Finite Group Databasebeta

← #1080644

Subgroups — #1080644

Order 512.

3354 conjugacy classes of subgroups.

The subgroup lattice has 1033 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2712C211yesmaximal, characteristic, complemented
2C2×#2388C211yesmaximal, characteristic
3#17186C212yesmaximal, complemented
4#16831C211yesmaximal, characteristic, complemented
5#16438C212yesmaximal, complemented
6#16318C211yesmaximal, characteristic, complemented
7#16294C212yesmaximal, complemented
8#15510C212yesmaximal, complemented
9#15498C212yesmaximal, complemented
10#15314C212yesmaximal, complemented
11#14889C212yesmaximal, complemented
12#14868C211yesmaximal, characteristic, complemented
13#14797C212yesmaximal, complemented
14#14521C211yesmaximal, characteristic, complemented
15#14220C212yesmaximal, complemented
16#14116C212yesmaximal, complemented
17#14027C212yesmaximal, complemented
18#14015C211yesmaximal, characteristic, complemented
19#14015C212yesmaximal, complemented
20C23×#41C2211yescharacteristic
21C22×#124C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C23×C4⋊C4C2211yescharacteristic
25#2712—28no—
26C2×#397C2211yescharacteristic
27C2×#397C2211yescharacteristic
28#2388—28no—
29C2×#395C2211yescharacteristic
30C2×#395C2212yes—
31C2×#394C2211yescharacteristic
32C2×#394C2212yes—
33C2×#394C2212yes—
34C2×#394C2212yes—
35C2×#394C2212yes—
36C2×#394C2212yes—
37C2×#393C2212yes—
38C2×#393C2212yes—
39C2×#393C2211yescharacteristic
40C2×#392C2212yes—
41C2×#392C2211yescharacteristic
42C2×#391C2212yes—
43C2×#391C2212yes—
44C2×#391C2212yes—
45C2×#390C2212yes—
46C2×#389C2211yescharacteristic
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2211yescharacteristic
52C2×#386C2211yescharacteristic
53C2×#385C2211yescharacteristic
54C2×#385C2212yes—
55C2×#385C2212yes—
56C2×#385C2212yes—
57C2×#385C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2211yescharacteristic
60#1446C2212yes—
61#1446C2212yes—
62#1445C2212yes—
63#1444C2212yes—
64#1444C2212yes—
65#1444C2212yes—
66#1443C2212yes—
67#1443C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1441C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1439C2211yescharacteristic
80#1439C2211yescharacteristic
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1438C2212yes—
89#1438C2212yes—
90#1438C2212yes—
91#1437C2212yes—
92#1437C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98C4⋊#95C2212yes—
99C4⋊#95C2212yes—
100#1434C2211yescharacteristic
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2212yes—
107C22⋊#95C2211yescharacteristic
108C4×#95C2212yes—
109C22×#41—24no—
110C22×#41—44no—
111C22×#41—42no—
112C22×#41—42no—
113C22×#41—44no—
114C23×Q8C2312yes—
115C23×Q8C2311yescharacteristic
116C23×D4C2311yescharacteristic
117C23×D4C2312yes—
118C23×D4C2312yes—
119C23×D4C2311yescharacteristic
120C24×C4C2312yes—
121C24×C4C2311yescharacteristic
122C24×C4C2311yescharacteristic
123C24×C4C2311yescharacteristic
124C24×C4C2311yescharacteristic
125C2×#124—28no—
126C2×#124—28no—
127C2×#124—44no—
128C2×C4×D4—28no—
129C2×C4×D4—24no—
130C2×C4×D4—42no—
131C2×C4×D4—44no—
132C2×C4×D4—44no—
133C2×C4×D4—42no—
134C22×C4⋊C4—42no—
135C22×C4⋊C4—44no—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2311yescharacteristic
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2312yes—
173C22×C42C2312yes—
174#397—24no—
175#397—42no—
176#395—24no—
177#395—44no—
178#394—24no—
179#394—28no—
180#394—28no—
181#394—44no—
182#394—44no—
183#394—44no—
184#393—24no—
185#393—28no—
186#393—28no—
187#392—28no—
188#392D418yes—
189#391—28no—
190#391—44no—
191#391—44no—
192#390—44no—
193#389—42no—
194#388—28no—
195#388—28no—
196#386—28no—
197#386—24no—
198#386—28no—
199#386—42no—
200#385—24no—
201#385—44no—
202#385—44no—
203#385—44no—
204#385—44no—
205C4×C22⋊C4—28no—
206C4×C22⋊C4—24no—
207C2×#95C2312yes—
208C2×#95C2311yescharacteristic
209C2×#95C2312yes—
210C2×#95C2311yescharacteristic
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×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2311yescharacteristic
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2311yescharacteristic
244C2×#95C2312yes—
245C25C2412yes—
246C25C2411yescharacteristic
247C25C2411yescharacteristic
248C2×#41—432no—
249C2×#41—416no—
250C2×#41—416no—
251C2×#41—432no—
252C2×#41—416no—
253C22×Q8—22no—
254C22×Q8—24no—
255C22×Q8—24no—
256C22×Q8—24no—
257C22×Q8—24no—
258C22×Q8—24no—
259C22×Q8—42no—
260C22×Q8—41no—
261C22×Q8—41no—
262C22×Q8—42no—
263C22×Q8—42no—
264C22×Q8—42no—
265C22×D4—24no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—24no—
269C22×D4—22no—
270C22×D4—24no—
271C22×D4—24no—
272C22×D4—22no—
273C22×D4—24no—
274C22×D4—24no—
275C22×D4—22no—
276C22×D4—24no—
277C22×D4—42no—
278C22×D4—42no—
279C22×D4—41no—
280C22×D4—41no—
281C22×D4—42no—
282C22×D4—42no—
283C22×D4—42no—
284C22×D4—42no—
285C22×D4—42no—
286C22×D4—41no—
287C22×D4—41no—
288C22×D4—42no—
289C22×D4C2×D418yes—
290C22×D4C2×D414yes—
291C23×C4—24no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—24no—
295C23×C4—22no—
296C23×C4—24no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—24no—
304C23×C4—22no—
305C23×C4—24no—
306C23×C4—41no—
307C23×C4—42no—
308C23×C4—41no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4—42no—
312C23×C4—41no—
313C23×C4—42no—
314C23×C4—41no—
315C23×C4—42no—
316C23×C4—42no—
317C23×C4—41no—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2412yes—
328C23×C4C2412yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2411yescharacteristic
332C23×C4C2412yes—
333C23×C4C2411yescharacteristic
334#124—432no—
335C4×D4—416no—
336C4×D4—432no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—41no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—416no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—41no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—41no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—41no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4C2×D418yes—
437C2×C22⋊C4C2×D414yes—
438C2×C22⋊C4#4114yescomplemented
439C2×C42—22no—
440C2×C42—24no—
441C2×C42—24no—
442C2×C42—24no—
443C2×C42—22no—
444C2×C42—24no—
445C2×C42—24no—
446C2×C42—42no—
447C2×C42—41no—
448C2×C42—42no—
449C2×C42—42no—
450C2×C42—42no—
451#95—24no—
452#95—24no—
453#95—22no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—22no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—24no—
465#95—24no—
466#95—24no—
467#95—24no—
468#95—24no—
469#95—42no—
470#95—42no—
471#95—42no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95—42no—
476#95—42no—
477#95—42no—
478#95—42no—
479#95—42no—
480#95—42no—
481#95—42no—
482#95—42no—
483#95—42no—
484#95—42no—
485#95—41no—
486#95—42no—
487#95C2×D414yes—
488#95#4118yescomplemented
489C24—22no—
490C24—22no—
491C24—21no—
492C24—21no—
493C24—22no—
494C24—22no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—22no—
504C24—21no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—21no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—22no—
520C24—21no—
521C24C22×D414yes—
522C24C22×D412yes—
523C24C2×#4112yes—
524C24H(5,𝔽2)12yes—
525C24H(5,𝔽2)12yes—
526C24C2511yescharacteristic
527#41—4128no—
528C2×Q8—48no—
529C2×Q8—44no—
530C2×Q8—48no—
531C2×Q8—48no—
532C2×Q8—48no—
533C2×Q8—44no—
534C2×Q8—48no—
535C2×Q8—44no—
536C2×Q8—48no—
537C2×Q8—84no—
538C2×Q8—84no—
539C2×Q8—84no—
540C2×D4—28no—
541C2×D4—216no—
542C2×D4—216no—
543C2×D4—48no—
544C2×D4—44no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—48no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—48no—
558C2×D4—44no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—44no—
562C2×D4—48no—
563C2×D4—44no—
564C2×D4—48no—
565C2×D4—44no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—216no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
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—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—44no—
661C22×C4—48no—
662C22×C4—48no—
663C22×C4—48no—
664C22×C4—48no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—44no—
670C22×C4—48no—
671C22×C4—44no—
672C22×C4—48no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—48no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—82no—
680C22×C4—84no—
681C22×C4—82no—
682C22×C4—84no—
683C22×C4—84no—
684C22×C4—82no—
685C22×C4C22×D412yes—
686C22×C4C22×D412yes—
687C22×C4C22×D414yes—
688C22×C4C2×#4114yes—
689C22×C4C2×#4114yes—
690C22×C4C2×#4114yes—
691C22×C4C2×#4114yes—
692C22×C4H(5,𝔽2)14yes—
693C22×C4H(5,𝔽2)12yes—
694C22×C4H(5,𝔽2)14yes—
695C22×C42−1+412yes—
696C22×C42−1+414yes—
697C4⋊C4—44no—
698C4⋊C4—48no—
699C4⋊C4—44no—
700C4⋊C4—48no—
701C4⋊C4—48no—
702C4⋊C4—84no—
703C4⋊C4—82no—
704C4⋊C4—84no—
705C4⋊C4—84no—
706C4⋊C4—84no—
707C4⋊C4—84no—
708C22⋊C4—28no—
709C22⋊C4—216no—
710C22⋊C4—44no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—48no—
714C22⋊C4—48no—
715C22⋊C4—44no—
716C22⋊C4—48no—
717C22⋊C4—48no—
718C22⋊C4—48no—
719C22⋊C4—48no—
720C22⋊C4—48no—
721C22⋊C4—48no—
722C22⋊C4—48no—
723C22⋊C4—84no—
724C22⋊C4—84no—
725C22⋊C4—84no—
726C22⋊C4—84no—
727C22⋊C4—84no—
728C22⋊C4—82no—
729C22⋊C4—84no—
730C22⋊C4—84no—
731C42—48no—
732C42—44no—
733C42—48no—
734C42—84no—
735C23—22no—
736C23—24no—
737C23—24no—
738C23—22no—
739C23—24no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—24no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—22no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—22no—
756C23—24no—
757C23—24no—
758C23—22no—
759C23—42no—
760C23—41no—
761C23—42no—
762C23—42no—
763C23—41no—
764C23—41no—
765C23—42no—
766C23—42no—
767C23—41no—
768C23—42no—
769C23—42no—
770C23—41no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—41no—
780C23—42no—
781C23—42no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—41no—
797C23—42no—
798C23—41no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—41no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—41no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23#54614yes—
816C23C23×D411yescharacteristic
817C23C22×#4111yescharacteristic
818C23C22×#4112yes—
819C23C2×H(5,𝔽2)12yes—
820C23C2×H(5,𝔽2)11yescharacteristic
821C23C2×H(5,𝔽2)11yescharacteristic
822C23C2×H(5,𝔽2)11yescharacteristic
823C23C2×H(5,𝔽2)12yes—
824C23C2×2−1+412yes—
825C23C2×2−1+411yescharacteristic
826C23#58511yescharacteristic
827Q8—416no—
828Q8—816no—
829D4—432no—
830D4—416no—
831D4—416no—
832D4—432no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—416no—
863C2×C4—432no—
864C2×C4—416no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—41no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—41no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—41no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—88no—
939C2×C4—88no—
940C2×C4#54718yes—
941C2×C4H(3,𝔽4)14yes—
942C22—24no—
943C22—28no—
944C22—42no—
945C22—42no—
946C22—44no—
947C22—42no—
948C22—44no—
949C22—44no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—44no—
954C22—42no—
955C22—44no—
956C22—44no—
957C22—42no—
958C22—44no—
959C22—44no—
960C22—44no—
961C22—44no—
962C22—42no—
963C22—44no—
964C22—44no—
965C22—82no—
966C22—81no—
967C22—82no—
968C22—81no—
969C22—82no—
970C22—82no—
971C22—82no—
972C22—82no—
973C22—82no—
974C22—82no—
975C22—81no—
976C22—82no—
977C22—81no—
978C22—82no—
979C22#346012yes—
980C22#346011yescharacteristic
981C22C2×#54611yescharacteristic
982C22C2×#54712yes—
983C22#348111yescharacteristic
984C22#348112yes—
985C22#348411yescharacteristic
986C22#348412yes—
987C22#348911yescharacteristic
988C22#349211yescharacteristic
989C22#351112yes—
990C22#351912yes—
991C22#352012yes—
992C22#352212yes—
993C22C2×H(3,𝔽4)11yescharacteristic
994C22#353211yescharacteristic
995C22#353212yes—
996C22#353411yescharacteristic
997C22#353611yescharacteristic
998C22#353612yes—
999C22#355012yes—
1000C22#355011yescharacteristic
1001C22#355412yes—
1002C4—24no—
1003C4—28no—
1004C4—44no—
1005C4—44no—
1006C4—42no—
1007C4—42no—
1008C4—44no—
1009C4—42no—
1010C4—44no—
1011C4—82no—
1012C4—82no—
1013C4—82no—
1014C4—81no—
1015C4—82no—
1016C4—82no—
1017C4—82no—
1018C2—44no—
1019C2—82no—
1020C2—84no—
1021C2#3774511yescharacteristic
1022C2#3779412yes—
1023C2#4117411yescharacteristic
1024C2#4129712yes—
1025C2#4421712yes—
1026C2#4432511yescharacteristic
1027C2#4543911yescharacteristic
1028C2#5229411yescharacteristic
1029C2#5295811yescharacteristic
1030C2#5907011yescharacteristic
1031C2#5909012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2388C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2712C2semidirect
3. #17186C2semidirect
4. #16831C2semidirect
5. #16438C2semidirect
6. #16318C2semidirect
7. #16294C2semidirect
8. #15510C2semidirect
9. #15498C2semidirect
10. #15314C2semidirect
11. #14889C2semidirect
12. #14868C2semidirect
13. #14797C2semidirect
14. #14521C2semidirect
15. #14220C2semidirect
16. #14116C2semidirect
17. #14027C2semidirect
18. #14015C2semidirect
19. #14015C2semidirect
438. C2×C22⋊C4#41semidirect
488. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#27122
C2×#23882
#171862
#168312
#164382
#163182
#162942
#155102
#154982
#153142
#148892
#148682
#147972
#145212
#142202
#141162
#140272
#140152