Finite Group Databasebeta

← #657605

Subgroups — #657605

Order 512.

4104 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2C2×#2857C211yesmaximal, characteristic, complemented
3C2×#2503C211yesmaximal, characteristic, complemented
4C2×#2417C211yesmaximal, characteristic
5#15940C214yesmaximal, complemented
6#15847C214yesmaximal, complemented
7#15238C211yesmaximal, characteristic, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15228C211yesmaximal, characteristic, complemented
10#15178C211yesmaximal, characteristic, complemented
11#14927C214yesmaximal
12#14139C211yesmaximal, characteristic, complemented
13#14138C211yesmaximal, characteristic, complemented
14#14024C211yesmaximal, characteristic, complemented
15#13978C211yesmaximal, characteristic, complemented
16#13879C211yesmaximal, characteristic, complemented
17#13878C214yesmaximal, complemented
18C4×#386C211yesmaximal, characteristic
19C2×C4⋊#95C211yesmaximal, characteristic, complemented
20C2×#552—28no—
21C2×#552—28no—
22C2×#552—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#126C2212yes—
25C22×#125C2211yescharacteristic
26C22×#125C2212yes—
27C22×#123C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×#117C2212yes—
35C22×#117C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38C23×C42C2211yescharacteristic
39#2857—28no—
40#2503—28no—
41#2417—28no—
42C2×#400C2214yes—
43C2×#398C2212yes—
44C2×#396C2212yes—
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#389C2214yes—
53C2×#389C2211yescharacteristic
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#384C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#381C2214yes—
60C2×#380C2214yes—
61C2×#380C2212yes—
62C2×#380C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C22×#95C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1440C2214yes—
77#1440C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1437C2212yes—
81#1436C2214yes—
82#1436C2214yes—
83#1436C2214yes—
84#1436C2214yes—
85#1436C2212yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C22⋊#95C2212yes—
94C22⋊#95C2214yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104C24×C4C2311yescharacteristic
105#552—2128no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—42no—
109C2×#126—28no—
110C2×#126—28no—
111C2×#126—28no—
112C2×#125—28no—
113C2×#125—28no—
114C2×#125—28no—
115C2×#125—24no—
116C2×#125—24no—
117C2×#125—24no—
118C2×#123—28no—
119C2×#123—28no—
120C2×#123—28no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—42no—
132C2×C22⋊Q8D418yes—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×D4—24no—
137C2×C4×D4—24no—
138C2×C4×D4D418yes—
139C2×#117—24no—
140C2×#117—28no—
141C2×#117—24no—
142C2×#117—24no—
143C2×#117—28no—
144C2×#117—28no—
145C22×C4⋊C4—24no—
146C22×C4⋊C4—24no—
147C22×C4⋊C4—24no—
148C22×C4⋊C4—24no—
149C22×C4⋊C4—42no—
150C22×C4⋊C4D418yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2314yes—
161C22×C4⋊C4C2314yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C42—24no—
182C22×C42—24no—
183C22×C42—42no—
184C22×C42C2311yescharacteristic
185C22×C42C2312yes—
186C22×C42C2312yes—
187C22×C42C2311yescharacteristic
188C22×C42C2311yescharacteristic
189C22×C42C2312yes—
190C22×C42C2311yescharacteristic
191C22×C42C2311yescharacteristic
192#400—216no—
193#398—28no—
194#396—28no—
195#391—24no—
196#391—24no—
197#391—24no—
198#391—24no—
199#391—24no—
200#391—24no—
201#391—42no—
202#389—216no—
203#389—24no—
204#386—28no—
205#386—28no—
206#384—24no—
207#382—24no—
208#382—24no—
209#381—216no—
210#380—24no—
211#380—216no—
212#380—28no—
213C4×C22⋊C4—24no—
214C4×C22⋊C4—24no—
215C4×C22⋊C4—42no—
216C2×#95—216no—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2312yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2312yes—
241C2×#95C2314yes—
242C25C2411yescharacteristic
243C25C2411yescharacteristic
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8C2×D414yes—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4C2×D414yes—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—28no—
271C23×C4—24no—
272C23×C4—28no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—28no—
283C23×C4—24no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—44no—
288C23×C4C2×D418yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4#4118yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2412yes—
305C23×C4C2411yescharacteristic
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2411yescharacteristic
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C4⋊Q8—416no—
312#126—264no—
313#125—264no—
314#125—232no—
315#123—264no—
316C22⋊Q8—232no—
317C22⋊Q8—232no—
318C22⋊Q8—416no—
319C22⋊Q8—416no—
320C4×Q8—232no—
321C4×D4—232no—
322#117—232no—
323#117—264no—
324C2×C4⋊C4—232no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
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—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—416no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D414yes—
377C2×C4⋊C4C2×D418yes—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4C2×D418yes—
381C2×C4⋊C4#4114yes—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4C2×D414yes—
412C2×C22⋊C4C2×D418yes—
413C2×C22⋊C4C2×D414yes—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—24no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—24no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—416no—
436C2×C42—42no—
437C2×C42C2×D414yes—
438C2×C42#4114yes—
439#95—24no—
440#95—24no—
441#95—28no—
442#95—28no—
443#95—24no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—24no—
449#95—24no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—28no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—28no—
458#95—24no—
459#95—44no—
460#95—44no—
461#95—42no—
462#95—42no—
463#95—44no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—21no—
476C24—22no—
477C24—21no—
478C24—22no—
479C24—22no—
480C24C22×D412yes—
481C24C22×D412yes—
482C24C22×D412yes—
483C24C22×D412yes—
484C24C2×#4114yes—
485C242−1+414yes—
486C24C2511yescharacteristic
487C2×Q8—28no—
488C2×Q8—28no—
489C2×Q8—28no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—28no—
504C2×D4—48no—
505C2×D4—48no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—216no—
521C22×C4—232no—
522C22×C4—216no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—216no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—416no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—416no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—48no—
615C22×C4—84no—
616C22×C4—88no—
617C22×C4#120116yes—
618C22×C4C22×D414yes—
619C22×C4C22×D412yes—
620C22×C4C22×D414yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D414yes—
624C22×C4C22×D414yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C2×#4114yes—
632C22×C4C2×#4114yes—
633C22×C4C2×#4114yes—
634C22×C4C2×#4114yes—
635C22×C4C2×#4112yes—
636C22×C4C2×#4112yes—
637C22×C4H(5,𝔽2)12yes—
638C22×C42−1+414yes—
639C22×C42−1+412yes—
640C4⋊C4—216no—
641C4⋊C4—216no—
642C4⋊C4—216no—
643C4⋊C4—216no—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—216no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—216no—
650C4⋊C4—28no—
651C4⋊C4—416no—
652C4⋊C4—48no—
653C4⋊C4—48no—
654C4⋊C4—416no—
655C4⋊C4—44no—
656C4⋊C4—48no—
657C4⋊C4—44no—
658C4⋊C4—84no—
659C22⋊C4—216no—
660C22⋊C4—216no—
661C22⋊C4—28no—
662C22⋊C4—216no—
663C22⋊C4—28no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—84no—
670C42—216no—
671C42—216no—
672C42—28no—
673C42—28no—
674C42—48no—
675C42—44no—
676C42—44no—
677C42—44no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—22no—
690C23—22no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23C2×#12014yes—
720C23#53214yes—
721C23#53614yes—
722C23#54718yes—
723C23#54818yes—
724C23C23×D411yescharacteristic
725C23C23×D411yescharacteristic
726C23C23×D411yescharacteristic
727C23C22×#4111yescharacteristic
728C23C22×#4111yescharacteristic
729C23C22×#4112yes—
730C23C2×H(5,𝔽2)11yescharacteristic
731C23C2×2−1+412yes—
732C23C2×2−1+411yescharacteristic
733C23C2×2−1+412yes—
734C23#58512yes—
735Q8—416no—
736Q8—88no—
737D4—416no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—232no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—432no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—432no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—416no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
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—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—816no—
837C2×C4C2×#12014yes—
838C2×C4C2×#12014yes—
839C2×C4#53214yes—
840C2×C4#53714yes—
841C2×C4#54614yes—
842C2×C4#54614yes—
843C2×C4#54714yes—
844C2×C4#54714yes—
845C2×C4#55218yescomplemented
846C22—24no—
847C22—28no—
848C22—24no—
849C22—24no—
850C22—28no—
851C22—28no—
852C22—24no—
853C22—24no—
854C22—28no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22#243218yes—
868C22C22×#12011yescharacteristic
869C22C2×#53211yescharacteristic
870C22C2×#53211yescharacteristic
871C22C2×#53611yescharacteristic
872C22C2×#53711yescharacteristic
873C22C2×#54611yescharacteristic
874C22C2×#54611yescharacteristic
875C22C2×#54712yes—
876C22C2×#54711yescharacteristic
877C22C2×#54711yescharacteristic
878C22C2×#54812yes—
879C22C2×#55212yes—
880C22#347512yes—
881C22#348912yes—
882C22#349512yes—
883C22#349712yes—
884C22#349911yescharacteristic
885C22#350011yescharacteristic
886C22#350512yes—
887C22#350912yes—
888C22#352312yes—
889C22#353812yes—
890C22#356312yes—
891C4—28no—
892C4—24no—
893C4—44no—
894C4—42no—
895C4—44no—
896C4—44no—
897C4—44no—
898C4—44no—
899C4—42no—
900C4—42no—
901C4—44no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4#243018yes—
908C2—28no—
909C2—82no—
910C2C2×#243211yescharacteristic
911C2C2×#243011yescharacteristic
912C2#3566011yescharacteristic
913C2#3618111yescharacteristic
914C2#3618612yes—
915C2#3638611yescharacteristic
916C2#3786511yescharacteristic
917C2#3808111yescharacteristic
918C2#3948712yes—
919C2#5901412yes—
920C2#5911112yes—
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
2. C2×#2857C2semidirect
3. C2×#2503C2semidirect
5. #15940C2semidirect
6. #15847C2semidirect
7. #15238C2semidirect
8. #15236C2semidirect
9. #15228C2semidirect
10. #15178C2semidirect
12. #14139C2semidirect
13. #14138C2semidirect
14. #14024C2semidirect
15. #13978C2semidirect
16. #13879C2semidirect
17. #13878C2semidirect
19. C2×C4⋊#95C2semidirect
845. C2×C4#552semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#28572
C2×#25032
C2×#24172
#159402
#158472
#152382
#152362
#152282
#151782
#149272
#141392
#141382
#140242
#139782
#138792
#138782
C4×#3862
C2×C4⋊#952