Finite Group Databasebeta

← #557127

Subgroups — #557127

Order 512.

2790 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic
2#14684C211yesmaximal, characteristic, complemented
3#14670C211yesmaximal, characteristic, complemented
4#14667C211yesmaximal, characteristic, complemented
5#14512C212yesmaximal, complemented
6#14509C212yesmaximal, complemented
7#14496C212yesmaximal, complemented
8#14479C212yesmaximal, complemented
9#14459C212yesmaximal, complemented
10#14431C212yesmaximal, complemented
11#14047C212yesmaximal, complemented
12#14023C212yesmaximal
13#14020C212yesmaximal, complemented
14#14016C212yesmaximal, complemented
15#13996C212yesmaximal, complemented
16#13968C212yesmaximal, complemented
17#13833C211yesmaximal, characteristic, complemented
18#13832C211yesmaximal, characteristic, complemented
19C2×#1434C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×#121C2211yescharacteristic
22C22×C4×D4C2212yes—
23C23×C42C2211yescharacteristic
24#2854C4116yescomplemented
25C2×#390C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#388C2212yes—
30C2×#388C2212yes—
31C2×#387C2212yes—
32C2×#386C2212yes—
33C2×#386C2212yes—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#385C2212yes—
38C2×#381C2212yes—
39C2×#380C2211yescharacteristic
40C2×C4×C22⋊C4C2212yes—
41C22×#95C2212yes—
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2212yes—
45#1445C2212yes—
46#1445C2212yes—
47#1445C2212yes—
48#1443C2212yes—
49#1443C2212yes—
50#1443C2212yes—
51#1442C2212yes—
52#1442C2212yes—
53#1442C2212yes—
54#1441C2212yes—
55#1441C2212yes—
56#1441C2212yes—
57#1441C2212yes—
58#1440C2212yes—
59#1440C2212yes—
60#1440C2212yes—
61#1440C2212yes—
62#1440C2212yes—
63#1439C2212yes—
64#1439C2212yes—
65#1439C2212yes—
66#1439C2212yes—
67#1439C2212yes—
68#1438C2212yes—
69#1437C2212yes—
70#1437C2212yes—
71#1437C2212yes—
72#1437C2212yes—
73#1437C2212yes—
74#1436C2212yes—
75#1436C2212yes—
76#1436C2212yes—
77#1436C2212yes—
78#1436C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83#1434C2211yescharacteristic
84#1434C2211yescharacteristic
85#1434C2211yescharacteristic
86#1434C2212yes—
87#1434C2211yescharacteristic
88#1434C2212yes—
89#1434C2211yescharacteristic
90#1434C2211yescharacteristic
91#1434C2212yes—
92#1434C2212yes—
93#1434C2212yes—
94#1434C2212yes—
95#1434C2212yes—
96#1434C2211yescharacteristic
97#1434C2211yescharacteristic
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2211yescharacteristic
101C22⋊#95C2211yescharacteristic
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2312yes—
116C2×#123—44no—
117C2×#123—44no—
118C2×#123C2×C4116yescomplemented
119C2×#121—44no—
120C2×#121C2×C418yes—
121C2×C4×D4—44no—
122C2×C4×D4—44no—
123C2×C4×D4—44no—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
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×C42—44no—
148C22×C42C2×C418yescomplemented
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#390C2×C418yescomplemented
157#390C2×C418yescomplemented
158#389C2×C418yescomplemented
159#389C2×C418yescomplemented
160#388C2×C4116yescomplemented
161#388C2×C4116yescomplemented
162#387—28no—
163#386—28no—
164#386—44no—
165#386—44no—
166#386—44no—
167#386C2×C4116yescomplemented
168#385—44no—
169#381—44no—
170#380C2×C418yescomplemented
171C4×C22⋊C4—44no—
172C2×#95—28no—
173C2×#95—42no—
174C2×#95—42no—
175C2×#95—44no—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2311yescharacteristic
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2311yescharacteristic
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2311yescharacteristic
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2312yes—
215C2×#95C2311yescharacteristic
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C25C2412yes—
226C25C2411yescharacteristic
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—42no—
235C22×D4—41no—
236C22×D4—41no—
237C22×D4C22×C418yes—
238C22×D4C22×C414yes—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—41no—
256C23×C4—41no—
257C23×C4—41no—
258C23×C4—41no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4C22×C414yes—
273C23×C4C22×C414yes—
274C23×C4C22×C414yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292#123—432no—
293#121—416no—
294C4×D4—432no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4C22×C414yes—
313C2×C4⋊C4C22×C414yes—
314C2×C4⋊C4C22×C418yes—
315C2×C4⋊C4C22×C418yes—
316C2×C4⋊C4C22×C414yes—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
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⋊C4C22×C418yes—
357C2×C22⋊C4C22×C418yes—
358C2×C22⋊C4C22×C418yes—
359C2×C22⋊C4C22×C418yes—
360C2×C22⋊C4C22×C418yes—
361C2×C22⋊C4C22×C418yes—
362C2×C42—24no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—416no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42C22×C414yes—
377C2×C42C22×C414yes—
378C2×C42C22×C414yes—
379C2×C42C22×C414yes—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—41no—
388#95—42no—
389#95—41no—
390#95—42no—
391#95—41no—
392#95—41no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—41no—
403#95—42no—
404#95—42no—
405#95—41no—
406#95—41no—
407#95—42no—
408#95—41no—
409#95—42no—
410#95—42no—
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—42no—
424#95—42no—
425#95C22×C418yes—
426#95C22×C418yes—
427#95C22×C418yes—
428#95#4118yes—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24C23×C414yes—
450C24C23×C412yes—
451C24H(5,𝔽2)14yes—
452C24H(5,𝔽2)14yes—
453C24H(5,𝔽2)12yes—
454C242−1+412yes—
455C24C2511yescharacteristic
456C2×D4—216no—
457C2×D4—216no—
458C2×D4—216no—
459C2×D4—28no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—84no—
467C2×D4—84no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
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—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—28no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
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—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—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—84no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4C23×C412yes—
600C22×C4C23×C412yes—
601C22×C4C23×C412yes—
602C22×C4C23×C414yes—
603C22×C4C23×C414yes—
604C22×C4C23×C414yes—
605C22×C4C23×C412yes—
606C22×C4C23×C412yes—
607C22×C4C23×C412yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4114yes—
610C22×C4C2×#4114yes—
611C4⋊C4—28no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—84no—
618C4⋊C4—84no—
619C22⋊C4—216no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C22⋊C4—84no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C42—44no—
635C42—44no—
636C42—44no—
637C42—44no—
638C42—48no—
639C42—84no—
640C42—84no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
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#51814yes—
695C23#51814yes—
696C23#52014yes—
697C23#56018yes—
698C23#56218yes—
699C23C24×C411yescharacteristic
700C23C22×#4112yes—
701C23C2×H(5,𝔽2)12yes—
702C23C2×H(5,𝔽2)12yes—
703C23C2×H(5,𝔽2)11yescharacteristic
704C23C2×2−1+411yescharacteristic
705C23#58511yescharacteristic
706C23#58511yescharacteristic
707C23#58511yescharacteristic
708C23#58511yescharacteristic
709C23#58512yes—
710D4—432no—
711D4—88no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—416no—
747C2×C4—416no—
748C2×C4—416no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
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—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
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—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—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—816no—
822C2×C4—816no—
823C2×C4—816no—
824C2×C4C4×#4114yes—
825C22—28no—
826C22—28no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—28no—
834C22—28no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22#237718yes—
851C22C2×C4×#4111yescharacteristic
852C22C2×#51811yescharacteristic
853C22C2×#51811yescharacteristic
854C22C2×#52011yescharacteristic
855C22#342811yescharacteristic
856C22#342811yescharacteristic
857C22#342811yescharacteristic
858C22#349412yes—
859C22#349412yes—
860C22#351312yes—
861C22#351312yes—
862C22#351312yes—
863C22#351612yes—
864C22C2×#56012yes—
865C22C2×#56212yes—
866C22#353312yes—
867C22#353312yes—
868C22#354511yescharacteristic
869C22#354511yescharacteristic
870C22#355311yescharacteristic
871C22#355311yescharacteristic
872C22#356012yes—
873C22#356012yes—
874C4—24no—
875C4—44no—
876C4—42no—
877C4—42no—
878C4—44no—
879C4—44no—
880C4—42no—
881C4—42no—
882C4—44no—
883C4—42no—
884C4—44no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C2—28no—
892C2—84no—
893C2#3422211yescharacteristic
894C2#3423011yescharacteristic
895C2#3423811yescharacteristic
896C2C2×#237711yescharacteristic
897C2#3438811yescharacteristic
898C2#3439011yescharacteristic
899C2#3439611yescharacteristic
900C2#4555612yes—
901C2#4555812yes—
902C2#4558612yes—
903C2#4558812yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14684C2semidirect
3. #14670C2semidirect
4. #14667C2semidirect
5. #14512C2semidirect
6. #14509C2semidirect
7. #14496C2semidirect
8. #14479C2semidirect
9. #14459C2semidirect
10. #14431C2semidirect
11. #14047C2semidirect
13. #14020C2semidirect
14. #14016C2semidirect
15. #13996C2semidirect
16. #13968C2semidirect
17. #13833C2semidirect
18. #13832C2semidirect
19. C2×#1434C2semidirect
24. #2854C4semidirect
118. C2×#123C2×C4semidirect
148. C22×C42C2×C4semidirect
156. #390C2×C4semidirect
157. #390C2×C4semidirect
158. #389C2×C4semidirect
159. #389C2×C4semidirect
160. #388C2×C4semidirect
161. #388C2×C4semidirect
167. #386C2×C4semidirect
170. #380C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
#146842
#146702
#146672
#145122
#145092
#144962
#144792
#144592
#144312
#140472
#140232
#140202
#140162
#139962
#139682
#138332
#138322
C2×#14342