Finite Group Databasebeta

← #515576

Subgroups — #515576

Order 512.

3116 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2322C211yesmaximal, characteristic
2C2×#2313C211yesmaximal, characteristic, complemented
3C2×#2290C211yesmaximal, characteristic
4#14158C212yesmaximal, complemented
5#14156C212yesmaximal, complemented
6#14146C212yesmaximal, complemented
7#14133C212yesmaximal, complemented
8#14078C212yesmaximal, complemented
9#14075C212yesmaximal, complemented
10#14073C212yesmaximal, complemented
11#14072C212yesmaximal, complemented
12#14004C212yesmaximal, complemented
13#13999C212yesmaximal
14#13996C212yesmaximal
15#13992C212yesmaximal, complemented
16#13784C211yesmaximal, characteristic
17C4×#385C211yesmaximal, characteristic, complemented
18C2×#1436C211yesmaximal, characteristic, complemented
19#13749C211yesmaximal, characteristic, complemented
20C22×#123C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2322C4116yescomplemented
26#2313—28no—
27C2×#389C2212yes—
28C2×#389C2212yes—
29#2290—28no—
30C2×#388C2212yes—
31C2×#388C2212yes—
32C2×#388C2212yes—
33C2×#387C2212yes—
34C2×#387C2212yes—
35C2×#387C2212yes—
36C2×#387C2212yes—
37C2×#387C2212yes—
38C2×#387C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2211yescharacteristic
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2211yescharacteristic
45C2×#385C2212yes—
46C2×#381C2212yes—
47C2×#381C2211yescharacteristic
48C2×#380C2212yes—
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2212yes—
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×#376C2211yescharacteristic
58C22×#95C2212yes—
59C22×#95C2211yescharacteristic
60C22×#95C2212yes—
61#1445C2212yes—
62#1445C2212yes—
63#1444C2212yes—
64#1443C2212yes—
65#1443C2212yes—
66#1443C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1442C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1440C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1437C2211yescharacteristic
78#1437C2212yes—
79#1437C2211yescharacteristic
80#1437C2212yes—
81#1437C2212yes—
82#1436C2211yescharacteristic
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2211yescharacteristic
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95C4⋊#95C2212yes—
96C4⋊#95C2212yes—
97C4⋊#95C2212yes—
98#1434C2212yes—
99#1434C2212yes—
100#1434C2212yes—
101#1434C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C4×#95C2212yes—
106C4×#95C2212yes—
107C4×#95C2212yes—
108C4×#95C2212yes—
109C4×#95C2212yes—
110C23×D4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2312yes—
116C24×C4C2311yescharacteristic
117C2×#123—28no—
118C2×#123C2×C418yes—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4C2×C418yes—
122C2×#117—24no—
123C2×#117—44no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4C2×C418yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C42—24no—
151C22×C42—44no—
152C22×C42C2311yescharacteristic
153C22×C42C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#389—44no—
166#389C2×C4116yescomplemented
167#388—28no—
168#388—44no—
169#388C2×C4116yescomplemented
170#387—28no—
171#387—28no—
172#387—28no—
173#387—28no—
174#387—28no—
175#387C2×C4116yescomplemented
176#386—28no—
177#386—28no—
178#386C2×C418yes—
179#385—28no—
180#385—28no—
181#385C2×C418yes—
182#385C2×C4116yescomplemented
183#381—28no—
184#381C2×C418yes—
185#380—28no—
186C4×C4⋊C4—24no—
187C4×C4⋊C4—44no—
188C4×C22⋊C4—24no—
189C4×C22⋊C4—28no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4—24no—
192C4×C22⋊C4C2×C418yes—
193C4×C22⋊C4D418yes—
194#376—24no—
195C2×#95—28no—
196C2×#95—24no—
197C2×#95—44no—
198C2×#95C2312yes—
199C2×#95C2311yescharacteristic
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
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×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C25C2411yescharacteristic
243C25C2411yescharacteristic
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4C22×C414yes—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4C22×C414yes—
277C23×C4C22×C414yes—
278C23×C4C22×C414yes—
279C23×C4C22×C414yes—
280C23×C4C2×D414yes—
281C23×C4#4118yes—
282C23×C4#4114yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300#123—232no—
301C4×D4—232no—
302#117—416no—
303C2×C4⋊C4—232no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
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—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4C22×C418yes—
333C2×C4⋊C4C22×C418yes—
334C2×C4⋊C4C22×C414yes—
335C2×C4⋊C4C22×C418yes—
336C2×C4⋊C4C22×C418yes—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4C22×C414yes—
364C2×C22⋊C4C22×C414yes—
365C2×C22⋊C4C22×C418yes—
366C2×C22⋊C4C22×C414yes—
367C2×C22⋊C4C22×C418yes—
368C2×C22⋊C4C22×C414yes—
369C2×C22⋊C4C2×D418yes—
370C2×C22⋊C4#4118yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—416no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42C22×C414yes—
402C2×C42C22×C418yes—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
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—22no—
422#95—22no—
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—24no—
434#95—24no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95C22×C418yes—
444#95C22×C418yes—
445#95C22×C418yes—
446#95C22×C418yes—
447#95C22×C418yes—
448#95C2×D418yes—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—21no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24C23×C412yes—
462C24C23×C412yes—
463C24C22×D412yes—
464C24C2×#4114yes—
465C24C2×#4112yes—
466C24C2×#4114yes—
467C24C2511yescharacteristic
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—48no—
472C2×D4—48no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—216no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
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—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—28no—
552C22×C4—216no—
553C22×C4—28no—
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—44no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—44no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4C4×D4116yes—
595C22×C4C23×C412yes—
596C22×C4C23×C414yes—
597C22×C4C23×C412yes—
598C22×C4C23×C414yes—
599C22×C4C23×C412yes—
600C22×C4C23×C414yes—
601C22×C4C23×C414yes—
602C22×C4C23×C412yes—
603C22×C4C23×C412yes—
604C22×C4C22×D414yes—
605C22×C4C22×D414yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4114yes—
610C22×C4C2×#4114yes—
611C22×C4C2×#4114yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4H(5,𝔽2)14yes—
615C22×C42−1+414yes—
616C4⋊C4—216no—
617C4⋊C4—216no—
618C4⋊C4—216no—
619C4⋊C4—28no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—28no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4#117116yescomplemented
639C42—28no—
640C42—28no—
641C42—48no—
642C42—44no—
643C42—44no—
644C42—48no—
645C42—44no—
646C42—82no—
647C42—82no—
648C42—84no—
649C42—84no—
650C42—84no—
651C42—84no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—42no—
674C23—42no—
675C23—41no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23C2×#11714yes—
690C23C2×C4×D414yes—
691C23C4×#4114yes—
692C23#52918yes—
693C23#53218yes—
694C23C24×C411yescharacteristic
695C23C23×D411yescharacteristic
696C23C22×#4112yes—
697C23C22×#4111yescharacteristic
698C23C22×#4112yes—
699C23C2×H(5,𝔽2)12yes—
700C23C2×2−1+412yes—
701C23#58512yes—
702C23#58512yes—
703D4—416no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
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—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—416no—
753C2×C4—416no—
754C2×C4—432no—
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—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
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—41no—
786C2×C4—41no—
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×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—416no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—816no—
815C2×C4—88no—
816C2×C4C2×#11718yes—
817C2×C4C2×C4×D414yes—
818C2×C4C2×C4×D414yes—
819C22—28no—
820C22—28no—
821C22—28no—
822C22—28no—
823C22—28no—
824C22—24no—
825C22—24no—
826C22—28no—
827C22—44no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22#229318yes—
837C22C22×#11711yescharacteristic
838C22C22×C4×D411yescharacteristic
839C22C2×C4×#4111yescharacteristic
840C22C4×H(5,𝔽2)12yes—
841C22C4×2−1+412yes—
842C22C2×#52912yes—
843C22C2×#53212yes—
844C22#348411yescharacteristic
845C22#348511yescharacteristic
846C22#348912yes—
847C22#349112yes—
848C22#349212yes—
849C22#350512yes—
850C22#350512yes—
851C22#350712yes—
852C22#350911yescharacteristic
853C22#351011yescharacteristic
854C22#351312yes—
855C22#351512yes—
856C22#352012yes—
857C22#352112yes—
858C4—28no—
859C4—24no—
860C4—24no—
861C4—44no—
862C4—44no—
863C4—44no—
864C4—44no—
865C4—44no—
866C4—44no—
867C4—42no—
868C4—44no—
869C4—42no—
870C4—44no—
871C4—42no—
872C4—44no—
873C4—82no—
874C4—82no—
875C2—28no—
876C2—82no—
877C2C2×#229311yescharacteristic
878C2#3426012yes—
879C2#3426411yescharacteristic
880C2#3426811yescharacteristic
881C2#3427812yes—
882C2#3537912yes—
883C2#3538012yes—
884C2#3539312yes—
885C2#3546412yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
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×#2313C2semidirect
4. #14158C2semidirect
5. #14156C2semidirect
6. #14146C2semidirect
7. #14133C2semidirect
8. #14078C2semidirect
9. #14075C2semidirect
10. #14073C2semidirect
11. #14072C2semidirect
12. #14004C2semidirect
15. #13992C2semidirect
17. C4×#385C2semidirect
18. C2×#1436C2semidirect
19. #13749C2semidirect
25. #2322C4semidirect
166. #389C2×C4semidirect
169. #388C2×C4semidirect
175. #387C2×C4semidirect
182. #385C2×C4semidirect
638. C22⋊C4#117semidirect

Maximal subgroups

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

subgroupindex
C2×#23222
C2×#23132
C2×#22902
#141582
#141562
#141462
#141332
#140782
#140752
#140732
#140722
#140042
#139992
#139962
#139922
#137842
C4×#3852
C2×#14362
#137492