Finite Group Databasebeta

← #155120

Subgroups — #155120

Order 512.

3150 conjugacy classes of subgroups.

The subgroup lattice has 995 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#398C211yesmaximal, characteristic
2C22×#389C211yesmaximal, characteristic
3C2×#1445C211yesmaximal, characteristic
4C2×#1441C212yesmaximal
5C2×#1436C211yesmaximal, characteristic
6C2×#1436C212yesmaximal
7C2×C4⋊#95C211yesmaximal, characteristic
8#7557C212yesmaximal
9#7557C211yesmaximal, characteristic
10#7556C212yesmaximal
11#7554C211yesmaximal, characteristic
12C23×C4⋊C4C2212yes—
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C2×#398—24no—
21C2×#398—24no—
22C2×#398C418yescomplemented
23C2×#389—24no—
24C2×#389—24no—
25C2×#389—24no—
26C22×#95C2211yescharacteristic
27C22×#95C2211yescharacteristic
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38C22×#95C2212yes—
39C22×#95C2211yescharacteristic
40C22×#95C2212yes—
41#1445—24no—
42#1441—28no—
43#1436—28no—
44#1436—24no—
45C4⋊#95—24no—
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2312yes—
50C24×C4C2311yescharacteristic
51C24×C4C2312yes—
52C24×C4C2311yescharacteristic
53C24×C4C2312yes—
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
56C24×C4C2311yescharacteristic
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—24no—
67C22×C4⋊C4—24no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—22no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—22no—
79C22×C4⋊C4—24no—
80C22×C4⋊C4—24no—
81C22×C4⋊C4—24no—
82C22×C4⋊C4—24no—
83C22×C4⋊C4—24no—
84C22×C4⋊C4—42no—
85C22×C4⋊C4—42no—
86C22×C4⋊C4—42no—
87C22×C4⋊C4C2×C414yes—
88C22×C4⋊C4C2×C418yes—
89C22×C4⋊C4C2×C414yes—
90C22×C4⋊C4D414yes—
91C22×C4⋊C4D414yes—
92C22×C4⋊C4D414yes—
93C22×C42—22no—
94C22×C42—22no—
95C22×C42—22no—
96C22×C42—22no—
97C22×C42—24no—
98C22×C42—22no—
99C22×C42—24no—
100C22×C42—22no—
101C22×C42—42no—
102C22×C42—42no—
103#398—232no—
104#389—232no—
105C2×#95—22no—
106C2×#95—22no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—22no—
113C2×#95—22no—
114C2×#95—22no—
115C2×#95—22no—
116C2×#95—22no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—22no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—22no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—22no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95C2×C418yes—
146C2×#95C2×C414yes—
147C2×#95D418yes—
148C2×#95D414yes—
149C2×#95Q818yes—
150C25C2411yescharacteristic
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—21no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
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—22no—
251C23×C4C22×C414yes—
252C23×C4C22×C412yes—
253C23×C4C22×C414yes—
254C23×C4C22×C412yes—
255C23×C4C22×C412yes—
256C23×C4C2×D412yes—
257C23×C4C2×D412yes—
258C23×C4C2×D414yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D414yes—
262C23×C4C2×D412yes—
263C23×C4C2×D412yes—
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D412yes—
267C23×C4C2×D412yes—
268C23×C4C2×D412yes—
269C23×C4C2×D412yes—
270C23×C4C2×D414yes—
271C23×C4C2×Q814yes—
272C23×C4C2×Q814yes—
273C23×C4C2×Q814yes—
274C23×C4#4114yes—
275C23×C4#4114yes—
276C23×C4#4114yes—
277C23×C4#4112yes—
278C23×C4#4112yes—
279C23×C4#4114yes—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—216no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—216no—
293C2×C4⋊C4—216no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—48no—
298C2×C4⋊C4—48no—
299C2×C4⋊C4—48no—
300C2×C4⋊C4—48no—
301C2×C4⋊C4—48no—
302C2×C4⋊C4—48no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—48no—
309C2×C4⋊C4—48no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—48no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—48no—
315C2×C4⋊C4C22⋊C4116yes—
316C2×C42—28no—
317C2×C42—28no—
318C2×C42—48no—
319C2×C42—48no—
320C2×C42—48no—
321C2×C42—48no—
322C2×C42—44no—
323C2×C42—44no—
324C2×C42—44no—
325C2×C42—44no—
326#95—216no—
327#95—28no—
328#95—28no—
329#95—216no—
330#95—28no—
331#95—216no—
332#95—216no—
333#95—48no—
334#95—48no—
335#95—48no—
336#95—48no—
337#95—48no—
338#95—48no—
339#95—48no—
340#95—44no—
341C24C23×C411yescharacteristic
342C24C22×D411yescharacteristic
343C24C22×D411yescharacteristic
344C24C22×D411yescharacteristic
345C24C22×D411yescharacteristic
346C24C22×D412yes—
347C24C22×Q812yes—
348C24C2×#4111yescharacteristic
349C24C2×#4111yescharacteristic
350C24C2×#4112yes—
351C24C2×#4112yes—
352C24C2×#4112yes—
353C24C2×#4112yes—
354C24H(5,𝔽2)12yes—
355C24H(5,𝔽2)12yes—
356C242−1+412yes—
357C242−1+412yes—
358C242−1+412yes—
359C242−1+412yes—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
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—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—42no—
498C22×C4—41no—
499C22×C4—42no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—42no—
505C22×C4—41no—
506C22×C4—42no—
507C22×C4—41no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—42no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—41no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4C2×C22⋊C414yes—
637C22×C4C2×C22⋊C414yes—
638C22×C4C2×C22⋊C414yes—
639C22×C4C4×D414yes—
640C22×C4C4×D414yes—
641C22×C4C4×D418yes—
642C22×C4C4×Q818yes—
643C22×C4#12014yes—
644C22×C4#12114yes—
645C22×C4#12114yes—
646C22×C4#12118yes—
647C22×C4C22⋊Q818yes—
648C22×C4#12314yes—
649C22×C4#12314yes—
650C22×C4#12414yes—
651C22×C4#12714yes—
652C22×C4C4⋊Q814yes—
653C4⋊C4—232no—
654C4⋊C4—416no—
655C4⋊C4—416no—
656C4⋊C4—416no—
657C4⋊C4—416no—
658C4⋊C4—432no—
659C42—416no—
660C42—416no—
661C23C22×C22⋊C411yescharacteristic
662C23C2×C4×D411yescharacteristic
663C23C2×C4×D411yescharacteristic
664C23C2×C4×D412yes—
665C23C2×C4×Q812yes—
666C23C4×#4112yes—
667C23#51912yes—
668C23#52012yes—
669C23#52012yes—
670C23C2×#12011yescharacteristic
671C23C2×#12112yes—
672C23C2×#12111yescharacteristic
673C23C2×#12111yescharacteristic
674C23C2×C22⋊Q812yes—
675C23C2×#12311yescharacteristic
676C23C2×#12311yescharacteristic
677C23#52511yescharacteristic
678C23#52512yes—
679C23C2×#12411yescharacteristic
680C23#52912yes—
681C23#52912yes—
682C23C2×#12711yescharacteristic
683C23C2×C4⋊Q811yescharacteristic
684C23#53211yescharacteristic
685C23#53312yes—
686C23#53312yes—
687C23#53411yescharacteristic
688C23#53511yescharacteristic
689C23#53611yescharacteristic
690C23#53611yescharacteristic
691C23#53612yes—
692C23#53611yescharacteristic
693C23#53611yescharacteristic
694C23#53712yes—
695C23#53712yes—
696C23#53912yes—
697C23#53912yes—
698C23#53912yes—
699C23#54012yes—
700C23#54112yes—
701C23#54112yes—
702C23#54112yes—
703C23#54112yes—
704C23#54112yes—
705C23#54212yes—
706C23#54412yes—
707C23#54412yes—
708C23D4212yes—
709C23D4212yes—
710C23#54612yes—
711C23#54612yes—
712C23#54612yes—
713C23#54612yes—
714C23#54712yes—
715C23#54712yes—
716C23#54712yes—
717C23#54712yes—
718C23#54712yes—
719C23#54712yes—
720C23#54712yes—
721C23#54812yes—
722C23#54812yes—
723C23#54812yes—
724C23#54812yes—
725C23#54812yes—
726C23D4×Q812yes—
727C23D4×Q812yes—
728C23D4×Q812yes—
729C23D4×Q812yes—
730C23#55112yes—
731C23#55212yes—
732C23#55212yes—
733C23#55212yes—
734C23#55212yes—
735C23#55312yes—
736C23#55312yes—
737C23#55312yes—
738C23#55412yes—
739C23#55412yes—
740C23#55612yes—
741C23#55612yes—
742C23#55712yes—
743C23#55712yes—
744C23#56212yes—
745C23#56312yes—
746C23#56312yes—
747C23#56412yes—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—28no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—24no—
779C2×C4—28no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—82no—
852C2×C4—82no—
853C2×C4—82no—
854C2×C4—82no—
855C2×C4—82no—
856C2×C4—82no—
857C2×C4—82no—
858C2×C4—82no—
859C2×C4—82no—
860C2×C4—82no—
861C2×C4—82no—
862C2×C4—82no—
863C2×C4—82no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4—82no—
867C2×C4—82no—
868C2×C4—82no—
869C2×C4—82no—
870C2×C4—82no—
871C2×C4—82no—
872C2×C4—82no—
873C2×C4—82no—
874C2×C4—82no—
875C2×C4#38618yes—
876C2×C4#39018yes—
877C22C2×#38611yescharacteristic
878C22C2×#39011yescharacteristic
879C22C4×#12311yescharacteristic
880C22C4×C22⋊Q812yes—
881C22C4×C4⋊Q811yescharacteristic
882C22#231111yescharacteristic
883C22#232211yescharacteristic
884C22#232312yes—
885C22#232711yescharacteristic
886C22#233012yes—
887C22#233612yes—
888C22#233912yes—
889C22Q8×C22⋊C412yes—
890C22#235912yes—
891C22#236012yes—
892C22#236112yes—
893C22#236112yes—
894C22#236212yes—
895C22#236512yes—
896C22#237012yes—
897C22#238212yes—
898C22#240511yescharacteristic
899C22#240611yescharacteristic
900C22#241512yes—
901C22#241612yes—
902C22#241612yes—
903C22#241712yes—
904C22#241912yes—
905C22#242512yes—
906C22#242712yes—
907C22#242912yes—
908C22#242912yes—
909C22#243211yescharacteristic
910C22#243311yescharacteristic
911C22#243411yescharacteristic
912C22#243611yescharacteristic
913C22#243812yes—
914C22#244012yes—
915C22#244312yes—
916C22#244612yes—
917C22#244612yes—
918C22#244912yes—
919C22#245312yes—
920C22#246212yes—
921C22#246412yes—
922C22#247512yes—
923C22#247812yes—
924C22#248611yescharacteristic
925C22#248912yes—
926C22#249212yes—
927C22#250111yescharacteristic
928C22#250411yescharacteristic
929C22#251912yes—
930C22#252212yes—
931C22#253411yescharacteristic
932C22#254012yes—
933C22#254212yes—
934C22#254511yescharacteristic
935C22#254611yescharacteristic
936C22#255012yes—
937C22#259012yes—
938C22#259412yes—
939C22#260612yes—
940C22#267112yes—
941C22#267712yes—
942C22#268012yes—
943C22#268112yes—
944C22#268912yes—
945C22#270412yes—
946C22#270712yes—
947C22#271112yes—
948C22#271312yes—
949C22#271612yes—
950C22#271912yes—
951C22#271912yes—
952C22#271912yes—
953C22#271912yes—
954C22#272012yes—
955C22#272212yes—
956C22#272512yes—
957C22#272612yes—
958C22#272612yes—
959C22#272912yes—
960C22#273912yes—
961C22#277612yes—
962C22#277712yes—
963C22#280212yes—
964C4—28no—
965C4—28no—
966C4—44no—
967C4—48no—
968C4—44no—
969C4—48no—
970C4—44no—
971C4—84no—
972C4—84no—
973C4—82no—
974C4—82no—
975C2#1396811yescharacteristic
976C2#1399712yes—
977C2#1402411yescharacteristic
978C2#1413711yescharacteristic
979C2#1419112yes—
980C2#1421112yes—
981C2#1445112yes—
982C2#1454812yes—
983C2#1455712yes—
984C2#1534011yescharacteristic
985C2#1534712yes—
986C2#1543011yescharacteristic
987C2#1543612yes—
988C2#1561812yes—
989C2#1562112yes—
990C2#1578311yescharacteristic
991C2#1580412yes—
992C2#1580612yes—
993C2#1588111yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
22. C2×#398C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3982
C22×#3892
C2×#14452
C2×#14412
C2×#14362
C2×C4⋊#952
#75572
#75562
#75542