Finite Group Databasebeta

← #158408

Subgroups — #158408

Order 512.

3436 conjugacy classes of subgroups.

The subgroup lattice has 1089 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#395C211yesmaximal, characteristic
2C22×#391C211yesmaximal, characteristic
3C2×#1446C211yesmaximal, characteristic
4C2×#1441C211yesmaximal, characteristic
5C2×#1441C212yesmaximal
6C2×#1436C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic
8#7557C211yesmaximal, characteristic
9#7557C212yesmaximal
10#7557C212yesmaximal
11#7556C212yesmaximal
12C24×Q8C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C4⋊C4C2212yes—
17C23×C42C2211yescharacteristic
18C2×#395—24no—
19C2×#395—24no—
20C2×#395—24no—
21C2×#391—24no—
22C2×#391—28no—
23C22×#95C2211yescharacteristic
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2212yes—
37C22×#95C2212yes—
38C22×#95C2212yes—
39C22×#95C2211yescharacteristic
40#1446—24no—
41#1441—28no—
42#1441—24no—
43#1436—24no—
44C4⋊#95—24no—
45C23×Q8—24no—
46C23×Q8—22no—
47C23×Q8—22no—
48C23×Q8—22no—
49C23×Q8—24no—
50C23×Q8—22no—
51C23×Q8—22no—
52C23×Q8—22no—
53C23×Q8—42no—
54C23×Q8—42no—
55C23×Q8D414yes—
56C24×C4C2311yescharacteristic
57C24×C4C2312yes—
58C24×C4C2312yes—
59C24×C4C2311yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2312yes—
62C24×C4C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C24×C4C2312yes—
65C24×C4C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C22×C4⋊C4—24no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—22no—
74C22×C4⋊C4—24no—
75C22×C4⋊C4—24no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—24no—
79C22×C4⋊C4—24no—
80C22×C4⋊C4—22no—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—24no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—24no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—42no—
87C22×C4⋊C4—42no—
88C22×C4⋊C4—42no—
89C22×C4⋊C4—42no—
90C22×C4⋊C4—42no—
91C22×C4⋊C4D414yes—
92C22×C4⋊C4Q818yescomplemented
93C22×C42—22no—
94C22×C42—24no—
95C22×C42—22no—
96C22×C42—42no—
97C22×C42D414yes—
98#395—232no—
99#391—232no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—22no—
104C2×#95—22no—
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—24no—
115C2×#95—22no—
116C2×#95—22no—
117C2×#95—22no—
118C2×#95—22no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—22no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—22no—
128C2×#95—24no—
129C2×#95—22no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—22no—
135C2×#95—42no—
136C2×#95—42no—
137C2×#95—42no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95D414yes—
146C2×#95D418yes—
147C2×#95Q814yescomplemented
148C2×#95Q814yescomplemented
149C25C2411yescharacteristic
150C22×Q8—28no—
151C22×Q8—216no—
152C22×Q8—28no—
153C22×Q8—28no—
154C22×Q8—216no—
155C22×Q8—28no—
156C22×Q8—28no—
157C22×Q8—48no—
158C22×Q8—48no—
159C22×Q8—48no—
160C22×Q8—48no—
161C22×Q8—48no—
162C22×Q8—48no—
163C22×Q8—48no—
164C22×Q8—48no—
165C22×Q8—48no—
166C22×Q8—44no—
167C22×Q8—44no—
168C22×Q8—48no—
169C22×Q8—44no—
170C22×Q8—44no—
171C22×Q8—44no—
172C22×Q8—44no—
173C23×C4—21no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—21no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—22no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—22no—
207C23×C4—21no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—21no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—21no—
257C23×C4—22no—
258C23×C4—21no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4C2×D412yes—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×D412yes—
291C23×C4C2×D412yes—
292C23×C4C2×D412yes—
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D414yes—
296C23×C4C2×D412yes—
297C23×C4C2×D412yes—
298C23×C4C2×Q814yes—
299C23×C4C2×Q812yes—
300C23×C4C2×Q812yes—
301C23×C4C2×Q814yes—
302C23×C4C2×Q812yes—
303C23×C4C2×Q812yes—
304C23×C4C2×Q812yes—
305C23×C4C2×Q814yes—
306C23×C4C2×Q812yes—
307C23×C4#4114yes—
308C23×C4#4114yes—
309C23×C4#4112yes—
310C23×C4#4112yes—
311C23×C4#4112yes—
312C23×C4#4112yes—
313C23×C4#4112yes—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—216no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—216no—
319C2×C4⋊C4—216no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—48no—
322C2×C4⋊C4—48no—
323C2×C4⋊C4—48no—
324C2×C4⋊C4—48no—
325C2×C4⋊C4—48no—
326C2×C4⋊C4—48no—
327C2×C4⋊C4—48no—
328C2×C4⋊C4—48no—
329C2×C4⋊C4—48no—
330C2×C4⋊C4—48no—
331C2×C4⋊C4—48no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—48no—
334C2×C4⋊C4—48no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C42—28no—
341C2×C42—28no—
342C2×C42—44no—
343C2×C42—48no—
344C2×C42—48no—
345#95—216no—
346#95—216no—
347#95—216no—
348#95—28no—
349#95—28no—
350#95—28no—
351#95—48no—
352#95—48no—
353#95—48no—
354#95—44no—
355#95—48no—
356#95—48no—
357#95—48no—
358#95—44no—
359#95—44no—
360#95—48no—
361#95—44no—
362C24C22×D411yescharacteristic
363C24C22×D411yescharacteristic
364C24C22×D411yescharacteristic
365C24C22×D412yes—
366C24C22×D411yescharacteristic
367C24C22×Q812yes—
368C24C22×Q811yescharacteristic
369C24C22×Q811yescharacteristic
370C24C2×#4111yescharacteristic
371C24C2×#4111yescharacteristic
372C24C2×#4111yescharacteristic
373C24C2×#4112yes—
374C24C2×#4111yescharacteristic
375C24C2×#4111yescharacteristic
376C24C2×#4112yes—
377C24H(5,𝔽2)12yes—
378C24H(5,𝔽2)12yes—
379C24H(5,𝔽2)11yescharacteristic
380C24H(5,𝔽2)11yescharacteristic
381C242−1+412yes—
382C242−1+411yescharacteristic
383C242−1+412yes—
384C242−1+411yescharacteristic
385C2×Q8—232no—
386C2×Q8—432no—
387C2×Q8—432no—
388C2×Q8—416no—
389C2×Q8—416no—
390C2×Q8—416no—
391C2×Q8—416no—
392C2×Q8—432no—
393C2×Q8—432no—
394C2×Q8—416no—
395C2×Q8—416no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—41no—
533C22×C4—42no—
534C22×C4—41no—
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—41no—
545C22×C4—41no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—42no—
554C22×C4—42no—
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—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—42no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—42no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—41no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
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×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—41no—
672C22×C4—42no—
673C22×C4—41no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4#12014yes—
694C22×C4#12014yes—
695C22×C4#12118yes—
696C22×C4#12114yes—
697C22×C4#12114yes—
698C22×C4#12114yes—
699C22×C4C22⋊Q814yes—
700C22×C4C22⋊Q818yes—
701C22×C4C22⋊Q814yes—
702C22×C4C22⋊Q818yes—
703C22×C4#12314yes—
704C22×C4#12314yes—
705C22×C4#12414yes—
706C22×C4C4⋊Q814yes—
707C22×C4C4⋊Q814yes—
708C22×C4C4⋊Q818yes—
709C4⋊C4—432no—
710C4⋊C4—416no—
711C4⋊C4—432no—
712C4⋊C4—416no—
713C42—416no—
714C23C2×#12011yescharacteristic
715C23C2×#12011yescharacteristic
716C23C2×#12111yescharacteristic
717C23C2×#12112yes—
718C23C2×#12111yescharacteristic
719C23C2×#12111yescharacteristic
720C23C2×C22⋊Q811yescharacteristic
721C23C2×C22⋊Q811yescharacteristic
722C23C2×C22⋊Q812yes—
723C23C2×C22⋊Q812yes—
724C23C2×#12311yescharacteristic
725C23C2×#12311yescharacteristic
726C23#52511yescharacteristic
727C23#52512yes—
728C23C2×#12411yescharacteristic
729C23#52912yes—
730C23C2×C4⋊Q811yescharacteristic
731C23C2×C4⋊Q812yes—
732C23C2×C4⋊Q811yescharacteristic
733C23#53211yescharacteristic
734C23#53211yescharacteristic
735C23#53312yes—
736C23#53312yes—
737C23#53311yescharacteristic
738C23#53311yescharacteristic
739C23#53411yescharacteristic
740C23#53412yes—
741C23#53511yescharacteristic
742C23#53511yescharacteristic
743C23#53611yescharacteristic
744C23#53612yes—
745C23#53612yes—
746C23#53611yescharacteristic
747C23#53611yescharacteristic
748C23#53711yescharacteristic
749C23#53711yescharacteristic
750C23#53712yes—
751C23#53812yes—
752C23#53812yes—
753C23#53912yes—
754C23#54112yes—
755C23#54112yes—
756C23#54211yescharacteristic
757C23#54211yescharacteristic
758C23#54212yes—
759C23#54212yes—
760C23#54212yes—
761C23#54312yes—
762C23#54412yes—
763C23#54412yes—
764C23#54412yes—
765C23D4212yes—
766C23D4212yes—
767C23#54612yes—
768C23#54612yes—
769C23#54612yes—
770C23#54612yes—
771C23#54611yescharacteristic
772C23#54611yescharacteristic
773C23#54612yes—
774C23#54712yes—
775C23#54812yes—
776C23#54812yes—
777C23#54812yes—
778C23D4×Q812yes—
779C23D4×Q812yes—
780C23D4×Q812yes—
781C23D4×Q811yescharacteristic
782C23D4×Q811yescharacteristic
783C23D4×Q811yescharacteristic
784C23D4×Q811yescharacteristic
785C23#55011yescharacteristic
786C23#55011yescharacteristic
787C23#55112yes—
788C23#55112yes—
789C23#55112yes—
790C23#55211yescharacteristic
791C23#55211yescharacteristic
792C23#55412yes—
793C23#55412yes—
794C23#55412yes—
795C23#55411yescharacteristic
796C23#55411yescharacteristic
797C23#55411yescharacteristic
798C23#55411yescharacteristic
799C23#55612yes—
800C23#55612yes—
801C23#55612yes—
802C23#55611yescharacteristic
803C23#55611yescharacteristic
804C23#55712yes—
805C23#55712yes—
806C23#55712yes—
807C23#55712yes—
808C23Q8212yes—
809C23#56212yes—
810C23#56212yes—
811C23#56312yes—
812C23#56312yes—
813Q8—464no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—28no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—24no—
826C2×C4—28no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—24no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—28no—
839C2×C4—28no—
840C2×C4—28no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—28no—
845C2×C4—24no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—42no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—44no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—44no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—44no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—44no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—44no—
910C2×C4—44no—
911C2×C4—44no—
912C2×C4—44no—
913C2×C4—44no—
914C2×C4—44no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—44no—
919C2×C4—82no—
920C2×C4—82no—
921C2×C4—81no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4—81no—
925C2×C4—82no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—82no—
929C2×C4—81no—
930C2×C4—82no—
931C2×C4—81no—
932C2×C4—82no—
933C2×C4—82no—
934C2×C4—82no—
935C2×C4—82no—
936C2×C4—82no—
937C2×C4—82no—
938C2×C4—82no—
939C2×C4—81no—
940C2×C4—82no—
941C2×C4—82no—
942C2×C4—82no—
943C2×C4—82no—
944C2×C4—82no—
945C2×C4—82no—
946C2×C4—82no—
947C2×C4—82no—
948C2×C4—82no—
949C2×C4—81no—
950C2×C4—81no—
951C2×C4—82no—
952C2×C4—81no—
953C2×C4#39418yes—
954C2×C4#39518yescomplemented
955C22C2×#39411yescharacteristic
956C22C2×#39511yescharacteristic
957C22#239611yescharacteristic
958C22#240811yescharacteristic
959C22#240911yescharacteristic
960C22#240912yes—
961C22#241011yescharacteristic
962C22#241012yes—
963C22#241111yescharacteristic
964C22#241212yes—
965C22#241711yescharacteristic
966C22#241711yescharacteristic
967C22#241812yes—
968C22#242311yescharacteristic
969C22#242311yescharacteristic
970C22#242612yes—
971C22#242912yes—
972C22#243011yescharacteristic
973C22#243111yescharacteristic
974C22#243411yescharacteristic
975C22#243712yes—
976C22#243812yes—
977C22#244012yes—
978C22#244612yes—
979C22#244612yes—
980C22#245012yes—
981C22#245112yes—
982C22#245112yes—
983C22#245212yes—
984C22#246512yes—
985C22#246912yes—
986C22#247212yes—
987C22#249211yescharacteristic
988C22#249211yescharacteristic
989C22#249911yescharacteristic
990C22#250211yescharacteristic
991C22#252012yes—
992C22#253411yescharacteristic
993C22#253811yescharacteristic
994C22#253811yescharacteristic
995C22#253812yes—
996C22#254511yescharacteristic
997C22#254511yescharacteristic
998C22#254611yescharacteristic
999C22#254611yescharacteristic
1000C22#254612yes—
1001C22#254912yes—
1002C22#255012yes—
1003C22#255012yes—
1004C22#255112yes—
1005C22#256012yes—
1006C22#256411yescharacteristic
1007C22#256711yescharacteristic
1008C22#256812yes—
1009C22#258112yes—
1010C22#258111yescharacteristic
1011C22#258412yes—
1012C22#258411yescharacteristic
1013C22#258612yes—
1014C22#258812yes—
1015C22#260512yes—
1016C22#261611yescharacteristic
1017C22#261711yescharacteristic
1018C22#262011yescharacteristic
1019C22#262111yescharacteristic
1020C22#262711yescharacteristic
1021C22#262811yescharacteristic
1022C22#263711yescharacteristic
1023C22#265911yescharacteristic
1024C22#266211yescharacteristic
1025C22#267412yes—
1026C22#267612yes—
1027C22#267712yes—
1028C22#268112yes—
1029C22#269012yes—
1030C22#269212yes—
1031C22#270012yes—
1032C22#270012yes—
1033C22#270412yes—
1034C22#271312yes—
1035C22#271312yes—
1036C22#271512yes—
1037C22#272912yes—
1038C22#273012yes—
1039C22#273212yes—
1040C22#273412yes—
1041C22#275512yes—
1042C22#275512yes—
1043C22#275912yes—
1044C22#276212yes—
1045C22#278812yes—
1046C22#279912yes—
1047C22#280512yes—
1048C22#280612yes—
1049C22#281411yescharacteristic
1050C22#282011yescharacteristic
1051C22#284711yescharacteristic
1052C22#285711yescharacteristic
1053C22#285711yescharacteristic
1054C4—28no—
1055C4—28no—
1056C4—44no—
1057C4—48no—
1058C4—44no—
1059C4—48no—
1060C4—82no—
1061C4—82no—
1062C4—84no—
1063C4—82no—
1064C4—84no—
1065C2#1472511yescharacteristic
1066C2#1475811yescharacteristic
1067C2#1487211yescharacteristic
1068C2#1487711yescharacteristic
1069C2#1512811yescharacteristic
1070C2#1515811yescharacteristic
1071C2#1516411yescharacteristic
1072C2#1518011yescharacteristic
1073C2#1518211yescharacteristic
1074C2#1528012yes—
1075C2#1531812yes—
1076C2#1533212yes—
1077C2#1538212yes—
1078C2#1550012yes—
1079C2#1562412yes—
1080C2#1569812yes—
1081C2#1585212yes—
1082C2#1626411yescharacteristic
1083C2#1650511yescharacteristic
1084C2#1656511yescharacteristic
1085C2#1680611yescharacteristic
1086C2#1690111yescharacteristic
1087C2#1707811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC25C24
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
92. C22×C4⋊C4Q8semidirect
147. C2×#95Q8semidirect
148. C2×#95Q8semidirect
954. C2×C4#395semidirect

Maximal subgroups

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

subgroupindex
C22×#3952
C22×#3912
C2×#14462
C2×#14412
C2×#14362
C2×C4⋊#952
#75572
#75562