Finite Group Databasebeta

← #612706

Subgroups — #612706

Order 512.

4416 conjugacy classes of subgroups.

The subgroup lattice has 969 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic, complemented
2C2×#2486C211yesmaximal, characteristic, complemented
3C2×#2416C211yesmaximal, characteristic
4C2×#2425C214yesmaximal, complemented
5C2×C42×D4C211yesmaximal, characteristic, complemented
6#15151C211yesmaximal, characteristic, complemented
7#15150C211yesmaximal, characteristic, complemented
8#15134C211yesmaximal, characteristic, complemented
9#15130C211yesmaximal, characteristic, complemented
10#14870C214yesmaximal, complemented
11#14839C214yesmaximal, complemented
12#14712C211yesmaximal, characteristic, complemented
13#14700C211yesmaximal, characteristic, complemented
14#14698C211yesmaximal, characteristic, complemented
15#14698C211yesmaximal, characteristic, complemented
16#14686C211yesmaximal, characteristic, complemented
17#13996C214yesmaximal, complemented
18#13880C211yesmaximal, characteristic, complemented
19C2×C4⋊#95C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×#123C2214yes—
22C22×#121C2211yescharacteristic
23C22×#121C2212yes—
24C22×#121C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2212yes—
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2501—28no—
32#2486—28no—
33#2425—232no—
34#2416—28no—
35C2×#399C2214yes—
36C2×#398C2212yes—
37C2×#398C2214yes—
38C2×#397C2214yes—
39C2×#397C2212yes—
40C2×#396C2212yes—
41C2×#396C2214yes—
42C2×#394C2214yes—
43C2×#394C2212yes—
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2214yes—
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388C2214yes—
54C2×#386C2214yes—
55C2×#386C2214yes—
56C2×#386C2212yes—
57C2×#385C2214yes—
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C2×#381C2212yes—
63C2×#380C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2214yes—
68C42×D4—28no—
69C2×C4×C4⋊C4C2212yes—
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2212yes—
73C2×C4×C22⋊C4C2212yes—
74C2×C4×C22⋊C4C2211yescharacteristic
75C22×#95C2214yes—
76C2×C43C2211yescharacteristic
77#1445C2214yes—
78#1445C2214yes—
79#1444C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1437C2214yes—
83#1437C2214yes—
84#1437C2214yes—
85C4⋊#95C2214yes—
86C4⋊#95C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2214yes—
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C23×D4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104C24×C4C2312yes—
105C24×C4C2311yescharacteristic
106C2×#123—216no—
107C2×#123—28no—
108C2×#123—216no—
109C2×#123—216no—
110C2×#123—216no—
111C2×#121—28no—
112C2×#121—216no—
113C2×#121—24no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—24no—
118C2×#121—42no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4—28no—
122C2×C4×D4—28no—
123C2×C4×D4D418yes—
124C2×C4×D4D4116yescomplemented
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—42no—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C42—24no—
166C22×C42—24no—
167C22×C42—24no—
168C22×C42—24no—
169C22×C42—42no—
170C22×C42—42no—
171C22×C42C2311yescharacteristic
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2312yes—
175C22×C42C2311yescharacteristic
176C22×C42C2312yes—
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180#399—216no—
181#398—216no—
182#398—28no—
183#397—216no—
184#397—28no—
185#396—28no—
186#396—216no—
187#394—28no—
188#394—216no—
189#390—24no—
190#390—24no—
191#390—24no—
192#390—24no—
193#390—42no—
194#389—24no—
195#389—216no—
196#389—24no—
197#389—24no—
198#388—216no—
199#386—216no—
200#386—216no—
201#386—28no—
202#385—216no—
203#384—24no—
204#384—24no—
205#384—24no—
206#384—42no—
207#381—28no—
208#380—24no—
209#380—216no—
210#380—24no—
211#380—24no—
212#380—24no—
213C4×C4⋊C4—24no—
214C4×C4⋊C4—28no—
215C4×C22⋊C4—28no—
216C4×C22⋊C4—24no—
217C4×C22⋊C4—28no—
218C4×C22⋊C4D418yescomplemented
219C2×#95—216no—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2314yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C43—24no—
239C25C2412yes—
240C25C2411yescharacteristic
241C25C2411yescharacteristic
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—28no—
248C22×D4—24no—
249C22×D4—28no—
250C22×D4—24no—
251C22×D4—28no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—42no—
261C22×D4—44no—
262C22×D4C2×D414yes—
263C22×D4C2×D418yes—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—28no—
285C23×C4—24no—
286C23×C4—28no—
287C23×C4—24no—
288C23×C4—28no—
289C23×C4—24no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—44no—
296C23×C4C2×D414yes—
297C23×C4C2×D418yes—
298C23×C4C2×D418yes—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4#4114yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318#123—432no—
319#123—464no—
320#121—416no—
321#121—432no—
322#121—416no—
323C4×D4—232no—
324C4×D4—264no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—416no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—416no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D418yes—
377C2×C4⋊C4#4114yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4C2×D414yes—
415C2×C22⋊C4C2×D414yes—
416C2×C22⋊C4C2×D418yes—
417C2×C22⋊C4C2×D418yes—
418C2×C22⋊C4C2×D418yes—
419C2×C22⋊C4#4118yes—
420C2×C42—24no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—24no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—24no—
433C2×C42—22no—
434C2×C42—24no—
435C2×C42—24no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—24no—
439C2×C42—416no—
440C2×C42—416no—
441C2×C42—42no—
442C2×C42—42no—
443C2×C42—42no—
444C2×C42C2×D414yes—
445C2×C42C2×D418yes—
446C2×C42C2×D414yes—
447C2×C42C2×D414yes—
448C2×C42#4114yes—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—28no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—28no—
463#95—28no—
464#95—24no—
465#95—28no—
466#95C2×D418yes—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—21no—
474C24—21no—
475C24—22no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—24no—
484C24—22no—
485C24—24no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—24no—
491C24—22no—
492C24—24no—
493C24C22×D412yes—
494C24C22×D414yes—
495C24C22×D412yes—
496C24C22×D412yes—
497C24C22×D414yes—
498C24C2×#4112yes—
499C24C2×#4114yes—
500C24C2511yescharacteristic
501C2×D4—28no—
502C2×D4—216no—
503C2×D4—28no—
504C2×D4—216no—
505C2×D4—48no—
506C2×D4—416no—
507C2×D4—48no—
508C2×D4—416no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—416no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—88no—
521C2×D4—84no—
522C2×D4#127116yes—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—216no—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—216no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—216no—
573C22×C4—216no—
574C22×C4—28no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—416no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—48no—
622C22×C4—416no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—416no—
627C22×C4—88no—
628C22×C4—84no—
629C22×C4#121116yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D414yes—
633C22×C4C22×D414yes—
634C22×C4C22×D412yes—
635C22×C4C22×D414yes—
636C22×C4C22×D414yes—
637C22×C4C22×D414yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C22×D414yes—
641C22×C4C22×D414yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C2×#4114yes—
645C22×C4C2×#4114yes—
646C22×C4C2×#4112yes—
647C22×C4C2×#4114yes—
648C22×C4C2×#4114yes—
649C22×C4C2×#4112yes—
650C22×C4C2×#4112yes—
651C22×C4C2×#4112yes—
652C22×C4H(5,𝔽2)12yes—
653C22×C42−1+414yes—
654C22×C42−1+412yes—
655C4⋊C4—28no—
656C4⋊C4—216no—
657C4⋊C4—28no—
658C4⋊C4—416no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—416no—
665C4⋊C4—416no—
666C4⋊C4—48no—
667C4⋊C4—48no—
668C4⋊C4—48no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—88no—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—216no—
676C22⋊C4—48no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—416no—
683C22⋊C4—416no—
684C22⋊C4—48no—
685C22⋊C4—416no—
686C22⋊C4—88no—
687C22⋊C4—84no—
688C22⋊C4#121132yescomplemented
689C42—216no—
690C42—28no—
691C42—28no—
692C42—28no—
693C42—28no—
694C42—48no—
695C42—48no—
696C42—48no—
697C42—44no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—24no—
720C23—22no—
721C23—24no—
722C23—22no—
723C23—24no—
724C23—24no—
725C23—22no—
726C23—24no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—44no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—44no—
744C23—42no—
745C23—44no—
746C23—42no—
747C23—42no—
748C23—44no—
749C23—42no—
750C23—42no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—42no—
757C23—44no—
758C23—42no—
759C23—44no—
760C23—44no—
761C23C2×#12114yes—
762C23C2×#12118yes—
763C23C2×#12714yes—
764C23C2×#12714yes—
765C23#53214yes—
766C23#53218yes—
767C23C23×D411yescharacteristic
768C23C23×D411yescharacteristic
769C23C23×D412yes—
770C23C22×#4111yescharacteristic
771C23C22×#4112yes—
772C23C22×#4111yescharacteristic
773C23C22×#4111yescharacteristic
774C23C2×H(5,𝔽2)11yescharacteristic
775C23C2×2−1+411yescharacteristic
776C23C2×2−1+412yes—
777C23#58512yes—
778D4—232no—
779D4—816no—
780D4—816no—
781D4—88no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—232no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—28no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—432no—
823C2×C4—432no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—416no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—44no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—42no—
855C2×C4—44no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—42no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—816no—
869C2×C4—816no—
870C2×C4C2×#12118yes—
871C2×C4C2×#12114yes—
872C2×C4C2×#12118yes—
873C2×C4C2×#12114yes—
874C2×C4#52914yes—
875C2×C4C2×#12714yes—
876C2×C4#53914yes—
877C2×C4#54614yes—
878C2×C4#54614yes—
879C2×C4#54718yes—
880C2×C4#54714yes—
881C2×C4#54714yes—
882C22—24no—
883C22—28no—
884C22—24no—
885C22—24no—
886C22—24no—
887C22—28no—
888C22—24no—
889C22—28no—
890C22—28no—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—42no—
903C22—82no—
904C22—82no—
905C22—84no—
906C22—82no—
907C22—82no—
908C22—82no—
909C22—84no—
910C22—82no—
911C22—84no—
912C22—84no—
913C22—82no—
914C22#285618yes—
915C22C22×#12112yes—
916C22C22×#12111yescharacteristic
917C22C2×#52911yescharacteristic
918C22C22×#12711yescharacteristic
919C22C2×#53211yescharacteristic
920C22C2×#53212yes—
921C22C2×#53911yescharacteristic
922C22#346112yes—
923C22C2×#54611yescharacteristic
924C22C2×#54611yescharacteristic
925C22C2×#54712yes—
926C22C2×#54711yescharacteristic
927C22C2×#54711yescharacteristic
928C22D4×#4112yes—
929C22#347512yes—
930C22#348212yes—
931C22#348912yes—
932C22#349612yes—
933C22#349911yescharacteristic
934C22#349912yes—
935C22#350011yescharacteristic
936C22#351512yes—
937C22#352012yes—
938C4—24no—
939C4—28no—
940C4—28no—
941C4—24no—
942C4—28no—
943C4—44no—
944C4—42no—
945C4—44no—
946C4—42no—
947C4—82no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4—82no—
952C4—82no—
953C4#242518yescomplemented
954C2—28no—
955C2—44no—
956C2—162no—
957C2C2×#242511yescharacteristic
958C2#3476312yes—
959C2#3500812yes—
960C2#3530811yescharacteristic
961C2#3615312yes—
962C2#3617911yescharacteristic
963C2#3618411yescharacteristic
964C2#3625912yes—
965C2#3626011yescharacteristic
966C2#3637611yescharacteristic
967C2C2×#285611yescharacteristic
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×#2501C2semidirect
2. C2×#2486C2semidirect
4. C2×#2425C2semidirect
5. C2×C42×D4C2semidirect
6. #15151C2semidirect
7. #15150C2semidirect
8. #15134C2semidirect
9. #15130C2semidirect
10. #14870C2semidirect
11. #14839C2semidirect
12. #14712C2semidirect
13. #14700C2semidirect
14. #14698C2semidirect
15. #14698C2semidirect
16. #14686C2semidirect
17. #13996C2semidirect
18. #13880C2semidirect
19. C2×C4⋊#95C2semidirect
124. C2×C4×D4D4semidirect
218. C4×C22⋊C4D4semidirect
688. C22⋊C4#121semidirect
953. C4#2425semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#24862
C2×#24162
C2×#24252
C2×C42×D42
#151512
#151502
#151342
#151302
#148702
#148392
#147122
#147002
#146982
#146862
#139962
#138802
C2×C4⋊#952