Finite Group Databasebeta

← C2×#14070 #514393

Subgroups — C2×#14070 #514393

Order 512.

5538 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#388C211yesmaximal, characteristic
2C22×#387C211yesmaximal, characteristic, complemented
3C22×#385C211yesmaximal, characteristic
4C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊C4C211yesmaximal, characteristic
6#14070C2116yesmaximal, direct product factor
7C2×#1442C211yesmaximal, characteristic, complemented
8C2×#1441C211yesmaximal, characteristic, complemented
9C2×#1440C211yesmaximal, characteristic
10C2×#1439C211yesmaximal, characteristic
11C2×#1437C211yesmaximal, characteristic
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×#1434C211yesmaximal, characteristic, complemented
14C2×#1434C211yesmaximal, characteristic, complemented
15C2×#1434C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C23×C42C2211yescharacteristic
31C23×C42C2211yescharacteristic
32C2×#388C4116yescomplemented
33C2×#388C2218yes—
34C2×#387—28no—
35C2×#387C2218yescomplemented
36C2×#385—28no—
37C2×#385C2218yes—
38C2×C4×C4⋊C4—28no—
39C2×C4×C4⋊C4C2218yescomplemented
40C2×C4×C22⋊C4—28no—
41C2×C4×C22⋊C4C2218yes—
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
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62#1442C2218yescomplemented
63#1441C2218yescomplemented
64#1440C2218yes—
65#1439C2218yes—
66#1437C2218yes—
67#1436C2218yescomplemented
68#1434C2218yescomplemented
69#1434C2218yescomplemented
70#1434C2218yescomplemented
71C22⋊#95C2218yes—
72C26C2311yescharacteristic
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—24no—
77C24×C4—24no—
78C24×C4—42no—
79C24×C4—42no—
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
94C24×C4C2311yescharacteristic
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—42no—
105C22×C4⋊C4C2×C418yescomplemented
106C22×C4⋊C4D418yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2314yes—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—42no—
125C22×C22⋊C4—42no—
126C22×C22⋊C4C2×C418yes—
127C22×C22⋊C4C2×C418yes—
128C22×C22⋊C4C2×C418yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C42—24no—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42—24no—
139C22×C42—24no—
140C22×C42—24no—
141C22×C42—42no—
142C22×C42—42no—
143C22×C42—42no—
144C22×C42—42no—
145C22×C42C2×C418yescomplemented
146C22×C42D418yes—
147C22×C42C2314yes—
148C22×C42C2314yes—
149C22×C42C2314yes—
150C22×C42C2314yes—
151#388C2×C4164yescomplemented
152#387—232no—
153#385—232no—
154C4×C4⋊C4—232no—
155C4×C22⋊C4—232no—
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—24no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95—24no—
168C2×#95—24no—
169C2×#95—24no—
170C2×#95—24no—
171C2×#95—42no—
172C2×#95—42no—
173C2×#95—42no—
174C2×#95C2×C418yescomplemented
175C2×#95C2×C418yescomplemented
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—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25C22×C414yes—
209C25#4114yes—
210C25#4114yes—
211C25C2412yes—
212C25C2411yescharacteristic
213C23×C4—22no—
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—232no—
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—28no—
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—28no—
282C23×C4—28no—
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—28no—
298C23×C4—28no—
299C23×C4—44no—
300C23×C4—44no—
301C23×C4—416no—
302C23×C4—416no—
303C23×C4—416no—
304C23×C4—416no—
305C23×C4—416no—
306C23×C4—416no—
307C23×C4C22×C414yes—
308C23×C4C22×C414yes—
309C23×C4C22×C414yes—
310C23×C4C22×C414yes—
311C23×C4C22×C414yes—
312C23×C4C22×C414yes—
313C23×C4C2×D414yes—
314C23×C4C2×D414yes—
315C23×C4C2×D414yes—
316C23×C4C2×D414yes—
317C23×C4C2×D414yes—
318C23×C4C2×D414yes—
319C23×C4#4114yes—
320C23×C4#4114yes—
321C23×C4#4114yes—
322C23×C4#4114yes—
323C23×C4#4114yes—
324C23×C4#4114yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2412yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2412yes—
332C23×C4C2412yes—
333C23×C4C2412yes—
334C23×C4C2412yes—
335C23×C4C2412yes—
336C23×C4C2412yes—
337C23×C4C2412yes—
338C23×C4C2412yes—
339C2×C4⋊C4—232no—
340C2×C4⋊C4—232no—
341C2×C4⋊C4—232no—
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—28no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—416no—
353C2×C4⋊C4C22×C4116yescomplemented
354C2×C4⋊C4C2×D4116yes—
355C2×C22⋊C4—232no—
356C2×C22⋊C4—232no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—232no—
361C2×C22⋊C4—232no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
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—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—416no—
375C2×C22⋊C4—416no—
376C2×C22⋊C4C22×C4116yes—
377C2×C22⋊C4C22×C4116yes—
378C2×C22⋊C4C22×C4116yes—
379C2×C42—232no—
380C2×C42—28no—
381C2×C42—28no—
382C2×C42—28no—
383C2×C42—28no—
384C2×C42—28no—
385C2×C42—28no—
386C2×C42—416no—
387C2×C42—44no—
388C2×C42—44no—
389C2×C42—44no—
390C2×C42—44no—
391C2×C42—416no—
392C2×C42—416no—
393C2×C42C22×C4116yescomplemented
394C2×C42C2×D4116yes—
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—28no—
404#95—28no—
405#95—28no—
406#95—28no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95C22×C4116yescomplemented
414#95C22×C4116yescomplemented
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—28no—
432C24—28no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
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—44no—
460C24—44no—
461C24#117116yes—
462C24C23×C414yes—
463C24C23×C412yes—
464C24C22×D412yes—
465C24C22×D412yes—
466C24C2×#4114yes—
467C24C2×#4114yes—
468C24C2×#4112yes—
469C24C2×#4112yes—
470C24C2×#4112yes—
471C24C2×#4112yes—
472C24C2×#4112yes—
473C24C2×#4112yes—
474C24C2×#4112yes—
475C24C2×#4112yes—
476C24H(5,𝔽2)12yes—
477C24H(5,𝔽2)12yes—
478C242−1+412yes—
479C242−1+412yes—
480C24C2511yescharacteristic
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—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—232no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
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—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—416no—
608C22×C4—416no—
609C22×C4—416no—
610C22×C4—416no—
611C22×C4—416no—
612C22×C4—4128no—
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—44no—
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—416no—
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×C4C4×D4116yes—
665C22×C4C4×D4116yes—
666C22×C4#121116yes—
667C22×C4C23×C414yes—
668C22×C4C23×C414yes—
669C22×C4C23×C414yes—
670C22×C4C23×C414yes—
671C22×C4C23×C414yes—
672C22×C4C23×C414yes—
673C22×C4C22×D414yes—
674C22×C4C22×D414yes—
675C22×C4C22×D414yes—
676C22×C4C22×D414yes—
677C22×C4C22×D414yes—
678C22×C4C22×D414yes—
679C22×C4C2×#4114yes—
680C22×C4C2×#4114yes—
681C22×C4C2×#4114yes—
682C22×C4C2×#4114yes—
683C22×C4C2×#4114yes—
684C22×C4C2×#4114yes—
685C4⋊C4—232no—
686C4⋊C4—232no—
687C4⋊C4—232no—
688C4⋊C4—416no—
689C22⋊C4—232no—
690C22⋊C4—232no—
691C22⋊C4—232no—
692C22⋊C4—232no—
693C22⋊C4—416no—
694C22⋊C4—416no—
695C42—232no—
696C42—416no—
697C42—416no—
698C42—416no—
699C23—232no—
700C23—232no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—232no—
720C23—416no—
721C23—416no—
722C23—416no—
723C23—416no—
724C23—416no—
725C23—416no—
726C23—416no—
727C23—416no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—416no—
745C23—416no—
746C23—416no—
747C23—416no—
748C23C2×#11718yes—
749C23C2×#11714yes—
750C23C2×C4×D414yes—
751C23C2×C4×D414yes—
752C23C4×#4114yes—
753C23C4×#4114yes—
754C23#52014yes—
755C23#52014yes—
756C23C2×#12114yes—
757C23#52514yes—
758C23#52514yes—
759C23#52514yes—
760C23#52914yes—
761C23#52914yes—
762C23#52914yes—
763C23#53214yes—
764C23#53414yes—
765C23#53614yes—
766C23#53914yes—
767C23#53914yes—
768C23#54614yes—
769C23#54614yes—
770C23#54814yes—
771C23#54814yes—
772C23#55114yes—
773C23#55114yes—
774C23#55114yes—
775C23#55214yes—
776C23#55214yes—
777C23#55214yes—
778C23#55214yes—
779C23#55314yes—
780C23#55314yes—
781C23#55614yes—
782C23#55614yes—
783C23#55914yes—
784C23C24×C411yescharacteristic
785C23C23×D411yescharacteristic
786C23C23×D411yescharacteristic
787C23C22×#4111yescharacteristic
788C23C22×#4111yescharacteristic
789C23C22×#4111yescharacteristic
790C23C22×#4111yescharacteristic
791C23C22×#4111yescharacteristic
792C23C22×#4111yescharacteristic
793C23C22×#4111yescharacteristic
794C23C22×#4111yescharacteristic
795C23C2×H(5,𝔽2)11yescharacteristic
796C23C2×H(5,𝔽2)11yescharacteristic
797C23C2×2−1+411yescharacteristic
798C23C2×2−1+411yescharacteristic
799C2×C4—232no—
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—24no—
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—232no—
819C2×C4—232no—
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—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
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—464no—
848C2×C4—416no—
849C2×C4—416no—
850C2×C4—416no—
851C2×C4—416no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
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—416no—
889C2×C4—416no—
890C2×C4—416no—
891C2×C4—416no—
892C2×C4—416no—
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—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—88no—
908C2×C4—88no—
909C2×C4C2×C4×D418yes—
910C2×C4C2×C4×D418yes—
911C2×C4C2×#12118yes—
912C22—28no—
913C22—28no—
914C22—28no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—464no—
928C22#229018yes—
929C22C4×#12118yes—
930C22#232218yes—
931C22#234318yes—
932C22#235218yes—
933C22#236718yes—
934C22#237318yes—
935C22#253418yes—
936C22#253618yes—
937C22#255818yes—
938C22#256018yes—
939C22#257518yes—
940C22#257718yes—
941C22#259918yes—
942C22#260018yes—
943C22C22×#11711yescharacteristic
944C22C22×C4×D411yescharacteristic
945C22C22×C4×D411yescharacteristic
946C22C2×C4×#4111yescharacteristic
947C22C2×C4×#4111yescharacteristic
948C22C2×#52011yescharacteristic
949C22C2×#52011yescharacteristic
950C22C22×#12111yescharacteristic
951C22C2×#52511yescharacteristic
952C22C2×#52511yescharacteristic
953C22C2×#52511yescharacteristic
954C22C2×#52911yescharacteristic
955C22C2×#52911yescharacteristic
956C22C2×#52911yescharacteristic
957C22C2×#53211yescharacteristic
958C22C2×#53411yescharacteristic
959C22C2×#53611yescharacteristic
960C22C2×#53911yescharacteristic
961C22C2×#53911yescharacteristic
962C22C2×#54611yescharacteristic
963C22C2×#54611yescharacteristic
964C22C2×#54811yescharacteristic
965C22C2×#54811yescharacteristic
966C22C2×#55111yescharacteristic
967C22C2×#55111yescharacteristic
968C22C2×#55111yescharacteristic
969C22C2×#55211yescharacteristic
970C22C2×#55211yescharacteristic
971C22C2×#55211yescharacteristic
972C22C2×#55211yescharacteristic
973C22C2×#55311yescharacteristic
974C22C2×#55311yescharacteristic
975C22C2×#55611yescharacteristic
976C22C2×#55611yescharacteristic
977C22C2×#55911yescharacteristic
978C4—28no—
979C4—28no—
980C4—28no—
981C4—44no—
982C4—44no—
983C4—44no—
984C4—44no—
985C4—44no—
986C4—44no—
987C4—44no—
988C4—44no—
989C4—44no—
990C4—82no—
991C4—82no—
992C2—48no—
993C2#14070116yesdirect product factor
994C2C2×#229011yescharacteristic
995C2C2×C4×#12111yescharacteristic
996C2C2×#232211yescharacteristic
997C2C2×#234311yescharacteristic
998C2C2×#235211yescharacteristic
999C2C2×#236711yescharacteristic
1000C2C2×#237311yescharacteristic
1001C2C2×#253411yescharacteristic
1002C2C2×#255811yescharacteristic
1003C2C2×#256011yescharacteristic
1004C2C2×#257511yescharacteristic
1005C2C2×#257711yescharacteristic
1006C2C2×#259911yescharacteristic
1007C2C2×#253611yescharacteristic
1008C2C2×#260011yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#387C2semidirect
4. C22×C4×C4⋊C4C2semidirect
6. #14070C2direct (N × H)
7. C2×#1442C2semidirect
8. C2×#1441C2semidirect
12. C2×#1436C2semidirect
13. C2×#1434C2semidirect
14. C2×#1434C2semidirect
15. C2×#1434C2semidirect
32. C2×#388C4semidirect
35. C2×#387C22semidirect
39. C2×C4×C4⋊C4C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
67. #1436C22semidirect
68. #1434C22semidirect
69. #1434C22semidirect
70. #1434C22semidirect
105. C22×C4⋊C4C2×C4semidirect
145. C22×C42C2×C4semidirect
151. #388C2×C4semidirect
174. C2×#95C2×C4semidirect
175. C2×#95C2×C4semidirect
353. C2×C4⋊C4C22×C4semidirect
393. C2×C42C22×C4semidirect
413. #95C22×C4semidirect
414. #95C22×C4semidirect
993. C2#14070direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3882
C22×#3872
C22×#3852
C22×C4×C4⋊C42
C22×C4×C22⋊C42
#140702
C2×#14422
C2×#14412
C2×#14402
C2×#14392
C2×#14372
C2×#14362
C2×#14342
C2×C22⋊#952