Finite Group Databasebeta

← #739704

Subgroups — #739704

Order 512.

4206 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic, complemented
2C2×#2538C211yesmaximal, characteristic, complemented
3C2×#2540C211yesmaximal, characteristic
4C2×#2398C211yesmaximal, characteristic, complemented
5#16674C212yesmaximal, complemented
6#16655C212yesmaximal, complemented
7#15913C214yesmaximal, complemented
8#15280C214yesmaximal, complemented
9#15215C212yesmaximal, complemented
10#15178C212yesmaximal, complemented
11#14893C212yesmaximal, complemented
12#14886C212yesmaximal, complemented
13#14273C211yesmaximal, characteristic, complemented
14#13970C212yesmaximal, complemented
15#13969C212yesmaximal, complemented
16#13926C211yesmaximal, characteristic, complemented
17#13786C211yesmaximal, characteristic, complemented
18C2×#556—28no—
19C2×#556—28no—
20C2×#556—28no—
21C22×C4⋊Q8C2211yescharacteristic
22C22×#126C2212yes—
23C22×#126C2212yes—
24C22×#124C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×C22⋊Q8C2212yes—
27C22×C22⋊Q8C2212yes—
28C22×C22⋊Q8C2212yes—
29C22×#121C2212yes—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×#117C2212yes—
36#2540—28no—
37#2538—28no—
38#2398—28no—
39C2×#400C2211yescharacteristic
40C2×#400C2211yescharacteristic
41C2×#399C2212yes—
42C2×#397C2212yes—
43C2×#396C2214yes—
44C2×#394C2211yescharacteristic
45C2×#394C2211yescharacteristic
46C2×#393C2212yes—
47C2×#392C2212yes—
48C2×#391C2212yes—
49C2×#391C2212yes—
50C2×#391C2212yes—
51C2×#390C2212yes—
52C2×#390C2214yes—
53C2×#390C2212yes—
54C2×#389C2212yes—
55C2×#386C2214yes—
56C2×#384C2211yescharacteristic
57C2×#380C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61C2×#376C2211yescharacteristic
62#1444C2214yes—
63#1444C2214yes—
64#1441C2212yes—
65#1441C2214yes—
66#1441C2212yes—
67#1440C2214yes—
68#1439C2214yes—
69#1439C2212yes—
70#1439C2214yes—
71#1439C2212yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1437C2214yes—
80#1436C2214yes—
81#1436C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86#1434C2212yes—
87#1434C2212yes—
88C22⋊#95C2214yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×Q8C2311yescharacteristic
92C23×D4C2311yescharacteristic
93C23×D4C2311yescharacteristic
94C23×D4C2314yes—
95C24×C4C2312yes—
96C24×C4C2312yes—
97#556—2128no—
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×#126—28no—
102C2×#126—28no—
103C2×#126—28no—
104C2×#126—28no—
105C2×#126—28no—
106C2×#126—28no—
107C2×#124—24no—
108C2×#124—24no—
109C2×#124—24no—
110C2×#124—24no—
111C2×#124—24no—
112C2×#124D418yes—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—28no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—44no—
120C2×C22⋊Q8—44no—
121C2×C22⋊Q8—44no—
122C2×#121—28no—
123C2×#121—28no—
124C2×#121—44no—
125C2×C4×Q8—24no—
126C2×C4×Q8—24no—
127C2×C4×Q8—24no—
128C2×C4×Q8—24no—
129C2×C4×Q8—24no—
130C2×C4×Q8—24no—
131C2×C4×Q8—24no—
132C2×C4×Q8D418yescomplemented
133C2×C4×Q8D418yescomplemented
134C2×C4×D4—24no—
135C2×C4×D4—24no—
136C2×C4×D4—24no—
137C2×C4×D4—24no—
138C2×C4×D4—24no—
139C2×C4×D4—24no—
140C2×#117—28no—
141C2×#117—28no—
142C2×#117—28no—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2314yes—
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2314yes—
172C22×C22⋊C4C2314yes—
173C22×C22⋊C4C2314yes—
174C22×C42C2312yes—
175C22×C42C2312yes—
176C22×C42C2312yes—
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2312yes—
180C22×C42C2311yescharacteristic
181#400—24no—
182#400—24no—
183#399—28no—
184#397—28no—
185#396—216no—
186#394—24no—
187#394—24no—
188#393—28no—
189#392—28no—
190#391—28no—
191#391—44no—
192#391—44no—
193#390—216no—
194#390—28no—
195#390—44no—
196#389—28no—
197#386—48no—
198#384—24no—
199#380—28no—
200C4×C4⋊C4—24no—
201C4×C22⋊C4—28no—
202C4×C22⋊C4—28no—
203#376—24no—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C25C2412yes—
224C25C2412yes—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—24no—
232C22×Q8—24no—
233C22×Q8—24no—
234C22×Q8—24no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—41no—
238C22×Q8—41no—
239C22×Q8C2×D414yes—
240C22×Q8C2×D414yes—
241C22×Q8C2×D414yes—
242C22×D4—24no—
243C22×D4—28no—
244C22×D4—28no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—28no—
252C22×D4—24no—
253C22×D4—42no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4C2×D414yes—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4C2414yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2414yes—
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C4⋊Q8—232no—
289#126—264no—
290#126—264no—
291#124—232no—
292#124—232no—
293C22⋊Q8—264no—
294C22⋊Q8—432no—
295C22⋊Q8—432no—
296#121—432no—
297C4×Q8—232no—
298C4×Q8—232no—
299C4×Q8—232no—
300C4×D4—232no—
301C4×D4—416no—
302#117—264no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
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—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4C2×D414yes—
342C2×C4⋊C4C2×D414yes—
343C2×C4⋊C4C2×D418yes—
344C2×C4⋊C4C2×D414yes—
345C2×C4⋊C4C2×D414yes—
346C2×C4⋊C4#4118yes—
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—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
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⋊C4C2×D418yes—
394C2×C22⋊C4C2×D418yes—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42C2×D418yes—
411C2×C42C2×D414yes—
412C2×C42C2×D414yes—
413C2×C42C2×D414yes—
414C2×C42C2×D414yes—
415C2×C42C2×D414yes—
416#95—24no—
417#95—22no—
418#95—22no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—28no—
425#95—28no—
426#95—28no—
427#95—28no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95—44no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—24no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—24no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—24no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—24no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C22×D414yes—
460C242−1+414yes—
461C24C2511yescharacteristic
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—216no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—216no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—44no—
485C2×D4—416no—
486C2×D4—416no—
487C2×D4—416no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—48no—
492C2×D4—88no—
493C2×D4—88no—
494C2×D4—88no—
495C2×D4—88no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—216no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
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—48no—
581C22×C4—48no—
582C22×C4C22×D412yes—
583C22×C4C22×D414yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C2×#4118yes—
599C22×C4C2×#4114yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4H(5,𝔽2)14yes—
602C22×C42−1+412yes—
603C4⋊C4—216no—
604C4⋊C4—216no—
605C4⋊C4—216no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—216no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—216no—
612C4⋊C4—416no—
613C4⋊C4—48no—
614C4⋊C4—416no—
615C4⋊C4—44no—
616C4⋊C4—48no—
617C4⋊C4—84no—
618C22⋊C4—216no—
619C22⋊C4—216no—
620C22⋊C4—216no—
621C22⋊C4—216no—
622C22⋊C4—216no—
623C22⋊C4—416no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—416no—
627C22⋊C4—48no—
628C22⋊C4—416no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—88no—
632C22⋊C4—88no—
633C22⋊C4—88no—
634C42—216no—
635C42—216no—
636C42—28no—
637C42—28no—
638C42—48no—
639C42—84no—
640C42#120116yes—
641C23—24no—
642C23—28no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—28no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—44no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—44no—
678C23—42no—
679C23—42no—
680C23—44no—
681C23—42no—
682C23—42no—
683C23—44no—
684C23—44no—
685C23—42no—
686C23—42no—
687C23—44no—
688C23—42no—
689C23—44no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—44no—
695C23—42no—
696C23—44no—
697C23—42no—
698C23—42no—
699C23C23×D411yescharacteristic
700C23C23×D411yescharacteristic
701C23C23×D411yescharacteristic
702C23C22×#4112yes—
703C23C2×H(5,𝔽2)12yes—
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×2−1+411yescharacteristic
706C23C2×2−1+412yes—
707C23#58511yescharacteristic
708C23#58511yescharacteristic
709C23#58512yes—
710Q8—416no—
711Q8—416no—
712Q8—416no—
713D4—416no—
714D4—416no—
715D4—832no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—432no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
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—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—816no—
803C2×C4C2×#12014yes—
804C2×C4C2×#12014yes—
805C2×C4C2×#12014yes—
806C2×C4#53214yes—
807C2×C4#53514yes—
808C2×C4#53714yes—
809C2×C4#54618yes—
810C2×C4#55018yes—
811C22—44no—
812C22—48no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—48no—
822C22—44no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—84no—
834C22—82no—
835C22—84no—
836C22—82no—
837C22C22×#12011yescharacteristic
838C22C2×#53211yescharacteristic
839C22C2×#53511yescharacteristic
840C22C2×#53711yescharacteristic
841C22#344911yescharacteristic
842C22C2×#54612yes—
843C22C2×#55012yes—
844C22#348611yescharacteristic
845C22#348711yescharacteristic
846C22#348811yescharacteristic
847C22#348811yescharacteristic
848C22#348912yes—
849C22#348911yescharacteristic
850C22#348912yes—
851C22#348911yescharacteristic
852C22#351612yes—
853C22#351812yes—
854C22#352012yes—
855C22#352112yes—
856C22#354612yes—
857C22#355212yes—
858C22#356112yes—
859C22#356212yes—
860C4—24no—
861C4—24no—
862C4—24no—
863C4—48no—
864C4—42no—
865C4—42no—
866C4—44no—
867C4—44no—
868C4—44no—
869C4—42no—
870C4—84no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4#243118yes—
875C2—84no—
876C2—84no—
877C2C2×#243111yescharacteristic
878C2#3525111yescharacteristic
879C2#3565911yescharacteristic
880C2#3590911yescharacteristic
881C2#3604811yescharacteristic
882C2#3913112yes—
883C2#3913612yes—
884C2#4281211yescharacteristic
885C2#4288911yescharacteristic
886C2#4508412yes—
887C2#4530712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2540C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#556C2semidirect
2. C2×#2538C2semidirect
4. C2×#2398C2semidirect
5. #16674C2semidirect
6. #16655C2semidirect
7. #15913C2semidirect
8. #15280C2semidirect
9. #15215C2semidirect
10. #15178C2semidirect
11. #14893C2semidirect
12. #14886C2semidirect
13. #14273C2semidirect
14. #13970C2semidirect
15. #13969C2semidirect
16. #13926C2semidirect
17. #13786C2semidirect
132. C2×C4×Q8D4semidirect
133. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5562
C2×#25382
C2×#25402
C2×#23982
#166742
#166552
#159132
#152802
#152152
#151782
#148932
#148862
#142732
#139702
#139692
#139262
#137862