Finite Group Databasebeta

← #584439

Subgroups — #584439

Order 512.

2450 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2735C211yesmaximal, characteristic
2#14673C211yesmaximal, characteristic
3#14671C212yesmaximal, complemented
4#14642C212yesmaximal, complemented
5#14636C211yesmaximal, characteristic, complemented
6#14633C212yesmaximal, complemented
7#14581C211yesmaximal, characteristic, complemented
8#14512C212yesmaximal, complemented
9#14433C212yesmaximal, complemented
10#14366C212yesmaximal
11#14310C212yesmaximal, complemented
12#14233C212yesmaximal, complemented
13#14230C211yesmaximal, characteristic, complemented
14#14119C212yesmaximal, complemented
15#14118C212yesmaximal, complemented
16#14077C212yesmaximal, complemented
17#13991C211yesmaximal, characteristic
18#13971C212yesmaximal
19C4×#397C211yesmaximal, characteristic, complemented
20C23×C22⋊C4C2211yescharacteristic
21#2735C4116yescomplemented
22C2×#399C2211yescharacteristic
23C2×#397C2211yescharacteristic
24C2×#397C2212yes—
25C2×#396C2212yes—
26C2×#389C2211yescharacteristic, complemented
27C2×#388C2212yes—
28C2×#388C2212yes—
29C2×#388C2212yes—
30C2×#388C2212yes—
31C2×#388C2212yes—
32C2×#388C2212yes—
33C2×#388C2212yes—
34C2×#388C2212yes—
35C2×#387C2212yescomplemented
36C2×#387C2212yescomplemented
37C2×#385C2212yes—
38C2×#385C2211yescharacteristic
39C2×#379C2211yescharacteristic
40C2×#379C2212yes—
41C2×#379C2212yes—
42C2×#379C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic, complemented
44C2×C4×C4⋊C4C2212yescomplemented
45C2×C4×C22⋊C4C2212yes—
46C2×C4×C22⋊C4C2211yescharacteristic
47#1445C2211yescharacteristic, complemented
48#1445C2211yescharacteristic, complemented
49#1444C2212yescomplemented
50#1444C2211yescharacteristic, complemented
51#1443C2212yescomplemented
52#1443C2212yescomplemented
53#1443C2212yescomplemented
54#1442C2211yescharacteristic, complemented
55#1442C2212yescomplemented
56#1442C2212yescomplemented
57#1442C2212yescomplemented
58#1441C2212yescomplemented
59#1441C2212yescomplemented
60#1441C2212yescomplemented
61#1441C2212yescomplemented
62#1441C2212yescomplemented
63#1441C2212yescomplemented
64#1440C2212yes—
65#1440C2212yes—
66#1440C2212yes—
67#1440C2212yes—
68#1440C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2211yescharacteristic
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2211yescharacteristic
82#1439C2212yes—
83#1437C2212yes—
84#1437C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1436C2212yescomplemented
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94C4⋊#95C2212yescomplemented
95C4⋊#95C2212yescomplemented
96C4⋊#95C2212yescomplemented
97#1434C2212yescomplemented
98#1434C2212yescomplemented
99#1434C2212yescomplemented
100#1434C2212yescomplemented
101C22⋊#95C2211yescharacteristic
102C22⋊#95C2212yes—
103C22⋊#95C2211yescharacteristic
104C22⋊#95C2212yes—
105C4×#95C2211yescharacteristic, complemented
106C4×#95C2212yescomplemented
107C4×#95C2211yescharacteristic, complemented
108C26C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C22⋊C4—42no—
124C22×C22⋊C4—44no—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2312yes—
154#399C2×C418yes—
155#397C2×C418yes—
156#397C2×C4116yescomplemented
157#396C2×C4116yescomplemented
158#389—42no—
159#388—44no—
160#388—44no—
161#388—44no—
162#388—44no—
163#388—44no—
164#388C2×C4116yes—
165#388C2×C4116yescomplemented
166#388C2×C4116yescomplemented
167#387—44no—
168#387—44no—
169#385—42no—
170#385—44no—
171#379—42no—
172#379—44no—
173#379C2×C4116yes—
174#379C2×C418yes—
175C4×C4⋊C4—44no—
176C4×C4⋊C4—42no—
177C4×C22⋊C4—42no—
178C4×C22⋊C4—44no—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2311yescharacteristic
186C2×#95C2312yes—
187C2×#95C2311yescharacteristic
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
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×#95C2311yescharacteristic
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2312yes—
220C2×#95C2311yescharacteristic
221C2×#95C2312yes—
222C25—22no—
223C25—22no—
224C25—42no—
225C25—41no—
226C25—42no—
227C25—41no—
228C25—42no—
229C25—42no—
230C25—41no—
231C25—41no—
232C25C22×C414yes—
233C25C2412yes—
234C25C2411yescharacteristic
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—41no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—41no—
243C23×C4—42no—
244C23×C4—41no—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2411yescharacteristic
250C23×C4C2412yes—
251C23×C4C2411yescharacteristic
252C23×C4C2412yes—
253C23×C4C2411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—41no—
267C2×C4⋊C4—41no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—41no—
273C2×C4⋊C4—41no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4C22×C418yes—
293C2×C4⋊C4C22×C414yes—
294C2×C4⋊C4C22×C418yes—
295C2×C4⋊C4C22×C414yes—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—41no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—416no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—41no—
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—41no—
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⋊C4C22×C418yes—
354C2×C22⋊C4C22×C414yes—
355C2×C22⋊C4C22×C418yes—
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×C22⋊C4C22×C414yes—
363C2×C42—22no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
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×C42—42no—
380C2×C42—42no—
381C2×C42C22×C418yes—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—41no—
398#95—41no—
399#95—41no—
400#95—42no—
401#95—42no—
402#95—41no—
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#95C22×C418yes—
421#95C22×C418yes—
422#95C22×C414yes—
423#95C22×C418yes—
424#95C22×C414yes—
425C24—21no—
426C24—22no—
427C24—21no—
428C24—22no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—21no—
433C24—22no—
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—28no—
448C24—44no—
449C24—48no—
450C24—48no—
451C24—44no—
452C24—44no—
453C24—48no—
454C24—44no—
455C24—84no—
456C24—84no—
457C24—82no—
458C24—82no—
459C24—82no—
460C24—84no—
461C24—82no—
462C24—84no—
463C24—82no—
464C24—84no—
465C24—84no—
466C24—82no—
467C24—84no—
468C24—84no—
469C24—84no—
470C24C23×C414yes—
471C24C23×C412yes—
472C24H(5,𝔽2)12yes—
473C242−1+412yes—
474C24C2511yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
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—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
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—21no—
506C22×C4—22no—
507C22×C4—21no—
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—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
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—21no—
545C22×C4—21no—
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—21no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—82no—
577C22×C4—84no—
578C22×C4—82no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—82no—
582C22×C4C23×C414yes—
583C22×C4C23×C412yes—
584C22×C4C23×C414yes—
585C22×C4C23×C414yes—
586C22×C4C23×C414yes—
587C22×C4C23×C414yes—
588C22×C4C23×C412yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C4H(5,𝔽2)14yes—
591C22×C4H(5,𝔽2)12yes—
592C4⋊C4—44no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—44no—
596C4⋊C4—48no—
597C4⋊C4—44no—
598C4⋊C4—48no—
599C4⋊C4—82no—
600C4⋊C4—84no—
601C4⋊C4—84no—
602C4⋊C4—84no—
603C4⋊C4—84no—
604C22⋊C4—216no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—44no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—84no—
619C22⋊C4—84no—
620C22⋊C4—82no—
621C22⋊C4—84no—
622C22⋊C4—84no—
623C22⋊C4—84no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C42—48no—
627C42—44no—
628C42—84no—
629C42—84no—
630C42—82no—
631C42—84no—
632C42—84no—
633C23—24no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—41no—
653C23—42no—
654C23—41no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—416no—
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—88no—
692C23—816no—
693C23—816no—
694C23—88no—
695C23—88no—
696C23—88no—
697C23—816no—
698C23—816no—
699C23—88no—
700C23—88no—
701C23#52014yes—
702C23C24×C411yescharacteristic
703C23C2×H(5,𝔽2)11yescharacteristic
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×H(5,𝔽2)12yes—
706C23C2×H(5,𝔽2)11yescharacteristic
707C23C2×2−1+411yescharacteristic
708C23#58512yes—
709C23#58512yes—
710C23#58512yes—
711C23#58511yescharacteristic
712C23#58511yescharacteristic
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—41no—
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—41no—
768C2×C4—42no—
769C2×C4—41no—
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—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
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—88no—
820C2×C4—88no—
821C2×C4#56014yes—
822C22—24no—
823C22—28no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—832no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22C2×#52011yescharacteristic
850C22#342812yes—
851C22C4×H(5,𝔽2)11yescharacteristic
852C22C4×H(5,𝔽2)12yes—
853C22C4×H(5,𝔽2)11yescharacteristic
854C22C2×#56011yescharacteristic
855C22#352912yes—
856C22#352911yescharacteristic
857C22#353312yes—
858C22#353412yes—
859C22#353411yescharacteristic
860C22#353611yescharacteristic
861C22#354511yescharacteristic
862C22#354512yes—
863C22#354612yes—
864C22#355111yescharacteristic
865C22#355811yescharacteristic
866C22#356012yes—
867C22#356112yes—
868C22#356411yescharacteristic
869C22#356412yes—
870C22#356612yes—
871C22#356612yes—
872C4—24no—
873C4—44no—
874C4—42no—
875C4—44no—
876C4—44no—
877C4—44no—
878C4—44no—
879C4—42no—
880C4—42no—
881C4—81no—
882C4—82no—
883C4—82no—
884C4—81no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C2—44no—
890C2—84no—
891C2C4×#56011yescharacteristic
892C2#3442411yescharacteristic
893C2#3444612yes—
894C2#3445812yes—
895C2#3450211yescharacteristic
896C2#5258611yescharacteristic
897C2#5258912yes—
898C2#5271711yescharacteristic
899C2#5284712yes—
900C2#5294111yescharacteristic
901C2#5301811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #14671C2semidirect
4. #14642C2semidirect
5. #14636C2semidirect
6. #14633C2semidirect
7. #14581C2semidirect
8. #14512C2semidirect
9. #14433C2semidirect
11. #14310C2semidirect
12. #14233C2semidirect
13. #14230C2semidirect
14. #14119C2semidirect
15. #14118C2semidirect
16. #14077C2semidirect
19. C4×#397C2semidirect
21. #2735C4semidirect
26. C2×#389C22semidirect
35. C2×#387C22semidirect
36. C2×#387C22semidirect
43. C2×C4×C4⋊C4C22semidirect
44. C2×C4×C4⋊C4C22semidirect
47. #1445C22semidirect
48. #1445C22semidirect
49. #1444C22semidirect
50. #1444C22semidirect
51. #1443C22semidirect
52. #1443C22semidirect
53. #1443C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1441C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
90. #1436C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. C4⋊#95C22semidirect
95. C4⋊#95C22semidirect
96. C4⋊#95C22semidirect
97. #1434C22semidirect
98. #1434C22semidirect
99. #1434C22semidirect
100. #1434C22semidirect
105. C4×#95C22semidirect
106. C4×#95C22semidirect
107. C4×#95C22semidirect
156. #397C2×C4semidirect
157. #396C2×C4semidirect
165. #388C2×C4semidirect
166. #388C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#27352
#146732
#146712
#146422
#146362
#146332
#145812
#145122
#144332
#143662
#143102
#142332
#142302
#141192
#141182
#140772
#139912
#139712
C4×#3972