Finite Group Databasebeta

← #4598717

Subgroups — #4598717

Order 512.

2834 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2820C211yesmaximal, characteristic, complemented
2C2×#2436C211yesmaximal, characteristic
3#17122C212yesmaximal, complemented
4#17106C212yesmaximal, complemented
5#16831C212yesmaximal, complemented
6#16695C211yesmaximal, characteristic, complemented
7#16611C212yesmaximal, complemented
8#16608C211yesmaximal, characteristic, complemented
9#16520C212yesmaximal, complemented
10#16380C212yesmaximal, complemented
11#16348C212yesmaximal, complemented
12#15328C212yesmaximal, complemented
13#15327C212yesmaximal, complemented
14#15311C212yesmaximal, complemented
15#15277C212yesmaximal
16#15017C211yesmaximal, characteristic, complemented
17#14916C211yesmaximal, characteristic, complemented
18#14874C212yesmaximal, complemented
19#14473C211yesmaximal, characteristic, complemented
20C24×Q8C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×#121C2211yescharacteristic
25#2820—28no—
26#2436—28no—
27C2×#399C2212yes—
28C2×#397C2212yes—
29C2×#397C2212yes—
30C2×#397C2212yes—
31C2×#396C2212yes—
32C2×#396C2212yes—
33C2×#395C2212yes—
34C2×#395C2212yes—
35C2×#395C2212yes—
36C2×#395C2212yes—
37C2×#394C2212yes—
38C2×#393C2212yes—
39C2×#393C2212yes—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#382C2211yescharacteristic
50C2×#380C2212yes—
51C2×C4×C22⋊C4C2211yescharacteristic
52#1446C2212yes—
53#1446C2212yes—
54#1446C2212yes—
55#1446C2212yes—
56#1445C2212yes—
57#1445C2212yes—
58#1444C2211yescharacteristic
59#1444C2211yescharacteristic
60#1444C2212yes—
61#1443C2212yes—
62#1443C2212yes—
63#1443C2212yes—
64#1443C2212yes—
65#1443C2212yes—
66#1443C2212yes—
67#1442C2212yes—
68#1442C2211yescharacteristic
69#1442C2212yes—
70#1442C2211yescharacteristic
71#1442C2212yes—
72#1442C2212yes—
73#1442C2212yes—
74#1442C2212yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2212yes—
78#1441C2212yes—
79#1441C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1440C2212yes—
83#1440C2212yes—
84#1440C2212yes—
85#1439C2212yes—
86#1439C2211yescharacteristic
87#1439C2211yescharacteristic
88#1439C2212yes—
89#1439C2212yes—
90#1439C2211yescharacteristic
91#1439C2212yes—
92#1439C2211yescharacteristic
93#1439C2212yes—
94#1439C2212yes—
95#1438C2212yes—
96#1438C2212yes—
97#1438C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100#1434C2211yescharacteristic
101#1434C2211yescharacteristic
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C23×Q8—24no—
110C23×Q8—42no—
111C23×Q8—42no—
112C23×Q8—44no—
113C23×Q8—44no—
114C23×Q8C2311yescharacteristic
115C23×Q8C2312yes—
116C23×Q8C2311yescharacteristic
117C23×D4C2312yes—
118C23×D4C2311yescharacteristic
119C24×C4C2311yescharacteristic
120C24×C4C2312yes—
121C24×C4C2312yes—
122C2×#125—24no—
123C2×#125—44no—
124C2×#124—24no—
125C2×#124—44no—
126C2×#124—44no—
127C2×#124D418yes—
128C2×#121—24no—
129C2×#121—42no—
130C2×#121—42no—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2311yescharacteristic
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×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#399—28no—
165#397—28no—
166#397—44no—
167#397—44no—
168#396—28no—
169#396—28no—
170#395—28no—
171#395—44no—
172#395—44no—
173#395—44no—
174#394—28no—
175#393—28no—
176#393—28no—
177#391—24no—
178#391—24no—
179#386—28no—
180#386—28no—
181#386—44no—
182#386—44no—
183#385—44no—
184#385—44no—
185#385—44no—
186#382—24no—
187#380—44no—
188C4×C22⋊C4—24no—
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
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×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C25C2412yes—
236C25C2411yescharacteristic
237C22×Q8—22no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×Q8—24no—
241C22×Q8—24no—
242C22×Q8—24no—
243C22×Q8—24no—
244C22×Q8—42no—
245C22×Q8—41no—
246C22×Q8—41no—
247C22×Q8—41no—
248C22×Q8—41no—
249C22×Q8—42no—
250C22×Q8—42no—
251C22×Q8—42no—
252C22×Q8—42no—
253C22×Q8—416no—
254C22×Q8—416no—
255C22×Q8—416no—
256C22×Q8—432no—
257C22×Q8—432no—
258C22×Q8C2×D414yes—
259C22×D4—24no—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—24no—
263C22×D4—24no—
264C22×D4—41no—
265C22×D4—41no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—42no—
270C22×D4C2×D414yes—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307#125—416no—
308#124—416no—
309#124—416no—
310#121—416no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—41no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
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×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
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—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
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⋊C4C2×D418yes—
399C2×C22⋊C4C2×D418yes—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—42no—
403C2×C42C2×D414yes—
404#95—22no—
405#95—22no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—41no—
422#95—41no—
423#95—41no—
424#95—41no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
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—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24C22×D414yes—
473C24H(5,𝔽2)12yes—
474C242−1+412yes—
475C242−1+412yes—
476C24C2511yescharacteristic
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—48no—
482C2×Q8—48no—
483C2×Q8—48no—
484C2×Q8—48no—
485C2×Q8—48no—
486C2×Q8—44no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—48no—
490C2×Q8—48no—
491C2×Q8—48no—
492C2×Q8—4128no—
493C2×Q8—48no—
494C2×Q8—44no—
495C2×D4—28no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—84no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—84no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—28no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
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—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
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—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—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
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—21no—
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—22no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—44no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—44no—
619C22×C4—84no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4—84no—
623C22×C4—84no—
624C22×C4—84no—
625C22×C4C22×D412yes—
626C22×C4C22×D414yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4H(5,𝔽2)12yes—
630C22×C4H(5,𝔽2)14yes—
631C22×C4H(5,𝔽2)14yes—
632C22×C42−1+414yes—
633C4⋊C4—44no—
634C4⋊C4—48no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—48no—
638C4⋊C4—84no—
639C4⋊C4—84no—
640C4⋊C4—82no—
641C4⋊C4—82no—
642C4⋊C4—84no—
643C4⋊C4—84no—
644C4⋊C4—84no—
645C4⋊C4—84no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C22⋊C4—84no—
659C22⋊C4—84no—
660C22⋊C4—84no—
661C22⋊C4—84no—
662C22⋊C4—84no—
663C22⋊C4—84no—
664C42—28no—
665C42—44no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
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—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23#56314yes—
724C23C23×D411yescharacteristic
725C23C2×H(5,𝔽2)12yes—
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×H(5,𝔽2)12yes—
728C23C2×H(5,𝔽2)11yescharacteristic
729C23C2×2−1+411yescharacteristic
730C23C2×2−1+411yescharacteristic
731C23C2×2−1+412yes—
732C23#58511yescharacteristic
733C23#58511yescharacteristic
734C23#58512yes—
735Q8—416no—
736Q8—416no—
737Q8—432no—
738D4—88no—
739D4—816no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—416no—
762C2×C4—432no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
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—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
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—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—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—816no—
849C2×C4#53414yes—
850C22—24no—
851C22—28no—
852C22—42no—
853C22—42no—
854C22—44no—
855C22—42no—
856C22—42no—
857C22—44no—
858C22—44no—
859C22—42no—
860C22—42no—
861C22—44no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22C2×#53411yescharacteristic
877C22#348411yescharacteristic
878C22#348411yescharacteristic
879C22#348911yescharacteristic
880C22#348911yescharacteristic
881C22#349911yescharacteristic
882C22#350011yescharacteristic
883C22C2×#56311yescharacteristic
884C22#353212yes—
885C22#353212yes—
886C22#353512yes—
887C22#354112yes—
888C22#354112yes—
889C22#354112yes—
890C22#354511yescharacteristic
891C22#354712yes—
892C22#355112yes—
893C22#355212yes—
894C22#355212yes—
895C22#356111yescharacteristic
896C22#356111yescharacteristic
897C22#356112yes—
898C22#356212yes—
899C4—24no—
900C4—44no—
901C4—42no—
902C4—44no—
903C4—44no—
904C4—42no—
905C4—42no—
906C4—81no—
907C4—81no—
908C4—82no—
909C4—82no—
910C4—82no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4—82no—
916C2—44no—
917C2—84no—
918C2#3670211yescharacteristic
919C2#4290811yescharacteristic
920C2#4291211yescharacteristic
921C2#4613611yescharacteristic
922C2#5120911yescharacteristic
923C2#5121311yescharacteristic
924C2#5154111yescharacteristic
925C2#5239912yes—
926C2#5489212yes—
927C2#5715512yes—
928C2#5721412yes—
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×#2820C2semidirect
3. #17122C2semidirect
4. #17106C2semidirect
5. #16831C2semidirect
6. #16695C2semidirect
7. #16611C2semidirect
8. #16608C2semidirect
9. #16520C2semidirect
10. #16380C2semidirect
11. #16348C2semidirect
12. #15328C2semidirect
13. #15327C2semidirect
14. #15311C2semidirect
16. #15017C2semidirect
17. #14916C2semidirect
18. #14874C2semidirect
19. #14473C2semidirect

Maximal subgroups

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

subgroupindex
C2×#28202
C2×#24362
#171222
#171062
#168312
#166952
#166112
#166082
#165202
#163802
#163482
#153282
#153272
#153112
#152772
#150172
#149162
#148742
#144732