—
202#385—216no—
203#384—24no—
204#384—24no—
205#384—24no—
206#382—24no—
207#382—24no—
208#380—24no—
209#380—24no—
210#380—48no—
211C4×C4⋊C4—24no—
212C4×C4⋊C4—24no—
213C4×C22⋊C4—42no—
214C4×C22⋊C4—42no—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C25C2412yes—
238C25C2411yescharacteristic
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—24no—
242C22×Q8—24no—
243C22×Q8—24no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—44no—
249C22×Q8—44no—
250C22×Q8C2×D414yes—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—24no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4C2×D414yes—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4C2×D414yes—
274C23×C4C2×D418yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C4⋊Q8—232no—
293#126—264no—
294#125—416no—
295#124—232no—
296#124—264no—
297#123—264no—
298C22⋊Q8—264no—
299C22⋊Q8—232no—
300#121—232no—
301C4×Q8—232no—
302C4×D4—232no—
303#117—232no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
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—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
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—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4C2×D414yes—
359C2×C4⋊C4C2×D414yes—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D418yes—
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—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4C2×D414yes—
404C2×C22⋊C4C2×D414yes—
405C2×C22⋊C4C2×D418yes—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42C2×D414yes—
423C2×C42C2×D418yes—
424C2×C42C2×D414yes—
425C2×C42C2×D414yes—
426C2×C42C2×D414yes—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—28no—
432#95—28no—
433#95—28no—
434#95—28no—
435#95—24no—
436#95—24no—
437#95—28no—
438#95—24no—
439#95—24no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—44no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—44no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—24no—
454C24—22no—
455C24—21no—
456C24—22no—
457C24—24no—
458C24—22no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—24no—
466C24—22no—
467C24—24no—
468C24—22no—
469C24C22×D414yes—
470C24C22×D412yes—
471C24C2511yescharacteristic
472C2×Q8—216no—
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—88no—
481C2×Q8—88no—
482C2×Q8—84no—
483C2×Q8—84no—
484C2×D4—216no—
485C2×D4—28no—
486C2×D4—28no—
487C2×D4—28no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—88no—
493C2×D4—88no—
494C2×D4—84no—
495C2×D4—84no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
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—24no—
539C22×C4—24no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—216no—
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—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—416no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—88no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4C22×D414yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D414yes—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4H(5,𝔽2)14yes—
602C22×C4H(5,𝔽2)12yes—
603C22×C42−1+414yes—
604C22×C42−1+412yes—
605C22×C42−1+412yes—
606C22×C42−1+412yes—
607C4⋊C4—216no—
608C4⋊C4—216no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—216no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—416no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—88no—
626C4⋊C4—84no—
627C4⋊C4—84no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—216no—
635C22⋊C4—416no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—88no—
639C22⋊C4—88no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—88no—
643C42—28no—
644C42—216no—
645C42—44no—
646C42—44no—
647C42—44no—
648C42—44no—
649C42#120116yes—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—28no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—44no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—44no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—44no—
682C23—42no—
683C23—44no—
684C23—42no—
685C23—44no—
686C23—42no—
687C23—44no—
688C23—42no—
689C23—44no—
690C23—42no—
691C23—44no—
692C23—42no—
693C23—42no—
694C23—44no—
695C23—44no—
696C23C23×D411yescharacteristic
697C23C23×D411yescharacteristic
698C23C23×D411yescharacteristic
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×H(5,𝔽2)12yes—
701C23C2×2−1+411yescharacteristic
702C23C2×2−1+411yescharacteristic
703C23C2×2−1+411yescharacteristic
704C23C2×2−1+412yes—
705C23#58512yes—
706C23#58512yes—
707Q8—416no—
708Q8—816no—
709D4—416no—
710D4—816no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—24no—
732C2×C4—28no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
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—416no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—816no—
803C2×C4C2×#12014yes—
804C2×C4C2×#12014yes—
805C2×C4C2×#12014yes—
806C2×C4#53614yes—
807C2×C4#53614yes—
808C2×C4#53614yes—
809C2×C4#53714yes—
810C2×C4#53714yes—
811C2×C4#53714yes—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—44no—
816C22—44no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—44no—
821C22—42no—
822C22—48no—
823C22—48no—
824C22—82no—
825C22—82no—
826C22—84no—
827C22—82no—
828C22—82no—
829C22—84no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22C22×#12011yescharacteristic
835C22C2×#53611yescharacteristic
836C22C2×#53611yescharacteristic
837C22C2×#53611yescharacteristic
838C22C2×#53711yescharacteristic
839C22C2×#53711yescharacteristic
840C22C2×#53711yescharacteristic
841C22#348812yes—
842C22#348912yes—
843C22#349612yes—
844C22#349712yes—
845C22#349811yescharacteristic
846C22#349911yescharacteristic
847C22#350011yescharacteristic
848C22#350011yescharacteristic
849C22#354112yes—
850C22#354212yes—
851C22#354412yes—
852C22#355212yes—
853C22#355412yes—
854C22#355512yes—
855C22#356512yes—
856C22#356512yes—
857C4—24no—
858C4—24no—
859C4—44no—
860C4—42no—
861C4—44no—
862C4—42no—
863C4—44no—
864C4—44no—
865C4—42no—
866C4—44no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4#261618yes—
874C2—82no—
875C2—84no—
876C2C2×#261611yescharacteristic
877C2#3551311yescharacteristic
878C2#3566011yescharacteristic
879C2#3730111yescharacteristic
880C2#3730311yescharacteristic
881C2#3738911yescharacteristic
882C2#3742311yescharacteristic
883C2#4244012yes—
884C2#4244212yes—
885C2#4279812yes—
886C2#4280412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2565C2semidirect
3. C2×#2566C2semidirect
4. C2×#2629C2semidirect
5. #16659C2semidirect
6. #16505C2semidirect
7. #16264C2semidirect
8. #16257C2semidirect
9. #15236C2semidirect
10. #15230C2semidirect
11. #15226C2semidirect
12. #15226C2semidirect
14. #15182C2semidirect
15. #15143C2semidirect
17. #13926C2semidirect
18. #13906C2semidirect
19. #13852C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5422
C2×#25652
C2×#25662
C2×#26292
#166592
#165052
#162642
#162572
#152362
#152302
#152262
#152192
#151822
#151432
#151302
#139262
#139062
#138522