Finite Group Databasebeta

← #522285

Subgroups — #522285

Order 512.

2662 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic
2#14459C212yesmaximal, complemented
3#14431C212yesmaximal, complemented
4#14372C212yesmaximal, complemented
5#14363C212yesmaximal
6#14293C212yesmaximal, complemented
7#14157C211yesmaximal, characteristic, complemented
8#14156C211yesmaximal, characteristic, complemented
9#14096C212yesmaximal, complemented
10#14095C212yesmaximal, complemented
11#14086C212yesmaximal, complemented
12#14085C212yesmaximal, complemented
13#14007C212yesmaximal, complemented
14#13984C212yesmaximal, complemented
15#13825C211yesmaximal, characteristic, complemented
16#13824C211yesmaximal, characteristic, complemented
17#13788C212yesmaximal, complemented
18C4×#381C211yesmaximal, characteristic, complemented
19C4×#381C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×#121C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#2854C4116yescomplemented
24C2×#390C2212yes—
25C2×#390C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#388C2212yes—
30C2×#388C2212yes—
31C2×#388C2212yes—
32C2×#388C2212yes—
33C2×#387C2212yes—
34C2×#387C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#381C2212yes—
39C2×#381C2211yescharacteristic
40C2×#381C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×C4×C4⋊C4C2212yes—
43C2×C4×C22⋊C4C2212yes—
44C2×C4×C22⋊C4C2212yes—
45C2×C4×C22⋊C4C2212yes—
46C2×C4×C22⋊C4C2212yes—
47#1445C2212yes—
48#1445C2212yes—
49#1443C2212yes—
50#1443C2212yes—
51#1442C2212yes—
52#1442C2212yes—
53#1441C2212yes—
54#1441C2212yes—
55#1441C2212yes—
56#1440C2212yes—
57#1440C2212yes—
58#1440C2212yes—
59#1439C2212yes—
60#1439C2212yes—
61#1439C2212yes—
62#1439C2212yes—
63#1439C2212yes—
64#1438C2212yes—
65#1438C2212yes—
66#1438C2212yes—
67#1437C2212yes—
68#1437C2212yes—
69#1437C2212yes—
70#1437C2212yes—
71#1437C2212yes—
72#1437C2212yes—
73#1437C2212yes—
74#1437C2212yes—
75#1437C2212yes—
76#1436C2212yes—
77#1436C2212yes—
78#1436C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85C4⋊#95C2212yes—
86#1434C2211yescharacteristic
87#1434C2211yescharacteristic
88#1434C2212yes—
89#1434C2212yes—
90#1434C2212yes—
91#1434C2212yes—
92#1434C2212yes—
93#1434C2211yescharacteristic
94#1434C2211yescharacteristic
95C22⋊#95C2212yes—
96C22⋊#95C2212yes—
97C22⋊#95C2211yescharacteristic
98C22⋊#95C2211yescharacteristic
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C4×#95C2211yescharacteristic
102C4×#95C2211yescharacteristic
103C4×#95C2211yescharacteristic
104C4×#95C2212yes—
105C4×#95C2212yes—
106C4×#95C2211yescharacteristic
107C4×#95C2212yes—
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C2×#123—44no—
115C2×#123—44no—
116C2×#123C2×C4116yescomplemented
117C2×#121—44no—
118C2×#121C2×C418yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
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×C42—44no—
145C22×C42C2×C418yescomplemented
146C22×C42C2312yes—
147C22×C42C2312yes—
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#390—44no—
158#390C2×C418yes—
159#390C2×C418yes—
160#389C2×C418yescomplemented
161#389C2×C418yescomplemented
162#388—28no—
163#388—44no—
164#388C2×C4116yescomplemented
165#388C2×C4116yescomplemented
166#387—28no—
167#387—44no—
168#386—28no—
169#386—44no—
170#386C2×C4116yescomplemented
171#381—24no—
172#381—28no—
173#381—24no—
174#380C2×C418yescomplemented
175C4×C4⋊C4—44no—
176C4×C22⋊C4—28no—
177C4×C22⋊C4—44no—
178C4×C22⋊C4—44no—
179C4×C22⋊C4—44no—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2311yescharacteristic
183C2×#95C2311yescharacteristic
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2311yescharacteristic
188C2×#95C2311yescharacteristic
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×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C25C2412yes—
226C25C2411yescharacteristic
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—42no—
231C22×D4—42no—
232C22×D4—42no—
233C22×D4—41no—
234C22×D4—41no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4C22×C418yes—
238C22×D4C22×C414yes—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—41no—
252C23×C4—41no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4C22×C414yes—
259C23×C4C22×C414yes—
260C23×C4C22×C414yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278#123—432no—
279#121—416no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4C22×C418yes—
298C2×C4⋊C4C22×C414yes—
299C2×C4⋊C4C22×C414yes—
300C2×C4⋊C4C22×C418yes—
301C2×C4⋊C4C22×C414yes—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
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⋊C4C22×C418yes—
348C2×C22⋊C4C22×C418yes—
349C2×C22⋊C4C22×C418yes—
350C2×C22⋊C4C22×C418yes—
351C2×C22⋊C4C22×C418yes—
352C2×C22⋊C4C22×C418yes—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—42no—
360C2×C42—416no—
361C2×C42—42no—
362C2×C42—42no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—42no—
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×C42—42no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42C22×C414yes—
380C2×C42C22×C414yes—
381C2×C42C22×C414yes—
382C2×C42C22×C414yes—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—22no—
390#95—22no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—22no—
397#95—22no—
398#95—22no—
399#95—22no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
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#95C22×C418yes—
423#95C22×C418yes—
424#95C22×C418yes—
425#95#4114yes—
426#95#4118yes—
427#95#4114yes—
428C24—22no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24—21no—
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—
449C24—22no—
450C24—22no—
451C24C23×C414yes—
452C24C23×C412yes—
453C24H(5,𝔽2)14yes—
454C24C2511yescharacteristic
455C2×D4—216no—
456C2×D4—28no—
457C2×D4—44no—
458C2×D4—48no—
459C2×D4—44no—
460C2×D4—48no—
461C2×D4—84no—
462C2×D4—84no—
463C2×D4—84no—
464C2×D4—84no—
465C2×D4—84no—
466C2×D4—84no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
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—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
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—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
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—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4C23×C412yes—
579C22×C4C23×C412yes—
580C22×C4C23×C414yes—
581C22×C4C23×C414yes—
582C22×C4C23×C414yes—
583C22×C4C23×C412yes—
584C22×C4C23×C412yes—
585C22×C4C23×C412yes—
586C22×C4C23×C412yes—
587C22×C4C2×#4114yes—
588C22×C4C2×#4114yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4114yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4H(5,𝔽2)12yes—
595C22×C4H(5,𝔽2)12yes—
596C4⋊C4—28no—
597C4⋊C4—216no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—84no—
603C4⋊C4—84no—
604C22⋊C4—216no—
605C22⋊C4—216no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—84no—
617C22⋊C4—84no—
618C22⋊C4—84no—
619C22⋊C4—84no—
620C22⋊C4—84no—
621C42—44no—
622C42—44no—
623C42—44no—
624C42—44no—
625C42—48no—
626C42—84no—
627C42—84no—
628C42—84no—
629C42—84no—
630C42—84no—
631C42—84no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
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#51814yes—
690C23C24×C411yescharacteristic
691C23C22×#4112yes—
692C23C22×#4111yescharacteristic
693C23C22×#4111yescharacteristic
694C23C2×H(5,𝔽2)11yescharacteristic
695C23C2×H(5,𝔽2)11yescharacteristic
696C23C2×H(5,𝔽2)12yes—
697C23#58512yes—
698C23#58512yes—
699C23#58511yescharacteristic
700C23#58511yescharacteristic
701D4—88no—
702D4—816no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
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—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—416no—
746C2×C4—416no—
747C2×C4—416no—
748C2×C4—42no—
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—816no—
811C2×C4C4×#4114yes—
812C2×C4C4×#4114yes—
813C2×C4#51814yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—42no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22C2×C4×#4111yescharacteristic
841C22C2×C4×#4111yescharacteristic
842C22C2×#51811yescharacteristic
843C22C2×#51811yescharacteristic
844C22#342811yescharacteristic
845C22#342811yescharacteristic
846C22#342811yescharacteristic
847C22#346012yes—
848C22#346012yes—
849C22#347512yes—
850C22#348012yes—
851C22#351312yes—
852C22#351312yes—
853C22#351312yes—
854C22#351312yes—
855C22#351411yescharacteristic
856C22#351411yescharacteristic
857C22#351711yescharacteristic
858C22#351711yescharacteristic
859C22#353412yes—
860C22#353412yes—
861C22#356612yes—
862C22#356612yes—
863C4—24no—
864C4—24no—
865C4—24no—
866C4—44no—
867C4—42no—
868C4—44no—
869C4—44no—
870C4—44no—
871C4—44no—
872C4—44no—
873C4—42no—
874C4—44no—
875C4—42no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C2—44no—
881C2—84no—
882C2#3408611yescharacteristic
883C2#3415111yescharacteristic
884C2#3422811yescharacteristic
885C2#3423211yescharacteristic
886C2#3423811yescharacteristic
887C2#3435811yescharacteristic
888C2#3439511yescharacteristic
889C2#3908512yes—
890C2#3908612yes—
891C2#3930012yes—
892C2#3930312yes—
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. #14459C2semidirect
3. #14431C2semidirect
4. #14372C2semidirect
6. #14293C2semidirect
7. #14157C2semidirect
8. #14156C2semidirect
9. #14096C2semidirect
10. #14095C2semidirect
11. #14086C2semidirect
12. #14085C2semidirect
13. #14007C2semidirect
14. #13984C2semidirect
15. #13825C2semidirect
16. #13824C2semidirect
17. #13788C2semidirect
18. C4×#381C2semidirect
19. C4×#381C2semidirect
23. #2854C4semidirect
116. C2×#123C2×C4semidirect
145. C22×C42C2×C4semidirect
160. #389C2×C4semidirect
161. #389C2×C4semidirect
164. #388C2×C4semidirect
165. #388C2×C4semidirect
170. #386C2×C4semidirect
174. #380C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
#144592
#144312
#143722
#143632
#142932
#141572
#141562
#140962
#140952
#140862
#140852
#140072
#139842
#138252
#138242
#137882
C4×#3812