Finite Group Databasebeta

← #154659

Subgroups — #154659

Order 512.

3210 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#398C211yesmaximal, characteristic
2C2×#1445C211yesmaximal, characteristic
3C2×#1444C211yesmaximal, characteristic
4C2×#1441C211yesmaximal, characteristic
5C2×#1436C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic
7C2×C4⋊#95C212yesmaximal
8C2×C4×#95C211yesmaximal, characteristic
9#7557C212yesmaximal
10#7557C212yesmaximal
11#7554C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C4⋊C4C2212yes—
17C23×C42C2211yescharacteristic
18C23×C42C2212yes—
19C2×#398—24no—
20C2×#398—24no—
21C2×#398C418yescomplemented
22C22×#95C2211yescharacteristic
23C22×#95C2212yes—
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38#1445—24no—
39#1444—24no—
40#1441—24no—
41#1436—24no—
42C4⋊#95—24no—
43C4⋊#95—28no—
44C4×#95—24no—
45C24×C4C2312yes—
46C24×C4C2311yescharacteristic
47C24×C4C2311yescharacteristic
48C24×C4C2312yes—
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2312yes—
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C24×C4C2312yes—
55C24×C4C2311yescharacteristic
56C22×C4⋊C4—24no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—22no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—24no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—24no—
81C22×C4⋊C4—42no—
82C22×C4⋊C4—42no—
83C22×C4⋊C4—42no—
84C22×C4⋊C4—42no—
85C22×C4⋊C4—42no—
86C22×C4⋊C4C2×C414yes—
87C22×C4⋊C4C2×C414yes—
88C22×C4⋊C4C2×C418yes—
89C22×C42—22no—
90C22×C42—24no—
91C22×C42—24no—
92C22×C42—22no—
93C22×C42—24no—
94C22×C42—24no—
95C22×C42—24no—
96C22×C42—42no—
97C22×C42—42no—
98C22×C42—42no—
99C22×C42D414yes—
100C22×C42Q818yes—
101#398—232no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—22no—
105C2×#95—24no—
106C2×#95—22no—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95—22no—
111C2×#95—22no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—22no—
119C2×#95—22no—
120C2×#95—22no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—22no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—22no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—42no—
135C2×#95—42no—
136C2×#95—42no—
137C2×#95—42no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95C2×C418yes—
142C2×#95C2×C414yes—
143C2×#95D414yes—
144C2×#95D414yes—
145C2×#95D414yes—
146C2×#95D414yes—
147C2×#95Q818yes—
148C25C2411yescharacteristic
149C23×C4—22no—
150C23×C4—21no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—21no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—21no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—22no—
172C23×C4—21no—
173C23×C4—22no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—21no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—21no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—21no—
203C23×C4—22no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—21no—
209C23×C4—22no—
210C23×C4—21no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—22no—
221C23×C4—22no—
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—22no—
233C23×C4—22no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—21no—
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—21no—
252C23×C4—21no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—21no—
257C23×C4—22no—
258C23×C4C22×C414yes—
259C23×C4C22×C412yes—
260C23×C4C22×C412yes—
261C23×C4C22×C412yes—
262C23×C4C22×C414yes—
263C23×C4C2×D412yes—
264C23×C4C2×D412yes—
265C23×C4C2×D414yes—
266C23×C4C2×D412yes—
267C23×C4C2×D412yes—
268C23×C4C2×D414yes—
269C23×C4C2×D412yes—
270C23×C4C2×D414yes—
271C23×C4C2×D412yes—
272C23×C4C2×D412yes—
273C23×C4C2×D412yes—
274C23×C4C2×D412yes—
275C23×C4C2×Q814yes—
276C23×C4C2×Q814yes—
277C23×C4C2×Q814yes—
278C23×C4C2×Q814yes—
279C23×C4C2×Q814yes—
280C23×C4C2×Q814yes—
281C23×C4#4114yes—
282C23×C4#4112yes—
283C23×C4#4112yes—
284C23×C4#4112yes—
285C23×C4#4112yes—
286C23×C4#4114yes—
287C23×C4#4114yes—
288C23×C4#4112yes—
289C23×C4#4114yes—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—216no—
292C2×C4⋊C4—216no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—216no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—48no—
301C2×C4⋊C4—48no—
302C2×C4⋊C4—48no—
303C2×C4⋊C4—48no—
304C2×C4⋊C4—48no—
305C2×C4⋊C4—48no—
306C2×C4⋊C4—48no—
307C2×C4⋊C4—48no—
308C2×C4⋊C4—48no—
309C2×C4⋊C4—48no—
310C2×C4⋊C4—48no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—48no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—48no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C42—28no—
324C2×C42—216no—
325C2×C42—216no—
326C2×C42—28no—
327C2×C42—44no—
328C2×C42—48no—
329C2×C42—48no—
330C2×C42—48no—
331C2×C42—48no—
332C2×C42—48no—
333C2×C42—48no—
334C2×C42—48no—
335#95—28no—
336#95—216no—
337#95—28no—
338#95—28no—
339#95—216no—
340#95—48no—
341#95—48no—
342#95—48no—
343#95—48no—
344#95—44no—
345#95—48no—
346#95—48no—
347#95—44no—
348#95—48no—
349#95—44no—
350#95C22⋊C4116yes—
351C24C23×C411yescharacteristic
352C24C22×D411yescharacteristic
353C24C22×D411yescharacteristic
354C24C22×D411yescharacteristic
355C24C22×D411yescharacteristic
356C24C22×D411yescharacteristic
357C24C22×Q812yes—
358C24C22×Q812yes—
359C24C2×#4111yescharacteristic
360C24C2×#4111yescharacteristic
361C24C2×#4111yescharacteristic
362C24C2×#4112yes—
363C24C2×#4112yes—
364C24C2×#4111yescharacteristic
365C24C2×#4112yes—
366C24C2×#4112yes—
367C24C2×#4111yescharacteristic
368C24H(5,𝔽2)11yescharacteristic
369C24H(5,𝔽2)11yescharacteristic
370C24H(5,𝔽2)12yes—
371C24H(5,𝔽2)11yescharacteristic
372C242−1+412yes—
373C242−1+411yescharacteristic
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
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—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—42no—
516C22×C4—41no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—41no—
522C22×C4—42no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—41no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—41no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—42no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—42no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—41no—
558C22×C4—42no—
559C22×C4—41no—
560C22×C4—42no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—41no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—41no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—41no—
585C22×C4—42no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—41no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—41no—
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—41no—
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—41no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—41no—
648C22×C4—41no—
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×C4C2×C22⋊C414yes—
666C22×C4C2×C22⋊C418yes—
667C22×C4C4×D414yes—
668C22×C4C4×D414yes—
669C22×C4C4×D414yes—
670C22×C4C4×Q818yes—
671C22×C4C4×Q818yes—
672C22×C4#12114yes—
673C22×C4#12114yes—
674C22×C4#12114yes—
675C22×C4C22⋊Q818yes—
676C22×C4C22⋊Q818yes—
677C22×C4C22⋊Q818yes—
678C22×C4#12314yes—
679C22×C4#12414yes—
680C22×C4#12418yes—
681C22×C4#12518yes—
682C22×C4#12714yes—
683C22×C4C4⋊Q814yes—
684C22×C4C4⋊Q818yes—
685C22×C4C4⋊Q818yes—
686C22×C4C4⋊Q814yes—
687C4⋊C4—432no—
688C4⋊C4—432no—
689C4⋊C4—416no—
690C4⋊C4—416no—
691C4⋊C4—416no—
692C42—416no—
693C42—432no—
694C23C22×C22⋊C411yescharacteristic
695C23C2×C4×D411yescharacteristic
696C23C2×C4×D411yescharacteristic
697C23C2×C4×D411yescharacteristic
698C23C2×C4×Q812yes—
699C23C2×C4×Q812yes—
700C23C4×#4111yescharacteristic
701C23C4×#4112yes—
702C23#51811yescharacteristic
703C23#52012yes—
704C23#52011yescharacteristic
705C23C2×#12111yescharacteristic
706C23C2×#12111yescharacteristic
707C23C2×#12111yescharacteristic
708C23C2×C22⋊Q812yes—
709C23C2×C22⋊Q812yes—
710C23C2×C22⋊Q812yes—
711C23C2×#12311yescharacteristic
712C23#52511yescharacteristic
713C23#52511yescharacteristic
714C23#52512yes—
715C23C2×#12412yes—
716C23C2×#12411yescharacteristic
717C23C2×#12512yes—
718C23#52912yes—
719C23#52912yes—
720C23#52911yescharacteristic
721C23#52912yes—
722C23#52912yes—
723C23C2×#12711yescharacteristic
724C23C2×C4⋊Q811yescharacteristic
725C23C2×C4⋊Q811yescharacteristic
726C23C2×C4⋊Q812yes—
727C23C2×C4⋊Q812yes—
728C23#53211yescharacteristic
729C23#53211yescharacteristic
730C23#53212yes—
731C23#53211yescharacteristic
732C23#53312yes—
733C23#53312yes—
734C23#53312yes—
735C23#53312yes—
736C23#53312yes—
737C23#53312yes—
738C23#53411yescharacteristic
739C23#53511yescharacteristic
740C23#53611yescharacteristic
741C23#53711yescharacteristic
742C23#53812yes—
743C23#53912yes—
744C23#53912yes—
745C23#54011yescharacteristic
746C23#54012yes—
747C23#54112yes—
748C23#54211yescharacteristic
749C23#54312yes—
750C23#54412yes—
751C23#54412yes—
752C23#54412yes—
753C23D4211yescharacteristic
754C23D4211yescharacteristic
755C23D4211yescharacteristic
756C23#54611yescharacteristic
757C23#54611yescharacteristic
758C23#54612yes—
759C23#54612yes—
760C23#54612yes—
761C23#54612yes—
762C23#54611yescharacteristic
763C23#54712yes—
764C23#54712yes—
765C23#54712yes—
766C23#54711yescharacteristic
767C23#54811yescharacteristic
768C23#54811yescharacteristic
769C23#54811yescharacteristic
770C23D4×Q812yes—
771C23#55011yescharacteristic
772C23#55011yescharacteristic
773C23#55011yescharacteristic
774C23#55112yes—
775C23#55112yes—
776C23#55112yes—
777C23#55212yes—
778C23#55212yes—
779C23#55212yes—
780C23#55212yes—
781C23#55311yescharacteristic
782C23#55312yes—
783C23#55312yes—
784C23#55311yescharacteristic
785C23#55412yes—
786C23#55412yes—
787C23#55412yes—
788C23#55412yes—
789C23#55412yes—
790C23#55511yescharacteristic
791C23#55712yes—
792C23#55712yes—
793C2×C4—28no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—28no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—28no—
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—28no—
812C2×C4—28no—
813C2×C4—28no—
814C2×C4—28no—
815C2×C4—28no—
816C2×C4—28no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—24no—
826C2×C4—28no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—28no—
833C2×C4—24no—
834C2×C4—28no—
835C2×C4—24no—
836C2×C4—44no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—44no—
842C2×C4—42no—
843C2×C4—44no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—42no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—42no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—42no—
879C2×C4—44no—
880C2×C4—42no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—44no—
896C2×C4—42no—
897C2×C4—82no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—82no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—82no—
907C2×C4—82no—
908C2×C4—82no—
909C2×C4—82no—
910C2×C4—82no—
911C2×C4—82no—
912C2×C4—82no—
913C2×C4—82no—
914C2×C4—82no—
915C2×C4—82no—
916C2×C4—82no—
917C2×C4—82no—
918C2×C4—82no—
919C2×C4—81no—
920C2×C4—81no—
921C2×C4—81no—
922C2×C4—82no—
923C2×C4—81no—
924C2×C4—81no—
925C2×C4—82no—
926C2×C4—82no—
927C2×C4—82no—
928C2×C4—82no—
929C2×C4—82no—
930C2×C4—82no—
931C2×C4#39018yes—
932C2×C4#391116yes—
933C2×C4#39818yescomplemented
934C22C2×#39011yescharacteristic
935C22C2×#39112yes—
936C22C4×#12111yescharacteristic
937C22C4×#12311yescharacteristic
938C22C4×C22⋊Q812yes—
939C22C4×#12512yes—
940C22C4×C4⋊Q811yescharacteristic
941C22C4×C4⋊Q812yes—
942C22C4×C4⋊Q811yescharacteristic
943C22#232211yescharacteristic
944C22#232411yescharacteristic
945C22#232912yes—
946C22#233012yes—
947C22D4×C22⋊C411yescharacteristic
948C22#233912yes—
949C22#234111yescharacteristic
950C22#235912yes—
951C22#236012yes—
952C22#236111yescharacteristic
953C22#236311yescharacteristic
954C22#236812yes—
955C22#237012yes—
956C22#237012yes—
957C22C2×#39811yescharacteristic
958C22#239211yescharacteristic
959C22#239511yescharacteristic
960C22#239612yes—
961C22#239911yescharacteristic
962C22#240212yes—
963C22#241211yescharacteristic
964C22#241311yescharacteristic
965C22#241411yescharacteristic
966C22#241611yescharacteristic
967C22#242512yes—
968C22#242611yescharacteristic
969C22#242811yescharacteristic
970C22#243712yes—
971C22#243812yes—
972C22#243812yes—
973C22#244012yes—
974C22#244012yes—
975C22#244112yes—
976C22#244212yes—
977C22#244912yes—
978C22#245012yes—
979C22#245312yes—
980C22#245412yes—
981C22#246212yes—
982C22#246412yes—
983C22#247212yes—
984C22#248812yes—
985C22#248812yes—
986C22#248912yes—
987C22#249012yes—
988C22#249011yescharacteristic
989C22#249111yescharacteristic
990C22#249811yescharacteristic
991C22#250111yescharacteristic
992C22#250211yescharacteristic
993C22#251912yes—
994C22#252012yes—
995C22#252212yes—
996C22#252212yes—
997C22#253911yescharacteristic
998C22#254011yescharacteristic
999C22#254111yescharacteristic
1000C22#254311yescharacteristic
1001C22#254611yescharacteristic
1002C22#254912yes—
1003C22#254912yes—
1004C22#255012yes—
1005C22#255012yes—
1006C22#255212yes—
1007C22#255212yes—
1008C22#255312yes—
1009C22#255412yes—
1010C22#255612yes—
1011C22#256912yes—
1012C22#257412yes—
1013C22#258311yescharacteristic
1014C22#258411yescharacteristic
1015C22#258512yes—
1016C22#258512yes—
1017C22#260311yescharacteristic
1018C22#260612yes—
1019C22#261111yescharacteristic
1020C22#261212yes—
1021C22#265911yescharacteristic
1022C22#266011yescharacteristic
1023C22#266111yescharacteristic
1024C22#266411yescharacteristic
1025C22#266612yes—
1026C22#266712yes—
1027C22#285712yes—
1028C22#285711yescharacteristic
1029C22#285711yescharacteristic
1030C22#285811yescharacteristic
1031C22#286212yes—
1032C22#286811yescharacteristic
1033C4—28no—
1034C4—28no—
1035C4—216no—
1036C4—44no—
1037C4—48no—
1038C4—44no—
1039C4—84no—
1040C4—82no—
1041C4—82no—
1042C4—82no—
1043C4—84no—
1044C2C4×#39811yescharacteristic
1045C2#1399611yescharacteristic
1046C2#1399811yescharacteristic
1047C2#1405212yes—
1048C2#1405412yes—
1049C2#1421112yes—
1050C2#1422611yescharacteristic
1051C2#1423712yes—
1052C2#1424411yescharacteristic
1053C2#1432811yescharacteristic
1054C2#1471411yescharacteristic
1055C2#1476611yescharacteristic
1056C2#1477112yes—
1057C2#1481811yescharacteristic
1058C2#1484011yescharacteristic
1059C2#1487112yes—
1060C2#1490311yescharacteristic
1061C2#1493712yes—
1062C2#1500711yescharacteristic
1063C2#1502011yescharacteristic
1064C2#1506712yes—
1065C2#1514511yescharacteristic
1066C2#1517311yescharacteristic
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
21. C2×#398C4semidirect
933. C2×C4#398semidirect

Maximal subgroups

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

subgroupindex
C22×#3982
C2×#14452
C2×#14442
C2×#14412
C2×#14362
C2×C4⋊#952
C2×C4×#952
#75572
#75542