Finite Group Databasebeta

← C2×#14731 #607662

Subgroups — C2×#14731 #607662

Order 512.

8046 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D4C211yesmaximal, characteristic
2C22×#397C211yesmaximal, characteristic, complemented
3C22×#394C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5C22×#385C211yesmaximal, characteristic, complemented
6C22×#381C211yesmaximal, characteristic, complemented
7#14731C2116yesmaximal, direct product factor
8C2×#1444C211yesmaximal, characteristic, complemented
9C2×#1441C211yesmaximal, characteristic, complemented
10C2×#1440C211yesmaximal, characteristic, complemented
11C2×#1440C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1438C211yesmaximal, characteristic
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×C4×D4—28no—
21C22×C4×D4—28no—
22C22×C4×D4—28no—
23C22×C4×D4C2218yes—
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊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×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C42C2211yescharacteristic
40C2×#397—28no—
41C2×#397C2218yescomplemented
42C2×#394—28no—
43C2×#394C2218yes—
44C2×#385—28no—
45C2×#385—28no—
46C2×#385C2218yescomplemented
47C2×#385C2218yescomplemented
48C2×#381—28no—
49C2×#381C2218yescomplemented
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
64C22×#95C2211yescharacteristic
65C22×#95C2211yescharacteristic
66#1444C2218yescomplemented
67#1441C2218yescomplemented
68#1440C2218yescomplemented
69#1440C2218yescomplemented
70#1439C2218yescomplemented
71#1438C2218yes—
72#1436C2218yescomplemented
73#1436C2218yescomplemented
74C22⋊#95C2218yescomplemented
75C26C2311yescharacteristic
76C26C2311yescharacteristic
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—24no—
83C23×D4D418yes—
84C23×D4C2314yes—
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—42no—
95C24×C4—42no—
96C24×C4—42no—
97C24×C4—42no—
98C24×C4D418yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2314yes—
111C24×C4C2314yes—
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C2×C4×D4—2128no—
115C2×C4×D4—232no—
116C2×C4×D4—232no—
117C2×C4×D4—232no—
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—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—42no—
131C22×C4⋊C4—42no—
132C22×C4⋊C4—42no—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2314yes—
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—24no—
150C22×C22⋊C4—24no—
151C22×C22⋊C4—24no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4—24no—
157C22×C22⋊C4—24no—
158C22×C22⋊C4—24no—
159C22×C22⋊C4—24no—
160C22×C22⋊C4—24no—
161C22×C22⋊C4—24no—
162C22×C22⋊C4—24no—
163C22×C22⋊C4—42no—
164C22×C22⋊C4—42no—
165C22×C22⋊C4—42no—
166C22×C22⋊C4—42no—
167C22×C22⋊C4D418yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2314yes—
172C22×C22⋊C4C2314yes—
173C22×C22⋊C4C2314yes—
174C22×C22⋊C4C2314yes—
175C22×C22⋊C4C2314yes—
176C22×C22⋊C4C2314yes—
177C22×C22⋊C4C2314yes—
178C22×C42—24no—
179C22×C42—24no—
180C22×C42—24no—
181C22×C42C2314yes—
182#397—232no—
183#394—232no—
184#385—232no—
185#385—232no—
186#381—232no—
187C2×#95—24no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95—24no—
191C2×#95—24no—
192C2×#95—24no—
193C2×#95—24no—
194C2×#95—24no—
195C2×#95—24no—
196C2×#95—24no—
197C2×#95—24no—
198C2×#95—24no—
199C2×#95—24no—
200C2×#95—24no—
201C2×#95—42no—
202C2×#95D418yescomplemented
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—
217C2×#95C2314yes—
218C2×#95C2314yes—
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—
241C25—22no—
242C25—22no—
243C25C2×D414yes—
244C25C2×D414yes—
245C25C2×D414yes—
246C25C2×D414yes—
247C25#4114yes—
248C25#4114yes—
249C25C2412yes—
250C25C2412yes—
251C25C2411yescharacteristic
252C22×D4—232no—
253C22×D4—232no—
254C22×D4—232no—
255C22×D4—232no—
256C22×D4—232no—
257C22×D4—232no—
258C22×D4—28no—
259C22×D4—28no—
260C22×D4—28no—
261C22×D4—28no—
262C22×D4—232no—
263C22×D4—28no—
264C22×D4—28no—
265C22×D4C2×D4116yes—
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—232no—
275C23×C4—232no—
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—28no—
289C23×C4—28no—
290C23×C4—28no—
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—232no—
322C23×C4—28no—
323C23×C4—28no—
324C23×C4—28no—
325C23×C4—28no—
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—22no—
340C23×C4—22no—
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—28no—
355C23×C4—28no—
356C23×C4—416no—
357C23×C4—44no—
358C23×C4—44no—
359C23×C4—44no—
360C23×C4—44no—
361C23×C4—416no—
362C23×C4—416no—
363C23×C4—416no—
364C23×C4—416no—
365C23×C4—416no—
366C23×C4—416no—
367C23×C4—416no—
368C23×C4—416no—
369C23×C4—416no—
370C23×C4—416no—
371C23×C4C2×D414yes—
372C23×C4C2×D414yes—
373C23×C4C2×D414yes—
374C23×C4C2×D414yes—
375C23×C4C2×D414yes—
376C23×C4C2×D4116yes—
377C23×C4C2×D414yes—
378C23×C4C2×D414yes—
379C23×C4C2×D414yes—
380C23×C4#4114yes—
381C23×C4#4114yes—
382C23×C4#4114yes—
383C23×C4#4114yes—
384C23×C4#4114yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C4×D4—2256no—
399C2×C4⋊C4—232no—
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—28no—
407C2×C4⋊C4—28no—
408C2×C4⋊C4—28no—
409C2×C4⋊C4—28no—
410C2×C4⋊C4—28no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—44no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4—416no—
416C2×C4⋊C4—416no—
417C2×C4⋊C4—416no—
418C2×C4⋊C4—416no—
419C2×C22⋊C4—232no—
420C2×C22⋊C4—232no—
421C2×C22⋊C4—232no—
422C2×C22⋊C4—232no—
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—28no—
435C2×C22⋊C4—28no—
436C2×C22⋊C4—28no—
437C2×C22⋊C4—28no—
438C2×C22⋊C4—28no—
439C2×C22⋊C4—28no—
440C2×C22⋊C4—28no—
441C2×C22⋊C4—28no—
442C2×C22⋊C4—28no—
443C2×C22⋊C4—28no—
444C2×C22⋊C4—28no—
445C2×C22⋊C4—28no—
446C2×C22⋊C4—28no—
447C2×C22⋊C4—28no—
448C2×C22⋊C4—44no—
449C2×C22⋊C4—44no—
450C2×C22⋊C4—44no—
451C2×C22⋊C4—44no—
452C2×C22⋊C4—416no—
453C2×C22⋊C4—416no—
454C2×C22⋊C4—416no—
455C2×C22⋊C4—416no—
456C2×C22⋊C4—416no—
457C2×C22⋊C4—416no—
458C2×C22⋊C4C2×D4116yes—
459C2×C42—232no—
460C2×C42—28no—
461C2×C42—28no—
462C2×C42—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—28no—
467#95—28no—
468#95—28no—
469#95—28no—
470#95—28no—
471#95—28no—
472#95—28no—
473#95—28no—
474#95—28no—
475#95—28no—
476#95—28no—
477#95—44no—
478#95C2×D4116yescomplemented
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—28no—
514C24—28no—
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—22no—
538C24—22no—
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—44no—
570C24—44no—
571C24#120116yes—
572C24#123116yes—
573C24C22×D414yes—
574C24C22×D414yes—
575C24C22×D414yes—
576C24C22×D414yes—
577C24C22×D412yes—
578C24C22×D412yes—
579C24C22×D412yes—
580C24C22×D412yes—
581C24C2×#4114yes—
582C24C2×#4114yes—
583C24C2×#4112yes—
584C24C2×#4112yes—
585C24C2×#4112yes—
586C24C2×#4112yes—
587C24C2×#4112yes—
588C24C2×#4112yes—
589C24C2×#4112yes—
590C24H(5,𝔽2)12yes—
591C24H(5,𝔽2)12yes—
592C242−1+412yes—
593C242−1+412yes—
594C24C2511yescharacteristic
595C2×D4—2256no—
596C2×D4—232no—
597C2×D4—232no—
598C2×D4—232no—
599C2×D4—232no—
600C2×D4—232no—
601C2×D4—232no—
602C2×D4—232no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—28no—
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—232no—
624C22×C4—28no—
625C22×C4—28no—
626C22×C4—28no—
627C22×C4—232no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—28no—
637C22×C4—28no—
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—28no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—28no—
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—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—232no—
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—416no—
718C22×C4—416no—
719C22×C4—416no—
720C22×C4—4128no—
721C22×C4—416no—
722C22×C4—416no—
723C22×C4—416no—
724C22×C4—416no—
725C22×C4—416no—
726C22×C4—416no—
727C22×C4—4128no—
728C22×C4—416no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
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—416no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
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×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4#121116yes—
787C22×C4#123116yes—
788C22×C4C22×D414yes—
789C22×C4C22×D414yes—
790C22×C4C22×D414yes—
791C22×C4C22×D414yes—
792C22×C4C22×D414yes—
793C22×C4C22×D414yes—
794C22×C4C22×D414yes—
795C22×C4C22×D414yes—
796C22×C4C2×#4114yes—
797C22×C4C2×#4114yes—
798C22×C4C2×#4114yes—
799C22×C4C2×#4114yes—
800C22×C4C2×#4114yes—
801C4⋊C4—232no—
802C4⋊C4—416no—
803C4⋊C4—416no—
804C4⋊C4—416no—
805C4⋊C4—416no—
806C22⋊C4—232no—
807C22⋊C4—232no—
808C22⋊C4—232no—
809C22⋊C4—232no—
810C22⋊C4—416no—
811C22⋊C4—416no—
812C22⋊C4—416no—
813C22⋊C4—416no—
814C22⋊C4—416no—
815C22⋊C4—416no—
816C42—232no—
817C23—232no—
818C23—232no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—232no—
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—232no—
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—24no—
857C23—24no—
858C23—24no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—416no—
863C23—416no—
864C23—416no—
865C23—416no—
866C23—42no—
867C23—416no—
868C23—42no—
869C23—42no—
870C23—416no—
871C23—416no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—416no—
878C23—42no—
879C23—416no—
880C23—416no—
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—416no—
896C23—42no—
897C23—42no—
898C23—416no—
899C23—416no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23—416no—
906C23—416no—
907C23—42no—
908C23—42no—
909C23—416no—
910C23—416no—
911C23—416no—
912C23—416no—
913C23—416no—
914C23—416no—
915C23C2×#12018yes—
916C23C2×#12014yes—
917C23C2×#12114yes—
918C23C2×#12318yes—
919C23C2×#12314yes—
920C23C2×#12314yes—
921C23#52514yes—
922C23#52514yes—
923C23#52514yes—
924C23#52514yes—
925C23#52514yes—
926C23#52514yes—
927C23#52914yes—
928C23#52914yes—
929C23#53214yes—
930C23#53414yes—
931C23#53614yes—
932C23#53914yes—
933C23#53914yes—
934C23#54214yes—
935C23#54214yes—
936C23D4214yes—
937C23D4214yes—
938C23#54614yes—
939C23#54614yes—
940C23#54714yes—
941C23#54714yes—
942C23#54714yes—
943C23#54714yes—
944C23#54714yes—
945C23#54814yes—
946C23#55114yes—
947C23#55214yes—
948C23#55314yes—
949C23#55314yes—
950C23#55614yes—
951C23#55914yes—
952C23C23×D411yescharacteristic
953C23C23×D411yescharacteristic
954C23C23×D411yescharacteristic
955C23C23×D411yescharacteristic
956C23C22×#4111yescharacteristic
957C23C22×#4111yescharacteristic
958C23C22×#4111yescharacteristic
959C23C22×#4111yescharacteristic
960C23C22×#4111yescharacteristic
961C23C22×#4111yescharacteristic
962C23C22×#4111yescharacteristic
963C23C2×H(5,𝔽2)11yescharacteristic
964C23C2×H(5,𝔽2)11yescharacteristic
965C23C2×2−1+411yescharacteristic
966C23C2×2−1+411yescharacteristic
967D4—2128no—
968C2×C4—232no—
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—24no—
987C2×C4—24no—
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—464no—
1004C2×C4—464no—
1005C2×C4—416no—
1006C2×C4—416no—
1007C2×C4—416no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—416no—
1011C2×C4—416no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—416no—
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—416no—
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—42no—
1068C2×C4—88no—
1069C2×C4—88no—
1070C2×C4—88no—
1071C2×C4—88no—
1072C2×C4C2×#12118yes—
1073C2×C4C2×#12318yes—
1074C22—28no—
1075C22—28no—
1076C22—28no—
1077C22—28no—
1078C22—28no—
1079C22—28no—
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—464no—
1100C22—464no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22—44no—
1105C22—44no—
1106C22#239218yes—
1107C22#240618yes—
1108C22#241018yes—
1109C22#241518yes—
1110C22#241918yes—
1111C22#242218yes—
1112C22#244318yes—
1113C22#244718yes—
1114C22#245518yes—
1115C22#246118yes—
1116C22#246618yes—
1117C22#246818yes—
1118C22#260018yes—
1119C22#263818yes—
1120C22#284918yes—
1121C22C22×#12011yescharacteristic
1122C22C22×#12111yescharacteristic
1123C22C22×#12311yescharacteristic
1124C22C22×#12311yescharacteristic
1125C22C2×#52511yescharacteristic
1126C22C2×#52511yescharacteristic
1127C22C2×#52511yescharacteristic
1128C22C2×#52511yescharacteristic
1129C22C2×#52511yescharacteristic
1130C22C2×#52511yescharacteristic
1131C22C2×#52911yescharacteristic
1132C22C2×#52911yescharacteristic
1133C22C2×#53211yescharacteristic
1134C22C2×#53411yescharacteristic
1135C22C2×#53611yescharacteristic
1136C22C2×#53911yescharacteristic
1137C22C2×#53911yescharacteristic
1138C22C2×#54211yescharacteristic
1139C22C2×#54211yescharacteristic
1140C22C2×D4211yescharacteristic
1141C22C2×D4211yescharacteristic
1142C22C2×#54611yescharacteristic
1143C22C2×#54611yescharacteristic
1144C22C2×#54711yescharacteristic
1145C22C2×#54711yescharacteristic
1146C22C2×#54711yescharacteristic
1147C22C2×#54711yescharacteristic
1148C22C2×#54711yescharacteristic
1149C22C2×#54811yescharacteristic
1150C22C2×#55111yescharacteristic
1151C22C2×#55211yescharacteristic
1152C22C2×#55311yescharacteristic
1153C22C2×#55311yescharacteristic
1154C22C2×#55611yescharacteristic
1155C22C2×#55911yescharacteristic
1156C4—28no—
1157C4—28no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C4—82no—
1166C4—82no—
1167C4—82no—
1168C4—82no—
1169C2—48no—
1170C2—48no—
1171C2#14731116yesdirect product factor
1172C2C2×#239211yescharacteristic
1173C2C2×#263811yescharacteristic
1174C2C2×#241011yescharacteristic
1175C2C2×#244311yescharacteristic
1176C2C2×#245511yescharacteristic
1177C2C2×#246611yescharacteristic
1178C2C2×#241911yescharacteristic
1179C2C2×#246111yescharacteristic
1180C2C2×#242211yescharacteristic
1181C2C2×#246811yescharacteristic
1182C2C2×#244711yescharacteristic
1183C2C2×#241511yescharacteristic
1184C2C2×#240611yescharacteristic
1185C2C2×#260011yescharacteristic
1186C2C2×#284911yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#397C2semidirect
4. C22×#385C2semidirect
5. C22×#385C2semidirect
6. C22×#381C2semidirect
7. #14731C2direct (N × H)
8. C2×#1444C2semidirect
9. C2×#1441C2semidirect
10. C2×#1440C2semidirect
11. C2×#1440C2semidirect
12. C2×#1439C2semidirect
14. C2×#1436C2semidirect
15. C2×#1436C2semidirect
16. C2×C22⋊#95C2semidirect
41. C2×#397C22semidirect
46. C2×#385C22semidirect
47. C2×#385C22semidirect
49. C2×#381C22semidirect
66. #1444C22semidirect
67. #1441C22semidirect
68. #1440C22semidirect
69. #1440C22semidirect
70. #1439C22semidirect
72. #1436C22semidirect
73. #1436C22semidirect
74. C22⋊#95C22semidirect
202. C2×#95D4semidirect
478. #95C2×D4semidirect
1171. C2#14731direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×D42
C22×#3972
C22×#3942
C22×#3852
C22×#3812
#147312
C2×#14442
C2×#14412
C2×#14402
C2×#14392
C2×#14382
C2×#14362
C2×C22⋊#952