Finite Group Databasebeta

← #155778

Subgroups — #155778

Order 512.

2622 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#382C211yesmaximal, characteristic
2C2×#1444C211yesmaximal, characteristic
3C2×#1442C211yesmaximal, characteristic
4C2×#1434C211yesmaximal, characteristic
5C2×#1434C211yesmaximal, characteristic
6#7557C212yesmaximal
7#7557C212yesmaximal
8#7557C211yesmaximal, characteristic
9#7557C211yesmaximal, characteristic
10#7556C212yesmaximal
11#7556C212yesmaximal
12C23×C4⋊C4C2212yes—
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C2×#382—24no—
17C2×#382—24no—
18C2×#382—24no—
19C22×#95C2211yescharacteristic
20C22×#95C2211yescharacteristic
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2211yescharacteristic
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2212yes—
37C22×#95C2212yes—
38#1444—24no—
39#1442—24no—
40#1434—24no—
41#1434C418yescomplemented
42C24×C4C2312yes—
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C24×C4C2311yescharacteristic
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2312yes—
52C24×C4C2311yescharacteristic
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—42no—
61C22×C4⋊C4—42no—
62C22×C4⋊C4—42no—
63C22×C4⋊C4—42no—
64C22×C4⋊C4—42no—
65C22×C4⋊C4—42no—
66C22×C4⋊C4—42no—
67C22×C4⋊C4—42no—
68C22×C4⋊C4D414yes—
69C22×C4⋊C4D414yes—
70C22×C42—22no—
71C22×C42—22no—
72C22×C42—22no—
73C22×C42—22no—
74C22×C42C2×C414yes—
75C22×C42D414yes—
76C22×C42Q814yes—
77#382—232no—
78C2×#95—22no—
79C2×#95—22no—
80C2×#95—22no—
81C2×#95—22no—
82C2×#95—24no—
83C2×#95—24no—
84C2×#95—24no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—22no—
103C2×#95—24no—
104C2×#95—22no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—22no—
112C2×#95—22no—
113C2×#95—42no—
114C2×#95—42no—
115C2×#95—42no—
116C2×#95—42no—
117C2×#95—42no—
118C2×#95—42no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—42no—
122C2×#95—42no—
123C2×#95—42no—
124C2×#95—42no—
125C2×#95—42no—
126C2×#95—42no—
127C2×#95—42no—
128C2×#95—42no—
129C2×#95C2×C418yes—
130C2×#95C2×C414yes—
131C2×#95C2×C414yes—
132C2×#95C2×C418yes—
133C25C2411yescharacteristic
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—22no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—21no—
161C23×C4—21no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—21no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
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—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—21no—
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—21no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—21no—
236C23×C4—21no—
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—21no—
247C23×C4—21no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4C22×C414yes—
253C23×C4C22×C412yes—
254C23×C4C22×C412yes—
255C23×C4C22×C414yes—
256C23×C4C22×C412yes—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4C2×D412yes—
263C23×C4C2×D412yes—
264C23×C4C2×Q812yes—
265C23×C4C2×Q812yes—
266C23×C4C2×Q812yes—
267C23×C4#4112yes—
268C23×C4#4112yes—
269C23×C4#4112yes—
270C23×C4#4112yes—
271C23×C4#4114yes—
272C23×C4#4114yes—
273C23×C4#4112yes—
274C23×C4#4112yes—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—48no—
278C2×C4⋊C4—48no—
279C2×C4⋊C4—48no—
280C2×C4⋊C4—48no—
281C2×C4⋊C4—48no—
282C2×C4⋊C4—48no—
283C2×C4⋊C4—48no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—48no—
289C2×C4⋊C4—48no—
290C2×C4⋊C4—48no—
291C2×C4⋊C4—48no—
292C2×C42—28no—
293C2×C42—28no—
294C2×C42—28no—
295C2×C42—28no—
296C2×C42—28no—
297C2×C42—28no—
298C2×C42C4⋊C4116yescomplemented
299#95—28no—
300#95—28no—
301#95—216no—
302#95—216no—
303#95—216no—
304#95—28no—
305#95—28no—
306#95—48no—
307#95—48no—
308#95—48no—
309#95—48no—
310#95—44no—
311#95—44no—
312#95—48no—
313#95—48no—
314#95—48no—
315#95—48no—
316#95—44no—
317#95—44no—
318C24C23×C411yescharacteristic
319C24C22×D411yescharacteristic
320C24C22×D411yescharacteristic
321C24C22×D411yescharacteristic
322C24C22×Q811yescharacteristic
323C24C2×#4112yes—
324C24C2×#4112yes—
325C24C2×#4111yescharacteristic
326C24C2×#4111yescharacteristic
327C24C2×#4111yescharacteristic
328C24C2×#4111yescharacteristic
329C24C2×#4111yescharacteristic
330C24C2×#4111yescharacteristic
331C24H(5,𝔽2)11yescharacteristic
332C24H(5,𝔽2)11yescharacteristic
333C24H(5,𝔽2)12yes—
334C24H(5,𝔽2)12yes—
335C24H(5,𝔽2)12yes—
336C242−1+411yescharacteristic
337C242−1+411yescharacteristic
338C242−1+412yes—
339C242−1+412yes—
340C242−1+412yes—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
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—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
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—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—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
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—41no—
459C22×C4—41no—
460C22×C4—42no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—42no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—41no—
495C22×C4—41no—
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—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—41no—
530C22×C4—42no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
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—41no—
581C22×C4—41no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—41no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—41no—
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—41no—
618C22×C4—41no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
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×C4C2×C4⋊C414yes—
645C22×C4C2×C4⋊C414yes—
646C22×C4C2×C4⋊C414yes—
647C22×C4#11718yes—
648C22×C4C4×D414yes—
649C22×C4C4×D414yes—
650C22×C4#12014yes—
651C22×C4C22⋊Q814yes—
652C22×C4C22⋊Q814yes—
653C22×C4#12314yes—
654C4⋊C4—416no—
655C4⋊C4—416no—
656C4⋊C4—432no—
657C42—232no—
658C23C22×C4⋊C411yescharacteristic
659C23C2×#11712yes—
660C23C2×C4×D411yescharacteristic
661C23C2×C4×D411yescharacteristic
662C23C4×#4111yescharacteristic
663C23C4×#4111yescharacteristic
664C23#51811yescharacteristic
665C23#51911yescharacteristic
666C23#52012yes—
667C23#52012yes—
668C23#52012yes—
669C23C2×#12011yescharacteristic
670C23C2×C22⋊Q811yescharacteristic
671C23C2×C22⋊Q811yescharacteristic
672C23C2×#12311yescharacteristic
673C23#52511yescharacteristic
674C23#52511yescharacteristic
675C23#53211yescharacteristic
676C23#53211yescharacteristic
677C23#53311yescharacteristic
678C23#53312yes—
679C23#53311yescharacteristic
680C23#53412yes—
681C23#53412yes—
682C23#53511yescharacteristic
683C23#53511yescharacteristic
684C23#53511yescharacteristic
685C23#53611yescharacteristic
686C23#53611yescharacteristic
687C23#53611yescharacteristic
688C23#53612yes—
689C23#53612yes—
690C23#53711yescharacteristic
691C23#53711yescharacteristic
692C23#53812yes—
693C23#53812yes—
694C23#53812yes—
695C23#53812yes—
696C23#53912yes—
697C23#53912yes—
698C23#53912yes—
699C23#53912yes—
700C23#53912yes—
701C23#53912yes—
702C23#53912yes—
703C23#53912yes—
704C23#54112yes—
705C23#54112yes—
706C23#54112yes—
707C23#54112yes—
708C23#54212yes—
709C23#54212yes—
710C23#54212yes—
711C23#54212yes—
712C23#54411yescharacteristic
713C23#54411yescharacteristic
714C23#54412yes—
715C23#54412yes—
716C23#54412yes—
717C23#54612yes—
718C23#54611yescharacteristic
719C23#54611yescharacteristic
720C23#54712yes—
721C23#54711yescharacteristic
722C23#54711yescharacteristic
723C23#54812yes—
724C23#54811yescharacteristic
725C23#54811yescharacteristic
726C23#55012yes—
727C23#55011yescharacteristic
728C23#55011yescharacteristic
729C23#55112yes—
730C23#55112yes—
731C23#55212yes—
732C23#55212yes—
733C23#55212yes—
734C23#55212yes—
735C23#55212yes—
736C23#55211yescharacteristic
737C23#55211yescharacteristic
738C23#55312yes—
739C23#55311yescharacteristic
740C23#55311yescharacteristic
741C23#55512yes—
742C23#55512yes—
743C23#55512yes—
744C23#55511yescharacteristic
745C23#55511yescharacteristic
746C23#55612yes—
747C23#55611yescharacteristic
748C23#55611yescharacteristic
749C23H(3,𝔽4)12yes—
750C23#56212yes—
751C23#56212yes—
752C23#56212yes—
753C23#56312yes—
754C23#56312yes—
755C23#56312yes—
756C23#56412yes—
757C2×C4—24no—
758C2×C4—24no—
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—24no—
768C2×C4—24no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—42no—
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—42no—
844C2×C4—42no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—81no—
850C2×C4—82no—
851C2×C4—81no—
852C2×C4—82no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—82no—
856C2×C4—82no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—82no—
862C2×C4—82no—
863C2×C4—82no—
864C2×C4—81no—
865C2×C4—82no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—82no—
870C2×C4—82no—
871C2×C4—81no—
872C2×C4—81no—
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—82no—
886C2×C4—82no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—82no—
890C2×C4—82no—
891C2×C4—82no—
892C2×C4—82no—
893C2×C4—82no—
894C2×C4—82no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4#38518yes—
898C22#228511yescharacteristic
899C22C2×#38511yescharacteristic
900C22#229611yescharacteristic
901C22#231611yescharacteristic
902C22#231711yescharacteristic
903C22#231711yescharacteristic
904C22#231711yescharacteristic
905C22#231812yes—
906C22#232012yes—
907C22#232212yes—
908C22#232212yes—
909C22#233412yes—
910C22#233412yes—
911C22#234312yes—
912C22#234612yes—
913C22#235212yes—
914C22#235412yes—
915C22#236211yescharacteristic
916C22#236211yescharacteristic
917C22#236311yescharacteristic
918C22#236311yescharacteristic
919C22#237912yes—
920C22#238212yes—
921C22#240711yescharacteristic
922C22#240711yescharacteristic
923C22#243111yescharacteristic
924C22#243211yescharacteristic
925C22#243911yescharacteristic
926C22#243912yes—
927C22#243911yescharacteristic
928C22#244111yescharacteristic
929C22#244112yes—
930C22#244111yescharacteristic
931C22#248511yescharacteristic
932C22#248511yescharacteristic
933C22#249911yescharacteristic
934C22#250011yescharacteristic
935C22#261011yescharacteristic
936C22#261011yescharacteristic
937C22#261111yescharacteristic
938C22#261111yescharacteristic
939C22#261212yes—
940C22#261212yes—
941C22#261311yescharacteristic
942C22#261411yescharacteristic
943C22#262311yescharacteristic
944C22#262311yescharacteristic
945C22#262712yes—
946C22#262712yes—
947C22#263111yescharacteristic
948C22#263211yescharacteristic
949C22#263311yescharacteristic
950C22#263411yescharacteristic
951C22#266211yescharacteristic
952C22#266211yescharacteristic
953C22#266411yescharacteristic
954C22#266411yescharacteristic
955C22#266612yes—
956C22#266612yes—
957C22#266612yes—
958C22#266612yes—
959C22#268412yes—
960C22#268612yes—
961C22#268612yes—
962C22#269012yes—
963C22#269012yes—
964C22#269412yes—
965C22#269412yes—
966C22#271712yes—
967C22#271912yes—
968C22#271912yes—
969C22#272112yes—
970C22#272112yes—
971C22#273012yes—
972C22#273012yes—
973C22#273112yes—
974C22#273312yes—
975C22#274412yes—
976C22#274412yes—
977C22#276512yes—
978C22#276512yes—
979C22#276712yes—
980C22#276712yes—
981C22#276912yes—
982C22#277512yes—
983C22#277512yes—
984C22#278112yes—
985C22#278112yes—
986C22#278212yes—
987C22#278312yes—
988C22#278312yes—
989C22#278512yes—
990C22#278912yes—
991C22#281911yescharacteristic
992C22#282011yescharacteristic
993C22#282011yescharacteristic
994C22#282211yescharacteristic
995C22#284412yes—
996C22#284512yes—
997C4—28no—
998C4—44no—
999C4—44no—
1000C4—48no—
1001C4—82no—
1002C4—84no—
1003C4—84no—
1004C4—82no—
1005C4—84no—
1006C4—82no—
1007C4—82no—
1008C2#1387911yescharacteristic
1009C2#1396311yescharacteristic
1010C2#1412911yescharacteristic
1011C2#1426311yescharacteristic
1012C2#1429811yescharacteristic
1013C2#1435611yescharacteristic
1014C2#1439312yes—
1015C2#1439412yes—
1016C2#1439912yes—
1017C2#1440012yes—
1018C2#1467711yescharacteristic
1019C2#1668011yescharacteristic
1020C2#1668111yescharacteristic
1021C2#1668211yescharacteristic
1022C2#1668311yescharacteristic
1023C2#1668612yes—
1024C2#1668712yes—
1025C2#1668712yes—
1026C2#1668912yes—
1027C2#1702911yescharacteristic
1028C2#1703111yescharacteristic
1029C2#1704611yescharacteristic
1030C2#1704811yescharacteristic
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
41. #1434C4semidirect
298. C2×C42C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3822
C2×#14442
C2×#14422
C2×#14342
#75572
#75562