Finite Group Databasebeta

← #636387

Subgroups — #636387

Order 512.

3922 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic, complemented
2C2×#2416C211yesmaximal, characteristic
3C2×#2618C212yesmaximal, complemented
4C2×C4×#123C211yesmaximal, characteristic, complemented
5C22×#384C211yesmaximal, characteristic, complemented
6#16515C214yesmaximal, complemented
7#16514C214yesmaximal, complemented
8#15134C212yesmaximal, complemented
9#15133C212yesmaximal, complemented
10#15131C212yesmaximal, complemented
11#15130C212yesmaximal, complemented
12#14729C212yesmaximal, complemented
13#14719C212yesmaximal, complemented
14#14256C212yesmaximal, complemented
15#14137C211yesmaximal, characteristic, complemented
16#13907C211yesmaximal, characteristic, complemented
17#13872C211yesmaximal, characteristic, complemented
18C22×#123C2212yes—
19C22×#123C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×#121C2212yes—
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2212yes—
27C23×C4⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2854—28no—
30#2618—216no—
31#2416—28no—
32C2×#398C2214yes—
33C2×#396C2214yes—
34C2×#396C2214yes—
35C2×#396C2212yes—
36C2×#396C2214yes—
37C2×#394C2214yes—
38C2×#394C2212yes—
39C2×#394C2214yes—
40C4×#123—28no—
41C2×#390C2212yes—
42C2×#390C2211yescharacteristic
43C2×#390C2212yes—
44C2×#389C2212yes—
45C2×#389C2211yescharacteristic
46C2×#389C2212yes—
47C2×#388C2214yes—
48C2×#388C2212yes—
49C2×#387C2212yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#386C2211yescharacteristic
55C2×#386C2212yes—
56C2×#385C2211yescharacteristic
57C2×#384—28no—
58C2×#384C2212yes—
59C2×#384C2212yes—
60C2×#384C2214yes—
61C2×#381C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×#380C2212yes—
65C2×#380C2212yes—
66C2×C4×C4⋊C4C2212yes—
67C2×C4×C22⋊C4C2212yes—
68C2×C4×C22⋊C4C2211yescharacteristic
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2212yes—
75#1441C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2212yes—
82#1439C2214yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2212yes—
88C23×D4C2312yes—
89C23×D4C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C23×D4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2312yes—
98C2×#123—24no—
99C2×#123—24no—
100C2×#123—28no—
101C2×#123—28no—
102C2×#123—28no—
103C2×#123D418yescomplemented
104C2×#121—28no—
105C2×#121—24no—
106C2×#121—28no—
107C2×#121—24no—
108C2×#121—24no—
109C2×#121—24no—
110C2×#121—44no—
111C2×#121—44no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C22×C4⋊C4—28no—
116C22×C4⋊C4—28no—
117C22×C4⋊C4—28no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—44no—
120C22×C4⋊C4—44no—
121C22×C4⋊C4—48no—
122C22×C4⋊C4—44no—
123C22×C4⋊C4D418yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C42—24no—
159C22×C42—24no—
160C22×C42D418yescomplemented
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2312yes—
165#398—216no—
166#396—216no—
167#396—28no—
168#396—216no—
169#396—48no—
170#394—28no—
171#394—216no—
172#394—48no—
173#390—24no—
174#390—28no—
175#390—44no—
176#389—24no—
177#389—28no—
178#389—44no—
179#388—216no—
180#388—28no—
181#387—28no—
182#386—28no—
183#386—28no—
184#386—28no—
185#386—24no—
186#386—28no—
187#386—44no—
188#385—24no—
189#384—28no—
190#384—28no—
191#384—216no—
192#381—24no—
193#380—24no—
194#380—24no—
195#380—28no—
196#380—44no—
197C4×C4⋊C4—28no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—28no—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C25C2412yes—
218C25C2411yescharacteristic
219C25C2411yescharacteristic
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—24no—
237C22×D4—22no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—44no—
241C22×D4—42no—
242C22×D4—44no—
243C22×D4C2×D414yes—
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—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—44no—
265C23×C4—44no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4C2×D414yes—
269C23×C4C2×D414yes—
270C23×C4C2×D414yes—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4C2×D418yes—
274C23×C4#4114yes—
275C23×C4#4114yes—
276C23×C4C2414yes—
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2414yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290#123—232no—
291#123—432no—
292#121—416no—
293#121—432no—
294#121—416no—
295C4×D4—416no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—432no—
339C2×C4⋊C4—432no—
340C2×C4⋊C4—416no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4C2×D414yes—
344C2×C4⋊C4C2×D414yes—
345C2×C4⋊C4C2×D418yes—
346C2×C4⋊C4C2×D418yes—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
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⋊C4—44no—
394C2×C22⋊C4C2×D414yes—
395C2×C22⋊C4C2×D418yes—
396C2×C42—232no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42C2×D418yes—
408C2×C42C2×D418yes—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—28no—
417#95—28no—
418#95—24no—
419#95—28no—
420#95—28no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—24no—
446C24—24no—
447C24—22no—
448C24—24no—
449C24—24no—
450C24—22no—
451C24C22×D412yes—
452C24C22×D412yes—
453C24C22×D412yes—
454C24C22×D412yes—
455C24C2×#4112yes—
456C24C2×#4112yes—
457C24H(5,𝔽2)12yes—
458C242−1+412yes—
459C24C2511yescharacteristic
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—84no—
482C2×D4—88no—
483C2×D4—88no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—216no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—216no—
507C22×C4—216no—
508C22×C4—216no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—216no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—24no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—88no—
579C22×C4—88no—
580C22×C4—88no—
581C22×C4—88no—
582C22×C4#121116yes—
583C22×C4#121116yescomplemented
584C22×C4C22×D414yes—
585C22×C4C22×D412yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D414yes—
590C22×C4C22×D412yes—
591C22×C4C22×D414yes—
592C22×C4C22×D414yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4114yes—
597C22×C4C2×#4112yes—
598C22×C4H(5,𝔽2)14yes—
599C22×C4H(5,𝔽2)14yes—
600C22×C42−1+414yes—
601C22×C42−1+414yes—
602C4⋊C4—216no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—48no—
606C4⋊C4—416no—
607C4⋊C4—416no—
608C4⋊C4—416no—
609C4⋊C4—416no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—416no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—88no—
619C22⋊C4—28no—
620C22⋊C4—216no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—44no—
625C22⋊C4—48no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—48no—
629C22⋊C4—416no—
630C22⋊C4—48no—
631C22⋊C4—416no—
632C22⋊C4—84no—
633C22⋊C4—88no—
634C22⋊C4—88no—
635C22⋊C4—88no—
636C42—216no—
637C42—216no—
638C42—44no—
639C42—48no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—42no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—44no—
684C23—42no—
685C23—44no—
686C23—44no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23C2×#12114yes—
703C23C2×#12114yes—
704C23#53714yes—
705C23D4214yes—
706C23#54714yes—
707C23#54814yes—
708C23#55314yes—
709C23C23×D411yescharacteristic
710C23C23×D411yescharacteristic
711C23C23×D411yescharacteristic
712C23C22×#4111yescharacteristic
713C23C22×#4111yescharacteristic
714C23C2×H(5,𝔽2)12yes—
715C23C2×H(5,𝔽2)11yescharacteristic
716C23C2×H(5,𝔽2)12yes—
717C23C2×2−1+412yes—
718C23C2×2−1+411yescharacteristic
719C23C2×2−1+412yes—
720D4—416no—
721D4—816no—
722D4—816no—
723D4—88no—
724C2×C4—232no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—232no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—232no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—41no—
768C2×C4—44no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—44no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—44no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—816no—
806C2×C4—816no—
807C2×C4—88no—
808C2×C4C2×#12114yes—
809C2×C4C2×#12118yes—
810C2×C4C2×#12114yes—
811C2×C4#53414yes—
812C2×C4#53614yes—
813C2×C4#53718yes—
814C2×C4#53718yes—
815C2×C4#53918yes—
816C22—24no—
817C22—24no—
818C22—28no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—28no—
823C22—28no—
824C22—28no—
825C22—24no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22—81no—
832C22—81no—
833C22—82no—
834C22—81no—
835C22—82no—
836C22—81no—
837C22—82no—
838C22—82no—
839C22—84no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—84no—
845C22—84no—
846C22—84no—
847C22—82no—
848C22#241618yes—
849C22C22×#12111yescharacteristic
850C22C22×#12111yescharacteristic
851C22C2×#53411yescharacteristic
852C22C2×#53611yescharacteristic
853C22C2×#53711yescharacteristic
854C22C2×#53712yes—
855C22C2×#53712yes—
856C22C2×#53912yes—
857C22C2×D4211yescharacteristic
858C22C2×#54711yescharacteristic
859C22C2×#54811yescharacteristic
860C22C2×#55311yescharacteristic
861C22#348411yescharacteristic
862C22#348611yescharacteristic
863C22#349212yes—
864C22#349812yes—
865C22#349912yes—
866C22#351112yes—
867C22#351112yes—
868C22#354312yes—
869C22#354412yes—
870C22#355212yes—
871C22#355212yes—
872C4—28no—
873C4—28no—
874C4—24no—
875C4—42no—
876C4—44no—
877C4—44no—
878C4—44no—
879C4—82no—
880C4—81no—
881C4—84no—
882C4—84no—
883C4—82no—
884C4—81no—
885C4#261818yescomplemented
886C2—28no—
887C2—82no—
888C2—162no—
889C2C2×#261811yescharacteristic
890C2C2×#241611yescharacteristic
891C2#3522311yescharacteristic
892C2#3527312yes—
893C2#3762012yes—
894C2#3933611yescharacteristic
895C2#3933711yescharacteristic
896C2#3934812yes—
897C2#3972011yescharacteristic
898C2#3972111yescharacteristic
899C2#3973212yes—
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
1. C2×#2854C2semidirect
3. C2×#2618C2semidirect
4. C2×C4×#123C2semidirect
5. C22×#384C2semidirect
6. #16515C2semidirect
7. #16514C2semidirect
8. #15134C2semidirect
9. #15133C2semidirect
10. #15131C2semidirect
11. #15130C2semidirect
12. #14729C2semidirect
13. #14719C2semidirect
14. #14256C2semidirect
15. #14137C2semidirect
16. #13907C2semidirect
17. #13872C2semidirect
103. C2×#123D4semidirect
160. C22×C42D4semidirect
583. C22×C4#121semidirect
885. C4#2618semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
C2×#24162
C2×#26182
C2×C4×#1232
C22×#3842
#165152
#165142
#151342
#151332
#151312
#151302
#147292
#147192
#142562
#141372
#139072
#138722