Finite Group Databasebeta

← #559278

Subgroups — #559278

Order 512.

3294 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2735C211yesmaximal, characteristic
2#14693C212yesmaximal
3#14636C211yesmaximal, characteristic, complemented
4#14627C211yesmaximal, characteristic, complemented
5#14586C212yesmaximal, complemented
6#14541C212yesmaximal, complemented
7#14488C212yesmaximal, complemented
8#14479C212yesmaximal, complemented
9#14366C212yesmaximal
10#14366C211yesmaximal, characteristic
11#14230C211yesmaximal, characteristic, complemented
12#14225C211yesmaximal, characteristic, complemented
13#14198C212yesmaximal, complemented
14#14197C212yesmaximal, complemented
15#14112C212yesmaximal, complemented
16#14070C212yesmaximal, complemented
17#14032C212yesmaximal, complemented
18#13831C212yesmaximal, complemented
19C4×#379C211yesmaximal, characteristic
20C25×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×#387C2212yescomplemented
34C2×#387C2212yescomplemented
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#379C2211yescharacteristic
42C2×#379C2212yes—
43C2×#379C2212yes—
44C2×#379C2211yescharacteristic
45C2×C4×C4⋊C4C2212yescomplemented
46C2×C4×C4⋊C4C2211yescharacteristic, complemented
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2211yescharacteristic
51#1445C2211yescharacteristic, complemented
52#1445C2211yescharacteristic, complemented
53#1444C2212yescomplemented
54#1444C2211yescharacteristic, complemented
55#1444C2211yescharacteristic, complemented
56#1443C2212yescomplemented
57#1443C2212yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1442C2212yescomplemented
61#1441C2212yescomplemented
62#1441C2212yescomplemented
63#1441C2212yescomplemented
64#1441C2212yescomplemented
65#1440C2212yes—
66#1440C2212yes—
67#1440C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2211yescharacteristic
71#1439C2211yescharacteristic
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1437C2212yes—
76#1437C2212yes—
77#1437C2212yes—
78#1437C2212yes—
79#1437C2212yes—
80#1437C2212yes—
81#1436C2212yescomplemented
82#1436C2212yescomplemented
83#1436C2212yescomplemented
84#1436C2212yescomplemented
85#1436C2212yescomplemented
86#1436C2212yescomplemented
87#1436C2212yescomplemented
88C4⋊#95C2212yescomplemented
89C4⋊#95C2212yescomplemented
90C4⋊#95C2212yescomplemented
91#1434C2212yescomplemented
92#1434C2212yescomplemented
93#1434C2212yescomplemented
94#1434C2212yescomplemented
95#1434C2212yescomplemented
96#1434C2211yescharacteristic, complemented
97C22⋊#95C2211yescharacteristic
98C22⋊#95C2212yes—
99C22⋊#95C2211yescharacteristic
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C4×#95C2211yescharacteristic, complemented
108C26C2311yescharacteristic
109C24×C4—24no—
110C24×C4—42no—
111C24×C4—44no—
112C24×C4—42no—
113C24×C4—44no—
114C24×C4C2311yescharacteristic
115C24×C4C2312yes—
116C24×C4C2312yes—
117C24×C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2312yes—
157#399C2×C418yescomplemented
158#397C2×C418yescomplemented
159#397C2×C4116yescomplemented
160#396C2×C4116yescomplemented
161#389—42no—
162#388—28no—
163#388—44no—
164#388—44no—
165#388C2×C4116yescomplemented
166#388C2×C4116yescomplemented
167#388C2×C4116yescomplemented
168#387—44no—
169#387—44no—
170#385—28no—
171#385—44no—
172#385—44no—
173#385—44no—
174#385—44no—
175#385—44no—
176#379—24no—
177#379—44no—
178#379C2×C418yes—
179#379C2×C4116yes—
180C4×C4⋊C4—42no—
181C4×C4⋊C4—44no—
182C4×C22⋊C4—42no—
183C4×C22⋊C4—42no—
184C4×C22⋊C4—44no—
185C4×C22⋊C4—44no—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2311yescharacteristic
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2311yescharacteristic
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2311yescharacteristic
229C25—22no—
230C25—22no—
231C25—24no—
232C25—24no—
233C25—42no—
234C25—41no—
235C25—41no—
236C25—41no—
237C25—42no—
238C25—41no—
239C25C22×C414yes—
240C25C2411yescharacteristic
241C25C2412yes—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—41no—
263C23×C4—41no—
264C23×C4—42no—
265C23×C4—416no—
266C23×C4—432no—
267C23×C4—432no—
268C23×C4—416no—
269C23×C4—416no—
270C23×C4#4114yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4C22×C414yescomplemented
319C2×C4⋊C4C22×C418yescomplemented
320C2×C4⋊C4C22×C418yescomplemented
321C2×C4⋊C4C22×C414yescomplemented
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—22no—
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—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—41no—
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⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4C22×C418yes—
372C2×C22⋊C4C22×C418yes—
373C2×C22⋊C4C22×C418yes—
374C2×C22⋊C4C22×C418yes—
375C2×C22⋊C4C22×C414yes—
376C2×C22⋊C4C22×C418yes—
377C2×C22⋊C4C22×C418yes—
378C2×C22⋊C4C22×C418yes—
379C2×C22⋊C4C22×C418yes—
380C2×C22⋊C4C22×C414yes—
381C2×C22⋊C4#4114yes—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—22no—
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×C42C22×C418yescomplemented
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—42no—
411#95—42no—
412#95—41no—
413#95—42no—
414#95—42no—
415#95—41no—
416#95—42no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—41no—
422#95—42no—
423#95—42no—
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#95C22×C418yescomplemented
440#95C22×C414yescomplemented
441#95C22×C418yescomplemented
442#95C22×C418yescomplemented
443#95C22×C414yescomplemented
444C24—22no—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—28no—
465C24—216no—
466C24—48no—
467C24—44no—
468C24—44no—
469C24—48no—
470C24—44no—
471C24—48no—
472C24—48no—
473C24—48no—
474C24—48no—
475C24—44no—
476C24—44no—
477C24—48no—
478C24—44no—
479C24—44no—
480C24—44no—
481C24—48no—
482C24—48no—
483C24—48no—
484C24—44no—
485C24—48no—
486C24—44no—
487C24C23×C412yes—
488C24C23×C414yes—
489C24C2×#4112yes—
490C24C2×#4112yes—
491C24H(5,𝔽2)14yes—
492C242−1+414yes—
493C24C2511yescharacteristic
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—216no—
498C22×C4—28no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
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—21no—
522C22×C4—22no—
523C22×C4—21no—
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—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—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
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—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—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—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—44no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—4128no—
607C22×C4—44no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—44no—
611C22×C4—48no—
612C22×C4—44no—
613C22×C4C23×C414yes—
614C22×C4C23×C412yes—
615C22×C4C23×C414yes—
616C22×C4C23×C414yes—
617C22×C4C23×C414yes—
618C22×C4C23×C414yes—
619C22×C4C23×C412yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4114yes—
623C22×C4H(5,𝔽2)12yes—
624C22×C4H(5,𝔽2)12yes—
625C22×C4H(5,𝔽2)14yes—
626C4⋊C4—44no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—44no—
630C4⋊C4—48no—
631C4⋊C4—44no—
632C4⋊C4—48no—
633C4⋊C4—84no—
634C4⋊C4—84no—
635C4⋊C4—84no—
636C4⋊C4—84no—
637C4⋊C4—82no—
638C22⋊C4—216no—
639C22⋊C4—216no—
640C22⋊C4—216no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—44no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—44no—
652C22⋊C4—84no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C42—48no—
659C42—44no—
660C42—84no—
661C42—82no—
662C42—84no—
663C42—84no—
664C42—84no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—416no—
696C23—432no—
697C23—432no—
698C23—416no—
699C23—416no—
700C23—416no—
701C23—432no—
702C23—416no—
703C23—416no—
704C23—432no—
705C23—416no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23C4×#4114yes—
733C23#52018yes—
734C23C24×C411yescharacteristic
735C23C22×#4111yescharacteristic
736C23C22×#4111yescharacteristic
737C23C2×H(5,𝔽2)12yes—
738C23C2×H(5,𝔽2)11yescharacteristic
739C23C2×H(5,𝔽2)11yescharacteristic
740C23C2×H(5,𝔽2)12yes—
741C23C2×2−1+412yes—
742C23#58511yescharacteristic
743C23#58511yescharacteristic
744C23#58512yes—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—432no—
778C2×C4—416no—
779C2×C4—416no—
780C2×C4—432no—
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—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
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—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4#56014yes—
856C22—28no—
857C22—28no—
858C22—24no—
859C22—28no—
860C22—28no—
861C22—464no—
862C22—44no—
863C22—42no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—42no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—42no—
872C22—44no—
873C22—42no—
874C22—44no—
875C22—42no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—42no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22C2×C4×#4111yescharacteristic
884C22C2×#52012yes—
885C22C4×H(5,𝔽2)12yes—
886C22C4×H(5,𝔽2)11yescharacteristic
887C22C4×H(5,𝔽2)11yescharacteristic
888C22#349012yes—
889C22#349011yescharacteristic
890C22#349311yescharacteristic
891C22#349512yes—
892C22#350511yescharacteristic
893C22#350611yescharacteristic
894C22#351312yes—
895C22#352012yes—
896C22C2×#56011yescharacteristic
897C22#352912yes—
898C22#352911yescharacteristic
899C22#353212yes—
900C22#353211yescharacteristic
901C22#353312yes—
902C22#353512yes—
903C22#353811yescharacteristic
904C22#354112yes—
905C22#354112yes—
906C4—24no—
907C4—44no—
908C4—42no—
909C4—42no—
910C4—44no—
911C4—44no—
912C4—42no—
913C4—44no—
914C4—42no—
915C4—42no—
916C4—44no—
917C4—44no—
918C4—82no—
919C4—82no—
920C4—82no—
921C4—82no—
922C4—82no—
923C2—48no—
924C2—44no—
925C2#3427711yescharacteristic
926C2#3429612yes—
927C2C4×#56011yescharacteristic
928C2#3441612yes—
929C2#3445711yescharacteristic
930C2#4545711yescharacteristic
931C2#4546612yes—
932C2#4547211yescharacteristic
933C2#4561512yes—
934C2#4562211yescharacteristic
935C2#4569311yescharacteristic
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. #14636C2semidirect
4. #14627C2semidirect
5. #14586C2semidirect
6. #14541C2semidirect
7. #14488C2semidirect
8. #14479C2semidirect
11. #14230C2semidirect
12. #14225C2semidirect
13. #14198C2semidirect
14. #14197C2semidirect
15. #14112C2semidirect
16. #14070C2semidirect
17. #14032C2semidirect
18. #13831C2semidirect
21. #2735C4semidirect
26. C2×#389C22semidirect
33. C2×#387C22semidirect
34. C2×#387C22semidirect
45. C2×C4×C4⋊C4C22semidirect
46. C2×C4×C4⋊C4C22semidirect
51. #1445C22semidirect
52. #1445C22semidirect
53. #1444C22semidirect
54. #1444C22semidirect
55. #1444C22semidirect
56. #1443C22semidirect
57. #1443C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
81. #1436C22semidirect
82. #1436C22semidirect
83. #1436C22semidirect
84. #1436C22semidirect
85. #1436C22semidirect
86. #1436C22semidirect
87. #1436C22semidirect
88. C4⋊#95C22semidirect
89. C4⋊#95C22semidirect
90. C4⋊#95C22semidirect
91. #1434C22semidirect
92. #1434C22semidirect
93. #1434C22semidirect
94. #1434C22semidirect
95. #1434C22semidirect
96. #1434C22semidirect
107. C4×#95C22semidirect
157. #399C2×C4semidirect
158. #397C2×C4semidirect
159. #397C2×C4semidirect
160. #396C2×C4semidirect
165. #388C2×C4semidirect
166. #388C2×C4semidirect
167. #388C2×C4semidirect
318. C2×C4⋊C4C22×C4semidirect
319. C2×C4⋊C4C22×C4semidirect
320. C2×C4⋊C4C22×C4semidirect
321. C2×C4⋊C4C22×C4semidirect
400. C2×C42C22×C4semidirect
439. #95C22×C4semidirect
440. #95C22×C4semidirect
441. #95C22×C4semidirect
442. #95C22×C4semidirect
443. #95C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#27352
#146932
#146362
#146272
#145862
#145412
#144882
#144792
#143662
#142302
#142252
#141982
#141972
#141122
#140702
#140322
#138312
C4×#3792