Finite Group Databasebeta

← #522420

Subgroups — #522420

Order 512.

2886 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2850C211yesmaximal, characteristic
2#14455C212yesmaximal, complemented
3#14421C212yesmaximal, complemented
4#14362C212yesmaximal, complemented
5#14361C212yesmaximal
6#14267C212yesmaximal, complemented
7#14162C211yesmaximal, characteristic, complemented
8#14157C211yesmaximal, characteristic, complemented
9#14124C212yesmaximal, complemented
10#14119C212yesmaximal, complemented
11#14116C212yesmaximal, complemented
12#14112C212yesmaximal, complemented
13#14071C212yesmaximal, complemented
14#14064C212yesmaximal, complemented
15#13826C211yesmaximal, characteristic, complemented
16#13824C211yesmaximal, characteristic, complemented
17#13791C212yesmaximal, complemented
18C4×#380C211yesmaximal, characteristic, complemented
19#13756C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#117C2212yes—
24C23×C42C2211yescharacteristic
25#2850C4116yescomplemented
26C2×#391C2212yes—
27C2×#391C2211yescharacteristic
28C2×#390C2212yes—
29C2×#390C2211yescharacteristic
30C2×#389C2212yes—
31C2×#388C2212yes—
32C2×#388C2212yes—
33C2×#388C2212yes—
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#387C2212yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#382C2211yescharacteristic
45C2×#380C2212yes—
46C2×C4×C4⋊C4C2212yes—
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2212yes—
50#1446C2212yes—
51#1444C2212yes—
52#1443C2212yes—
53#1442C2212yes—
54#1442C2212yes—
55#1441C2212yes—
56#1441C2212yes—
57#1441C2212yes—
58#1441C2212yes—
59#1440C2212yes—
60#1439C2212yes—
61#1439C2212yes—
62#1439C2212yes—
63#1439C2212yes—
64#1439C2212yes—
65#1439C2212yes—
66#1439C2212yes—
67#1438C2212yes—
68#1438C2212yes—
69#1438C2212yes—
70#1437C2212yes—
71#1437C2212yes—
72#1437C2212yes—
73#1437C2212yes—
74#1437C2212yes—
75#1437C2212yes—
76#1437C2212yes—
77#1436C2212yes—
78#1436C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2212yes—
91#1434C2212yes—
92#1434C2212yes—
93#1434C2212yes—
94#1434C2212yes—
95C22⋊#95C2212yes—
96C22⋊#95C2212yes—
97C22⋊#95C2211yescharacteristic
98C22⋊#95C2211yescharacteristic
99C22⋊#95C2211yescharacteristic
100C22⋊#95C2211yescharacteristic
101C4×#95C2211yescharacteristic
102C4×#95C2211yescharacteristic
103C4×#95C2212yes—
104C4×#95C2212yes—
105C4×#95C2211yescharacteristic
106C4×#95C2212yes—
107C4×#95C2211yescharacteristic
108C23×Q8C2311yescharacteristic
109C23×D4C2311yescharacteristic
110C23×D4C2312yes—
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C24×C4C2311yescharacteristic
115C2×#124—44no—
116C2×#124C2×C418yes—
117C2×C22⋊Q8—42no—
118C2×C22⋊Q8—42no—
119C2×C22⋊Q8C2×C418yescomplemented
120C2×#121—42no—
121C2×#121—42no—
122C2×#121C2×C418yes—
123C2×#117—28no—
124C2×#117—44no—
125C2×#117—44no—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
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×C42—44no—
154C22×C42C2×C418yescomplemented
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#391—28no—
167#391C2×C418yescomplemented
168#390—28no—
169#390C2×C418yes—
170#389—44no—
171#388—44no—
172#388—44no—
173#388—44no—
174#388—44no—
175#388C2×C4116yescomplemented
176#388C2×C4116yescomplemented
177#387—44no—
178#386—28no—
179#386—28no—
180#386C2×C4116yescomplemented
181#386C2×C4116yescomplemented
182#385—44no—
183#385—44no—
184#382C2×C418yescomplemented
185#380—28no—
186C4×C4⋊C4—44no—
187C4×C22⋊C4—44no—
188C4×C22⋊C4—44no—
189C4×C22⋊C4—44no—
190C2×#95C2311yescharacteristic
191C2×#95C2311yescharacteristic
192C2×#95C2311yescharacteristic
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
195C2×#95C2311yescharacteristic
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
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×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C25C2412yes—
233C25C2411yescharacteristic
234C22×Q8—24no—
235C22×Q8—41no—
236C22×Q8—41no—
237C22×Q8—42no—
238C22×Q8C22×C414yes—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—41no—
243C22×D4—41no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4C22×C414yes—
250C22×D4C22×C418yes—
251C23×C4—24no—
252C23×C4—22no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
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×C4C22×C414yes—
271C23×C4C22×C414yes—
272C23×C4C22×C414yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290#124—416no—
291C22⋊Q8—416no—
292#121—416no—
293#117—432no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
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⋊C4C22×C418yes—
322C2×C4⋊C4C22×C414yes—
323C2×C4⋊C4C22×C414yes—
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—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⋊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⋊C4C22×C418yes—
369C2×C22⋊C4C22×C418yes—
370C2×C22⋊C4C22×C418yes—
371C2×C22⋊C4C22×C418yes—
372C2×C22⋊C4C22×C418yes—
373C2×C22⋊C4C22×C418yes—
374C2×C22⋊C4#4118yes—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—416no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42C22×C414yes—
402C2×C42C22×C414yes—
403C2×C42C22×C414yes—
404C2×C42C22×C414yes—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—22no—
413#95—22no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
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—
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#95C22×C418yes—
443#95C22×C418yes—
444#95C22×C418yes—
445#95C22×C418yes—
446#95#4118yes—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C23×C414yes—
471C24C23×C412yes—
472C24C2×#4114yes—
473C24C2511yescharacteristic
474C2×Q8—28no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—84no—
478C2×Q8—84no—
479C2×D4—216no—
480C2×D4—28no—
481C2×D4—44no—
482C2×D4—48no—
483C2×D4—44no—
484C2×D4—48no—
485C2×D4—84no—
486C2×D4—84no—
487C2×D4—84no—
488C2×D4—84no—
489C2×D4—84no—
490C2×D4—84no—
491C22×C4—216no—
492C22×C4—216no—
493C22×C4—28no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
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—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
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—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—28no—
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—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—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4C23×C414yes—
600C22×C4C23×C412yes—
601C22×C4C23×C414yes—
602C22×C4C23×C414yes—
603C22×C4C23×C412yes—
604C22×C4C23×C412yes—
605C22×C4C23×C412yes—
606C22×C4C23×C412yes—
607C22×C4C23×C412yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4114yes—
610C22×C4C2×#4114yes—
611C22×C4C2×#4114yes—
612C22×C4C2×#4114yes—
613C22×C4H(5,𝔽2)14yes—
614C22×C4H(5,𝔽2)12yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C42−1+412yes—
619C22×C42−1+412yes—
620C4⋊C4—216no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—84no—
628C4⋊C4—84no—
629C4⋊C4—84no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—216no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—84no—
645C22⋊C4—84no—
646C22⋊C4—84no—
647C42—28no—
648C42—28no—
649C42—44no—
650C42—44no—
651C42—48no—
652C42—48no—
653C42—84no—
654C42—84no—
655C42—84no—
656C42—84no—
657C42—84no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
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—
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—
715C23C4×#4114yes—
716C23C24×C411yescharacteristic
717C23C22×#4112yes—
718C23C22×#4112yes—
719C23C2×H(5,𝔽2)12yes—
720C23C2×H(5,𝔽2)11yescharacteristic
721C23C2×H(5,𝔽2)11yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×2−1+411yescharacteristic
725C23C2×2−1+411yescharacteristic
726C23#58512yes—
727Q8—88no—
728D4—88no—
729D4—816no—
730C2×C4—232no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—416no—
776C2×C4—416no—
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—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—816no—
836C2×C4C4×#4114yes—
837C2×C4#51814yes—
838C2×C4#51814yes—
839C2×C4#52014yes—
840C2×C4#52014yes—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—44no—
848C22—44no—
849C22—42no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22C2×C4×#4111yescharacteristic
868C22C2×C4×#4111yescharacteristic
869C22C2×#51811yescharacteristic
870C22C2×#51811yescharacteristic
871C22C2×#52011yescharacteristic
872C22C2×#52011yescharacteristic
873C22#342811yescharacteristic
874C22#346012yes—
875C22#346112yes—
876C22#348112yes—
877C22#348212yes—
878C22#349012yes—
879C22#349212yes—
880C22#351412yes—
881C22#351412yes—
882C22#351912yes—
883C22#351912yes—
884C22#354112yes—
885C22#354212yes—
886C22#354811yescharacteristic
887C22#354811yescharacteristic
888C22#354911yescharacteristic
889C22#355011yescharacteristic
890C4—24no—
891C4—24no—
892C4—24no—
893C4—24no—
894C4—24no—
895C4—42no—
896C4—44no—
897C4—44no—
898C4—44no—
899C4—44no—
900C4—44no—
901C4—44no—
902C4—44no—
903C4—82no—
904C4—82no—
905C4—82no—
906C4—82no—
907C2—44no—
908C2—84no—
909C2#3408411yescharacteristic
910C2#3415311yescharacteristic
911C2#3421811yescharacteristic
912C2#3424011yescharacteristic
913C2#3424611yescharacteristic
914C2#3436211yescharacteristic
915C2#3436811yescharacteristic
916C2#3883712yes—
917C2#3883812yes—
918C2#3886812yes—
919C2#3887112yes—
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. #14455C2semidirect
3. #14421C2semidirect
4. #14362C2semidirect
6. #14267C2semidirect
7. #14162C2semidirect
8. #14157C2semidirect
9. #14124C2semidirect
10. #14119C2semidirect
11. #14116C2semidirect
12. #14112C2semidirect
13. #14071C2semidirect
14. #14064C2semidirect
15. #13826C2semidirect
16. #13824C2semidirect
17. #13791C2semidirect
18. C4×#380C2semidirect
19. #13756C2semidirect
25. #2850C4semidirect
119. C2×C22⋊Q8C2×C4semidirect
154. C22×C42C2×C4semidirect
167. #391C2×C4semidirect
175. #388C2×C4semidirect
176. #388C2×C4semidirect
180. #386C2×C4semidirect
181. #386C2×C4semidirect
184. #382C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#28502
#144552
#144212
#143622
#143612
#142672
#141622
#141572
#141242
#141192
#141162
#141122
#140712
#140642
#138262
#138242
#137912
C4×#3802
#137562