Finite Group Databasebeta

← #572018

Subgroups — #572018

Order 512.

2570 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2482C211yesmaximal, characteristic
2#14618C212yesmaximal, complemented
3#14616C212yesmaximal, complemented
4#14515C211yesmaximal, characteristic, complemented
5#14412C212yesmaximal, complemented
6#14368C212yesmaximal, complemented
7#14366C212yesmaximal
8#14365C211yesmaximal, characteristic
9#14332C212yesmaximal, complemented
10#14194C212yesmaximal, complemented
11#14125C212yesmaximal, complemented
12#14079C212yesmaximal, complemented
13#14067C212yesmaximal, complemented
14#14031C212yesmaximal, complemented
15#13957C211yesmaximal, characteristic, complemented
16#13873C212yesmaximal
17#13827C211yesmaximal, characteristic
18#13823C211yesmaximal, characteristic, complemented
19#13777C211yesmaximal, characteristic, complemented
20C22×#117C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22#2482C4116yescomplemented
23C2×#399C2212yes—
24C2×#397C2212yes—
25C2×#388C2212yes—
26C2×#388C2212yes—
27C2×#388C2212yes—
28C2×#388C2212yes—
29C2×#388C2212yes—
30C2×#388C2212yes—
31C2×#388C2212yes—
32C2×#385C2211yescharacteristic
33C2×#385C2211yescharacteristic
34C2×#382C2211yescharacteristic, complemented
35C2×#381C2211yescharacteristic
36C2×#380C2212yes—
37C2×#379C2212yes—
38C2×#379C2212yes—
39C2×#379C2211yescharacteristic
40C2×#379C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic, complemented
42C2×C4×C4⋊C4C2212yescomplemented
43C2×C4×C4⋊C4C2212yescomplemented
44C2×C4×C4⋊C4C2211yescharacteristic, complemented
45C2×C4×C22⋊C4C2212yes—
46C2×#376C2211yescharacteristic, complemented
47#1445C2212yescomplemented
48#1445C2212yescomplemented
49#1444C2212yescomplemented
50#1443C2212yescomplemented
51#1443C2212yescomplemented
52#1443C2212yescomplemented
53#1442C2212yescomplemented
54#1442C2212yescomplemented
55#1441C2212yescomplemented
56#1440C2212yes—
57#1440C2212yes—
58#1440C2212yes—
59#1440C2212yes—
60#1440C2212yes—
61#1439C2212yes—
62#1439C2212yes—
63#1439C2212yes—
64#1439C2212yes—
65#1439C2212yes—
66#1439C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1437C2212yes—
70#1437C2212yes—
71#1437C2212yes—
72#1437C2212yes—
73#1437C2212yes—
74#1437C2211yescharacteristic
75#1437C2211yescharacteristic
76#1437C2212yes—
77#1437C2212yes—
78#1437C2212yes—
79#1437C2212yes—
80#1437C2211yescharacteristic
81#1437C2211yescharacteristic
82#1437C2212yes—
83#1437C2212yes—
84#1437C2212yes—
85#1436C2211yescharacteristic, complemented
86#1436C2212yescomplemented
87#1436C2212yescomplemented
88#1436C2212yescomplemented
89#1436C2211yescharacteristic, complemented
90#1436C2212yescomplemented
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94#1436C2212yescomplemented
95#1436C2212yescomplemented
96#1436C2212yescomplemented
97#1436C2212yescomplemented
98#1436C2212yescomplemented
99#1436C2211yescharacteristic, complemented
100#1436C2211yescharacteristic, complemented
101C4⋊#95C2212yescomplemented
102#1434C2212yescomplemented
103#1434C2212yescomplemented
104#1434C2212yescomplemented
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C4×#95C2212yescomplemented
108C26C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C2×#117—42no—
112C2×#117—42no—
113C2×#117C2×C418yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C22⋊C4—42no—
124C22×C22⋊C4—42no—
125C22×C22⋊C4C2×C418yes—
126C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159#399C2×C4116yes—
160#397C2×C4116yes—
161#388—28no—
162#388—44no—
163#388—44no—
164#388—44no—
165#388—44no—
166#388C2×C4116yes—
167#388C2×C4116yes—
168#385C2×C418yes—
169#385C2×C418yes—
170#382—42no—
171#381C2×C418yes—
172#380—28no—
173#379—28no—
174#379—44no—
175#379C2×C418yes—
176#379C2×C418yes—
177C4×C4⋊C4—44no—
178C4×C4⋊C4—44no—
179C4×C4⋊C4—42no—
180C4×C4⋊C4—42no—
181C4×C22⋊C4—44no—
182#376—42no—
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×#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×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2312yes—
220C2×#95C2311yescharacteristic
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C25—24no—
226C25—41no—
227C25—41no—
228C25—42no—
229C25—42no—
230C25—42no—
231C25—42no—
232C25—42no—
233C25C22×C414yes—
234C25C2412yes—
235C25C2411yescharacteristic
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—42no—
240C23×C4—41no—
241C23×C4—41no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4C22×C414yes—
245C23×C4C22×C414yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2411yescharacteristic
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263#117—416no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—41no—
279C2×C4⋊C4—41no—
280C2×C4⋊C4—41no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4C22×C414yes—
288C2×C4⋊C4C22×C414yes—
289C2×C4⋊C4C22×C418yes—
290C2×C4⋊C4C22×C418yes—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—416no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
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—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—41no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4—41no—
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⋊C4C22×C418yes—
346C2×C22⋊C4C22×C414yes—
347C2×C22⋊C4C22×C418yes—
348C2×C22⋊C4C22×C414yes—
349C2×C22⋊C4C22×C414yes—
350C2×C22⋊C4C22×C414yes—
351C2×C22⋊C4C22×C418yes—
352C2×C22⋊C4C22×C418yes—
353C2×C22⋊C4C22×C418yes—
354C2×C22⋊C4C22×C418yes—
355C2×C22⋊C4#4118yes—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—41no—
364C2×C42—41no—
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—41no—
375C2×C42—42no—
376C2×C42—41no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42C22×C414yes—
384C2×C42C22×C414yes—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
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—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—41no—
413#95—42no—
414#95—41no—
415#95—42no—
416#95—41no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95C22×C418yes—
424#95C22×C418yes—
425#95C22×C418yes—
426#95C22×C418yes—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
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—22no—
448C24—28no—
449C24—44no—
450C24—48no—
451C24—44no—
452C24—48no—
453C24—48no—
454C24—44no—
455C24—44no—
456C24—84no—
457C24—84no—
458C24—84no—
459C24—84no—
460C24—84no—
461C24—84no—
462C24—84no—
463C24—82no—
464C24—82no—
465C24—84no—
466C24—84no—
467C24—84no—
468C24—84no—
469C24C23×C414yes—
470C24C23×C412yes—
471C24C2×#4114yes—
472C24C2511yescharacteristic
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
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—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
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—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—28no—
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—44no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—84no—
576C22×C4C23×C414yes—
577C22×C4C23×C414yes—
578C22×C4C23×C412yes—
579C22×C4C23×C412yes—
580C22×C4C23×C412yes—
581C22×C4C23×C414yes—
582C22×C4C23×C412yes—
583C22×C4C23×C412yes—
584C22×C4C23×C412yes—
585C22×C4C2×#4114yes—
586C22×C4C2×#4114yes—
587C22×C4H(5,𝔽2)14yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4H(5,𝔽2)12yes—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—84no—
599C22⋊C4—28no—
600C22⋊C4—216no—
601C22⋊C4—48no—
602C22⋊C4—44no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—84no—
612C22⋊C4—84no—
613C22⋊C4—84no—
614C22⋊C4—84no—
615C22⋊C4—84no—
616C22⋊C4—84no—
617C22⋊C4—84no—
618C22⋊C4—84no—
619C22⋊C4—84no—
620C22⋊C4—84no—
621C42—28no—
622C42—28no—
623C42—44no—
624C42—48no—
625C42—48no—
626C42—44no—
627C42—84no—
628C42—84no—
629C42—82no—
630C42—82no—
631C42—84no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—42no—
650C23—41no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—416no—
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—816no—
689C23—88no—
690C23—88no—
691C23—816no—
692C23—816no—
693C23—816no—
694C23—816no—
695C23—816no—
696C23C4×#4114yes—
697C23C24×C411yescharacteristic
698C23C22×#4112yes—
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×H(5,𝔽2)11yescharacteristic
701C23C2×H(5,𝔽2)12yes—
702C23#58512yes—
703C23#58512yes—
704C23#58512yes—
705C23#58512yes—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—416no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
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—88no—
814C2×C4#51814yes—
815C22—28no—
816C22—24no—
817C22—42no—
818C22—44no—
819C22—44no—
820C22—42no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—832no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22C2×C4×#4111yescharacteristic
841C22C2×#51811yescharacteristic
842C22#342812yes—
843C22#342811yescharacteristic
844C22C4×H(5,𝔽2)12yes—
845C22#350512yes—
846C22#351012yes—
847C22#351312yes—
848C22#351312yes—
849C22#351312yes—
850C22#352112yes—
851C22#353312yes—
852C22#353711yescharacteristic
853C22#353912yes—
854C22#354011yescharacteristic
855C22#354011yescharacteristic
856C22#354012yes—
857C22#354011yescharacteristic
858C22#354612yes—
859C22#356612yes—
860C22#356612yes—
861C4—24no—
862C4—44no—
863C4—42no—
864C4—42no—
865C4—44no—
866C4—44no—
867C4—42no—
868C4—42no—
869C4—44no—
870C4—42no—
871C4—44no—
872C4—44no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—82no—
878C2—44no—
879C2—84no—
880C2#3423811yescharacteristic
881C2#3431512yes—
882C2#3436111yescharacteristic
883C2#3441111yescharacteristic
884C2#3450812yes—
885C2#5040712yes—
886C2#5040812yes—
887C2#5052212yes—
888C2#5152012yes—
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
2. #14618C2semidirect
3. #14616C2semidirect
4. #14515C2semidirect
5. #14412C2semidirect
6. #14368C2semidirect
9. #14332C2semidirect
10. #14194C2semidirect
11. #14125C2semidirect
12. #14079C2semidirect
13. #14067C2semidirect
14. #14031C2semidirect
15. #13957C2semidirect
18. #13823C2semidirect
19. #13777C2semidirect
22. #2482C4semidirect
34. C2×#382C22semidirect
41. C2×C4×C4⋊C4C22semidirect
42. C2×C4×C4⋊C4C22semidirect
43. C2×C4×C4⋊C4C22semidirect
44. C2×C4×C4⋊C4C22semidirect
46. C2×#376C22semidirect
47. #1445C22semidirect
48. #1445C22semidirect
49. #1444C22semidirect
50. #1443C22semidirect
51. #1443C22semidirect
52. #1443C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1441C22semidirect
85. #1436C22semidirect
86. #1436C22semidirect
87. #1436C22semidirect
88. #1436C22semidirect
89. #1436C22semidirect
90. #1436C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. #1436C22semidirect
96. #1436C22semidirect
97. #1436C22semidirect
98. #1436C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. C4⋊#95C22semidirect
102. #1434C22semidirect
103. #1434C22semidirect
104. #1434C22semidirect
107. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24822
#146182
#146162
#145152
#144122
#143682
#143662
#143652
#143322
#141942
#141252
#140792
#140672
#140312
#139572
#138732
#138272
#138232
#137772