Finite Group Databasebeta

← #558743

Subgroups — #558743

Order 512.

3060 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2482C211yesmaximal, characteristic
2#14695C212yesmaximal, complemented
3#14652C211yesmaximal, characteristic, complemented
4#14646C211yesmaximal, characteristic, complemented
5#14610C211yesmaximal, characteristic, complemented
6#14584C212yesmaximal, complemented
7#14543C211yesmaximal, characteristic, complemented
8#14542C212yesmaximal, complemented
9#14500C212yesmaximal, complemented
10#14447C212yesmaximal, complemented
11#14433C212yesmaximal, complemented
12#14127C212yesmaximal
13#14044C212yesmaximal, complemented
14#13991C212yesmaximal
15#13972C212yesmaximal, complemented
16#13962C212yesmaximal, complemented
17#13869C211yesmaximal, characteristic
18#13831C212yesmaximal, complemented
19C2×#1437C211yesmaximal, characteristic
20C22×#117C2211yescharacteristic
21C23×C22⋊C4C2212yes—
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2482C4116yescomplemented
26C2×#399C2211yescharacteristic
27C2×#399C2211yescharacteristic
28C2×#397C2211yescharacteristic
29C2×#397C2211yescharacteristic
30C2×#388C2212yes—
31C2×#388C2212yes—
32C2×#388C2212yes—
33C2×#388C2212yes—
34C2×#387C2212yescomplemented
35C2×#387C2212yescomplemented
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#381C2212yes—
43C2×#381C2211yescharacteristic
44C2×#379C2211yescharacteristic
45C2×#379C2212yes—
46C2×C4×C22⋊C4C2212yes—
47C22×#95C2212yes—
48C22×#95C2211yescharacteristic
49#1443C2212yescomplemented
50#1443C2212yescomplemented
51#1442C2212yescomplemented
52#1442C2212yescomplemented
53#1442C2212yescomplemented
54#1442C2212yescomplemented
55#1441C2212yescomplemented
56#1441C2212yescomplemented
57#1441C2212yescomplemented
58#1441C2212yescomplemented
59#1441C2212yescomplemented
60#1441C2212yescomplemented
61#1440C2211yescharacteristic
62#1440C2211yescharacteristic
63#1440C2211yescharacteristic
64#1440C2211yescharacteristic
65#1440C2212yes—
66#1440C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1437C2211yescharacteristic
74#1437C2212yes—
75#1437C2212yes—
76#1437C2211yescharacteristic
77#1437C2211yescharacteristic
78#1437C2211yescharacteristic
79#1437C2212yes—
80#1437C2212yes—
81#1436C2212yescomplemented
82#1436C2212yescomplemented
83#1436C2212yescomplemented
84#1436C2212yescomplemented
85#1436C2212yescomplemented
86#1436C2212yescomplemented
87#1436C2212yescomplemented
88#1436C2212yescomplemented
89C4⋊#95C2212yescomplemented
90C4⋊#95C2212yescomplemented
91C4⋊#95C2212yescomplemented
92C4⋊#95C2212yescomplemented
93#1434C2212yescomplemented
94#1434C2212yescomplemented
95#1434C2212yescomplemented
96#1434C2212yescomplemented
97#1434C2212yescomplemented
98#1434C2212yescomplemented
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C26C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C2×#117—42no—
115C2×#117—42no—
116C2×#117C2×C418yescomplemented
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C22⋊C4—28no—
128C22×C22⋊C4—44no—
129C22×C22⋊C4—44no—
130C22×C22⋊C4—42no—
131C22×C22⋊C4—42no—
132C22×C22⋊C4—42no—
133C22×C22⋊C4—44no—
134C22×C22⋊C4C2×C418yes—
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⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C42—44no—
157C22×C42—42no—
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164#399C2×C418yescomplemented
165#399C2×C418yescomplemented
166#397C2×C418yescomplemented
167#397C2×C418yescomplemented
168#388—28no—
169#388—44no—
170#388C2×C4116yescomplemented
171#388C2×C4116yescomplemented
172#387—44no—
173#387—44no—
174#385—28no—
175#385—44no—
176#385—44no—
177#385—44no—
178#385—44no—
179#385C2×C4116yescomplemented
180#381—44no—
181#381C2×C418yescomplemented
182#379—42no—
183#379C2×C4116yes—
184C4×C22⋊C4—44no—
185C2×#95—44no—
186C2×#95—42no—
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×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2311yescharacteristic
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C25—24no—
232C25—22no—
233C25—24no—
234C25—22no—
235C25—24no—
236C25—42no—
237C25—42no—
238C25—42no—
239C25C22×C414yes—
240C25C2411yescharacteristic
241C25C2411yescharacteristic
242C25C2411yescharacteristic
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
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×C4—42no—
271C23×C4—42no—
272C23×C4C22×C414yes—
273C23×C4C22×C414yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290#117—416no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
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⋊C4C22×C414yes—
318C2×C4⋊C4C22×C414yes—
319C2×C4⋊C4C22×C418yes—
320C2×C4⋊C4C22×C418yes—
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—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—416no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—41no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—41no—
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—41no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—41no—
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—432no—
365C2×C22⋊C4—416no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4C22×C418yes—
373C2×C22⋊C4C22×C418yes—
374C2×C22⋊C4C22×C418yes—
375C2×C22⋊C4C22×C414yes—
376C2×C22⋊C4C22×C414yes—
377C2×C22⋊C4C22×C414yes—
378C2×C22⋊C4C22×C414yes—
379C2×C22⋊C4C22×C418yes—
380C2×C22⋊C4C22×C418yes—
381C2×C22⋊C4C22×C418yes—
382C2×C22⋊C4#4118yes—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—41no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—41no—
393C2×C42—416no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42C22×C418yes—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—41no—
412#95—42no—
413#95—41no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
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#95—42no—
438#95—42no—
439#95C22×C418yes—
440#95C22×C414yes—
441#95C22×C414yes—
442#95C22×C418yes—
443#95C22×C418yes—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—28no—
456C24—22no—
457C24—22no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—28no—
465C24—216no—
466C24—44no—
467C24—48no—
468C24—48no—
469C24—48no—
470C24—48no—
471C24—48no—
472C24—48no—
473C24—48no—
474C24—44no—
475C24—48no—
476C24—44no—
477C24—82no—
478C24—82no—
479C24—84no—
480C24—84no—
481C24—84no—
482C24—84no—
483C24—84no—
484C24C23×C412yes—
485C24C23×C412yes—
486C24C23×C412yes—
487C24C2×#4114yes—
488C24H(5,𝔽2)12yes—
489C24H(5,𝔽2)12yes—
490C24H(5,𝔽2)14yes—
491C242−1+414yes—
492C24C2511yescharacteristic
493C22×C4—216no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—216no—
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—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
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—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
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—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—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4—84no—
612C22×C4—84no—
613C22×C4—84no—
614C22×C4—84no—
615C22×C4—84no—
616C22×C4—84no—
617C22×C4C23×C414yes—
618C22×C4C23×C414yes—
619C22×C4C23×C412yes—
620C22×C4C23×C414yes—
621C22×C4C23×C412yes—
622C22×C4C23×C412yes—
623C22×C4C23×C412yes—
624C22×C4C23×C414yes—
625C22×C4C2×#4114yes—
626C22×C4C2×#4114yes—
627C22×C4H(5,𝔽2)14yes—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—84no—
633C4⋊C4—84no—
634C4⋊C4—84no—
635C4⋊C4—84no—
636C4⋊C4—84no—
637C4⋊C4—84no—
638C22⋊C4—216no—
639C22⋊C4—216no—
640C22⋊C4—216no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—84no—
657C22⋊C4—82no—
658C22⋊C4—82no—
659C42—48no—
660C42—44no—
661C42—48no—
662C42—44no—
663C42—84no—
664C42—84no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—24no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—22no—
692C23—22no—
693C23—24no—
694C23—22no—
695C23—24no—
696C23—416no—
697C23—432no—
698C23—41no—
699C23—42no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—416no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—41no—
716C23—42no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—88no—
726C23—816no—
727C23—816no—
728C23—816no—
729C23—816no—
730C23—816no—
731C23C4×#4114yes—
732C23#51814yes—
733C23#52018yes—
734C23#56014yes—
735C23#56218yes—
736C23#56314yes—
737C23C24×C411yescharacteristic
738C23C22×#4112yes—
739C23C2×H(5,𝔽2)11yescharacteristic
740C23C2×H(5,𝔽2)11yescharacteristic
741C23C2×H(5,𝔽2)12yes—
742C23C2×H(5,𝔽2)12yes—
743C23C2×2−1+412yes—
744C23#58512yes—
745C23#58512yes—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
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—24no—
775C2×C4—416no—
776C2×C4—432no—
777C2×C4—416no—
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—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
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—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—816no—
854C2×C4—816no—
855C22—28no—
856C22—24no—
857C22—28no—
858C22—24no—
859C22—28no—
860C22—28no—
861C22—28no—
862C22—28no—
863C22—24no—
864C22—28no—
865C22—42no—
866C22—44no—
867C22—42no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—42no—
873C22—42no—
874C22—44no—
875C22—42no—
876C22—44no—
877C22—832no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22#237618yes—
883C22C2×C4×#4111yescharacteristic
884C22C2×#51811yescharacteristic
885C22C2×#52012yes—
886C22#342811yescharacteristic
887C22C4×H(5,𝔽2)12yes—
888C22#349012yes—
889C22#349512yes—
890C22#351312yes—
891C22#351312yes—
892C22#351312yes—
893C22#352012yes—
894C22C2×#56011yescharacteristic
895C22C2×#56212yes—
896C22C2×#56311yescharacteristic
897C22#353211yescharacteristic
898C22#353311yescharacteristic
899C22#353512yes—
900C22#354212yes—
901C22#354212yes—
902C22#354512yes—
903C22#356412yes—
904C4—42no—
905C4—42no—
906C4—44no—
907C4—42no—
908C4—42no—
909C4—44no—
910C4—44no—
911C4—44no—
912C4—44no—
913C4—44no—
914C4—44no—
915C4—82no—
916C4—82no—
917C4—82no—
918C4—82no—
919C4—82no—
920C2—28no—
921C2—44no—
922C2—82no—
923C2#3422811yescharacteristic
924C2#3429612yes—
925C2C2×#237611yescharacteristic
926C2#3440611yescharacteristic
927C2#3447912yes—
928C2#4552812yes—
929C2#4555712yes—
930C2#4616812yes—
931C2#4633412yes—
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. #14695C2semidirect
3. #14652C2semidirect
4. #14646C2semidirect
5. #14610C2semidirect
6. #14584C2semidirect
7. #14543C2semidirect
8. #14542C2semidirect
9. #14500C2semidirect
10. #14447C2semidirect
11. #14433C2semidirect
13. #14044C2semidirect
15. #13972C2semidirect
16. #13962C2semidirect
18. #13831C2semidirect
25. #2482C4semidirect
34. C2×#387C22semidirect
35. C2×#387C22semidirect
49. #1443C22semidirect
50. #1443C22semidirect
51. #1442C22semidirect
52. #1442C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1441C22semidirect
56. #1441C22semidirect
57. #1441C22semidirect
58. #1441C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
81. #1436C22semidirect
82. #1436C22semidirect
83. #1436C22semidirect
84. #1436C22semidirect
85. #1436C22semidirect
86. #1436C22semidirect
87. #1436C22semidirect
88. #1436C22semidirect
89. C4⋊#95C22semidirect
90. C4⋊#95C22semidirect
91. C4⋊#95C22semidirect
92. C4⋊#95C22semidirect
93. #1434C22semidirect
94. #1434C22semidirect
95. #1434C22semidirect
96. #1434C22semidirect
97. #1434C22semidirect
98. #1434C22semidirect
116. C2×#117C2×C4semidirect
164. #399C2×C4semidirect
165. #399C2×C4semidirect
166. #397C2×C4semidirect
167. #397C2×C4semidirect
170. #388C2×C4semidirect
171. #388C2×C4semidirect
179. #385C2×C4semidirect
181. #381C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24822
#146952
#146522
#146462
#146102
#145842
#145432
#145422
#145002
#144472
#144332
#141272
#140442
#139912
#139722
#139622
#138692
#138312
C2×#14372