Finite Group Databasebeta

← #616469

Subgroups — #616469

Order 512.

3566 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2857C211yesmaximal, characteristic, complemented
3C2×#2285C211yesmaximal, characteristic, complemented
4C2×C42×D4C211yesmaximal, characteristic
5#15221C212yesmaximal, complemented
6#15220C212yesmaximal, complemented
7#15183C212yesmaximal, complemented
8#15181C212yesmaximal
9#15179C212yesmaximal, complemented
10#15177C212yesmaximal
11#14714C211yesmaximal, characteristic, complemented
12#14712C211yesmaximal, characteristic, complemented
13#14686C211yesmaximal, characteristic, complemented
14#14045C212yesmaximal, complemented
15#14021C212yesmaximal, complemented
16#13997C212yesmaximal, complemented
17#13973C212yesmaximal, complemented
18#13951C212yesmaximal, complemented
19#13871C212yesmaximal
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2212yes—
22C22×C22⋊Q8C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×#117C2212yes—
27C23×C42C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2857—28no—
30#2857—28no—
31C2×#391C2212yes—
32C2×#391C2212yes—
33C2×#391C2212yes—
34C2×#391C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#389C2212yes—
42#2285—28no—
43C2×#384C2211yescharacteristic
44C2×#384C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#382C2212yes—
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C42×D4—28no—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C43C2211yescharacteristic
69#1445C2214yes—
70#1444C2214yes—
71#1443C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1441C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1436C2214yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C4⋊#95C2212yes—
88C4⋊#95C2212yes—
89C4⋊#95C2212yes—
90C4⋊#95C2212yes—
91C4⋊#95C2212yes—
92C4⋊#95C2212yes—
93C4⋊#95C2214yes—
94#1434C2214yes—
95C23×Q8C2312yes—
96C23×D4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C22⋊Q8—28no—
107C2×C22⋊Q8—28no—
108C2×C22⋊Q8—28no—
109C2×C22⋊Q8—44no—
110C2×C22⋊Q8—44no—
111C2×C22⋊Q8—44no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4Q818yescomplemented
121C2×#117—28no—
122C2×#117—28no—
123C2×#117—44no—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2314yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C42—24no—
152C22×C42—24no—
153C22×C42—24no—
154C22×C42—24no—
155C22×C42—24no—
156C22×C42D418yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2314yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171#391—28no—
172#391—28no—
173#391—28no—
174#391—44no—
175#389—28no—
176#389—28no—
177#389—28no—
178#389—28no—
179#389—28no—
180#389—44no—
181#389—44no—
182#384—24no—
183#384—24no—
184#384D418yescomplemented
185#382—28no—
186#380—28no—
187#380—28no—
188#380—28no—
189#380—28no—
190#380—28no—
191#380—28no—
192#380—28no—
193#380—44no—
194#380—44no—
195C4×C4⋊C4—28no—
196C4×C4⋊C4—28no—
197C4×C4⋊C4—24no—
198C4×C4⋊C4—24no—
199C4×C4⋊C4—24no—
200C4×C22⋊C4—24no—
201C4×C22⋊C4—24no—
202C4×C22⋊C4—24no—
203C4×C22⋊C4—24no—
204C4×C22⋊C4—24no—
205C4×C22⋊C4—24no—
206C2×#95C2311yescharacteristic
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2311yescharacteristic
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C43—24no—
229C25C2411yescharacteristic
230C25C2411yescharacteristic
231C22×Q8—24no—
232C22×Q8—24no—
233C22×Q8—24no—
234C22×Q8—24no—
235C22×Q8—24no—
236C22×Q8—24no—
237C22×Q8—24no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4C2×Q814yes—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
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—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×Q814yes—
283C23×C4C2×Q814yes—
284C23×C4#4114yes—
285C23×C4#4114yes—
286C23×C4#4114yes—
287C23×C4C2414yes—
288C23×C4C2414yes—
289C23×C4C2414yes—
290C23×C4C2414yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C4⋊Q8—416no—
305C22⋊Q8—432no—
306C22⋊Q8—432no—
307C4×D4—232no—
308C4×D4—232no—
309C4×D4—232no—
310#117—432no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
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—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4C2×D418yes—
359C2×C4⋊C4C2×D418yes—
360C2×C4⋊C4C2×D418yes—
361C2×C4⋊C4C2×Q814yes—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4C2×Q814yes—
391C2×C22⋊C4C2×Q814yes—
392C2×C42—22no—
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—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—232no—
405C2×C42—28no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—28no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—44no—
426C2×C42—416no—
427C2×C42C2×D414yes—
428C2×C42C2×D414yes—
429C2×C42C2×D414yes—
430C2×C42C2×D414yes—
431C2×C42C2×D414yes—
432C2×C42C2×Q814yes—
433C2×C42#4114yes—
434C2×C42#4114yes—
435C2×C42#4114yes—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—28no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—44no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95—44no—
457#95—44no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24C22×D412yes—
483C24C22×Q812yes—
484C24C22×Q812yes—
485C24C2×#4112yes—
486C24C2×#4112yes—
487C24C2×#4112yes—
488C24C2511yescharacteristic
489C2×Q8—48no—
490C2×Q8—48no—
491C2×Q8—48no—
492C2×Q8—48no—
493C2×Q8—48no—
494C2×Q8—48no—
495C2×Q8—48no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—28no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4C22⋊Q8116yescomplemented
628C22×C4C22×D412yes—
629C22×C4C22×D418yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×D412yes—
636C22×C4C22×D412yes—
637C22×C4C22×D412yes—
638C22×C4C22×Q812yes—
639C22×C4C22×Q812yes—
640C22×C4C22×Q812yes—
641C22×C4C22×Q812yes—
642C22×C4C22×Q812yes—
643C22×C4C2×#4112yes—
644C22×C4C2×#4112yes—
645C22×C4C2×#4112yes—
646C22×C4C2×#4112yes—
647C22×C4C2×#4112yes—
648C22×C4C2×#4112yes—
649C22×C4C2×#4112yes—
650C22×C4C2×#4112yes—
651C22×C4C2×#4112yes—
652C22×C4C2×#4112yes—
653C22×C4C2×#4112yes—
654C22×C4C2×#4112yes—
655C22×C4C2×#4112yes—
656C22×C4C2×#4112yes—
657C22×C4C2×#4112yes—
658C22×C4H(5,𝔽2)12yes—
659C22×C4H(5,𝔽2)12yes—
660C22×C4H(5,𝔽2)12yes—
661C22×C42−1+412yes—
662C22×C42−1+412yes—
663C22×C42−1+412yes—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—28no—
667C4⋊C4—216no—
668C4⋊C4—216no—
669C4⋊C4—216no—
670C4⋊C4—416no—
671C4⋊C4—416no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—48no—
677C4⋊C4—48no—
678C4⋊C4—48no—
679C4⋊C4—48no—
680C4⋊C4—88no—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—416no—
688C22⋊C4—416no—
689C22⋊C4—416no—
690C22⋊C4—88no—
691C42—28no—
692C42—28no—
693C42—28no—
694C42—28no—
695C42—28no—
696C42—28no—
697C42—416no—
698C42—44no—
699C42—44no—
700C42—44no—
701C42—44no—
702C42—44no—
703C42—44no—
704C42#121116yes—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23C2×C22⋊Q814yes—
774C23#53314yes—
775C23C23×D411yescharacteristic
776C23C23×D411yescharacteristic
777C23C23×Q811yescharacteristic
778C23C22×#4111yescharacteristic
779C23C22×#4111yescharacteristic
780C23C22×#4111yescharacteristic
781C23C22×#4111yescharacteristic
782C23C22×#4111yescharacteristic
783C23C22×#4111yescharacteristic
784C23C2×H(5,𝔽2)11yescharacteristic
785C23C2×H(5,𝔽2)11yescharacteristic
786C23C2×H(5,𝔽2)11yescharacteristic
787C23C2×2−1+411yescharacteristic
788C23C2×2−1+411yescharacteristic
789C23C2×2−1+411yescharacteristic
790Q8—816no—
791D4—232no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—232no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—22no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—44no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—44no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—416no—
869C2×C4—416no—
870C2×C4—416no—
871C2×C4—416no—
872C2×C4—416no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4C2×#12114yes—
895C2×C4C2×#12114yes—
896C2×C4C2×#12114yes—
897C2×C4C2×C22⋊Q814yes—
898C2×C4C2×C22⋊Q814yes—
899C2×C4#52514yes—
900C2×C4#52514yes—
901C2×C4#53314yes—
902C2×C4#53514yes—
903C2×C4#53614yes—
904C2×C4#53714yes—
905C2×C4#54614yes—
906C2×C4#54614yes—
907C2×C4#54714yes—
908C2×C4#54814yes—
909C2×C4D4×Q814yes—
910C2×C4#55014yes—
911C2×C4#55214yes—
912C2×C4#55214yes—
913C2×C4#55314yes—
914C2×C4#55414yes—
915C2×C4#55514yes—
916C2×C4#55614yes—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—24no—
921C22—24no—
922C22—24no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22C22×#12111yescharacteristic
948C22C22×C22⋊Q811yescharacteristic
949C22C2×#52511yescharacteristic
950C22C2×#52511yescharacteristic
951C22C2×#53311yescharacteristic
952C22C2×#53311yescharacteristic
953C22#344411yescharacteristic
954C22#344411yescharacteristic
955C22C2×#53511yescharacteristic
956C22C2×#53611yescharacteristic
957C22C2×#53711yescharacteristic
958C22C2×#54611yescharacteristic
959C22C2×#54611yescharacteristic
960C22C2×#54711yescharacteristic
961C22C2×#54811yescharacteristic
962C22C2×D4×Q811yescharacteristic
963C22C2×#55011yescharacteristic
964C22C2×#55211yescharacteristic
965C22C2×#55211yescharacteristic
966C22C2×#55311yescharacteristic
967C22C2×#55411yescharacteristic
968C22C2×#55511yescharacteristic
969C22C2×#55611yescharacteristic
970C22#350311yescharacteristic
971C22#350311yescharacteristic
972C22#350811yescharacteristic
973C22#350811yescharacteristic
974C22#350911yescharacteristic
975C22#350911yescharacteristic
976C22#351111yescharacteristic
977C22#351111yescharacteristic
978C22#351111yescharacteristic
979C22#351111yescharacteristic
980C22#351111yescharacteristic
981C22#351111yescharacteristic
982C4—24no—
983C4—24no—
984C4—48no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—84no—
994C4—84no—
995C4—84no—
996C4#241418yes—
997C4#241518yes—
998C4#241718yes—
999C2—44no—
1000C2—44no—
1001C2C2×#241711yescharacteristic
1002C2C2×#241411yescharacteristic
1003C2C2×#241511yescharacteristic
1004C2#3527911yescharacteristic
1005C2#3529211yescharacteristic
1006C2#3529711yescharacteristic
1007C2#3612911yescharacteristic
1008C2#3613411yescharacteristic
1009C2#3614911yescharacteristic
1010C2#3615011yescharacteristic
1011C2#3618911yescharacteristic
1012C2#3619411yescharacteristic
1013C2#3620911yescharacteristic
1014C2#3621011yescharacteristic
1015C2#3662511yescharacteristic
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
1. C2×#2857C2semidirect
2. C2×#2857C2semidirect
3. C2×#2285C2semidirect
5. #15221C2semidirect
6. #15220C2semidirect
7. #15183C2semidirect
9. #15179C2semidirect
11. #14714C2semidirect
12. #14712C2semidirect
13. #14686C2semidirect
14. #14045C2semidirect
15. #14021C2semidirect
16. #13997C2semidirect
17. #13973C2semidirect
18. #13951C2semidirect
120. C2×C4×D4Q8semidirect
184. #384D4semidirect
627. C22×C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#22852
C2×C42×D42
#152212
#152202
#151832
#151812
#151792
#151772
#147142
#147122
#146862
#140452
#140212
#139972
#139732
#139512
#138712