Finite Group Databasebeta

← #725996

Subgroups — #725996

Order 512.

4292 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic, complemented
2C2×#2538C211yesmaximal, characteristic, complemented
3C2×#2562C211yesmaximal, characteristic, complemented
4C2×#2397C211yesmaximal, characteristic
5#16674C212yesmaximal, complemented
6#16655C212yesmaximal, complemented
7#15846C214yesmaximal, complemented
8#15272C214yesmaximal, complemented
9#15177C212yesmaximal, complemented
10#15177C212yesmaximal, complemented
11#14893C212yesmaximal, complemented
12#14886C212yesmaximal, complemented
13#14283C211yesmaximal, characteristic, complemented
14#13906C211yesmaximal, characteristic, complemented
15#13872C212yesmaximal, complemented
16#13871C212yesmaximal, complemented
17#13786C211yesmaximal, characteristic, complemented
18C2×#552—28no—
19C2×#552—28no—
20C2×#552—28no—
21C22×#126C2212yes—
22C22×#125C2212yes—
23C22×#125C2211yescharacteristic
24C22×#123C2212yes—
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2212yes—
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yes—
31C22×C4×D4C2212yes—
32C22×C4×D4C2211yescharacteristic
33C22×#117C2212yes—
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#2562—28no—
37#2538—28no—
38#2397—28no—
39C2×#400C2212yes—
40C2×#399C2211yescharacteristic
41C2×#399C2211yescharacteristic
42C2×#399C2212yes—
43C2×#396C2214yes—
44C2×#394C2212yes—
45C2×#392C2211yescharacteristic
46C2×#392C2211yescharacteristic
47C2×#392C2212yes—
48C2×#391C2212yes—
49C2×#390C2212yes—
50C2×#390C2212yes—
51C2×#389C2212yes—
52C2×#388C2214yes—
53C2×#386C2214yes—
54C2×#384C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2212yes—
59C2×#380C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×#376C2211yescharacteristic
62#1444C2214yes—
63#1444C2214yes—
64#1441C2212yes—
65#1441C2212yes—
66#1441C2214yes—
67#1441C2214yes—
68#1440C2214yes—
69#1439C2212yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2212yes—
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×D4C2311yescharacteristic
91C23×D4C2312yes—
92C23×D4C2311yescharacteristic
93C23×D4C2312yes—
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98#552—2128no—
99C2×#126—28no—
100C2×#126—28no—
101C2×#126—28no—
102C2×#125—28no—
103C2×#125—28no—
104C2×#125—28no—
105C2×#125—24no—
106C2×#125—24no—
107C2×#125D418yescomplemented
108C2×#123—28no—
109C2×#123—28no—
110C2×#123—28no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—44no—
119C2×C22⋊Q8—44no—
120C2×C4×Q8—24no—
121C2×C4×Q8—24no—
122C2×C4×Q8D418yescomplemented
123C2×C4×D4—28no—
124C2×C4×D4—28no—
125C2×C4×D4—24no—
126C2×C4×D4—24no—
127C2×C4×D4—24no—
128C2×C4×D4—24no—
129C2×C4×D4—24no—
130C2×C4×D4—28no—
131C2×C4×D4—28no—
132C2×C4×D4—44no—
133C2×C4×D4—44no—
134C2×C4×D4D418yes—
135C2×#117—24no—
136C2×#117—24no—
137C2×#117—24no—
138C2×#117—28no—
139C2×#117—28no—
140C2×#117—28no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4—24no—
143C22×C4⋊C4—24no—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2314yes—
161C22×C4⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2314yes—
174C22×C22⋊C4C2314yes—
175C22×C22⋊C4C2314yes—
176C22×C22⋊C4C2314yes—
177C22×C22⋊C4C2314yes—
178C22×C42C2312yes—
179C22×C42C2312yes—
180C22×C42C2312yes—
181C22×C42C2312yes—
182C22×C42C2311yescharacteristic
183#400—28no—
184#399—28no—
185#399—24no—
186#399—24no—
187#396—216no—
188#394—28no—
189#392—28no—
190#392—24no—
191#392—24no—
192#391—28no—
193#390—28no—
194#390—44no—
195#389—28no—
196#388—216no—
197#386—48no—
198#384—24no—
199#380—28no—
200#380—28no—
201#380—28no—
202#380—44no—
203#380—44no—
204C4×C4⋊C4—24no—
205#376—24no—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C25C2411yescharacteristic
224C25C2412yes—
225C25C2411yescharacteristic
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—24no—
229C22×Q8—24no—
230C22×Q8C2×D414yes—
231C22×D4—24no—
232C22×D4—22no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4—41no—
250C22×D4—41no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—42no—
256C22×D4C2×D414yes—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2414yes—
282C23×C4C2414yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295#126—264no—
296#125—264no—
297#125—232no—
298#123—264no—
299C22⋊Q8—232no—
300C22⋊Q8—232no—
301C22⋊Q8—432no—
302C4×Q8—232no—
303C4×D4—232no—
304C4×D4—432no—
305C4×D4—432no—
306C4×D4—416no—
307#117—232no—
308#117—264no—
309C2×C4⋊C4—232no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
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—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4C2×D414yes—
357C2×C4⋊C4C2×D414yes—
358C2×C4⋊C4C2×D414yes—
359C2×C4⋊C4C2×D418yes—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D418yes—
362C2×C4⋊C4C2×D418yes—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4C2×D414yes—
410C2×C22⋊C4C2×D414yes—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42C2×D418yes—
422C2×C42C2×D414yes—
423C2×C42C2×D414yes—
424C2×C42C2×D414yes—
425C2×C42#4118yes—
426#95—22no—
427#95—22no—
428#95—24no—
429#95—24no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—28no—
434#95—28no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95—44no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—21no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24C22×D412yes—
476C24C22×D412yes—
477C24H(5,𝔽2)12yes—
478C242−1+414yes—
479C242−1+412yes—
480C24C2511yescharacteristic
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—28no—
484C2×Q8—48no—
485C2×Q8—48no—
486C2×D4—28no—
487C2×D4—216no—
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—44no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—44no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—44no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—216no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—24no—
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—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
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—28no—
560C22×C4—28no—
561C22×C4—216no—
562C22×C4—216no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4C22×D414yes—
604C22×C4C22×D414yes—
605C22×C4C22×D414yes—
606C22×C4C22×D412yes—
607C22×C4C22×D414yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C2×#4114yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4114yes—
621C22×C4H(5,𝔽2)14yes—
622C4⋊C4—216no—
623C4⋊C4—216no—
624C4⋊C4—216no—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—216no—
629C4⋊C4—28no—
630C4⋊C4—216no—
631C4⋊C4—216no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—416no—
636C4⋊C4—44no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—84no—
640C22⋊C4—216no—
641C22⋊C4—216no—
642C22⋊C4—216no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—416no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—416no—
651C22⋊C4—48no—
652C22⋊C4—88no—
653C22⋊C4—88no—
654C22⋊C4—88no—
655C22⋊C4—88no—
656C42—216no—
657C42—216no—
658C42—216no—
659C42—84no—
660C42#120116yes—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—41no—
686C23—41no—
687C23—42no—
688C23—41no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—41no—
698C23—42no—
699C23—41no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23#53714yes—
742C23C23×D411yescharacteristic
743C23C23×D411yescharacteristic
744C23C23×D411yescharacteristic
745C23C22×#4112yes—
746C23C2×H(5,𝔽2)12yes—
747C23C2×H(5,𝔽2)11yescharacteristic
748C23C2×2−1+411yescharacteristic
749C23C2×2−1+412yes—
750C23#58511yescharacteristic
751C23#58511yescharacteristic
752C23#58512yes—
753Q8—416no—
754D4—416no—
755D4—416no—
756D4—432no—
757D4—432no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—28no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—432no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
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—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—416no—
818C2×C4—416no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—816no—
841C2×C4C2×#12014yes—
842C2×C4C2×#12014yes—
843C2×C4C2×#12014yes—
844C2×C4#53214yes—
845C2×C4#53514yes—
846C2×C4#54618yes—
847C2×C4#55018yes—
848C22—24no—
849C22—28no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—44no—
854C22—42no—
855C22—42no—
856C22—44no—
857C22—44no—
858C22—42no—
859C22—44no—
860C22—44no—
861C22—42no—
862C22—44no—
863C22—44no—
864C22—42no—
865C22—42no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—81no—
872C22—81no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—81no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22C22×#12011yescharacteristic
886C22C2×#53211yescharacteristic
887C22C2×#53511yescharacteristic
888C22C2×#53711yescharacteristic
889C22#344911yescharacteristic
890C22C2×#54612yes—
891C22C2×#55012yes—
892C22#348611yescharacteristic
893C22#348711yescharacteristic
894C22#348811yescharacteristic
895C22#348811yescharacteristic
896C22#348911yescharacteristic
897C22#348912yes—
898C22#348912yes—
899C22#348911yescharacteristic
900C22#349212yes—
901C22#349312yes—
902C22#349512yes—
903C22#349512yes—
904C22#353812yes—
905C22#353912yes—
906C22#354112yes—
907C22#354212yes—
908C4—24no—
909C4—24no—
910C4—44no—
911C4—42no—
912C4—42no—
913C4—44no—
914C4—44no—
915C4—44no—
916C4—44no—
917C4—44no—
918C4—84no—
919C4—82no—
920C4—84no—
921C4#243118yes—
922C2—44no—
923C2—84no—
924C2—82no—
925C2C2×#243111yescharacteristic
926C2#3525111yescharacteristic
927C2#3565911yescharacteristic
928C2#3592611yescharacteristic
929C2#3606511yescharacteristic
930C2#3783712yes—
931C2#3784712yes—
932C2#4280811yescharacteristic
933C2#4288511yescharacteristic
934C2#4498012yes—
935C2#4543212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2397C2
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×#552C2semidirect
2. C2×#2538C2semidirect
3. C2×#2562C2semidirect
5. #16674C2semidirect
6. #16655C2semidirect
7. #15846C2semidirect
8. #15272C2semidirect
9. #15177C2semidirect
10. #15177C2semidirect
11. #14893C2semidirect
12. #14886C2semidirect
13. #14283C2semidirect
14. #13906C2semidirect
15. #13872C2semidirect
16. #13871C2semidirect
17. #13786C2semidirect
107. C2×#125D4semidirect
122. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#25382
C2×#25622
C2×#23972
#166742
#166552
#158462
#152722
#151772
#148932
#148862
#142832
#139062
#138722
#138712
#137862