Finite Group Databasebeta

← #696743

Subgroups — #696743

Order 512.

3800 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2C2×#2502C211yesmaximal, characteristic, complemented
3C2×#2415C211yesmaximal, characteristic
4C2×#2621C211yesmaximal, characteristic, complemented
5#16657C214yesmaximal
6#15912C214yesmaximal, complemented
7#15848C214yesmaximal, complemented
8#15238C211yesmaximal, characteristic, complemented
9#15228C211yesmaximal, characteristic, complemented
10#15182C211yesmaximal, characteristic, complemented
11#15178C211yesmaximal, characteristic, complemented
12#14892C214yesmaximal, complemented
13#14138C211yesmaximal, characteristic, complemented
14#14138C211yesmaximal, characteristic, complemented
15#14024C211yesmaximal, characteristic, complemented
16#13976C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18#13839C211yesmaximal, characteristic
19#13795C211yesmaximal, 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
36C22×#117C2211yescharacteristic
37C22×#117C2211yescharacteristic
38C23×C4⋊C4C2211yescharacteristic
39#2621—28no—
40#2502—28no—
41#2415—28no—
42C2×#398C2214yes—
43C2×#398C2214yes—
44C2×#397C2214yes—
45C2×#397C2212yes—
46C2×#394C2212yes—
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2212yes—
56C2×#388C2212yes—
57C2×#385C2214yes—
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#382C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65#1444C2214yes—
66#1444C2214yes—
67#1444C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1441C2212yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1440C2212yes—
75#1440C2214yes—
76#1440C2214yes—
77#1439C2212yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2212yes—
82#1436C2214yes—
83#1436C2214yes—
84#1436C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87C4⋊#95C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C22⋊#95C2214yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103#552—2128no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—42no—
107C2×#126—28no—
108C2×#126—28no—
109C2×#126—28no—
110C2×#125—28no—
111C2×#125—28no—
112C2×#125—28no—
113C2×#125—24no—
114C2×#125—24no—
115C2×#125—24no—
116C2×#123—28no—
117C2×#123—28no—
118C2×#123—28no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
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—42no—
130C2×C22⋊Q8D418yes—
131C2×C4×Q8—24no—
132C2×C4×Q8—24no—
133C2×C4×Q8—24no—
134C2×C4×D4—24no—
135C2×C4×D4—24no—
136C2×C4×D4D418yes—
137C2×#117—24no—
138C2×#117—28no—
139C2×#117—24no—
140C2×#117—24no—
141C2×#117—24no—
142C2×#117—24no—
143C2×#117—24no—
144C2×#117—28no—
145C2×#117—28no—
146C2×#117—24no—
147C2×#117—42no—
148C2×#117—42no—
149C22×C4⋊C4—24no—
150C22×C4⋊C4—24no—
151C22×C4⋊C4D418yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2314yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2314yes—
171C22×C4⋊C4C2314yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C42C2312yes—
186C22×C42C2312yes—
187C22×C42C2311yescharacteristic
188C22×C42C2311yescharacteristic
189C22×C42C2311yescharacteristic
190C22×C42C2312yes—
191C22×C42C2311yescharacteristic
192C22×C42C2311yescharacteristic
193#398—216no—
194#398—216no—
195#397—216no—
196#397—28no—
197#394—28no—
198#391—24no—
199#391—24no—
200#391—24no—
201#391—24no—
202#391—24no—
203#391—24no—
204#391—42no—
205#389—28no—
206#389—24no—
207#388—28no—
208#385—216no—
209#384—24no—
210#384—24no—
211#382—24no—
212#380—24no—
213C4×C22⋊C4—24no—
214C4×C22⋊C4—24no—
215C4×C22⋊C4—42no—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2312yes—
240C25C2411yescharacteristic
241C25C2411yescharacteristic
242C22×Q8—22no—
243C22×Q8—22no—
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×Q8C2×D414yes—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4C2×D414yes—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2×D418yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C4⋊Q8—416no—
298#126—264no—
299#125—264no—
300#125—232no—
301#123—264no—
302C22⋊Q8—232no—
303C22⋊Q8—232no—
304C22⋊Q8—416no—
305C22⋊Q8—416no—
306C4×Q8—232no—
307C4×D4—232no—
308#117—232no—
309#117—264no—
310#117—416no—
311#117—416no—
312C2×C4⋊C4—232no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
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—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4C2×D414yes—
366C2×C4⋊C4C2×D414yes—
367C2×C4⋊C4C2×D418yes—
368C2×C4⋊C4C2×D414yes—
369C2×C4⋊C4C2×D414yes—
370C2×C4⋊C4C2×D418yes—
371C2×C4⋊C4#4114yes—
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—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
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—24no—
391C2×C22⋊C4—24no—
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—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4C2×D414yes—
408C2×C22⋊C4C2×D418yes—
409C2×C22⋊C4C2×D414yes—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—42no—
432C2×C42C2×D414yes—
433C2×C42#4114yes—
434#95—24no—
435#95—24no—
436#95—28no—
437#95—28no—
438#95—28no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—28no—
443#95—28no—
444#95—24no—
445#95—28no—
446#95—24no—
447#95—28no—
448#95—24no—
449#95—28no—
450#95—42no—
451#95—44no—
452#95—44no—
453#95—44no—
454#95—42no—
455#95—44no—
456#95—42no—
457#95—44no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—22no—
463C24—21no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24C22×D412yes—
477C24C22×D412yes—
478C24C22×D412yes—
479C24C22×D412yes—
480C24C2511yescharacteristic
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—28no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×D4—28no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—48no—
499C2×D4—48no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—216no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—22no—
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—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—416no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—416no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4#120116yes—
601C22×C4C22×D412yes—
602C22×C4C22×D414yes—
603C22×C4C22×D414yes—
604C22×C4C22×D412yes—
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×C4C2×#4114yes—
615C22×C4C2×#4114yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4H(5,𝔽2)12yes—
619C22×C42−1+414yes—
620C22×C42−1+414yes—
621C22×C42−1+412yes—
622C4⋊C4—216no—
623C4⋊C4—216no—
624C4⋊C4—216no—
625C4⋊C4—216no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—216no—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—216no—
632C4⋊C4—28no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—416no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—48no—
639C4⋊C4—44no—
640C4⋊C4—88no—
641C4⋊C4—88no—
642C22⋊C4—216no—
643C22⋊C4—216no—
644C22⋊C4—216no—
645C22⋊C4—28no—
646C22⋊C4—216no—
647C22⋊C4—28no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C42—216no—
656C42—216no—
657C42—28no—
658C42—28no—
659C42—48no—
660C42—44no—
661C42—44no—
662C42—44no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23C2×#12014yes—
709C23C23×D411yescharacteristic
710C23C23×D411yescharacteristic
711C23C23×D411yescharacteristic
712C23C22×#4111yescharacteristic
713C23C22×#4111yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×2−1+411yescharacteristic
716C23C2×2−1+412yes—
717C23C2×2−1+412yes—
718C23#58512yes—
719C23#58512yes—
720Q8—416no—
721Q8—88no—
722D4—416no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—232no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—432no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—416no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
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—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4C2×#12014yes—
822C2×C4C2×#12014yes—
823C2×C4#53214yes—
824C2×C4#53714yes—
825C2×C4#54614yes—
826C2×C4#54614yes—
827C2×C4#54714yes—
828C2×C4#54714yes—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22C22×#12011yescharacteristic
852C22C2×#53211yescharacteristic
853C22C2×#53711yescharacteristic
854C22#344911yescharacteristic
855C22#344911yescharacteristic
856C22C2×#54611yescharacteristic
857C22C2×#54611yescharacteristic
858C22C2×#54711yescharacteristic
859C22C2×#54711yescharacteristic
860C22#348512yes—
861C22#348612yes—
862C22#348712yes—
863C22#349512yes—
864C22#349911yescharacteristic
865C22#349911yescharacteristic
866C22#349912yes—
867C22#350712yes—
868C22#351512yes—
869C22#351612yes—
870C22#354112yes—
871C22#354712yes—
872C22#355512yes—
873C22#356312yes—
874C4—24no—
875C4—44no—
876C4—44no—
877C4—42no—
878C4—42no—
879C4—44no—
880C4—42no—
881C4—44no—
882C4—44no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4#243018yes—
891C2—44no—
892C2—82no—
893C2C2×#243011yescharacteristic
894C2#3514911yescharacteristic
895C2#3566611yescharacteristic
896C2#3577312yes—
897C2#3786811yescharacteristic
898C2#3808811yescharacteristic
899C2#3894611yescharacteristic
900C2#3948411yescharacteristic
901C2#4267512yes—
902C2#4523712yes—
903C2#4523812yes—
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×#2502C2semidirect
4. C2×#2621C2semidirect
6. #15912C2semidirect
7. #15848C2semidirect
8. #15238C2semidirect
9. #15228C2semidirect
10. #15182C2semidirect
11. #15178C2semidirect
12. #14892C2semidirect
13. #14138C2semidirect
14. #14138C2semidirect
15. #14024C2semidirect
16. #13976C2semidirect
17. #13879C2semidirect
19. #13795C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#25022
C2×#24152
C2×#26212
#166572
#159122
#158482
#152382
#152282
#151822
#151782
#148922
#141382
#140242
#139762
#138792
#138392
#137952