Finite Group Databasebeta

← #158438

Subgroups — #158438

Order 512.

3208 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#391C211yesmaximal, characteristic
2C2×#1446C212yesmaximal
3C2×#1445C212yesmaximal
4C2×#1441C211yesmaximal, characteristic
5C2×#1436C212yesmaximal
6#7557C211yesmaximal, characteristic
7#7557C212yesmaximal
8#7557C212yesmaximal
9#7556C212yesmaximal
10C24×Q8C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2212yes—
13C23×C4⋊C4C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C2×#391—28no—
16C2×#391—24no—
17C22×#95C2211yescharacteristic
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33#1446—28no—
34#1445—28no—
35#1441—24no—
36#1436—28no—
37C23×Q8—24no—
38C23×Q8—22no—
39C23×Q8—24no—
40C23×Q8—24no—
41C23×Q8—22no—
42C23×Q8—24no—
43C23×Q8—41no—
44C23×Q8—41no—
45C23×Q8—41no—
46C23×Q8—41no—
47C23×Q8Q814yes—
48C24×C4C2311yescharacteristic
49C24×C4C2312yes—
50C24×C4C2312yes—
51C24×C4C2312yes—
52C24×C4C2311yescharacteristic
53C24×C4C2312yes—
54C24×C4C2312yes—
55C24×C4C2312yes—
56C24×C4C2311yescharacteristic
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—22no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—41no—
66C22×C4⋊C4—41no—
67C22×C4⋊C4—42no—
68C22×C4⋊C4—42no—
69C22×C4⋊C4—41no—
70C22×C4⋊C4—42no—
71C22×C4⋊C4—41no—
72C22×C4⋊C4D414yes—
73C22×C4⋊C4Q818yescomplemented
74C22×C42—24no—
75C22×C42—22no—
76C22×C42—24no—
77C22×C42—41no—
78C22×C42—41no—
79#391—232no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—24no—
83C2×#95—24no—
84C2×#95—24no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—22no—
95C2×#95—24no—
96C2×#95—24no—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—42no—
113C2×#95—42no—
114C2×#95—42no—
115C2×#95—42no—
116C2×#95—42no—
117C2×#95—42no—
118C2×#95—41no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—41no—
122C2×#95—42no—
123C2×#95D418yes—
124C2×#95D418yes—
125C25C2411yescharacteristic
126C22×Q8—28no—
127C22×Q8—216no—
128C22×Q8—28no—
129C22×Q8—216no—
130C22×Q8—28no—
131C22×Q8—216no—
132C22×Q8—44no—
133C22×Q8—44no—
134C22×Q8—48no—
135C22×Q8—48no—
136C22×Q8—48no—
137C22×Q8—48no—
138C22×Q8—48no—
139C22×Q8—48no—
140C22×Q8—48no—
141C22×Q8—48no—
142C22×Q8—44no—
143C22×Q8—44no—
144C22×Q8—44no—
145C22×Q8—44no—
146C22×Q8—48no—
147C22×Q8—44no—
148C22×Q8—44no—
149C23×C4—22no—
150C23×C4—22no—
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—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—21no—
181C23×C4—21no—
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—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—21no—
225C23×C4—21no—
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×C4C2×D412yes—
249C23×C4C2×D414yes—
250C23×C4C2×D412yes—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4C2×D414yes—
254C23×C4C2×D414yes—
255C23×C4C2×D412yes—
256C23×C4C2×D414yes—
257C23×C4C2×Q814yes—
258C23×C4C2×Q814yes—
259C23×C4C2×Q814yes—
260C23×C4C2×Q814yes—
261C23×C4C2×Q812yes—
262C23×C4#4114yes—
263C23×C4#4114yes—
264C23×C4#4114yes—
265C23×C4#4114yes—
266C23×C4#4114yes—
267C23×C4#4112yes—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—216no—
270C2×C4⋊C4—216no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—48no—
274C2×C4⋊C4—48no—
275C2×C4⋊C4—48no—
276C2×C4⋊C4—48no—
277C2×C4⋊C4—48no—
278C2×C4⋊C4—48no—
279C2×C4⋊C4—48no—
280C2×C4⋊C4—48no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—48no—
284C2×C4⋊C4—44no—
285C2×C42—28no—
286C2×C42—48no—
287C2×C42—48no—
288C2×C42—44no—
289C2×C42—44no—
290#95—216no—
291#95—216no—
292#95—216no—
293#95—216no—
294#95—48no—
295#95—48no—
296#95—48no—
297#95—48no—
298#95—48no—
299#95—48no—
300#95—48no—
301#95—44no—
302#95—48no—
303#95—44no—
304#95—44no—
305#95—48no—
306C24C22×D412yes—
307C24C22×D411yescharacteristic
308C24C22×D412yes—
309C24C22×Q811yescharacteristic
310C24C22×Q812yes—
311C24C2×#4111yescharacteristic
312C24C2×#4112yes—
313C24C2×#4112yes—
314C24C2×#4112yes—
315C24C2×#4112yes—
316C24C2×#4112yes—
317C24H(5,𝔽2)11yescharacteristic
318C24H(5,𝔽2)11yescharacteristic
319C24H(5,𝔽2)11yescharacteristic
320C24H(5,𝔽2)11yescharacteristic
321C24H(5,𝔽2)12yes—
322C242−1+412yes—
323C242−1+412yes—
324C242−1+412yes—
325C2×Q8—232no—
326C2×Q8—432no—
327C2×Q8—432no—
328C2×Q8—416no—
329C2×Q8—416no—
330C2×Q8—432no—
331C2×Q8—432no—
332C2×Q8—416no—
333C2×Q8—416no—
334C2×Q8—416no—
335C2×Q8—416no—
336C22×C4—22no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
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—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
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—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—22no—
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—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
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—41no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—41no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—41no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
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—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—41no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—41no—
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—41no—
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—41no—
602C22×C4#12014yes—
603C22×C4C22⋊Q818yes—
604C22×C4C22⋊Q818yes—
605C22×C4C22⋊Q818yes—
606C22×C4C22⋊Q814yes—
607C22×C4C22⋊Q818yes—
608C22×C4#12318yes—
609C22×C4#12314yes—
610C22×C4#12714yes—
611C4⋊C4—416no—
612C4⋊C4—432no—
613C4⋊C4—416no—
614C42—416no—
615C23C2×#12011yescharacteristic
616C23C2×C22⋊Q812yes—
617C23C2×C22⋊Q812yes—
618C23C2×C22⋊Q812yes—
619C23C2×C22⋊Q812yes—
620C23C2×C22⋊Q811yescharacteristic
621C23C2×#12312yes—
622C23C2×#12311yescharacteristic
623C23#52512yes—
624C23#52512yes—
625C23#52511yescharacteristic
626C23#52912yes—
627C23#52912yes—
628C23#52912yes—
629C23C2×#12711yescharacteristic
630C23#53212yes—
631C23#53312yes—
632C23#53312yes—
633C23#53312yes—
634C23#53411yescharacteristic
635C23#53511yescharacteristic
636C23#53612yes—
637C23#53612yes—
638C23#53712yes—
639C23#53712yes—
640C23#53811yescharacteristic
641C23#53811yescharacteristic
642C23#53812yes—
643C23#53912yes—
644C23#54112yes—
645C23#54112yes—
646C23#54112yes—
647C23#54212yes—
648C23#54212yes—
649C23#54212yes—
650C23#54212yes—
651C23#54212yes—
652C23#54212yes—
653C23#54212yes—
654C23#54312yes—
655C23#54311yescharacteristic
656C23#54311yescharacteristic
657C23#54412yes—
658C23D4212yes—
659C23D4212yes—
660C23#54612yes—
661C23#54612yes—
662C23#54612yes—
663C23#54612yes—
664C23#54612yes—
665C23#54612yes—
666C23#54612yes—
667C23#54712yes—
668C23#54712yes—
669C23#54712yes—
670C23#54812yes—
671C23#54812yes—
672C23#54812yes—
673C23D4×Q812yes—
674C23D4×Q812yes—
675C23D4×Q812yes—
676C23#55112yes—
677C23#55111yescharacteristic
678C23#55111yescharacteristic
679C23#55112yes—
680C23#55112yes—
681C23#55212yes—
682C23#55212yes—
683C23#55412yes—
684C23#55511yescharacteristic
685C23#55612yes—
686C23#55612yes—
687C23#55712yes—
688C23#55712yes—
689C23#55712yes—
690C23#55712yes—
691C23#55712yes—
692C23Q8212yes—
693C23Q8211yescharacteristic
694C23#55912yes—
695C23#55912yes—
696C23H(3,𝔽4)11yescharacteristic
697C23#56212yes—
698C23#56311yescharacteristic
699C23#56312yes—
700C23#56311yescharacteristic
701C23#56311yescharacteristic
702Q8—464no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—24no—
709C2×C4—28no—
710C2×C4—28no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—82no—
794C2×C4—82no—
795C2×C4—82no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4—82no—
799C2×C4—82no—
800C2×C4—82no—
801C2×C4—82no—
802C2×C4—82no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—82no—
818C2×C4—82no—
819C2×C4—82no—
820C2×C4—82no—
821C2×C4#39918yes—
822C22C2×#39911yescharacteristic
823C22#239612yes—
824C22#240511yescharacteristic
825C22#240912yes—
826C22#241812yes—
827C22#241812yes—
828C22#243012yes—
829C22#243311yescharacteristic
830C22#243712yes—
831C22#243712yes—
832C22#243712yes—
833C22#243812yes—
834C22#243912yes—
835C22#244612yes—
836C22#244612yes—
837C22#244712yes—
838C22#244712yes—
839C22#244912yes—
840C22#245112yes—
841C22#245112yes—
842C22#245112yes—
843C22#245112yes—
844C22#245112yes—
845C22#245212yes—
846C22#245312yes—
847C22#245312yes—
848C22#245312yes—
849C22#245812yes—
850C22#245812yes—
851C22#245912yes—
852C22#246112yes—
853C22#246212yes—
854C22#246212yes—
855C22#247712yes—
856C22#248211yescharacteristic
857C22#252012yes—
858C22#252112yes—
859C22#252712yes—
860C22#253911yescharacteristic
861C22#254012yes—
862C22#254212yes—
863C22#255712yes—
864C22#256512yes—
865C22#257211yescharacteristic
866C22#258112yes—
867C22#258212yes—
868C22#258212yes—
869C22#258611yescharacteristic
870C22#258812yes—
871C22#260712yes—
872C22#262512yes—
873C22#262611yescharacteristic
874C22#263712yes—
875C22#265012yes—
876C22#266512yes—
877C22#267212yes—
878C22#267412yes—
879C22#268112yes—
880C22#268312yes—
881C22#268411yescharacteristic
882C22#269212yes—
883C22#269812yes—
884C22#270212yes—
885C22#271212yes—
886C22#271212yes—
887C22#271312yes—
888C22#271312yes—
889C22#271512yes—
890C22#271612yes—
891C22#271711yescharacteristic
892C22#272312yes—
893C22#273111yescharacteristic
894C22#273411yescharacteristic
895C22#275412yes—
896C22#275812yes—
897C22#279812yes—
898C22#279912yes—
899C22#279911yescharacteristic
900C22#279912yes—
901C22#279911yescharacteristic
902C22#280612yes—
903C22#280911yescharacteristic
904C22#281111yescharacteristic
905C22#283211yescharacteristic
906C22#283311yescharacteristic
907C22#284811yescharacteristic
908C22#285512yes—
909C4—28no—
910C4—48no—
911C4—44no—
912C4—48no—
913C4—48no—
914C4—84no—
915C4—82no—
916C4—84no—
917C4—84no—
918C2#1473411yescharacteristic
919C2#1476812yes—
920C2#1478712yes—
921C2#1487812yes—
922C2#1519312yes—
923C2#1532512yes—
924C2#1533612yes—
925C2#1533712yes—
926C2#1578411yescharacteristic
927C2#1583311yescharacteristic
928C2#1585611yescharacteristic
929C2#1596312yes—
930C2#1596412yes—
931C2#1606612yes—
932C2#1609311yescharacteristic
933C2#1628012yes—
934C2#1628112yes—
935C2#1663011yescharacteristic
936C2#1665311yescharacteristic
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
73. C22×C4⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#3912
C2×#14462
C2×#14452
C2×#14412
C2×#14362
#75572
#75562