Finite Group Databasebeta

← #154116

Subgroups — #154116

Order 512.

3050 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C4⋊C4C211yesmaximal, characteristic
2C2×#1441C212yesmaximal
3C2×C4⋊#95C211yesmaximal, characteristic
4C2×#1434C211yesmaximal, characteristic
5C2×#1434C211yesmaximal, characteristic
6C2×#1434C211yesmaximal, characteristic
7#7557C212yesmaximal
8#7557C212yesmaximal
9#7556C212yesmaximal
10#7554C211yesmaximal, characteristic
11#7554C211yesmaximal, characteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2212yes—
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C2×C4×C4⋊C4—28no—
19C2×C4×C4⋊C4C418yescomplemented
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2211yescharacteristic
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2212yes—
36C22×#95C2212yes—
37#1441—28no—
38C4⋊#95—24no—
39#1434—24no—
40#1434—24no—
41#1434—24no—
42C24×C4C2312yes—
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2312yes—
46C24×C4C2311yescharacteristic
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C22×C4⋊C4—24no—
54C22×C4⋊C4—24no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—24no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—42no—
66C22×C4⋊C4—42no—
67C22×C4⋊C4C2×C414yes—
68C22×C4⋊C4C2×C414yes—
69C22×C4⋊C4D418yes—
70C22×C42—24no—
71C22×C42—24no—
72C22×C42—22no—
73C22×C42—22no—
74C22×C42—24no—
75C22×C42—24no—
76C22×C42—22no—
77C22×C42—22no—
78C22×C42—42no—
79C22×C42—42no—
80C22×C42C2×C414yes—
81C22×C42C2×C414yes—
82C22×C42C2×C414yes—
83C22×C42D414yes—
84C22×C42Q814yes—
85C4×C4⋊C4—232no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—24no—
106C2×#95—22no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—22no—
120C2×#95—22no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—42no—
124C2×#95—42no—
125C2×#95—42no—
126C2×#95—42no—
127C2×#95—42no—
128C2×#95—42no—
129C2×#95—42no—
130C2×#95—42no—
131C2×#95C2×C414yes—
132C2×#95C2×C414yes—
133C2×#95D414yes—
134C2×#95Q814yes—
135C25C2411yescharacteristic
136C23×C4—21no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—22no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—21no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—22no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—22no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
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—22no—
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×C4C22×C412yes—
243C23×C4C22×C412yes—
244C23×C4C22×C412yes—
245C23×C4C22×C412yes—
246C23×C4C22×C412yes—
247C23×C4C22×C412yes—
248C23×C4C22×C412yes—
249C23×C4C2×D414yes—
250C23×C4C2×D414yes—
251C23×C4C2×D412yes—
252C23×C4C2×D414yes—
253C23×C4C2×D414yes—
254C23×C4C2×D412yes—
255C23×C4C2×D412yes—
256C23×C4C2×D412yes—
257C23×C4C2×Q814yes—
258C23×C4C2×Q812yes—
259C23×C4C2×Q812yes—
260C23×C4C2×Q812yes—
261C23×C4C2×Q812yes—
262C23×C4#4114yes—
263C23×C4#4114yes—
264C23×C4#4114yes—
265C23×C4#4112yes—
266C23×C4#4112yes—
267C23×C4#4114yes—
268C23×C4#4112yes—
269C23×C4#4114yes—
270C23×C4#4112yes—
271C23×C4#4112yes—
272C23×C4#4112yes—
273C2×C4⋊C4—216no—
274C2×C4⋊C4—216no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—216no—
281C2×C4⋊C4—216no—
282C2×C4⋊C4—216no—
283C2×C4⋊C4—48no—
284C2×C4⋊C4—48no—
285C2×C4⋊C4—48no—
286C2×C4⋊C4—48no—
287C2×C4⋊C4—48no—
288C2×C4⋊C4—48no—
289C2×C4⋊C4C22⋊C4116yes—
290C2×C42—28no—
291C2×C42—28no—
292C2×C42—216no—
293C2×C42—216no—
294C2×C42—28no—
295C2×C42—28no—
296C2×C42—28no—
297C2×C42—28no—
298C2×C42—44no—
299C2×C42—44no—
300C2×C42—48no—
301C2×C42—48no—
302C2×C42—48no—
303C2×C42—48no—
304C2×C42C4⋊C4116yescomplemented
305#95—216no—
306#95—216no—
307#95—28no—
308#95—28no—
309#95—28no—
310#95—28no—
311#95—48no—
312#95—48no—
313#95—48no—
314#95—48no—
315#95—48no—
316#95—48no—
317#95—48no—
318#95—48no—
319#95—44no—
320#95—44no—
321#95—48no—
322C24C23×C411yescharacteristic
323C24C22×D412yes—
324C24C22×D411yescharacteristic
325C24C22×D411yescharacteristic
326C24C22×Q811yescharacteristic
327C24C22×Q811yescharacteristic
328C24C2×#4112yes—
329C24C2×#4112yes—
330C24C2×#4111yescharacteristic
331C24C2×#4111yescharacteristic
332C24C2×#4112yes—
333C24C2×#4111yescharacteristic
334C24C2×#4111yescharacteristic
335C24C2×#4111yescharacteristic
336C24C2×#4111yescharacteristic
337C24C2×#4112yes—
338C24C2×#4112yes—
339C24H(5,𝔽2)12yes—
340C24H(5,𝔽2)11yescharacteristic
341C24H(5,𝔽2)11yescharacteristic
342C242−1+412yes—
343C242−1+411yescharacteristic
344C242−1+411yescharacteristic
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
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—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
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—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—42no—
507C22×C4—41no—
508C22×C4—41no—
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—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
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—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4C2×C22⋊C414yes—
626C22×C4C2×C22⋊C414yes—
627C22×C4C2×C22⋊C414yes—
628C22×C4C2×C4⋊C414yes—
629C22×C4C2×C4⋊C414yes—
630C22×C4C2×C4⋊C414yes—
631C22×C4#11714yes—
632C22×C4#11714yes—
633C22×C4#11714yes—
634C22×C4#11714yes—
635C22×C4#11714yes—
636C22×C4C4×D414yes—
637C22×C4C4×Q814yes—
638C22×C4#12118yes—
639C22×C4#12114yes—
640C22×C4C22⋊Q818yes—
641C22×C4C22⋊Q814yes—
642C22×C4#12318yes—
643C22×C4#12318yes—
644C22×C4#12514yes—
645C22×C4C4⋊Q814yes—
646C4⋊C4—232no—
647C4⋊C4—232no—
648C4⋊C4—432no—
649C42—232no—
650C42—416no—
651C42—416no—
652C23C22×C22⋊C411yescharacteristic
653C23C22×C4⋊C411yescharacteristic
654C23C2×#11711yescharacteristic
655C23C2×#11711yescharacteristic
656C23C2×#11711yescharacteristic
657C23C2×#11711yescharacteristic
658C23C2×#11711yescharacteristic
659C23C2×C4×D411yescharacteristic
660C23C2×C4×Q811yescharacteristic
661C23C4×#4111yescharacteristic
662C23C4×#4111yescharacteristic
663C23#51811yescharacteristic
664C23#51911yescharacteristic
665C23#52011yescharacteristic
666C23#52011yescharacteristic
667C23C2×#12112yes—
668C23C2×#12111yescharacteristic
669C23C2×C22⋊Q811yescharacteristic
670C23C2×C22⋊Q812yes—
671C23C2×#12312yes—
672C23C2×#12312yes—
673C23#52512yes—
674C23#52512yes—
675C23#52512yes—
676C23#52512yes—
677C23#52512yes—
678C23C2×#12511yescharacteristic
679C23#52912yes—
680C23#52912yes—
681C23#52912yes—
682C23#52912yes—
683C23#52912yes—
684C23#52912yes—
685C23#52912yes—
686C23#52912yes—
687C23C2×C4⋊Q811yescharacteristic
688C23#53211yescharacteristic
689C23#53211yescharacteristic
690C23#53212yes—
691C23#53311yescharacteristic
692C23#53311yescharacteristic
693C23#53312yes—
694C23#53312yes—
695C23#53312yes—
696C23#53312yes—
697C23#53511yescharacteristic
698C23#53611yescharacteristic
699C23#53712yes—
700C23#53812yes—
701C23#53812yes—
702C23#53912yes—
703C23#53912yes—
704C23#54112yes—
705C23#54112yes—
706C23#54212yes—
707C23#54212yes—
708C23#54411yescharacteristic
709C23#54411yescharacteristic
710C23#54412yes—
711C23D4212yes—
712C23#54612yes—
713C23#54612yes—
714C23#54611yescharacteristic
715C23#54611yescharacteristic
716C23#54712yes—
717C23#54712yes—
718C23#54812yes—
719C23#54812yes—
720C23#54811yescharacteristic
721C23#54811yescharacteristic
722C23D4×Q812yes—
723C23#55012yes—
724C23#55112yes—
725C23#55112yes—
726C23#55211yescharacteristic
727C23#55211yescharacteristic
728C23#55212yes—
729C23#55212yes—
730C23#55212yes—
731C23#55212yes—
732C23#55311yescharacteristic
733C23#55311yescharacteristic
734C23#55312yes—
735C23#55312yes—
736C23#55312yes—
737C23#55312yes—
738C23#55411yescharacteristic
739C23#55411yescharacteristic
740C23#55412yes—
741C23#55512yes—
742C23#55611yescharacteristic
743C23#55611yescharacteristic
744C23#55612yes—
745C23#55612yes—
746C23#55612yes—
747C23#55711yescharacteristic
748C23#55711yescharacteristic
749C23#55911yescharacteristic
750C23#55911yescharacteristic
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—28no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
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—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
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—44no—
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—82no—
876C2×C4—82no—
877C2×C4—82no—
878C2×C4—82no—
879C2×C4—82no—
880C2×C4—82no—
881C2×C4—82no—
882C2×C4—82no—
883C2×C4—82no—
884C2×C4—82no—
885C2×C4#38018yes—
886C2×C4#38118yes—
887C2×C4#38918yes—
888C22C2×#38011yescharacteristic
889C22C2×#38111yescharacteristic
890C22#228011yescharacteristic
891C22#228311yescharacteristic
892C22#228311yescharacteristic
893C22#228511yescharacteristic
894C22#228511yescharacteristic
895C22#229011yescharacteristic
896C22#229011yescharacteristic
897C22C2×#38911yescharacteristic
898C22#229511yescharacteristic
899C22#229511yescharacteristic
900C22#229611yescharacteristic
901C22#231611yescharacteristic
902C22#231711yescharacteristic
903C22#231811yescharacteristic
904C22#231811yescharacteristic
905C22#232011yescharacteristic
906C22#232011yescharacteristic
907C22D4×C22⋊C411yescharacteristic
908C22#233911yescharacteristic
909C22Q8×C22⋊C411yescharacteristic
910C22#234111yescharacteristic
911C22#234411yescharacteristic
912C22#234511yescharacteristic
913C22#234611yescharacteristic
914C22#234711yescharacteristic
915C22#235211yescharacteristic
916C22#235211yescharacteristic
917C22#235311yescharacteristic
918C22#235311yescharacteristic
919C22#235511yescharacteristic
920C22#235511yescharacteristic
921C22#235611yescharacteristic
922C22#235611yescharacteristic
923C22#239212yes—
924C22#239612yes—
925C22#239912yes—
926C22#240212yes—
927C22#241412yes—
928C22#241512yes—
929C22#241612yes—
930C22#241712yes—
931C22#241812yes—
932C22#241912yes—
933C22#242112yes—
934C22#242312yes—
935C22#243912yes—
936C22#244012yes—
937C22#244112yes—
938C22#244212yes—
939C22#244312yes—
940C22#244412yes—
941C22#244612yes—
942C22#244812yes—
943C22#245612yes—
944C22#245812yes—
945C22#246012yes—
946C22#246212yes—
947C22#246312yes—
948C22#246512yes—
949C22#246712yes—
950C22#246812yes—
951C22#246912yes—
952C22#246912yes—
953C22#247412yes—
954C22#247512yes—
955C22#252412yes—
956C22#252512yes—
957C22#252812yes—
958C22#252912yes—
959C22#254411yescharacteristic
960C22#254511yescharacteristic
961C22#255011yescharacteristic
962C22#255011yescharacteristic
963C22#256511yescharacteristic
964C22#256611yescharacteristic
965C22#257011yescharacteristic
966C22#257011yescharacteristic
967C22#257312yes—
968C22#257412yes—
969C22#258512yes—
970C22#258712yes—
971C22#258812yes—
972C22#259312yes—
973C22#259412yes—
974C22#259512yes—
975C22#260112yes—
976C22#260112yes—
977C22#260512yes—
978C22#260612yes—
979C22#266212yes—
980C22#266412yes—
981C22#266612yes—
982C22#266612yes—
983C22#285412yes—
984C22#285412yes—
985C22#285512yes—
986C22#285512yes—
987C4—28no—
988C4—28no—
989C4—28no—
990C4—44no—
991C4—44no—
992C4—44no—
993C4—44no—
994C4—84no—
995C4—84no—
996C4—84no—
997C4—84no—
998C2#1384811yescharacteristic
999C2#1389011yescharacteristic
1000C2#1389311yescharacteristic
1001C2#1389411yescharacteristic
1002C2#1389711yescharacteristic
1003C2#1390711yescharacteristic
1004C2#1390911yescharacteristic
1005C2#1392711yescharacteristic
1006C2#1392811yescharacteristic
1007C2#1393111yescharacteristic
1008C2#1393211yescharacteristic
1009C2#1395111yescharacteristic
1010C2#1396411yescharacteristic
1011C2#1435611yescharacteristic
1012C2#1468511yescharacteristic
1013C2#1479912yes—
1014C2#1480012yes—
1015C2#1480412yes—
1016C2#1480512yes—
1017C2#1486112yes—
1018C2#1486212yes—
1019C2#1486312yes—
1020C2#1486412yes—
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
19. C2×C4×C4⋊C4C4semidirect
304. C2×C42C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C4⋊C42
C2×#14412
C2×C4⋊#952
C2×#14342
#75572
#75562
#75542