Finite Group Databasebeta

← #538038

Subgroups — #538038

Order 512.

6218 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2403C211yesmaximal, characteristic
2C2×#2358C212yesmaximal, complemented
3C2×D4×C22⋊C4C212yesmaximal, complemented
4#14521C212yesmaximal, complemented
5#14520C212yesmaximal, complemented
6#14519C212yesmaximal, complemented
7#14410C211yesmaximal, characteristic, complemented
8#14358C211yesmaximal, characteristic, complemented
9#14187C212yesmaximal, complemented
10#14145C211yesmaximal, characteristic, complemented
11#14134C211yesmaximal, characteristic, complemented
12#14016C212yesmaximal, complemented
13#13991C212yesmaximal, complemented
14#13988C212yesmaximal, complemented
15#13967C212yesmaximal, complemented
16#13967C212yesmaximal, complemented
17#13867C211yesmaximal, characteristic, complemented
18C2×#1438C211yesmaximal, characteristic, complemented
19#13784C212yesmaximal, complemented
20C24×D4C2211yescharacteristic
21C24×D4C2211yescharacteristic
22C22×#120C2212yes—
23C22×#120C2211yescharacteristic
24C22×#120C2211yescharacteristic
25C22×C4×D4C2212yes—
26C22×C4×D4C2212yes—
27C22×C4×D4C2212yescomplemented
28C23×C22⋊C4C2212yes—
29C23×C22⋊C4C2211yescharacteristic, complemented
30C23×C22⋊C4C2212yescomplemented
31C23×C22⋊C4C2212yescomplemented
32#2403C4116yescomplemented
33C2×#392C2212yes—
34C2×#392C2212yes—
35#2358—216no—
36D4×C22⋊C4—216no—
37C2×#390C2212yescomplemented
38C2×#390C2212yescomplemented
39C2×#390C2212yescomplemented
40C2×#388C2212yescomplemented
41C2×#388C2212yescomplemented
42C2×#388C2212yescomplemented
43C2×#388C2212yescomplemented
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2211yescharacteristic
47C2×#386C2211yescharacteristic
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yescomplemented
51C2×#386C2212yescomplemented
52C2×#386C2212yescomplemented
53C2×#386C2212yescomplemented
54C2×#386C2212yescomplemented
55C2×#386C2212yescomplemented
56C2×#386C2212yescomplemented
57C2×#385C2212yescomplemented
58C2×#385C2212yescomplemented
59C2×#380C2212yescomplemented
60C2×#379C2212yes—
61C2×#379C2211yescharacteristic
62C2×#379C2212yescomplemented
63C2×#379C2211yescharacteristic, complemented
64C2×C4×C22⋊C4C2212yescomplemented
65C2×C4×C22⋊C4C2212yescomplemented
66C2×C4×C22⋊C4C2212yescomplemented
67C22×#95C2211yescharacteristic, complemented
68C22×#95C2211yescharacteristic, complemented
69#1442C2212yescomplemented
70#1442C2212yescomplemented
71#1440C2212yescomplemented
72#1440C2212yescomplemented
73#1439C2212yescomplemented
74#1439C2212yescomplemented
75#1439C2212yescomplemented
76#1439C2212yescomplemented
77#1439C2212yescomplemented
78#1439C2212yescomplemented
79#1438C2211yescharacteristic
80#1438C2211yescharacteristic
81#1438C2212yes—
82#1438C2211yescharacteristic
83#1438C2211yescharacteristic
84#1438C2211yescharacteristic, complemented
85#1438C2211yescharacteristic, complemented
86#1438C2212yescomplemented
87#1438C2212yescomplemented
88#1438C2211yescharacteristic, complemented
89#1438C2211yescharacteristic, complemented
90#1438C2212yescomplemented
91#1437C2212yescomplemented
92#1437C2212yescomplemented
93#1437C2212yescomplemented
94#1437C2212yescomplemented
95#1437C2212yescomplemented
96#1437C2212yescomplemented
97#1436C2212yescomplemented
98#1436C2212yescomplemented
99#1436C2212yescomplemented
100#1436C2212yescomplemented
101#1434C2212yescomplemented
102#1434C2212yescomplemented
103C22⋊#95C2212yescomplemented
104C22⋊#95C2212yescomplemented
105C22⋊#95C2212yescomplemented
106C22⋊#95C2212yescomplemented
107C22⋊#95C2212yescomplemented
108C22⋊#95C2212yescomplemented
109C22⋊#95C2212yescomplemented
110C26C2311yescharacteristic
111C26C2311yescharacteristic
112C26C2311yescharacteristic
113C23×D4—28no—
114C23×D4—28no—
115C23×D4—42no—
116C23×D4—42no—
117C23×D4—42no—
118C23×D4—42no—
119C23×D4—44no—
120C23×D4—44no—
121C23×D4C2×C418yescomplemented
122C23×D4C2×C418yescomplemented
123C23×D4C2312yes—
124C23×D4C2311yescharacteristic
125C23×D4C2312yes—
126C23×D4C2312yes—
127C23×D4C2311yescharacteristic
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2311yescharacteristic
131C24×C4C2312yes—
132C24×C4C2311yescharacteristic
133C24×C4C2312yes—
134C24×C4C2312yes—
135C24×C4C2312yes—
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138C2×#120—28no—
139C2×#120—28no—
140C2×#120—44no—
141C2×#120—44no—
142C2×#120C2×C4116yescomplemented
143C2×#120C2×C418yescomplemented
144C2×#120C2×C418yescomplemented
145C2×C4×D4—28no—
146C2×C4×D4—28no—
147C2×C4×D4—28no—
148C2×C4×D4—28no—
149C2×C4×D4—28no—
150C2×C4×D4—44no—
151C2×C4×D4—44no—
152C2×C4×D4—44no—
153C2×C4×D4—44no—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4—28no—
159C22×C22⋊C4—28no—
160C22×C22⋊C4—28no—
161C22×C22⋊C4—28no—
162C22×C22⋊C4—44no—
163C22×C22⋊C4—44no—
164C22×C22⋊C4—44no—
165C22×C22⋊C4—44no—
166C22×C22⋊C4—44no—
167C22×C22⋊C4—42no—
168C22×C22⋊C4—44no—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C42C2312yes—
203C22×C42C2312yes—
204C22×C42C2312yes—
205C22×C42C2312yes—
206#392C2×C4116yescomplemented
207#392C2×C4116yescomplemented
208#390—28no—
209#390—28no—
210#390—28no—
211#388—28no—
212#388—28no—
213#388—44no—
214#388—44no—
215#386—28no—
216#386—28no—
217#386—28no—
218#386—28no—
219#386—28no—
220#386—44no—
221#386—44no—
222#386—44no—
223#386—44no—
224#386C2×C418yescomplemented
225#386C2×C4116yescomplemented
226#386C2×C418yescomplemented
227#386D4116yescomplemented
228#385—28no—
229#385—28no—
230#380—28no—
231#379—28no—
232#379—28no—
233#379—42no—
234#379C2×C418yescomplemented
235C4×C22⋊C4—28no—
236C4×C22⋊C4—28no—
237C4×C22⋊C4—28no—
238C2×#95—42no—
239C2×#95—42no—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2311yescharacteristic
249C2×#95C2312yes—
250C2×#95C2311yescharacteristic
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C25—24no—
269C25—24no—
270C25—24no—
271C25—24no—
272C25—24no—
273C25—24no—
274C25—24no—
275C25—24no—
276C25—24no—
277C25—22no—
278C25—22no—
279C25—22no—
280C25—22no—
281C25—42no—
282C25—42no—
283C25—42no—
284C25—42no—
285C25—42no—
286C25—41no—
287C25—41no—
288C25—42no—
289C25—42no—
290C25—42no—
291C25—42no—
292C25C22×C414yes—
293C25C22×C414yes—
294C25C22×C414yes—
295C25C2411yescharacteristic
296C25C2411yescharacteristic
297C25C2412yes—
298C25C2411yescharacteristic
299C25C2411yescharacteristic
300C25C2411yescharacteristic
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—24no—
317C22×D4—264no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—42no—
321C22×D4—416no—
322C22×D4—42no—
323C22×D4—42no—
324C22×D4—41no—
325C22×D4—41no—
326C22×D4—41no—
327C22×D4—41no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4—41no—
331C22×D4—41no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—416no—
342C22×D4—416no—
343C22×D4—416no—
344C22×D4—416no—
345C22×D4—432no—
346C22×D4—416no—
347C22×D4—432no—
348C22×D4—432no—
349C22×D4C22×C418yes—
350C22×D4C22×C414yes—
351C22×D4C22×C418yes—
352C22×D4C22×C418yes—
353C22×D4C22×C418yes—
354C22×D4C22×C414yes—
355C22×D4C22×C414yes—
356C22×D4C22×C414yes—
357C22×D4C2×D418yes—
358C22×D4#4118yes—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4C22×C414yes—
402C23×C4C22×C414yes—
403C23×C4C2×D418yes—
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417#120—264no—
418#120—416no—
419#120—416no—
420C4×D4—432no—
421C4×D4—432no—
422C4×D4—432no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—416no—
480C2×C22⋊C4—432no—
481C2×C22⋊C4—432no—
482C2×C22⋊C4—432no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—41no—
488C2×C22⋊C4—41no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4C22×C418yes—
522C2×C22⋊C4C22×C414yes—
523C2×C22⋊C4C22×C418yes—
524C2×C22⋊C4C22×C418yes—
525C2×C22⋊C4C22×C414yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C22×C418yes—
529C2×C22⋊C4C2×D418yes—
530C2×C22⋊C4C2×D418yescomplemented
531C2×C22⋊C4C2×D418yescomplemented
532C2×C42—24no—
533C2×C42—24no—
534C2×C42—24no—
535C2×C42—24no—
536C2×C42—24no—
537C2×C42—24no—
538C2×C42—42no—
539C2×C42—42no—
540C2×C42—42no—
541C2×C42—42no—
542C2×C42—42no—
543C2×C42—42no—
544#95—24no—
545#95—24no—
546#95—24no—
547#95—24no—
548#95—24no—
549#95—24no—
550#95—24no—
551#95—41no—
552#95—41no—
553#95—42no—
554#95—42no—
555#95—41no—
556#95—41no—
557#95—42no—
558#95—42no—
559#95—42no—
560#95—42no—
561#95—42no—
562#95—42no—
563#95—42no—
564#95—42no—
565#95—42no—
566#95—42no—
567#95—42no—
568#95C22×C418yes—
569#95C22×C418yes—
570#95C2×D418yescomplemented
571#95C2×D418yescomplemented
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—21no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—28no—
603C24—28no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—21no—
612C24—21no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—22no—
620C24—216no—
621C24—216no—
622C24—216no—
623C24—28no—
624C24—28no—
625C24—28no—
626C24—44no—
627C24—44no—
628C24—44no—
629C24—48no—
630C24—48no—
631C24—48no—
632C24—44no—
633C24—48no—
634C24—48no—
635C24—48no—
636C24—48no—
637C24—48no—
638C24—48no—
639C24—48no—
640C24—44no—
641C24—48no—
642C24—44no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—48no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—48no—
652C24—44no—
653C24—44no—
654C24—48no—
655C24—48no—
656C24—44no—
657C24—44no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—82no—
669C24—82no—
670C24—82no—
671C24—82no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—82no—
680C24—82no—
681C24C23×C412yes—
682C24C23×C412yes—
683C24C23×C414yes—
684C24C23×C412yes—
685C24C23×C412yes—
686C24C23×C412yes—
687C24C22×D414yes—
688C24C22×D414yes—
689C24C2×#4114yes—
690C24C2×#4114yes—
691C24H(5,𝔽2)14yes—
692C24H(5,𝔽2)14yes—
693C24H(5,𝔽2)12yes—
694C24H(5,𝔽2)12yes—
695C24C2511yescharacteristic
696C2×D4—216no—
697C2×D4—216no—
698C2×D4—216no—
699C2×D4—216no—
700C2×D4—216no—
701C2×D4—216no—
702C2×D4—216no—
703C2×D4—216no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—216no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—216no—
710C2×D4—216no—
711C2×D4—48no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—4128no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—4128no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4C4×D4132yescomplemented
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—28no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—216no—
802C22×C4—216no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—48no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—84no—
847C22×C4—84no—
848C22×C4—84no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4—84no—
859C22×C4—84no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4C23×C412yes—
867C22×C4C23×C412yes—
868C22×C4C23×C414yes—
869C22×C4C23×C414yes—
870C22×C4C23×C414yes—
871C22×C4C22×D414yes—
872C22×C4C22×D414yes—
873C22×C4C22×D414yes—
874C22×C4C22×D414yes—
875C22×C4C22×D414yes—
876C22×C4C2×#4114yes—
877C22×C4H(5,𝔽2)14yes—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—84no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—216no—
885C22⋊C4—28no—
886C22⋊C4—216no—
887C22⋊C4—216no—
888C22⋊C4—216no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—44no—
894C22⋊C4—48no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—84no—
910C22⋊C4—84no—
911C22⋊C4—84no—
912C22⋊C4—84no—
913C22⋊C4—82no—
914C22⋊C4—82no—
915C42—48no—
916C42—48no—
917C42—48no—
918C42—84no—
919C23—22no—
920C23—22no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—22no—
934C23—22no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—22no—
939C23—24no—
940C23—24no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—22no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—24no—
982C23—24no—
983C23—416no—
984C23—416no—
985C23—416no—
986C23—432no—
987C23—432no—
988C23—432no—
989C23—41no—
990C23—41no—
991C23—42no—
992C23—42no—
993C23—41no—
994C23—41no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—42no—
1024C23—41no—
1025C23—416no—
1026C23—416no—
1027C23—41no—
1028C23—41no—
1029C23—42no—
1030C23—42no—
1031C23—41no—
1032C23—41no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—88no—
1060C23—88no—
1061C23—816no—
1062C23—816no—
1063C23—88no—
1064C23—816no—
1065C23—816no—
1066C23—816no—
1067C23—816no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23—816no—
1072C23—816no—
1073C23—816no—
1074C23—816no—
1075C23—88no—
1076C23—816no—
1077C23—816no—
1078C23C2×C4×D418yes—
1079C23C2×C4×D418yes—
1080C23#51814yes—
1081C23#51814yes—
1082C23#51814yes—
1083C23D4214yes—
1084C23#54618yes—
1085C23#55114yes—
1086C23C24×C411yescharacteristic
1087C23C23×D412yes—
1088C23C22×#4112yes—
1089C23C2×H(5,𝔽2)11yescharacteristic
1090C23C2×H(5,𝔽2)11yescharacteristic
1091C23C2×H(5,𝔽2)12yes—
1092C23C2×H(5,𝔽2)12yes—
1093C23C2×H(5,𝔽2)12yes—
1094C23#58512yes—
1095D4—264no—
1096D4—432no—
1097D4—432no—
1098D4—416no—
1099D4—416no—
1100D4—416no—
1101D4—416no—
1102D4—816no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—416no—
1137C2×C4—416no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—816no—
1192C2×C4—816no—
1193C2×C4—816no—
1194C2×C4—816no—
1195C2×C4—816no—
1196C2×C4C2×C4×D418yes—
1197C22—24no—
1198C22—28no—
1199C22—28no—
1200C22—24no—
1201C22—28no—
1202C22—28no—
1203C22—28no—
1204C22—28no—
1205C22—24no—
1206C22—24no—
1207C22—28no—
1208C22—28no—
1209C22—28no—
1210C22—28no—
1211C22—28no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—42no—
1225C22—42no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—832no—
1249C22—832no—
1250C22—832no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22#235818yes—
1260C22C22×C4×D412yes—
1261C22C2×#51811yescharacteristic
1262C22C2×#51811yescharacteristic
1263C22C2×#51811yescharacteristic
1264C22C4×H(5,𝔽2)12yes—
1265C22C2×D4211yescharacteristic
1266C22C2×#54612yes—
1267C22C2×#55111yescharacteristic
1268C22#348412yes—
1269C22#348412yes—
1270C22#348812yes—
1271C22#348812yes—
1272C22#351312yes—
1273C22#351312yes—
1274C22#351912yes—
1275C22#351912yes—
1276C22#353212yes—
1277C22#353212yes—
1278C22#353412yes—
1279C22#354311yescharacteristic
1280C22#354511yescharacteristic
1281C4—28no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—44no—
1286C4—44no—
1287C4—44no—
1288C4—44no—
1289C4—44no—
1290C4—44no—
1291C4—82no—
1292C4—82no—
1293C4—82no—
1294C2—28no—
1295C2—44no—
1296C2—48no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2C2×#235811yescharacteristic
1301C2#3429012yes—
1302C2#3429012yes—
1303C2#3435611yescharacteristic
1304C2#3440811yescharacteristic
1305C2#4309512yes—
1306C2#4309812yes—
1307C2#4319712yes—
1308C2#4400112yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2403C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2358C2semidirect
3. C2×D4×C22⋊C4C2semidirect
4. #14521C2semidirect
5. #14520C2semidirect
6. #14519C2semidirect
7. #14410C2semidirect
8. #14358C2semidirect
9. #14187C2semidirect
10. #14145C2semidirect
11. #14134C2semidirect
12. #14016C2semidirect
13. #13991C2semidirect
14. #13988C2semidirect
15. #13967C2semidirect
16. #13967C2semidirect
17. #13867C2semidirect
18. C2×#1438C2semidirect
19. #13784C2semidirect
27. C22×C4×D4C22semidirect
29. C23×C22⋊C4C22semidirect
30. C23×C22⋊C4C22semidirect
31. C23×C22⋊C4C22semidirect
32. #2403C4semidirect
37. C2×#390C22semidirect
38. C2×#390C22semidirect
39. C2×#390C22semidirect
40. C2×#388C22semidirect
41. C2×#388C22semidirect
42. C2×#388C22semidirect
43. C2×#388C22semidirect
50. C2×#386C22semidirect
51. C2×#386C22semidirect
52. C2×#386C22semidirect
53. C2×#386C22semidirect
54. C2×#386C22semidirect
55. C2×#386C22semidirect
56. C2×#386C22semidirect
57. C2×#385C22semidirect
58. C2×#385C22semidirect
59. C2×#380C22semidirect
62. C2×#379C22semidirect
63. C2×#379C22semidirect
64. C2×C4×C22⋊C4C22semidirect
65. C2×C4×C22⋊C4C22semidirect
66. C2×C4×C22⋊C4C22semidirect
67. C22×#95C22semidirect
68. C22×#95C22semidirect
69. #1442C22semidirect
70. #1442C22semidirect
71. #1440C22semidirect
72. #1440C22semidirect
73. #1439C22semidirect
74. #1439C22semidirect
75. #1439C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
84. #1438C22semidirect
85. #1438C22semidirect
86. #1438C22semidirect
87. #1438C22semidirect
88. #1438C22semidirect
89. #1438C22semidirect
90. #1438C22semidirect
91. #1437C22semidirect
92. #1437C22semidirect
93. #1437C22semidirect
94. #1437C22semidirect
95. #1437C22semidirect
96. #1437C22semidirect
97. #1436C22semidirect
98. #1436C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. #1434C22semidirect
102. #1434C22semidirect
103. C22⋊#95C22semidirect
104. C22⋊#95C22semidirect
105. C22⋊#95C22semidirect
106. C22⋊#95C22semidirect
107. C22⋊#95C22semidirect
108. C22⋊#95C22semidirect
109. C22⋊#95C22semidirect
121. C23×D4C2×C4semidirect
122. C23×D4C2×C4semidirect
142. C2×#120C2×C4semidirect
143. C2×#120C2×C4semidirect
144. C2×#120C2×C4semidirect
206. #392C2×C4semidirect
207. #392C2×C4semidirect
224. #386C2×C4semidirect
225. #386C2×C4semidirect
226. #386C2×C4semidirect
227. #386D4semidirect
234. #379C2×C4semidirect
530. C2×C22⋊C4C2×D4semidirect
531. C2×C22⋊C4C2×D4semidirect
570. #95C2×D4semidirect
571. #95C2×D4semidirect
745. C2×D4C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24032
C2×#23582
C2×D4×C22⋊C42
#145212
#145202
#145192
#144102
#143582
#141872
#141452
#141342
#140162
#139912
#139882
#139672
#138672
C2×#14382
#137842