Finite Group Databasebeta

← #4035833

Subgroups — #4035833

Order 512.

2995 conjugacy classes of subgroups.

The subgroup lattice has 947 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2763C211yesmaximal, characteristic, complemented
2C2×#2436C211yesmaximal, characteristic
3#17198C211yesmaximal, characteristic, complemented
4#17153C212yesmaximal, complemented
5#16094C212yesmaximal, complemented
6#15851C212yesmaximal, complemented
7#15673C211yesmaximal, characteristic
8#15568C211yesmaximal, characteristic, complemented
9#15510C212yesmaximal, complemented
10#15311C212yesmaximal, complemented
11#15269C212yesmaximal, complemented
12#15260C211yesmaximal, characteristic
13#14968C212yesmaximal, complemented
14#14922C212yesmaximal, complemented
15#14833C212yesmaximal, complemented
16#14537C211yesmaximal, characteristic, complemented
17#14421C212yesmaximal, complemented
18#14378C212yesmaximal, complemented
19#13922C212yesmaximal, complemented
20C24×Q8C2211yescharacteristic
21C22×#124C2212yes—
22C22×#124C2211yescharacteristic
23C22×#123C2211yescharacteristic
24C22×#121C2211yescharacteristic
25#2763—28no—
26#2436—28no—
27C2×#400C2212yes—
28C2×#397C2212yes—
29C2×#396C2212yes—
30C2×#395C2212yes—
31C2×#395C2211yescharacteristic
32C2×#394C2212yes—
33C2×#394C2212yes—
34C2×#393C2211yescharacteristic
35C2×#393C2211yescharacteristic
36C2×#393C2211yescharacteristic
37C2×#393C2211yescharacteristic
38C2×#393C2211yescharacteristic
39C2×#391C2212yes—
40C2×#391C2212yes—
41C2×#391C2212yes—
42C2×#391C2212yes—
43C2×#391C2212yes—
44C2×#388C2212yes—
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2211yescharacteristic
50C2×#385C2212yes—
51C2×#385C2211yescharacteristic
52C2×#382C2212yes—
53C2×#380C2212yes—
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56#1446C2212yes—
57#1446C2212yes—
58#1446C2212yes—
59#1446C2212yes—
60#1446C2212yes—
61#1444C2212yes—
62#1444C2212yes—
63#1444C2212yes—
64#1443C2212yes—
65#1443C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1441C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2211yescharacteristic
76#1440C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1438C2211yescharacteristic
89#1438C2212yes—
90#1438C2211yescharacteristic
91#1438C2211yescharacteristic
92#1437C2211yescharacteristic
93#1437C2212yes—
94#1436C2211yescharacteristic
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100C4⋊#95C2212yes—
101C4⋊#95C2212yes—
102#1434C2212yes—
103#1434C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C23×Q8—24no—
110C23×Q8—28no—
111C23×Q8—42no—
112C23×Q8—42no—
113C23×Q8—44no—
114C23×Q8C2311yescharacteristic
115C23×Q8C2312yes—
116C23×Q8C2311yescharacteristic
117C23×Q8C2311yescharacteristic
118C23×D4C2311yescharacteristic
119C23×D4C2311yescharacteristic
120C23×D4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C24×C4C2312yes—
123C24×C4C2311yescharacteristic
124C2×#124—28no—
125C2×#124—28no—
126C2×#124—42no—
127C2×#124—44no—
128C2×#124—44no—
129C2×#123—42no—
130C2×#123—44no—
131C2×#121—24no—
132C2×#121—42no—
133C2×#121—42no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2311yescharacteristic
168#400—28no—
169#397—44no—
170#396—44no—
171#395—28no—
172#395—42no—
173#394—44no—
174#394—44no—
175#393—24no—
176#393—24no—
177#393—24no—
178#393—24no—
179#393D418yes—
180#391—28no—
181#391—28no—
182#391—28no—
183#391—44no—
184#391—44no—
185#388—28no—
186#388—44no—
187#388—44no—
188#386—28no—
189#386—28no—
190#386—42no—
191#385—28no—
192#385—24no—
193#382—28no—
194#380—44no—
195C4×C22⋊C4—24no—
196C4×C22⋊C4—44no—
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2311yescharacteristic
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2311yescharacteristic
239C2×#95C2312yes—
240C25C2411yescharacteristic
241C25C2411yescharacteristic
242C25C2411yescharacteristic
243C22×Q8—24no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—24no—
247C22×Q8—24no—
248C22×Q8—24no—
249C22×Q8—24no—
250C22×Q8—24no—
251C22×Q8—24no—
252C22×Q8—41no—
253C22×Q8—42no—
254C22×Q8—41no—
255C22×Q8—42no—
256C22×Q8—41no—
257C22×Q8—42no—
258C22×Q8—41no—
259C22×Q8—42no—
260C22×Q8—41no—
261C22×Q8—42no—
262C22×Q8—41no—
263C22×Q8—416no—
264C22×Q8—432no—
265C22×Q8—432no—
266C22×Q8—416no—
267C22×Q8—416no—
268C22×Q8C2×D414yes—
269C22×Q8#4118yes—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—24no—
275C22×D4—24no—
276C22×D4—22no—
277C22×D4—24no—
278C22×D4—22no—
279C22×D4—41no—
280C22×D4—41no—
281C22×D4—41no—
282C22×D4—42no—
283C22×D4—42no—
284C22×D4—42no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—22no—
288C23×C4—24no—
289C23×C4—22no—
290C23×C4—24no—
291C23×C4—22no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—41no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—41no—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318#124—432no—
319#124—416no—
320#123—416no—
321#121—416no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
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—24no—
366C2×C22⋊C4—22no—
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—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—41no—
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—41no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4C2×D418yes—
408C2×C22⋊C4C2×D414yes—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—41no—
418C2×C42—42no—
419C2×C42—42no—
420#95—22no—
421#95—22no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
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—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—41no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95C2×D414yes—
462#95C2×D418yes—
463C24—21no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—21no—
474C24—21no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24C22×D412yes—
488C24H(5,𝔽2)14yes—
489C24H(5,𝔽2)12yes—
490C24C2511yescharacteristic
491C2×Q8—216no—
492C2×Q8—216no—
493C2×Q8—216no—
494C2×Q8—44no—
495C2×Q8—48no—
496C2×Q8—48no—
497C2×Q8—44no—
498C2×Q8—48no—
499C2×Q8—48no—
500C2×Q8—48no—
501C2×Q8—44no—
502C2×Q8—48no—
503C2×Q8—48no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—48no—
507C2×Q8—4128no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—82no—
511C2×Q8—84no—
512C2×Q8—82no—
513C2×Q8—84no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—44no—
519C2×D4—48no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—84no—
524C2×D4—82no—
525C2×D4—82no—
526C2×D4—84no—
527C2×D4—82no—
528C2×D4—84no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—28no—
537C22×C4—216no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
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—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
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—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—44no—
632C22×C4—48no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—82no—
636C22×C4—84no—
637C22×C4—82no—
638C22×C4—84no—
639C22×C4C22×D412yes—
640C22×C4C22×D414yes—
641C22×C4C22×D412yes—
642C22×C4C22×D414yes—
643C22×C4C2×#4114yes—
644C22×C4C2×#4114yes—
645C22×C4C2×#4114yes—
646C22×C4H(5,𝔽2)14yes—
647C22×C4H(5,𝔽2)12yes—
648C22×C42−1+414yes—
649C22×C42−1+414yes—
650C4⋊C4—44no—
651C4⋊C4—48no—
652C4⋊C4—84no—
653C4⋊C4—84no—
654C4⋊C4—84no—
655C4⋊C4—84no—
656C4⋊C4—84no—
657C4⋊C4—84no—
658C4⋊C4—84no—
659C4⋊C4—84no—
660C22⋊C4—28no—
661C22⋊C4—216no—
662C22⋊C4—44no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—84no—
676C22⋊C4—84no—
677C22⋊C4—84no—
678C22⋊C4—82no—
679C22⋊C4—84no—
680C42—48no—
681C42—44no—
682C42—48no—
683C42—84no—
684C23—22no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—24no—
694C23—24no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—42no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—41no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23H(3,𝔽4)14yes—
747C23C23×D411yescharacteristic
748C23C22×#4112yes—
749C23C2×H(5,𝔽2)12yes—
750C23C2×H(5,𝔽2)11yescharacteristic
751C23C2×H(5,𝔽2)11yescharacteristic
752C23C2×H(5,𝔽2)12yes—
753C23C2×2−1+412yes—
754C23C2×2−1+412yes—
755C23#58512yes—
756Q8—416no—
757Q8—432no—
758Q8—416no—
759Q8—88no—
760D4—88no—
761D4—88no—
762D4—88no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—432no—
790C2×C4—416no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—42no—
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—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—41no—
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—42no—
855C2×C4—42no—
856C2×C4—41no—
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—42no—
866C2×C4—42no—
867C2×C4—88no—
868C2×C4#54618yes—
869C2×C4#55114yes—
870C22—28no—
871C22—24no—
872C22—44no—
873C22—44no—
874C22—42no—
875C22—44no—
876C22—42no—
877C22—44no—
878C22—44no—
879C22—42no—
880C22—44no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—81no—
892C22—82no—
893C22—81no—
894C22—81no—
895C22—82no—
896C22—82no—
897C22C2×#54612yes—
898C22C2×#55111yescharacteristic
899C22#348411yescharacteristic
900C22#348611yescharacteristic
901C22#348812yes—
902C22#349012yes—
903C22#349911yescharacteristic
904C22#351612yes—
905C22#351812yes—
906C22#352212yes—
907C22#352212yes—
908C22C2×H(3,𝔽4)11yescharacteristic
909C22#353211yescharacteristic
910C22#353612yes—
911C22#353612yes—
912C22#354112yes—
913C22#354412yes—
914C22#354511yescharacteristic
915C22#354712yes—
916C22#355212yes—
917C22#355812yes—
918C4—28no—
919C4—24no—
920C4—44no—
921C4—44no—
922C4—44no—
923C4—42no—
924C4—42no—
925C4—44no—
926C4—82no—
927C4—82no—
928C4—82no—
929C4—82no—
930C4—82no—
931C4—81no—
932C4—82no—
933C4—82no—
934C2—44no—
935C2—82no—
936C2—161no—
937C2#4529212yes—
938C2#4530312yes—
939C2#4541712yes—
940C2#4597711yescharacteristic
941C2#4609912yes—
942C2#4642611yescharacteristic
943C2#4765612yes—
944C2#5889712yes—
945C2#5900611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2763C2semidirect
3. #17198C2semidirect
4. #17153C2semidirect
5. #16094C2semidirect
6. #15851C2semidirect
8. #15568C2semidirect
9. #15510C2semidirect
10. #15311C2semidirect
11. #15269C2semidirect
13. #14968C2semidirect
14. #14922C2semidirect
15. #14833C2semidirect
16. #14537C2semidirect
17. #14421C2semidirect
18. #14378C2semidirect
19. #13922C2semidirect

Maximal subgroups

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

subgroupindex
C2×#27632
C2×#24362
#171982
#171532
#160942
#158512
#156732
#155682
#155102
#153112
#152692
#152602
#149682
#149222
#148332
#145372
#144212
#143782
#139222