Finite Group Databasebeta

← #616998

Subgroups — #616998

Order 512.

5524 conjugacy classes of subgroups.

The subgroup lattice has 1151 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#537C211yesmaximal, characteristic
2C2×#2857C211yesmaximal, characteristic, complemented
3C2×#2432C211yesmaximal, characteristic, complemented
4C2×#2620C211yesmaximal, characteristic, complemented
5C2×#2616C211yesmaximal, characteristic, complemented
6C2×#2297C211yesmaximal, characteristic, complemented
7#15316C214yesmaximal, complemented
8#15276C214yesmaximal, complemented
9#15274C214yesmaximal, complemented
10#15274C214yesmaximal, complemented
11#15215C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic, complemented
13#15178C211yesmaximal, characteristic, complemented
14#15130C211yesmaximal, characteristic, complemented
15#14698C211yesmaximal, characteristic, complemented
16#14258C211yesmaximal, characteristic, complemented
17#14139C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19#13880C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C23×#41C2211yescharacteristic
22C2×#537—28no—
23C2×#537—28no—
24C2×#537—28no—
25C22×C4⋊Q8C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2212yes—
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C22×#121C2212yes—
35C22×#121C2212yes—
36C22×#121C2212yes—
37C22×#121C2211yescharacteristic
38C22×#117C2211yescharacteristic
39C23×C4⋊C4C2211yescharacteristic
40C23×C42C2211yescharacteristic
41#2857—28no—
42#2620—28no—
43#2616—28no—
44#2432—28no—
45C2×#396C2214yes—
46C2×#395C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2212yes—
50C2×#394C2214yes—
51C2×#394C2214yes—
52C2×#394C2214yes—
53#2297—28no—
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#391C2212yes—
59C2×#391C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#390C2212yes—
63C2×#390C2211yescharacteristic
64C2×#389C2214yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2214yes—
68C2×#385C2214yes—
69C2×#385C2214yes—
70C2×#384C2211yescharacteristic
71C2×#384C2211yescharacteristic
72C2×#380C2214yes—
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80#1444C2214yes—
81#1444C2214yes—
82#1441C2214yes—
83#1441C2214yes—
84#1441C2214yes—
85#1440C2214yes—
86#1439C2214yes—
87#1439C2214yes—
88#1439C2214yes—
89#1439C2214yes—
90#1438C2214yes—
91#1438C2214yes—
92#1437C2214yes—
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96C4⋊#95C2211yescharacteristic
97C22⋊#95C2214yes—
98C22⋊#95C2214yes—
99C22×#41—24no—
100C22×#41—24no—
101C22×#41—24no—
102C22×#41—24no—
103C22×#41—24no—
104C22×#41—24no—
105C22×#41—24no—
106C22×#41—24no—
107C22×#41—24no—
108C22×#41—42no—
109C22×#41—42no—
110C22×#41—42no—
111C22×#41—42no—
112C22×#41D418yes—
113C23×Q8C2311yescharacteristic
114C23×Q8C2311yescharacteristic
115C23×Q8C2311yescharacteristic
116C23×D4C2311yescharacteristic
117C23×D4C2312yes—
118C23×D4C2311yescharacteristic
119C23×D4C2311yescharacteristic
120C23×D4C2311yescharacteristic
121C23×D4C2312yes—
122C23×D4C2312yes—
123C24×C4C2311yescharacteristic
124C24×C4C2312yes—
125C24×C4C2312yes—
126C24×C4C2311yescharacteristic
127C24×C4C2311yescharacteristic
128C24×C4C2312yes—
129#537—2128no—
130C2×C4⋊Q8—24no—
131C2×C4⋊Q8—24no—
132C2×C4⋊Q8—42no—
133C2×#124—24no—
134C2×#124—24no—
135C2×#124—42no—
136C2×C22⋊Q8—24no—
137C2×C22⋊Q8—28no—
138C2×C22⋊Q8—24no—
139C2×C22⋊Q8—24no—
140C2×C22⋊Q8—24no—
141C2×C22⋊Q8—24no—
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8—24no—
144C2×C22⋊Q8—24no—
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—28no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—28no—
151C2×C22⋊Q8—42no—
152C2×C22⋊Q8—42no—
153C2×C22⋊Q8D418yes—
154C2×#121—24no—
155C2×#121—28no—
156C2×#121—28no—
157C2×#121—28no—
158C2×#121—28no—
159C2×#121—28no—
160C2×#121—24no—
161C2×#121—24no—
162C2×#121—24no—
163C2×#121—24no—
164C2×#121—28no—
165C2×#121—28no—
166C2×#121—28no—
167C2×#121—28no—
168C2×#121D418yes—
169C2×#117—24no—
170C2×#117—24no—
171C2×#117—42no—
172C22×C4⋊C4—24no—
173C22×C4⋊C4—24no—
174C22×C4⋊C4—24no—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2314yes—
183C22×C4⋊C4C2314yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2314yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2314yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2314yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2314yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2314yes—
209C22×C42—24no—
210C22×C42—24no—
211C22×C42—42no—
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217#396—216no—
218#395—28no—
219#394—28no—
220#394—28no—
221#394—28no—
222#394—216no—
223#394—216no—
224#394—48no—
225#391—24no—
226#391—24no—
227#391—24no—
228#391—24no—
229#391—28no—
230#391—42no—
231#390—24no—
232#390—28no—
233#390—24no—
234#390—42no—
235#389—216no—
236#386—28no—
237#386—28no—
238#386—48no—
239#385—216no—
240#385—48no—
241#384—24no—
242#384—24no—
243#380—24no—
244#380—24no—
245#380—24no—
246#380—216no—
247C4×C22⋊C4—24no—
248C4×C22⋊C4—24no—
249C4×C22⋊C4—24no—
250C4×C22⋊C4D418yescomplemented
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2314yes—
255C2×#95C2314yes—
256C2×#95C2312yes—
257C2×#95C2314yes—
258C2×#95C2314yes—
259C2×#95C2314yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2314yes—
263C2×#95C2314yes—
264C2×#95C2314yes—
265C2×#95C2314yes—
266C2×#95C2312yes—
267C25C2411yescharacteristic
268C25C2412yes—
269C25C2411yescharacteristic
270C25C2411yescharacteristic
271C2×#41—232no—
272C2×#41—232no—
273C2×#41—232no—
274C2×#41—416no—
275C2×#41—416no—
276C2×#41—416no—
277C2×#41—416no—
278C2×#41—416no—
279C2×#41—416no—
280C2×#41—416no—
281C2×#41—416no—
282C2×#41—416no—
283C2×#41—416no—
284C2×#41—416no—
285C22×Q8—22no—
286C22×Q8—22no—
287C22×Q8—22no—
288C22×Q8—22no—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8—22no—
297C22×Q8—22no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—41no—
303C22×Q8—41no—
304C22×Q8C2×D414yes—
305C22×Q8C2×D414yes—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—24no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4—41no—
337C22×D4—41no—
338C22×D4—42no—
339C22×D4—41no—
340C22×D4—41no—
341C22×D4—42no—
342C22×D4—44no—
343C22×D4—44no—
344C22×D4—44no—
345C22×D4—44no—
346C22×D4C2×D414yes—
347C22×D4C2×D414yes—
348C22×D4C2×D414yes—
349C22×D4C2×D414yes—
350C22×D4C2×D418yes—
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—24no—
360C23×C4—24no—
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—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—44no—
383C23×C4—44no—
384C23×C4C2×D414yes—
385C23×C4C2×D414yes—
386C23×C4C2×D414yes—
387C23×C4C2×D414yes—
388C23×C4C2×D414yes—
389C23×C4C2×D414yes—
390C23×C4#4114yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C4⋊Q8—416no—
407#124—416no—
408C22⋊Q8—232no—
409C22⋊Q8—264no—
410C22⋊Q8—232no—
411C22⋊Q8—416no—
412C22⋊Q8—416no—
413C22⋊Q8—416no—
414#121—232no—
415#121—264no—
416#121—264no—
417#121—264no—
418#121—232no—
419#117—416no—
420C2×C4⋊C4—232no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
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—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
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—28no—
448C2×C4⋊C4—28no—
449C2×C4⋊C4—28no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—28no—
455C2×C4⋊C4—28no—
456C2×C4⋊C4—44no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—44no—
461C2×C4⋊C4—44no—
462C2×C4⋊C4—44no—
463C2×C4⋊C4C2×D414yes—
464C2×C4⋊C4C2×D414yes—
465C2×C4⋊C4C2×D418yes—
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—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—28no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—28no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—28no—
493C2×C22⋊C4—28no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—28no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—28no—
503C2×C22⋊C4—28no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4—44no—
511C2×C22⋊C4—44no—
512C2×C22⋊C4—44no—
513C2×C22⋊C4—44no—
514C2×C22⋊C4—44no—
515C2×C22⋊C4—44no—
516C2×C22⋊C4—44no—
517C2×C22⋊C4C2×D418yes—
518C2×C22⋊C4C2×D418yes—
519C2×C22⋊C4C2×D418yes—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—24no—
528C2×C42—24no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—416no—
533C2×C42—42no—
534C2×C42C2×D414yes—
535C2×C42C2×D414yes—
536#95—24no—
537#95—24no—
538#95—24no—
539#95—28no—
540#95—28no—
541#95—24no—
542#95—24no—
543#95—24no—
544#95—28no—
545#95—28no—
546#95—28no—
547#95—44no—
548#95—44no—
549#95—44no—
550#95—44no—
551#95C2×D418yes—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—22no—
557C24—21no—
558C24—22no—
559C24—21no—
560C24—21no—
561C24—21no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—21no—
569C24—22no—
570C24—22no—
571C24—21no—
572C24—22no—
573C24—21no—
574C24—21no—
575C24—22no—
576C24—24no—
577C24—22no—
578C24—21no—
579C24—21no—
580C24—22no—
581C24—22no—
582C24—24no—
583C24—22no—
584C24—22no—
585C24—24no—
586C24—24no—
587C24—22no—
588C24C22×D412yes—
589C24C22×D414yes—
590C24C22×D412yes—
591C24C22×D412yes—
592C24C22×D412yes—
593C24C22×D412yes—
594C24C22×D412yes—
595C24C2×#4112yes—
596C24C2511yescharacteristic
597#41—4128no—
598#41—4128no—
599C2×Q8—28no—
600C2×Q8—28no—
601C2×Q8—28no—
602C2×Q8—28no—
603C2×Q8—28no—
604C2×Q8—44no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—44no—
616C2×Q8—44no—
617C2×Q8—44no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×D4—216no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—28no—
624C2×D4—28no—
625C2×D4—216no—
626C2×D4—216no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—416no—
646C2×D4—44no—
647C2×D4—44no—
648C2×D4—48no—
649C2×D4—44no—
650C2×D4—44no—
651C2×D4—48no—
652C2×D4—48no—
653C2×D4—48no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—88no—
659C2×D4—88no—
660C2×D4—88no—
661C2×D4—84no—
662C2×D4—84no—
663C2×D4—84no—
664C2×D4—84no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—28no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—216no—
690C22×C4—216no—
691C22×C4—22no—
692C22×C4—21no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—21no—
705C22×C4—22no—
706C22×C4—24no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—24no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—216no—
724C22×C4—28no—
725C22×C4—28no—
726C22×C4—28no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—24no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—24no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—24no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—24no—
754C22×C4—22no—
755C22×C4—24no—
756C22×C4—48no—
757C22×C4—48no—
758C22×C4—48no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4—48no—
765C22×C4—48no—
766C22×C4—48no—
767C22×C4—48no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—88no—
773C22×C4—88no—
774C22×C4—84no—
775C22×C4—84no—
776C22×C4#120116yes—
777C22×C4#121116yes—
778C22×C4C22×D414yes—
779C22×C4C22×D412yes—
780C22×C4C22×D414yes—
781C22×C4C22×D414yes—
782C22×C4C22×D414yes—
783C22×C4C22×D412yes—
784C22×C4C22×D412yes—
785C22×C4C22×D412yes—
786C22×C4C22×D412yes—
787C22×C4C22×D412yes—
788C22×C4C22×D414yes—
789C22×C4C22×D412yes—
790C22×C4C22×D412yes—
791C22×C4C22×D412yes—
792C22×C4C22×D412yes—
793C22×C4C2×#4112yes—
794C22×C4C2×#4112yes—
795C22×C4H(5,𝔽2)14yes—
796C22×C4H(5,𝔽2)12yes—
797C22×C4H(5,𝔽2)12yes—
798C22×C42−1+414yes—
799C22×C42−1+414yes—
800C4⋊C4—216no—
801C4⋊C4—216no—
802C4⋊C4—28no—
803C4⋊C4—28no—
804C4⋊C4—216no—
805C4⋊C4—416no—
806C4⋊C4—48no—
807C4⋊C4—416no—
808C4⋊C4—48no—
809C4⋊C4—44no—
810C4⋊C4—48no—
811C4⋊C4—44no—
812C4⋊C4—48no—
813C4⋊C4—44no—
814C4⋊C4—88no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—216no—
818C22⋊C4—216no—
819C22⋊C4—216no—
820C22⋊C4—48no—
821C22⋊C4—48no—
822C22⋊C4—48no—
823C22⋊C4—416no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—416no—
829C22⋊C4—88no—
830C22⋊C4—88no—
831C22⋊C4—84no—
832C22⋊C4—84no—
833C22⋊C4—84no—
834C42—28no—
835C42—28no—
836C42—48no—
837C42—44no—
838C42—44no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—24no—
844C23—24no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—22no—
858C23—22no—
859C23—24no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—24no—
867C23—22no—
868C23—24no—
869C23—22no—
870C23—22no—
871C23—24no—
872C23—24no—
873C23—28no—
874C23—22no—
875C23—28no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—44no—
898C23—42no—
899C23—44no—
900C23—42no—
901C23—42no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—42no—
906C23—41no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—44no—
913C23—42no—
914C23—42no—
915C23—42no—
916C23—42no—
917C23—42no—
918C23—42no—
919C23—44no—
920C23—42no—
921C23—44no—
922C23—42no—
923C23—44no—
924C23—42no—
925C23—42no—
926C23—44no—
927C23—44no—
928C23—42no—
929C23C2×#12014yes—
930C23C2×#12114yes—
931C23C23×D411yescharacteristic
932C23C23×D411yescharacteristic
933C23C23×D411yescharacteristic
934C23C23×D411yescharacteristic
935C23C22×#4111yescharacteristic
936C23C2×H(5,𝔽2)11yescharacteristic
937C23C2×H(5,𝔽2)11yescharacteristic
938C23C2×H(5,𝔽2)12yes—
939C23C2×2−1+412yes—
940C23C2×2−1+412yes—
941C23#58512yes—
942Q8—416no—
943Q8—416no—
944Q8—88no—
945D4—416no—
946D4—416no—
947D4—416no—
948D4—432no—
949D4—416no—
950D4—816no—
951D4—816no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—232no—
971C2×C4—232no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—28no—
987C2×C4—24no—
988C2×C4—432no—
989C2×C4—432no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—42no—
997C2×C4—41no—
998C2×C4—42no—
999C2×C4—41no—
1000C2×C4—42no—
1001C2×C4—44no—
1002C2×C4—42no—
1003C2×C4—44no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—416no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—44no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—44no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—44no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—44no—
1038C2×C4—44no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—44no—
1042C2×C4—816no—
1043C2×C4C2×#12014yes—
1044C2×C4C2×#12014yes—
1045C2×C4C2×#12114yes—
1046C2×C4C2×#12114yes—
1047C2×C4#53414yes—
1048C2×C4#53718yescomplemented
1049C2×C4D4214yes—
1050C2×C4D4214yes—
1051C2×C4#54614yes—
1052C2×C4#54614yes—
1053C22—24no—
1054C22—24no—
1055C22—24no—
1056C22—24no—
1057C22—24no—
1058C22—24no—
1059C22—44no—
1060C22—44no—
1061C22—42no—
1062C22—42no—
1063C22—44no—
1064C22—44no—
1065C22—42no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—48no—
1076C22—42no—
1077C22—44no—
1078C22—42no—
1079C22—44no—
1080C22—42no—
1081C22—48no—
1082C22—42no—
1083C22—44no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—82no—
1088C22—82no—
1089C22—82no—
1090C22—84no—
1091C22—84no—
1092C22—82no—
1093C22—82no—
1094C22—82no—
1095C22—82no—
1096C22—82no—
1097C22C22×#12011yescharacteristic
1098C22C22×#12111yescharacteristic
1099C22C2×#53411yescharacteristic
1100C22C2×#53712yes—
1101C22#346112yes—
1102C22C2×D4211yescharacteristic
1103C22C2×D4211yescharacteristic
1104C22C2×#54611yescharacteristic
1105C22C2×#54611yescharacteristic
1106C22#348612yes—
1107C22#348812yes—
1108C22#348912yes—
1109C22#349612yes—
1110C22#349811yescharacteristic
1111C22#349912yes—
1112C22#349911yescharacteristic
1113C22#349911yescharacteristic
1114C22#350011yescharacteristic
1115C22#351112yes—
1116C22#353612yes—
1117C22#354112yes—
1118C22#354712yes—
1119C22#354812yes—
1120C4—28no—
1121C4—24no—
1122C4—24no—
1123C4—44no—
1124C4—42no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—82no—
1130C4—82no—
1131C4—82no—
1132C4—82no—
1133C4—82no—
1134C4#241018yes—
1135C2—44no—
1136C2—44no—
1137C2—84no—
1138C2—82no—
1139C2C2×#241011yescharacteristic
1140C2#3527311yescharacteristic
1141C2#3530811yescharacteristic
1142C2#3551311yescharacteristic
1143C2#3566611yescharacteristic
1144C2#3729611yescharacteristic
1145C2#3738811yescharacteristic
1146C2#3764912yes—
1147C2#3778112yes—
1148C2#3934012yes—
1149C2#3943212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#537C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2857C2semidirect
3. C2×#2432C2semidirect
4. C2×#2620C2semidirect
5. C2×#2616C2semidirect
6. C2×#2297C2semidirect
7. #15316C2semidirect
8. #15276C2semidirect
9. #15274C2semidirect
10. #15274C2semidirect
11. #15215C2semidirect
12. #15182C2semidirect
13. #15178C2semidirect
14. #15130C2semidirect
15. #14698C2semidirect
16. #14258C2semidirect
17. #14139C2semidirect
18. #13937C2semidirect
19. #13880C2semidirect
250. C4×C22⋊C4D4semidirect
1048. C2×C4#537semidirect

Maximal subgroups

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

subgroupindex
C22×#5372
C2×#28572
C2×#24322
C2×#26202
C2×#26162
C2×#22972
#153162
#152762
#152742
#152152
#151822
#151782
#151302
#146982
#142582
#141392
#139372
#138802