Finite Group Databasebeta

← C2×#13988 #514271

Subgroups — C2×#13988 #514271

Order 512.

7474 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#388C211yesmaximal, characteristic, complemented
2C22×#386C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5C22×#380C211yesmaximal, characteristic, complemented
6C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
8#13988C2116yesmaximal, direct product factor
9C2×#1442C211yesmaximal, characteristic, complemented
10C2×#1440C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1438C211yesmaximal, characteristic
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×#1434C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊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×#388—28no—
37C2×#388C2218yescomplemented
38C2×#386—28no—
39C2×#386C4116yescomplemented
40C2×#386C2218yes—
41C2×#386C2218yes—
42C2×#385—28no—
43C2×#385C2218yescomplemented
44C2×#380—28no—
45C2×#380C2218yescomplemented
46C2×C4×C22⋊C4—28no—
47C2×C4×C22⋊C4—28no—
48C2×C4×C22⋊C4C2218yescomplemented
49C2×C4×C22⋊C4C2218yescomplemented
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#1442C2218yescomplemented
67#1440C2218yescomplemented
68#1439C2218yescomplemented
69#1438C2218yes—
70#1437C2218yescomplemented
71#1436C2218yescomplemented
72#1436C2218yescomplemented
73#1434C2218yescomplemented
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—42no—
94C24×C4—42no—
95C24×C4—42no—
96C24×C4—42no—
97C24×C4C2×C418yescomplemented
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2314yes—
109C24×C4C2314yes—
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
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—42no—
148C22×C22⋊C4—42no—
149C22×C22⋊C4—42no—
150C22×C22⋊C4—42no—
151C22×C22⋊C4C2×C418yes—
152C22×C22⋊C4C2×C418yes—
153C22×C22⋊C4C2×C418yescomplemented
154C22×C22⋊C4D418yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C42—24no—
166C22×C42—24no—
167C22×C42—24no—
168C22×C42—24no—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42—42no—
172C22×C42—42no—
173C22×C42—42no—
174C22×C42C2314yes—
175C22×C42C2314yes—
176C22×C42C2314yes—
177#388—232no—
178#386—232no—
179#386C2×C4164yescomplemented
180#385—232no—
181#380—232no—
182C4×C22⋊C4—232no—
183C4×C22⋊C4—232no—
184C2×#95—24no—
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—42no—
194C2×#95—42no—
195C2×#95—42no—
196C2×#95C2×C418yescomplemented
197C2×#95C2×C418yescomplemented
198C2×#95D418yescomplemented
199C2×#95D418yescomplemented
200C2×#95C2314yes—
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—
216C25—22no—
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—
240C25C22×C414yes—
241C25C22×C414yes—
242C25C2×D414yes—
243C25#4114yes—
244C25#4114yes—
245C25#4114yes—
246C25C2412yes—
247C25C2412yes—
248C25C2411yescharacteristic
249C22×D4—232no—
250C22×D4—232no—
251C22×D4—28no—
252C22×D4—28no—
253C22×D4—28no—
254C22×D4—28no—
255C22×D4—416no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—416no—
259C22×D4—416no—
260C22×D4—416no—
261C22×D4—416no—
262C22×D4C22×C4116yes—
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—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—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—28no—
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×C4—232no—
326C23×C4—232no—
327C23×C4—28no—
328C23×C4—28no—
329C23×C4—28no—
330C23×C4—28no—
331C23×C4—28no—
332C23×C4—28no—
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—28no—
348C23×C4—28no—
349C23×C4—416no—
350C23×C4—44no—
351C23×C4—44no—
352C23×C4—44no—
353C23×C4—44no—
354C23×C4—416no—
355C23×C4—416no—
356C23×C4—416no—
357C23×C4—416no—
358C23×C4—416no—
359C23×C4—416no—
360C23×C4—416no—
361C23×C4—416no—
362C23×C4—416no—
363C23×C4—416no—
364C23×C4C22×C414yes—
365C23×C4C22×C414yes—
366C23×C4C22×C414yes—
367C23×C4C22×C414yes—
368C23×C4C22×C414yes—
369C23×C4C22×C4116yescomplemented
370C23×C4C2×D414yes—
371C23×C4C2×D414yes—
372C23×C4C2×D414yes—
373C23×C4C2×D414yes—
374C23×C4C2×D414yes—
375C23×C4C2×D414yes—
376C23×C4C2×D414yes—
377C23×C4C2×D414yes—
378C23×C4#4114yes—
379C23×C4#4114yes—
380C23×C4#4114yes—
381C23×C4#4114yes—
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2412yes—
395C2×C4⋊C4—28no—
396C2×C4⋊C4—28no—
397C2×C4⋊C4—28no—
398C2×C4⋊C4—28no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—28no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—416no—
405C2×C4⋊C4—416no—
406C2×C4⋊C4—416no—
407C2×C22⋊C4—232no—
408C2×C22⋊C4—232no—
409C2×C22⋊C4—232no—
410C2×C22⋊C4—28no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—28no—
414C2×C22⋊C4—232no—
415C2×C22⋊C4—232no—
416C2×C22⋊C4—232no—
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—28no—
435C2×C22⋊C4—44no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4—416no—
440C2×C22⋊C4—416no—
441C2×C22⋊C4—416no—
442C2×C22⋊C4—416no—
443C2×C22⋊C4C22×C4116yes—
444C2×C22⋊C4C22×C4116yes—
445C2×C22⋊C4C22×C4116yescomplemented
446C2×C22⋊C4C2×D4116yes—
447C2×C42—28no—
448C2×C42—28no—
449C2×C42—28no—
450C2×C42—28no—
451C2×C42—28no—
452C2×C42—28no—
453C2×C42—44no—
454C2×C42—44no—
455C2×C42—44no—
456C2×C42—416no—
457C2×C42—416no—
458C2×C42—416no—
459#95—28no—
460#95—28no—
461#95—28no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—28no—
467#95—28no—
468#95—44no—
469#95—44no—
470#95—44no—
471#95C22×C4116yescomplemented
472#95C22×C4116yescomplemented
473#95C2×D4116yescomplemented
474#95C2×D4116yescomplemented
475C24—28no—
476C24—28no—
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—22no—
512C24—22no—
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—44no—
536C24—44no—
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#117116yes—
568C24C4×D4116yes—
569C24C23×C414yes—
570C24C23×C414yes—
571C24C23×C412yes—
572C24C22×D414yes—
573C24C22×D412yes—
574C24C22×D412yes—
575C24C22×D412yes—
576C24C2×#4114yes—
577C24C2×#4114yes—
578C24C2×#4114yes—
579C24C2×#4112yes—
580C24C2×#4112yes—
581C24C2×#4112yes—
582C24C2×#4112yes—
583C24C2×#4112yes—
584C24C2×#4112yes—
585C24C2×#4112yes—
586C24H(5,𝔽2)12yes—
587C24H(5,𝔽2)12yes—
588C24H(5,𝔽2)12yes—
589C242−1+412yes—
590C24C2511yescharacteristic
591C2×D4—232no—
592C2×D4—232no—
593C2×D4—416no—
594C2×D4—4128no—
595C2×D4—416no—
596C2×D4—416no—
597C2×D4—416no—
598C2×D4—416no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—28no—
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—28no—
616C22×C4—28no—
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—232no—
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—28no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—28no—
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—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—232no—
703C22×C4—232no—
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—416no—
719C22×C4—4128no—
720C22×C4—416no—
721C22×C4—416no—
722C22×C4—416no—
723C22×C4—416no—
724C22×C4—416no—
725C22×C4—416no—
726C22×C4—416no—
727C22×C4—416no—
728C22×C4—4128no—
729C22×C4—416no—
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—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—416no—
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×C4C4×D4116yes—
778C22×C4C4×D4116yes—
779C22×C4#121116yes—
780C22×C4C23×C414yes—
781C22×C4C23×C414yes—
782C22×C4C23×C414yes—
783C22×C4C23×C414yes—
784C22×C4C23×C414yes—
785C22×C4C22×D414yes—
786C22×C4C22×D414yes—
787C22×C4C22×D414yes—
788C22×C4C22×D414yes—
789C22×C4C22×D414yes—
790C22×C4C22×D414yes—
791C22×C4C22×D414yes—
792C22×C4C22×D414yes—
793C22×C4C2×#4114yes—
794C22×C4C2×#4114yes—
795C22×C4C2×#4114yes—
796C22×C4C2×#4114yes—
797C4⋊C4—416no—
798C4⋊C4—416no—
799C4⋊C4—416no—
800C22⋊C4—232no—
801C22⋊C4—232no—
802C22⋊C4—232no—
803C22⋊C4—232no—
804C22⋊C4—232no—
805C22⋊C4—232no—
806C22⋊C4—416no—
807C22⋊C4—416no—
808C22⋊C4—416no—
809C22⋊C4—416no—
810C42—416no—
811C42—416no—
812C42—416no—
813C23—232no—
814C23—232no—
815C23—232no—
816C23—232no—
817C23—24no—
818C23—24no—
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—232no—
854C23—232no—
855C23—416no—
856C23—416no—
857C23—416no—
858C23—416no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—416no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—416no—
872C23—416no—
873C23—42no—
874C23—42no—
875C23—416no—
876C23—416no—
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—416no—
900C23—416no—
901C23—416no—
902C23—416no—
903C23—416no—
904C23—416no—
905C23—416no—
906C23—416no—
907C23—416no—
908C23—416no—
909C23—416no—
910C23—416no—
911C23C2×#11718yes—
912C23C2×#11714yes—
913C23C2×C4×D418yes—
914C23C2×C4×D414yes—
915C23C2×C4×D414yes—
916C23C2×C4×D414yes—
917C23C4×#4114yes—
918C23#51814yes—
919C23#52014yes—
920C23C2×#12114yes—
921C23#52514yes—
922C23#52514yes—
923C23#52514yes—
924C23#52914yes—
925C23#52914yes—
926C23#52914yes—
927C23#53214yes—
928C23#53814yes—
929C23#53914yes—
930C23#54014yes—
931C23#54214yes—
932C23D4214yes—
933C23D4214yes—
934C23#54614yes—
935C23#54614yes—
936C23#54614yes—
937C23#54614yes—
938C23#54614yes—
939C23#54714yes—
940C23#54814yes—
941C23#54814yes—
942C23#55114yes—
943C23#55114yes—
944C23#55114yes—
945C23#55214yes—
946C23#55314yes—
947C23#55314yes—
948C23C24×C411yescharacteristic
949C23C23×D411yescharacteristic
950C23C23×D411yescharacteristic
951C23C23×D411yescharacteristic
952C23C22×#4111yescharacteristic
953C23C22×#4111yescharacteristic
954C23C22×#4111yescharacteristic
955C23C22×#4111yescharacteristic
956C23C22×#4111yescharacteristic
957C23C22×#4111yescharacteristic
958C23C22×#4111yescharacteristic
959C23C2×H(5,𝔽2)11yescharacteristic
960C23C2×H(5,𝔽2)11yescharacteristic
961C23C2×H(5,𝔽2)11yescharacteristic
962C23C2×2−1+411yescharacteristic
963D4—464no—
964C2×C4—232no—
965C2×C4—232no—
966C2×C4—24no—
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—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—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—464no—
1010C2×C4—464no—
1011C2×C4—416no—
1012C2×C4—416no—
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—416no—
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—416no—
1048C2×C4—416no—
1049C2×C4—416no—
1050C2×C4—416no—
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—88no—
1066C2×C4—88no—
1067C2×C4C2×C4×D418yes—
1068C2×C4C2×C4×D418yes—
1069C2×C4C2×#12118yes—
1070C22—28no—
1071C22—28no—
1072C22—28no—
1073C22—28no—
1074C22—28no—
1075C22—28no—
1076C22—44no—
1077C22—44no—
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—464no—
1099C22—464no—
1100C22—44no—
1101C22—44no—
1102C22#229018yes—
1103C22C4×#12118yes—
1104C22#233518yes—
1105C22#234218yes—
1106C22#235218yes—
1107C22#235818yes—
1108C22#236118yes—
1109C22#242418yes—
1110C22#242718yes—
1111C22#245718yes—
1112C22#246318yes—
1113C22#246418yes—
1114C22#247718yes—
1115C22#255318yes—
1116C22#257818yes—
1117C22C22×#11711yescharacteristic
1118C22C22×C4×D411yescharacteristic
1119C22C22×C4×D411yescharacteristic
1120C22C22×C4×D411yescharacteristic
1121C22C2×C4×#4111yescharacteristic
1122C22C2×#51811yescharacteristic
1123C22C2×#52011yescharacteristic
1124C22C22×#12111yescharacteristic
1125C22C2×#52511yescharacteristic
1126C22C2×#52511yescharacteristic
1127C22C2×#52511yescharacteristic
1128C22C2×#52911yescharacteristic
1129C22C2×#52911yescharacteristic
1130C22C2×#52911yescharacteristic
1131C22C2×#53211yescharacteristic
1132C22C2×#53811yescharacteristic
1133C22C2×#53911yescharacteristic
1134C22C2×#54011yescharacteristic
1135C22C2×#54211yescharacteristic
1136C22C2×D4211yescharacteristic
1137C22C2×D4211yescharacteristic
1138C22C2×#54611yescharacteristic
1139C22C2×#54611yescharacteristic
1140C22C2×#54611yescharacteristic
1141C22C2×#54611yescharacteristic
1142C22C2×#54611yescharacteristic
1143C22C2×#54711yescharacteristic
1144C22C2×#54811yescharacteristic
1145C22C2×#54811yescharacteristic
1146C22C2×#55111yescharacteristic
1147C22C2×#55111yescharacteristic
1148C22C2×#55111yescharacteristic
1149C22C2×#55211yescharacteristic
1150C22C2×#55311yescharacteristic
1151C22C2×#55311yescharacteristic
1152C4—28no—
1153C4—28no—
1154C4—28no—
1155C4—44no—
1156C4—44no—
1157C4—44no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—82no—
1164C4—82no—
1165C2—48no—
1166C2—48no—
1167C2#13988116yesdirect product factor
1168C2C2×#229011yescharacteristic
1169C2C2×C4×#12111yescharacteristic
1170C2C2×#233511yescharacteristic
1171C2C2×#234211yescharacteristic
1172C2C2×#235211yescharacteristic
1173C2C2×#235811yescharacteristic
1174C2C2×#236111yescharacteristic
1175C2C2×#242411yescharacteristic
1176C2C2×#246311yescharacteristic
1177C2C2×#246411yescharacteristic
1178C2C2×#245711yescharacteristic
1179C2C2×#242711yescharacteristic
1180C2C2×#247711yescharacteristic
1181C2C2×#255311yescharacteristic
1182C2C2×#257811yescharacteristic
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. C22×#388C2semidirect
4. C22×#385C2semidirect
5. C22×#380C2semidirect
6. C22×C4×C22⋊C4C2semidirect
7. C22×C4×C22⋊C4C2semidirect
8. #13988C2direct (N × H)
9. C2×#1442C2semidirect
10. C2×#1440C2semidirect
11. C2×#1439C2semidirect
13. C2×#1437C2semidirect
14. C2×#1436C2semidirect
15. C2×#1436C2semidirect
16. C2×#1434C2semidirect
37. C2×#388C22semidirect
39. C2×#386C4semidirect
43. C2×#385C22semidirect
45. C2×#380C22semidirect
48. C2×C4×C22⋊C4C22semidirect
49. C2×C4×C22⋊C4C22semidirect
66. #1442C22semidirect
67. #1440C22semidirect
68. #1439C22semidirect
70. #1437C22semidirect
71. #1436C22semidirect
72. #1436C22semidirect
73. #1434C22semidirect
97. C24×C4C2×C4semidirect
153. C22×C22⋊C4C2×C4semidirect
179. #386C2×C4semidirect
196. C2×#95C2×C4semidirect
197. C2×#95C2×C4semidirect
198. C2×#95D4semidirect
199. C2×#95D4semidirect
369. C23×C4C22×C4semidirect
445. C2×C22⋊C4C22×C4semidirect
471. #95C22×C4semidirect
472. #95C22×C4semidirect
473. #95C2×D4semidirect
474. #95C2×D4semidirect
1167. C2#13988direct (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×#3862
C22×#3852
C22×#3802
C22×C4×C22⋊C42
#139882
C2×#14422
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×#14342