Finite Group Databasebeta

← C2×#14187 #514672

Subgroups — C2×#14187 #514672

Order 512.

10006 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D4C211yesmaximal, characteristic, complemented
2C22×#392C211yesmaximal, characteristic
3C22×#390C211yesmaximal, characteristic, complemented
4C22×#388C211yesmaximal, characteristic, complemented
5C22×#386C211yesmaximal, characteristic, complemented
6C22×#386C211yesmaximal, characteristic, complemented
7C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
8#14187C2116yesmaximal, direct product factor
9C2×#1439C211yesmaximal, characteristic, complemented
10C2×#1438C211yesmaximal, characteristic, complemented
11C2×#1438C211yesmaximal, characteristic, complemented
12C2×#1437C211yesmaximal, characteristic, complemented
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C24×D4C2211yescharacteristic
19C24×D4C2211yescharacteristic
20C25×C4C2211yescharacteristic
21C25×C4C2211yescharacteristic
22C22×C4×D4—28no—
23C22×C4×D4—28no—
24C22×C4×D4—28no—
25C22×C4×D4C2218yescomplemented
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊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×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C22⋊C4C2211yescharacteristic
40C23×C22⋊C4C2211yescharacteristic
41C23×C42C2211yescharacteristic
42C23×C42C2211yescharacteristic
43C23×C42C2211yescharacteristic
44C2×#392C4116yescomplemented
45C2×#392C2218yes—
46C2×#390—28no—
47C2×#390C2218yescomplemented
48C2×#388—28no—
49C2×#388C2218yescomplemented
50C2×#386—28no—
51C2×#386—28no—
52C2×#386C2218yescomplemented
53C2×#386C2218yescomplemented
54C2×C4×C22⋊C4—28no—
55C2×C4×C22⋊C4C2218yescomplemented
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2211yescharacteristic
66C22×#95C2211yescharacteristic
67C22×#95C2211yescharacteristic
68#1439C2218yescomplemented
69#1438C2218yescomplemented
70#1438C2218yescomplemented
71#1437C2218yescomplemented
72#1437C2218yescomplemented
73#1436C2218yescomplemented
74#1436C2218yescomplemented
75C22⋊#95C2218yescomplemented
76C26C2311yescharacteristic
77C26C2311yescharacteristic
78C26C2311yescharacteristic
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—24no—
85C23×D4—24no—
86C23×D4—24no—
87C23×D4—24no—
88C23×D4—24no—
89C23×D4—24no—
90C23×D4—24no—
91C23×D4—42no—
92C23×D4—42no—
93C23×D4—42no—
94C23×D4—42no—
95C23×D4—42no—
96C23×D4—42no—
97C23×D4C2×C418yes—
98C23×D4C2×C418yescomplemented
99C23×D4C2×C418yescomplemented
100C23×D4C2314yes—
101C23×D4C2314yes—
102C23×D4C2314yes—
103C24×C4—24no—
104C24×C4—24no—
105C24×C4—24no—
106C24×C4—24no—
107C24×C4—24no—
108C24×C4—24no—
109C24×C4—24no—
110C24×C4—24no—
111C24×C4—24no—
112C24×C4—42no—
113C24×C4—42no—
114C24×C4—42no—
115C24×C4—42no—
116C24×C4D418yescomplemented
117C24×C4C2311yescharacteristic
118C24×C4C2311yescharacteristic
119C24×C4C2311yescharacteristic
120C24×C4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C24×C4C2311yescharacteristic
123C24×C4C2311yescharacteristic
124C24×C4C2311yescharacteristic
125C24×C4C2314yes—
126C24×C4C2314yes—
127C24×C4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2311yescharacteristic
131C2×C4×D4—2128no—
132C2×C4×D4—232no—
133C2×C4×D4—232no—
134C2×C4×D4—232no—
135C22×C4⋊C4—24no—
136C22×C4⋊C4—24no—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—24no—
139C22×C4⋊C4—42no—
140C22×C4⋊C4D418yescomplemented
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2314yes—
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—24no—
164C22×C22⋊C4—24no—
165C22×C22⋊C4—24no—
166C22×C22⋊C4—24no—
167C22×C22⋊C4—24no—
168C22×C22⋊C4—24no—
169C22×C22⋊C4—24no—
170C22×C22⋊C4—42no—
171C22×C22⋊C4—42no—
172C22×C22⋊C4—42no—
173C22×C22⋊C4—42no—
174C22×C22⋊C4—42no—
175C22×C22⋊C4—42no—
176C22×C22⋊C4—42no—
177C22×C22⋊C4—42no—
178C22×C22⋊C4C2×C418yescomplemented
179C22×C22⋊C4C2×C418yescomplemented
180C22×C22⋊C4C2×C418yescomplemented
181C22×C22⋊C4D418yescomplemented
182C22×C22⋊C4C2314yes—
183C22×C22⋊C4C2314yes—
184C22×C22⋊C4C2314yes—
185C22×C22⋊C4C2314yes—
186C22×C22⋊C4C2314yes—
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C2314yes—
189C22×C22⋊C4C2314yes—
190C22×C22⋊C4C2314yes—
191C22×C22⋊C4C2314yes—
192C22×C22⋊C4C2314yes—
193C22×C22⋊C4C2314yes—
194C22×C22⋊C4C2314yes—
195C22×C42—24no—
196C22×C42—24no—
197C22×C42—24no—
198C22×C42—24no—
199C22×C42—24no—
200C22×C42—24no—
201C22×C42—24no—
202C22×C42—42no—
203C22×C42—42no—
204C22×C42C2314yes—
205C22×C42C2314yes—
206C22×C42C2314yes—
207#392C2×C4164yescomplemented
208#390—232no—
209#388—232no—
210#386—232no—
211#386—232no—
212C4×C22⋊C4—232no—
213C2×#95—24no—
214C2×#95—24no—
215C2×#95—24no—
216C2×#95—24no—
217C2×#95—24no—
218C2×#95—24no—
219C2×#95—24no—
220C2×#95—42no—
221C2×#95—42no—
222C2×#95—42no—
223C2×#95C2×C418yescomplemented
224C2×#95D418yescomplemented
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C25—22no—
238C25—22no—
239C25—22no—
240C25—22no—
241C25—22no—
242C25—22no—
243C25—22no—
244C25—22no—
245C25—22no—
246C25—22no—
247C25—22no—
248C25—22no—
249C25—22no—
250C25—22no—
251C25—22no—
252C25—22no—
253C25—22no—
254C25—22no—
255C25—22no—
256C25—22no—
257C25—22no—
258C25—22no—
259C25—22no—
260C25—22no—
261C25—22no—
262C25—22no—
263C25—22no—
264C25—22no—
265C25—22no—
266C25—22no—
267C25—22no—
268C25—22no—
269C25—22no—
270C25—22no—
271C25—22no—
272C25—22no—
273C25—22no—
274C25—22no—
275C25C22×C414yes—
276C25C22×C414yes—
277C25C22×C414yes—
278C25C2×D414yes—
279C25C2×D414yes—
280C25#4114yes—
281C25#4114yes—
282C25C2412yes—
283C25C2412yes—
284C25C2412yes—
285C25C2411yescharacteristic
286C22×D4—232no—
287C22×D4—232no—
288C22×D4—232no—
289C22×D4—232no—
290C22×D4—232no—
291C22×D4—232no—
292C22×D4—28no—
293C22×D4—28no—
294C22×D4—28no—
295C22×D4—28no—
296C22×D4—232no—
297C22×D4—232no—
298C22×D4—28no—
299C22×D4—28no—
300C22×D4—28no—
301C22×D4—28no—
302C22×D4—232no—
303C22×D4—232no—
304C22×D4—28no—
305C22×D4—28no—
306C22×D4—28no—
307C22×D4—28no—
308C22×D4—416no—
309C22×D4—416no—
310C22×D4—416no—
311C22×D4—44no—
312C22×D4—44no—
313C22×D4—44no—
314C22×D4—44no—
315C22×D4—44no—
316C22×D4—44no—
317C22×D4—416no—
318C22×D4—416no—
319C22×D4—416no—
320C22×D4—416no—
321C22×D4—416no—
322C22×D4—416no—
323C22×D4—416no—
324C22×D4—416no—
325C22×D4C22×C4116yes—
326C22×D4C22×C4116yescomplemented
327C22×D4C22×C4116yescomplemented
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—232no—
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—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—232no—
383C23×C4—232no—
384C23×C4—28no—
385C23×C4—28no—
386C23×C4—28no—
387C23×C4—28no—
388C23×C4—28no—
389C23×C4—28no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—28no—
405C23×C4—28no—
406C23×C4—416no—
407C23×C4—44no—
408C23×C4—44no—
409C23×C4—44no—
410C23×C4—44no—
411C23×C4—416no—
412C23×C4—416no—
413C23×C4—416no—
414C23×C4—416no—
415C23×C4—416no—
416C23×C4—416no—
417C23×C4—416no—
418C23×C4—416no—
419C23×C4—416no—
420C23×C4—416no—
421C23×C4C22×C414yes—
422C23×C4C22×C414yes—
423C23×C4C22×C414yes—
424C23×C4C22×C414yes—
425C23×C4C2×D414yes—
426C23×C4C2×D414yes—
427C23×C4C2×D414yes—
428C23×C4C2×D414yes—
429C23×C4C2×D414yes—
430C23×C4C2×D414yes—
431C23×C4C2×D414yes—
432C23×C4C2×D414yes—
433C23×C4C2×D414yes—
434C23×C4C2×D414yes—
435C23×C4C2×D4116yescomplemented
436C23×C4#4114yes—
437C23×C4#4114yes—
438C23×C4#4114yes—
439C23×C4#4114yes—
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2412yes—
451C23×C4C2412yes—
452C4×D4—2256no—
453C2×C4⋊C4—232no—
454C2×C4⋊C4—28no—
455C2×C4⋊C4—28no—
456C2×C4⋊C4—28no—
457C2×C4⋊C4—28no—
458C2×C4⋊C4—44no—
459C2×C4⋊C4—416no—
460C2×C4⋊C4C2×D4116yescomplemented
461C2×C22⋊C4—232no—
462C2×C22⋊C4—232no—
463C2×C22⋊C4—28no—
464C2×C22⋊C4—28no—
465C2×C22⋊C4—232no—
466C2×C22⋊C4—232no—
467C2×C22⋊C4—232no—
468C2×C22⋊C4—28no—
469C2×C22⋊C4—28no—
470C2×C22⋊C4—28no—
471C2×C22⋊C4—28no—
472C2×C22⋊C4—28no—
473C2×C22⋊C4—28no—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—28no—
476C2×C22⋊C4—28no—
477C2×C22⋊C4—28no—
478C2×C22⋊C4—28no—
479C2×C22⋊C4—28no—
480C2×C22⋊C4—28no—
481C2×C22⋊C4—28no—
482C2×C22⋊C4—28no—
483C2×C22⋊C4—28no—
484C2×C22⋊C4—28no—
485C2×C22⋊C4—28no—
486C2×C22⋊C4—28no—
487C2×C22⋊C4—28no—
488C2×C22⋊C4—28no—
489C2×C22⋊C4—28no—
490C2×C22⋊C4—28no—
491C2×C22⋊C4—28no—
492C2×C22⋊C4—28no—
493C2×C22⋊C4—416no—
494C2×C22⋊C4—44no—
495C2×C22⋊C4—44no—
496C2×C22⋊C4—44no—
497C2×C22⋊C4—44no—
498C2×C22⋊C4—44no—
499C2×C22⋊C4—44no—
500C2×C22⋊C4—44no—
501C2×C22⋊C4—44no—
502C2×C22⋊C4—416no—
503C2×C22⋊C4—416no—
504C2×C22⋊C4—416no—
505C2×C22⋊C4—416no—
506C2×C22⋊C4—416no—
507C2×C22⋊C4—416no—
508C2×C22⋊C4—416no—
509C2×C22⋊C4C22×C4116yescomplemented
510C2×C22⋊C4C22×C4116yescomplemented
511C2×C22⋊C4C22×C4116yescomplemented
512C2×C22⋊C4C2×D4116yescomplemented
513C2×C42—232no—
514C2×C42—28no—
515C2×C42—28no—
516C2×C42—28no—
517C2×C42—28no—
518C2×C42—28no—
519C2×C42—28no—
520C2×C42—28no—
521C2×C42—44no—
522C2×C42—44no—
523C2×C42—416no—
524C2×C42—416no—
525#95—28no—
526#95—28no—
527#95—28no—
528#95—28no—
529#95—28no—
530#95—28no—
531#95—28no—
532#95—44no—
533#95—44no—
534#95—44no—
535#95C22×C4116yescomplemented
536#95C2×D4116yescomplemented
537C24—28no—
538C24—28no—
539C24—28no—
540C24—28no—
541C24—28no—
542C24—28no—
543C24—28no—
544C24—28no—
545C24—28no—
546C24—28no—
547C24—28no—
548C24—28no—
549C24—28no—
550C24—28no—
551C24—28no—
552C24—28no—
553C24—28no—
554C24—28no—
555C24—28no—
556C24—28no—
557C24—28no—
558C24—28no—
559C24—28no—
560C24—28no—
561C24—28no—
562C24—28no—
563C24—28no—
564C24—28no—
565C24—28no—
566C24—28no—
567C24—28no—
568C24—28no—
569C24—28no—
570C24—28no—
571C24—28no—
572C24—28no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—28no—
598C24—28no—
599C24—28no—
600C24—28no—
601C24—28no—
602C24—28no—
603C24—28no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—44no—
619C24—44no—
620C24—44no—
621C24—44no—
622C24—44no—
623C24—44no—
624C24—44no—
625C24—44no—
626C24—44no—
627C24—44no—
628C24—44no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24—44no—
634C24—44no—
635C24—44no—
636C24—44no—
637C24—44no—
638C24—44no—
639C24—44no—
640C24—44no—
641C24—44no—
642C24—44no—
643C24—44no—
644C24—44no—
645C24—44no—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—44no—
652C24—44no—
653C24—44no—
654C24—44no—
655C24—44no—
656C24—44no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24—44no—
665C24—44no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24C4×D4116yes—
679C24C4×D4116yes—
680C24C23×C414yes—
681C24C23×C414yes—
682C24C23×C414yes—
683C24C23×C412yes—
684C24C22×D414yes—
685C24C22×D414yes—
686C24C22×D412yes—
687C24C22×D412yes—
688C24C22×D412yes—
689C24C22×D412yes—
690C24C2×#4114yes—
691C24C2×#4114yes—
692C24C2×#4112yes—
693C24C2×#4112yes—
694C24C2×#4112yes—
695C24C2×#4112yes—
696C24C2×#4112yes—
697C24C2×#4112yes—
698C24H(5,𝔽2)12yes—
699C24H(5,𝔽2)12yes—
700C24H(5,𝔽2)12yes—
701C24H(5,𝔽2)12yes—
702C24C2511yescharacteristic
703C2×D4—232no—
704C2×D4—232no—
705C2×D4—232no—
706C2×D4—232no—
707C2×D4—2256no—
708C2×D4—232no—
709C2×D4—232no—
710C2×D4—232no—
711C2×D4—232no—
712C2×D4—232no—
713C2×D4—232no—
714C2×D4—416no—
715C2×D4—416no—
716C2×D4—416no—
717C2×D4—4128no—
718C2×D4—416no—
719C2×D4—416no—
720C2×D4—416no—
721C2×D4—416no—
722C2×D4—4128no—
723C2×D4—416no—
724C2×D4—416no—
725C2×D4—416no—
726C2×D4—416no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—232no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—232no—
823C22×C4—232no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—416no—
839C22×C4—4128no—
840C22×C4—416no—
841C22×C4—416no—
842C22×C4—416no—
843C22×C4—416no—
844C22×C4—416no—
845C22×C4—416no—
846C22×C4—416no—
847C22×C4—416no—
848C22×C4—4128no—
849C22×C4—416no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—416no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4C4×D4116yes—
890C22×C4C4×D4116yescomplemented
891C22×C4#120116yes—
892C22×C4#121116yes—
893C22×C4C23×C414yes—
894C22×C4C23×C414yes—
895C22×C4C23×C414yes—
896C22×C4C23×C414yes—
897C22×C4C22×D414yes—
898C22×C4C22×D414yes—
899C22×C4C22×D414yes—
900C22×C4C22×D414yes—
901C22×C4C22×D414yes—
902C22×C4C22×D414yes—
903C22×C4C22×D414yes—
904C22×C4C22×D414yes—
905C22×C4C22×D414yes—
906C22×C4C22×D414yes—
907C22×C4C2×#4114yes—
908C22×C4C2×#4114yes—
909C22×C4C2×#4114yes—
910C22×C4C2×#4114yes—
911C4⋊C4—232no—
912C4⋊C4—416no—
913C22⋊C4—232no—
914C22⋊C4—232no—
915C22⋊C4—232no—
916C22⋊C4—232no—
917C22⋊C4—232no—
918C22⋊C4—416no—
919C22⋊C4—416no—
920C22⋊C4—416no—
921C22⋊C4—416no—
922C22⋊C4—416no—
923C22⋊C4—416no—
924C22⋊C4—416no—
925C22⋊C4—416no—
926C42—232no—
927C42—416no—
928C42—416no—
929C23—232no—
930C23—232no—
931C23—232no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—232no—
969C23—232no—
970C23—232no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—416no—
979C23—416no—
980C23—416no—
981C23—416no—
982C23—416no—
983C23—416no—
984C23—416no—
985C23—416no—
986C23—416no—
987C23—42no—
988C23—416no—
989C23—416no—
990C23—42no—
991C23—416no—
992C23—416no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—416no—
1000C23—416no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—416no—
1026C23—416no—
1027C23—416no—
1028C23—416no—
1029C23—416no—
1030C23—416no—
1031C23—416no—
1032C23—416no—
1033C23—416no—
1034C23—416no—
1035C23—416no—
1036C23—416no—
1037C23—416no—
1038C23—416no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—416no—
1068C23—416no—
1069C23—88no—
1070C23—88no—
1071C23—88no—
1072C23—88no—
1073C23—88no—
1074C23—88no—
1075C23—88no—
1076C23—88no—
1077C23C2×C4×D418yes—
1078C23C2×C4×D418yes—
1079C23C2×C4×D414yes—
1080C23C2×C4×D414yes—
1081C23C2×C4×D414yes—
1082C23C2×C4×D414yes—
1083C23C4×#4114yes—
1084C23#51814yes—
1085C23#51814yes—
1086C23C2×#12014yes—
1087C23C2×#12114yes—
1088C23#52514yes—
1089C23#52514yes—
1090C23#52514yes—
1091C23#52514yes—
1092C23#52914yes—
1093C23#53214yes—
1094C23#53414yes—
1095C23#53514yes—
1096C23#53814yes—
1097C23#53814yes—
1098C23D4214yes—
1099C23D4214yes—
1100C23#54614yes—
1101C23#54614yes—
1102C23#54614yes—
1103C23#54614yes—
1104C23#54614yes—
1105C23#55014yes—
1106C23#55014yes—
1107C23#55014yes—
1108C23#55114yes—
1109C23#55314yes—
1110C23#55314yes—
1111C23#55314yes—
1112C23#55514yes—
1113C23#55914yes—
1114C23C24×C411yescharacteristic
1115C23C23×D411yescharacteristic
1116C23C23×D411yescharacteristic
1117C23C23×D411yescharacteristic
1118C23C23×D411yescharacteristic
1119C23C22×#4111yescharacteristic
1120C23C22×#4111yescharacteristic
1121C23C22×#4111yescharacteristic
1122C23C22×#4111yescharacteristic
1123C23C22×#4111yescharacteristic
1124C23C22×#4111yescharacteristic
1125C23C2×H(5,𝔽2)11yescharacteristic
1126C23C2×H(5,𝔽2)11yescharacteristic
1127C23C2×H(5,𝔽2)11yescharacteristic
1128C23C2×H(5,𝔽2)11yescharacteristic
1129D4—2128no—
1130D4—464no—
1131D4—464no—
1132C2×C4—232no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—232no—
1141C2×C4—232no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—232no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—464no—
1179C2×C4—464no—
1180C2×C4—416no—
1181C2×C4—416no—
1182C2×C4—42no—
1183C2×C4—416no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—416no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—416no—
1209C2×C4—416no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—88no—
1225C2×C4—88no—
1226C2×C4C2×C4×D418yes—
1227C2×C4C2×C4×D418yescomplemented
1228C2×C4C2×#12018yes—
1229C2×C4C2×#12118yes—
1230C22—28no—
1231C22—28no—
1232C22—28no—
1233C22—28no—
1234C22—28no—
1235C22—28no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—464no—
1256C22—464no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22—82no—
1275C22—832no—
1276C22—82no—
1277C22—82no—
1278C22C4×#12018yes—
1279C22C4×#12118yes—
1280C22#232118yes—
1281C22#235818yes—
1282C22#236318yes—
1283C22#236418yes—
1284C22#236618yes—
1285C22#241018yes—
1286C22#241418yes—
1287C22#243118yes—
1288C22#245618yes—
1289C22#245618yes—
1290C22#245918yes—
1291C22#246718yes—
1292C22#260218yes—
1293C22C22×C4×D411yescharacteristic
1294C22C22×C4×D411yescharacteristic
1295C22C22×C4×D411yescharacteristic
1296C22C22×C4×D411yescharacteristic
1297C22C2×C4×#4111yescharacteristic
1298C22C2×#51811yescharacteristic
1299C22C2×#51811yescharacteristic
1300C22C22×#12011yescharacteristic
1301C22C22×#12111yescharacteristic
1302C22C2×#52511yescharacteristic
1303C22C2×#52511yescharacteristic
1304C22C2×#52511yescharacteristic
1305C22C2×#52511yescharacteristic
1306C22C2×#52911yescharacteristic
1307C22C2×#53211yescharacteristic
1308C22C2×#53411yescharacteristic
1309C22C2×#53511yescharacteristic
1310C22C2×#53811yescharacteristic
1311C22C2×#53811yescharacteristic
1312C22C2×D4211yescharacteristic
1313C22C2×D4211yescharacteristic
1314C22C2×#54611yescharacteristic
1315C22C2×#54611yescharacteristic
1316C22C2×#54611yescharacteristic
1317C22C2×#54611yescharacteristic
1318C22C2×#54611yescharacteristic
1319C22C2×#55011yescharacteristic
1320C22C2×#55011yescharacteristic
1321C22C2×#55011yescharacteristic
1322C22C2×#55111yescharacteristic
1323C22C2×#55311yescharacteristic
1324C22C2×#55311yescharacteristic
1325C22C2×#55311yescharacteristic
1326C22C2×#55511yescharacteristic
1327C22C2×#55911yescharacteristic
1328C4—28no—
1329C4—28no—
1330C4—28no—
1331C4—28no—
1332C4—44no—
1333C4—44no—
1334C4—44no—
1335C4—44no—
1336C4—44no—
1337C4—44no—
1338C4—82no—
1339C4—82no—
1340C2—48no—
1341C2—48no—
1342C2—84no—
1343C2#14187116yesdirect product factor
1344C2C2×C4×#12011yescharacteristic
1345C2C2×C4×#12111yescharacteristic
1346C2C2×#232111yescharacteristic
1347C2C2×#235811yescharacteristic
1348C2C2×#236311yescharacteristic
1349C2C2×#236411yescharacteristic
1350C2C2×#236611yescharacteristic
1351C2C2×#241011yescharacteristic
1352C2C2×#245611yescharacteristic
1353C2C2×#245611yescharacteristic
1354C2C2×#245911yescharacteristic
1355C2C2×#246711yescharacteristic
1356C2C2×#241411yescharacteristic
1357C2C2×#243111yescharacteristic
1358C2C2×#260211yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC22×#392C2
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×C4×D4C2semidirect
3. C22×#390C2semidirect
4. C22×#388C2semidirect
5. C22×#386C2semidirect
6. C22×#386C2semidirect
7. C22×C4×C22⋊C4C2semidirect
8. #14187C2direct (N × H)
9. C2×#1439C2semidirect
10. C2×#1438C2semidirect
11. C2×#1438C2semidirect
12. C2×#1437C2semidirect
13. C2×#1437C2semidirect
14. C2×#1436C2semidirect
15. C2×#1436C2semidirect
16. C2×C22⋊#95C2semidirect
25. C22×C4×D4C22semidirect
44. C2×#392C4semidirect
47. C2×#390C22semidirect
49. C2×#388C22semidirect
52. C2×#386C22semidirect
53. C2×#386C22semidirect
55. C2×C4×C22⋊C4C22semidirect
68. #1439C22semidirect
69. #1438C22semidirect
70. #1438C22semidirect
71. #1437C22semidirect
72. #1437C22semidirect
73. #1436C22semidirect
74. #1436C22semidirect
75. C22⋊#95C22semidirect
98. C23×D4C2×C4semidirect
99. C23×D4C2×C4semidirect
116. C24×C4D4semidirect
140. C22×C4⋊C4D4semidirect
178. C22×C22⋊C4C2×C4semidirect
179. C22×C22⋊C4C2×C4semidirect
180. C22×C22⋊C4C2×C4semidirect
181. C22×C22⋊C4D4semidirect
207. #392C2×C4semidirect
223. C2×#95C2×C4semidirect
224. C2×#95D4semidirect
326. C22×D4C22×C4semidirect
327. C22×D4C22×C4semidirect
435. C23×C4C2×D4semidirect
460. C2×C4⋊C4C2×D4semidirect
509. C2×C22⋊C4C22×C4semidirect
510. C2×C22⋊C4C22×C4semidirect
511. C2×C22⋊C4C22×C4semidirect
512. C2×C22⋊C4C2×D4semidirect
535. #95C22×C4semidirect
536. #95C2×D4semidirect
890. C22×C4C4×D4semidirect
1227. C2×C4C2×C4×D4semidirect
1343. C2#14187direct (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×#3922
C22×#3902
C22×#3882
C22×#3862
C22×C4×C22⋊C42
#141872
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C22⋊#952