Finite Group Databasebeta

← #3531631

Subgroups — #3531631

Order 512.

2214 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17217C212yesmaximal, complemented
2#17072C211yesmaximal, characteristic, complemented
3#16952C212yesmaximal, complemented
4#16832C212yesmaximal, complemented
5#16684C211yesmaximal, characteristic, complemented
6#16587C212yesmaximal, complemented
7#15944C212yesmaximal, complemented
8#15772C212yesmaximal, complemented
9#15673C212yesmaximal
10#15311C212yesmaximal, complemented
11#15311C212yesmaximal, complemented
12#14968C212yesmaximal, complemented
13#14922C212yesmaximal, complemented
14#14719C211yesmaximal, characteristic
15#14632C211yesmaximal, characteristic, complemented
16#14494C211yesmaximal, characteristic, complemented
17#14412C212yesmaximal, complemented
18#13923C211yesmaximal, characteristic, complemented
19#13881C211yesmaximal, characteristic, complemented
20C22×#124C2212yes—
21C22×#121C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C2×#397C2212yes—
24C2×#396C2212yes—
25C2×#395C2212yes—
26C2×#395C2212yes—
27C2×#395C2212yes—
28C2×#394C2211yescharacteristic
29C2×#394C2212yes—
30C2×#394C2212yes—
31C2×#394C2211yescharacteristic
32C2×#393C2212yes—
33C2×#388C2212yes—
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#382C2211yescharacteristic
39C2×#382C2211yescharacteristic
40C2×#382C2212yes—
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2211yescharacteristic
45#1446C2212yes—
46#1446C2212yes—
47#1445C2212yes—
48#1443C2212yes—
49#1443C2212yes—
50#1442C2212yes—
51#1442C2212yes—
52#1442C2212yes—
53#1442C2212yes—
54#1442C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1441C2211yescharacteristic
59#1441C2211yescharacteristic
60#1441C2211yescharacteristic
61#1441C2212yes—
62#1441C2211yescharacteristic
63#1441C2212yes—
64#1441C2211yescharacteristic
65#1441C2211yescharacteristic
66#1441C2212yes—
67#1440C2212yes—
68#1440C2212yes—
69#1440C2212yes—
70#1440C2212yes—
71#1440C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1438C2212yes—
86#1438C2212yes—
87#1438C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98C4⋊#95C2211yescharacteristic
99C4⋊#95C2211yescharacteristic
100C4⋊#95C2212yes—
101#1434C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C23×Q8C2312yes—
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C2×#124—44no—
114C2×#124—44no—
115C2×#124—44no—
116C2×#121—44no—
117C2×#121—42no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
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×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2311yescharacteristic
158#397—44no—
159#396—44no—
160#395—44no—
161#395—44no—
162#395—44no—
163#394—24no—
164#394—42no—
165#394—44no—
166#394—44no—
167#393—44no—
168#388—28no—
169#388—44no—
170#388—44no—
171#386—44no—
172#386—44no—
173#382—24no—
174#382—44no—
175#382—42no—
176#380—42no—
177#380—42no—
178C4×C22⋊C4—24no—
179C4×C22⋊C4—42no—
180C2×#95C2312yes—
181C2×#95C2311yescharacteristic
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2311yescharacteristic
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×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C25C2412yes—
225C25C2411yescharacteristic
226C22×Q8—24no—
227C22×Q8—42no—
228C22×Q8—42no—
229C22×Q8—42no—
230C22×Q8—42no—
231C22×Q8—42no—
232C22×Q8—42no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—42no—
239C22×D4—42no—
240C22×D4—41no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—41no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—41no—
256C23×C4—41no—
257C23×C4—41no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279#124—432no—
280#121—416no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—416no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4#4114yes—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
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×C42—22no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—41no—
386C2×C42—42no—
387C2×C42—41no—
388C2×C42—42no—
389C2×C42#4114yes—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—22no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—41no—
410#95—41no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424#95—42no—
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—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—21no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24H(5,𝔽2)14yes—
459C24H(5,𝔽2)12yes—
460C24C2511yescharacteristic
461C2×Q8—48no—
462C2×Q8—84no—
463C2×Q8—84no—
464C2×Q8—84no—
465C2×Q8—84no—
466C2×Q8—84no—
467C2×Q8—84no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—44no—
472C2×D4—48no—
473C2×D4—82no—
474C2×D4—84no—
475C2×D4—84no—
476C2×D4—84no—
477C2×D4—84no—
478C2×D4—84no—
479C2×D4—82no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—28no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
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—21no—
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—21no—
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—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—84no—
598C22×C4C2×#4112yes—
599C22×C4C2×#4114yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4H(5,𝔽2)14yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C4H(5,𝔽2)12yes—
606C22×C42−1+412yes—
607C22×C42−1+414yes—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—82no—
614C4⋊C4—82no—
615C4⋊C4—84no—
616C4⋊C4—84no—
617C4⋊C4—84no—
618C4⋊C4—84no—
619C4⋊C4—82no—
620C4⋊C4—84no—
621C4⋊C4—82no—
622C4⋊C4—84no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C42—44no—
642C42—48no—
643C42—48no—
644C42—44no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
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—
702C23H(3,𝔽4)14yes—
703C23C22×#4111yescharacteristic
704C23C22×#4111yescharacteristic
705C23C2×H(5,𝔽2)11yescharacteristic
706C23C2×H(5,𝔽2)11yescharacteristic
707C23C2×H(5,𝔽2)11yescharacteristic
708C23C2×H(5,𝔽2)12yes—
709C23C2×H(5,𝔽2)12yes—
710C23C2×2−1+411yescharacteristic
711C23C2×2−1+412yes—
712C23#58511yescharacteristic
713C23#58512yes—
714Q8—816no—
715D4—816no—
716D4—88no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—416no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
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—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
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—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—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—88no—
829C2×C4—88no—
830C2×C4#55514yes—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—42no—
841C22—44no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22#345911yescharacteristic
858C22C2×#55511yescharacteristic
859C22#349011yescharacteristic
860C22#349211yescharacteristic
861C22#349412yes—
862C22#349511yescharacteristic
863C22#351112yes—
864C22#351412yes—
865C22#352212yes—
866C22C2×H(3,𝔽4)11yescharacteristic
867C22#353211yescharacteristic
868C22#353411yescharacteristic
869C22#353412yes—
870C22#353612yes—
871C22#353611yescharacteristic
872C22#353712yes—
873C22#354112yes—
874C22#354212yes—
875C22#354411yescharacteristic
876C22#354511yescharacteristic
877C22#355212yes—
878C22#355912yes—
879C22#356512yes—
880C4—24no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—44no—
886C4—44no—
887C4—44no—
888C4—82no—
889C4—81no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—82no—
897C2—44no—
898C2—162no—
899C2#3794811yescharacteristic
900C2#4208512yes—
901C2#4520812yes—
902C2#4599111yescharacteristic
903C2#4609911yescharacteristic
904C2#4775011yescharacteristic
905C2#4892211yescharacteristic
906C2#5077212yes—
907C2#5241011yescharacteristic
908C2#5362412yes—
909C2#5561311yescharacteristic
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. #17217C2semidirect
2. #17072C2semidirect
3. #16952C2semidirect
4. #16832C2semidirect
5. #16684C2semidirect
6. #16587C2semidirect
7. #15944C2semidirect
8. #15772C2semidirect
10. #15311C2semidirect
11. #15311C2semidirect
12. #14968C2semidirect
13. #14922C2semidirect
15. #14632C2semidirect
16. #14494C2semidirect
17. #14412C2semidirect
18. #13923C2semidirect
19. #13881C2semidirect

Maximal subgroups

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

subgroupindex
#172172
#170722
#169522
#168322
#166842
#165872
#159442
#157722
#156732
#153112
#149682
#149222
#147192
#146322
#144942
#144122
#139232
#138812