Finite Group Databasebeta

← #617195

Subgroups — #617195

Order 512.

3432 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2503C211yesmaximal, characteristic, complemented
2C2×#2616C211yesmaximal, characteristic
3C2×#2311C211yesmaximal, characteristic
4C2×#2297C211yesmaximal, characteristic
5#15702C214yesmaximal, complemented
6#15538C214yesmaximal, complemented
7#15503C214yesmaximal, complemented
8#15495C214yesmaximal, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15233C211yesmaximal, characteristic, complemented
11#15233C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic, complemented
13#14702C211yesmaximal, characteristic, complemented
14#14682C211yesmaximal, characteristic, complemented
15#14340C211yesmaximal, characteristic, complemented
16#14258C211yesmaximal, characteristic, complemented
17#14138C211yesmaximal, characteristic, complemented
18#13924C211yesmaximal, characteristic, complemented
19#13879C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2616—28no—
29#2503—28no—
30C2×#400C2214yes—
31C2×#395C2212yes—
32C2×#394C2212yes—
33C2×#394C2212yes—
34C2×#394C2212yes—
35#2311—28no—
36#2297—28no—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2212yes—
40C2×#391C2212yes—
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#390C2212yes—
44C2×#390C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#384C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#381C2214yes—
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65#1445C2214yes—
66#1443C2214yes—
67#1443C2214yes—
68#1442C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1436C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91#1434C2214yes—
92C22⋊#95C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—42no—
100C22×#41—42no—
101C22×#41D418yes—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×D4C2311yescharacteristic
105C23×D4C2311yescharacteristic
106C23×D4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
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—42no—
125C2×#117—42no—
126C2×#117—42no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
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×C22⋊C4C2312yes—
159C22×C42—24no—
160C22×C42—24no—
161C22×C42—42no—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2312yes—
168#400—216no—
169#395—28no—
170#394—28no—
171#394—28no—
172#394—28no—
173#391—28no—
174#391—24no—
175#391—24no—
176#391—28no—
177#391—42no—
178#391—42no—
179#390—28no—
180#390—28no—
181#386—28no—
182#386—28no—
183#386—28no—
184#386—28no—
185#384—42no—
186#382—24no—
187#382—24no—
188#382—42no—
189#381—216no—
190#380—24no—
191#380—24no—
192#380—24no—
193#380—24no—
194#380—24no—
195#380—24no—
196#380—24no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—24no—
200C4×C22⋊C4D418yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C25C2411yescharacteristic
228C25C2411yescharacteristic
229C25C2411yescharacteristic
230C2×#41—232no—
231C2×#41—232no—
232C2×#41—416no—
233C2×#41—416no—
234C2×#41—416no—
235C2×#41—416no—
236C2×#41—416no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—41no—
249C22×Q8—41no—
250C22×Q8C2×D414yes—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—41no—
264C22×D4—41no—
265C22×D4—41no—
266C22×D4—41no—
267C22×D4—41no—
268C22×D4—41no—
269C22×D4C2×D414yes—
270C22×D4C2×D414yes—
271C22×D4C2×D414yes—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
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—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4#4114yes—
303C23×C4#4114yes—
304C23×C4#4114yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C23×C4C2412yes—
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C22⋊Q8—416no—
322C22⋊Q8—416no—
323C22⋊Q8—416no—
324#117—416no—
325#117—416no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—416no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
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—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—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4C2×D418yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—22no—
414C2×C42—24no—
415C2×C42—22no—
416C2×C42—24no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—416no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42C2×D414yes—
425C2×C42C2×D414yes—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—28no—
437#95—28no—
438#95—28no—
439#95—28no—
440#95—28no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—44no—
449#95—44no—
450#95—44no—
451#95C2×D418yes—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24C22×D412yes—
479C24C22×D412yes—
480C24C22×D412yes—
481C24C22×D412yes—
482C24C2×#4112yes—
483C24C2×#4112yes—
484C24C2×#4112yes—
485C24C2511yescharacteristic
486#41—4128no—
487C2×Q8—28no—
488C2×Q8—28no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—28no—
504C2×D4—28no—
505C2×D4—28no—
506C2×D4—28no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
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—28no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
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—24no—
601C22×C4—24no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—416no—
630C22×C4—48no—
631C22×C4—84no—
632C22×C4—84no—
633C22×C4—88no—
634C22×C4#121116yes—
635C22×C4#123116yes—
636C22×C4C22×D412yes—
637C22×C4C22×D414yes—
638C22×C4C22×D414yes—
639C22×C4C22×D412yes—
640C22×C4C22×D412yes—
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C2×#4112yes—
645C22×C4C2×#4112yes—
646C22×C4C2×#4112yes—
647C22×C4C2×#4112yes—
648C22×C4C2×#4112yes—
649C22×C4C2×#4112yes—
650C22×C4H(5,𝔽2)12yes—
651C22×C4H(5,𝔽2)12yes—
652C22×C42−1+414yes—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—48no—
660C4⋊C4—44no—
661C4⋊C4—48no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—88no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—84no—
676C22⋊C4—84no—
677C22⋊C4—84no—
678C22⋊C4—84no—
679C22⋊C4—84no—
680C22⋊C4—84no—
681C22⋊C4—84no—
682C42—28no—
683C42—28no—
684C42—48no—
685C42—48no—
686C42—44no—
687C42—44no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23C2×#12114yes—
756C23C2×#12314yes—
757C23C23×D411yescharacteristic
758C23C23×D411yescharacteristic
759C23C22×#4111yescharacteristic
760C23C22×#4111yescharacteristic
761C23C22×#4111yescharacteristic
762C23C2×H(5,𝔽2)11yescharacteristic
763C23C2×H(5,𝔽2)11yescharacteristic
764C23C2×2−1+412yes—
765C23#58512yes—
766C23#58512yes—
767C23#58512yes—
768Q8—416no—
769Q8—88no—
770D4—416no—
771D4—416no—
772D4—416no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—232no—
786C2×C4—232no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—432no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—416no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—42no—
866C2×C4—816no—
867C2×C4C2×#12114yes—
868C2×C4C2×#12114yes—
869C2×C4C2×#12314yes—
870C2×C4C2×#12314yes—
871C2×C4#53414yes—
872C2×C4#54614yes—
873C2×C4#54614yes—
874C2×C4#55114yes—
875C2×C4#55114yes—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—44no—
887C22—44no—
888C22—42no—
889C22—42no—
890C22—44no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—44no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—82no—
906C22—82no—
907C22—82no—
908C22—82no—
909C22C22×#12111yescharacteristic
910C22C22×#12311yescharacteristic
911C22C2×#53411yescharacteristic
912C22#344912yes—
913C22#346112yes—
914C22C2×#54611yescharacteristic
915C22C2×#54611yescharacteristic
916C22C2×#55111yescharacteristic
917C22C2×#55111yescharacteristic
918C22#348912yes—
919C22#349312yes—
920C22#349512yes—
921C22#349911yescharacteristic
922C22#350011yescharacteristic
923C22#350011yescharacteristic
924C22#350011yescharacteristic
925C22#350712yes—
926C22#351012yes—
927C22#351212yes—
928C22#353912yes—
929C22#354112yes—
930C22#354712yes—
931C22#355112yes—
932C4—24no—
933C4—24no—
934C4—44no—
935C4—42no—
936C4—44no—
937C4—44no—
938C4—82no—
939C4—82no—
940C4—82no—
941C4—82no—
942C4—82no—
943C4—82no—
944C4—82no—
945C4—82no—
946C4—82no—
947C4#241218yes—
948C2—44no—
949C2—44no—
950C2—82no—
951C2C2×#241211yescharacteristic
952C2#3530811yescharacteristic
953C2#3532711yescharacteristic
954C2#3561811yescharacteristic
955C2#3561911yescharacteristic
956C2#3738811yescharacteristic
957C2#3741811yescharacteristic
958C2#3784712yes—
959C2#3797412yes—
960C2#3946312yes—
961C2#3956612yes—
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
1. C2×#2503C2semidirect
5. #15702C2semidirect
6. #15538C2semidirect
7. #15503C2semidirect
8. #15495C2semidirect
9. #15236C2semidirect
10. #15233C2semidirect
11. #15233C2semidirect
12. #15182C2semidirect
13. #14702C2semidirect
14. #14682C2semidirect
15. #14340C2semidirect
16. #14258C2semidirect
17. #14138C2semidirect
18. #13924C2semidirect
19. #13879C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25032
C2×#26162
C2×#23112
C2×#22972
#157022
#155382
#155032
#154952
#152362
#152332
#151822
#147022
#146822
#143402
#142582
#141382
#139242
#138792