Finite Group Databasebeta

← #609836

Subgroups — #609836

Order 512.

2962 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2392C211yesmaximal, characteristic
2C2×#2285C211yesmaximal, characteristic, complemented
3#15945C211yesmaximal, characteristic, complemented
4#15943C212yesmaximal, complemented
5#15941C211yesmaximal, characteristic, complemented
6#15790C211yesmaximal, characteristic, complemented
7#15771C212yesmaximal, complemented
8#15643C211yesmaximal, characteristic, complemented
9#15487C212yesmaximal, complemented
10#15474C212yesmaximal, complemented
11#15304C212yesmaximal
12#15291C212yesmaximal, complemented
13C4×#400C212yesmaximal, complemented
14C4×#394C212yesmaximal, complemented
15#13842C212yesmaximal, complemented
16#13839C212yesmaximal, complemented
17C4×#388C212yesmaximal, complemented
18C4×#386C212yesmaximal, complemented
19#13761C211yesmaximal, characteristic, complemented
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C42C2211yescharacteristic
25C2×#400C2212yes—
26#2392—28no—
27C2×#398C2211yescharacteristic
28C2×#397C2211yescharacteristic
29C2×#396C2212yes—
30C2×#394C2212yes—
31C2×#394C2211yescharacteristic
32C2×#394C2212yes—
33C2×#392C2211yescharacteristic
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38#2285—28no—
39C2×#384C2211yescharacteristic
40C2×#384C2211yescharacteristic
41C2×#382C2211yescharacteristic
42C2×#382C2211yescharacteristic
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C4⋊C4C2212yes—
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2212yes—
50C2×C4×C22⋊C4C2212yes—
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53C2×C4×C22⋊C4C2212yes—
54C2×#376C2211yescharacteristic
55C2×C43C2211yescharacteristic
56#1445C2212yes—
57#1443C2212yes—
58#1443C2212yes—
59#1443C2212yes—
60#1443C2212yes—
61#1442C2212yes—
62#1442C2212yes—
63#1442C2212yes—
64#1442C2212yes—
65#1442C2212yes—
66#1442C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2212yes—
70#1441C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1438C2212yes—
84#1438C2212yes—
85#1438C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1437C2211yescharacteristic
91#1437C2212yes—
92#1437C2211yescharacteristic
93#1436C2211yescharacteristic
94#1436C2211yescharacteristic
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100#1434C2212yes—
101#1434C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C4×#95C2212yes—
105C4×#95C2212yes—
106C4×#95C2212yes—
107C4×#95C2212yes—
108C4×#95C2212yes—
109C23×D4C2312yes—
110C23×D4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C2×C4×D4—28no—
115C2×C4×D4—28no—
116C2×C4×D4—28no—
117C2×C4×D4—24no—
118C2×C4×D4—42no—
119C2×C4×D4—42no—
120C2×#117—24no—
121C2×#117—42no—
122C2×#117—42no—
123C2×#117—42no—
124C2×#117—42no—
125C2×#117D418yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2311yescharacteristic
155C22×C42—24no—
156C22×C42—28no—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2311yescharacteristic
169#400—28no—
170#398—24no—
171#397—24no—
172#396—28no—
173#394—24no—
174#394—28no—
175#394—28no—
176#392—24no—
177#388—28no—
178#388—28no—
179#386—28no—
180#386—28no—
181#384—24no—
182#384—24no—
183#382—24no—
184#382—24no—
185#380—28no—
186#380—28no—
187C4×C4⋊C4—24no—
188C4×C4⋊C4—28no—
189C4×C4⋊C4—28no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4—28no—
192C4×C22⋊C4—28no—
193C4×C22⋊C4—28no—
194C4×C22⋊C4—44no—
195C4×C22⋊C4—44no—
196#376—42no—
197C2×#95C2311yescharacteristic
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2312yes—
234C2×#95C2311yescharacteristic
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C43—42no—
239C25C2412yes—
240C25C2411yescharacteristic
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—24no—
248C22×D4—41no—
249C22×D4—41no—
250C22×D4—42no—
251C22×D4—42no—
252C22×D4—42no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4C2×D414yes—
271C23×C4#4118yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C4×D4—416no—
290C4×D4—432no—
291#117—416no—
292#117—416no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4C2×D414yes—
325C2×C4⋊C4C2×D414yes—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4C2×D414yes—
379C2×C22⋊C4#4118yes—
380C2×C42—232no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—41no—
406C2×C42—42no—
407C2×C42—41no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42C2×D414yes—
411C2×C42C2×D414yes—
412C2×C42#4118yes—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—22no—
420#95—22no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—41no—
447#95—42no—
448#95—41no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95#4118yes—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24C22×D412yes—
476C24C2×#4114yes—
477C24C2×#4114yes—
478C24C2511yescharacteristic
479C2×D4—216no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—44no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—44no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—44no—
490C2×D4—48no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—216no—
501C22×C4—216no—
502C22×C4—216no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
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—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
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—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
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—22no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4#124116yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4114yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4114yes—
610C22×C4C2×#4114yes—
611C22×C4C2×#4114yes—
612C22×C4C2×#4114yes—
613C22×C4C2×#4114yes—
614C22×C4C2×#4114yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C4H(5,𝔽2)12yes—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—48no—
628C22⋊C4—216no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C42—28no—
647C42—28no—
648C42—216no—
649C42—28no—
650C42—28no—
651C42—44no—
652C42—48no—
653C42—44no—
654C42—48no—
655C42—48no—
656C42—48no—
657C42—48no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—41no—
683C23—41no—
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—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23C2×#12414yes—
714C23C23×D411yescharacteristic
715C23C22×#4112yes—
716C23C22×#4112yes—
717C23C22×#4112yes—
718C23C22×#4112yes—
719C23C2×H(5,𝔽2)11yescharacteristic
720C23C2×H(5,𝔽2)11yescharacteristic
721C23#58512yes—
722C23#58512yes—
723D4—432no—
724D4—416no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—232no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—432no—
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—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
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—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—816no—
828C2×C4#52514yes—
829C2×C4C2×#12414yes—
830C2×C4C2×#12414yes—
831C2×C4#52918yes—
832C2×C4#53414yes—
833C2×C4#55318yes—
834C2×C4#55318yes—
835C22—24no—
836C22—28no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—42no—
842C22—42no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22C2×#52511yescharacteristic
860C22C22×#12411yescharacteristic
861C22C2×#52912yes—
862C22#344412yes—
863C22C2×#53411yescharacteristic
864C22#345512yes—
865C22#345512yes—
866C22#346012yes—
867C22#346012yes—
868C22D4×#4112yes—
869C22D4×#4112yes—
870C22C2×#55312yes—
871C22C2×#55312yes—
872C22#347512yes—
873C22#347512yes—
874C22#347512yes—
875C22#347512yes—
876C22#348111yescharacteristic
877C22#348311yescharacteristic
878C22#352911yescharacteristic
879C22#352911yescharacteristic
880C4—24no—
881C4—28no—
882C4—44no—
883C4—44no—
884C4—44no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—44no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4#259118yes—
897C2—44no—
898C2—84no—
899C2#3474012yes—
900C2#3479712yes—
901C2#3481312yes—
902C2C2×#259111yescharacteristic
903C2#3491712yes—
904C2#5216511yescharacteristic
905C2#5216711yescharacteristic
906C2#5224212yes—
907C2#5224212yes—
subgroupG/H
centerC23×C4C24
commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2285C2semidirect
3. #15945C2semidirect
4. #15943C2semidirect
5. #15941C2semidirect
6. #15790C2semidirect
7. #15771C2semidirect
8. #15643C2semidirect
9. #15487C2semidirect
10. #15474C2semidirect
12. #15291C2semidirect
13. C4×#400C2semidirect
14. C4×#394C2semidirect
15. #13842C2semidirect
16. #13839C2semidirect
17. C4×#388C2semidirect
18. C4×#386C2semidirect
19. #13761C2semidirect

Maximal subgroups

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

subgroupindex
C2×#23922
C2×#22852
#159452
#159432
#159412
#157902
#157712
#156432
#154872
#154742
#153042
#152912
C4×#4002
C4×#3942
#138422
#138392
C4×#3882
C4×#3862
#137612