Finite Group Databasebeta

← #946431

Subgroups — #946431

Order 512.

3318 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2547C211yesmaximal, characteristic, complemented
2C2×#2436C211yesmaximal, characteristic
3C2×#2420C211yesmaximal, characteristic
4C2×#2434C211yesmaximal, characteristic, complemented
5#17097C214yesmaximal, complemented
6#16299C214yesmaximal, complemented
7#16267C214yesmaximal, complemented
8#15958C214yesmaximal, complemented
9#15243C211yesmaximal, characteristic, complemented
10#15241C211yesmaximal, characteristic, complemented
11#15215C211yesmaximal, characteristic
12#15188C211yesmaximal, characteristic, complemented
13#15184C211yesmaximal, characteristic, complemented
14#15182C211yesmaximal, characteristic, complemented
15#14274C211yesmaximal, characteristic, complemented
16#14273C211yesmaximal, characteristic, complemented
17#14027C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic, complemented
19#13842C211yesmaximal, characteristic, complemented
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×#124C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29#2547—28no—
30#2436—28no—
31#2434—28no—
32#2420—28no—
33C2×#397C2214yes—
34C2×#397C2212yes—
35C2×#395C2212yes—
36C2×#395C2212yes—
37C2×#394C2212yes—
38C2×#393C2214yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#386C2212yes—
54C2×#386C2214yes—
55C2×#385C2212yes—
56C2×#385C2212yes—
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#381C2212yes—
60C2×#380C2211yescharacteristic
61C2×#380C2214yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×#376C2211yescharacteristic
67#1446C2214yes—
68#1445C2214yes—
69#1445C2214yes—
70#1443C2212yes—
71#1443C2214yes—
72#1443C2214yes—
73#1442C2212yes—
74#1442C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1440C2212yes—
80#1440C2214yes—
81#1439C2212yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1439C2214yes—
86#1439C2214yes—
87#1439C2214yes—
88#1438C2214yes—
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×Q8C2312yes—
106C23×D4C2311yescharacteristic
107C23×D4C2312yes—
108C24×C4C2311yescharacteristic
109C24×C4C2312yes—
110C24×C4C2312yes—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—42no—
116C2×C4⋊Q8—42no—
117C2×#124—24no—
118C2×#124—24no—
119C2×#124—24no—
120C2×#124—42no—
121C2×#124—42no—
122C2×#124—42no—
123C2×#124—42no—
124C2×#124—42no—
125C2×#124D418yes—
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×#121—24no—
130C2×#121—24no—
131C2×#121—42no—
132C2×C4×D4—24no—
133C2×C4×D4—24no—
134C2×C4×D4—42no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#397—216no—
168#397—28no—
169#395—28no—
170#395—28no—
171#394—28no—
172#393—216no—
173#391—24no—
174#391—24no—
175#391—24no—
176#391—24no—
177#391—24no—
178#391—24no—
179#391—42no—
180#391—42no—
181#391—42no—
182#391—42no—
183#391—42no—
184#390—24no—
185#390—42no—
186#389—24no—
187#386—28no—
188#386—216no—
189#385—28no—
190#385—28no—
191#384—42no—
192#382—24no—
193#381—28no—
194#380—24no—
195#380—216no—
196C4×C4⋊C4—24no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—42no—
199C4×C22⋊C4D418yes—
200#376—42no—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C25C2412yes—
232C25C2411yescharacteristic
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—24no—
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×Q8—42no—
256C22×Q8—42no—
257C22×Q8—42no—
258C22×Q8—42no—
259C22×Q8—416no—
260C22×Q8—416no—
261C22×Q8—416no—
262C22×Q8—416no—
263C22×Q8—416no—
264C22×Q8—416no—
265C22×Q8—416no—
266C22×Q8C2×D414yes—
267C22×Q8#4114yes—
268C22×D4—24no—
269C22×D4—24no—
270C22×D4—28no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—42no—
278C22×D4—44no—
279C22×D4C2×D414yes—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—28no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—44no—
298C23×C4C2×D414yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C4⋊Q8—416no—
317C4⋊Q8—416no—
318#124—416no—
319#124—416no—
320#124—416no—
321C22⋊Q8—416no—
322#121—416no—
323C4×D4—416no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
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—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
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—42no—
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×D414yes—
394C2×C22⋊C4C2×D414yes—
395C2×C22⋊C4C2×D4116yes—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42C2×D414yes—
412C2×C42C2×D414yes—
413C2×C42C2×D414yes—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—28no—
418#95—28no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—28no—
427#95—28no—
428#95—24no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—44no—
433#95—44no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—44no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95C2×D414yes—
443#95C2×D414yes—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—24no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24C22×D414yes—
464C24C22×D412yes—
465C242−1+414yes—
466C24C2511yescharacteristic
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—28no—
472C2×Q8—28no—
473C2×Q8—48no—
474C2×Q8—48no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×Q8—4128no—
480C2×Q8—48no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
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×Q8—44no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—48no—
500C2×D4—416no—
501C2×D4—48no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—84no—
507C2×D4—88no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
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—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—22no—
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—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
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—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—416no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—48no—
612C22×C4—84no—
613C22×C4—88no—
614C22×C4C22×D414yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D414yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C2×#4114yes—
624C22×C4C2×#4112yes—
625C22×C4H(5,𝔽2)12yes—
626C22×C4H(5,𝔽2)12yes—
627C22×C4H(5,𝔽2)12yes—
628C22×C4H(5,𝔽2)12yes—
629C22×C42−1+414yes—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—84no—
641C4⋊C4—88no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—416no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—416no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—416no—
652C22⋊C4—84no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—88no—
656C42—28no—
657C42—28no—
658C42—28no—
659C42—44no—
660C42—44no—
661C42—44no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—28no—
678C23—28no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—44no—
697C23—44no—
698C23—42no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23#53614yes—
708C23C23×D411yescharacteristic
709C23C23×D411yescharacteristic
710C23C22×#4111yescharacteristic
711C23C2×H(5,𝔽2)11yescharacteristic
712C23C2×H(5,𝔽2)11yescharacteristic
713C23C2×H(5,𝔽2)11yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×2−1+412yes—
716C23C2×2−1+412yes—
717C23#58512yes—
718C23#58512yes—
719Q8—432no—
720Q8—416no—
721Q8—416no—
722Q8—88no—
723D4—416no—
724D4—816no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—432no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—416no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
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—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
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—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—816no—
823C2×C4#53414yes—
824C2×C4#53514yes—
825C2×C4#53614yes—
826C2×C4#53814yes—
827C2×C4D4214yes—
828C2×C4#54614yes—
829C2×C4#54614yes—
830C2×C4#56014yes—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—44no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—44no—
839C22—42no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—48no—
846C22—48no—
847C22—84no—
848C22—82no—
849C22—82no—
850C22—84no—
851C22—82no—
852C22—82no—
853C22C2×#53411yescharacteristic
854C22C2×#53511yescharacteristic
855C22C2×#53611yescharacteristic
856C22C2×#53611yescharacteristic
857C22C2×#53811yescharacteristic
858C22C2×D4211yescharacteristic
859C22C2×#54611yescharacteristic
860C22C2×#54611yescharacteristic
861C22#348912yes—
862C22#348912yes—
863C22#350011yescharacteristic
864C22#350011yescharacteristic
865C22#351612yes—
866C22#351812yes—
867C22C2×#56011yescharacteristic
868C22#354112yes—
869C22#354712yes—
870C22#355212yes—
871C22#355212yes—
872C22#356112yes—
873C22#356112yes—
874C22#356212yes—
875C22#356212yes—
876C4—24no—
877C4—42no—
878C4—42no—
879C4—44no—
880C4—42no—
881C4—44no—
882C4—44no—
883C4—42no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4#267818yes—
893C2—44no—
894C2—84no—
895C2#3742211yescharacteristic
896C2#3761711yescharacteristic
897C2#3767611yescharacteristic
898C2#3767611yescharacteristic
899C2#3808511yescharacteristic
900C2#3895811yescharacteristic
901C2#4284712yes—
902C2#4292612yes—
903C2#4530712yes—
904C2C2×#267811yescharacteristic
905C2#5302212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2547C2semidirect
4. C2×#2434C2semidirect
5. #17097C2semidirect
6. #16299C2semidirect
7. #16267C2semidirect
8. #15958C2semidirect
9. #15243C2semidirect
10. #15241C2semidirect
12. #15188C2semidirect
13. #15184C2semidirect
14. #15182C2semidirect
15. #14274C2semidirect
16. #14273C2semidirect
17. #14027C2semidirect
18. #13922C2semidirect
19. #13842C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25472
C2×#24362
C2×#24202
C2×#24342
#170972
#162992
#162672
#159582
#152432
#152412
#152152
#151882
#151842
#151822
#142742
#142732
#140272
#139222
#138422