Finite Group Databasebeta

← #612710

Subgroups — #612710

Order 512.

3458 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2503C211yesmaximal, characteristic, complemented
2C2×#2486C211yesmaximal, characteristic
3C2×#2417C211yesmaximal, characteristic
4C2×C42×D4C211yesmaximal, characteristic
5#15237C211yesmaximal, characteristic, complemented
6#15236C211yesmaximal, characteristic, complemented
7#15234C211yesmaximal, characteristic, complemented
8#15233C211yesmaximal, characteristic, complemented
9#14846C214yesmaximal, complemented
10#14833C214yesmaximal, complemented
11#14707C211yesmaximal, characteristic, complemented
12#14703C211yesmaximal, characteristic, complemented
13#14702C211yesmaximal, characteristic, complemented
14#14702C211yesmaximal, characteristic, complemented
15#14682C211yesmaximal, characteristic, complemented
16#13968C214yesmaximal
17#13881C211yesmaximal, characteristic, complemented
18#13874C214yesmaximal, complemented
19C2×C4⋊#95C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C42C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2503—28no—
30#2486—28no—
31#2417—28no—
32C2×#400C2214yes—
33C2×#398C2212yes—
34C2×#398C2212yes—
35C2×#397C2212yes—
36C2×#396C2212yes—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#386C2212yes—
46C2×#382C2211yescharacteristic
47C2×#382C2211yescharacteristic
48C2×#382C2211yescharacteristic
49C2×#382C2211yescharacteristic
50C2×#381C2212yes—
51C2×#381C2214yes—
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C42×D4—28no—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2211yescharacteristic
64C22×#95C2214yes—
65C2×C43C2211yescharacteristic
66#1443C2214yes—
67#1443C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1436C2214yes—
76#1436C2214yes—
77#1436C2214yes—
78#1436C2214yes—
79#1436C2214yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2214yes—
89#1434C2214yes—
90#1434C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2312yes—
101C24×C4C2312yes—
102C24×C4C2311yescharacteristic
103C2×#123—28no—
104C2×#123—216no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—42no—
111C2×C4×D4—28no—
112C2×C4×D4—24no—
113C2×C4×D4—28no—
114C2×C4×D4—24no—
115C2×C4×D4—28no—
116C2×C4×D4D418yes—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C42—24no—
150C22×C42—24no—
151C22×C42—24no—
152C22×C42—24no—
153C22×C42—42no—
154C22×C42—42no—
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#400—216no—
165#398—28no—
166#398—28no—
167#397—28no—
168#396—28no—
169#391—24no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—42no—
174#389—24no—
175#389—24no—
176#389—24no—
177#386—28no—
178#382—24no—
179#382—24no—
180#382—24no—
181#382—42no—
182#381—28no—
183#381—216no—
184#380—24no—
185#380—24no—
186#380—24no—
187#380—24no—
188#380—28no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—28no—
191C4×C22⋊C4—28no—
192C4×C22⋊C4—24no—
193C4×C22⋊C4—28no—
194C4×C22⋊C4D418yes—
195C2×#95—216no—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C43—24no—
225C25C2411yescharacteristic
226C25C2411yescharacteristic
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—24no—
237C22×D4C2×D414yes—
238C22×D4#4118yes—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—28no—
260C23×C4—28no—
261C23×C4—24no—
262C23×C4—28no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—44no—
272C23×C4C2×D414yes—
273C23×C4C2×D414yes—
274C23×C4C2×D414yes—
275C23×C4#4118yes—
276C23×C4#4114yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294#123—432no—
295C22⋊Q8—416no—
296C22⋊Q8—416no—
297C4×D4—264no—
298C4×D4—232no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—416no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—416no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2×D414yes—
345C2×C4⋊C4#4114yes—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4C2×D418yes—
370C2×C22⋊C4C2×D414yes—
371C2×C22⋊C4C2×D414yes—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—416no—
393C2×C42—416no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42C2×D414yes—
398C2×C42C2×D414yes—
399C2×C42C2×D414yes—
400C2×C42#4114yes—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—28no—
410#95—24no—
411#95—24no—
412#95—28no—
413#95—28no—
414#95—24no—
415#95—24no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—28no—
421#95—28no—
422#95—28no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95C2×D418yes—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—22no—
443C24—22no—
444C24C22×D412yes—
445C24C22×D412yes—
446C24C22×D412yes—
447C24C2×#4114yes—
448C24C2×#4112yes—
449C24C2×#4114yes—
450C24C2×#4114yes—
451C24C2511yescharacteristic
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×D4—28no—
460C2×D4—216no—
461C2×D4—216no—
462C2×D4—28no—
463C2×D4#124116yes—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—216no—
482C22×C4—216no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—216no—
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—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
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—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—416no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—416no—
575C22×C4—48no—
576C22×C4—416no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—84no—
580C22×C4—88no—
581C22×C4#121116yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D414yes—
585C22×C4C22×D414yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4114yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4114yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C42−1+414yes—
602C22×C42−1+412yes—
603C4⋊C4—216no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—84no—
619C22⋊C4—216no—
620C22⋊C4—28no—
621C22⋊C4—216no—
622C22⋊C4—28no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—84no—
629C42—216no—
630C42—28no—
631C42—28no—
632C42—28no—
633C42—28no—
634C42—48no—
635C42—48no—
636C42—48no—
637C42—44no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23C2×#12114yes—
679C23#52518yes—
680C23C2×#12414yes—
681C23C2×#12414yes—
682C23#52918yes—
683C23#53214yes—
684C23C23×D411yescharacteristic
685C23C23×D411yescharacteristic
686C23C22×#4111yescharacteristic
687C23C22×#4112yes—
688C23C22×#4112yes—
689C23C22×#4111yescharacteristic
690C23C22×#4111yescharacteristic
691C23C2×H(5,𝔽2)11yescharacteristic
692C23C2×2−1+411yescharacteristic
693C23C2×2−1+412yes—
694C23#58512yes—
695Q8—88no—
696D4—232no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—432no—
732C2×C4—432no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—416no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—816no—
793C2×C4—816no—
794C2×C4C2×#12114yes—
795C2×C4C2×#12114yes—
796C2×C4C2×#12414yes—
797C2×C4#52914yes—
798C2×C4#53914yes—
799C2×C4#54614yes—
800C2×C4#54614yes—
801C2×C4#54714yes—
802C2×C4#54714yes—
803C2×C4#55218yes—
804C22—28no—
805C22—24no—
806C22—28no—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—24no—
811C22—28no—
812C22—28no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—44no—
818C22—42no—
819C22—44no—
820C22—42no—
821C22—42no—
822C22—44no—
823C22—44no—
824C22—42no—
825C22#285018yes—
826C22C22×#12111yescharacteristic
827C22C2×#52512yes—
828C22C22×#12411yescharacteristic
829C22C2×#52912yes—
830C22C2×#52911yescharacteristic
831C22C2×#53211yescharacteristic
832C22C2×#53911yescharacteristic
833C22#346112yes—
834C22C2×#54611yescharacteristic
835C22C2×#54611yescharacteristic
836C22C2×#54711yescharacteristic
837C22C2×#54711yescharacteristic
838C22C2×#55212yes—
839C22#347512yes—
840C22#347512yes—
841C22#348212yes—
842C22#348912yes—
843C22#349911yescharacteristic
844C22#350011yescharacteristic
845C22#350512yes—
846C22#350912yes—
847C22#351512yes—
848C22#352012yes—
849C4—24no—
850C4—28no—
851C4—24no—
852C4—44no—
853C4—44no—
854C4—44no—
855C4—44no—
856C4—42no—
857C4—42no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4#242518yes—
866C2—28no—
867C2—44no—
868C2C2×#242511yescharacteristic
869C2#3478012yes—
870C2#3502612yes—
871C2#3530811yescharacteristic
872C2#3615612yes—
873C2#3616411yescharacteristic
874C2#3618111yescharacteristic
875C2#3630311yescharacteristic
876C2#3637512yes—
877C2#3638611yescharacteristic
878C2C2×#285011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2503C2semidirect
5. #15237C2semidirect
6. #15236C2semidirect
7. #15234C2semidirect
8. #15233C2semidirect
9. #14846C2semidirect
10. #14833C2semidirect
11. #14707C2semidirect
12. #14703C2semidirect
13. #14702C2semidirect
14. #14702C2semidirect
15. #14682C2semidirect
17. #13881C2semidirect
18. #13874C2semidirect
19. C2×C4⋊#95C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25032
C2×#24862
C2×#24172
C2×C42×D42
#152372
#152362
#152342
#152332
#148462
#148332
#147072
#147032
#147022
#146822
#139682
#138812
#138742
C2×C4⋊#952