Finite Group Databasebeta

← #678425

Subgroups — #678425

Order 512.

4136 conjugacy classes of subgroups.

The subgroup lattice has 949 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#553C211yesmaximal, characteristic
2C2×#2859C211yesmaximal, characteristic, complemented
3C2×#2562C211yesmaximal, characteristic, complemented
4C2×#2566C211yesmaximal, characteristic, complemented
5#15940C214yesmaximal, complemented
6#15316C214yesmaximal, complemented
7#15219C211yesmaximal, characteristic, complemented
8#15219C211yesmaximal, characteristic, complemented
9#15130C211yesmaximal, characteristic, complemented
10#15130C211yesmaximal, characteristic, complemented
11#14761C214yesmaximal, complemented
12#14185C214yesmaximal, complemented
13#14160C211yesmaximal, characteristic, complemented
14#13881C211yesmaximal, characteristic, complemented
15#13880C211yesmaximal, characteristic, complemented
16#13879C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18C4×#390C211yesmaximal, characteristic, complemented
19C4×#390C211yesmaximal, characteristic, complemented
20C2×#553—28no—
21C2×#553—28no—
22C2×#553—28no—
23C22×#126C2212yes—
24C22×#125C2211yescharacteristic
25C22×#125C2211yescharacteristic
26C22×#123C2212yes—
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#121C2212yes—
30C22×C4×D4C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35#2859—28no—
36#2566—28no—
37#2562—28no—
38C2×#400C2212yes—
39C2×#396C2214yes—
40C2×#394C2214yes—
41C2×#394C2212yes—
42C2×#394C2214yes—
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2212yes—
48C2×#389C2214yes—
49C2×#389C2214yes—
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#385C2214yes—
53C2×#385C2214yes—
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2214yes—
71C2×C43C2211yescharacteristic
72#1444C2214yes—
73#1442C2214yes—
74#1441C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2214yes—
82#1438C2214yes—
83#1437C2214yes—
84#1437C2212yes—
85#1437C2212yes—
86#1436C2214yes—
87#1436C2214yes—
88#1436C2214yes—
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2212yes—
96C22⋊#95C2214yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C23×D4C2311yescharacteristic
100C23×D4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2312yes—
104C24×C4C2312yes—
105#553—2128no—
106C2×#126—28no—
107C2×#126—28no—
108C2×#126—28no—
109C2×#125—24no—
110C2×#125—24no—
111C2×#125—24no—
112C2×#125—24no—
113C2×#125—24no—
114C2×#125D418yes—
115C2×#123—28no—
116C2×#123—28no—
117C2×#123—28no—
118C2×#121—28no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121—24no—
122C2×#121—24no—
123C2×#121—28no—
124C2×#121—24no—
125C2×#121—24no—
126C2×#121—28no—
127C2×C4×D4—28no—
128C2×C4×D4—28no—
129C2×C4×D4—28no—
130C2×C4×D4—24no—
131C2×C4×D4—24no—
132C2×C4×D4—24no—
133C2×C4×D4—24no—
134C2×C4×D4D418yes—
135C2×C4×D4D418yes—
136C2×#117—24no—
137C2×#117—24no—
138C2×#117—24no—
139C22×C4⋊C4—24no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2314yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2314yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2314yes—
177C22×C42C2312yes—
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2312yes—
181C22×C42C2312yes—
182C22×C42C2311yescharacteristic
183C22×C42C2311yescharacteristic
184C22×C42C2312yes—
185C22×C42C2311yescharacteristic
186#400—28no—
187#396—216no—
188#394—28no—
189#394—216no—
190#394—48no—
191#390—24no—
192#390—24no—
193#390—28no—
194#390—24no—
195#390—24no—
196#389—216no—
197#389—216no—
198#388—28no—
199#388—28no—
200#385—216no—
201#385—48no—
202#384—24no—
203#384—24no—
204#384—24no—
205#382—24no—
206#382—24no—
207#382—24no—
208#380—24no—
209#380—24no—
210#380—24no—
211#380—24no—
212C4×C4⋊C4—24no—
213C4×C4⋊C4—24no—
214C4×C22⋊C4—24no—
215C4×C22⋊C4—24no—
216C4×C22⋊C4—24no—
217C4×C22⋊C4—24no—
218C4×C22⋊C4—48no—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C43—24no—
239C25C2411yescharacteristic
240C25C2412yes—
241C25C2411yescharacteristic
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—28no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—24no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—42no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4C2×D414yes—
263C22×D4C2×D414yes—
264C23×C4—24no—
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—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2×D418yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304#126—264no—
305#125—232no—
306#125—416no—
307#123—264no—
308#121—264no—
309#121—232no—
310#121—232no—
311C4×D4—264no—
312C4×D4—232no—
313C4×D4—232no—
314#117—232no—
315C2×C4⋊C4—232no—
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—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D414yes—
363C2×C4⋊C4C2×D414yes—
364C2×C4⋊C4C2×D418yes—
365C2×C4⋊C4C2×D414yes—
366C2×C4⋊C4C2×D418yes—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
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—28no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4C2×D414yes—
414C2×C22⋊C4C2×D418yes—
415C2×C22⋊C4C2×D414yes—
416C2×C22⋊C4#4118yes—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—24no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—44no—
438C2×C42C2×D414yes—
439C2×C42C2×D414yes—
440C2×C42C2×D414yes—
441C2×C42#4114yes—
442C2×C42#4114yes—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—28no—
457#95—28no—
458#95—44no—
459#95—44no—
460#95—44no—
461#95—44no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—21no—
468C24—21no—
469C24—22no—
470C24—22no—
471C24—21no—
472C24—22no—
473C24—21no—
474C24—22no—
475C24—21no—
476C24—21no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—24no—
481C24—24no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—24no—
489C24—24no—
490C24—22no—
491C24C22×D414yes—
492C24C22×D412yes—
493C24C22×D412yes—
494C24C2×#4114yes—
495C24C2511yescharacteristic
496C2×D4—216no—
497C2×D4—28no—
498C2×D4—216no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—44no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—416no—
507C2×D4—416no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—88no—
515C2×D4—88no—
516C2×D4—84no—
517C2×D4—84no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—216no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—216no—
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—24no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—416no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—88no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—88no—
610C22×C4—88no—
611C22×C4—84no—
612C22×C4—84no—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D414yes—
616C22×C4C22×D414yes—
617C22×C4C22×D414yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4114yes—
629C22×C4C2×#4114yes—
630C22×C4C2×#4114yes—
631C22×C4C2×#4112yes—
632C22×C4C2×#4112yes—
633C22×C4H(5,𝔽2)14yes—
634C22×C42−1+412yes—
635C22×C42−1+412yes—
636C4⋊C4—216no—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—28no—
640C4⋊C4—216no—
641C4⋊C4—28no—
642C4⋊C4—216no—
643C4⋊C4—416no—
644C4⋊C4—48no—
645C4⋊C4—416no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—88no—
653C22⋊C4—216no—
654C22⋊C4—216no—
655C22⋊C4—216no—
656C22⋊C4—28no—
657C22⋊C4—216no—
658C22⋊C4—28no—
659C22⋊C4—216no—
660C22⋊C4—48no—
661C22⋊C4—416no—
662C22⋊C4—48no—
663C22⋊C4—416no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—416no—
668C22⋊C4—88no—
669C22⋊C4—84no—
670C22⋊C4—84no—
671C42—216no—
672C42—28no—
673C42—28no—
674C42—48no—
675C42—48no—
676C42—44no—
677C42—44no—
678C42—84no—
679C42#120116yes—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—22no—
689C23—22no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—24no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—28no—
701C23—28no—
702C23—22no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—41no—
715C23—42no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—44no—
726C23—42no—
727C23—42no—
728C23—44no—
729C23—42no—
730C23—44no—
731C23—44no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—44no—
737C23—42no—
738C23—44no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—44no—
743C23—42no—
744C23—44no—
745C23—42no—
746C23—44no—
747C23—42no—
748C23#53214yes—
749C23C23×D411yescharacteristic
750C23C23×D411yescharacteristic
751C23C23×D411yescharacteristic
752C23C22×#4111yescharacteristic
753C23C22×#4111yescharacteristic
754C23C22×#4112yes—
755C23C2×H(5,𝔽2)12yes—
756C23C2×2−1+411yescharacteristic
757C23C2×2−1+411yescharacteristic
758C23#58512yes—
759C23#58512yes—
760D4—416no—
761D4—432no—
762D4—416no—
763D4—816no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—28no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—24no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—416no—
822C2×C4—416no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—44no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—44no—
850C2×C4—816no—
851C2×C4—816no—
852C2×C4C2×#12014yes—
853C2×C4C2×#12014yes—
854C2×C4C2×#12014yes—
855C2×C4#53214yes—
856C2×C4#53614yes—
857C2×C4#54714yes—
858C2×C4#54714yes—
859C2×C4#54814yes—
860C2×C4#54814yes—
861C2×C4#55318yescomplemented
862C22—24no—
863C22—24no—
864C22—24no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22—42no—
869C22—42no—
870C22—44no—
871C22—42no—
872C22—42no—
873C22—48no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—48no—
879C22—42no—
880C22—44no—
881C22—42no—
882C22—44no—
883C22—44no—
884C22—42no—
885C22—82no—
886C22—84no—
887C22—82no—
888C22—84no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22C22×#12011yescharacteristic
896C22C2×#53211yescharacteristic
897C22C2×#53211yescharacteristic
898C22C2×#53611yescharacteristic
899C22#344911yescharacteristic
900C22C2×#54711yescharacteristic
901C22C2×#54711yescharacteristic
902C22C2×#54811yescharacteristic
903C22C2×#54811yescharacteristic
904C22D4×#4112yes—
905C22D4×#4112yes—
906C22C2×#55312yes—
907C22#347512yes—
908C22#348812yes—
909C22#349612yes—
910C22#349811yescharacteristic
911C22#350011yescharacteristic
912C22#350612yes—
913C22#351112yes—
914C22#351212yes—
915C22#351512yes—
916C22#355912yes—
917C22#356512yes—
918C4—28no—
919C4—24no—
920C4—24no—
921C4—44no—
922C4—44no—
923C4—42no—
924C4—42no—
925C4—44no—
926C4—44no—
927C4—44no—
928C4—82no—
929C4—82no—
930C4—82no—
931C4—82no—
932C4—82no—
933C4#243218yes—
934C2—44no—
935C2—84no—
936C2—82no—
937C2C2×#243211yescharacteristic
938C2#3473811yescharacteristic
939C2#3551311yescharacteristic
940C2#3618211yescharacteristic
941C2#3618411yescharacteristic
942C2#3646812yes—
943C2#3948311yescharacteristic
944C2#3948511yescharacteristic
945C2#3995212yes—
946C2#5913712yes—
947C2#5913912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#553C2
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×#2859C2semidirect
3. C2×#2562C2semidirect
4. C2×#2566C2semidirect
5. #15940C2semidirect
6. #15316C2semidirect
7. #15219C2semidirect
8. #15219C2semidirect
9. #15130C2semidirect
10. #15130C2semidirect
11. #14761C2semidirect
12. #14185C2semidirect
13. #14160C2semidirect
14. #13881C2semidirect
15. #13880C2semidirect
16. #13879C2semidirect
17. #13879C2semidirect
18. C4×#390C2semidirect
19. C4×#390C2semidirect
861. C2×C4#553semidirect

Maximal subgroups

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

subgroupindex
C22×#5532
C2×#28592
C2×#25622
C2×#25662
#159402
#153162
#152192
#151302
#147612
#141852
#141602
#138812
#138802
#138792
C4×#3902