Finite Group Databasebeta

← C2×#14114 #514443

Subgroups — C2×#14114 #514443

Order 512.

5258 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#388C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic
3C22×C4×C22⋊C4C211yesmaximal, characteristic
4#14114C2116yesmaximal, direct product factor
5C2×#1442C211yesmaximal, characteristic, complemented
6C2×#1441C211yesmaximal, characteristic, complemented
7C2×#1439C211yesmaximal, characteristic
8C2×#1439C211yesmaximal, characteristic
9C2×#1436C211yesmaximal, characteristic, complemented
10C2×#1436C211yesmaximal, characteristic, complemented
11C2×#1436C211yesmaximal, characteristic, complemented
12C2×C4⋊#95C211yesmaximal, characteristic, complemented
13C2×#1434C211yesmaximal, characteristic, complemented
14C2×C22⋊#95C211yesmaximal, characteristic
15C2×C22⋊#95C211yesmaximal, characteristic
16C2×C4×#95C211yesmaximal, characteristic, complemented
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×#388—28no—
33C2×#388C4116yescomplemented
34C2×#388C2218yes—
35C2×#388C2218yes—
36C2×C4×C22⋊C4—28no—
37C2×C4×C22⋊C4C2218yes—
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
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
58#1442C2218yescomplemented
59#1441C2218yescomplemented
60#1439C2218yes—
61#1439C2218yes—
62#1436C2218yescomplemented
63#1436C2218yescomplemented
64#1436C2218yescomplemented
65C4⋊#95C2218yescomplemented
66#1434C2218yescomplemented
67C22⋊#95C2218yes—
68C22⋊#95C2218yes—
69C4×#95C2218yescomplemented
70C26C2311yescharacteristic
71C24×C4—24no—
72C24×C4—24no—
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—42no—
77C24×C4—42no—
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2314yes—
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4—42no—
100C22×C4⋊C4—42no—
101C22×C4⋊C4—42no—
102C22×C4⋊C4—42no—
103C22×C4⋊C4—42no—
104C22×C4⋊C4C2×C418yescomplemented
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2314yes—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—42no—
117C22×C22⋊C4—42no—
118C22×C22⋊C4—42no—
119C22×C22⋊C4—42no—
120C22×C22⋊C4—42no—
121C22×C22⋊C4—42no—
122C22×C22⋊C4C2×C418yes—
123C22×C22⋊C4C2×C418yes—
124C22×C22⋊C4C2×C418yes—
125C22×C22⋊C4D418yes—
126C22×C22⋊C4Q818yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C42—24no—
134C22×C42—24no—
135C22×C42—24no—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42—24no—
139C22×C42—42no—
140C22×C42—42no—
141C22×C42—42no—
142C22×C42—42no—
143C22×C42—42no—
144C22×C42C2×C418yescomplemented
145C22×C42C2314yes—
146C22×C42C2314yes—
147C22×C42C2314yes—
148C22×C42C2314yes—
149#388—232no—
150#388C2×C4164yescomplemented
151C4×C22⋊C4—232no—
152C2×#95—24no—
153C2×#95—24no—
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—24no—
165C2×#95—42no—
166C2×#95—42no—
167C2×#95—42no—
168C2×#95—42no—
169C2×#95—42no—
170C2×#95C2×C418yescomplemented
171C2×#95C2×C418yescomplemented
172C2×#95C2314yes—
173C2×#95C2314yes—
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—
192C25—22no—
193C25—22no—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25C22×C414yes—
205C25C2×D414yes—
206C25C2×Q814yes—
207C25C2412yes—
208C25C2411yescharacteristic
209C23×C4—22no—
210C23×C4—22no—
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—22no—
220C23×C4—22no—
221C23×C4—232no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—28no—
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×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—28no—
278C23×C4—28no—
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—28no—
294C23×C4—28no—
295C23×C4—44no—
296C23×C4—44no—
297C23×C4—416no—
298C23×C4—416no—
299C23×C4—416no—
300C23×C4—416no—
301C23×C4—416no—
302C23×C4—416no—
303C23×C4C22×C414yes—
304C23×C4C22×C414yes—
305C23×C4C22×C414yes—
306C23×C4C22×C414yes—
307C23×C4C22×C414yes—
308C23×C4C22×C414yes—
309C23×C4C2×D414yes—
310C23×C4C2×D414yes—
311C23×C4C2×Q814yes—
312C23×C4C2×Q814yes—
313C23×C4#4114yes—
314C23×C4#4114yes—
315C23×C4#4114yes—
316C23×C4#4114yes—
317C23×C4#4114yes—
318C23×C4#4114yes—
319C23×C4#4114yes—
320C23×C4#4114yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2412yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2412yes—
332C23×C4C2412yes—
333C23×C4C2412yes—
334C23×C4C2412yes—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—416no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—416no—
348C2×C4⋊C4—416no—
349C2×C4⋊C4—416no—
350C2×C4⋊C4C22×C4116yescomplemented
351C2×C22⋊C4—232no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—416no—
360C2×C22⋊C4—416no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—416no—
368C2×C22⋊C4—416no—
369C2×C22⋊C4C4⋊C4164yescomplemented
370C2×C22⋊C4C22×C4116yes—
371C2×C22⋊C4C22×C4116yes—
372C2×C22⋊C4C22×C4116yes—
373C2×C22⋊C4C2×D4116yes—
374C2×C22⋊C4C2×Q8116yes—
375C2×C42—28no—
376C2×C42—28no—
377C2×C42—28no—
378C2×C42—28no—
379C2×C42—28no—
380C2×C42—28no—
381C2×C42—416no—
382C2×C42—44no—
383C2×C42—44no—
384C2×C42—44no—
385C2×C42—44no—
386C2×C42—44no—
387C2×C42—416no—
388C2×C42—416no—
389C2×C42—416no—
390C2×C42C22×C4116yescomplemented
391#95—28no—
392#95—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—28no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95C22×C4116yescomplemented
410#95C22×C4116yescomplemented
411C24—28no—
412C24—28no—
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—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—44no—
442C24—44no—
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—
457C24C2×C4⋊C4116yes—
458C24C23×C414yes—
459C24C23×C412yes—
460C24C22×D414yes—
461C24C22×D412yes—
462C24C22×Q814yes—
463C24C22×Q812yes—
464C24C2×#4112yes—
465C24C2×#4112yes—
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—
476C24C2511yescharacteristic
477C22×C4—28no—
478C22×C4—28no—
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—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
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—232no—
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—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—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—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—416no—
604C22×C4—416no—
605C22×C4—416no—
606C22×C4—416no—
607C22×C4—416no—
608C22×C4—4128no—
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—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—416no—
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×C4C2×C4⋊C4116yes—
661C22×C4C2×C4⋊C4116yes—
662C22×C4#126116yes—
663C22×C4C23×C414yes—
664C22×C4C23×C414yes—
665C22×C4C23×C414yes—
666C22×C4C23×C414yes—
667C22×C4C23×C414yes—
668C22×C4C23×C414yes—
669C22×C4C22×D414yes—
670C22×C4C22×D414yes—
671C22×C4C22×Q814yes—
672C22×C4C22×Q814yes—
673C22×C4C2×#4114yes—
674C22×C4C2×#4114yes—
675C22×C4C2×#4114yes—
676C22×C4C2×#4114yes—
677C22×C4C2×#4114yes—
678C22×C4C2×#4114yes—
679C22×C4C2×#4114yes—
680C22×C4C2×#4114yes—
681C4⋊C4—416no—
682C4⋊C4—416no—
683C4⋊C4—416no—
684C4⋊C4—416no—
685C22⋊C4—232no—
686C22⋊C4—416no—
687C22⋊C4—416no—
688C22⋊C4—416no—
689C22⋊C4—416no—
690C22⋊C4C2×C4⋊C4164yescomplemented
691C42—416no—
692C42—416no—
693C42—416no—
694C42—416no—
695C23—232no—
696C23—232no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
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—232no—
716C23—416no—
717C23—416no—
718C23—416no—
719C23—416no—
720C23—416no—
721C23—416no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—416no—
739C23—416no—
740C23—416no—
741C23—416no—
742C23—416no—
743C23—416no—
744C23C22×C4⋊C418yes—
745C23C22×C4⋊C414yes—
746C23C4×#4114yes—
747C23C4×#4114yes—
748C23C4×#4114yes—
749C23C4×#4114yes—
750C23#51814yes—
751C23#51814yes—
752C23#52514yes—
753C23#52514yes—
754C23C2×#12614yes—
755C23#52914yes—
756C23#52914yes—
757C23#52914yes—
758C23#53314yes—
759C23#53314yes—
760C23#53814yes—
761C23#53814yes—
762C23#54014yes—
763C23#54014yes—
764C23#54614yes—
765C23#54614yes—
766C23#54614yes—
767C23#54614yes—
768C23#55114yes—
769C23#55114yes—
770C23#55114yes—
771C23#55314yes—
772C23#55314yes—
773C23#55414yes—
774C23#55414yes—
775C23#55414yes—
776C23#55414yes—
777C23#55514yes—
778C23#55514yes—
779C23#55914yes—
780C23C24×C411yescharacteristic
781C23C23×D411yescharacteristic
782C23C23×Q811yescharacteristic
783C23C22×#4111yescharacteristic
784C23C22×#4111yescharacteristic
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
795C2×C4—232no—
796C2×C4—232no—
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—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—232no—
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—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—464no—
844C2×C4—416no—
845C2×C4—416no—
846C2×C4—416no—
847C2×C4—416no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
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—416no—
885C2×C4—416no—
886C2×C4—416no—
887C2×C4—416no—
888C2×C4—416no—
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—42no—
903C2×C4—88no—
904C2×C4—88no—
905C2×C4C22×C4⋊C418yes—
906C2×C4C22×C4⋊C418yes—
907C2×C4C2×#12618yes—
908C22—28no—
909C22—28no—
910C22—28no—
911C22—44no—
912C22—44no—
913C22—44no—
914C22—464no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22#229618yes—
925C22C4×#12618yes—
926C22#233318yes—
927C22#234918yes—
928C22#234918yes—
929C22#237218yes—
930C22#237418yes—
931C22#245718yes—
932C22#245918yes—
933C22#247618yes—
934C22#248018yes—
935C22#249718yes—
936C22#252218yes—
937C22#257418yes—
938C22#258918yes—
939C22C23×C4⋊C411yescharacteristic
940C22C2×C4×#4111yescharacteristic
941C22C2×C4×#4111yescharacteristic
942C22C2×C4×#4111yescharacteristic
943C22C2×C4×#4111yescharacteristic
944C22C2×#51811yescharacteristic
945C22C2×#51811yescharacteristic
946C22C2×#52511yescharacteristic
947C22C2×#52511yescharacteristic
948C22C22×#12611yescharacteristic
949C22C2×#52911yescharacteristic
950C22C2×#52911yescharacteristic
951C22C2×#52911yescharacteristic
952C22C2×#53311yescharacteristic
953C22C2×#53311yescharacteristic
954C22C2×#53811yescharacteristic
955C22C2×#53811yescharacteristic
956C22C2×#54011yescharacteristic
957C22C2×#54011yescharacteristic
958C22C2×#54611yescharacteristic
959C22C2×#54611yescharacteristic
960C22C2×#54611yescharacteristic
961C22C2×#54611yescharacteristic
962C22C2×#55111yescharacteristic
963C22C2×#55111yescharacteristic
964C22C2×#55111yescharacteristic
965C22C2×#55311yescharacteristic
966C22C2×#55311yescharacteristic
967C22C2×#55411yescharacteristic
968C22C2×#55411yescharacteristic
969C22C2×#55411yescharacteristic
970C22C2×#55411yescharacteristic
971C22C2×#55511yescharacteristic
972C22C2×#55511yescharacteristic
973C22C2×#55911yescharacteristic
974C4—28no—
975C4—28no—
976C4—28no—
977C4—44no—
978C4—44no—
979C4—44no—
980C4—44no—
981C4—44no—
982C4—44no—
983C4—44no—
984C4—44no—
985C4—44no—
986C4—82no—
987C4—82no—
988C2—48no—
989C2#14114116yesdirect product factor
990C2C2×#229611yescharacteristic
991C2C2×C4×#12611yescharacteristic
992C2C2×#233311yescharacteristic
993C2C2×#234911yescharacteristic
994C2C2×#234911yescharacteristic
995C2C2×#237211yescharacteristic
996C2C2×#237411yescharacteristic
997C2C2×#248011yescharacteristic
998C2C2×#245911yescharacteristic
999C2C2×#245711yescharacteristic
1000C2C2×#247611yescharacteristic
1001C2C2×#252211yescharacteristic
1002C2C2×#249711yescharacteristic
1003C2C2×#257411yescharacteristic
1004C2C2×#258911yescharacteristic
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
4. #14114C2direct (N × H)
5. C2×#1442C2semidirect
6. C2×#1441C2semidirect
9. C2×#1436C2semidirect
10. C2×#1436C2semidirect
11. C2×#1436C2semidirect
12. C2×C4⋊#95C2semidirect
13. C2×#1434C2semidirect
16. C2×C4×#95C2semidirect
33. C2×#388C4semidirect
58. #1442C22semidirect
59. #1441C22semidirect
62. #1436C22semidirect
63. #1436C22semidirect
64. #1436C22semidirect
65. C4⋊#95C22semidirect
66. #1434C22semidirect
69. C4×#95C22semidirect
104. C22×C4⋊C4C2×C4semidirect
144. C22×C42C2×C4semidirect
150. #388C2×C4semidirect
170. C2×#95C2×C4semidirect
171. C2×#95C2×C4semidirect
350. C2×C4⋊C4C22×C4semidirect
369. C2×C22⋊C4C4⋊C4semidirect
390. C2×C42C22×C4semidirect
409. #95C22×C4semidirect
410. #95C22×C4semidirect
690. C22⋊C4C2×C4⋊C4semidirect
989. C2#14114direct (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×C4×C22⋊C42
#141142
C2×#14422
C2×#14412
C2×#14392
C2×#14362
C2×C4⋊#952
C2×#14342
C2×C22⋊#952
C2×C4×#952