Finite Group Databasebeta

← #156390

Subgroups — #156390

Order 512.

2458 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1443C212yesmaximal
2C2×#1442C211yesmaximal, characteristic
3C2×#1441C211yesmaximal, characteristic
4C2×#1441C211yesmaximal, characteristic
5C2×#1436C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic
7#7557C211yesmaximal, characteristic
8#7556C212yesmaximal
9#7556C212yesmaximal
10#7556C212yesmaximal
11#7554C211yesmaximal, characteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C22×#95C2211yescharacteristic
17C22×#95C2211yescharacteristic
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2211yescharacteristic
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2211yescharacteristic
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35#1443—28no—
36#1442—24no—
37#1441—24no—
38#1441C418yescomplemented
39#1436—24no—
40C4⋊#95—24no—
41C24×C4C2311yescharacteristic
42C24×C4C2312yes—
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—42no—
63C22×C4⋊C4—42no—
64C22×C4⋊C4—42no—
65C22×C4⋊C4—42no—
66C22×C4⋊C4C2×C414yes—
67C22×C4⋊C4C2×C414yes—
68C22×C4⋊C4D414yes—
69C22×C42—22no—
70C22×C42—22no—
71C22×C42—42no—
72C22×C42—42no—
73C22×C42D414yes—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95—22no—
77C2×#95—24no—
78C2×#95—22no—
79C2×#95—22no—
80C2×#95—24no—
81C2×#95—22no—
82C2×#95—22no—
83C2×#95—24no—
84C2×#95—24no—
85C2×#95—22no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—22no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—22no—
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—22no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95—42no—
111C2×#95—42no—
112C2×#95—42no—
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×#95C2×C418yes—
126C2×#95C2×C414yes—
127C2×#95C2×C418yes—
128C2×#95D414yes—
129C25C2411yescharacteristic
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—22no—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—22no—
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—22no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—21no—
176C23×C4—22no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—22no—
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—21no—
195C23×C4—21no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—21no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—21no—
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—21no—
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—21no—
245C23×C4—21no—
246C23×C4—22no—
247C23×C4—21no—
248C23×C4—22no—
249C23×C4C22×C412yes—
250C23×C4C22×C414yes—
251C23×C4C22×C414yes—
252C23×C4C22×C412yes—
253C23×C4C22×C412yes—
254C23×C4C2×D414yes—
255C23×C4C2×D412yes—
256C23×C4C2×D412yes—
257C23×C4C2×D412yes—
258C23×C4C2×D412yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4#4112yes—
263C23×C4#4114yes—
264C23×C4#4112yes—
265C23×C4#4112yes—
266C23×C4#4114yes—
267C23×C4#4112yes—
268C23×C4#4112yes—
269C23×C4#4112yes—
270C23×C4#4112yes—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—48no—
277C2×C4⋊C4—48no—
278C2×C4⋊C4—44no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—44no—
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×C42—28no—
289C2×C42—44no—
290C2×C42—44no—
291C2×C42—48no—
292C2×C42—48no—
293#95—28no—
294#95—216no—
295#95—28no—
296#95—28no—
297#95—48no—
298#95—48no—
299#95—48no—
300#95—48no—
301#95—48no—
302#95—48no—
303#95—44no—
304#95—44no—
305#95—48no—
306#95—48no—
307#95—48no—
308#95—48no—
309#95—44no—
310#95—48no—
311#95—44no—
312C24C23×C411yescharacteristic
313C24C22×D411yescharacteristic
314C24C22×D411yescharacteristic
315C24C22×D411yescharacteristic
316C24C2×#4111yescharacteristic
317C24C2×#4111yescharacteristic
318C24C2×#4111yescharacteristic
319C24C2×#4111yescharacteristic
320C24C2×#4111yescharacteristic
321C24C2×#4111yescharacteristic
322C24C2×#4111yescharacteristic
323C24C2×#4112yes—
324C24C2×#4112yes—
325C24H(5,𝔽2)12yes—
326C24H(5,𝔽2)12yes—
327C24H(5,𝔽2)12yes—
328C24H(5,𝔽2)11yescharacteristic
329C242−1+412yes—
330C242−1+412yes—
331C242−1+411yescharacteristic
332C242−1+411yescharacteristic
333C242−1+412yes—
334C242−1+411yescharacteristic
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—22no—
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—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—24no—
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—22no—
415C22×C4—24no—
416C22×C4—22no—
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—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—42no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—42no—
467C22×C4—41no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—41no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—41no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—42no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—42no—
512C22×C4—41no—
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—41no—
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—41no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—41no—
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—41no—
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—41no—
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×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#11714yes—
639C22×C4C4×D414yes—
640C22×C4C4×D414yes—
641C22×C4C4×D414yes—
642C22×C4#12114yes—
643C22×C4#12114yes—
644C22×C4#12314yes—
645C22×C4#12414yes—
646C22×C4#12414yes—
647C22×C4#12614yes—
648C4⋊C4—416no—
649C4⋊C4—416no—
650C4⋊C4—416no—
651C42—416no—
652C23C2×#11711yescharacteristic
653C23C2×C4×D411yescharacteristic
654C23C2×C4×D411yescharacteristic
655C23C2×C4×D411yescharacteristic
656C23C4×#4112yes—
657C23C4×#4111yescharacteristic
658C23#51812yes—
659C23#51912yes—
660C23#51911yescharacteristic
661C23#52012yes—
662C23#52011yescharacteristic
663C23C2×#12111yescharacteristic
664C23C2×#12111yescharacteristic
665C23C2×#12311yescharacteristic
666C23#52511yescharacteristic
667C23C2×#12411yescharacteristic
668C23C2×#12411yescharacteristic
669C23C2×#12611yescharacteristic
670C23#52911yescharacteristic
671C23#52912yes—
672C23#53211yescharacteristic
673C23#53211yescharacteristic
674C23#53411yescharacteristic
675C23#53411yescharacteristic
676C23#53412yes—
677C23#53511yescharacteristic
678C23#53611yescharacteristic
679C23#53611yescharacteristic
680C23#53611yescharacteristic
681C23#53611yescharacteristic
682C23#53612yes—
683C23#53711yescharacteristic
684C23#53712yes—
685C23#53712yes—
686C23#53812yes—
687C23#53812yes—
688C23#53812yes—
689C23#53812yes—
690C23#53812yes—
691C23#53912yes—
692C23#53912yes—
693C23#53912yes—
694C23#53912yes—
695C23#53912yes—
696C23#53912yes—
697C23#53912yes—
698C23#53912yes—
699C23#53912yes—
700C23#54112yes—
701C23#54111yescharacteristic
702C23#54112yes—
703C23#54112yes—
704C23#54112yes—
705C23#54112yes—
706C23#54112yes—
707C23#54112yes—
708C23#54211yescharacteristic
709C23#54212yes—
710C23#54212yes—
711C23D4211yescharacteristic
712C23#54612yes—
713C23#54711yescharacteristic
714C23#54711yescharacteristic
715C23#54711yescharacteristic
716C23#54712yes—
717C23#54711yescharacteristic
718C23#54811yescharacteristic
719C23#54812yes—
720C23#54811yescharacteristic
721C23#55012yes—
722C23#55112yes—
723C23#55211yescharacteristic
724C23#55211yescharacteristic
725C23#55211yescharacteristic
726C23#55211yescharacteristic
727C23#55212yes—
728C23#55212yes—
729C23#55212yes—
730C23#55211yescharacteristic
731C23#55312yes—
732C23#55312yes—
733C23#55312yes—
734C23#55311yescharacteristic
735C23#55512yes—
736C23#55511yescharacteristic
737C23#55511yescharacteristic
738C23#55612yes—
739C23#55612yes—
740C23#55612yes—
741C23#55611yescharacteristic
742C23#55912yes—
743C23#56212yes—
744C23#56212yes—
745C23#56312yes—
746C23#56312yes—
747C23#56312yes—
748C23#56312yes—
749C23#56312yes—
750C23#56312yes—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—28no—
755C2×C4—24no—
756C2×C4—24no—
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—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—44no—
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—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—82no—
842C2×C4—81no—
843C2×C4—82no—
844C2×C4—82no—
845C2×C4—82no—
846C2×C4—82no—
847C2×C4—82no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—82no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—82no—
856C2×C4—82no—
857C2×C4—82no—
858C2×C4—82no—
859C2×C4—81no—
860C2×C4—81no—
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—81no—
883C2×C4—81no—
884C2×C4—82no—
885C2×C4—82no—
886C2×C4—82no—
887C2×C4—82no—
888C2×C4—82no—
889C2×C4—82no—
890C2×C4—81no—
891C2×C4#38818yes—
892C22C2×#38811yescharacteristic
893C22C4×#12111yescharacteristic
894C22C4×#12411yescharacteristic
895C22#231812yes—
896C22#232111yescharacteristic
897C22#232211yescharacteristic
898C22#232311yescharacteristic
899C22#232312yes—
900C22#232512yes—
901C22#232711yescharacteristic
902C22#233412yes—
903C22#233612yes—
904C22#233612yes—
905C22#234411yescharacteristic
906C22#234611yescharacteristic
907C22#235612yes—
908C22#236111yescharacteristic
909C22#236211yescharacteristic
910C22#236212yes—
911C22#236312yes—
912C22#237412yes—
913C22#237812yes—
914C22#238112yes—
915C22#248511yescharacteristic
916C22#248611yescharacteristic
917C22#248911yescharacteristic
918C22#248912yes—
919C22#249111yescharacteristic
920C22#249511yescharacteristic
921C22#249611yescharacteristic
922C22#249911yescharacteristic
923C22#250311yescharacteristic
924C22#251412yes—
925C22#253611yescharacteristic
926C22#253711yescharacteristic
927C22#254311yescharacteristic
928C22#254511yescharacteristic
929C22#254711yescharacteristic
930C22#254811yescharacteristic
931C22#255412yes—
932C22#259111yescharacteristic
933C22#259312yes—
934C22#261011yescharacteristic
935C22#261711yescharacteristic
936C22#261811yescharacteristic
937C22#261811yescharacteristic
938C22#262111yescharacteristic
939C22#262211yescharacteristic
940C22#262311yescharacteristic
941C22#263411yescharacteristic
942C22#263811yescharacteristic
943C22#263911yescharacteristic
944C22#263912yes—
945C22#264211yescharacteristic
946C22#264312yes—
947C22#265212yes—
948C22#265512yes—
949C22#265512yes—
950C22#266311yescharacteristic
951C22#266411yescharacteristic
952C22#266412yes—
953C22#268112yes—
954C22#268212yes—
955C22#268912yes—
956C22#269512yes—
957C22#271512yes—
958C22#272112yes—
959C22#272112yes—
960C22#272412yes—
961C22#272512yes—
962C22#272512yes—
963C22#272512yes—
964C22#272712yes—
965C22#272812yes—
966C22#273112yes—
967C22#274412yes—
968C22#274512yes—
969C22#276912yes—
970C22#277012yes—
971C22#277012yes—
972C22#277512yes—
973C22#277612yes—
974C22#277612yes—
975C22#277912yes—
976C22#278112yes—
977C22#278312yes—
978C22#278312yes—
979C22#278712yes—
980C22#278712yes—
981C22#278912yes—
982C22#279412yes—
983C22#279412yes—
984C22#280812yes—
985C22#281411yescharacteristic
986C22#281711yescharacteristic
987C22#282011yescharacteristic
988C22#282111yescharacteristic
989C22#283112yes—
990C22#283312yes—
991C4—28no—
992C4—44no—
993C4—44no—
994C4—44no—
995C4—82no—
996C4—84no—
997C4—84no—
998C4—82no—
999C4—82no—
1000C4—84no—
1001C4—84no—
1002C2#1399411yescharacteristic
1003C2#1400311yescharacteristic
1004C2#1422711yescharacteristic
1005C2#1425911yescharacteristic
1006C2#1431411yescharacteristic
1007C2#1432611yescharacteristic
1008C2#1438712yes—
1009C2#1451112yes—
1010C2#1456512yes—
1011C2#1459012yes—
1012C2#1462611yescharacteristic
1013C2#1681511yescharacteristic
1014C2#1682111yescharacteristic
1015C2#1686312yes—
1016C2#1687012yes—
1017C2#1700511yescharacteristic
1018C2#1701011yescharacteristic
1019C2#1701312yes—
1020C2#1701412yes—
1021C2#1702311yescharacteristic
1022C2#1703111yescharacteristic
1023C2#1706311yescharacteristic
1024C2#1706911yescharacteristic
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
38. #1441C4semidirect

Maximal subgroups

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

subgroupindex
C2×#14432
C2×#14422
C2×#14412
C2×#14362
C2×C4⋊#952
#75572
#75562
#75542