Finite Group Databasebeta

← C2×#14064 #514387

Subgroups — C2×#14064 #514387

Order 512.

8306 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#117C211yesmaximal, characteristic, complemented
2C22×#386C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
6#14064C2116yesmaximal, direct product factor
7C2×#1442C211yesmaximal, characteristic, complemented
8C2×#1439C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic, complemented
10C2×#1438C211yesmaximal, characteristic
11C2×#1437C211yesmaximal, characteristic, complemented
12C2×#1437C211yesmaximal, characteristic, complemented
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1434C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×#117—28no—
21C22×#117—28no—
22C22×#117—28no—
23C22×#117C2218yescomplemented
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊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×C22⋊C4C2211yescharacteristic
37C23×C42C2211yescharacteristic
38C23×C42C2211yescharacteristic
39C23×C42C2211yescharacteristic
40C2×#386—28no—
41C2×#386C4116yescomplemented
42C2×#386C2218yes—
43C2×#386C2218yes—
44C2×#385—28no—
45C2×#385C2218yescomplemented
46C2×C4×C22⋊C4—28no—
47C2×C4×C22⋊C4C2218yescomplemented
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
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64#1442C2218yescomplemented
65#1439C2218yescomplemented
66#1439C2218yescomplemented
67#1438C2218yes—
68#1437C2218yescomplemented
69#1437C2218yescomplemented
70#1436C2218yescomplemented
71#1436C2218yescomplemented
72#1434C2218yescomplemented
73C22⋊#95C2218yescomplemented
74C26C2311yescharacteristic
75C26C2311yescharacteristic
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—42no—
81C23×D4—42no—
82C23×D4C2×C418yes—
83C23×D4C2314yes—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—24no—
92C24×C4—24no—
93C24×C4—24no—
94C24×C4—24no—
95C24×C4—42no—
96C24×C4—42no—
97C24×C4C2×C418yescomplemented
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2314yes—
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2314yes—
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C2×#117—2128no—
114C2×#117—232no—
115C2×#117—232no—
116C2×#117—232no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4D418yescomplemented
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
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—24no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—24no—
147C22×C22⋊C4—24no—
148C22×C22⋊C4—24no—
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⋊C4C2×C418yes—
156C22×C22⋊C4C2×C418yes—
157C22×C22⋊C4C2×C418yescomplemented
158C22×C22⋊C4D418yes—
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×C22⋊C4C2314yes—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42—24no—
172C22×C42—24no—
173C22×C42—24no—
174C22×C42—24no—
175C22×C42—42no—
176C22×C42—42no—
177C22×C42D418yescomplemented
178C22×C42C2314yes—
179C22×C42C2314yes—
180C22×C42C2314yes—
181#386—232no—
182#386C2×C4164yescomplemented
183#385—232no—
184C4×C22⋊C4—232no—
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×#95—42no—
197C2×#95—42no—
198C2×#95—42no—
199C2×#95C2×C418yescomplemented
200C2×#95C2×C418yescomplemented
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
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—22no—
239C25—22no—
240C25—22no—
241C25C22×C414yes—
242C25C22×C414yes—
243C25C2×D414yes—
244C25#4114yes—
245C25#4114yes—
246C25#4114yes—
247C25C2412yes—
248C25C2412yes—
249C25C2411yescharacteristic
250C22×D4—232no—
251C22×D4—232no—
252C22×D4—28no—
253C22×D4—28no—
254C22×D4—28no—
255C22×D4—28no—
256C22×D4—416no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—416no—
260C22×D4—416no—
261C22×D4—416no—
262C22×D4—416no—
263C22×D4C22×C4116yes—
264C23×C4—232no—
265C23×C4—232no—
266C23×C4—232no—
267C23×C4—232no—
268C23×C4—232no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—28no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—28no—
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—232no—
284C23×C4—232no—
285C23×C4—28no—
286C23×C4—28no—
287C23×C4—28no—
288C23×C4—28no—
289C23×C4—232no—
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—28no—
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×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—28no—
340C23×C4—28no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—28no—
356C23×C4—28no—
357C23×C4—44no—
358C23×C4—44no—
359C23×C4—416no—
360C23×C4—416no—
361C23×C4—416no—
362C23×C4—416no—
363C23×C4—416no—
364C23×C4—416no—
365C23×C4C22×C414yes—
366C23×C4C22×C414yes—
367C23×C4C22×C414yes—
368C23×C4C22×C414yes—
369C23×C4C22×C414yes—
370C23×C4C22×C4116yescomplemented
371C23×C4C2×D414yes—
372C23×C4C2×D414yes—
373C23×C4C2×D414yes—
374C23×C4C2×D414yes—
375C23×C4C2×D414yes—
376C23×C4C2×D414yes—
377C23×C4C2×D414yes—
378C23×C4C2×D414yes—
379C23×C4#4114yes—
380C23×C4#4114yes—
381C23×C4#4114yes—
382C23×C4#4114yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396#117—2256no—
397C2×C4⋊C4—232no—
398C2×C4⋊C4—232no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—28no—
402C2×C4⋊C4—28no—
403C2×C4⋊C4—28no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—28no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4—416no—
408C2×C4⋊C4C2×D4116yescomplemented
409C2×C22⋊C4—232no—
410C2×C22⋊C4—232no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—232no—
414C2×C22⋊C4—232no—
415C2×C22⋊C4—232no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—28no—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—28no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—28no—
433C2×C22⋊C4—28no—
434C2×C22⋊C4—416no—
435C2×C22⋊C4—44no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4—44no—
441C2×C22⋊C4—416no—
442C2×C22⋊C4—416no—
443C2×C22⋊C4—416no—
444C2×C22⋊C4—416no—
445C2×C22⋊C4C22×C4116yes—
446C2×C22⋊C4C22×C4116yes—
447C2×C22⋊C4C22×C4116yescomplemented
448C2×C22⋊C4C2×D4116yes—
449C2×C42—232no—
450C2×C42—232no—
451C2×C42—28no—
452C2×C42—28no—
453C2×C42—28no—
454C2×C42—28no—
455C2×C42—28no—
456C2×C42—28no—
457C2×C42—44no—
458C2×C42—44no—
459C2×C42—416no—
460C2×C42C2×D4116yescomplemented
461#95—28no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—28no—
467#95—28no—
468#95—28no—
469#95—28no—
470#95—44no—
471#95—44no—
472#95—44no—
473#95—44no—
474#95—44no—
475#95C22×C4116yescomplemented
476#95C22×C4116yescomplemented
477C24—28no—
478C24—28no—
479C24—28no—
480C24—28no—
481C24—28no—
482C24—28no—
483C24—28no—
484C24—28no—
485C24—28no—
486C24—28no—
487C24—28no—
488C24—28no—
489C24—28no—
490C24—28no—
491C24—28no—
492C24—28no—
493C24—28no—
494C24—28no—
495C24—28no—
496C24—28no—
497C24—28no—
498C24—28no—
499C24—28no—
500C24—28no—
501C24—28no—
502C24—28no—
503C24—28no—
504C24—28no—
505C24—28no—
506C24—28no—
507C24—28no—
508C24—28no—
509C24—28no—
510C24—28no—
511C24—28no—
512C24—28no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
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—
553C24—44no—
554C24—44no—
555C24—44no—
556C24—44no—
557C24—44no—
558C24—44no—
559C24—44no—
560C24—44no—
561C24—44no—
562C24—44no—
563C24—44no—
564C24—44no—
565C24—44no—
566C24—44no—
567C24—44no—
568C24—44no—
569C24#117116yescomplemented
570C24C4×D4116yes—
571C24C23×C414yes—
572C24C23×C414yes—
573C24C23×C412yes—
574C24C22×D414yes—
575C24C22×D412yes—
576C24C22×D412yes—
577C24C22×D412yes—
578C24C2×#4114yes—
579C24C2×#4114yes—
580C24C2×#4114yes—
581C24C2×#4112yes—
582C24C2×#4112yes—
583C24C2×#4112yes—
584C24C2×#4112yes—
585C24C2×#4112yes—
586C24C2×#4112yes—
587C24C2×#4112yes—
588C24H(5,𝔽2)12yes—
589C24H(5,𝔽2)12yes—
590C24H(5,𝔽2)12yes—
591C242−1+412yes—
592C24C2511yescharacteristic
593C2×D4—232no—
594C2×D4—232no—
595C2×D4—416no—
596C2×D4—4128no—
597C2×D4—416no—
598C2×D4—416no—
599C2×D4—416no—
600C2×D4—416no—
601C22×C4—232no—
602C22×C4—232no—
603C22×C4—232no—
604C22×C4—232no—
605C22×C4—2256no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—232no—
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—28no—
621C22×C4—28no—
622C22×C4—28no—
623C22×C4—28no—
624C22×C4—28no—
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—232no—
638C22×C4—232no—
639C22×C4—232no—
640C22×C4—28no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—28no—
654C22×C4—28no—
655C22×C4—28no—
656C22×C4—28no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—28no—
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—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—416no—
727C22×C4—416no—
728C22×C4—416no—
729C22×C4—416no—
730C22×C4—4128no—
731C22×C4—416no—
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—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—416no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4C4×D4116yes—
780C22×C4C4×D4116yes—
781C22×C4#120116yes—
782C22×C4C23×C414yes—
783C22×C4C23×C414yes—
784C22×C4C23×C414yes—
785C22×C4C23×C414yes—
786C22×C4C23×C414yes—
787C22×C4C22×D414yes—
788C22×C4C22×D414yes—
789C22×C4C22×D414yes—
790C22×C4C22×D414yes—
791C22×C4C22×D414yes—
792C22×C4C22×D414yes—
793C22×C4C22×D414yes—
794C22×C4C22×D414yes—
795C22×C4C2×#4114yes—
796C22×C4C2×#4114yes—
797C22×C4C2×#4114yes—
798C22×C4C2×#4114yes—
799C4⋊C4—232no—
800C4⋊C4—232no—
801C4⋊C4—416no—
802C22⋊C4—232no—
803C22⋊C4—232no—
804C22⋊C4—232no—
805C22⋊C4—232no—
806C22⋊C4—232no—
807C22⋊C4—416no—
808C22⋊C4—416no—
809C22⋊C4—416no—
810C22⋊C4—416no—
811C22⋊C4—416no—
812C42—232no—
813C42—232no—
814C42—416no—
815C23—232no—
816C23—232no—
817C23—232no—
818C23—232no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—232no—
856C23—232no—
857C23—416no—
858C23—416no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—416no—
863C23—416no—
864C23—416no—
865C23—416no—
866C23—416no—
867C23—416no—
868C23—416no—
869C23—416no—
870C23—416no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—416no—
904C23—416no—
905C23—416no—
906C23—416no—
907C23—416no—
908C23—416no—
909C23—416no—
910C23—416no—
911C23—416no—
912C23—416no—
913C23C2×#11714yes—
914C23C2×#11718yescomplemented
915C23C2×C4×D418yes—
916C23C2×C4×D414yes—
917C23C2×C4×D414yes—
918C23C2×C4×D414yes—
919C23C4×#4114yes—
920C23#51814yes—
921C23#52014yes—
922C23C2×#12014yes—
923C23#52514yes—
924C23#52514yes—
925C23#52514yes—
926C23#52514yes—
927C23#52514yes—
928C23#52914yes—
929C23#52914yes—
930C23#53514yes—
931C23#53714yes—
932C23#54014yes—
933C23#54214yes—
934C23#54614yes—
935C23#54614yes—
936C23#54614yes—
937C23#54614yes—
938C23#54614yes—
939C23#54714yes—
940C23#54814yes—
941C23#55014yes—
942C23#55114yes—
943C23#55114yes—
944C23#55114yes—
945C23#55214yes—
946C23#55214yes—
947C23#55314yes—
948C23#55314yes—
949C23#55514yes—
950C23C24×C411yescharacteristic
951C23C23×D411yescharacteristic
952C23C23×D411yescharacteristic
953C23C23×D411yescharacteristic
954C23C22×#4111yescharacteristic
955C23C22×#4111yescharacteristic
956C23C22×#4111yescharacteristic
957C23C22×#4111yescharacteristic
958C23C22×#4111yescharacteristic
959C23C22×#4111yescharacteristic
960C23C22×#4111yescharacteristic
961C23C2×H(5,𝔽2)11yescharacteristic
962C23C2×H(5,𝔽2)11yescharacteristic
963C23C2×H(5,𝔽2)11yescharacteristic
964C23C2×2−1+411yescharacteristic
965D4—464no—
966C2×C4—2128no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—232no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—232no—
987C2×C4—232no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—464no—
1013C2×C4—416no—
1014C2×C4—416no—
1015C2×C4—416no—
1016C2×C4—416no—
1017C2×C4—416no—
1018C2×C4—416no—
1019C2×C4—416no—
1020C2×C4—416no—
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—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—42no—
1065C2×C4—42no—
1066C2×C4—42no—
1067C2×C4—88no—
1068C2×C4—88no—
1069C2×C4C2×C4×D418yes—
1070C2×C4C2×C4×D418yes—
1071C2×C4C2×#12018yes—
1072C22—28no—
1073C22—28no—
1074C22—28no—
1075C22—28no—
1076C22—28no—
1077C22—28no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—44no—
1092C22—44no—
1093C22—44no—
1094C22—44no—
1095C22—44no—
1096C22—44no—
1097C22—44no—
1098C22—44no—
1099C22—44no—
1100C22—44no—
1101C22—44no—
1102C22—464no—
1103C22—464no—
1104C22#229018yes—
1105C22C4×#12018yes—
1106C22#232418yes—
1107C22#234218yes—
1108C22#235218yes—
1109C22#235918yes—
1110C22#236318yes—
1111C22#240418yes—
1112C22#240718yes—
1113C22#247018yes—
1114C22#247118yes—
1115C22#247618yes—
1116C22#247718yes—
1117C22#259818yes—
1118C22#260918yes—
1119C22C22×#11711yescharacteristic
1120C22C22×C4×D411yescharacteristic
1121C22C22×C4×D411yescharacteristic
1122C22C22×C4×D411yescharacteristic
1123C22C2×C4×#4111yescharacteristic
1124C22C2×#51811yescharacteristic
1125C22C2×#52011yescharacteristic
1126C22C22×#12011yescharacteristic
1127C22C2×#52511yescharacteristic
1128C22C2×#52511yescharacteristic
1129C22C2×#52511yescharacteristic
1130C22C2×#52511yescharacteristic
1131C22C2×#52511yescharacteristic
1132C22C2×#52911yescharacteristic
1133C22C2×#52911yescharacteristic
1134C22C2×#53511yescharacteristic
1135C22C2×#53711yescharacteristic
1136C22C2×#54011yescharacteristic
1137C22C2×#54211yescharacteristic
1138C22C2×#54611yescharacteristic
1139C22C2×#54611yescharacteristic
1140C22C2×#54611yescharacteristic
1141C22C2×#54611yescharacteristic
1142C22C2×#54611yescharacteristic
1143C22C2×#54711yescharacteristic
1144C22C2×#54811yescharacteristic
1145C22C2×#55011yescharacteristic
1146C22C2×#55111yescharacteristic
1147C22C2×#55111yescharacteristic
1148C22C2×#55111yescharacteristic
1149C22C2×#55211yescharacteristic
1150C22C2×#55211yescharacteristic
1151C22C2×#55311yescharacteristic
1152C22C2×#55311yescharacteristic
1153C22C2×#55511yescharacteristic
1154C4—28no—
1155C4—28no—
1156C4—28no—
1157C4—44no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C4—82no—
1166C4—82no—
1167C2—48no—
1168C2—48no—
1169C2#14064116yesdirect product factor
1170C2C2×#229011yescharacteristic
1171C2C2×C4×#12011yescharacteristic
1172C2C2×#232411yescharacteristic
1173C2C2×#234211yescharacteristic
1174C2C2×#235211yescharacteristic
1175C2C2×#235911yescharacteristic
1176C2C2×#236311yescharacteristic
1177C2C2×#240711yescharacteristic
1178C2C2×#247611yescharacteristic
1179C2C2×#247711yescharacteristic
1180C2C2×#247011yescharacteristic
1181C2C2×#247111yescharacteristic
1182C2C2×#240411yescharacteristic
1183C2C2×#259811yescharacteristic
1184C2C2×#260911yescharacteristic
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
1. C23×#117C2semidirect
4. C22×#385C2semidirect
5. C22×C4×C22⋊C4C2semidirect
6. #14064C2direct (N × H)
7. C2×#1442C2semidirect
8. C2×#1439C2semidirect
9. C2×#1439C2semidirect
11. C2×#1437C2semidirect
12. C2×#1437C2semidirect
13. C2×#1436C2semidirect
14. C2×#1436C2semidirect
15. C2×#1434C2semidirect
16. C2×C22⋊#95C2semidirect
23. C22×#117C22semidirect
41. C2×#386C4semidirect
45. C2×#385C22semidirect
47. C2×C4×C22⋊C4C22semidirect
64. #1442C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
68. #1437C22semidirect
69. #1437C22semidirect
70. #1436C22semidirect
71. #1436C22semidirect
72. #1434C22semidirect
73. C22⋊#95C22semidirect
97. C24×C4C2×C4semidirect
125. C22×C4⋊C4D4semidirect
157. C22×C22⋊C4C2×C4semidirect
177. C22×C42D4semidirect
182. #386C2×C4semidirect
199. C2×#95C2×C4semidirect
200. C2×#95C2×C4semidirect
370. C23×C4C22×C4semidirect
408. C2×C4⋊C4C2×D4semidirect
447. C2×C22⋊C4C22×C4semidirect
460. C2×C42C2×D4semidirect
475. #95C22×C4semidirect
476. #95C22×C4semidirect
569. C24#117semidirect
914. C23C2×#117semidirect
1169. C2#14064direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1172
C22×#3862
C22×#3852
C22×C4×C22⋊C42
#140642
C2×#14422
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×#14342
C2×C22⋊#952