Finite Group Databasebeta

← #517907

Subgroups — #517907

Order 512.

3126 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2273C211yesmaximal, characteristic
2#14355C211yesmaximal, characteristic, complemented
3#14351C212yesmaximal, complemented
4#13947C212yesmaximal, complemented
5#13917C212yesmaximal, complemented
6#13915C212yesmaximal, complemented
7#13903C211yesmaximal, characteristic
8#13895C212yesmaximal, complemented
9#13891C212yesmaximal, complemented
10#13875C212yesmaximal, complemented
11#13873C212yesmaximal
12#13873C212yesmaximal
13#13868C211yesmaximal, characteristic
14#13844C211yesmaximal, characteristic, complemented
15#13842C212yesmaximal, complemented
16#13822C212yesmaximal, complemented
17#13816C212yesmaximal, complemented
18#13807C211yesmaximal, characteristic, complemented
19#13801C211yesmaximal, characteristic, complemented
20C22×#117C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C2×#388C2212yes—
24C2×#388C2212yes—
25C2×#388C2212yes—
26C2×#388C2212yes—
27C2×#382C2212yescomplemented
28C2×#381C2211yescharacteristic
29C2×#381C2211yescharacteristic
30C2×#381C2211yescharacteristic
31C2×#380C2211yescharacteristic
32C2×#380C2212yes—
33C2×#380C2212yes—
34C2×#379C2212yes—
35C2×#379C2211yescharacteristic
36C2×#379C2211yescharacteristic
37#2273C4116yescomplemented
38C2×C4×C4⋊C4C2212yescomplemented
39C2×C4×C4⋊C4C2212yescomplemented
40C2×C4×C22⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4C2212yes—
42C2×C4×C22⋊C4C2212yes—
43C2×C4×C22⋊C4C2212yes—
44C2×C4×C22⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4C2212yes—
46C2×C4×C22⋊C4C2212yes—
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2212yes—
50C2×#376C2212yescomplemented
51#1444C2212yescomplemented
52#1444C2211yescharacteristic, complemented
53#1444C2211yescharacteristic, complemented
54#1443C2212yescomplemented
55#1443C2212yescomplemented
56#1443C2212yescomplemented
57#1443C2212yescomplemented
58#1442C2211yescharacteristic, complemented
59#1442C2212yescomplemented
60#1442C2211yescharacteristic, complemented
61#1440C2212yes—
62#1440C2212yes—
63#1440C2212yes—
64#1440C2212yes—
65#1439C2212yes—
66#1439C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1437C2212yes—
74#1437C2212yes—
75#1437C2212yes—
76#1437C2212yes—
77#1437C2212yes—
78#1437C2212yes—
79#1437C2212yes—
80#1437C2212yes—
81#1436C2212yescomplemented
82#1436C2212yescomplemented
83#1436C2212yescomplemented
84#1436C2212yescomplemented
85C4⋊#95C2212yescomplemented
86C4⋊#95C2212yescomplemented
87C4⋊#95C2212yescomplemented
88#1434C2212yescomplemented
89#1434C2212yescomplemented
90#1434C2212yescomplemented
91#1434C2212yescomplemented
92#1434C2211yescharacteristic, complemented
93#1434C2212yescomplemented
94#1434C2212yescomplemented
95#1434C2212yescomplemented
96#1434C2211yescharacteristic, complemented
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C4×#95C2212yescomplemented
103C4×#95C2212yescomplemented
104C4×#95C2212yescomplemented
105C4×#95C2212yescomplemented
106C4×#95C2211yescharacteristic, complemented
107C4×#95C2211yescharacteristic, complemented
108C26C2311yescharacteristic
109C24×C4C2312yes—
110C24×C4C2312yes—
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C2×#117—24no—
114C2×#117—44no—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—28no—
125C22×C22⋊C4—28no—
126C22×C22⋊C4C2×C418yes—
127C22×C22⋊C4C2×C4116yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159#388—28no—
160#388—28no—
161#388—28no—
162#388—28no—
163#382—44no—
164#381—24no—
165#381—42no—
166#381—42no—
167#380—24no—
168#380—44no—
169#380—44no—
170#379—44no—
171#379—42no—
172#379—42no—
173C4×C4⋊C4—44no—
174C4×C4⋊C4—44no—
175C4×C22⋊C4—24no—
176C4×C22⋊C4—44no—
177C4×C22⋊C4—44no—
178C4×C22⋊C4C2×C4116yes—
179C4×C22⋊C4C2×C4116yes—
180C4×C22⋊C4C2×C4116yes—
181C4×C22⋊C4C2×C418yes—
182C4×C22⋊C4C2×C418yes—
183C4×C22⋊C4C2×C4116yes—
184C4×C22⋊C4C2×C4116yes—
185#376—44no—
186C2×#95C2311yescharacteristic
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2311yescharacteristic
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C25—22no—
231C25—22no—
232C25—24no—
233C25—24no—
234C25—42no—
235C25—41no—
236C25—41no—
237C25—42no—
238C25—41no—
239C25—41no—
240C25C22×C414yes—
241C25C2411yescharacteristic
242C25C2412yes—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—41no—
256C23×C4—41no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—41no—
262C23×C4—41no—
263C23×C4C22×C414yes—
264C23×C4C22×C418yes—
265C23×C4C22×C418yes—
266C23×C4C22×C414yes—
267C23×C4#4114yes—
268C23×C4#4114yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286#117—416no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—232no—
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—264no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—24no—
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—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—42no—
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—41no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4C22×C418yes—
361C2×C22⋊C4C22×C418yes—
362C2×C22⋊C4C22×C418yes—
363C2×C22⋊C4C22×C418yes—
364C2×C22⋊C4C22×C418yes—
365C2×C22⋊C4C22×C418yes—
366C2×C22⋊C4#4118yes—
367C2×C22⋊C4#4118yes—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
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×C42C22×C418yes—
396C2×C42C22×C418yes—
397C2×C42C22×C418yes—
398C2×C42C22×C418yes—
399#95—22no—
400#95—22no—
401#95—24no—
402#95—22no—
403#95—22no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—42no—
420#95—42no—
421#95—42no—
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#95C22×C418yes—
438#95C22×C414yes—
439#95C22×C414yes—
440#95C22×C418yes—
441#95C22×C414yes—
442#95C22×C414yes—
443C24—28no—
444C24—216no—
445C24—28no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—21no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—28no—
467C24—216no—
468C24—48no—
469C24—44no—
470C24—44no—
471C24—82no—
472C24—82no—
473C24—82no—
474C24—82no—
475C24—84no—
476C24—82no—
477C24—82no—
478C24—84no—
479C24—84no—
480C24—84no—
481C24—84no—
482C24—84no—
483C24—84no—
484C24—84no—
485C24—84no—
486C24C23×C412yes—
487C24C23×C414yes—
488C24C2×#4114yes—
489C24C2×#4114yes—
490C24C2×#4112yes—
491C24C2×#4112yes—
492C24C2511yescharacteristic
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—21no—
506C22×C4—21no—
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—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—28no—
538C22×C4—216no—
539C22×C4—216no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
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—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4—84no—
602C22×C4—84no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4#117116yes—
608C22×C4C23×C414yes—
609C22×C4C23×C414yes—
610C22×C4C23×C414yes—
611C22×C4C23×C412yes—
612C22×C4C23×C412yes—
613C22×C4C23×C414yes—
614C22×C4C23×C414yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4114yes—
617C22×C4C2×#4114yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4114yes—
621C22×C4C2×#4114yes—
622C22×C4C2×#4112yes—
623C22×C4H(5,𝔽2)12yes—
624C22×C4H(5,𝔽2)12yes—
625C22×C4H(5,𝔽2)14yes—
626C4⋊C4—28no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—44no—
631C4⋊C4—84no—
632C4⋊C4—84no—
633C22⋊C4—216no—
634C22⋊C4—216no—
635C22⋊C4—216no—
636C22⋊C4—216no—
637C22⋊C4—216no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—84no—
646C22⋊C4—82no—
647C22⋊C4—82no—
648C22⋊C4—84no—
649C22⋊C4—84no—
650C22⋊C4—84no—
651C22⋊C4—84no—
652C22⋊C4#117132yescomplemented
653C42—48no—
654C42—48no—
655C42—48no—
656C42—48no—
657C42—48no—
658C42—48no—
659C42—48no—
660C42—82no—
661C42—82no—
662C42—84no—
663C42—84no—
664C23—232no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
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—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—88no—
722C23—88no—
723C23—816no—
724C23—816no—
725C23—88no—
726C23—816no—
727C23—88no—
728C23—88no—
729C23—816no—
730C23—88no—
731C23C2×#11718yes—
732C23C2×#11714yes—
733C23C24×C411yescharacteristic
734C23C22×#4111yescharacteristic
735C23C22×#4111yescharacteristic
736C23C22×#4112yes—
737C23C22×#4112yes—
738C23C2×H(5,𝔽2)12yes—
739C23C2×H(5,𝔽2)11yescharacteristic
740C23C2×H(5,𝔽2)11yescharacteristic
741C23#58512yes—
742C23#58511yescharacteristic
743C23#58511yescharacteristic
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
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—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—416no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
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—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
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—816no—
849C2×C4—816no—
850C2×C4—88no—
851C2×C4C2×#11714yes—
852C2×C4C2×#11714yes—
853C2×C4C2×#11718yes—
854C2×C4C2×#11718yes—
855C22—24no—
856C22—24no—
857C22—28no—
858C22—28no—
859C22—24no—
860C22—28no—
861C22—42no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—42no—
867C22—44no—
868C22—42no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—42no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—832no—
882C22C22×#11711yescharacteristic
883C22C22×#11712yes—
884C22C4×H(5,𝔽2)12yes—
885C22C4×H(5,𝔽2)11yescharacteristic
886C22C4×H(5,𝔽2)11yescharacteristic
887C22#344411yescharacteristic
888C22#344412yes—
889C22#344411yescharacteristic
890C22#349011yescharacteristic
891C22#349111yescharacteristic
892C22#349411yescharacteristic
893C22#349411yescharacteristic
894C22#350512yes—
895C22#350811yescharacteristic
896C22#351011yescharacteristic
897C22#351312yes—
898C22#351312yes—
899C22#351412yes—
900C22#351412yes—
901C22#351912yes—
902C22#351912yes—
903C22#352112yes—
904C22#352112yes—
905C4—24no—
906C4—24no—
907C4—28no—
908C4—28no—
909C4—42no—
910C4—44no—
911C4—42no—
912C4—44no—
913C4—44no—
914C4—44no—
915C4—82no—
916C4—82no—
917C4—82no—
918C4—81no—
919C4—82no—
920C4—82no—
921C4—81no—
922C2—44no—
923C2—48no—
924C2#3401211yescharacteristic
925C2#3425111yescharacteristic
926C2#3425511yescharacteristic
927C2#3426112yes—
928C2#3426112yes—
929C2#3585111yescharacteristic
930C2#3586312yes—
931C2#3590711yescharacteristic
932C2#3594411yescharacteristic
933C2#3596712yes—
934C2#3604611yescharacteristic
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. #14355C2semidirect
3. #14351C2semidirect
4. #13947C2semidirect
5. #13917C2semidirect
6. #13915C2semidirect
8. #13895C2semidirect
9. #13891C2semidirect
10. #13875C2semidirect
14. #13844C2semidirect
15. #13842C2semidirect
16. #13822C2semidirect
17. #13816C2semidirect
18. #13807C2semidirect
19. #13801C2semidirect
27. C2×#382C22semidirect
37. #2273C4semidirect
38. C2×C4×C4⋊C4C22semidirect
39. C2×C4×C4⋊C4C22semidirect
50. C2×#376C22semidirect
51. #1444C22semidirect
52. #1444C22semidirect
53. #1444C22semidirect
54. #1443C22semidirect
55. #1443C22semidirect
56. #1443C22semidirect
57. #1443C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
81. #1436C22semidirect
82. #1436C22semidirect
83. #1436C22semidirect
84. #1436C22semidirect
85. C4⋊#95C22semidirect
86. C4⋊#95C22semidirect
87. C4⋊#95C22semidirect
88. #1434C22semidirect
89. #1434C22semidirect
90. #1434C22semidirect
91. #1434C22semidirect
92. #1434C22semidirect
93. #1434C22semidirect
94. #1434C22semidirect
95. #1434C22semidirect
96. #1434C22semidirect
102. C4×#95C22semidirect
103. C4×#95C22semidirect
104. C4×#95C22semidirect
105. C4×#95C22semidirect
106. C4×#95C22semidirect
107. C4×#95C22semidirect
652. C22⋊C4#117semidirect

Maximal subgroups

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

subgroupindex
C2×#22732
#143552
#143512
#139472
#139172
#139152
#139032
#138952
#138912
#138752
#138732
#138682
#138442
#138422
#138222
#138162
#138072
#138012