Finite Group Databasebeta

← #153751

Subgroups — #153751

Order 512.

5226 conjugacy classes of subgroups.

The subgroup lattice has 1035 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#380C212yesmaximal
2C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊C4C211yesmaximal, characteristic
4C2×#1437C212yesmaximal
5C2×C4⋊#95C212yesmaximal, complemented
6C2×C4⋊#95C211yesmaximal, characteristic, complemented
7#7556C212yesmaximal, complemented
8#7555C212yesmaximal
9#7554C212yesmaximal, complemented
10C25×C4C2211yescharacteristic
11C23×C4⋊C4C2212yes—
12C23×C4⋊C4C2212yes—
13C23×C22⋊C4C2211yescharacteristic
14C23×C22⋊C4C2214yes—
15C23×C22⋊C4C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C23×C42C2212yes—
18C23×C42C2211yescharacteristic
19C2×#380—28no—
20C2×#380—28no—
21C2×#380C4116yescomplemented
22C2×C4×C4⋊C4—24no—
23C2×C4×C4⋊C4—28no—
24C2×C4×C22⋊C4—24no—
25C2×C4×C22⋊C4—24no—
26C2×C4×C22⋊C4C418yescomplemented
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2214yes—
30C22×#95C2214yes—
31C22×#95C2211yescharacteristic
32C22×#95C2214yes—
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35#1437—28no—
36C4⋊#95—24no—
37C4⋊#95—28no—
38C26C2311yescharacteristic
39C24×C4—22no—
40C24×C4—22no—
41C24×C4—24no—
42C24×C4—24no—
43C24×C4—24no—
44C24×C4—24no—
45C24×C4—24no—
46C24×C4C2×C414yes—
47C24×C4C2×C418yes—
48C24×C4C2314yes—
49C24×C4C2311yescharacteristic
50C24×C4C2314yes—
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
56C22×C4⋊C4—24no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—24no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—24no—
66C22×C4⋊C4C2×C418yes—
67C22×C4⋊C4C2×C418yes—
68C22×C4⋊C4D418yes—
69C22×C4⋊C4D418yes—
70C22×C22⋊C4—24no—
71C22×C22⋊C4—22no—
72C22×C22⋊C4—22no—
73C22×C22⋊C4—22no—
74C22×C22⋊C4—22no—
75C22×C22⋊C4—24no—
76C22×C22⋊C4—22no—
77C22×C22⋊C4—22no—
78C22×C22⋊C4—28no—
79C22×C22⋊C4—28no—
80C22×C22⋊C4—28no—
81C22×C22⋊C4—28no—
82C22×C22⋊C4—44no—
83C22×C22⋊C4—44no—
84C22×C22⋊C4C2×C414yes—
85C22×C22⋊C4C2×C4116yes—
86C22×C22⋊C4C2×C414yes—
87C22×C22⋊C4D414yes—
88C22×C22⋊C4Q814yes—
89C22×C42—24no—
90C22×C42—24no—
91C22×C42—24no—
92C22×C42—22no—
93C22×C42—22no—
94C22×C42—28no—
95C22×C42—24no—
96C22×C42—24no—
97C22×C42—24no—
98C22×C42—24no—
99C22×C42—44no—
100C22×C42C2×C414yes—
101C22×C42C2×C414yes—
102C22×C42D414yes—
103C22×C42D414yes—
104#380—264no—
105C4×C4⋊C4—232no—
106C4×C22⋊C4—232no—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95—22no—
111C2×#95—24no—
112C2×#95—28no—
113C2×#95—28no—
114C2×#95—28no—
115C2×#95—28no—
116C2×#95—28no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—28no—
120C2×#95—24no—
121C2×#95—28no—
122C2×#95—24no—
123C2×#95—44no—
124C2×#95—44no—
125C2×#95—44no—
126C2×#95C2×C414yes—
127C2×#95C2×C414yes—
128C2×#95C2×C4116yes—
129C25—21no—
130C25—21no—
131C25—22no—
132C25—22no—
133C25—21no—
134C25—21no—
135C25—22no—
136C25—22no—
137C25—22no—
138C25—22no—
139C25—22no—
140C25—22no—
141C25—22no—
142C25—22no—
143C25C22×C412yes—
144C25C22×C414yes—
145C25C2×D412yes—
146C25C2×Q812yes—
147C25#4114yes—
148C25C2411yescharacteristic
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—24no—
158C23×C4—24no—
159C23×C4—24no—
160C23×C4—21no—
161C23×C4—22no—
162C23×C4—21no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—24no—
173C23×C4—24no—
174C23×C4—24no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—24no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—24no—
183C23×C4—24no—
184C23×C4—24no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—24no—
189C23×C4—22no—
190C23×C4—24no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—28no—
194C23×C4—216no—
195C23×C4—28no—
196C23×C4—216no—
197C23×C4—216no—
198C23×C4—216no—
199C23×C4—216no—
200C23×C4—216no—
201C23×C4—216no—
202C23×C4—216no—
203C23×C4—24no—
204C23×C4—24no—
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—44no—
218C23×C4—48no—
219C23×C4—48no—
220C23×C4—48no—
221C23×C4—44no—
222C23×C4—48no—
223C23×C4—44no—
224C23×C4—48no—
225C23×C4—48no—
226C23×C4—44no—
227C23×C4C42116yescomplemented
228C23×C4C22×C418yes—
229C23×C4C22×C412yes—
230C23×C4C22×C414yes—
231C23×C4C22×C418yes—
232C23×C4C22×C412yes—
233C23×C4C22×C412yes—
234C23×C4C22×C412yes—
235C23×C4C22×C412yes—
236C23×C4C22×C414yes—
237C23×C4C22×C412yes—
238C23×C4C2×D418yes—
239C23×C4C2×D418yes—
240C23×C4C2×D412yes—
241C23×C4C2×D412yes—
242C23×C4C2×D412yes—
243C23×C4C2×D412yes—
244C23×C4C2×D412yes—
245C23×C4C2×D412yes—
246C23×C4C2×D414yes—
247C23×C4C2×D412yes—
248C23×C4C2×D414yes—
249C23×C4C2×D412yes—
250C23×C4C2×Q812yes—
251C23×C4C2×Q812yes—
252C23×C4#4114yes—
253C23×C4#4112yes—
254C23×C4#4112yes—
255C23×C4#4114yes—
256C23×C4#4114yes—
257C23×C4#4114yes—
258C2×C4⋊C4—216no—
259C2×C4⋊C4—216no—
260C2×C4⋊C4—216no—
261C2×C4⋊C4—216no—
262C2×C4⋊C4—216no—
263C2×C4⋊C4—216no—
264C2×C4⋊C4—216no—
265C2×C4⋊C4—216no—
266C2×C4⋊C4—216no—
267C2×C4⋊C4—48no—
268C2×C4⋊C4—48no—
269C2×C4⋊C4—48no—
270C2×C4⋊C4—48no—
271C2×C4⋊C4C22⋊C4132yescomplemented
272C2×C22⋊C4—216no—
273C2×C22⋊C4—216no—
274C2×C22⋊C4—28no—
275C2×C22⋊C4—28no—
276C2×C22⋊C4—28no—
277C2×C22⋊C4—28no—
278C2×C22⋊C4—28no—
279C2×C22⋊C4—28no—
280C2×C22⋊C4—28no—
281C2×C22⋊C4—28no—
282C2×C22⋊C4—28no—
283C2×C22⋊C4—232no—
284C2×C22⋊C4—232no—
285C2×C22⋊C4—416no—
286C2×C22⋊C4—416no—
287C2×C22⋊C4—416no—
288C2×C22⋊C4—416no—
289C2×C22⋊C4—416no—
290C2×C22⋊C4C4⋊C4116yescomplemented
291C2×C42—216no—
292C2×C42—28no—
293C2×C42—216no—
294C2×C42—28no—
295C2×C42—216no—
296C2×C42—28no—
297C2×C42—216no—
298C2×C42—416no—
299C2×C42—416no—
300C2×C42—48no—
301C2×C42—48no—
302C2×C42—48no—
303C2×C42—44no—
304C2×C42—44no—
305C2×C42C22⋊C4116yescomplemented
306#95—216no—
307#95—28no—
308#95—28no—
309#95—232no—
310#95—416no—
311#95—416no—
312#95—48no—
313#95—48no—
314C24—24no—
315C24—22no—
316C24—22no—
317C24—22no—
318C24—24no—
319C24—22no—
320C24—24no—
321C24—24no—
322C24—24no—
323C24—24no—
324C24—24no—
325C24—24no—
326C24—24no—
327C24—24no—
328C24—24no—
329C24—24no—
330C24—24no—
331C24—24no—
332C24—24no—
333C24—24no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—24no—
339C24—24no—
340C24—24no—
341C24—24no—
342C24—24no—
343C24—24no—
344C24—24no—
345C24—24no—
346C24—24no—
347C24—24no—
348C24—24no—
349C24—24no—
350C24—24no—
351C24—24no—
352C24—24no—
353C24—24no—
354C24—24no—
355C24—24no—
356C24—24no—
357C24—24no—
358C24—24no—
359C24—24no—
360C24—41no—
361C24—42no—
362C24—42no—
363C24—42no—
364C24—42no—
365C24—41no—
366C24—41no—
367C24—42no—
368C24—42no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—42no—
375C24—42no—
376C24—42no—
377C24—42no—
378C24—42no—
379C24—42no—
380C24—42no—
381C24—42no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24—42no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24C2×C4214yes—
397C24C2×C4⋊C414yes—
398C24#11714yes—
399C24C4×D418yes—
400C24C4×Q818yes—
401C24C23×C411yescharacteristic
402C24C23×C412yes—
403C24C22×D411yescharacteristic
404C24C22×D412yes—
405C24C22×D411yescharacteristic
406C24C22×D412yes—
407C24C22×D411yescharacteristic
408C24C22×Q811yescharacteristic
409C24C2×#4112yes—
410C24C2×#4112yes—
411C24C2×#4112yes—
412C24C2×#4112yes—
413C24C2×#4111yescharacteristic
414C24C2×#4111yescharacteristic
415C24C2×#4112yes—
416C24H(5,𝔽2)12yes—
417C24H(5,𝔽2)12yes—
418C242−1+412yes—
419C242−1+412yes—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—24no—
461C22×C4—28no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—28no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—28no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—24no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—232no—
499C22×C4—264no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—41no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—41no—
516C22×C4—44no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—44no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—44no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—44no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—44no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—44no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—416no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—416no—
567C22×C4—432no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4C2×C4214yes—
597C22×C4C2×C4214yes—
598C22×C4C2×C22⋊C414yes—
599C22×C4C2×C22⋊C4116yes—
600C22×C4C2×C22⋊C414yes—
601C22×C4C2×C22⋊C414yes—
602C22×C4C2×C22⋊C418yes—
603C22×C4C2×C4⋊C414yes—
604C22×C4C2×C4⋊C414yes—
605C22×C4#11714yes—
606C22×C4#11714yes—
607C22×C4#11714yes—
608C22×C4#11718yes—
609C22×C4C4×D418yes—
610C22×C4C4×D418yes—
611C22×C4C4×D418yes—
612C22×C4C4×D418yes—
613C22×C4C4×D418yes—
614C22×C4C4×D418yes—
615C22×C4#12014yes—
616C22×C4#12114yes—
617C22×C4#12114yes—
618C22×C4#12118yes—
619C22×C4#12118yes—
620C22×C4#12118yes—
621C22×C4C22⋊Q814yes—
622C22×C4C22⋊Q814yes—
623C22×C4#12314yes—
624C22×C4#12318yes—
625C22×C4#12414yes—
626C22×C4#12418yes—
627C22×C4#12618yes—
628C22×C4#12714yes—
629C4⋊C4—264no—
630C4⋊C4—432no—
631C22⋊C4—232no—
632C22⋊C4—232no—
633C22⋊C4—464no—
634C42—232no—
635C42—432no—
636C42—416no—
637C23—28no—
638C23—28no—
639C23—28no—
640C23—28no—
641C23—28no—
642C23—28no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—24no—
650C23—28no—
651C23—24no—
652C23—28no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—42no—
684C23—42no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—42no—
721C23—42no—
722C23—44no—
723C23C4×C4⋊C418yescomplemented
724C23C22×C4211yescharacteristic
725C23C22×C22⋊C411yescharacteristic
726C23C22×C22⋊C412yes—
727C23C22×C4⋊C411yescharacteristic
728C23C2×#11711yescharacteristic
729C23C2×#11712yes—
730C23C2×#11711yescharacteristic
731C23C2×#11711yescharacteristic
732C23C2×#11711yescharacteristic
733C23C2×C4×D412yes—
734C23C2×C4×D412yes—
735C23C2×C4×D412yes—
736C23C2×C4×D412yes—
737C23C2×C4×D412yes—
738C23C2×C4×D412yes—
739C23C2×C4×D412yes—
740C23C2×C4×Q812yes—
741C23C4×#4112yes—
742C23C4×#4112yes—
743C23#51812yes—
744C23#51912yes—
745C23#52012yes—
746C23#52012yes—
747C23#52012yes—
748C23#52012yes—
749C23C2×#12011yescharacteristic
750C23C2×#12111yescharacteristic
751C23C2×#12112yes—
752C23C2×#12111yescharacteristic
753C23C2×#12112yes—
754C23C2×#12112yes—
755C23C2×C22⋊Q811yescharacteristic
756C23C2×C22⋊Q811yescharacteristic
757C23C2×#12312yes—
758C23C2×#12311yescharacteristic
759C23#52512yes—
760C23#52512yes—
761C23C2×#12411yescharacteristic
762C23C2×#12412yes—
763C23C2×#12612yes—
764C23#52912yes—
765C23#52912yes—
766C23C2×#12711yescharacteristic
767C23#53212yes—
768C23#53312yes—
769C23#53511yescharacteristic
770C23#53511yescharacteristic
771C23#53611yescharacteristic
772C23#53611yescharacteristic
773C23#53712yes—
774C23#53712yes—
775C23#54012yes—
776C23#54112yes—
777C23#54212yes—
778C23#54212yes—
779C23D4212yes—
780C23D4212yes—
781C23#54612yes—
782C23#54612yes—
783C23#54612yes—
784C23#54612yes—
785C23#54712yes—
786C23#54712yes—
787C23#54712yes—
788C23#54712yes—
789C23#54812yes—
790C23#54812yes—
791C23#54812yes—
792C23#54812yes—
793C23D4×Q812yes—
794C23D4×Q812yes—
795C23#55012yes—
796C23#55012yes—
797C23#55212yes—
798C23#55212yes—
799C23#55212yes—
800C23#55212yes—
801C23#55312yes—
802C23#55312yes—
803C23#55312yes—
804C23#55312yes—
805C23#55412yes—
806C23#55412yes—
807C23#55512yes—
808C23#55512yes—
809C23#55612yes—
810C23#55612yes—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—28no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—28no—
817C2×C4—28no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—216no—
823C2×C4—216no—
824C2×C4—28no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—28no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—216no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—48no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—48no—
843C2×C4—48no—
844C2×C4—44no—
845C2×C4—48no—
846C2×C4—48no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—48no—
850C2×C4—48no—
851C2×C4—48no—
852C2×C4—48no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—48no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—48no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—48no—
874C2×C4—464no—
875C2×C4—48no—
876C2×C4—48no—
877C2×C4—48no—
878C2×C4—48no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—84no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4—84no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4—84no—
889C2×C4—84no—
890C2×C4C4×C22⋊C418yes—
891C2×C4C4×C22⋊C4116yes—
892C2×C4#38018yescomplemented
893C2×C4#38618yes—
894C2×C4#386116yes—
895C2×C4#388116yes—
896C2×C4#388116yes—
897C2×C4#388116yes—
898C2×C4#39018yes—
899C2×C4#390116yes—
900C22—28no—
901C22—216no—
902C22—44no—
903C22—44no—
904C22—48no—
905C22—48no—
906C22—44no—
907C22—44no—
908C22—48no—
909C22—48no—
910C22—48no—
911C22—48no—
912C22—48no—
913C22—48no—
914C22—48no—
915C22—48no—
916C22—44no—
917C22—44no—
918C22—48no—
919C22C2×C4×C22⋊C411yescharacteristic
920C22C2×C4×C22⋊C412yes—
921C22C2×C4×C4⋊C411yescharacteristic
922C22C4×#11711yescharacteristic
923C22#227412yes—
924C22C2×#38011yescharacteristic
925C22#228011yescharacteristic
926C22#228311yescharacteristic
927C22#228511yescharacteristic
928C22C2×#38611yescharacteristic
929C22C2×#38612yes—
930C22C2×#38812yes—
931C22C2×#38812yes—
932C22C2×#38812yes—
933C22C2×#39011yescharacteristic
934C22C2×#39012yes—
935C22C4×#12112yes—
936C22C4×#12112yes—
937C22C4×C22⋊Q812yes—
938C22C4×C22⋊Q812yes—
939C22#231111yescharacteristic
940C22#231111yescharacteristic
941C22#231412yes—
942C22#232312yes—
943C22#232312yes—
944C22#232412yes—
945C22#232412yes—
946C22D4×C22⋊C412yes—
947C22#233912yes—
948C22Q8×C22⋊C412yes—
949C22#234112yes—
950C22#234412yes—
951C22#234512yes—
952C22#234612yes—
953C22#234712yes—
954C22D4×C4⋊C412yes—
955C22D4×C4⋊C412yes—
956C22#235212yes—
957C22#235212yes—
958C22#235212yes—
959C22#235212yes—
960C22#235412yes—
961C22#235412yes—
962C22#236012yes—
963C22#236012yes—
964C22#236112yes—
965C22#236112yes—
966C22#236212yes—
967C22#236212yes—
968C22#236312yes—
969C22#236312yes—
970C22#240712yes—
971C22#240811yescharacteristic
972C22#240911yescharacteristic
973C22#241412yes—
974C22#241512yes—
975C22#241612yes—
976C22#241712yes—
977C22#242012yes—
978C22#242112yes—
979C22#242212yes—
980C22#242312yes—
981C22#242612yes—
982C22#242712yes—
983C22#242812yes—
984C22#242912yes—
985C22#248512yes—
986C22#248611yescharacteristic
987C22#248711yescharacteristic
988C22#248912yes—
989C22#249012yes—
990C22#249112yes—
991C22#249212yes—
992C22#249412yes—
993C22#249512yes—
994C22#249612yes—
995C22#249712yes—
996C22#253512yes—
997C22#253612yes—
998C22#253712yes—
999C22#253812yes—
1000C22#254012yes—
1001C22#254111yescharacteristic
1002C22#254211yescharacteristic
1003C22#254711yescharacteristic
1004C22#256212yes—
1005C22#256311yescharacteristic
1006C4—28no—
1007C4—44no—
1008C4—44no—
1009C4—44no—
1010C4—416no—
1011C4—44no—
1012C4—88no—
1013C4#1437116yescomplemented
1014C2—48no—
1015C2C2×#143711yescharacteristic
1016C2C4×#38011yescharacteristic
1017C2#1377711yescharacteristic
1018C2C22⋊C4×C4⋊C412yes—
1019C2#1380112yes—
1020C2#1387111yescharacteristic
1021C2#1387211yescharacteristic
1022C2#1387512yes—
1023C2#1387612yes—
1024C2#1390511yescharacteristic
1025C2#1390611yescharacteristic
1026C2#1396912yes—
1027C2#1397012yes—
1028C2#1397312yes—
1029C2#1397412yes—
1030C2#1399312yes—
1031C2#1399412yes—
1032C2#1399712yes—
1033C2#1399812yes—
subgroupG/H
center, Frattini, socle, cosocleC25C24
commutatorC23C22×C42
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×C4×C4⋊C4C2semidirect
5. C2×C4⋊#95C2semidirect
6. C2×C4⋊#95C2semidirect
7. #7556C2semidirect
9. #7554C2semidirect
21. C2×#380C4semidirect
26. C2×C4×C22⋊C4C4semidirect
227. C23×C4C42semidirect
271. C2×C4⋊C4C22⋊C4semidirect
290. C2×C22⋊C4C4⋊C4semidirect
305. C2×C42C22⋊C4semidirect
723. C23C4×C4⋊C4semidirect
892. C2×C4#380semidirect
1013. C4#1437semidirect

Maximal subgroups

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

subgroupindex
C22×#3802
C22×C4×C4⋊C42
C22×C4×C22⋊C42
C2×#14372
C2×C4⋊#952
#75562
#75552
#75542