Finite Group Databasebeta

← #612646

Subgroups — #612646

Order 512.

4346 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2499C211yesmaximal, characteristic, complemented
3C2×#2280C211yesmaximal, characteristic
4C22×C4×C22⋊C4C211yesmaximal, characteristic
5#15236C211yesmaximal, characteristic, complemented
6#15233C211yesmaximal, characteristic, complemented
7#15182C211yesmaximal, characteristic, complemented
8#15150C211yesmaximal, characteristic, complemented
9#14837C214yesmaximal, complemented
10#14820C214yesmaximal
11#14702C211yesmaximal, characteristic, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14686C211yesmaximal, characteristic, complemented
14#14682C211yesmaximal, characteristic, complemented
15#14202C214yesmaximal, complemented
16#14138C211yesmaximal, characteristic, complemented
17#14047C214yesmaximal, complemented
18#13939C211yesmaximal, characteristic, complemented
19#13879C211yesmaximal, characteristic, complemented
20C25×C4C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C22⋊C4C2212yes—
27C23×C42C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2848—28no—
30#2499—28no—
31C2×#397C2214yes—
32C2×#397C2214yes—
33C2×#391C2211yescharacteristic, complemented
34C2×#391C2211yescharacteristic, complemented
35C2×#391C2211yescharacteristic, complemented
36C2×#391C2211yescharacteristic, complemented
37C2×#387C2214yescomplemented
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#384C2211yescharacteristic, complemented
42C2×#384C2211yescharacteristic, complemented
43C2×#382C2211yescharacteristic, complemented
44C2×#382C2211yescharacteristic, complemented
45#2280—28no—
46C2×#381C2212yes—
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2214yes—
55C2×#379C2212yes—
56C2×#379C2212yes—
57C2×C4×C22⋊C4—28no—
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2212yes—
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2212yes—
65C2×C4×C22⋊C4C2211yescharacteristic
66C22×#95C2212yes—
67#1445C2214yescomplemented
68#1443C2214yescomplemented
69#1442C2214yescomplemented
70#1441C2214yescomplemented
71#1440C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1436C2214yescomplemented
78#1436C2214yescomplemented
79#1436C2214yescomplemented
80#1436C2214yescomplemented
81C4⋊#95C2211yescharacteristic, complemented
82C4⋊#95C2211yescharacteristic, complemented
83C4⋊#95C2211yescharacteristic, complemented
84C4⋊#95C2211yescharacteristic, complemented
85C4⋊#95C2211yescharacteristic, complemented
86C4⋊#95C2211yescharacteristic, complemented
87C4⋊#95C2211yescharacteristic, complemented
88C4⋊#95C2214yescomplemented
89C4⋊#95C2211yescharacteristic, complemented
90#1434C2214yescomplemented
91#1434C2214yescomplemented
92C22⋊#95C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C26C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C24×C4—24no—
98C24×C4—24no—
99C24×C4—24no—
100C24×C4—24no—
101C24×C4—42no—
102C24×C4—42no—
103C24×C4D418yes—
104C24×C4C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2312yes—
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—42no—
120C2×C22⋊Q8—42no—
121C2×#117—24no—
122C2×#117—24no—
123C2×#117—24no—
124C2×#117—24no—
125C2×#117—42no—
126C2×#117—42no—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C22⋊C4—28no—
140C22×C22⋊C4—28no—
141C22×C22⋊C4—28no—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C42—24no—
159C22×C42—24no—
160C22×C42—24no—
161C22×C42—24no—
162C22×C42—42no—
163C22×C42—42no—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2312yes—
172#397—216no—
173#397—216no—
174#391—24no—
175#391—24no—
176#391—42no—
177#391—42no—
178#387—216no—
179#385—28no—
180#385—28no—
181#385—28no—
182#384—24no—
183#384—42no—
184#382—24no—
185#382—42no—
186#381—28no—
187#380—24no—
188#380—24no—
189#380—24no—
190#380—24no—
191#380—24no—
192#380—24no—
193#380—24no—
194#380—216no—
195#379—28no—
196#379—28no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—28no—
199C4×C22⋊C4—28no—
200C4×C22⋊C4—28no—
201C4×C22⋊C4—24no—
202C4×C22⋊C4—24no—
203C4×C22⋊C4—28no—
204C4×C22⋊C4D418yes—
205C2×#95—28no—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C25—22no—
232C25—24no—
233C25—24no—
234C25—22no—
235C25—22no—
236C25—22no—
237C25—24no—
238C25—41no—
239C25—41no—
240C25—42no—
241C25C2×D414yes—
242C25C2411yescharacteristic
243C25C2411yescharacteristic
244C25C2411yescharacteristic
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—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—24no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—232no—
268C23×C4—232no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—416no—
290C23×C4—41no—
291C23×C4—41no—
292C23×C4—41no—
293C23×C4—41no—
294C23×C4—41no—
295C23×C4—41no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—416no—
301C23×C4—416no—
302C23×C4—416no—
303C23×C4—416no—
304C23×C4C2×D414yes—
305C23×C4C2×D414yes—
306C23×C4C2×D414yes—
307C23×C4C2×D414yes—
308C23×C4C2×D414yes—
309C23×C4C2×D414yes—
310C23×C4C2×D414yes—
311C23×C4#4118yes—
312C23×C4#4114yes—
313C23×C4#4114yes—
314C23×C4#4114yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2411yescharacteristic
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2411yescharacteristic
328C23×C4C2412yes—
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331C22⋊Q8—416no—
332C22⋊Q8—416no—
333C22⋊Q8—416no—
334#117—416no—
335#117—416no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
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—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C22⋊C4—264no—
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—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4C2×D418yes—
413C2×C22⋊C4#4118yes—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—416no—
433C2×C42—416no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42C2×D414yes—
439C2×C42C2×D414yes—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—28no—
454#95—28no—
455#95—28no—
456#95—28no—
457#95—28no—
458#95—44no—
459#95—44no—
460#95—44no—
461#95—44no—
462#95—44no—
463#95—44no—
464#95C2×D418yes—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—21no—
469C24—21no—
470C24—22no—
471C24—216no—
472C24—216no—
473C24—28no—
474C24—28no—
475C24—28no—
476C24—21no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—28no—
494C24—28no—
495C24—44no—
496C24—44no—
497C24—44no—
498C24—44no—
499C24—44no—
500C24—44no—
501C24—48no—
502C24—48no—
503C24—48no—
504C24—48no—
505C24—48no—
506C24—48no—
507C24—48no—
508C24—48no—
509C24—48no—
510C24—48no—
511C24C22×D412yes—
512C24C22×D412yes—
513C24C22×D412yes—
514C24C22×D412yes—
515C24C2×#4112yes—
516C24C2×#4114yes—
517C24C2×#4112yes—
518C24C2×#4112yes—
519C24C2×#4114yes—
520C242−1+414yes—
521C24C2511yescharacteristic
522C2×Q8—44no—
523C2×Q8—44no—
524C2×Q8—44no—
525C2×Q8—44no—
526C2×Q8—44no—
527C2×Q8—44no—
528C2×Q8—44no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—216no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—216no—
557C22×C4—21no—
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—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—216no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—48no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—4128no—
640C22×C4—48no—
641C22×C4—48no—
642C22×C4—48no—
643C22×C4—48no—
644C22×C4—48no—
645C22×C4—48no—
646C22×C4—48no—
647C22×C4—48no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—48no—
657C22×C4—48no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4#121116yes—
663C22×C4#123116yes—
664C22×C4C22×D412yes—
665C22×C4C22×D414yes—
666C22×C4C22×D412yes—
667C22×C4C22×D412yes—
668C22×C4C22×D412yes—
669C22×C4C22×D414yes—
670C22×C4C22×D412yes—
671C22×C4C22×D412yes—
672C22×C4C2×#4114yes—
673C22×C4C2×#4114yes—
674C22×C4C2×#4112yes—
675C22×C4C2×#4112yes—
676C22×C4C2×#4112yes—
677C22×C4C2×#4114yes—
678C22×C4C2×#4114yes—
679C22×C4C2×#4112yes—
680C22×C4C2×#4112yes—
681C22×C4C2×#4112yes—
682C22×C4H(5,𝔽2)12yes—
683C22×C4H(5,𝔽2)12yes—
684C4⋊C4—48no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—48no—
689C4⋊C4—44no—
690C4⋊C4—48no—
691C4⋊C4—416no—
692C4⋊C4—44no—
693C4⋊C4—44no—
694C4⋊C4—44no—
695C4⋊C4—88no—
696C22⋊C4—216no—
697C22⋊C4—216no—
698C22⋊C4—216no—
699C22⋊C4—216no—
700C22⋊C4—48no—
701C22⋊C4—48no—
702C22⋊C4—48no—
703C22⋊C4—48no—
704C22⋊C4—48no—
705C22⋊C4—48no—
706C22⋊C4—48no—
707C22⋊C4—48no—
708C22⋊C4—48no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C42—28no—
713C42—28no—
714C42—48no—
715C42—48no—
716C42—48no—
717C42—48no—
718C42—44no—
719C42—44no—
720C23—22no—
721C23—24no—
722C23—22no—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—232no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—24no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—24no—
748C23—24no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—416no—
766C23—416no—
767C23—416no—
768C23—416no—
769C23—432no—
770C23—432no—
771C23—432no—
772C23—432no—
773C23—416no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—416no—
793C23C2×#12114yes—
794C23C2×#12314yes—
795C23#53214yes—
796C23#53214yes—
797C23#53614yes—
798C23#55218yes—
799C23#55618yes—
800C23C23×D411yescharacteristic
801C23C23×D411yescharacteristic
802C23C22×#4111yescharacteristic
803C23C22×#4111yescharacteristic
804C23C22×#4111yescharacteristic
805C23C22×#4112yes—
806C23C22×#4112yes—
807C23C2×H(5,𝔽2)11yescharacteristic
808C23C2×H(5,𝔽2)11yescharacteristic
809C23C2×2−1+412yes—
810C23#58512yes—
811Q8—88no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—232no—
831C2×C4—232no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—416no—
845C2×C4—432no—
846C2×C4—416no—
847C2×C4—416no—
848C2×C4—432no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
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—416no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4C2×#12114yes—
909C2×C4C2×#12114yes—
910C2×C4C2×#12314yes—
911C2×C4C2×#12314yes—
912C2×C4#52518yes—
913C2×C4#53414yes—
914C2×C4#54614yes—
915C2×C4#54614yes—
916C2×C4#55114yes—
917C2×C4#55114yes—
918C22—24no—
919C22—24no—
920C22—28no—
921C22—28no—
922C22—24no—
923C22—28no—
924C22—28no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—464no—
935C22—42no—
936C22—44no—
937C22—44no—
938C22—44no—
939C22—44no—
940C22—42no—
941C22—44no—
942C22—44no—
943C22—44no—
944C22—44no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22#249918yescomplemented
952C22C22×#12111yescharacteristic
953C22C22×#12311yescharacteristic
954C22C2×#52512yes—
955C22C2×#53211yescharacteristic
956C22C2×#53211yescharacteristic
957C22#344412yes—
958C22C2×#53411yescharacteristic
959C22C2×#53611yescharacteristic
960C22#344911yescharacteristic
961C22C2×#54611yescharacteristic
962C22C2×#54611yescharacteristic
963C22C2×#55111yescharacteristic
964C22C2×#55111yescharacteristic
965C22C2×#55212yes—
966C22C2×#55612yes—
967C22#347512yes—
968C22#347512yes—
969C22#348912yes—
970C22#349512yes—
971C22#350512yes—
972C22#350612yes—
973C22#352012yes—
974C22#352012yes—
975C4—28no—
976C4—24no—
977C4—24no—
978C4—44no—
979C4—44no—
980C4—44no—
981C4—42no—
982C4—82no—
983C4—82no—
984C4—82no—
985C4—82no—
986C4—82no—
987C4—82no—
988C4—82no—
989C4—82no—
990C4#241218yes—
991C2—28no—
992C2—44no—
993C2—44no—
994C2C2×#241211yescharacteristic
995C2C2×#249911yescharacteristic
996C2#3481011yescharacteristic
997C2#3503211yescharacteristic
998C2#3508511yescharacteristic
999C2#3530611yescharacteristic
1000C2#3615612yes—
1001C2#3616112yes—
1002C2#3620412yes—
1003C2#3620712yes—
1004C2#3662411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
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×#2499C2semidirect
5. #15236C2semidirect
6. #15233C2semidirect
7. #15182C2semidirect
8. #15150C2semidirect
9. #14837C2semidirect
11. #14702C2semidirect
12. #14702C2semidirect
13. #14686C2semidirect
14. #14682C2semidirect
15. #14202C2semidirect
16. #14138C2semidirect
17. #14047C2semidirect
18. #13939C2semidirect
19. #13879C2semidirect
33. C2×#391C22semidirect
34. C2×#391C22semidirect
35. C2×#391C22semidirect
36. C2×#391C22semidirect
37. C2×#387C22semidirect
41. C2×#384C22semidirect
42. C2×#384C22semidirect
43. C2×#382C22semidirect
44. C2×#382C22semidirect
67. #1445C22semidirect
68. #1443C22semidirect
69. #1442C22semidirect
70. #1441C22semidirect
77. #1436C22semidirect
78. #1436C22semidirect
79. #1436C22semidirect
80. #1436C22semidirect
81. C4⋊#95C22semidirect
82. C4⋊#95C22semidirect
83. C4⋊#95C22semidirect
84. C4⋊#95C22semidirect
85. C4⋊#95C22semidirect
86. C4⋊#95C22semidirect
87. C4⋊#95C22semidirect
88. C4⋊#95C22semidirect
89. C4⋊#95C22semidirect
90. #1434C22semidirect
91. #1434C22semidirect
951. C22#2499semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#24992
C2×#22802
C22×C4×C22⋊C42
#152362
#152332
#151822
#151502
#148372
#148202
#147022
#146862
#146822
#142022
#141382
#140472
#139392
#138792