Finite Group Databasebeta

← #153806

Subgroups — #153806

Order 512.

3678 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C4⋊C4C212yesmaximal
2C2×#1444C211yesmaximal, characteristic
3C2×#1436C212yesmaximal
4C2×#1436C212yesmaximal
5C2×#1436C212yesmaximal
6#7557C212yesmaximal
7#7556C211yesmaximal, characteristic
8#7554C212yesmaximal
9#7554C211yesmaximal, characteristic
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2212yes—
13C23×C42C2212yes—
14C23×C42C2212yes—
15C23×C42C2211yescharacteristic
16C2×C4×C4⋊C4—28no—
17C2×C4×C4⋊C4—28no—
18C2×C4×C4⋊C4—28no—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2211yescharacteristic
22C22×#95C2212yes—
23C22×#95C2211yescharacteristic
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34#1444C418yescomplemented
35#1436—28no—
36#1436—28no—
37#1436C4116yescomplemented
38C24×C4C2311yescharacteristic
39C24×C4C2312yes—
40C24×C4C2311yescharacteristic
41C24×C4C2312yes—
42C24×C4C2311yescharacteristic
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2312yes—
46C24×C4C2312yes—
47C22×C4⋊C4—24no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—24no—
53C22×C4⋊C4—24no—
54C22×C4⋊C4—24no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—41no—
60C22×C4⋊C4—41no—
61C22×C4⋊C4C2×C418yes—
62C22×C4⋊C4C2×C414yes—
63C22×C4⋊C4C2×C418yes—
64C22×C4⋊C4D418yes—
65C22×C4⋊C4Q818yes—
66C22×C42—24no—
67C22×C42—24no—
68C22×C42—24no—
69C22×C42—24no—
70C22×C42—24no—
71C22×C42—24no—
72C22×C42—24no—
73C22×C42—24no—
74C22×C42—24no—
75C22×C42—24no—
76C22×C42—24no—
77C22×C42—24no—
78C22×C42—24no—
79C22×C42—41no—
80C22×C42—41no—
81C22×C42—42no—
82C22×C42—42no—
83C22×C42C2×C418yes—
84C22×C42D414yes—
85C4×C4⋊C4—264no—
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—24no—
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—22no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—41no—
112C2×#95—41no—
113C2×#95—42no—
114C2×#95—41no—
115C2×#95—41no—
116C2×#95—42no—
117C2×#95—41no—
118C2×#95—41no—
119C2×#95C2×C418yes—
120C2×#95C2×C418yes—
121C2×#95C2×C418yes—
122C2×#95C2×C418yes—
123C2×#95C2×C418yes—
124C2×#95C2×C414yes—
125C2×#95C2×C418yes—
126C2×#95C2×C414yes—
127C2×#95D418yes—
128C25C2411yescharacteristic
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
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—21no—
178C23×C4—21no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—21no—
182C23×C4—22no—
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—21no—
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—21no—
212C23×C4—21no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4C22×C414yes—
219C23×C4C22×C412yes—
220C23×C4C22×C412yes—
221C23×C4C22×C414yes—
222C23×C4C22×C414yes—
223C23×C4C22×C414yes—
224C23×C4C22×C412yes—
225C23×C4C22×C414yes—
226C23×C4C22×C414yes—
227C23×C4C22×C414yes—
228C23×C4C22×C414yes—
229C23×C4C22×C414yes—
230C23×C4C2×D414yes—
231C23×C4C2×D412yes—
232C23×C4C2×D414yes—
233C23×C4C2×D414yes—
234C23×C4C2×D414yes—
235C23×C4C2×D414yes—
236C23×C4C2×D414yes—
237C23×C4C2×D414yes—
238C23×C4C2×Q814yes—
239C23×C4C2×Q814yes—
240C23×C4C2×Q814yes—
241C23×C4#4112yes—
242C23×C4#4114yes—
243C23×C4#4114yes—
244C23×C4#4114yes—
245C23×C4#4114yes—
246C23×C4#4114yes—
247C23×C4#4114yes—
248C2×C4⋊C4—216no—
249C2×C4⋊C4—216no—
250C2×C4⋊C4—216no—
251C2×C4⋊C4—216no—
252C2×C4⋊C4—216no—
253C2×C4⋊C4—216no—
254C2×C4⋊C4—216no—
255C2×C4⋊C4—216no—
256C2×C4⋊C4—216no—
257C2×C4⋊C4—216no—
258C2×C4⋊C4—216no—
259C2×C4⋊C4—216no—
260C2×C4⋊C4—216no—
261C2×C4⋊C4—216no—
262C2×C4⋊C4—44no—
263C2×C4⋊C4—44no—
264C2×C4⋊C4—48no—
265C2×C4⋊C4—44no—
266C2×C4⋊C4C4⋊C4132yescomplemented
267C2×C42—216no—
268C2×C42—216no—
269C2×C42—216no—
270C2×C42—216no—
271C2×C42—216no—
272C2×C42—216no—
273C2×C42—216no—
274C2×C42—216no—
275C2×C42—216no—
276C2×C42—44no—
277C2×C42—44no—
278C2×C42—48no—
279C2×C42—44no—
280C2×C42—48no—
281C2×C42—48no—
282C2×C42—48no—
283C2×C42—48no—
284C2×C42—48no—
285C2×C42—48no—
286#95—216no—
287#95—216no—
288#95—216no—
289#95—216no—
290#95—216no—
291#95—216no—
292#95—216no—
293#95—44no—
294#95—44no—
295#95—48no—
296#95—48no—
297#95—44no—
298#95—44no—
299#95—48no—
300#95C42116yescomplemented
301C24C23×C412yes—
302C24C23×C411yescharacteristic
303C24C22×D412yes—
304C24C22×D411yescharacteristic
305C24C22×D412yes—
306C24C22×Q812yes—
307C24C2×#4112yes—
308C24C2×#4112yes—
309C24C2×#4112yes—
310C24C2×#4112yes—
311C24C2×#4111yescharacteristic
312C24C2×#4112yes—
313C24C2×#4112yes—
314C24H(5,𝔽2)11yescharacteristic
315C24H(5,𝔽2)11yescharacteristic
316C24H(5,𝔽2)11yescharacteristic
317C242−1+412yes—
318C242−1+411yescharacteristic
319C242−1+412yes—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
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—24no—
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—24no—
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—22no—
401C22×C4—22no—
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—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
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—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
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—42no—
487C22×C4—42no—
488C22×C4—41no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—41no—
494C22×C4—42no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
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—41no—
516C22×C4—41no—
517C22×C4—41no—
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—41no—
530C22×C4—42no—
531C22×C4—41no—
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—41no—
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—41no—
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—41no—
574C22×C4—42no—
575C22×C4—41no—
576C22×C4C2×C4214yes—
577C22×C4C2×C4218yes—
578C22×C4C2×C4⋊C418yes—
579C22×C4C2×C4⋊C418yes—
580C22×C4C2×C4⋊C418yes—
581C22×C4#11718yes—
582C22×C4C4×D418yes—
583C22×C4C4×D414yes—
584C22×C4C4×D418yes—
585C22×C4C4×D418yes—
586C22×C4C4×D418yes—
587C22×C4C4×D418yes—
588C22×C4C4×D418yes—
589C22×C4C4×Q818yes—
590C22×C4C4×Q818yes—
591C22×C4#12018yes—
592C22×C4C22⋊Q818yes—
593C22×C4C22⋊Q818yes—
594C22×C4#12318yes—
595C4⋊C4—264no—
596C4⋊C4—264no—
597C4⋊C4—416no—
598C42—264no—
599C42—416no—
600C42—432no—
601C23C22×C4211yescharacteristic
602C23C22×C4⋊C412yes—
603C23C2×#11712yes—
604C23C2×C4×D412yes—
605C23C2×C4×D411yescharacteristic
606C23C2×C4×D412yes—
607C23C2×C4×D412yes—
608C23C2×C4×D412yes—
609C23C2×C4×D412yes—
610C23C2×C4×D412yes—
611C23C2×C4×Q812yes—
612C23C2×C4×Q812yes—
613C23C4×#4111yescharacteristic
614C23C4×#4112yes—
615C23C4×#4112yes—
616C23C4×#4112yes—
617C23C4×#4112yes—
618C23#51811yescharacteristic
619C23#51912yes—
620C23#51911yescharacteristic
621C23#51911yescharacteristic
622C23#52012yes—
623C23#52012yes—
624C23#52012yes—
625C23#52011yescharacteristic
626C23C2×#12012yes—
627C23C2×C22⋊Q812yes—
628C23C2×C22⋊Q812yes—
629C23C2×#12312yes—
630C23#52512yes—
631C23#52512yes—
632C23#52512yes—
633C23#52512yes—
634C23#52512yes—
635C23#52512yes—
636C23#52912yes—
637C23#52912yes—
638C23#52912yes—
639C23#52912yes—
640C23#53312yes—
641C23#53312yes—
642C23#53411yescharacteristic
643C23#53612yes—
644C23#53711yescharacteristic
645C23#53811yescharacteristic
646C23#53912yes—
647C23#53912yes—
648C23#53911yescharacteristic
649C23#54112yes—
650C23#54112yes—
651C23#54212yes—
652C23D4211yescharacteristic
653C23D4212yes—
654C23D4211yescharacteristic
655C23#54612yes—
656C23#54712yes—
657C23#54712yes—
658C23#54712yes—
659C23#54712yes—
660C23#54712yes—
661C23#54812yes—
662C23#54812yes—
663C23#54812yes—
664C23D4×Q812yes—
665C23D4×Q812yes—
666C23#55012yes—
667C23#55111yescharacteristic
668C23#55111yescharacteristic
669C23#55212yes—
670C23#55212yes—
671C23#55212yes—
672C23#55312yes—
673C23#55312yes—
674C23#55312yes—
675C23#55412yes—
676C23#55412yes—
677C23#55511yescharacteristic
678C23#55612yes—
679C23#55612yes—
680C23#55612yes—
681C23#55612yes—
682C23#55712yes—
683C23#55712yes—
684C23#55712yes—
685C23Q8211yescharacteristic
686C23#55911yescharacteristic
687C23#55911yescharacteristic
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—24no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—24no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
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—42no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
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—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
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×C4C4×C4⋊C4116yescomplemented
806C2×C4#385116yes—
807C22C2×C4×C4⋊C412yes—
808C22C42×D411yescharacteristic
809C22C42×D412yes—
810C22#227411yescharacteristic
811C22#227611yescharacteristic
812C22C2×#38512yes—
813C22#229012yes—
814C22#229012yes—
815C22#229612yes—
816C22C4×#12012yes—
817C22C4×#12012yes—
818C22C4×#12312yes—
819C22C4×#12312yes—
820C22C4×C22⋊Q812yes—
821C22C4×C22⋊Q812yes—
822C22C4×C22⋊Q812yes—
823C22C4×C22⋊Q812yes—
824C22#232212yes—
825C22#232312yes—
826C22#232511yescharacteristic
827C22#232711yescharacteristic
828C22#233211yescharacteristic
829C22#233412yes—
830C22#233612yes—
831C22#233611yescharacteristic
832C22#234412yes—
833C22#234712yes—
834C22D4×C4⋊C412yes—
835C22D4×C4⋊C412yes—
836C22Q8×C4⋊C412yes—
837C22#235112yes—
838C22#235412yes—
839C22#235512yes—
840C22#235811yescharacteristic
841C22#235912yes—
842C22#236112yes—
843C22#236112yes—
844C22#236112yes—
845C22#236212yes—
846C22#236212yes—
847C22#236212yes—
848C22#236512yes—
849C22#236512yes—
850C22#236512yes—
851C22#236611yescharacteristic
852C22#236712yes—
853C22#236911yescharacteristic
854C22#237012yes—
855C22#237012yes—
856C22#237312yes—
857C22#237411yescharacteristic
858C22#240311yescharacteristic
859C22#240612yes—
860C22#240712yes—
861C22#240912yes—
862C22#244312yes—
863C22#244312yes—
864C22#244612yes—
865C22#244812yes—
866C22#244912yes—
867C22#244912yes—
868C22#245112yes—
869C22#245312yes—
870C22#245511yescharacteristic
871C22#245612yes—
872C22#246212yes—
873C22#246212yes—
874C22#246311yescharacteristic
875C22#246912yes—
876C22#246912yes—
877C22#247412yes—
878C22#247512yes—
879C22#247812yes—
880C22#247912yes—
881C22#257912yes—
882C22#258112yes—
883C22#258211yescharacteristic
884C22#258512yes—
885C22#258611yescharacteristic
886C22#258812yes—
887C22#259012yes—
888C22#259311yescharacteristic
889C22#259412yes—
890C22#259612yes—
891C22#259912yes—
892C22#260011yescharacteristic
893C22#260911yescharacteristic
894C4—216no—
895C4—216no—
896C4—44no—
897C4—48no—
898C4—48no—
899C4—48no—
900C4—44no—
901C4—82no—
902C4—84no—
903C2C4×#38512yes—
904C2#1379011yescharacteristic
905C2C4⋊C4211yescharacteristic
906C2#1382112yes—
907C2#1382311yescharacteristic
908C2#1401512yes—
909C2#1401712yes—
910C2#1403112yes—
911C2#1403512yes—
912C2#1406312yes—
913C2#1406912yes—
914C2#1411112yes—
915C2#1411712yes—
916C2#1417111yescharacteristic
917C2#1417412yes—
918C2#1419112yes—
919C2#1419411yescharacteristic
920C2#1421911yescharacteristic
921C2#1423811yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC23C22×C42
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
34. #1444C4semidirect
37. #1436C4semidirect
266. C2×C4⋊C4C4⋊C4semidirect
300. #95C42semidirect
805. C2×C4C4×C4⋊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×#14442
C2×#14362
#75572
#75562
#75542