Finite Group Databasebeta

← #154451

Subgroups — #154451

Order 512.

3482 conjugacy classes of subgroups.

The subgroup lattice has 1085 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C22×C4×C4⋊C4C211yesmaximal, characteristic
3C2×#1444C212yesmaximal
4C2×#1444C211yesmaximal, characteristic
5C2×#1441C211yesmaximal, characteristic
6C2×#1441C211yesmaximal, characteristic
7C2×#1436C212yesmaximal
8#7557C211yesmaximal, characteristic
9#7557C212yesmaximal
10#7554C212yesmaximal
11#7554C211yesmaximal, characteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C4⋊C4C2212yes—
17C23×C4⋊C4C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C2×#389—24no—
22C2×#389—28no—
23C2×C4×C4⋊C4—24no—
24C2×C4×C4⋊C4—24no—
25C2×C4×C4⋊C4—24no—
26C22×#95C2212yes—
27C22×#95C2211yescharacteristic
28C22×#95C2211yescharacteristic
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2212yes—
37C22×#95C2211yescharacteristic
38C22×#95C2212yes—
39C22×#95C2212yes—
40#1444—24no—
41#1444—28no—
42#1441—24no—
43#1441C418yescomplemented
44#1436—28no—
45C24×C4C2312yes—
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2312yes—
49C24×C4C2312yes—
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—24no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—24no—
76C22×C4⋊C4—24no—
77C22×C4⋊C4—24no—
78C22×C4⋊C4—22no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—24no—
81C22×C4⋊C4—24no—
82C22×C4⋊C4—24no—
83C22×C4⋊C4—24no—
84C22×C4⋊C4—42no—
85C22×C4⋊C4—42no—
86C22×C4⋊C4—42no—
87C22×C4⋊C4—42no—
88C22×C4⋊C4—42no—
89C22×C4⋊C4C2×C414yes—
90C22×C4⋊C4C2×C414yes—
91C22×C4⋊C4D414yes—
92C22×C4⋊C4D414yes—
93C22×C4⋊C4Q814yes—
94C22×C42—22no—
95C22×C42—22no—
96C22×C42—22no—
97C22×C42—22no—
98C22×C42—22no—
99C22×C42—22no—
100C22×C42—22no—
101C22×C42—22no—
102C22×C42—22no—
103C22×C42—22no—
104C22×C42—22no—
105C22×C42—24no—
106C22×C42—24no—
107C22×C42—42no—
108C22×C42—42no—
109C22×C42D414yes—
110C22×C42Q814yes—
111#389—232no—
112C4×C4⋊C4—232no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—22no—
116C2×#95—24no—
117C2×#95—22no—
118C2×#95—22no—
119C2×#95—22no—
120C2×#95—22no—
121C2×#95—22no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—24no—
125C2×#95—22no—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—22no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—24no—
142C2×#95—22no—
143C2×#95—22no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95—42no—
147C2×#95—42no—
148C2×#95—42no—
149C2×#95C2×C418yes—
150C2×#95C2×C418yes—
151C2×#95C2×C414yes—
152C2×#95D418yes—
153C2×#95D414yes—
154C2×#95Q818yes—
155C25C2411yescharacteristic
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—22no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—21no—
162C23×C4—21no—
163C23×C4—22no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
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—22no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
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—21no—
213C23×C4—21no—
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—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×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4C22×C412yes—
259C23×C4C22×C414yes—
260C23×C4C22×C414yes—
261C23×C4C22×C412yes—
262C23×C4C22×C412yes—
263C23×C4C2×D414yes—
264C23×C4C2×D412yes—
265C23×C4C2×D414yes—
266C23×C4C2×D412yes—
267C23×C4C2×D412yes—
268C23×C4C2×D412yes—
269C23×C4C2×D412yes—
270C23×C4C2×D412yes—
271C23×C4C2×D412yes—
272C23×C4C2×D412yes—
273C23×C4C2×D412yes—
274C23×C4C2×D412yes—
275C23×C4C2×D412yes—
276C23×C4C2×D414yes—
277C23×C4C2×D412yes—
278C23×C4C2×Q814yes—
279C23×C4C2×Q812yes—
280C23×C4C2×Q814yes—
281C23×C4C2×Q812yes—
282C23×C4C2×Q812yes—
283C23×C4C2×Q812yes—
284C23×C4C2×Q812yes—
285C23×C4C2×Q814yes—
286C23×C4C2×Q812yes—
287C23×C4#4114yes—
288C23×C4#4114yes—
289C23×C4#4112yes—
290C23×C4#4112yes—
291C23×C4#4112yes—
292C23×C4#4112yes—
293C23×C4#4112yes—
294C23×C4#4112yes—
295C23×C4#4112yes—
296C23×C4#4112yes—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—216no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—216no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—216no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—216no—
318C2×C4⋊C4—48no—
319C2×C4⋊C4—48no—
320C2×C4⋊C4—48no—
321C2×C4⋊C4—48no—
322C2×C4⋊C4—48no—
323C2×C4⋊C4—48no—
324C2×C4⋊C4—48no—
325C2×C4⋊C4—48no—
326C2×C4⋊C4—48no—
327C2×C4⋊C4—48no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—48no—
330C2×C4⋊C4—48no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—48no—
333C2×C4⋊C4—48no—
334C2×C4⋊C4C4⋊C4116yescomplemented
335C2×C42—28no—
336C2×C42—28no—
337C2×C42—28no—
338C2×C42—28no—
339C2×C42—28no—
340C2×C42—28no—
341C2×C42—28no—
342C2×C42—28no—
343C2×C42—28no—
344C2×C42—28no—
345C2×C42—44no—
346C2×C42—48no—
347C2×C42—48no—
348C2×C42—48no—
349C2×C42—48no—
350C2×C42—44no—
351C2×C42—44no—
352#95—28no—
353#95—216no—
354#95—28no—
355#95—216no—
356#95—28no—
357#95—216no—
358#95—216no—
359#95—48no—
360#95—48no—
361#95—48no—
362#95—48no—
363#95—48no—
364#95—48no—
365#95—44no—
366C24C23×C411yescharacteristic
367C24C22×D411yescharacteristic
368C24C22×D411yescharacteristic
369C24C22×D411yescharacteristic
370C24C22×D412yes—
371C24C22×D411yescharacteristic
372C24C22×Q811yescharacteristic
373C24C22×Q811yescharacteristic
374C24C22×Q812yes—
375C24C2×#4111yescharacteristic
376C24C2×#4111yescharacteristic
377C24C2×#4111yescharacteristic
378C24C2×#4112yes—
379C24C2×#4111yescharacteristic
380C24C2×#4112yes—
381C24C2×#4111yescharacteristic
382C24C2×#4111yescharacteristic
383C24C2×#4111yescharacteristic
384C24C2×#4111yescharacteristic
385C24H(5,𝔽2)12yes—
386C24H(5,𝔽2)12yes—
387C242−1+412yes—
388C242−1+412yes—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
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—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—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—41no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—42no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
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—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×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×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4C2×C4⋊C414yes—
678C22×C4C2×C4⋊C414yes—
679C22×C4C2×C4⋊C414yes—
680C22×C4C4×D418yes—
681C22×C4C4×D414yes—
682C22×C4C4×D414yes—
683C22×C4C4×D414yes—
684C22×C4C4×Q818yes—
685C22×C4C4×Q814yes—
686C22×C4#12014yes—
687C22×C4#12014yes—
688C22×C4#12114yes—
689C22×C4#12114yes—
690C22×C4#12114yes—
691C22×C4C22⋊Q814yes—
692C22×C4C22⋊Q814yes—
693C22×C4C22⋊Q814yes—
694C22×C4C22⋊Q814yes—
695C22×C4C22⋊Q818yes—
696C22×C4C22⋊Q814yes—
697C22×C4#12314yes—
698C22×C4#12514yes—
699C22×C4C4⋊Q814yes—
700C22×C4C4⋊Q814yes—
701C22×C4C4⋊Q818yes—
702C4⋊C4—232no—
703C4⋊C4—232no—
704C4⋊C4—232no—
705C4⋊C4—416no—
706C4⋊C4—432no—
707C4⋊C4—432no—
708C42—232no—
709C42—416no—
710C42—416no—
711C23C22×C4⋊C411yescharacteristic
712C23C2×C4×D411yescharacteristic
713C23C2×C4×D412yes—
714C23C2×C4×D411yescharacteristic
715C23C2×C4×D411yescharacteristic
716C23C2×C4×Q811yescharacteristic
717C23C2×C4×Q812yes—
718C23C4×#4111yescharacteristic
719C23C4×#4111yescharacteristic
720C23#52012yes—
721C23#52012yes—
722C23C2×#12011yescharacteristic
723C23C2×#12011yescharacteristic
724C23C2×#12111yescharacteristic
725C23C2×#12111yescharacteristic
726C23C2×#12111yescharacteristic
727C23C2×C22⋊Q811yescharacteristic
728C23C2×C22⋊Q811yescharacteristic
729C23C2×C22⋊Q811yescharacteristic
730C23C2×C22⋊Q811yescharacteristic
731C23C2×C22⋊Q811yescharacteristic
732C23C2×C22⋊Q812yes—
733C23C2×#12311yescharacteristic
734C23#52511yescharacteristic
735C23#52511yescharacteristic
736C23#52511yescharacteristic
737C23#52511yescharacteristic
738C23#52511yescharacteristic
739C23#52511yescharacteristic
740C23#52511yescharacteristic
741C23#52512yes—
742C23#52512yes—
743C23C2×#12511yescharacteristic
744C23#52911yescharacteristic
745C23#52911yescharacteristic
746C23#52912yes—
747C23#52911yescharacteristic
748C23#52911yescharacteristic
749C23C2×C4⋊Q811yescharacteristic
750C23C2×C4⋊Q812yes—
751C23C2×C4⋊Q811yescharacteristic
752C23#53211yescharacteristic
753C23#53212yes—
754C23#53211yescharacteristic
755C23#53211yescharacteristic
756C23#53312yes—
757C23#53312yes—
758C23#53312yes—
759C23#53311yescharacteristic
760C23#53312yes—
761C23#53311yescharacteristic
762C23#53311yescharacteristic
763C23#53311yescharacteristic
764C23#53411yescharacteristic
765C23#53511yescharacteristic
766C23#53611yescharacteristic
767C23#53611yescharacteristic
768C23#53812yes—
769C23#53912yes—
770C23#53912yes—
771C23#54012yes—
772C23#54112yes—
773C23#54112yes—
774C23#54212yes—
775C23#54212yes—
776C23#54412yes—
777C23#54412yes—
778C23D4212yes—
779C23D4212yes—
780C23D4212yes—
781C23#54612yes—
782C23#54612yes—
783C23#54612yes—
784C23#54712yes—
785C23#54712yes—
786C23#54712yes—
787C23#54712yes—
788C23#54812yes—
789C23#54812yes—
790C23D4×Q812yes—
791C23D4×Q812yes—
792C23D4×Q812yes—
793C23D4×Q812yes—
794C23#55012yes—
795C23#55112yes—
796C23#55212yes—
797C23#55212yes—
798C23#55212yes—
799C23#55212yes—
800C23#55312yes—
801C23#55312yes—
802C23#55312yes—
803C23#55412yes—
804C23#55412yes—
805C23#55412yes—
806C23#55412yes—
807C23#55712yes—
808C23#55712yes—
809C23Q8212yes—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—28no—
823C2×C4—28no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—28no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—28no—
848C2×C4—28no—
849C2×C4—28no—
850C2×C4—28no—
851C2×C4—28no—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—28no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—28no—
858C2×C4—28no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—44no—
883C2×C4—42no—
884C2×C4—44no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—44no—
896C2×C4—44no—
897C2×C4—44no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—44no—
910C2×C4—44no—
911C2×C4—44no—
912C2×C4—44no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—44no—
916C2×C4—44no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—82no—
933C2×C4—82no—
934C2×C4—82no—
935C2×C4—82no—
936C2×C4—82no—
937C2×C4—82no—
938C2×C4—82no—
939C2×C4—82no—
940C2×C4—82no—
941C2×C4—82no—
942C2×C4—82no—
943C2×C4—82no—
944C2×C4—82no—
945C2×C4—82no—
946C2×C4—82no—
947C2×C4—82no—
948C2×C4#38518yes—
949C2×C4#38918yescomplemented
950C2×C4#39518yes—
951C22C2×#38511yescharacteristic
952C22C2×#38911yescharacteristic
953C22#229611yescharacteristic
954C22C4×#12011yescharacteristic
955C22C4×#12111yescharacteristic
956C22C4×#12111yescharacteristic
957C22C4×C22⋊Q812yes—
958C22C4×C22⋊Q811yescharacteristic
959C22C4×C22⋊Q811yescharacteristic
960C22C4×C4⋊Q812yes—
961C22C4×C4⋊Q811yescharacteristic
962C22#232211yescharacteristic
963C22#232611yescharacteristic
964C22#233012yes—
965C22#233412yes—
966C22D4×C4⋊C412yes—
967C22Q8×C4⋊C412yes—
968C22#235912yes—
969C22#236012yes—
970C22#236012yes—
971C22#236112yes—
972C22#236112yes—
973C22#237012yes—
974C22C2×#39511yescharacteristic
975C22#238811yescharacteristic
976C22#239611yescharacteristic
977C22#239612yes—
978C22#239911yescharacteristic
979C22#239912yes—
980C22#240311yescharacteristic
981C22#240611yescharacteristic
982C22#240611yescharacteristic
983C22#240811yescharacteristic
984C22#240911yescharacteristic
985C22#242312yes—
986C22#242412yes—
987C22#242812yes—
988C22#242912yes—
989C22#242912yes—
990C22#243111yescharacteristic
991C22#243411yescharacteristic
992C22#243812yes—
993C22#244012yes—
994C22#244012yes—
995C22#244112yes—
996C22#244312yes—
997C22#244912yes—
998C22#244912yes—
999C22#244912yes—
1000C22#245112yes—
1001C22#245112yes—
1002C22#245212yes—
1003C22#245612yes—
1004C22#246112yes—
1005C22#246212yes—
1006C22#246212yes—
1007C22#246212yes—
1008C22#246412yes—
1009C22#246812yes—
1010C22#247012yes—
1011C22#247512yes—
1012C22#247912yes—
1013C22#250612yes—
1014C22#250712yes—
1015C22#251912yes—
1016C22#252212yes—
1017C22#253611yescharacteristic
1018C22#254311yescharacteristic
1019C22#254611yescharacteristic
1020C22#255012yes—
1021C22#255012yes—
1022C22#255112yes—
1023C22#255612yes—
1024C22#255812yes—
1025C22#256511yescharacteristic
1026C22#256711yescharacteristic
1027C22#257911yescharacteristic
1028C22#258311yescharacteristic
1029C22#258512yes—
1030C22#258612yes—
1031C22#258712yes—
1032C22#259012yes—
1033C22#259811yescharacteristic
1034C22#260612yes—
1035C22#261111yescharacteristic
1036C22#262711yescharacteristic
1037C22#262811yescharacteristic
1038C22#263411yescharacteristic
1039C22#263511yescharacteristic
1040C22#265412yes—
1041C22#266612yes—
1042C22#284711yescharacteristic
1043C22#284811yescharacteristic
1044C22#285111yescharacteristic
1045C22#285111yescharacteristic
1046C22#285411yescharacteristic
1047C22#285511yescharacteristic
1048C22#285711yescharacteristic
1049C22#285711yescharacteristic
1050C4—28no—
1051C4—28no—
1052C4—28no—
1053C4—44no—
1054C4—48no—
1055C4—48no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4—84no—
1060C4—84no—
1061C2C4×#39511yescharacteristic
1062C2#1397611yescharacteristic
1063C2#1400512yes—
1064C2#1401511yescharacteristic
1065C2#1411112yes—
1066C2#1417611yescharacteristic
1067C2#1420412yes—
1068C2#1421112yes—
1069C2#1422611yescharacteristic
1070C2#1431811yescharacteristic
1071C2#1469711yescharacteristic
1072C2#1472011yescharacteristic
1073C2#1472211yescharacteristic
1074C2#1478812yes—
1075C2#1479012yes—
1076C2#1480412yes—
1077C2#1481612yes—
1078C2#1488011yescharacteristic
1079C2#1489311yescharacteristic
1080C2#1507111yescharacteristic
1081C2#1509811yescharacteristic
1082C2#1512811yescharacteristic
1083C2#1516611yescharacteristic
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
43. #1441C4semidirect
334. C2×C4⋊C4C4⋊C4semidirect
949. C2×C4#389semidirect

Maximal subgroups

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

subgroupindex
C22×#3892
C22×C4×C4⋊C42
C2×#14442
C2×#14412
C2×#14362
#75572
#75542