Finite Group Databasebeta

← #687693

Subgroups — #687693

Order 512.

3410 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2565C211yesmaximal, characteristic, complemented
2C2×#2442C211yesmaximal, characteristic, complemented
3C2×#2341C211yesmaximal, characteristic
4C2×#2311C211yesmaximal, characteristic
5#16305C214yesmaximal, complemented
6#15355C214yesmaximal, complemented
7#15330C214yesmaximal, complemented
8#15244C211yesmaximal, characteristic, complemented
9#15229C211yesmaximal, characteristic, complemented
10#15134C211yesmaximal, characteristic, complemented
11#15134C211yesmaximal, characteristic, complemented
12#14774C214yesmaximal, complemented
13#14340C211yesmaximal, characteristic, complemented
14#13976C211yesmaximal, characteristic, complemented
15#13976C211yesmaximal, characteristic, complemented
16#13942C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic
18#13880C211yesmaximal, characteristic, complemented
19#13844C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26#2565—28no—
27#2442—28no—
28C2×#400C2212yes—
29C2×#398C2214yes—
30C2×#398C2212yes—
31C2×#396C2214yes—
32C2×#396C2214yes—
33#2341—28no—
34#2311—28no—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2212yes—
44C2×#390C2212yes—
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#387C2214yes—
50C2×#386C2214yes—
51C2×#385C2212yes—
52C2×#385C2214yes—
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2212yes—
61C2×#380C2212yes—
62C2×#380C2214yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2212yes—
67C2×C4×C22⋊C4C2211yescharacteristic
68#1444C2212yes—
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1442C2212yes—
73#1441C2214yes—
74#1441C2214yes—
75#1439C2214yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1438C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91#1434C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—42no—
100C22×#41—42no—
101C22×#41Q818yes—
102C23×Q8C2311yescharacteristic
103C23×D4C2311yescharacteristic
104C23×D4C2312yes—
105C24×C4C2312yes—
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C2×#125—24no—
109C2×#125—24no—
110C2×#125—42no—
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×#117—24no—
118C2×#117—24no—
119C2×#117—42no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#400—28no—
165#398—216no—
166#398—28no—
167#396—48no—
168#396—48no—
169#391—24no—
170#391—24no—
171#391—24no—
172#391D418yes—
173#390—24no—
174#390—28no—
175#390—28no—
176#390—24no—
177#390—24no—
178#390—24no—
179#390—42no—
180#390—42no—
181#389—24no—
182#389—24no—
183#387—216no—
184#386—216no—
185#385—28no—
186#385—48no—
187#384—24no—
188#384—42no—
189#384—42no—
190#382—24no—
191#382—24no—
192#380—24no—
193#380—24no—
194#380—28no—
195#380—216no—
196#380—28no—
197C4×C4⋊C4—24no—
198C4×C4⋊C4—42no—
199C4×C22⋊C4—24no—
200C4×C22⋊C4—28no—
201C4×C22⋊C4D418yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2311yescharacteristic
224C2×#95C2314yes—
225C2×#95C2311yescharacteristic
226C25C2412yes—
227C25C2411yescharacteristic
228C2×#41—232no—
229C2×#41—232no—
230C2×#41—416no—
231C2×#41—416no—
232C2×#41—416no—
233C2×#41—416no—
234C2×#41—416no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8C2×D414yes—
240C22×Q8C2×Q814yes—
241C22×Q8#4114yes—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—24no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4C2×Q814yes—
255C22×D4C2×Q818yes—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4C2×D414yes—
272C23×C4C2×Q818yes—
273C23×C4C2×Q814yes—
274C23×C4#4114yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292#125—416no—
293C4×Q8—416no—
294C4×Q8—416no—
295#117—416no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—416no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4C2×D414yes—
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—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4C2×D414yes—
385C2×C22⋊C4C2×D414yes—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42C2×D414yes—
408C2×C42C2×D414yes—
409C2×C42C2×D414yes—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—28no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—28no—
418#95—24no—
419#95—28no—
420#95—24no—
421#95—28no—
422#95—28no—
423#95—24no—
424#95—24no—
425#95—42no—
426#95—42no—
427#95—44no—
428#95—42no—
429#95—44no—
430#95—44no—
431#95C2×D414yes—
432#95C2×D414yes—
433#95C2×D4116yes—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—24no—
447C24—22no—
448C24—22no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24C22×D412yes—
453C24C22×Q814yes—
454C24C22×Q812yes—
455C24C2×#4112yes—
456C24C2511yescharacteristic
457#41—4128no—
458C2×Q8—28no—
459C2×Q8—28no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8C22⋊Q8116yes—
465C2×D4—216no—
466C2×D4—216no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—216no—
532C22×C4—216no—
533C22×C4—22no—
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—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—88no—
573C22×C4—84no—
574C22×C4—88no—
575C22×C4C22⋊Q8116yes—
576C22×C4C22×D412yes—
577C22×C4C22×D414yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D414yes—
581C22×C4C22×D412yes—
582C22×C4C22×D414yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×Q812yes—
587C22×C4C22×Q814yes—
588C22×C4C22×Q812yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4H(5,𝔽2)14yes—
594C22×C4H(5,𝔽2)12yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C42−1+414yes—
597C4⋊C4—28no—
598C4⋊C4—48no—
599C4⋊C4—416no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—84no—
613C4⋊C4—84no—
614C4⋊C4—88no—
615C4⋊C4—88no—
616C22⋊C4—216no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—88no—
624C22⋊C4—88no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C22⋊C4—84no—
630C42—28no—
631C42—28no—
632C42—28no—
633C42—48no—
634C42—48no—
635C42—44no—
636C42—44no—
637C42—44no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—28no—
656C23—28no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—42no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23C2×C22⋊Q814yes—
684C23C23×D411yescharacteristic
685C23C23×D411yescharacteristic
686C23C23×Q811yescharacteristic
687C23C22×#4111yescharacteristic
688C23C22×#4111yescharacteristic
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×H(5,𝔽2)11yescharacteristic
691C23C2×H(5,𝔽2)12yes—
692C23C2×2−1+412yes—
693C23#58512yes—
694C23#58512yes—
695Q8—232no—
696D4—432no—
697D4—416no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—232no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—28no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—432no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—816no—
791C2×C4C2×C22⋊Q814yes—
792C2×C4C2×C22⋊Q818yes—
793C2×C4C2×C22⋊Q814yes—
794C2×C4C2×C22⋊Q814yes—
795C2×C4#54314yes—
796C2×C4D4214yes—
797C2×C4#54614yes—
798C2×C4#54614yes—
799C2×C4#55114yes—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—42no—
808C22—42no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—48no—
814C22—44no—
815C22—48no—
816C22—82no—
817C22—82no—
818C22—84no—
819C22—84no—
820C22—82no—
821C22—82no—
822C22C22×C22⋊Q811yescharacteristic
823C22C22×C22⋊Q811yescharacteristic
824C22#344911yescharacteristic
825C22#344911yescharacteristic
826C22C2×#54311yescharacteristic
827C22C2×D4211yescharacteristic
828C22C2×#54611yescharacteristic
829C22C2×#54611yescharacteristic
830C22C2×#55111yescharacteristic
831C22#348812yes—
832C22#349212yes—
833C22#349712yes—
834C22#349811yescharacteristic
835C22#349911yescharacteristic
836C22#350312yes—
837C22#350412yes—
838C22#351212yes—
839C22#351612yes—
840C22#351712yes—
841C22#354212yes—
842C22#354612yes—
843C22#354712yes—
844C22#356112yes—
845C4—24no—
846C4—28no—
847C4—42no—
848C4—42no—
849C4—44no—
850C4—44no—
851C4—44no—
852C4—44no—
853C4—42no—
854C4—42no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4#243718yes—
862C2—44no—
863C2—84no—
864C2C2×#243711yescharacteristic
865C2#3533311yescharacteristic
866C2#3553211yescharacteristic
867C2#3581612yes—
868C2#3768111yescharacteristic
869C2#3808911yescharacteristic
870C2#3894611yescharacteristic
871C2#3935611yescharacteristic
872C2#4295412yes—
873C2#4491312yes—
874C2#4491812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
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×#2565C2semidirect
2. C2×#2442C2semidirect
5. #16305C2semidirect
6. #15355C2semidirect
7. #15330C2semidirect
8. #15244C2semidirect
9. #15229C2semidirect
10. #15134C2semidirect
11. #15134C2semidirect
12. #14774C2semidirect
13. #14340C2semidirect
14. #13976C2semidirect
15. #13976C2semidirect
16. #13942C2semidirect
18. #13880C2semidirect
19. #13844C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25652
C2×#24422
C2×#23412
C2×#23112
#163052
#153552
#153302
#152442
#152292
#151342
#147742
#143402
#139762
#139422
#139372
#138802
#138442