Finite Group Databasebeta

← #156713

Subgroups — #156713

Order 512.

3664 conjugacy classes of subgroups.

The subgroup lattice has 1021 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#395C211yesmaximal, characteristic
2C22×#395C211yesmaximal, characteristic
3C22×#389C211yesmaximal, characteristic
4C2×#1446C211yesmaximal, characteristic
5C2×#1444C212yesmaximal
6C2×#1436C212yesmaximal
7#7557C212yesmaximal
8#7557C212yesmaximal
9#7557C211yesmaximal, characteristic
10#7557C211yesmaximal, characteristic
11#7556C211yesmaximal, characteristic
12C24×Q8C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C4⋊C4C2212yes—
17C23×C4⋊C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C2×#395—28no—
21C2×#395—28no—
22C2×#395—24no—
23C2×#395—24no—
24C2×#389—24no—
25C2×#389—24no—
26C2×#389—24no—
27C22×#95C2212yes—
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38C22×#95C2212yes—
39C22×#95C2212yes—
40C22×#95C2212yes—
41C22×#95C2211yescharacteristic
42#1446—24no—
43#1444—28no—
44#1436—28no—
45C23×Q8—22no—
46C23×Q8—22no—
47C23×Q8—24no—
48C23×Q8—24no—
49C23×Q8—22no—
50C23×Q8—24no—
51C23×Q8—42no—
52C23×Q8—42no—
53C23×Q8—42no—
54C24×C4C2311yescharacteristic
55C24×C4C2312yes—
56C24×C4C2311yescharacteristic
57C24×C4C2311yescharacteristic
58C24×C4C2312yes—
59C24×C4C2311yescharacteristic
60C24×C4C2312yes—
61C24×C4C2311yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2312yes—
64C24×C4C2311yescharacteristic
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—24no—
75C22×C4⋊C4—24no—
76C22×C4⋊C4—24no—
77C22×C4⋊C4—24no—
78C22×C4⋊C4—24no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—22no—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—22no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—24no—
87C22×C4⋊C4—24no—
88C22×C4⋊C4—24no—
89C22×C4⋊C4—24no—
90C22×C4⋊C4—42no—
91C22×C4⋊C4—42no—
92C22×C4⋊C4—42no—
93C22×C4⋊C4—42no—
94C22×C4⋊C4—42no—
95C22×C4⋊C4—42no—
96C22×C4⋊C4—42no—
97C22×C4⋊C4D418yes—
98C22×C4⋊C4D414yes—
99C22×C4⋊C4D414yes—
100C22×C4⋊C4Q814yescomplemented
101C22×C42—22no—
102C22×C42—22no—
103C22×C42—22no—
104C22×C42—24no—
105C22×C42—42no—
106#395—232no—
107#395—232no—
108#389—232no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—22no—
114C2×#95—22no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—22no—
122C2×#95—22no—
123C2×#95—22no—
124C2×#95—22no—
125C2×#95—22no—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—22no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95—42no—
147C2×#95D418yes—
148C2×#95D414yes—
149C2×#95Q818yescomplemented
150C2×#95Q818yescomplemented
151C25C2411yescharacteristic
152C22×Q8—28no—
153C22×Q8—28no—
154C22×Q8—28no—
155C22×Q8—48no—
156C22×Q8—48no—
157C22×Q8—48no—
158C22×Q8—48no—
159C22×Q8—48no—
160C22×Q8—48no—
161C22×Q8—48no—
162C22×Q8—48no—
163C22×Q8—48no—
164C22×Q8—44no—
165C22×Q8—44no—
166C22×Q8—48no—
167C22×Q8—44no—
168C22×Q8—48no—
169C22×Q8—48no—
170C22×Q8—48no—
171C22×Q8—44no—
172C22×Q8—48no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
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—21no—
202C23×C4—21no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
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×C4—22no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
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×C4C2×D412yes—
274C23×C4C2×D414yes—
275C23×C4C2×D412yes—
276C23×C4C2×D412yes—
277C23×C4C2×D412yes—
278C23×C4C2×D412yes—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2×D412yes—
286C23×C4C2×D412yes—
287C23×C4C2×D414yes—
288C23×C4C2×Q814yes—
289C23×C4C2×Q812yes—
290C23×C4C2×Q812yes—
291C23×C4C2×Q814yes—
292C23×C4C2×Q814yes—
293C23×C4C2×Q814yes—
294C23×C4C2×Q814yes—
295C23×C4C2×Q812yes—
296C23×C4C2×Q814yes—
297C23×C4#4114yes—
298C23×C4#4112yes—
299C23×C4#4112yes—
300C23×C4#4114yes—
301C23×C4#4112yes—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—216no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—216no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—216no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—48no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—48no—
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—48no—
333C2×C4⋊C4—48no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—48no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—48no—
338C2×C42—28no—
339C2×C42—48no—
340C2×C42—48no—
341C2×C42—44no—
342C2×C42—44no—
343#95—216no—
344#95—28no—
345#95—216no—
346#95—28no—
347#95—28no—
348#95—28no—
349#95—216no—
350#95—216no—
351#95—216no—
352#95—48no—
353#95—48no—
354#95—48no—
355#95—48no—
356#95—48no—
357#95—44no—
358C24C22×D411yescharacteristic
359C24C22×D411yescharacteristic
360C24C22×D412yes—
361C24C22×D412yes—
362C24C22×D411yescharacteristic
363C24C22×Q811yescharacteristic
364C24C22×Q812yes—
365C24C22×Q812yes—
366C24C2×#4112yes—
367C24C2×#4111yescharacteristic
368C24C2×#4111yescharacteristic
369C24C2×#4111yescharacteristic
370C24C2×#4112yes—
371C24H(5,𝔽2)12yes—
372C24H(5,𝔽2)12yes—
373C24H(5,𝔽2)12yes—
374C242−1+412yes—
375C242−1+412yes—
376C242−1+412yes—
377C2×Q8—416no—
378C2×Q8—416no—
379C2×Q8—416no—
380C2×Q8—432no—
381C2×Q8—432no—
382C2×Q8—432no—
383C2×Q8—432no—
384C2×Q8—432no—
385C2×Q8—432no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
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—24no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
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—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—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
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—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—41no—
539C22×C4—42no—
540C22×C4—41no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
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—41no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—41no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
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—41no—
623C22×C4—42no—
624C22×C4—41no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—41no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—41no—
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#12014yes—
667C22×C4#12014yes—
668C22×C4#12014yes—
669C22×C4#12118yes—
670C22×C4C22⋊Q818yes—
671C22×C4C22⋊Q814yes—
672C22×C4C22⋊Q814yes—
673C22×C4C22⋊Q818yes—
674C22×C4C22⋊Q814yes—
675C22×C4C4⋊Q818yes—
676C22×C4C4⋊Q814yes—
677C22×C4C4⋊Q814yes—
678C22×C4C4⋊Q818yes—
679C4⋊C4—232no—
680C4⋊C4—416no—
681C4⋊C4—416no—
682C4⋊C4—432no—
683C4⋊C4—416no—
684C4⋊C4—432no—
685C42—416no—
686C23C2×#12011yescharacteristic
687C23C2×#12011yescharacteristic
688C23C2×#12011yescharacteristic
689C23C2×#12112yes—
690C23C2×C22⋊Q811yescharacteristic
691C23C2×C22⋊Q811yescharacteristic
692C23C2×C22⋊Q812yes—
693C23C2×C22⋊Q811yescharacteristic
694C23C2×C22⋊Q812yes—
695C23#52511yescharacteristic
696C23#52511yescharacteristic
697C23#52512yes—
698C23#52511yescharacteristic
699C23#52511yescharacteristic
700C23C2×C4⋊Q812yes—
701C23C2×C4⋊Q811yescharacteristic
702C23C2×C4⋊Q812yes—
703C23C2×C4⋊Q811yescharacteristic
704C23#53211yescharacteristic
705C23#53212yes—
706C23#53312yes—
707C23#53312yes—
708C23#53312yes—
709C23#53411yescharacteristic
710C23#53411yescharacteristic
711C23#53412yes—
712C23#53512yes—
713C23#53511yescharacteristic
714C23#53611yescharacteristic
715C23#53611yescharacteristic
716C23#53612yes—
717C23#53611yescharacteristic
718C23#53612yes—
719C23#53812yes—
720C23#53912yes—
721C23#53912yes—
722C23#53912yes—
723C23#54112yes—
724C23#54212yes—
725C23#54212yes—
726C23#54212yes—
727C23#54212yes—
728C23#54412yes—
729C23#54412yes—
730C23#54412yes—
731C23#54412yes—
732C23#54412yes—
733C23D4212yes—
734C23D4212yes—
735C23D4212yes—
736C23D4212yes—
737C23D4212yes—
738C23#54612yes—
739C23#54612yes—
740C23#54612yes—
741C23#54612yes—
742C23#54712yes—
743C23#54712yes—
744C23#54712yes—
745C23#54812yes—
746C23#54812yes—
747C23#54812yes—
748C23D4×Q812yes—
749C23D4×Q812yes—
750C23D4×Q812yes—
751C23D4×Q812yes—
752C23D4×Q812yes—
753C23D4×Q812yes—
754C23D4×Q812yes—
755C23D4×Q812yes—
756C23#55112yes—
757C23#55212yes—
758C23#55412yes—
759C23#55412yes—
760C23#55412yes—
761C23#55412yes—
762C23#55412yes—
763C23#55412yes—
764C23#55612yes—
765C23#55712yes—
766C23#55712yes—
767C23Q8212yes—
768C23Q8212yes—
769C23#56012yes—
770C23#56312yes—
771C23#56312yes—
772C23#56312yes—
773Q8—464no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—28no—
783C2×C4—28no—
784C2×C4—24no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—28no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—28no—
803C2×C4—28no—
804C2×C4—28no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—82no—
891C2×C4—82no—
892C2×C4—82no—
893C2×C4—82no—
894C2×C4—82no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4—82no—
899C2×C4—82no—
900C2×C4—82no—
901C2×C4—82no—
902C2×C4#39518yescomplemented
903C22C2×#39511yescharacteristic
904C22#238811yescharacteristic
905C22#239911yescharacteristic
906C22#240311yescharacteristic
907C22#240311yescharacteristic
908C22#240411yescharacteristic
909C22#240611yescharacteristic
910C22#240812yes—
911C22#240912yes—
912C22#240911yescharacteristic
913C22#241012yes—
914C22#241512yes—
915C22#242412yes—
916C22#242912yes—
917C22#243211yescharacteristic
918C22#243411yescharacteristic
919C22#243411yescharacteristic
920C22#243412yes—
921C22#243812yes—
922C22#244012yes—
923C22#244012yes—
924C22#244012yes—
925C22#244912yes—
926C22#244912yes—
927C22#244912yes—
928C22#244912yes—
929C22#245112yes—
930C22#245112yes—
931C22#245112yes—
932C22#245212yes—
933C22#245212yes—
934C22#245212yes—
935C22#246112yes—
936C22#246212yes—
937C22#246312yes—
938C22#246512yes—
939C22#246512yes—
940C22#246512yes—
941C22#254612yes—
942C22#255012yes—
943C22#255012yes—
944C22#255012yes—
945C22#255112yes—
946C22#255112yes—
947C22#255112yes—
948C22#255612yes—
949C22#255612yes—
950C22#256411yescharacteristic
951C22#256711yescharacteristic
952C22#256712yes—
953C22#258111yescharacteristic
954C22#258312yes—
955C22#258311yescharacteristic
956C22#258612yes—
957C22#262711yescharacteristic
958C22#262812yes—
959C22#263211yescharacteristic
960C22#263811yescharacteristic
961C22#266312yes—
962C22#266612yes—
963C22#266812yes—
964C22#266912yes—
965C22#267412yes—
966C22#267412yes—
967C22#267712yes—
968C22#267712yes—
969C22#267712yes—
970C22#267812yes—
971C22#268912yes—
972C22#269012yes—
973C22#271312yes—
974C22#271312yes—
975C22#272012yes—
976C22#272012yes—
977C22#272312yes—
978C22#272912yes—
979C22#272912yes—
980C22#273412yes—
981C22#273412yes—
982C22#274212yes—
983C22#277412yes—
984C22#279212yes—
985C22#279212yes—
986C22#280512yes—
987C22#283812yes—
988C22#284811yescharacteristic
989C22#285712yes—
990C4—28no—
991C4—44no—
992C4—44no—
993C4—44no—
994C4—44no—
995C4—48no—
996C4—44no—
997C4—48no—
998C4—48no—
999C4—82no—
1000C4—84no—
1001C2#1472011yescharacteristic
1002C2#1472311yescharacteristic
1003C2#1476312yes—
1004C2#1481612yes—
1005C2#1488111yescharacteristic
1006C2#1512812yes—
1007C2#1525711yescharacteristic
1008C2#1526511yescharacteristic
1009C2#1531812yes—
1010C2#1535412yes—
1011C2#1536012yes—
1012C2#1562512yes—
1013C2#1562712yes—
1014C2#1576211yescharacteristic
1015C2#1577912yes—
1016C2#1584911yescharacteristic
1017C2#1632512yes—
1018C2#1632712yes—
1019C2#1655312yes—
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
100. C22×C4⋊C4Q8semidirect
149. C2×#95Q8semidirect
150. C2×#95Q8semidirect
902. 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×#3892
C2×#14462
C2×#14442
C2×#14362
#75572
#75562