Finite Group Databasebeta

← #617258

Subgroups — #617258

Order 512.

3340 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2500C211yesmaximal, characteristic, complemented
2C2×#2485C211yesmaximal, characteristic, complemented
3C2×#2416C211yesmaximal, characteristic
4C2×#2290C211yesmaximal, characteristic, complemented
5#15866C214yesmaximal, complemented
6#15577C214yesmaximal, complemented
7#15303C214yesmaximal, complemented
8#15274C214yesmaximal, complemented
9#15233C211yesmaximal, characteristic, complemented
10#15196C211yesmaximal, characteristic, complemented
11#15134C211yesmaximal, characteristic, complemented
12#15130C211yesmaximal, characteristic, complemented
13#14698C211yesmaximal, characteristic, complemented
14#14686C211yesmaximal, characteristic, complemented
15#14276C211yesmaximal, characteristic, complemented
16#14260C211yesmaximal, characteristic, complemented
17#14257C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19#13795C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2500—28no—
29#2485—28no—
30#2416—28no—
31C2×#397C2212yes—
32C2×#396C2212yes—
33C2×#396C2214yes—
34C2×#394C2212yes—
35C2×#394C2212yes—
36C2×#394C2214yes—
37C2×#394C2214yes—
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46#2290—28no—
47C2×#388C2212yes—
48C2×#388C2214yes—
49C2×#388C2212yes—
50C2×#387C2212yes—
51C2×#387C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#386C2214yes—
55C2×#385C2212yes—
56C2×#385C2214yes—
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#382C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×#380C2214yes—
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×#376C2211yescharacteristic
70#1444C2214yes—
71#1444C2214yes—
72#1443C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1440C2214yes—
77#1440C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1438C2214yes—
83#1437C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2214yes—
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C2×#121—28no—
104C2×#121—24no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#121—24no—
108C2×#121—24no—
109C2×#121—48no—
110C2×#121—42no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4D418yes—
114C2×#117—24no—
115C2×#117—24no—
116C2×#117—24no—
117C2×#117—24no—
118C2×#117—24no—
119C2×#117—42no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C42—24no—
159C22×C42—24no—
160C22×C42—42no—
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#397—28no—
169#396—28no—
170#396—48no—
171#394—28no—
172#394—28no—
173#394—216no—
174#394—48no—
175#390—24no—
176#390—24no—
177#390—24no—
178#390—24no—
179#390—42no—
180#389—24no—
181#389—24no—
182#389—24no—
183#388—28no—
184#388—28no—
185#388—216no—
186#387—28no—
187#387—28no—
188#386—28no—
189#386—28no—
190#386—48no—
191#385—28no—
192#385—48no—
193#384—24no—
194#384—24no—
195#384—42no—
196#382—24no—
197#380—24no—
198#380—24no—
199#380—24no—
200#380—24no—
201#380—48no—
202C4×C4⋊C4—24no—
203C4×C22⋊C4—24no—
204C4×C22⋊C4D418yescomplemented
205#376—24no—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C25C2412yes—
228C25C2411yescharacteristic
229C25C2411yescharacteristic
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—28no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4C2×D414yes—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4#4114yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294#121—416no—
295#121—432no—
296#121—416no—
297C4×D4—232no—
298#117—416no—
299#117—416no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—416no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4#4114yes—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
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—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4C2×D414yes—
395C2×C22⋊C4C2×D414yes—
396C2×C22⋊C4C2×D418yes—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—22no—
413C2×C42—416no—
414C2×C42—42no—
415C2×C42C2×D414yes—
416C2×C42C2×D414yes—
417C2×C42C2×D414yes—
418C2×C42#4114yes—
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—28no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—28no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95—44no—
439#95C2×D418yes—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—21no—
450C24—22no—
451C24—22no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—24no—
463C24—24no—
464C24—22no—
465C24—24no—
466C24—22no—
467C24—24no—
468C24C22×D412yes—
469C24C22×D412yes—
470C24C22×D412yes—
471C24C2×#4112yes—
472C24H(5,𝔽2)14yes—
473C24C2511yescharacteristic
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—44no—
477C2×D4—48no—
478C2×D4—416no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—84no—
493C2×D4—88no—
494C2×D4—88no—
495C2×D4—88no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—216no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
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—24no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—48no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—48no—
593C22×C4—88no—
594C22×C4—84no—
595C22×C4—88no—
596C22×C4#121116yes—
597C22×C4C22×D412yes—
598C22×C4C22×D414yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D414yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4114yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4H(5,𝔽2)14yes—
613C22×C4H(5,𝔽2)12yes—
614C22×C42−1+414yes—
615C22×C42−1+412yes—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—48no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—88no—
630C4⋊C4—88no—
631C4⋊C4—84no—
632C4⋊C4—88no—
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—416no—
645C22⋊C4—88no—
646C22⋊C4—88no—
647C22⋊C4—84no—
648C22⋊C4—84no—
649C22⋊C4—84no—
650C22⋊C4—88no—
651C42—28no—
652C42—28no—
653C42—28no—
654C42—28no—
655C42—48no—
656C42—48no—
657C42—44no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—44no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—42no—
717C23—42no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23C2×#12114yes—
726C23#53514yes—
727C23C23×D411yescharacteristic
728C23C23×D411yescharacteristic
729C23C22×#4111yescharacteristic
730C23C22×#4111yescharacteristic
731C23C22×#4111yescharacteristic
732C23C2×H(5,𝔽2)12yes—
733C23C2×H(5,𝔽2)12yes—
734C23C2×H(5,𝔽2)11yescharacteristic
735C23C2×2−1+412yes—
736C23C2×2−1+411yescharacteristic
737C23#58512yes—
738D4—416no—
739D4—816no—
740D4—816no—
741D4—88no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—232no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—28no—
772C2×C4—432no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
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—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—416no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
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—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—816no—
831C2×C4C2×#12114yes—
832C2×C4C2×#12114yes—
833C2×C4#52914yes—
834C2×C4#53718yes—
835C2×C4#53914yes—
836C2×C4#54614yes—
837C2×C4#54614yes—
838C2×C4#54714yes—
839C2×C4#54714yes—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—84no—
863C22—84no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—84no—
870C22—84no—
871C22—82no—
872C22—82no—
873C22C22×#12111yescharacteristic
874C22C2×#52911yescharacteristic
875C22C2×#53511yescharacteristic
876C22C2×#53712yes—
877C22#344911yescharacteristic
878C22C2×#53911yescharacteristic
879C22C2×#54611yescharacteristic
880C22C2×#54611yescharacteristic
881C22C2×#54711yescharacteristic
882C22C2×#54711yescharacteristic
883C22#348812yes—
884C22#349212yes—
885C22#349412yes—
886C22#349412yes—
887C22#349811yescharacteristic
888C22#349911yescharacteristic
889C22#351112yes—
890C22#351812yes—
891C22#351912yes—
892C22#353712yes—
893C22#354112yes—
894C22#354412yes—
895C22#354712yes—
896C4—24no—
897C4—28no—
898C4—44no—
899C4—42no—
900C4—42no—
901C4—44no—
902C4—42no—
903C4—44no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4—82no—
909C4—82no—
910C4—82no—
911C4#242518yes—
912C2—44no—
913C2—44no—
914C2—162no—
915C2C2×#242511yescharacteristic
916C2#3525211yescharacteristic
917C2#3527311yescharacteristic
918C2#3558912yes—
919C2#3733912yes—
920C2#3783612yes—
921C2#3786311yescharacteristic
922C2#3786911yescharacteristic
923C2#3808011yescharacteristic
924C2#3809111yescharacteristic
925C2#3892212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
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×#2500C2semidirect
2. C2×#2485C2semidirect
4. C2×#2290C2semidirect
5. #15866C2semidirect
6. #15577C2semidirect
7. #15303C2semidirect
8. #15274C2semidirect
9. #15233C2semidirect
10. #15196C2semidirect
11. #15134C2semidirect
12. #15130C2semidirect
13. #14698C2semidirect
14. #14686C2semidirect
15. #14276C2semidirect
16. #14260C2semidirect
17. #14257C2semidirect
18. #13880C2semidirect
19. #13795C2semidirect
204. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25002
C2×#24852
C2×#24162
C2×#22902
#158662
#155772
#153032
#152742
#152332
#151962
#151342
#151302
#146982
#146862
#142762
#142602
#142572
#138802
#137952