Finite Group Databasebeta

← C2×#15458 #608998

Subgroups — C2×#15458 #608998

Order 512.

5634 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#396C211yesmaximal, characteristic, complemented
2C22×#394C211yesmaximal, characteristic
3C22×#390C211yesmaximal, characteristic
4C22×#389C211yesmaximal, characteristic, complemented
5C22×#388C211yesmaximal, characteristic, complemented
6C22×#387C211yesmaximal, characteristic, complemented
7#15458C2116yesmaximal, direct product factor
8C2×#1441C211yesmaximal, characteristic, complemented
9C2×#1440C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1439C211yesmaximal, characteristic, complemented
14C2×#1438C211yesmaximal, characteristic
15C2×#1437C211yesmaximal, characteristic, complemented
16C2×#1434C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C42C2211yescharacteristic
37C23×C42C2211yescharacteristic
38C2×#396—28no—
39C2×#396C2218yescomplemented
40C2×#394—28no—
41C2×#394C2218yes—
42C2×#390—28no—
43C2×#390C2218yes—
44C2×#389—28no—
45C2×#389C2218yescomplemented
46C2×#388—28no—
47C2×#388C2218yescomplemented
48C2×#387—28no—
49C2×#387C2218yescomplemented
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64#1441C2218yescomplemented
65#1440C2218yescomplemented
66#1439C2218yescomplemented
67#1439C2218yescomplemented
68#1439C2218yescomplemented
69#1439C2218yescomplemented
70#1438C2218yes—
71#1437C2218yescomplemented
72#1434C2218yescomplemented
73C26C2311yescharacteristic
74C26C2311yescharacteristic
75C23×D4—24no—
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—42no—
81C23×D4—42no—
82C23×D4C2314yes—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—42no—
105C22×C4⋊C4—42no—
106C22×C4⋊C4—42no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—42no—
110C22×C4⋊C4—42no—
111C22×C4⋊C4D418yes—
112C22×C4⋊C4D418yes—
113C22×C4⋊C4D418yescomplemented
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—24no—
138C22×C22⋊C4—24no—
139C22×C22⋊C4—24no—
140C22×C22⋊C4—24no—
141C22×C22⋊C4—24no—
142C22×C22⋊C4—24no—
143C22×C22⋊C4—24no—
144C22×C22⋊C4—42no—
145C22×C22⋊C4—42no—
146C22×C22⋊C4—42no—
147C22×C22⋊C4—42no—
148C22×C22⋊C4—42no—
149C22×C22⋊C4—42no—
150C22×C22⋊C4—42no—
151C22×C22⋊C4—42no—
152C22×C22⋊C4—42no—
153C22×C22⋊C4—42no—
154C22×C22⋊C4—42no—
155C22×C22⋊C4—42no—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2314yes—
168C22×C42—24no—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42—24no—
172C22×C42—24no—
173C22×C42—42no—
174C22×C42C2314yes—
175C22×C42C2314yes—
176#396—232no—
177#394—232no—
178#390—232no—
179#389—232no—
180#388—232no—
181#387—232no—
182C2×#95—24no—
183C2×#95—24no—
184C2×#95—24no—
185C2×#95—24no—
186C2×#95—24no—
187C2×#95—24no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95—24no—
191C2×#95—24no—
192C2×#95—24no—
193C2×#95—24no—
194C2×#95—42no—
195C2×#95—42no—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—22no—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—22no—
234C25—22no—
235C25—22no—
236C25—22no—
237C25—22no—
238C25#4114yes—
239C25#4114yes—
240C25C2412yes—
241C25C2412yes—
242C25C2411yescharacteristic
243C22×D4—232no—
244C22×D4—28no—
245C22×D4—28no—
246C22×D4—28no—
247C22×D4—28no—
248C22×D4—28no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—416no—
252C22×D4—416no—
253C22×D4—416no—
254C22×D4—416no—
255C22×D4—416no—
256C22×D4—416no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4C2×D414yes—
336C23×C4C2×D414yes—
337C23×C4C2×D414yes—
338C23×C4C2×D414yes—
339C23×C4C2×D414yes—
340C23×C4C2×D414yes—
341C23×C4C2×D414yes—
342C23×C4C2×D414yes—
343C23×C4C2×D414yes—
344C23×C4#4114yes—
345C23×C4#4114yes—
346C23×C4#4114yes—
347C23×C4#4114yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2412yes—
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C2×C4⋊C4—232no—
362C2×C4⋊C4—232no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—416no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—416no—
380C2×C4⋊C4—416no—
381C2×C4⋊C4—416no—
382C2×C4⋊C4C2×D4116yes—
383C2×C4⋊C4C2×D4116yes—
384C2×C4⋊C4C2×D4116yescomplemented
385C2×C22⋊C4—232no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—416no—
423C2×C22⋊C4—416no—
424C2×C22⋊C4—416no—
425C2×C22⋊C4—416no—
426C2×C22⋊C4—416no—
427C2×C22⋊C4—416no—
428C2×C22⋊C4—416no—
429C2×C22⋊C4—416no—
430C2×C22⋊C4—416no—
431C2×C22⋊C4—416no—
432C2×C22⋊C4—416no—
433C2×C42—28no—
434C2×C42—28no—
435C2×C42—28no—
436C2×C42—28no—
437C2×C42—28no—
438C2×C42—44no—
439C2×C42—416no—
440C2×C42—416no—
441#95—28no—
442#95—28no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—44no—
454#95—44no—
455C24—28no—
456C24—28no—
457C24—28no—
458C24—28no—
459C24—28no—
460C24—28no—
461C24—28no—
462C24—28no—
463C24—28no—
464C24—28no—
465C24—28no—
466C24—28no—
467C24—28no—
468C24—28no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—44no—
498C24—44no—
499C24—44no—
500C24—44no—
501C24—44no—
502C24—44no—
503C24—44no—
504C24—44no—
505C24—44no—
506C24—44no—
507C24—44no—
508C24—44no—
509C24—44no—
510C24—44no—
511C24—44no—
512C24—44no—
513C24—44no—
514C24—44no—
515C24—44no—
516C24—44no—
517C24—44no—
518C24—44no—
519C24—44no—
520C24—44no—
521C24—44no—
522C24—44no—
523C24—44no—
524C24—44no—
525C24—44no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—44no—
530C24—44no—
531C24—44no—
532C24—44no—
533C24—44no—
534C24—44no—
535C24—44no—
536C24—44no—
537C24—44no—
538C24—44no—
539C24—44no—
540C24—44no—
541C24—44no—
542C24—44no—
543C24—44no—
544C24—44no—
545C24—44no—
546C24—44no—
547C24—44no—
548C24—44no—
549C24—44no—
550C24—44no—
551C24—44no—
552C24—44no—
553C24C22×D412yes—
554C24C22×D412yes—
555C24C22×D412yes—
556C24C2×#4114yes—
557C24C2×#4114yes—
558C24C2×#4112yes—
559C24C2×#4112yes—
560C24C2×#4112yes—
561C24C2×#4112yes—
562C24C2×#4112yes—
563C24C2×#4112yes—
564C24H(5,𝔽2)12yes—
565C24H(5,𝔽2)12yes—
566C24H(5,𝔽2)12yes—
567C24H(5,𝔽2)12yes—
568C242−1+412yes—
569C242−1+412yes—
570C24C2511yescharacteristic
571C2×D4—232no—
572C2×D4—416no—
573C2×D4—416no—
574C2×D4—416no—
575C2×D4—416no—
576C2×D4—416no—
577C2×D4—4128no—
578C2×D4—416no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4#121116yes—
747C22×C4#121116yes—
748C22×C4C22×D414yes—
749C22×C4C22×D414yes—
750C22×C4C22×D414yes—
751C22×C4C22×D414yes—
752C22×C4C22×D414yes—
753C22×C4C22×D414yes—
754C22×C4C22×D414yes—
755C22×C4C22×D414yes—
756C22×C4C22×D414yes—
757C22×C4C2×#4114yes—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2×#4114yes—
761C4⋊C4—232no—
762C4⋊C4—232no—
763C4⋊C4—416no—
764C4⋊C4—416no—
765C4⋊C4—416no—
766C4⋊C4—416no—
767C22⋊C4—232no—
768C22⋊C4—416no—
769C22⋊C4—416no—
770C22⋊C4—416no—
771C22⋊C4—416no—
772C22⋊C4—416no—
773C22⋊C4—416no—
774C22⋊C4—416no—
775C22⋊C4—416no—
776C22⋊C4—416no—
777C22⋊C4—416no—
778C22⋊C4—416no—
779C42—416no—
780C42—416no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—416no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—416no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—416no—
848C23—42no—
849C23—42no—
850C23—416no—
851C23—416no—
852C23—416no—
853C23—416no—
854C23—416no—
855C23—416no—
856C23—416no—
857C23—416no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—416no—
863C23—416no—
864C23—416no—
865C23—88no—
866C23—88no—
867C23—88no—
868C23—88no—
869C23—88no—
870C23—88no—
871C23—88no—
872C23—88no—
873C23—88no—
874C23—88no—
875C23—88no—
876C23—88no—
877C23—88no—
878C23—88no—
879C23—88no—
880C23—88no—
881C23C2×#12114yes—
882C23C2×#12114yes—
883C23#52514yes—
884C23#52514yes—
885C23#52914yes—
886C23#52914yes—
887C23#53414yes—
888C23#53514yes—
889C23#53714yes—
890C23#53914yes—
891C23#53914yes—
892C23#54014yes—
893C23#54214yes—
894C23#54214yes—
895C23#54214yes—
896C23D4214yes—
897C23#54614yes—
898C23#54614yes—
899C23#54614yes—
900C23#54714yes—
901C23#54814yes—
902C23#54814yes—
903C23#54814yes—
904C23#54814yes—
905C23#55014yes—
906C23#55014yes—
907C23#55114yes—
908C23#55114yes—
909C23#55114yes—
910C23#55214yes—
911C23#55314yes—
912C23#55314yes—
913C23#55514yes—
914C23#56014yes—
915C23#56314yes—
916C23C23×D411yescharacteristic
917C23C23×D411yescharacteristic
918C23C23×D411yescharacteristic
919C23C22×#4111yescharacteristic
920C23C22×#4111yescharacteristic
921C23C22×#4111yescharacteristic
922C23C22×#4111yescharacteristic
923C23C22×#4111yescharacteristic
924C23C22×#4111yescharacteristic
925C23C2×H(5,𝔽2)11yescharacteristic
926C23C2×H(5,𝔽2)11yescharacteristic
927C23C2×H(5,𝔽2)11yescharacteristic
928C23C2×H(5,𝔽2)11yescharacteristic
929C23C2×2−1+411yescharacteristic
930C23C2×2−1+411yescharacteristic
931D4—464no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—232no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—232no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—416no—
972C2×C4—416no—
973C2×C4—416no—
974C2×C4—416no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—416no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—416no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—416no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—88no—
1031C2×C4—88no—
1032C2×C4—88no—
1033C2×C4—88no—
1034C2×C4C2×#12118yes—
1035C2×C4C2×#12118yes—
1036C22—44no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—44no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—44no—
1050C22—832no—
1051C22—832no—
1052C22—82no—
1053C22—82no—
1054C22—82no—
1055C22—82no—
1056C22—82no—
1057C22—82no—
1058C22—82no—
1059C22—82no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—82no—
1065C22—82no—
1066C22—82no—
1067C22—82no—
1068C22#241418yes—
1069C22#241618yes—
1070C22#242618yes—
1071C22#242618yes—
1072C22#246018yes—
1073C22#246318yes—
1074C22#247918yes—
1075C22#252618yes—
1076C22#253418yes—
1077C22#267318yes—
1078C22#270518yes—
1079C22#270718yes—
1080C22#272318yes—
1081C22#273118yes—
1082C22#275718yes—
1083C22C22×#12111yescharacteristic
1084C22C22×#12111yescharacteristic
1085C22C2×#52511yescharacteristic
1086C22C2×#52511yescharacteristic
1087C22C2×#52911yescharacteristic
1088C22C2×#52911yescharacteristic
1089C22C2×#53411yescharacteristic
1090C22C2×#53511yescharacteristic
1091C22C2×#53711yescharacteristic
1092C22C2×#53911yescharacteristic
1093C22C2×#53911yescharacteristic
1094C22C2×#54011yescharacteristic
1095C22C2×#54211yescharacteristic
1096C22C2×#54211yescharacteristic
1097C22C2×#54211yescharacteristic
1098C22C2×D4211yescharacteristic
1099C22C2×#54611yescharacteristic
1100C22C2×#54611yescharacteristic
1101C22C2×#54611yescharacteristic
1102C22C2×#54711yescharacteristic
1103C22C2×#54811yescharacteristic
1104C22C2×#54811yescharacteristic
1105C22C2×#54811yescharacteristic
1106C22C2×#54811yescharacteristic
1107C22C2×#55011yescharacteristic
1108C22C2×#55011yescharacteristic
1109C22C2×#55111yescharacteristic
1110C22C2×#55111yescharacteristic
1111C22C2×#55111yescharacteristic
1112C22C2×#55211yescharacteristic
1113C22C2×#55311yescharacteristic
1114C22C2×#55311yescharacteristic
1115C22C2×#55511yescharacteristic
1116C22C2×#56011yescharacteristic
1117C22C2×#56311yescharacteristic
1118C4—28no—
1119C4—28no—
1120C4—44no—
1121C4—44no—
1122C4—44no—
1123C4—44no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—82no—
1128C4—82no—
1129C4—82no—
1130C4—82no—
1131C2—84no—
1132C2—84no—
1133C2#15458116yesdirect product factor
1134C2C2×#246311yescharacteristic
1135C2C2×#246011yescharacteristic
1136C2C2×#241611yescharacteristic
1137C2C2×#242611yescharacteristic
1138C2C2×#242611yescharacteristic
1139C2C2×#241411yescharacteristic
1140C2C2×#247911yescharacteristic
1141C2C2×#252611yescharacteristic
1142C2C2×#253411yescharacteristic
1143C2C2×#267311yescharacteristic
1144C2C2×#270511yescharacteristic
1145C2C2×#270711yescharacteristic
1146C2C2×#272311yescharacteristic
1147C2C2×#273111yescharacteristic
1148C2C2×#275711yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#396C2semidirect
4. C22×#389C2semidirect
5. C22×#388C2semidirect
6. C22×#387C2semidirect
7. #15458C2direct (N × H)
8. C2×#1441C2semidirect
9. C2×#1440C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
12. C2×#1439C2semidirect
13. C2×#1439C2semidirect
15. C2×#1437C2semidirect
16. C2×#1434C2semidirect
39. C2×#396C22semidirect
45. C2×#389C22semidirect
47. C2×#388C22semidirect
49. C2×#387C22semidirect
64. #1441C22semidirect
65. #1440C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
71. #1437C22semidirect
72. #1434C22semidirect
113. C22×C4⋊C4D4semidirect
384. C2×C4⋊C4C2×D4semidirect
1133. C2#15458direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3962
C22×#3942
C22×#3902
C22×#3892
C22×#3882
C22×#3872
#154582
C2×#14412
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14342