Finite Group Databasebeta

← #535007

Subgroups — #535007

Order 512.

3294 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2677C211yesmaximal, characteristic
2C2×#2365C212yesmaximal, complemented
3C2×C4×C22⋊Q8C212yesmaximal
4#14402C211yesmaximal, characteristic
5#14362C212yesmaximal
6#14230C211yesmaximal, characteristic
7#14219C212yesmaximal, complemented
8#14215C211yesmaximal, characteristic
9#14213C211yesmaximal, characteristic
10#14211C212yesmaximal, complemented
11#14203C212yesmaximal, complemented
12#14186C212yesmaximal, complemented
13#14172C211yesmaximal, characteristic
14#14112C212yesmaximal
15#14111C212yesmaximal, complemented
16#14053C212yesmaximal, complemented
17#13825C212yesmaximal, complemented
18#13823C212yesmaximal
19C4×#385C211yesmaximal, characteristic
20C22×C4⋊Q8C2212yes—
21C22×C22⋊Q8C2212yes—
22C22×C4×Q8C2211yescharacteristic
23C22×C4×Q8C2212yes—
24C23×C42C2211yescharacteristic
25#2677C4116yescomplemented
26C2×#399C2211yescharacteristic
27C2×#398C2212yes—
28C2×#395C2212yes—
29C2×#393C2211yescharacteristic
30#2365—216no—
31C4×C22⋊Q8—216no—
32C2×#391C2212yes—
33C2×#391C2212yes—
34C2×#391C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2211yescharacteristic
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#387C2212yes—
43C2×#387C2212yes—
44C2×#387C2212yes—
45C2×#387C2212yes—
46C2×#387C2212yes—
47C2×#387C2212yes—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#385C2211yescharacteristic
51C2×#385C2211yescharacteristic
52C2×#380C2212yes—
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2212yes—
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2211yescharacteristic
64#1446C2212yes—
65#1446C2211yescharacteristic
66#1445C2211yescharacteristic
67#1444C2211yescharacteristic
68#1444C2212yes—
69#1444C2212yes—
70#1444C2211yescharacteristic
71#1441C2212yes—
72#1441C2212yes—
73#1441C2212yes—
74#1441C2212yes—
75#1441C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2211yescharacteristic
79#1439C2211yescharacteristic
80#1437C2212yes—
81#1437C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99C4⋊#95C2212yes—
100C4⋊#95C2212yes—
101C4⋊#95C2212yes—
102#1434C2211yescharacteristic
103#1434C2212yes—
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2211yescharacteristic
106C4×#95C2211yescharacteristic
107C4×#95C2212yes—
108C4×#95C2212yes—
109C4×#95C2212yes—
110C23×Q8C2311yescharacteristic
111C23×Q8C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C2×C4⋊Q8—28no—
116C2×C4⋊Q8—28no—
117C2×C4⋊Q8C2×C4116yescomplemented
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—28no—
120C2×C22⋊Q8C2×C4116yes—
121C2×C4×Q8—28no—
122C2×C4×Q8—28no—
123C2×C4×Q8—28no—
124C2×C4×Q8—44no—
125C2×C4×Q8—42no—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C42—28no—
154C22×C42—42no—
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2311yescharacteristic
168#399C2×C418yes—
169#398C2×C4116yescomplemented
170#395C2×C4116yescomplemented
171#393C2×C418yes—
172#391—28no—
173#391—28no—
174#391—28no—
175#389—28no—
176#389—28no—
177#389—28no—
178#389—28no—
179#389—42no—
180#388—28no—
181#388C2×C4116yes—
182#387—28no—
183#387—28no—
184#387—28no—
185#387—28no—
186#387C2×C4116yescomplemented
187#387D4116yes—
188#385—28no—
189#385—28no—
190#385C2×C418yes—
191#385Q818yescomplemented
192#380—28no—
193C4×C4⋊C4—28no—
194C4×C4⋊C4—28no—
195C4×C4⋊C4—28no—
196C4×C4⋊C4—28no—
197C4×C4⋊C4—28no—
198C4×C4⋊C4—28no—
199C4×C4⋊C4—28no—
200C4×C22⋊C4—24no—
201C4×C22⋊C4—28no—
202C4×C22⋊C4—28no—
203C4×C22⋊C4—42no—
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×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2311yescharacteristic
225C2×#95C2312yes—
226C2×#95C2311yescharacteristic
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2311yescharacteristic
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2311yescharacteristic
235C2×#95C2312yes—
236C2×#95C2311yescharacteristic
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2311yescharacteristic
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C25C2411yescharacteristic
247C22×Q8—24no—
248C22×Q8—24no—
249C22×Q8—24no—
250C22×Q8—24no—
251C22×Q8—24no—
252C22×Q8—24no—
253C22×Q8—42no—
254C22×Q8—41no—
255C22×Q8—42no—
256C22×Q8—41no—
257C22×Q8C22×C418yes—
258C22×Q8C22×C414yes—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—41no—
268C23×C4—42no—
269C23×C4—41no—
270C23×C4—41no—
271C23×C4—41no—
272C23×C4C22×C414yes—
273C23×C4C2×Q814yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C4⋊Q8—264no—
293C22⋊Q8—264no—
294C4×Q8—432no—
295C4×Q8—416no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—41no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—41no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4C22×C418yes—
341C2×C4⋊C4C22×C418yes—
342C2×C4⋊C4C22×C418yes—
343C2×C4⋊C4C22×C418yes—
344C2×C4⋊C4C22×C418yes—
345C2×C4⋊C4C22×C414yes—
346C2×C4⋊C4C22×C418yes—
347C2×C4⋊C4C2×D418yes—
348C2×C4⋊C4C2×D418yes—
349C2×C4⋊C4C2×Q818yes—
350C2×C4⋊C4#4118yes—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4C22×C418yes—
369C2×C22⋊C4C22×C418yes—
370C2×C22⋊C4C22×C414yes—
371C2×C22⋊C4C22×C414yes—
372C2×C22⋊C4C2×Q814yes—
373C2×C22⋊C4C2×Q814yes—
374C2×C22⋊C4#4114yes—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—416no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42C22×C418yes—
412C2×C42C2×D418yes—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—41no—
439#95—41no—
440#95—42no—
441#95—41no—
442#95—41no—
443#95—42no—
444#95C22×C418yes—
445#95C22×C414yes—
446#95C22×C418yes—
447#95C22×C418yes—
448#95C22×C418yes—
449#95C22×C414yes—
450#95C2×D418yes—
451#95C2×D418yes—
452#95C2×D418yes—
453#95C2×D418yes—
454#95C2×Q818yes—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—22no—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—21no—
463C24C23×C412yes—
464C24C22×Q812yes—
465C24C2×#4112yes—
466C24C2511yescharacteristic
467C2×Q8—216no—
468C2×Q8—216no—
469C2×Q8—216no—
470C2×Q8—48no—
471C2×Q8—44no—
472C2×Q8—48no—
473C2×Q8—44no—
474C2×Q8—48no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—44no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—28no—
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—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—216no—
548C22×C4—216no—
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—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—44no—
579C22×C4—48no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4C23×C412yes—
583C22×C4C23×C414yes—
584C22×C4C23×C414yes—
585C22×C4C23×C412yes—
586C22×C4C23×C414yes—
587C22×C4C23×C414yes—
588C22×C4C23×C414yes—
589C22×C4C23×C414yes—
590C22×C4C22×D414yes—
591C22×C4C22×D414yes—
592C22×C4C22×D414yes—
593C22×C4C22×D414yes—
594C22×C4C22×D414yes—
595C22×C4C22×D414yes—
596C22×C4C22×D414yes—
597C22×C4C22×Q812yes—
598C22×C4C22×Q812yes—
599C22×C4C22×Q814yes—
600C22×C4C22×Q814yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4114yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4114yes—
605C22×C4H(5,𝔽2)12yes—
606C22×C42−1+412yes—
607C22×C42−1+414yes—
608C4⋊C4—216no—
609C4⋊C4—216no—
610C4⋊C4—216no—
611C4⋊C4—216no—
612C4⋊C4—216no—
613C4⋊C4—216no—
614C4⋊C4—216no—
615C4⋊C4—44no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—44no—
623C4⋊C4—48no—
624C4⋊C4—84no—
625C4⋊C4—82no—
626C4⋊C4C4×D4132yes—
627C22⋊C4—216no—
628C22⋊C4—216no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—44no—
634C22⋊C4C4×Q8116yescomplemented
635C42—216no—
636C42—216no—
637C42—48no—
638C42—48no—
639C42—48no—
640C42—48no—
641C42—48no—
642C42—48no—
643C42—48no—
644C42—48no—
645C42—44no—
646C42—84no—
647C42—82no—
648C23—24no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—42no—
670C23C2×C4×Q814yes—
671C23C24×C411yescharacteristic
672C23C23×D412yes—
673C23C23×Q811yescharacteristic
674C23C22×#4112yes—
675C23C22×#4111yescharacteristic
676C23C2×H(5,𝔽2)11yescharacteristic
677C23C2×2−1+412yes—
678C23C2×2−1+411yescharacteristic
679C23#58511yescharacteristic
680C23#58512yes—
681C23#58511yescharacteristic
682Q8—432no—
683Q8—416no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—416no—
741C2×C4—416no—
742C2×C4—416no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
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—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4C2×C4×D418yes—
796C2×C4C2×C4×D418yes—
797C2×C4C2×C4×D418yes—
798C2×C4C2×C4×Q818yes—
799C2×C4D4214yes—
800C2×C4D4×Q818yes—
801C22—28no—
802C22—24no—
803C22—44no—
804C22—42no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22C22×C4×D412yes—
813C22C22×C4×Q811yescharacteristic
814C22C4×H(5,𝔽2)11yescharacteristic
815C22C4×2−1+412yes—
816C22C4×2−1+411yescharacteristic
817C22C2×D4211yescharacteristic
818C22C2×D4×Q812yes—
819C22D4×#4112yes—
820C22D4×#4112yes—
821C22Q8×#4112yes—
822C22#348111yescharacteristic
823C22#348212yes—
824C22#348912yes—
825C22#348912yes—
826C22#349211yescharacteristic
827C22#349311yescharacteristic
828C22#350111yescharacteristic
829C22#350211yescharacteristic
830C22#350912yes—
831C22#351012yes—
832C22#353311yescharacteristic
833C22#353811yescharacteristic
834C22#356512yes—
835C4—28no—
836C4—28no—
837C4—28no—
838C4—24no—
839C4—28no—
840C4—28no—
841C4—42no—
842C4—44no—
843C4—44no—
844C4—42no—
845C4—44no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—44no—
850C4—82no—
851C4—82no—
852C4—82no—
853C2—44no—
854C2C4×D4211yescharacteristic
855C2C4×D4×Q812yes—
856C2#3426812yes—
857C2#3427111yescharacteristic
858C2#3451411yescharacteristic
859C2#5899311yescharacteristic
860C2#5899811yescharacteristic
861C2#5915212yes—
862C2#5917112yes—
863C2#5993811yescharacteristic
864C2#6003011yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC25C24
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×#2365C2semidirect
7. #14219C2semidirect
10. #14211C2semidirect
11. #14203C2semidirect
12. #14186C2semidirect
15. #14111C2semidirect
16. #14053C2semidirect
17. #13825C2semidirect
25. #2677C4semidirect
117. C2×C4⋊Q8C2×C4semidirect
169. #398C2×C4semidirect
170. #395C2×C4semidirect
186. #387C2×C4semidirect
191. #385Q8semidirect
634. C22⋊C4C4×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#26772
C2×#23652
C2×C4×C22⋊Q82
#144022
#143622
#142302
#142192
#142152
#142132
#142112
#142032
#141862
#141722
#141122
#141112
#140532
#138252
#138232
C4×#3852