Finite Group Databasebeta

← C2×#15431 #608969

Subgroups — C2×#15431 #608969

Order 512.

4930 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#398C211yesmaximal, characteristic, complemented
2C22×#385C211yesmaximal, characteristic
3C22×#382C211yesmaximal, characteristic, complemented
4C22×#380C211yesmaximal, characteristic
5#15431C2116yesmaximal, direct product factor
6C2×#1442C211yesmaximal, characteristic, complemented
7C2×#1442C211yesmaximal, characteristic, complemented
8C2×#1442C211yesmaximal, characteristic, complemented
9C2×#1441C211yesmaximal, characteristic, complemented
10C2×#1441C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic
12C2×#1439C211yesmaximal, characteristic
13C2×#1439C211yesmaximal, characteristic
14C2×#1437C211yesmaximal, characteristic
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C42C2211yescharacteristic
32C2×#398—28no—
33C2×#398C2218yescomplemented
34C2×#385—28no—
35C2×#385C2218yes—
36C2×#382—28no—
37C2×#382C2218yescomplemented
38C2×#380—28no—
39C2×#380C2218yes—
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1442C2218yescomplemented
61#1442C2218yescomplemented
62#1442C2218yescomplemented
63#1441C2218yescomplemented
64#1441C2218yescomplemented
65#1439C2218yes—
66#1439C2218yes—
67#1439C2218yes—
68#1437C2218yes—
69#1436C2218yescomplemented
70C22⋊#95C2218yes—
71C26C2311yescharacteristic
72C24×C4—24no—
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—24no—
77C24×C4—42no—
78C24×C4—42no—
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2314yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
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—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—42no—
110C22×C4⋊C4—42no—
111C22×C4⋊C4—42no—
112C22×C4⋊C4—42no—
113C22×C4⋊C4—42no—
114C22×C4⋊C4—42no—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
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—42no—
134C22×C22⋊C4—42no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4Q818yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42—24no—
149C22×C42C2314yes—
150#398—232no—
151#385—232no—
152#382—232no—
153#380—232no—
154C2×#95—24no—
155C2×#95—24no—
156C2×#95—24no—
157C2×#95—24no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—24no—
163C2×#95—24no—
164C2×#95—42no—
165C2×#95—42no—
166C2×#95—42no—
167C2×#95—42no—
168C2×#95—42no—
169C2×#95—42no—
170C2×#95—42no—
171C2×#95—42no—
172C2×#95D418yes—
173C2×#95D418yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25C2×Q814yes—
207C25#4114yes—
208C25#4114yes—
209C25C2412yes—
210C25C2411yescharacteristic
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—232no—
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—28no—
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—28no—
258C23×C4—28no—
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—28no—
302C23×C4—28no—
303C23×C4—44no—
304C23×C4—44no—
305C23×C4—416no—
306C23×C4—416no—
307C23×C4—416no—
308C23×C4—416no—
309C23×C4—416no—
310C23×C4—416no—
311C23×C4C2×D414yes—
312C23×C4C2×D414yes—
313C23×C4C2×D414yes—
314C23×C4C2×D414yes—
315C23×C4C2×D414yes—
316C23×C4C2×D414yes—
317C23×C4C2×Q814yes—
318C23×C4C2×Q814yes—
319C23×C4#4114yes—
320C23×C4#4114yes—
321C23×C4#4114yes—
322C23×C4#4114yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2412yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2412yes—
332C23×C4C2412yes—
333C23×C4C2412yes—
334C23×C4C2412yes—
335C23×C4C2412yes—
336C23×C4C2412yes—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—416no—
359C2×C4⋊C4—416no—
360C2×C4⋊C4—416no—
361C2×C4⋊C4—416no—
362C2×C4⋊C4—416no—
363C2×C4⋊C4—416no—
364C2×C4⋊C4—416no—
365C2×C22⋊C4—232no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—416no—
384C2×C22⋊C4—416no—
385C2×C22⋊C4—416no—
386C2×C22⋊C4—416no—
387C2×C22⋊C4—416no—
388C2×C22⋊C4C2×Q8116yes—
389C2×C42—232no—
390C2×C42—28no—
391C2×C42—28no—
392C2×C42—28no—
393#95—28no—
394#95—28no—
395#95—28no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95C2×D4116yes—
412#95C2×D4116yes—
413C24—28no—
414C24—28no—
415C24—28no—
416C24—28no—
417C24—28no—
418C24—28no—
419C24—28no—
420C24—28no—
421C24—28no—
422C24—28no—
423C24—28no—
424C24—28no—
425C24—28no—
426C24—28no—
427C24—28no—
428C24—28no—
429C24—28no—
430C24—28no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—44no—
444C24—44no—
445C24—44no—
446C24—44no—
447C24—44no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—44no—
452C24—44no—
453C24—44no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24#125116yes—
460C24C22×D412yes—
461C24C22×D412yes—
462C24C22×Q814yes—
463C24C22×Q812yes—
464C24C2×#4114yes—
465C24C2×#4114yes—
466C24C2×#4112yes—
467C24C2×#4112yes—
468C24C2×#4112yes—
469C24C2×#4112yes—
470C24C2×#4112yes—
471C24C2×#4112yes—
472C24H(5,𝔽2)12yes—
473C24H(5,𝔽2)12yes—
474C24H(5,𝔽2)12yes—
475C24H(5,𝔽2)12yes—
476C242−1+412yes—
477C242−1+412yes—
478C24C2511yescharacteristic
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—232no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—416no—
597C22×C4—416no—
598C22×C4—416no—
599C22×C4—416no—
600C22×C4—416no—
601C22×C4—4128no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—416no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4C22⋊Q8116yes—
670C22×C4#124116yes—
671C22×C4C22×D414yes—
672C22×C4C22×D414yes—
673C22×C4C22×D414yes—
674C22×C4C22×D414yes—
675C22×C4C22×D414yes—
676C22×C4C22×D414yes—
677C22×C4C22×Q814yes—
678C22×C4C22×Q814yes—
679C22×C4C2×#4114yes—
680C22×C4C2×#4114yes—
681C22×C4C2×#4114yes—
682C22×C4C2×#4114yes—
683C4⋊C4—416no—
684C4⋊C4—416no—
685C4⋊C4—416no—
686C4⋊C4—416no—
687C4⋊C4—416no—
688C4⋊C4—416no—
689C4⋊C4—416no—
690C22⋊C4—232no—
691C22⋊C4—416no—
692C22⋊C4—416no—
693C22⋊C4—416no—
694C22⋊C4—416no—
695C22⋊C4—416no—
696C42—232no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—232no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—232no—
717C23—232no—
718C23—416no—
719C23—416no—
720C23—42no—
721C23—42no—
722C23—416no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—416no—
734C23—416no—
735C23—42no—
736C23—42no—
737C23—416no—
738C23—416no—
739C23—416no—
740C23—416no—
741C23—416no—
742C23—42no—
743C23—42no—
744C23—416no—
745C23—416no—
746C23C2×C22⋊Q814yes—
747C23#52514yes—
748C23#52514yes—
749C23C2×#12414yes—
750C23C2×#12518yes—
751C23C2×#12514yes—
752C23#52914yes—
753C23#53514yes—
754C23#53714yes—
755C23#53814yes—
756C23#53814yes—
757C23#53914yes—
758C23#53914yes—
759C23#54014yes—
760C23#54114yes—
761C23#54414yes—
762C23D4214yes—
763C23#54614yes—
764C23#54614yes—
765C23#54614yes—
766C23#54714yes—
767C23#54814yes—
768C23D4×Q814yes—
769C23#55114yes—
770C23#55114yes—
771C23#55214yes—
772C23#55214yes—
773C23#55214yes—
774C23#55314yes—
775C23#55414yes—
776C23#55414yes—
777C23#55414yes—
778C23#55514yes—
779C23#55514yes—
780C23#56214yes—
781C23#56214yes—
782C23C23×D411yescharacteristic
783C23C23×D411yescharacteristic
784C23C23×Q811yescharacteristic
785C23C22×#4111yescharacteristic
786C23C22×#4111yescharacteristic
787C23C22×#4111yescharacteristic
788C23C22×#4111yescharacteristic
789C23C22×#4111yescharacteristic
790C23C22×#4111yescharacteristic
791C23C2×H(5,𝔽2)11yescharacteristic
792C23C2×H(5,𝔽2)11yescharacteristic
793C23C2×H(5,𝔽2)11yescharacteristic
794C23C2×H(5,𝔽2)11yescharacteristic
795C23C2×2−1+411yescharacteristic
796C23C2×2−1+411yescharacteristic
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—232no—
810C2×C4—232no—
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—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—464no—
830C2×C4—416no—
831C2×C4—416no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—416no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—416no—
856C2×C4—416no—
857C2×C4—416no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
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—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—88no—
903C2×C4—88no—
904C2×C4—88no—
905C2×C4—88no—
906C2×C4—88no—
907C2×C4—88no—
908C2×C4C2×C22⋊Q818yes—
909C2×C4C2×#12418yes—
910C22—28no—
911C22—28no—
912C22—28no—
913C22—44no—
914C22—464no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22#244218yes—
927C22#244918yes—
928C22#247218yes—
929C22#247318yes—
930C22#247618yes—
931C22#248918yes—
932C22#250518yes—
933C22#256318yes—
934C22#260918yes—
935C22#267618yes—
936C22#270418yes—
937C22#270618yes—
938C22#274418yes—
939C22#276818yes—
940C22#278118yes—
941C22C22×C22⋊Q811yescharacteristic
942C22C2×#52511yescharacteristic
943C22C2×#52511yescharacteristic
944C22C22×#12411yescharacteristic
945C22C22×#12511yescharacteristic
946C22C2×#52911yescharacteristic
947C22C2×#53511yescharacteristic
948C22C2×#53711yescharacteristic
949C22C2×#53811yescharacteristic
950C22C2×#53811yescharacteristic
951C22C2×#53911yescharacteristic
952C22C2×#53911yescharacteristic
953C22C2×#54011yescharacteristic
954C22C2×#54111yescharacteristic
955C22C2×#54411yescharacteristic
956C22C2×D4211yescharacteristic
957C22C2×#54611yescharacteristic
958C22C2×#54611yescharacteristic
959C22C2×#54611yescharacteristic
960C22C2×#54711yescharacteristic
961C22C2×#54811yescharacteristic
962C22C2×D4×Q811yescharacteristic
963C22C2×#55111yescharacteristic
964C22C2×#55111yescharacteristic
965C22C2×#55211yescharacteristic
966C22C2×#55211yescharacteristic
967C22C2×#55211yescharacteristic
968C22C2×#55311yescharacteristic
969C22C2×#55411yescharacteristic
970C22C2×#55411yescharacteristic
971C22C2×#55411yescharacteristic
972C22C2×#55511yescharacteristic
973C22C2×#55511yescharacteristic
974C22C2×#56211yescharacteristic
975C22C2×#56211yescharacteristic
976C4—28no—
977C4—28no—
978C4—44no—
979C4—44no—
980C4—44no—
981C4—44no—
982C4—44no—
983C4—44no—
984C4—82no—
985C4—82no—
986C4—82no—
987C4—82no—
988C4—82no—
989C4—82no—
990C2—48no—
991C2#15431116yesdirect product factor
992C2C2×#244911yescharacteristic
993C2C2×#247211yescharacteristic
994C2C2×#247311yescharacteristic
995C2C2×#244211yescharacteristic
996C2C2×#247611yescharacteristic
997C2C2×#250511yescharacteristic
998C2C2×#248911yescharacteristic
999C2C2×#260911yescharacteristic
1000C2C2×#256311yescharacteristic
1001C2C2×#267611yescharacteristic
1002C2C2×#270411yescharacteristic
1003C2C2×#270611yescharacteristic
1004C2C2×#274411yescharacteristic
1005C2C2×#276811yescharacteristic
1006C2C2×#278111yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC26C23
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×#398C2semidirect
3. C22×#382C2semidirect
5. #15431C2direct (N × H)
6. C2×#1442C2semidirect
7. C2×#1442C2semidirect
8. C2×#1442C2semidirect
9. C2×#1441C2semidirect
10. C2×#1441C2semidirect
15. C2×#1436C2semidirect
33. C2×#398C22semidirect
37. C2×#382C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
69. #1436C22semidirect
991. C2#15431direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3982
C22×#3852
C22×#3822
C22×#3802
#154312
C2×#14422
C2×#14412
C2×#14392
C2×#14372
C2×#14362
C2×C22⋊#952