Finite Group Databasebeta

← #155687

Subgroups — #155687

Order 512.

2802 conjugacy classes of subgroups.

The subgroup lattice has 1017 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×#1441C212yesmaximal
5C2×C4⋊#95C211yesmaximal, characteristic
6C2×#1434C211yesmaximal, characteristic
7#7557C211yesmaximal, characteristic
8#7557C211yesmaximal, characteristic
9#7557C212yesmaximal
10#7557C212yesmaximal
11#7556C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C4⋊C4C2212yes—
16C23×C42C2211yescharacteristic
17C2×#382—24no—
18C2×#382—28no—
19C22×#95C2211yescharacteristic
20C22×#95C2212yes—
21C22×#95C2211yescharacteristic
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2212yes—
34C22×#95C2211yescharacteristic
35C22×#95C2212yes—
36C22×#95C2212yes—
37#1444—24no—
38#1442—24no—
39#1441—28no—
40C4⋊#95C418yescomplemented
41#1434—24no—
42C24×C4C2312yes—
43C24×C4C2312yes—
44C24×C4C2311yescharacteristic
45C24×C4C2312yes—
46C24×C4C2311yescharacteristic
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2312yes—
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C22×C4⋊C4—24no—
54C22×C4⋊C4—24no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—24no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—24no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—42no—
69C22×C4⋊C4—42no—
70C22×C4⋊C4—42no—
71C22×C4⋊C4—42no—
72C22×C4⋊C4—42no—
73C22×C4⋊C4—42no—
74C22×C4⋊C4—42no—
75C22×C4⋊C4—42no—
76C22×C4⋊C4C2×C418yes—
77C22×C42—24no—
78C22×C42—24no—
79C22×C42C2×C414yes—
80C22×C42D414yes—
81C22×C42Q814yes—
82#382—232no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95—22no—
86C2×#95—22no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—22no—
93C2×#95—22no—
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—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—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×#95—42no—
126C2×#95—42no—
127C2×#95C2×C414yes—
128C2×#95C2×C414yes—
129C2×#95C2×C418yes—
130C2×#95D418yes—
131C2×#95D414yes—
132C2×#95Q814yes—
133C25C2411yescharacteristic
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—22no—
141C23×C4—21no—
142C23×C4—21no—
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—21no—
156C23×C4—21no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—21no—
160C23×C4—21no—
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—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
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—21no—
199C23×C4—21no—
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—21no—
216C23×C4—21no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
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—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4C22×C414yes—
247C23×C4C22×C412yes—
248C23×C4C22×C414yes—
249C23×C4C22×C412yes—
250C23×C4C22×C412yes—
251C23×C4C2×D414yes—
252C23×C4C2×D412yes—
253C23×C4C2×D414yes—
254C23×C4C2×D412yes—
255C23×C4C2×D412yes—
256C23×C4C2×D412yes—
257C23×C4C2×D412yes—
258C23×C4C2×D414yes—
259C23×C4C2×D412yes—
260C23×C4C2×Q812yes—
261C23×C4C2×Q812yes—
262C23×C4C2×Q812yes—
263C23×C4C2×Q812yes—
264C23×C4C2×Q812yes—
265C23×C4C2×Q812yes—
266C23×C4#4114yes—
267C23×C4#4114yes—
268C23×C4#4114yes—
269C23×C4#4112yes—
270C23×C4#4112yes—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—216no—
274C2×C4⋊C4—216no—
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—48no—
282C2×C4⋊C4—48no—
283C2×C4⋊C4—48no—
284C2×C4⋊C4—48no—
285C2×C4⋊C4—48no—
286C2×C4⋊C4—48no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—48no—
290C2×C4⋊C4—48no—
291C2×C4⋊C4—48no—
292C2×C4⋊C4—48no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C42—216no—
296C2×C42—28no—
297C2×C42—216no—
298C2×C42—28no—
299C2×C42C4⋊C4116yescomplemented
300#95—216no—
301#95—28no—
302#95—28no—
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×D412yes—
321C24C22×D411yescharacteristic
322C24C22×Q811yescharacteristic
323C24C22×Q811yescharacteristic
324C24C2×#4112yes—
325C24C2×#4112yes—
326C24C2×#4112yes—
327C24C2×#4111yescharacteristic
328C24C2×#4111yescharacteristic
329C24H(5,𝔽2)11yescharacteristic
330C24H(5,𝔽2)11yescharacteristic
331C24H(5,𝔽2)11yescharacteristic
332C24H(5,𝔽2)11yescharacteristic
333C24H(5,𝔽2)12yes—
334C24H(5,𝔽2)12yes—
335C242−1+411yescharacteristic
336C242−1+411yescharacteristic
337C242−1+411yescharacteristic
338C242−1+411yescharacteristic
339C242−1+412yes—
340C242−1+412yes—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
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—22no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—24no—
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—22no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
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—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—41no—
473C22×C4—41no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
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—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—41no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—41no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
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—41no—
540C22×C4—41no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
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—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×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4C2×C4⋊C414yes—
629C22×C4C2×C4⋊C414yes—
630C22×C4C2×C4⋊C414yes—
631C22×C4#11718yes—
632C22×C4C4×D418yes—
633C22×C4C4×D414yes—
634C22×C4C4×Q814yes—
635C22×C4#12014yes—
636C22×C4#12114yes—
637C22×C4C22⋊Q818yes—
638C22×C4C22⋊Q814yes—
639C22×C4#12314yes—
640C22×C4#12514yes—
641C22×C4C4⋊Q814yes—
642C4⋊C4—432no—
643C4⋊C4—416no—
644C4⋊C4—416no—
645C4⋊C4—432no—
646C42—232no—
647C23C22×C4⋊C411yescharacteristic
648C23C2×#11712yes—
649C23C2×C4×D412yes—
650C23C2×C4×D411yescharacteristic
651C23C2×C4×Q811yescharacteristic
652C23#51811yescharacteristic
653C23#51811yescharacteristic
654C23#51911yescharacteristic
655C23#51911yescharacteristic
656C23#52012yes—
657C23#52012yes—
658C23C2×#12011yescharacteristic
659C23C2×#12111yescharacteristic
660C23C2×C22⋊Q811yescharacteristic
661C23C2×C22⋊Q812yes—
662C23C2×#12311yescharacteristic
663C23C2×#12511yescharacteristic
664C23C2×C4⋊Q811yescharacteristic
665C23#53211yescharacteristic
666C23#53211yescharacteristic
667C23#53312yes—
668C23#53511yescharacteristic
669C23#53511yescharacteristic
670C23#53512yes—
671C23#53511yescharacteristic
672C23#53511yescharacteristic
673C23#53611yescharacteristic
674C23#53611yescharacteristic
675C23#53612yes—
676C23#53611yescharacteristic
677C23#53611yescharacteristic
678C23#53711yescharacteristic
679C23#53711yescharacteristic
680C23#53711yescharacteristic
681C23#53711yescharacteristic
682C23#53712yes—
683C23#53712yes—
684C23#53812yes—
685C23#53812yes—
686C23#53912yes—
687C23#53912yes—
688C23#54012yes—
689C23#54011yescharacteristic
690C23#54011yescharacteristic
691C23#54112yes—
692C23#54112yes—
693C23#54112yes—
694C23#54111yescharacteristic
695C23#54111yescharacteristic
696C23#54212yes—
697C23#54212yes—
698C23#54212yes—
699C23#54212yes—
700C23#54211yescharacteristic
701C23#54211yescharacteristic
702C23#54211yescharacteristic
703C23#54211yescharacteristic
704C23#54412yes—
705C23#54411yescharacteristic
706C23#54411yescharacteristic
707C23#54411yescharacteristic
708C23#54411yescharacteristic
709C23#54412yes—
710C23#54411yescharacteristic
711C23#54411yescharacteristic
712C23#54411yescharacteristic
713C23#54411yescharacteristic
714C23D4212yes—
715C23#54612yes—
716C23#54612yes—
717C23#54612yes—
718C23#54612yes—
719C23#54712yes—
720C23#54712yes—
721C23#54712yes—
722C23#54812yes—
723C23#54812yes—
724C23D4×Q812yes—
725C23#55112yes—
726C23#55112yes—
727C23#55212yes—
728C23#55212yes—
729C23#55212yes—
730C23#55212yes—
731C23#55312yes—
732C23#55312yes—
733C23#55412yes—
734C23#55412yes—
735C23#55612yes—
736C23#55712yes—
737C23#55912yes—
738C23H(3,𝔽4)12yes—
739C23#56212yes—
740C23#56212yes—
741C23#56212yes—
742C23#56312yes—
743C23#56312yes—
744C23#56312yes—
745C23#56412yes—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
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—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—82no—
836C2×C4—81no—
837C2×C4—82no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—82no—
842C2×C4—82no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—82no—
847C2×C4—81no—
848C2×C4—82no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—82no—
852C2×C4—82no—
853C2×C4—82no—
854C2×C4—82no—
855C2×C4—82no—
856C2×C4—82no—
857C2×C4—81no—
858C2×C4—81no—
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—81no—
874C2×C4—81no—
875C2×C4—82no—
876C2×C4—82no—
877C2×C4—82no—
878C2×C4—82no—
879C2×C4—82no—
880C2×C4—82no—
881C2×C4#38518yes—
882C2×C4#38918yes—
883C22#228511yescharacteristic
884C22C2×#38511yescharacteristic
885C22C2×#38911yescharacteristic
886C22#231611yescharacteristic
887C22#231611yescharacteristic
888C22#231711yescharacteristic
889C22#231711yescharacteristic
890C22#231812yes—
891C22#232012yes—
892C22#232312yes—
893C22#232412yes—
894C22#232711yescharacteristic
895C22#232811yescharacteristic
896C22#233111yescharacteristic
897C22#233111yescharacteristic
898C22#234212yes—
899C22#234412yes—
900C22#235212yes—
901C22#235512yes—
902C22#236012yes—
903C22#236112yes—
904C22#237912yes—
905C22#238212yes—
906C22#240811yescharacteristic
907C22#240911yescharacteristic
908C22#243011yescharacteristic
909C22#243011yescharacteristic
910C22#243812yes—
911C22#243812yes—
912C22#244012yes—
913C22#244212yes—
914C22#248611yescharacteristic
915C22#248711yescharacteristic
916C22#249811yescharacteristic
917C22#249811yescharacteristic
918C22#254411yescharacteristic
919C22#254511yescharacteristic
920C22#255012yes—
921C22#256511yescharacteristic
922C22#256611yescharacteristic
923C22#257012yes—
924C22#261511yescharacteristic
925C22#261611yescharacteristic
926C22#262011yescharacteristic
927C22#262011yescharacteristic
928C22#262411yescharacteristic
929C22#262511yescharacteristic
930C22#262812yes—
931C22#262911yescharacteristic
932C22#262911yescharacteristic
933C22#262912yes—
934C22#264711yescharacteristic
935C22#264711yescharacteristic
936C22#266011yescharacteristic
937C22#266011yescharacteristic
938C22#266211yescharacteristic
939C22#266211yescharacteristic
940C22#266411yescharacteristic
941C22#266411yescharacteristic
942C22#266612yes—
943C22#266612yes—
944C22#267012yes—
945C22#267212yes—
946C22#267412yes—
947C22#267612yes—
948C22#269812yes—
949C22#270012yes—
950C22#270412yes—
951C22#270612yes—
952C22#270712yes—
953C22#271012yes—
954C22#271112yes—
955C22#271212yes—
956C22#271312yes—
957C22#271512yes—
958C22#271912yes—
959C22#271912yes—
960C22#272012yes—
961C22#272312yes—
962C22#272512yes—
963C22#272612yes—
964C22#275312yes—
965C22#275412yes—
966C22#275512yes—
967C22#276112yes—
968C22#276212yes—
969C22#276312yes—
970C22#276612yes—
971C22#276712yes—
972C22#276812yes—
973C22#277212yes—
974C22#277312yes—
975C22#277412yes—
976C22#281911yescharacteristic
977C22#282011yescharacteristic
978C22#282011yescharacteristic
979C22#282211yescharacteristic
980C22#284412yes—
981C22#284512yes—
982C4—28no—
983C4—28no—
984C4—48no—
985C4—44no—
986C4—84no—
987C4—82no—
988C4—82no—
989C4—84no—
990C4—82no—
991C4—84no—
992C4—82no—
993C2#1387811yescharacteristic
994C2#1390911yescharacteristic
995C2#1413011yescharacteristic
996C2#1426411yescharacteristic
997C2#1427611yescharacteristic
998C2#1435611yescharacteristic
999C2#1437712yes—
1000C2#1437812yes—
1001C2#1438512yes—
1002C2#1438612yes—
1003C2#1467711yescharacteristic
1004C2#1650411yescharacteristic
1005C2#1650511yescharacteristic
1006C2#1652412yes—
1007C2#1652512yes—
1008C2#1657112yes—
1009C2#1657212yes—
1010C2#1660411yescharacteristic
1011C2#1660511yescharacteristic
1012C2#1670011yescharacteristic
1013C2#1670111yescharacteristic
1014C2#1670411yescharacteristic
1015C2#1670511yescharacteristic
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
40. C4⋊#95C4semidirect
299. 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×#14412
C2×C4⋊#952
C2×#14342
#75572
#75562