Finite Group Databasebeta

← C2×#14566 #521027

Subgroups — C2×#14566 #521027

Order 512.

5330 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#394C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic, complemented
3C22×#388C211yesmaximal, characteristic, complemented
4#14566C2116yesmaximal, direct product factor
5C2×#1443C211yesmaximal, characteristic, complemented
6C2×#1439C211yesmaximal, characteristic, complemented
7C2×#1439C211yesmaximal, characteristic, complemented
8C2×#1438C211yesmaximal, characteristic
9C2×#1438C211yesmaximal, characteristic
10C2×#1437C211yesmaximal, characteristic, complemented
11C2×#1437C211yesmaximal, characteristic, complemented
12C2×#1437C211yesmaximal, characteristic, complemented
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C4⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊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×C42C2211yescharacteristic
34C23×C42C2211yescharacteristic
35C23×C42C2211yescharacteristic
36C2×#394C4116yescomplemented
37C2×#394C2218yes—
38C2×#388—28no—
39C2×#388—28no—
40C2×#388C2218yescomplemented
41C2×#388C2218yescomplemented
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#1443C2218yescomplemented
59#1439C2218yescomplemented
60#1439C2218yescomplemented
61#1438C2218yes—
62#1438C2218yes—
63#1437C2218yescomplemented
64#1437C2218yescomplemented
65#1437C2218yescomplemented
66#1437C2218yescomplemented
67#1436C2218yescomplemented
68#1436C2218yescomplemented
69C4⋊#95C2218yescomplemented
70C26C2311yescharacteristic
71C26C2311yescharacteristic
72C23×D4—42no—
73C23×D4—42no—
74C23×D4—42no—
75C23×D4—42no—
76C23×D4—42no—
77C23×D4—42no—
78C23×D4C2×C418yes—
79C23×D4C2314yes—
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
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—42no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4—42no—
100C22×C4⋊C4—42no—
101C22×C4⋊C4C2×C418yes—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2314yes—
105C22×C22⋊C4—24no—
106C22×C22⋊C4—24no—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—24no—
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—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—42no—
122C22×C22⋊C4—42no—
123C22×C22⋊C4—42no—
124C22×C22⋊C4—42no—
125C22×C22⋊C4—42no—
126C22×C22⋊C4—42no—
127C22×C22⋊C4—42no—
128C22×C22⋊C4—42no—
129C22×C22⋊C4—42no—
130C22×C22⋊C4—42no—
131C22×C22⋊C4—42no—
132C22×C22⋊C4—42no—
133C22×C22⋊C4—42no—
134C22×C22⋊C4—42no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4C2×C418yes—
138C22×C22⋊C4C2×C418yes—
139C22×C22⋊C4C2×C418yes—
140C22×C22⋊C4C2×C418yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C42—24no—
154C22×C42—24no—
155C22×C42—24no—
156C22×C42—42no—
157C22×C42—42no—
158C22×C42—42no—
159C22×C42—42no—
160C22×C42—42no—
161C22×C42—42no—
162C22×C42C2314yes—
163C22×C42C2314yes—
164C22×C42C2314yes—
165#394C2×C4164yescomplemented
166#388—232no—
167#388—232no—
168C2×#95—24no—
169C2×#95—24no—
170C2×#95—24no—
171C2×#95—24no—
172C2×#95—42no—
173C2×#95—42no—
174C2×#95—42no—
175C2×#95—42no—
176C2×#95—42no—
177C2×#95—42no—
178C2×#95—42no—
179C2×#95—42no—
180C2×#95—42no—
181C2×#95—42no—
182C2×#95C2×C418yes—
183C2×#95D418yescomplemented
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
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—
228C25C22×C414yes—
229C25C22×C414yes—
230C25C2412yes—
231C25C2412yes—
232C25C2411yescharacteristic
233C22×D4—416no—
234C22×D4—416no—
235C22×D4—416no—
236C22×D4—44no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—416no—
243C22×D4—416no—
244C22×D4—416no—
245C22×D4—416no—
246C22×D4C22×C4116yes—
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—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×C4C22×C414yes—
326C23×C4C22×C414yes—
327C23×C4C22×C414yes—
328C23×C4C22×C414yes—
329C23×C4C22×C414yes—
330C23×C4C2×D414yes—
331C23×C4C2×D414yes—
332C23×C4C2×D414yes—
333C23×C4#4114yes—
334C23×C4#4114yes—
335C23×C4#4114yes—
336C23×C4#4114yes—
337C23×C4#4114yes—
338C23×C4C2412yes—
339C23×C4C2412yes—
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2412yes—
343C23×C4C2412yes—
344C23×C4C2412yes—
345C23×C4C2412yes—
346C23×C4C2412yes—
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2412yes—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—416no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—416no—
361C2×C4⋊C4—416no—
362C2×C4⋊C4C22×C4116yes—
363C2×C22⋊C4—232no—
364C2×C22⋊C4—232no—
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—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—416no—
382C2×C22⋊C4—416no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—416no—
400C2×C22⋊C4—416no—
401C2×C22⋊C4—416no—
402C2×C22⋊C4—416no—
403C2×C22⋊C4—416no—
404C2×C22⋊C4—416no—
405C2×C22⋊C4—416no—
406C2×C22⋊C4—416no—
407C2×C22⋊C4C22×C4116yes—
408C2×C22⋊C4C22×C4116yes—
409C2×C22⋊C4C22×C4116yes—
410C2×C22⋊C4C22×C4116yes—
411C2×C42—28no—
412C2×C42—28no—
413C2×C42—28no—
414C2×C42—44no—
415C2×C42—44no—
416C2×C42—44no—
417C2×C42—44no—
418C2×C42—44no—
419C2×C42—44no—
420C2×C42—416no—
421C2×C42—416no—
422C2×C42—416no—
423#95—28no—
424#95—28no—
425#95—28no—
426#95—28no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95C22×C4116yes—
438#95C2×D4116yescomplemented
439C24—28no—
440C24—28no—
441C24—28no—
442C24—28no—
443C24—28no—
444C24—28no—
445C24—28no—
446C24—28no—
447C24—28no—
448C24—28no—
449C24—28no—
450C24—28no—
451C24—28no—
452C24—28no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
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—44no—
482C24—44no—
483C24—44no—
484C24—44no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24—44no—
489C24—44no—
490C24—44no—
491C24—44no—
492C24—44no—
493C24—44no—
494C24—44no—
495C24—44no—
496C24—44no—
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—
537C24C23×C414yes—
538C24C23×C414yes—
539C24C23×C412yes—
540C24C22×D412yes—
541C24C2×#4112yes—
542C24C2×#4112yes—
543C24C2×#4112yes—
544C24C2×#4112yes—
545C24C2×#4112yes—
546C24H(5,𝔽2)12yes—
547C24H(5,𝔽2)12yes—
548C24H(5,𝔽2)12yes—
549C24H(5,𝔽2)12yes—
550C24H(5,𝔽2)12yes—
551C24H(5,𝔽2)12yes—
552C24H(5,𝔽2)12yes—
553C242−1+412yes—
554C24C2511yescharacteristic
555C2×D4—416no—
556C2×D4—416no—
557C2×D4—416no—
558C2×D4—4128no—
559C2×D4—416no—
560C2×D4—416no—
561C2×D4—416no—
562C2×D4—416no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
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—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
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—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
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×C4C4×D4116yes—
732C22×C4C23×C414yes—
733C22×C4C23×C414yes—
734C22×C4C23×C414yes—
735C22×C4C23×C414yes—
736C22×C4C23×C414yes—
737C22×C4C22×D414yes—
738C22×C4C22×D414yes—
739C22×C4C22×D414yes—
740C22×C4C2×#4114yes—
741C22×C4C2×#4114yes—
742C22×C4C2×#4114yes—
743C22×C4C2×#4114yes—
744C22×C4C2×#4114yes—
745C4⋊C4—416no—
746C4⋊C4—416no—
747C4⋊C4—416no—
748C22⋊C4—232no—
749C22⋊C4—232no—
750C22⋊C4—416no—
751C22⋊C4—416no—
752C22⋊C4—416no—
753C22⋊C4—416no—
754C22⋊C4—416no—
755C22⋊C4—416no—
756C22⋊C4—416no—
757C22⋊C4—416no—
758C22⋊C4—416no—
759C22⋊C4—416no—
760C42—416no—
761C42—416no—
762C42—416no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—416no—
778C23—416no—
779C23—416no—
780C23—416no—
781C23—416no—
782C23—416no—
783C23—416no—
784C23—416no—
785C23—416no—
786C23—416no—
787C23—416no—
788C23—416no—
789C23—416no—
790C23—416no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
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—88no—
848C23—88no—
849C23—88no—
850C23—88no—
851C23—88no—
852C23—88no—
853C23—88no—
854C23—88no—
855C23—88no—
856C23—88no—
857C23—88no—
858C23—88no—
859C23—88no—
860C23—88no—
861C23—88no—
862C23—88no—
863C23C2×C4×D414yes—
864C23C4×#4114yes—
865C23C4×#4114yes—
866C23#51814yes—
867C23#51814yes—
868C23#51814yes—
869C23#52014yes—
870C23#53514yes—
871C23#53714yes—
872C23#53814yes—
873C23#53814yes—
874C23#53814yes—
875C23#53914yes—
876C23#54014yes—
877C23#54014yes—
878C23#54214yes—
879C23#54214yes—
880C23#54214yes—
881C23#54214yes—
882C23#54614yes—
883C23#54614yes—
884C23#54614yes—
885C23#55014yes—
886C23#55114yes—
887C23#55314yes—
888C23#55314yes—
889C23#55314yes—
890C23#55314yes—
891C23#55314yes—
892C23#55514yes—
893C23#55914yes—
894C23#56014yes—
895C23#56014yes—
896C23#56014yes—
897C23H(3,𝔽4)14yes—
898C23C24×C411yescharacteristic
899C23C23×D411yescharacteristic
900C23C22×#4111yescharacteristic
901C23C22×#4111yescharacteristic
902C23C22×#4111yescharacteristic
903C23C22×#4111yescharacteristic
904C23C22×#4111yescharacteristic
905C23C2×H(5,𝔽2)11yescharacteristic
906C23C2×H(5,𝔽2)11yescharacteristic
907C23C2×H(5,𝔽2)11yescharacteristic
908C23C2×H(5,𝔽2)11yescharacteristic
909C23C2×H(5,𝔽2)11yescharacteristic
910C23C2×H(5,𝔽2)11yescharacteristic
911C23C2×H(5,𝔽2)11yescharacteristic
912C23C2×2−1+411yescharacteristic
913D4—464no—
914C2×C4—232no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
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—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—416no—
954C2×C4—416no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—416no—
977C2×C4—416no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—416no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—416no—
985C2×C4—416no—
986C2×C4—416no—
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—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
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—88no—
1016C2×C4—88no—
1017C2×C4C2×C4×D418yes—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—44no—
1031C22—44no—
1032C22—82no—
1033C22—82no—
1034C22—82no—
1035C22—82no—
1036C22—82no—
1037C22—82no—
1038C22—82no—
1039C22—82no—
1040C22—82no—
1041C22—82no—
1042C22—82no—
1043C22—82no—
1044C22—82no—
1045C22—82no—
1046C22—82no—
1047C22—82no—
1048C22—832no—
1049C22—832no—
1050C22#232418yes—
1051C22#233518yes—
1052C22#233718yes—
1053C22#236318yes—
1054C22#236418yes—
1055C22#237418yes—
1056C22#237518yes—
1057C22#270318yes—
1058C22#270518yes—
1059C22#271218yes—
1060C22#271418yes—
1061C22#275318yes—
1062C22#279518yes—
1063C22#280118yes—
1064C22#280318yes—
1065C22C22×C4×D411yescharacteristic
1066C22C2×C4×#4111yescharacteristic
1067C22C2×C4×#4111yescharacteristic
1068C22C2×#51811yescharacteristic
1069C22C2×#51811yescharacteristic
1070C22C2×#51811yescharacteristic
1071C22C2×#52011yescharacteristic
1072C22C2×#53511yescharacteristic
1073C22C2×#53711yescharacteristic
1074C22C2×#53811yescharacteristic
1075C22C2×#53811yescharacteristic
1076C22C2×#53811yescharacteristic
1077C22C2×#53911yescharacteristic
1078C22C2×#54011yescharacteristic
1079C22C2×#54011yescharacteristic
1080C22C2×#54211yescharacteristic
1081C22C2×#54211yescharacteristic
1082C22C2×#54211yescharacteristic
1083C22C2×#54211yescharacteristic
1084C22C2×#54611yescharacteristic
1085C22C2×#54611yescharacteristic
1086C22C2×#54611yescharacteristic
1087C22C2×#55011yescharacteristic
1088C22C2×#55111yescharacteristic
1089C22C2×#55311yescharacteristic
1090C22C2×#55311yescharacteristic
1091C22C2×#55311yescharacteristic
1092C22C2×#55311yescharacteristic
1093C22C2×#55311yescharacteristic
1094C22C2×#55511yescharacteristic
1095C22C2×#55911yescharacteristic
1096C22C2×#56011yescharacteristic
1097C22C2×#56011yescharacteristic
1098C22C2×#56011yescharacteristic
1099C22C2×H(3,𝔽4)11yescharacteristic
1100C4—28no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C4—44no—
1106C4—44no—
1107C4—44no—
1108C4—44no—
1109C4—44no—
1110C4—44no—
1111C4—82no—
1112C4—82no—
1113C2—84no—
1114C2—84no—
1115C2#14566116yesdirect product factor
1116C2C2×#232411yescharacteristic
1117C2C2×#233511yescharacteristic
1118C2C2×#233711yescharacteristic
1119C2C2×#236311yescharacteristic
1120C2C2×#236411yescharacteristic
1121C2C2×#237411yescharacteristic
1122C2C2×#237511yescharacteristic
1123C2C2×#270311yescharacteristic
1124C2C2×#270511yescharacteristic
1125C2C2×#271211yescharacteristic
1126C2C2×#271411yescharacteristic
1127C2C2×#275311yescharacteristic
1128C2C2×#279511yescharacteristic
1129C2C2×#280111yescharacteristic
1130C2C2×#280311yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC24×D4C22
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×#388C2semidirect
3. C22×#388C2semidirect
4. #14566C2direct (N × H)
5. C2×#1443C2semidirect
6. C2×#1439C2semidirect
7. C2×#1439C2semidirect
10. C2×#1437C2semidirect
11. C2×#1437C2semidirect
12. C2×#1437C2semidirect
13. C2×#1437C2semidirect
14. C2×#1436C2semidirect
15. C2×#1436C2semidirect
16. C2×C4⋊#95C2semidirect
36. C2×#394C4semidirect
40. C2×#388C22semidirect
41. C2×#388C22semidirect
58. #1443C22semidirect
59. #1439C22semidirect
60. #1439C22semidirect
63. #1437C22semidirect
64. #1437C22semidirect
65. #1437C22semidirect
66. #1437C22semidirect
67. #1436C22semidirect
68. #1436C22semidirect
69. C4⋊#95C22semidirect
165. #394C2×C4semidirect
183. C2×#95D4semidirect
438. #95C2×D4semidirect
1115. C2#14566direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3942
C22×#3882
#145662
C2×#14432
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C4⋊#952