Finite Group Databasebeta

← #687628

Subgroups — #687628

Order 512.

3444 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic, complemented
2C2×#2416C211yesmaximal, characteristic
3C2×#2352C211yesmaximal, characteristic, complemented
4C2×#2317C211yesmaximal, characteristic, complemented
5#16317C214yesmaximal, complemented
6#15950C214yesmaximal, complemented
7#15345C214yesmaximal, complemented
8#15244C211yesmaximal, characteristic, complemented
9#15233C211yesmaximal, characteristic, complemented
10#15231C211yesmaximal, characteristic, complemented
11#15219C211yesmaximal, characteristic, complemented
12#14761C214yesmaximal, complemented
13#14257C211yesmaximal, characteristic, complemented
14#14136C211yesmaximal, characteristic, complemented
15#14048C211yesmaximal, characteristic, complemented
16#14001C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic, complemented
20C22×#123C2214yes—
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#121C2212yes—
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29#2501—28no—
30#2416—28no—
31C2×#399C2214yes—
32C2×#396C2212yes—
33C2×#394C2212yes—
34#2352—28no—
35#2317—28no—
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#389C2214yes—
42C2×#389C2211yescharacteristic
43C2×#388C2212yes—
44C2×#388C2214yes—
45C2×#387C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#385C2214yes—
49C2×#385C2214yes—
50C2×#385C2214yes—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2212yes—
66#1444C2214yes—
67#1444C2214yes—
68#1443C2214yes—
69#1442C2214yes—
70#1441C2212yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2212yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2212yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2212yes—
82#1438C2214yes—
83#1438C2214yes—
84#1438C2214yes—
85#1437C2214yes—
86#1436C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C2×#123—216no—
104C2×#123—48no—
105C2×#123—48no—
106C2×#121—28no—
107C2×#121—24no—
108C2×#121—24no—
109C2×#121—24no—
110C2×#121—24no—
111C2×#121—24no—
112C2×#121—48no—
113C2×#121—42no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4D418yes—
117C2×#117—24no—
118C2×#117—24no—
119C2×#117—24no—
120C2×#117—24no—
121C2×#117—24no—
122C2×#117—42no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—42no—
128C22×C4⋊C4—42no—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2314yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2312yes—
170#399—216no—
171#396—28no—
172#394—28no—
173#390—24no—
174#390—24no—
175#390—24no—
176#390—24no—
177#390—42no—
178#389—216no—
179#389—24no—
180#388—28no—
181#388—48no—
182#387—28no—
183#386—28no—
184#386—28no—
185#385—216no—
186#385—48no—
187#385—48no—
188#384—24no—
189#384—24no—
190#384—42no—
191#384D418yescomplemented
192#382—24no—
193#382—24no—
194#382—24no—
195#380—24no—
196#380—24no—
197#380—24no—
198C4×C4⋊C4—24no—
199C4×C22⋊C4—24no—
200C4×C22⋊C4—28no—
201C4×C22⋊C4—24no—
202C4×C22⋊C4—24no—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C25C2412yes—
226C25C2411yescharacteristic
227C25C2411yescharacteristic
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—28no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4C2×D414yes—
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—24no—
261C23×C4—24no—
262C23×C4—28no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4C2×D414yes—
271C23×C4C2×D414yes—
272C23×C4#4114yes—
273C23×C4#4114yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290#123—464no—
291#121—416no—
292#121—432no—
293#121—416no—
294C4×D4—232no—
295#117—232no—
296#117—416no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—416no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4C2×D414yes—
343C2×C4⋊C4C2×D414yes—
344C2×C4⋊C4C2×D414yes—
345C2×C4⋊C4C2×D4116yes—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
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⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4C2×D414yes—
394C2×C22⋊C4C2×D414yes—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—42no—
411C2×C42—44no—
412C2×C42C2×D414yes—
413C2×C42C2×D414yes—
414C2×C42#4114yes—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—28no—
422#95—28no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—28no—
428#95—24no—
429#95—24no—
430#95—42no—
431#95—42no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—21no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—24no—
460C24—24no—
461C24—22no—
462C24—24no—
463C24—22no—
464C24—24no—
465C24C22×D412yes—
466C24C22×D412yes—
467C24C2×#4112yes—
468C24C2×#4112yes—
469C24H(5,𝔽2)14yes—
470C24C2511yescharacteristic
471C2×D4—28no—
472C2×D4—28no—
473C2×D4—44no—
474C2×D4—48no—
475C2×D4—416no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—84no—
490C2×D4—88no—
491C2×D4—88no—
492C2×D4—88no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
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—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—416no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—88no—
587C22×C4—84no—
588C22×C4—84no—
589C22×C4—88no—
590C22×C4—88no—
591C22×C4#123116yescomplemented
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D414yes—
596C22×C4C22×D414yes—
597C22×C4C22×D414yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4H(5,𝔽2)14yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C42−1+414yes—
610C22×C42−1+412yes—
611C4⋊C4—216no—
612C4⋊C4—28no—
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—416no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—416no—
619C4⋊C4—48no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—88no—
626C4⋊C4—88no—
627C22⋊C4—216no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—48no—
634C22⋊C4—416no—
635C22⋊C4—48no—
636C22⋊C4—416no—
637C22⋊C4—48no—
638C22⋊C4—416no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—84no—
643C22⋊C4—88no—
644C22⋊C4—84no—
645C42—28no—
646C42—28no—
647C42—28no—
648C42—48no—
649C42—44no—
650C42—44no—
651C42—84no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—42no—
712C23—42no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23C2×#12314yes—
720C23#53514yes—
721C23C23×D411yescharacteristic
722C23C23×D411yescharacteristic
723C23C22×#4111yescharacteristic
724C23C22×#4111yescharacteristic
725C23C22×#4111yescharacteristic
726C23C2×H(5,𝔽2)12yes—
727C23C2×H(5,𝔽2)11yescharacteristic
728C23C2×H(5,𝔽2)12yes—
729C23C2×2−1+411yescharacteristic
730C23C2×2−1+412yes—
731C23#58512yes—
732D4—416no—
733D4—816no—
734D4—816no—
735D4—88no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—232no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—416no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—816no—
825C2×C4—816no—
826C2×C4C2×#12314yes—
827C2×C4C2×#12314yes—
828C2×C4#52514yes—
829C2×C4#53914yes—
830C2×C4D4214yes—
831C2×C4#54714yes—
832C2×C4#54814yes—
833C2×C4#55314yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—44no—
844C22—44no—
845C22—42no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—42no—
851C22—42no—
852C22—44no—
853C22—44no—
854C22—42no—
855C22—42no—
856C22—82no—
857C22—82no—
858C22—84no—
859C22—82no—
860C22—84no—
861C22—84no—
862C22—82no—
863C22—82no—
864C22—84no—
865C22—82no—
866C22—82no—
867C22C22×#12311yescharacteristic
868C22C2×#52511yescharacteristic
869C22C2×#53511yescharacteristic
870C22#344911yescharacteristic
871C22C2×#53911yescharacteristic
872C22C2×D4211yescharacteristic
873C22C2×#54711yescharacteristic
874C22C2×#54811yescharacteristic
875C22C2×#55311yescharacteristic
876C22#348412yes—
877C22#349212yes—
878C22#349212yes—
879C22#349412yes—
880C22#349412yes—
881C22#349712yes—
882C22#349811yescharacteristic
883C22#349911yescharacteristic
884C22#350612yes—
885C22#351112yes—
886C22#354312yes—
887C22#354412yes—
888C22#355912yes—
889C22#356112yes—
890C4—24no—
891C4—44no—
892C4—44no—
893C4—44no—
894C4—42no—
895C4—44no—
896C4—44no—
897C4—44no—
898C4—42no—
899C4—42no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4#244318yes—
906C2—44no—
907C2—44no—
908C2—162no—
909C2C2×#244311yescharacteristic
910C2#3526211yescharacteristic
911C2#3553011yescharacteristic
912C2#3568212yes—
913C2#3767411yescharacteristic
914C2#3786311yescharacteristic
915C2#3935611yescharacteristic
916C2#3948311yescharacteristic
917C2#4294612yes—
918C2#4487812yes—
919C2#4492212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
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×#2501C2semidirect
3. C2×#2352C2semidirect
4. C2×#2317C2semidirect
5. #16317C2semidirect
6. #15950C2semidirect
7. #15345C2semidirect
8. #15244C2semidirect
9. #15233C2semidirect
10. #15231C2semidirect
11. #15219C2semidirect
12. #14761C2semidirect
13. #14257C2semidirect
14. #14136C2semidirect
15. #14048C2semidirect
16. #14001C2semidirect
17. #13880C2semidirect
18. #13880C2semidirect
19. #13839C2semidirect
191. #384D4semidirect
591. C22×C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#24162
C2×#23522
C2×#23172
#163172
#159502
#153452
#152442
#152332
#152312
#152192
#147612
#142572
#141362
#140482
#140012
#138802
#138392