Finite Group Databasebeta

← #873674

Subgroups — #873674

Order 512.

3748 conjugacy classes of subgroups.

The subgroup lattice has 985 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2538C211yesmaximal, characteristic, complemented
3C2×#2432C211yesmaximal, characteristic, complemented
4C2×#2407C211yesmaximal, characteristic
5#16549C214yesmaximal, complemented
6#15493C214yesmaximal, complemented
7#15439C214yesmaximal, complemented
8#15215C211yesmaximal, characteristic, complemented
9#15185C211yesmaximal, characteristic, complemented
10#15182C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic, complemented
12#15155C211yesmaximal, characteristic, complemented
13#15150C211yesmaximal, characteristic, complemented
14#14698C211yesmaximal, characteristic, complemented
15#14551C214yesmaximal, complemented
16#14026C211yesmaximal, characteristic, complemented
17#14024C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2857—28no—
31#2538—28no—
32#2432—28no—
33#2407—28no—
34C2×#399C2214yes—
35C2×#399C2214yes—
36C2×#397C2214yes—
37C2×#396C2212yes—
38C2×#396C2212yes—
39C2×#394C2214yes—
40C2×#394C2212yes—
41C2×#392C2212yes—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2212yes—
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389C2214yes—
54C2×#389C2212yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2214yes—
58C2×#385C2214yes—
59C2×#385C2212yes—
60C2×#384C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C2×#380C2214yes—
64C2×#380C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2211yescharacteristic
70#1445C2214yes—
71#1445C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1438C2214yes—
82#1437C2214yes—
83#1437C2214yes—
84#1437C2212yes—
85#1436C2214yes—
86#1436C2212yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C22⋊#95C2212yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—42no—
99C22×#41—42no—
100C22×#41—42no—
101C22×#41—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×D4C2311yescharacteristic
105C23×D4C2312yes—
106C23×D4C2311yescharacteristic
107C23×D4C2312yes—
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C2×C4⋊Q8—42no—
113C2×C4⋊Q8—42no—
114C2×C4⋊Q8D418yescomplemented
115C2×#124—24no—
116C2×#124—24no—
117C2×#124—42no—
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×C22⋊Q8—42no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8—42no—
127C2×#121—24no—
128C2×#121—24no—
129C2×#121—42no—
130C2×C4×Q8—24no—
131C2×C4×Q8—42no—
132C2×C4×Q8—42no—
133C2×C4×D4—42no—
134C2×C4×D4—42no—
135C2×C4×D4D418yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2311yescharacteristic
169C22×C42—24no—
170C22×C42—42no—
171C22×C42—42no—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2312yes—
178C22×C42C2312yes—
179#399—216no—
180#399—48no—
181#397—48no—
182#396—28no—
183#396—28no—
184#394—216no—
185#394—28no—
186#392—28no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—24no—
191#391—42no—
192#391—42no—
193#390—28no—
194#390—24no—
195#390—24no—
196#390—42no—
197#390—42no—
198#389—216no—
199#389—28no—
200#386—28no—
201#386—28no—
202#386—48no—
203#385—28no—
204#385—216no—
205#384—24no—
206#384—24no—
207#384—42no—
208#380—24no—
209#380—24no—
210#380—24no—
211#380—216no—
212C4×C22⋊C4—24no—
213C4×C22⋊C4—42no—
214C4×C22⋊C4—42no—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2312yes—
234C2×#95C2314yes—
235C2×#95C2312yes—
236C25C2411yescharacteristic
237C25C2412yes—
238C25C2411yescharacteristic
239C2×#41—416no—
240C2×#41—416no—
241C2×#41—416no—
242C2×#41—416no—
243C2×#41—416no—
244C2×#41—416no—
245C2×#41—416no—
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×Q8C2×D414yes—
259C22×Q8C2×D414yes—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—24no—
263C22×D4—24no—
264C22×D4—24no—
265C22×D4—28no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—24no—
269C22×D4—24no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—41no—
275C22×D4—41no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4—42no—
279C22×D4—42no—
280C22×D4—42no—
281C22×D4—44no—
282C22×D4C2×D414yes—
283C22×D4#4114yes—
284C23×C4—24no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—24no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—24no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4C2×D414yes—
311C23×C4C2×D414yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2411yescharacteristic
326C23×C4C2412yes—
327C23×C4C2411yescharacteristic
328C4⋊Q8—416no—
329#124—416no—
330C22⋊Q8—416no—
331C22⋊Q8—416no—
332C22⋊Q8—416no—
333#121—416no—
334C4×Q8—416no—
335C4×D4—416no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D4116yes—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—41no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4C2×D414yes—
427C2×C22⋊C4C2×D414yes—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—24no—
433C2×C42—22no—
434C2×C42—24no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—416no—
444C2×C42—42no—
445C2×C42—42no—
446C2×C42—42no—
447C2×C42—42no—
448C2×C42C2×D414yes—
449C2×C42C2×D414yes—
450#95—24no—
451#95—24no—
452#95—28no—
453#95—28no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—28no—
458#95—24no—
459#95—24no—
460#95—28no—
461#95—24no—
462#95—24no—
463#95—42no—
464#95—42no—
465#95—44no—
466#95—44no—
467#95—44no—
468#95—44no—
469#95—44no—
470#95#4118yescomplemented
471C24—21no—
472C24—22no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—21no—
478C24—21no—
479C24—22no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—24no—
484C24—22no—
485C24—21no—
486C24—22no—
487C24—24no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—24no—
497C24—22no—
498C24—22no—
499C24—24no—
500C24C22×D412yes—
501C24C22×D412yes—
502C24C2×#4114yes—
503C242−1+414yes—
504C24C2511yescharacteristic
505#41—4128no—
506C2×Q8—28no—
507C2×Q8—28no—
508C2×Q8—28no—
509C2×Q8—28no—
510C2×Q8—28no—
511C2×Q8—28no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×D4—28no—
521C2×D4—28no—
522C2×D4—28no—
523C2×D4—28no—
524C2×D4—28no—
525C2×D4—44no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—416no—
537C2×D4—48no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—84no—
543C2×D4—88no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—216no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—48no—
639C22×C4—48no—
640C22×C4—48no—
641C22×C4—48no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—48no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4C22×D414yes—
652C22×C4C22×D412yes—
653C22×C4C22×D412yes—
654C22×C4C22×D414yes—
655C22×C4C22×D412yes—
656C22×C4C22×D412yes—
657C22×C4C22×D414yes—
658C22×C4C22×D412yes—
659C22×C4C22×D412yes—
660C22×C4C2×#4114yes—
661C22×C4C2×#4114yes—
662C22×C4C2×#4114yes—
663C22×C4C2×#4112yes—
664C22×C4H(5,𝔽2)14yes—
665C22×C4H(5,𝔽2)12yes—
666C22×C4H(5,𝔽2)12yes—
667C22×C4H(5,𝔽2)12yes—
668C22×C4H(5,𝔽2)12yes—
669C22×C42−1+414yes—
670C4⋊C4—44no—
671C4⋊C4—416no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—48no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—416no—
683C4⋊C4—84no—
684C4⋊C4—88no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C22⋊C4—48no—
692C22⋊C4—48no—
693C22⋊C4—416no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C22⋊C4—416no—
697C22⋊C4—84no—
698C22⋊C4—88no—
699C22⋊C4—88no—
700C22⋊C4—84no—
701C22⋊C4—84no—
702C22⋊C4—84no—
703C42—28no—
704C42—28no—
705C42—48no—
706C42—48no—
707C42—44no—
708C42—44no—
709C42—44no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—24no—
715C23—22no—
716C23—22no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—22no—
727C23—24no—
728C23—24no—
729C23—22no—
730C23—28no—
731C23—22no—
732C23—22no—
733C23—28no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—41no—
748C23—42no—
749C23—41no—
750C23—42no—
751C23—41no—
752C23—42no—
753C23—44no—
754C23—42no—
755C23—42no—
756C23—44no—
757C23—42no—
758C23—42no—
759C23—44no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—42no—
768C23—42no—
769C23—41no—
770C23—44no—
771C23—44no—
772C23—42no—
773C23—42no—
774C23—44no—
775C23—42no—
776C23—42no—
777C23—44no—
778C23#53614yes—
779C23C23×D411yescharacteristic
780C23C23×D411yescharacteristic
781C23C22×#4112yes—
782C23C22×#4111yescharacteristic
783C23C2×H(5,𝔽2)11yescharacteristic
784C23C2×H(5,𝔽2)11yescharacteristic
785C23C2×H(5,𝔽2)11yescharacteristic
786C23C2×H(5,𝔽2)11yescharacteristic
787C23C2×H(5,𝔽2)12yes—
788C23C2×2−1+412yes—
789C23C2×2−1+412yes—
790Q8—416no—
791Q8—416no—
792D4—416no—
793D4—432no—
794D4—416no—
795D4—816no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—432no—
828C2×C4—432no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—416no—
856C2×C4—416no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—44no—
868C2×C4—42no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—42no—
888C2×C4—44no—
889C2×C4#53214yes—
890C2×C4#53414yes—
891C2×C4#53414yes—
892C2×C4#53814yes—
893C2×C4D4214yes—
894C2×C4#54614yes—
895C2×C4#54614yes—
896C2×C4#55018yes—
897C2×C4#56014yes—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—42no—
902C22—42no—
903C22—44no—
904C22—42no—
905C22—44no—
906C22—44no—
907C22—42no—
908C22—44no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—44no—
914C22—44no—
915C22—42no—
916C22—48no—
917C22—48no—
918C22—42no—
919C22—44no—
920C22—42no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22—84no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—84no—
931C22C2×#53211yescharacteristic
932C22C2×#53411yescharacteristic
933C22C2×#53411yescharacteristic
934C22C2×#53611yescharacteristic
935C22C2×#53811yescharacteristic
936C22C2×D4211yescharacteristic
937C22C2×#54611yescharacteristic
938C22C2×#54611yescharacteristic
939C22C2×#55012yes—
940C22#348212yes—
941C22#348612yes—
942C22#349811yescharacteristic
943C22#349911yescharacteristic
944C22#350812yes—
945C22#352012yes—
946C22#352012yes—
947C22#352012yes—
948C22#352012yes—
949C22C2×#56011yescharacteristic
950C22#353612yes—
951C22#353612yes—
952C22#354812yes—
953C22#355212yes—
954C4—24no—
955C4—28no—
956C4—44no—
957C4—42no—
958C4—42no—
959C4—44no—
960C4—44no—
961C4—42no—
962C4—44no—
963C4—82no—
964C4—82no—
965C4—82no—
966C4—82no—
967C4—82no—
968C4—82no—
969C4#266818yes—
970C2—44no—
971C2—82no—
972C2—84no—
973C2#3508511yescharacteristic
974C2#3612811yescharacteristic
975C2#3640611yescharacteristic
976C2#3729611yescharacteristic
977C2#3767511yescharacteristic
978C2#3807811yescharacteristic
979C2#3913312yes—
980C2#4007612yes—
981C2#4563212yes—
982C2C2×#266811yescharacteristic
983C2#5904012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2407C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2857C2semidirect
2. C2×#2538C2semidirect
3. C2×#2432C2semidirect
5. #16549C2semidirect
6. #15493C2semidirect
7. #15439C2semidirect
8. #15215C2semidirect
9. #15185C2semidirect
10. #15182C2semidirect
11. #15182C2semidirect
12. #15155C2semidirect
13. #15150C2semidirect
14. #14698C2semidirect
15. #14551C2semidirect
16. #14026C2semidirect
17. #14024C2semidirect
18. #13937C2semidirect
19. C4×#386C2semidirect
114. C2×C4⋊Q8D4semidirect
470. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25382
C2×#24322
C2×#24072
#165492
#154932
#154392
#152152
#151852
#151822
#151552
#151502
#146982
#145512
#140262
#140242
#139372
C4×#3862