Finite Group Databasebeta

← #686325

Subgroups — #686325

Order 512.

3680 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2406C211yesmaximal, characteristic
2C22×#398C211yesmaximal, characteristic, complemented
3C2×#2339C211yesmaximal, characteristic
4C2×#2322C211yesmaximal, characteristic, complemented
5#16279C212yesmaximal, complemented
6#16271C212yesmaximal, complemented
7#15698C212yesmaximal, complemented
8#15387C212yesmaximal, complemented
9#15294C212yesmaximal, complemented
10#15286C212yesmaximal, complemented
11#15073C211yesmaximal, characteristic, complemented
12#14927C211yesmaximal, characteristic, complemented
13#14919C211yesmaximal, characteristic, complemented
14#14777C211yesmaximal, characteristic, complemented
15#14744C212yesmaximal, complemented
16#14736C212yesmaximal, complemented
17#14256C211yesmaximal, characteristic, complemented
18#14019C211yesmaximal, characteristic, complemented
19#14015C211yesmaximal, characteristic, complemented
20#13968C211yesmaximal, characteristic, complemented
21#13956C211yesmaximal, characteristic
22#13874C211yesmaximal, characteristic, complemented
23#13872C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33#2406—28no—
34C2×#399C2212yes—
35C2×#398—28no—
36C2×#398C2212yes—
37C2×#398C2212yes—
38C2×#398C2212yes—
39C2×#398C2212yes—
40C2×#395C2212yes—
41C2×#394C2212yes—
42#2339—28no—
43#2322—28no—
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#389C2212yes—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#387C2212yes—
50C2×#386C2211yescharacteristic
51C2×#386C2211yescharacteristic
52C2×#386C2211yescharacteristic
53C2×#386C2211yescharacteristic
54C2×#386C2211yescharacteristic
55C2×#386C2211yescharacteristic
56C2×#386C2211yescharacteristic
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2211yescharacteristic
60C2×#385C2211yescharacteristic
61C2×#385C2212yes—
62C2×#385C2212yes—
63C2×#385C2212yes—
64C2×#385C2212yes—
65C2×#385C2211yescharacteristic
66C2×#381C2211yescharacteristic
67C2×#381C2211yescharacteristic
68C2×#381C2211yescharacteristic
69C2×#381C2211yescharacteristic
70C2×#381C2211yescharacteristic
71C2×#381C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#380C2212yes—
74C2×#380C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C22×#95C2211yescharacteristic
78C22×#95C2211yescharacteristic
79C22×#95C2211yescharacteristic
80C22×#95C2211yescharacteristic
81#1446C2212yes—
82#1445C2212yes—
83#1445C2212yes—
84#1444C2212yes—
85#1444C2212yes—
86#1443C2212yes—
87#1443C2212yes—
88#1443C2212yes—
89#1442C2212yes—
90#1442C2212yes—
91#1442C2212yes—
92#1442C2212yes—
93#1442C2212yes—
94#1442C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2212yes—
98#1441C2212yes—
99#1441C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1440C2212yes—
103#1440C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yes—
109#1439C2212yes—
110#1439C2212yes—
111#1438C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115#1436C2212yes—
116C4⋊#95C2212yes—
117#1434C2212yes—
118C22⋊#95C2212yes—
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C22×#41—24no—
128C22×#41—24no—
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—42no—
133C22×#41—42no—
134C23×Q8C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C2×#123—24no—
150C2×#123—24no—
151C2×#123—24no—
152C2×#123—24no—
153C2×#123—42no—
154C2×#123D418yes—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—24no—
159C2×C4×D4—42no—
160C2×C4×D4—42no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—24no—
163C22×C4⋊C4—24no—
164C22×C4⋊C4—24no—
165C22×C4⋊C4—24no—
166C22×C4⋊C4—24no—
167C22×C4⋊C4—44no—
168C22×C4⋊C4—44no—
169C22×C4⋊C4—42no—
170C22×C4⋊C4—42no—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2312yes—
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2312yes—
209#399—44no—
210#398—28no—
211#398—28no—
212#398—28no—
213#398—28no—
214#395—28no—
215#394—28no—
216#391—24no—
217#391—24no—
218#389—28no—
219#388—28no—
220#388—44no—
221#387—28no—
222#386—24no—
223#386—24no—
224#386—24no—
225#386—24no—
226#386—24no—
227#386—24no—
228#386—24no—
229#386—24no—
230#386—24no—
231#386—42no—
232#385—28no—
233#385—28no—
234#385—24no—
235#385—28no—
236#385—42no—
237#385—44no—
238#381—24no—
239#381—24no—
240#381—24no—
241#381—24no—
242#381—42no—
243#381—42no—
244#380—24no—
245#380—44no—
246#380—42no—
247C4×C22⋊C4—24no—
248C4×C22⋊C4—24no—
249C2×#95—24no—
250C2×#95—24no—
251C2×#95—24no—
252C2×#95D418yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2311yescharacteristic
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C25C2411yescharacteristic
300C25C2411yescharacteristic
301C25C2411yescharacteristic
302C2×#41—232no—
303C2×#41—416no—
304C2×#41—416no—
305C2×#41—416no—
306C2×#41—416no—
307C2×#41—416no—
308C2×#41—416no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—41no—
315C22×Q8—41no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4C2×D414yes—
334C22×D4#4114yes—
335C22×D4#4114yes—
336C22×D4#4114yes—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—41no—
384C23×C4—41no—
385C23×C4—41no—
386C23×C4—41no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—41no—
390C23×C4—41no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4C2×D414yes—
397C23×C4C2×D414yes—
398C23×C4C2×D414yes—
399C23×C4C2×D414yes—
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2412yes—
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420#123—232no—
421#123—416no—
422C4×D4—416no—
423C4×D4—416no—
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—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—416no—
463C2×C4⋊C4—416no—
464C2×C4⋊C4—416no—
465C2×C4⋊C4—416no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4C2×D418yes—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4C2×D414yes—
528C2×C22⋊C4C2×D418yes—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—24no—
534C2×C42—41no—
535C2×C42—41no—
536C2×C42—42no—
537C2×C42—42no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—24no—
542#95—24no—
543#95—24no—
544#95—24no—
545#95—22no—
546#95—24no—
547#95—24no—
548#95—24no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—24no—
554#95—24no—
555#95—24no—
556#95—24no—
557#95—24no—
558#95—24no—
559#95—24no—
560#95—24no—
561#95—24no—
562#95—24no—
563#95—24no—
564#95—24no—
565#95—42no—
566#95—42no—
567#95—42no—
568#95—42no—
569#95—42no—
570#95—42no—
571#95—42no—
572#95—42no—
573#95—42no—
574#95—42no—
575#95—42no—
576#95—42no—
577#95—42no—
578#95—42no—
579#95—42no—
580#95C2×D414yes—
581#95C2×D414yes—
582#95C2×D414yes—
583#95C2×D414yes—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—21no—
589C24—21no—
590C24—22no—
591C24—21no—
592C24—21no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—22no—
601C24—21no—
602C24—21no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24C22×D412yes—
607C24C22×D412yes—
608C24C22×D412yes—
609C24C2×#4112yes—
610C24C2×#4112yes—
611C24C2×#4112yes—
612C24C2×#4112yes—
613C24C2×#4112yes—
614C24C2×#4112yes—
615C24H(5,𝔽2)12yes—
616C24H(5,𝔽2)12yes—
617C24C2511yescharacteristic
618#41—4128no—
619C2×Q8—28no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8—44no—
625C2×Q8—44no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—28no—
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—28no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4#123116yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—22no—
654C22×C4—28no—
655C22×C4—28no—
656C22×C4—28no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—28no—
664C22×C4—28no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—21no—
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—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—48no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—48no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—48no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—82no—
811C22×C4—84no—
812C22×C4—82no—
813C22×C4—84no—
814C22×C4—84no—
815C22×C4—84no—
816C22×C4—84no—
817C22×C4—84no—
818C22×C4—84no—
819C22×C4C22×D414yes—
820C22×C4C22×D412yes—
821C22×C4C22×D412yes—
822C22×C4C22×D412yes—
823C22×C4C22×D414yes—
824C22×C4C22×D412yes—
825C22×C4C22×D412yes—
826C22×C4C22×D412yes—
827C22×C4C22×D412yes—
828C22×C4C2×#4112yes—
829C22×C4C2×#4112yes—
830C22×C4C2×#4112yes—
831C22×C4H(5,𝔽2)14yes—
832C22×C42−1+414yes—
833C22×C42−1+414yes—
834C4⋊C4—216no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C4⋊C4—84no—
847C4⋊C4—84no—
848C4⋊C4—84no—
849C22⋊C4—28no—
850C22⋊C4—216no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—48no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—82no—
866C22⋊C4—82no—
867C22⋊C4—84no—
868C22⋊C4—84no—
869C42—44no—
870C42—44no—
871C42—84no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—24no—
877C23—24no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23—24no—
884C23—24no—
885C23—24no—
886C23—24no—
887C23—24no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—24no—
895C23—24no—
896C23—24no—
897C23—24no—
898C23—24no—
899C23—24no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—24no—
904C23—24no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—42no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—42no—
930C23—42no—
931C23—42no—
932C23—42no—
933C23C2×#12314yes—
934C23C2×#12314yes—
935C23#52514yes—
936C23#53814yes—
937C23D4214yes—
938C23#54614yes—
939C23#54614yes—
940C23#55114yes—
941C23C23×D411yescharacteristic
942C23C23×D411yescharacteristic
943C23C22×#4111yescharacteristic
944C23C22×#4111yescharacteristic
945C23C22×#4111yescharacteristic
946C23C2×H(5,𝔽2)11yescharacteristic
947C23C2×H(5,𝔽2)11yescharacteristic
948C23C2×H(5,𝔽2)12yes—
949C23C2×2−1+412yes—
950C23C2×2−1+412yes—
951C23#58512yes—
952Q8—416no—
953D4—232no—
954D4—416no—
955D4—416no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—416no—
997C2×C4—416no—
998C2×C4—416no—
999C2×C4—416no—
1000C2×C4—416no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—416no—
1007C2×C4—416no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—42no—
1014C2×C4—41no—
1015C2×C4—42no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—42no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—42no—
1046C2×C4—41no—
1047C2×C4—42no—
1048C2×C4—41no—
1049C2×C4—42no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—42no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—42no—
1065C2×C4—42no—
1066C2×C4—42no—
1067C2×C4—42no—
1068C2×C4—42no—
1069C2×C4—42no—
1070C2×C4—42no—
1071C2×C4—42no—
1072C2×C4—42no—
1073C2×C4—42no—
1074C2×C4—42no—
1075C2×C4—42no—
1076C2×C4—42no—
1077C2×C4—42no—
1078C2×C4—42no—
1079C2×C4—42no—
1080C2×C4—42no—
1081C2×C4—42no—
1082C2×C4—42no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—88no—
1086C2×C4—88no—
1087C2×C4—88no—
1088C2×C4—88no—
1089C2×C4C2×#12314yes—
1090C2×C4#53614yes—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—28no—
1095C22—24no—
1096C22—24no—
1097C22—28no—
1098C22—28no—
1099C22—24no—
1100C22—28no—
1101C22—24no—
1102C22—28no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—44no—
1107C22—42no—
1108C22—42no—
1109C22—44no—
1110C22—42no—
1111C22—44no—
1112C22—42no—
1113C22—42no—
1114C22—44no—
1115C22—42no—
1116C22—44no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—82no—
1121C22—82no—
1122C22—81no—
1123C22#241818yes—
1124C22C22×#12311yescharacteristic
1125C22C2×#52511yescharacteristic
1126C22C2×#53611yescharacteristic
1127C22#344911yescharacteristic
1128C22C2×#53811yescharacteristic
1129C22C2×D4211yescharacteristic
1130C22C2×#54611yescharacteristic
1131C22C2×#54611yescharacteristic
1132C22C2×#55111yescharacteristic
1133C22#348411yescharacteristic
1134C22#348611yescharacteristic
1135C22#348812yes—
1136C22#349912yes—
1137C22#351512yes—
1138C22#351512yes—
1139C22#351512yes—
1140C22#352012yes—
1141C22#352012yes—
1142C22#352012yes—
1143C22#353412yes—
1144C22#353612yes—
1145C22#354412yes—
1146C22#355912yes—
1147C4—24no—
1148C4—24no—
1149C4—44no—
1150C4—42no—
1151C4—42no—
1152C4—44no—
1153C4—44no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—44no—
1159C4—81no—
1160C4—82no—
1161C4—81no—
1162C4—81no—
1163C4—82no—
1164C4—81no—
1165C4—82no—
1166C4—82no—
1167C2—28no—
1168C2—44no—
1169C2—82no—
1170C2C2×#241811yescharacteristic
1171C2#3513811yescharacteristic
1172C2#3535711yescharacteristic
1173C2#3599812yes—
1174C2#3765211yescharacteristic
1175C2#3802111yescharacteristic
1176C2#3802911yescharacteristic
1177C2#3933711yescharacteristic
1178C2#4084512yes—
1179C2#4334212yes—
1180C2#4397412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#398C2semidirect
4. C2×#2322C2semidirect
5. #16279C2semidirect
6. #16271C2semidirect
7. #15698C2semidirect
8. #15387C2semidirect
9. #15294C2semidirect
10. #15286C2semidirect
11. #15073C2semidirect
12. #14927C2semidirect
13. #14919C2semidirect
14. #14777C2semidirect
15. #14744C2semidirect
16. #14736C2semidirect
17. #14256C2semidirect
18. #14019C2semidirect
19. #14015C2semidirect
20. #13968C2semidirect
22. #13874C2semidirect
23. #13872C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24062
C22×#3982
C2×#23392
C2×#23222
#162792
#162712
#156982
#153872
#152942
#152862
#150732
#149272
#149192
#147772
#147442
#147362
#142562
#140192
#140152
#139682
#139562
#138742
#138722