Finite Group Databasebeta

← #617000

Subgroups — #617000

Order 512.

5144 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#536C211yesmaximal, characteristic
2C2×#2857C211yesmaximal, characteristic, complemented
3C2×#2434C211yesmaximal, characteristic, complemented
4C2×#2621C211yesmaximal, characteristic, complemented
5C2×#2616C211yesmaximal, characteristic
6C2×#2297C211yesmaximal, characteristic
7#15318C214yesmaximal, complemented
8#15311C214yesmaximal, complemented
9#15271C214yesmaximal, complemented
10#15269C214yesmaximal, complemented
11#15236C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic, complemented
13#15178C211yesmaximal, characteristic, complemented
14#15178C211yesmaximal, characteristic, complemented
15#14702C211yesmaximal, characteristic, complemented
16#14258C211yesmaximal, characteristic, complemented
17#14138C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic, complemented
19#13879C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C24×Q8C2211yescharacteristic
22C2×#536—28no—
23C2×#536—28no—
24C2×#536—28no—
25C22×C4⋊Q8C2212yes—
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C22×#124C2212yes—
29C22×#123C2212yes—
30C22×#123C2212yes—
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C22×C22⋊Q8C2211yescharacteristic
37C22×C22⋊Q8C2211yescharacteristic
38C22×#117C2211yescharacteristic
39C22×#117C2211yescharacteristic
40C23×C42C2211yescharacteristic
41#2857—28no—
42#2621—28no—
43#2616—28no—
44#2434—28no—
45C2×#398C2214yes—
46C2×#397C2214yes—
47C2×#395C2212yes—
48C2×#395C2214yes—
49C2×#394C2212yes—
50C2×#394C2212yes—
51C2×#394C2212yes—
52#2297—28no—
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#391C2211yescharacteristic
59C2×#391C2212yes—
60C2×#391C2211yescharacteristic
61C2×#391C2211yescharacteristic
62C2×#390C2212yes—
63C2×#389C2214yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#385C2214yes—
67C2×#384C2211yescharacteristic
68C2×#382C2211yescharacteristic
69C2×#380C2214yes—
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77#1446C2214yes—
78#1444C2214yes—
79#1444C2214yes—
80#1442C2214yes—
81#1441C2214yes—
82#1441C2214yes—
83#1440C2214yes—
84#1440C2214yes—
85#1440C2214yes—
86#1439C2214yes—
87#1439C2214yes—
88#1439C2214yes—
89#1439C2214yes—
90#1436C2214yes—
91#1436C2214yes—
92#1436C2214yes—
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96C4⋊#95C2211yescharacteristic
97C22⋊#95C2214yes—
98C22⋊#95C2214yes—
99C22×#41—24no—
100C22×#41—24no—
101C22×#41—24no—
102C22×#41—24no—
103C22×#41—42no—
104C22×#41—42no—
105C22×#41D418yes—
106C23×Q8—24no—
107C23×Q8—24no—
108C23×Q8—24no—
109C23×Q8—24no—
110C23×Q8—24no—
111C23×Q8—42no—
112C23×Q8—42no—
113C23×Q8C2311yescharacteristic
114C23×Q8C2311yescharacteristic
115C23×Q8C2311yescharacteristic
116C23×Q8C2312yes—
117C23×Q8C2311yescharacteristic
118C23×D4C2311yescharacteristic
119C23×D4C2311yescharacteristic
120C23×D4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C24×C4C2312yes—
123C24×C4C2312yes—
124C24×C4C2311yescharacteristic
125C24×C4C2311yescharacteristic
126#536—2128no—
127C2×C4⋊Q8—28no—
128C2×C4⋊Q8—24no—
129C2×C4⋊Q8—24no—
130C2×C4⋊Q8—28no—
131C2×C4⋊Q8—28no—
132C2×C4⋊Q8—24no—
133C2×C4⋊Q8—24no—
134C2×C4⋊Q8—42no—
135C2×C4⋊Q8—42no—
136C2×#124—28no—
137C2×#124—28no—
138C2×#124—28no—
139C2×#123—28no—
140C2×#123—28no—
141C2×#123—28no—
142C2×#123—28no—
143C2×#123—28no—
144C2×#123—28no—
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—24no—
151C2×C22⋊Q8—24no—
152C2×C22⋊Q8—24no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—24no—
156C2×C22⋊Q8—24no—
157C2×C22⋊Q8—24no—
158C2×C22⋊Q8—24no—
159C2×C22⋊Q8—24no—
160C2×C22⋊Q8—24no—
161C2×C22⋊Q8—24no—
162C2×C22⋊Q8—42no—
163C2×C22⋊Q8—42no—
164C2×C22⋊Q8D418yes—
165C2×C22⋊Q8D418yes—
166C2×#117—24no—
167C2×#117—24no—
168C2×#117—24no—
169C2×#117—24no—
170C2×#117—24no—
171C2×#117—42no—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2314yes—
180C22×C4⋊C4C2314yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2314yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C42—24no—
205C22×C42—24no—
206C22×C42—42no—
207C22×C42C2311yescharacteristic
208C22×C42C2312yes—
209C22×C42C2311yescharacteristic
210C22×C42C2312yes—
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213#398—216no—
214#397—216no—
215#395—28no—
216#395—216no—
217#394—28no—
218#394—28no—
219#394—28no—
220#391—24no—
221#391—24no—
222#391—24no—
223#391—24no—
224#391—24no—
225#391—24no—
226#391—28no—
227#391—42no—
228#391—42no—
229#390—28no—
230#389—216no—
231#386—28no—
232#386—28no—
233#385—216no—
234#384—24no—
235#382—24no—
236#380—24no—
237#380—24no—
238#380—24no—
239#380—216no—
240C4×C22⋊C4—24no—
241C4×C22⋊C4—24no—
242C4×C22⋊C4—24no—
243C4×C22⋊C4D418yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2314yes—
248C2×#95C2314yes—
249C2×#95C2314yes—
250C2×#95C2314yes—
251C2×#95C2314yes—
252C2×#95C2314yes—
253C2×#95C2314yes—
254C2×#95C2314yes—
255C2×#95C2312yes—
256C2×#95C2314yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2314yes—
260C2×#95C2314yes—
261C2×#95C2314yes—
262C2×#95C2314yes—
263C2×#95C2312yes—
264C25C2411yescharacteristic
265C25C2411yescharacteristic
266C25C2411yescharacteristic
267C2×#41—232no—
268C2×#41—232no—
269C2×#41—416no—
270C2×#41—416no—
271C2×#41—416no—
272C2×#41—416no—
273C2×#41—416no—
274C22×Q8—232no—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8—24no—
280C22×Q8—24no—
281C22×Q8—24no—
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8—22no—
285C22×Q8—22no—
286C22×Q8—22no—
287C22×Q8—22no—
288C22×Q8—22no—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8—24no—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8—24no—
297C22×Q8—22no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—22no—
303C22×Q8—42no—
304C22×Q8—42no—
305C22×Q8—41no—
306C22×Q8—41no—
307C22×Q8—416no—
308C22×Q8—416no—
309C22×Q8—416no—
310C22×Q8—416no—
311C22×Q8—416no—
312C22×Q8—416no—
313C22×Q8C2×D414yes—
314C22×Q8C2×D414yes—
315C22×Q8C2×D414yes—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4—41no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4—41no—
334C22×D4C2×D414yes—
335C22×D4C2×D414yes—
336C22×D4C2×D414yes—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—24no—
350C23×C4—24no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—42no—
362C23×C4—42no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4C2×D414yes—
366C23×C4C2×D414yes—
367C23×C4C2×D414yes—
368C23×C4C2×D414yes—
369C23×C4C2×D414yes—
370C23×C4C2×D414yes—
371C23×C4#4114yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2412yes—
382C23×C4C2411yescharacteristic
383C23×C4C2412yes—
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2412yes—
387C23×C4C2411yescharacteristic
388C4⋊Q8—264no—
389C4⋊Q8—416no—
390C4⋊Q8—416no—
391#124—264no—
392#123—264no—
393#123—264no—
394C22⋊Q8—232no—
395C22⋊Q8—232no—
396C22⋊Q8—232no—
397C22⋊Q8—232no—
398C22⋊Q8—416no—
399C22⋊Q8—416no—
400C22⋊Q8—416no—
401#117—232no—
402#117—416no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—28no—
432C2×C4⋊C4—28no—
433C2×C4⋊C4—28no—
434C2×C4⋊C4—28no—
435C2×C4⋊C4—28no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—28no—
441C2×C4⋊C4—44no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—44no—
446C2×C4⋊C4—44no—
447C2×C4⋊C4C2×D414yes—
448C2×C4⋊C4C2×D414yes—
449C2×C4⋊C4C2×D418yes—
450C2×C4⋊C4C2×D418yes—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—44no—
491C2×C22⋊C4—44no—
492C2×C22⋊C4—44no—
493C2×C22⋊C4C2×D418yes—
494C2×C22⋊C4C2×D418yes—
495C2×C22⋊C4C2×D418yes—
496C2×C42—24no—
497C2×C42—24no—
498C2×C42—24no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—24no—
507C2×C42—24no—
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—416no—
512C2×C42—42no—
513C2×C42C2×D414yes—
514C2×C42C2×D414yes—
515#95—24no—
516#95—24no—
517#95—24no—
518#95—28no—
519#95—28no—
520#95—24no—
521#95—24no—
522#95—24no—
523#95—28no—
524#95—28no—
525#95—28no—
526#95—28no—
527#95—28no—
528#95—28no—
529#95—28no—
530#95—44no—
531#95—44no—
532#95—44no—
533#95—44no—
534#95C2×D418yes—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—21no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24C22×D412yes—
562C24C22×D412yes—
563C24C22×D412yes—
564C24C22×D412yes—
565C24C22×D412yes—
566C24C22×D412yes—
567C24C2×#4112yes—
568C24C2511yescharacteristic
569#41—4128no—
570C2×Q8—216no—
571C2×Q8—28no—
572C2×Q8—28no—
573C2×Q8—28no—
574C2×Q8—28no—
575C2×Q8—28no—
576C2×Q8—28no—
577C2×Q8—28no—
578C2×Q8—28no—
579C2×Q8—44no—
580C2×Q8—48no—
581C2×Q8—48no—
582C2×Q8—48no—
583C2×Q8—48no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8—48no—
589C2×Q8—4128no—
590C2×Q8—44no—
591C2×Q8—48no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—44no—
595C2×Q8—44no—
596C2×Q8—44no—
597C2×Q8—44no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×Q8—44no—
603C2×Q8—44no—
604C2×Q8—44no—
605C2×Q8—44no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—44no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—28no—
640C22×C4—28no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—216no—
652C22×C4—216no—
653C22×C4—22no—
654C22×C4—21no—
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—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—24no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—24no—
690C22×C4—22no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—28no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—24no—
719C22×C4—22no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—48no—
724C22×C4—48no—
725C22×C4—48no—
726C22×C4—48no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—48no—
733C22×C4—48no—
734C22×C4—48no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4#120116yes—
740C22×C4#121116yes—
741C22×C4C22×D414yes—
742C22×C4C22×D414yes—
743C22×C4C22×D414yes—
744C22×C4C22×D414yes—
745C22×C4C22×D414yes—
746C22×C4C22×D412yes—
747C22×C4C22×D412yes—
748C22×C4C22×D412yes—
749C22×C4C22×D412yes—
750C22×C4C22×D412yes—
751C22×C4C22×D412yes—
752C22×C4C22×D414yes—
753C22×C4C22×D412yes—
754C22×C4C22×D412yes—
755C22×C4C22×D412yes—
756C22×C4C22×D412yes—
757C22×C4C2×#4112yes—
758C22×C4C2×#4112yes—
759C22×C4H(5,𝔽2)12yes—
760C22×C4H(5,𝔽2)12yes—
761C22×C42−1+414yes—
762C22×C42−1+414yes—
763C22×C42−1+414yes—
764C4⋊C4—216no—
765C4⋊C4—216no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—216no—
769C4⋊C4—216no—
770C4⋊C4—416no—
771C4⋊C4—48no—
772C4⋊C4—416no—
773C4⋊C4—416no—
774C4⋊C4—48no—
775C4⋊C4—44no—
776C4⋊C4—48no—
777C4⋊C4—44no—
778C4⋊C4—48no—
779C4⋊C4—44no—
780C22⋊C4—216no—
781C22⋊C4—216no—
782C22⋊C4—216no—
783C22⋊C4—216no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—84no—
794C22⋊C4—84no—
795C22⋊C4—84no—
796C42—216no—
797C42—28no—
798C42—28no—
799C42—48no—
800C42—44no—
801C42—44no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—24no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—22no—
821C23—22no—
822C23—24no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23C2×#12014yes—
870C23C2×#12114yes—
871C23C23×D411yescharacteristic
872C23C23×D411yescharacteristic
873C23C23×D411yescharacteristic
874C23C23×D411yescharacteristic
875C23C22×#4111yescharacteristic
876C23C2×H(5,𝔽2)11yescharacteristic
877C23C2×H(5,𝔽2)11yescharacteristic
878C23C2×2−1+412yes—
879C23C2×2−1+412yes—
880C23C2×2−1+412yes—
881C23#58512yes—
882Q8—416no—
883Q8—432no—
884Q8—416no—
885Q8—416no—
886Q8—88no—
887D4—416no—
888D4—416no—
889D4—416no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—232no—
909C2×C4—232no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—28no—
927C2×C4—28no—
928C2×C4—24no—
929C2×C4—432no—
930C2×C4—432no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—44no—
946C2×C4—42no—
947C2×C4—44no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—416no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—44no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—44no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—44no—
984C2×C4—44no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4C2×#12014yes—
988C2×C4C2×#12014yes—
989C2×C4C2×#12114yes—
990C2×C4C2×#12114yes—
991C2×C4#53414yes—
992C2×C4#53618yescomplemented
993C2×C4D4214yes—
994C2×C4D4214yes—
995C2×C4#54614yes—
996C2×C4#54614yes—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—42no—
1004C22—42no—
1005C22—44no—
1006C22—44no—
1007C22—42no—
1008C22—42no—
1009C22—44no—
1010C22—44no—
1011C22—42no—
1012C22—42no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—82no—
1027C22—82no—
1028C22—82no—
1029C22—82no—
1030C22C22×#12011yescharacteristic
1031C22C22×#12111yescharacteristic
1032C22C2×#53411yescharacteristic
1033C22C2×#53612yes—
1034C22#346112yes—
1035C22C2×D4211yescharacteristic
1036C22C2×D4211yescharacteristic
1037C22C2×#54611yescharacteristic
1038C22C2×#54611yescharacteristic
1039C22#348612yes—
1040C22#348912yes—
1041C22#348912yes—
1042C22#349712yes—
1043C22#349911yescharacteristic
1044C22#349911yescharacteristic
1045C22#349912yes—
1046C22#349911yescharacteristic
1047C22#350011yescharacteristic
1048C22#350912yes—
1049C22#353812yes—
1050C22#354112yes—
1051C22#354712yes—
1052C22#355012yes—
1053C4—28no—
1054C4—24no—
1055C4—24no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4—42no—
1060C4—44no—
1061C4—44no—
1062C4—44no—
1063C4—82no—
1064C4—82no—
1065C4—82no—
1066C4—82no—
1067C4—82no—
1068C4#241018yes—
1069C2—44no—
1070C2—44no—
1071C2—82no—
1072C2C2×#241011yescharacteristic
1073C2#3530811yescharacteristic
1074C2#3531611yescharacteristic
1075C2#3566011yescharacteristic
1076C2#3566611yescharacteristic
1077C2#3738611yescharacteristic
1078C2#3738811yescharacteristic
1079C2#3765112yes—
1080C2#3778312yes—
1081C2#3934312yes—
1082C2#3943512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
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×#2857C2semidirect
3. C2×#2434C2semidirect
4. C2×#2621C2semidirect
7. #15318C2semidirect
8. #15311C2semidirect
9. #15271C2semidirect
10. #15269C2semidirect
11. #15236C2semidirect
12. #15182C2semidirect
13. #15178C2semidirect
14. #15178C2semidirect
15. #14702C2semidirect
16. #14258C2semidirect
17. #14138C2semidirect
18. #13922C2semidirect
19. #13879C2semidirect
992. C2×C4#536semidirect

Maximal subgroups

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

subgroupindex
C22×#5362
C2×#28572
C2×#24342
C2×#26212
C2×#26162
C2×#22972
#153182
#153112
#152712
#152692
#152362
#151822
#151782
#147022
#142582
#141382
#139222
#138792