Finite Group Databasebeta

← #705202

Subgroups — #705202

Order 512.

3068 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2416C211yesmaximal, characteristic
2C2×#2352C211yesmaximal, characteristic, complemented
3#16441C214yesmaximal, complemented
4#15967C214yesmaximal, complemented
5#15277C214yesmaximal, complemented
6#15239C211yesmaximal, characteristic, complemented
7#15224C211yesmaximal, characteristic, complemented
8#15150C211yesmaximal, characteristic, complemented
9#15130C211yesmaximal, characteristic, complemented
10#14741C214yesmaximal, complemented
11#14257C211yesmaximal, characteristic, complemented
12#14137C211yesmaximal, characteristic, complemented
13#14136C211yesmaximal, characteristic, complemented
14#14048C211yesmaximal, characteristic, complemented
15#14001C211yesmaximal, characteristic, complemented
16#13924C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13839C211yesmaximal, characteristic, complemented
19#13795C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2416—28no—
29C2×#397C2214yes—
30C2×#396C2212yes—
31C2×#394C2212yes—
32C2×#394C2214yes—
33#2352—28no—
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#388C2212yes—
41C2×#388C2214yes—
42C2×#387C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2214yes—
46C2×#385C2214yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#382C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58#1445C2214yes—
59#1445C2214yes—
60#1444C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1441C2212yes—
64#1441C2214yes—
65#1440C2212yes—
66#1440C2214yes—
67#1440C2214yes—
68#1439C2212yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1438C2212yes—
74#1438C2214yes—
75#1438C2214yes—
76#1437C2214yes—
77#1436C2214yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×D4C2311yescharacteristic
94C23×D4C2312yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2312yes—
101C2×#121—28no—
102C2×#121—24no—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#121—48no—
108C2×#121—42no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4D418yes—
112C2×#117—24no—
113C2×#117—24no—
114C2×#117—24no—
115C2×#117—42no—
116C2×#117—42no—
117C2×#117—42no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊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⋊C4C2314yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163#397—48no—
164#396—28no—
165#394—28no—
166#394—48no—
167#390—24no—
168#390—24no—
169#390—42no—
170#390—42no—
171#390—42no—
172#389—24no—
173#388—28no—
174#388—48no—
175#387—28no—
176#386—28no—
177#386—28no—
178#386—48no—
179#385—48no—
180#384—24no—
181#384—42no—
182#382—24no—
183#380—24no—
184#380—24no—
185#380—24no—
186C4×C4⋊C4—24no—
187C4×C22⋊C4—24no—
188C4×C22⋊C4—28no—
189C4×C22⋊C4—42no—
190C4×C22⋊C4—42no—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C25C2411yescharacteristic
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—28no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4—44no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4C2×D414yes—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—44no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4C2×D414yes—
261C23×C4C2×D414yes—
262C23×C4#4114yes—
263C23×C4#4114yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280#121—416no—
281#121—432no—
282#121—416no—
283C4×D4—232no—
284#117—416no—
285#117—416no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—416no—
316C2×C4⋊C4—416no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4C2×D414yes—
327C2×C4⋊C4#4114yes—
328C2×C4⋊C4#4114yes—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
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—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
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—28no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4C2×D414yes—
377C2×C22⋊C4C2×D414yes—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—42no—
396C2×C42—44no—
397C2×C42C2×D414yes—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—24no—
408#95—24no—
409#95—42no—
410#95—44no—
411#95—42no—
412#95—44no—
413#95—42no—
414#95—42no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95—44no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—24no—
447C24—22no—
448C24—24no—
449C24—24no—
450C24C22×D412yes—
451C24C22×D412yes—
452C24C2×#4112yes—
453C24C2×#4112yes—
454C24H(5,𝔽2)14yes—
455C24C2511yescharacteristic
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—44no—
459C2×D4—48no—
460C2×D4—416no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—84no—
475C2×D4—88no—
476C2×D4—88no—
477C2×D4—88no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
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—24no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
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—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—88no—
573C22×C4—88no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—88no—
577C22×C4—88no—
578C22×C4#123116yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C2×#4114yes—
585C22×C4C2×#4114yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4H(5,𝔽2)14yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4H(5,𝔽2)12yes—
595C22×C42−1+414yes—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—48no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—88no—
609C4⋊C4—88no—
610C22⋊C4—216no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—416no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—84no—
624C22⋊C4—88no—
625C22⋊C4—84no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C42—28no—
629C42—48no—
630C42—44no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42—84no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23C2×#12314yes—
703C23#53514yes—
704C23C23×D411yescharacteristic
705C23C22×#4111yescharacteristic
706C23C22×#4111yescharacteristic
707C23C22×#4111yescharacteristic
708C23C22×#4111yescharacteristic
709C23C2×H(5,𝔽2)12yes—
710C23C2×H(5,𝔽2)11yescharacteristic
711C23C2×H(5,𝔽2)11yescharacteristic
712C23C2×H(5,𝔽2)12yes—
713C23C2×2−1+412yes—
714C23#58512yes—
715D4—416no—
716D4—816no—
717D4—816no—
718D4—88no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—232no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—28no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
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—44no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—416no—
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—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—816no—
808C2×C4—816no—
809C2×C4C2×#12314yes—
810C2×C4C2×#12314yes—
811C2×C4#52914yes—
812C2×C4#53814yes—
813C2×C4#54614yes—
814C2×C4#54614yes—
815C2×C4#55314yes—
816C2×C4#55314yes—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—42no—
832C22—44no—
833C22—44no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—44no—
838C22—44no—
839C22—82no—
840C22—82no—
841C22—84no—
842C22—84no—
843C22—82no—
844C22—84no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—84no—
850C22C22×#12311yescharacteristic
851C22C2×#52911yescharacteristic
852C22C2×#53511yescharacteristic
853C22#344911yescharacteristic
854C22C2×#53811yescharacteristic
855C22C2×#54611yescharacteristic
856C22C2×#54611yescharacteristic
857C22C2×#55311yescharacteristic
858C22C2×#55311yescharacteristic
859C22#349212yes—
860C22#349412yes—
861C22#349412yes—
862C22#349811yescharacteristic
863C22#349911yescharacteristic
864C22#351112yes—
865C22#351312yes—
866C22#351612yes—
867C22#351912yes—
868C22#352212yes—
869C22#353612yes—
870C22#353712yes—
871C22#354612yes—
872C22#354712yes—
873C4—24no—
874C4—44no—
875C4—44no—
876C4—44no—
877C4—42no—
878C4—42no—
879C4—44no—
880C4—42no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4#244418yes—
889C2—44no—
890C2—44no—
891C2—162no—
892C2C2×#244411yescharacteristic
893C2#3526211yescharacteristic
894C2#3553011yescharacteristic
895C2#3598912yes—
896C2#3807911yescharacteristic
897C2#3808011yescharacteristic
898C2#3894511yescharacteristic
899C2#3894611yescharacteristic
900C2#4298912yes—
901C2#4537312yes—
902C2#4537412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
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×#2352C2semidirect
3. #16441C2semidirect
4. #15967C2semidirect
5. #15277C2semidirect
6. #15239C2semidirect
7. #15224C2semidirect
8. #15150C2semidirect
9. #15130C2semidirect
10. #14741C2semidirect
11. #14257C2semidirect
12. #14137C2semidirect
13. #14136C2semidirect
14. #14048C2semidirect
15. #14001C2semidirect
16. #13924C2semidirect
17. #13880C2semidirect
18. #13839C2semidirect
19. #13795C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24162
C2×#23522
#164412
#159672
#152772
#152392
#152242
#151502
#151302
#147412
#142572
#141372
#141362
#140482
#140012
#139242
#138802
#138392
#137952