Finite Group Databasebeta

← C2×#14540 #520997

Subgroups — C2×#14540 #520997

Order 512.

6222 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#394C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic, complemented
3C22×#388C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic
5C22×#385C211yesmaximal, characteristic, complemented
6#14540C2116yesmaximal, direct product factor
7C2×#1442C211yesmaximal, characteristic, complemented
8C2×#1442C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1438C211yesmaximal, characteristic
12C2×#1437C211yesmaximal, characteristic, complemented
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×C4⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C23×C4⋊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×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35C23×C42C2211yescharacteristic
36C2×#394C4116yescomplemented
37C2×#394C2218yes—
38C2×#388—28no—
39C2×#388—28no—
40C2×#388C2218yescomplemented
41C2×#388C2218yescomplemented
42C2×#386—28no—
43C2×#386C2218yes—
44C2×#385—28no—
45C2×#385C2218yescomplemented
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
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
62#1442C2218yescomplemented
63#1442C2218yescomplemented
64#1439C2218yescomplemented
65#1439C2218yescomplemented
66#1438C2218yes—
67#1437C2218yescomplemented
68#1437C2218yescomplemented
69#1436C2218yescomplemented
70C4⋊#95C2218yescomplemented
71C22⋊#95C2218yescomplemented
72C26C2311yescharacteristic
73C26C2311yescharacteristic
74C23×D4—24no—
75C23×D4—24no—
76C23×D4—42no—
77C23×D4—42no—
78C23×D4—42no—
79C23×D4—42no—
80C23×D4C2×C418yes—
81C23×D4C2314yes—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—42no—
86C24×C4—42no—
87C24×C4—42no—
88C24×C4—42no—
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2314yes—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—42no—
110C22×C4⋊C4—42no—
111C22×C4⋊C4—42no—
112C22×C4⋊C4—42no—
113C22×C4⋊C4—42no—
114C22×C4⋊C4C2×C418yescomplemented
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2314yes—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
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—42no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4—42no—
140C22×C22⋊C4—42no—
141C22×C22⋊C4—42no—
142C22×C22⋊C4—42no—
143C22×C22⋊C4—42no—
144C22×C22⋊C4—42no—
145C22×C22⋊C4—42no—
146C22×C22⋊C4—42no—
147C22×C22⋊C4C2×C418yes—
148C22×C22⋊C4C2×C418yes—
149C22×C22⋊C4C2×C418yescomplemented
150C22×C22⋊C4C2×C418yescomplemented
151C22×C22⋊C4D418yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
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×C42—24no—
164C22×C42—24no—
165C22×C42—24no—
166C22×C42—42no—
167C22×C42—42no—
168C22×C42—42no—
169C22×C42C2314yes—
170C22×C42C2314yes—
171#394C2×C4164yescomplemented
172#388—232no—
173#388—232no—
174#386—232no—
175#385—232no—
176C2×#95—24no—
177C2×#95—24no—
178C2×#95—24no—
179C2×#95—24no—
180C2×#95—24no—
181C2×#95—24no—
182C2×#95—24no—
183C2×#95—42no—
184C2×#95—42no—
185C2×#95—42no—
186C2×#95—42no—
187C2×#95—42no—
188C2×#95—42no—
189C2×#95—42no—
190C2×#95C2×C418yescomplemented
191C2×#95D418yescomplemented
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—22no—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—22no—
234C25C22×C414yes—
235C25C22×C414yes—
236C25C2×D414yes—
237C25#4114yes—
238C25C2412yes—
239C25C2412yes—
240C25C2411yescharacteristic
241C22×D4—232no—
242C22×D4—28no—
243C22×D4—28no—
244C22×D4—416no—
245C22×D4—416no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—416no—
251C22×D4—416no—
252C22×D4—416no—
253C22×D4—416no—
254C22×D4C22×C4116yes—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—28no—
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—28no—
335C23×C4—28no—
336C23×C4—44no—
337C23×C4—44no—
338C23×C4—44no—
339C23×C4—44no—
340C23×C4—416no—
341C23×C4—416no—
342C23×C4—416no—
343C23×C4—416no—
344C23×C4—416no—
345C23×C4—416no—
346C23×C4—416no—
347C23×C4C22×C414yes—
348C23×C4C22×C414yes—
349C23×C4C22×C414yes—
350C23×C4C22×C414yes—
351C23×C4C22×C414yes—
352C23×C4C2×D414yes—
353C23×C4C2×D414yes—
354C23×C4C2×D414yes—
355C23×C4C2×D414yes—
356C23×C4C2×D414yes—
357C23×C4#4114yes—
358C23×C4#4114yes—
359C23×C4#4114yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2412yes—
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—416no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—416no—
386C2×C4⋊C4—416no—
387C2×C4⋊C4—416no—
388C2×C4⋊C4C22×C4116yescomplemented
389C2×C22⋊C4—232no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—232no—
393C2×C22⋊C4—232no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—416no—
409C2×C22⋊C4—416no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—416no—
423C2×C22⋊C4—416no—
424C2×C22⋊C4—416no—
425C2×C22⋊C4—416no—
426C2×C22⋊C4—416no—
427C2×C22⋊C4—416no—
428C2×C22⋊C4C22×C4116yes—
429C2×C22⋊C4C22×C4116yes—
430C2×C22⋊C4C22×C4116yescomplemented
431C2×C22⋊C4C22×C4116yescomplemented
432C2×C22⋊C4C2×D4116yes—
433C2×C42—28no—
434C2×C42—28no—
435C2×C42—28no—
436C2×C42—44no—
437C2×C42—44no—
438C2×C42—44no—
439C2×C42—416no—
440C2×C42—416no—
441#95—28no—
442#95—28no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—44no—
449#95—44no—
450#95—44no—
451#95—44no—
452#95—44no—
453#95—44no—
454#95—44no—
455#95C22×C4116yescomplemented
456#95C2×D4116yescomplemented
457C24—28no—
458C24—28no—
459C24—28no—
460C24—28no—
461C24—28no—
462C24—28no—
463C24—28no—
464C24—28no—
465C24—28no—
466C24—28no—
467C24—28no—
468C24—28no—
469C24—28no—
470C24—28no—
471C24—28no—
472C24—28no—
473C24—28no—
474C24—28no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—28no—
488C24—28no—
489C24—28no—
490C24—28no—
491C24—28no—
492C24—28no—
493C24—28no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—44no—
509C24—44no—
510C24—44no—
511C24—44no—
512C24—44no—
513C24—44no—
514C24—44no—
515C24—44no—
516C24—44no—
517C24—44no—
518C24—44no—
519C24—44no—
520C24—44no—
521C24—44no—
522C24—44no—
523C24—44no—
524C24—44no—
525C24—44no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—44no—
530C24—44no—
531C24—44no—
532C24—44no—
533C24—44no—
534C24—44no—
535C24—44no—
536C24—44no—
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—
552C24C4×D4116yes—
553C24C23×C414yes—
554C24C23×C414yes—
555C24C23×C412yes—
556C24C22×D414yes—
557C24C22×D412yes—
558C24C22×D412yes—
559C24C2×#4114yes—
560C24C2×#4112yes—
561C24C2×#4112yes—
562C24C2×#4112yes—
563C24C2×#4112yes—
564C24H(5,𝔽2)12yes—
565C24H(5,𝔽2)12yes—
566C24H(5,𝔽2)12yes—
567C24H(5,𝔽2)12yes—
568C24H(5,𝔽2)12yes—
569C24H(5,𝔽2)12yes—
570C242−1+412yes—
571C242−1+412yes—
572C24C2511yescharacteristic
573C2×D4—232no—
574C2×D4—416no—
575C2×D4—416no—
576C2×D4—4128no—
577C2×D4—416no—
578C2×D4—416no—
579C2×D4—416no—
580C2×D4—416no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—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—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—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—416no—
696C22×C4—416no—
697C22×C4—416no—
698C22×C4—416no—
699C22×C4—416no—
700C22×C4—416no—
701C22×C4—4128no—
702C22×C4—416no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×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×C4C4×D4116yes—
758C22×C4C23×C414yes—
759C22×C4C23×C414yes—
760C22×C4C23×C414yes—
761C22×C4C23×C414yes—
762C22×C4C23×C414yes—
763C22×C4C22×D414yes—
764C22×C4C22×D414yes—
765C22×C4C22×D414yes—
766C22×C4C22×D414yes—
767C22×C4C22×D414yes—
768C22×C4C2×#4114yes—
769C22×C4C2×#4114yes—
770C22×C4C2×#4114yes—
771C4⋊C4—416no—
772C4⋊C4—416no—
773C4⋊C4—416no—
774C4⋊C4—416no—
775C22⋊C4—232no—
776C22⋊C4—232no—
777C22⋊C4—232no—
778C22⋊C4—416no—
779C22⋊C4—416no—
780C22⋊C4—416no—
781C22⋊C4—416no—
782C22⋊C4—416no—
783C22⋊C4—416no—
784C22⋊C4—416no—
785C22⋊C4—416no—
786C42—416no—
787C42—416no—
788C23—232no—
789C23—232no—
790C23—232no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—416no—
817C23—416no—
818C23—416no—
819C23—416no—
820C23—416no—
821C23—416no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—416no—
833C23—416no—
834C23—416no—
835C23—42no—
836C23—42no—
837C23—416no—
838C23—416no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—416no—
844C23—416no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—416no—
849C23—416no—
850C23—416no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—88no—
880C23—88no—
881C23—88no—
882C23—88no—
883C23—88no—
884C23—88no—
885C23—88no—
886C23—88no—
887C23C2×C4×D418yes—
888C23C2×C4×D414yes—
889C23C2×C4×D414yes—
890C23C4×#4114yes—
891C23#51814yes—
892C23#51814yes—
893C23#52014yes—
894C23#52014yes—
895C23#53414yes—
896C23#53514yes—
897C23#53514yes—
898C23#53714yes—
899C23#53814yes—
900C23#53814yes—
901C23#53814yes—
902C23#53914yes—
903C23#54014yes—
904C23#54014yes—
905C23#54214yes—
906C23#54214yes—
907C23D4214yes—
908C23#54614yes—
909C23#54614yes—
910C23#54614yes—
911C23#54714yes—
912C23#54714yes—
913C23#54814yes—
914C23#55114yes—
915C23#55214yes—
916C23#55314yes—
917C23#55314yes—
918C23#55314yes—
919C23H(3,𝔽4)14yes—
920C23#56214yes—
921C23#56214yes—
922C23#56314yes—
923C23C24×C411yescharacteristic
924C23C23×D411yescharacteristic
925C23C23×D411yescharacteristic
926C23C22×#4111yescharacteristic
927C23C22×#4111yescharacteristic
928C23C22×#4111yescharacteristic
929C23C22×#4111yescharacteristic
930C23C2×H(5,𝔽2)11yescharacteristic
931C23C2×H(5,𝔽2)11yescharacteristic
932C23C2×H(5,𝔽2)11yescharacteristic
933C23C2×H(5,𝔽2)11yescharacteristic
934C23C2×H(5,𝔽2)11yescharacteristic
935C23C2×H(5,𝔽2)11yescharacteristic
936C23C2×2−1+411yescharacteristic
937C23C2×2−1+411yescharacteristic
938D4—464no—
939C2×C4—232no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—464no—
977C2×C4—416no—
978C2×C4—416no—
979C2×C4—416no—
980C2×C4—416no—
981C2×C4—416no—
982C2×C4—416no—
983C2×C4—416no—
984C2×C4—416no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—416no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—416no—
1019C2×C4—42no—
1020C2×C4—42no—
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—88no—
1042C2×C4—88no—
1043C2×C4C2×C4×D418yes—
1044C22—28no—
1045C22—28no—
1046C22—28no—
1047C22—44no—
1048C22—44no—
1049C22—44no—
1050C22—44no—
1051C22—44no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—464no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—82no—
1068C22—82no—
1069C22—82no—
1070C22—82no—
1071C22—82no—
1072C22—82no—
1073C22—832no—
1074C22—82no—
1075C22—82no—
1076C22#232118yes—
1077C22#232418yes—
1078C22#233518yes—
1079C22#235918yes—
1080C22#236118yes—
1081C22#236418yes—
1082C22#237918yes—
1083C22#267018yes—
1084C22#267118yes—
1085C22#269618yes—
1086C22#270118yes—
1087C22#270218yes—
1088C22#271818yes—
1089C22#275318yes—
1090C22#277918yes—
1091C22C22×C4×D411yescharacteristic
1092C22C22×C4×D411yescharacteristic
1093C22C2×C4×#4111yescharacteristic
1094C22C2×#51811yescharacteristic
1095C22C2×#51811yescharacteristic
1096C22C2×#52011yescharacteristic
1097C22C2×#52011yescharacteristic
1098C22C2×#53411yescharacteristic
1099C22C2×#53511yescharacteristic
1100C22C2×#53511yescharacteristic
1101C22C2×#53711yescharacteristic
1102C22C2×#53811yescharacteristic
1103C22C2×#53811yescharacteristic
1104C22C2×#53811yescharacteristic
1105C22C2×#53911yescharacteristic
1106C22C2×#54011yescharacteristic
1107C22C2×#54011yescharacteristic
1108C22C2×#54211yescharacteristic
1109C22C2×#54211yescharacteristic
1110C22C2×D4211yescharacteristic
1111C22C2×#54611yescharacteristic
1112C22C2×#54611yescharacteristic
1113C22C2×#54611yescharacteristic
1114C22C2×#54711yescharacteristic
1115C22C2×#54711yescharacteristic
1116C22C2×#54811yescharacteristic
1117C22C2×#55111yescharacteristic
1118C22C2×#55211yescharacteristic
1119C22C2×#55311yescharacteristic
1120C22C2×#55311yescharacteristic
1121C22C2×#55311yescharacteristic
1122C22C2×H(3,𝔽4)11yescharacteristic
1123C22C2×#56211yescharacteristic
1124C22C2×#56211yescharacteristic
1125C22C2×#56311yescharacteristic
1126C4—28no—
1127C4—44no—
1128C4—44no—
1129C4—44no—
1130C4—44no—
1131C4—44no—
1132C4—44no—
1133C4—44no—
1134C4—44no—
1135C4—44no—
1136C4—44no—
1137C4—82no—
1138C4—82no—
1139C2—48no—
1140C2—84no—
1141C2#14540116yesdirect product factor
1142C2C2×#232111yescharacteristic
1143C2C2×#232411yescharacteristic
1144C2C2×#233511yescharacteristic
1145C2C2×#235911yescharacteristic
1146C2C2×#236111yescharacteristic
1147C2C2×#236411yescharacteristic
1148C2C2×#237911yescharacteristic
1149C2C2×#267011yescharacteristic
1150C2C2×#267111yescharacteristic
1151C2C2×#269611yescharacteristic
1152C2C2×#270111yescharacteristic
1153C2C2×#270211yescharacteristic
1154C2C2×#271811yescharacteristic
1155C2C2×#275311yescharacteristic
1156C2C2×#277911yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#388C2semidirect
3. C22×#388C2semidirect
5. C22×#385C2semidirect
6. #14540C2direct (N × H)
7. C2×#1442C2semidirect
8. C2×#1442C2semidirect
9. C2×#1439C2semidirect
10. C2×#1439C2semidirect
12. C2×#1437C2semidirect
13. C2×#1437C2semidirect
14. C2×#1436C2semidirect
15. C2×C4⋊#95C2semidirect
16. C2×C22⋊#95C2semidirect
36. C2×#394C4semidirect
40. C2×#388C22semidirect
41. C2×#388C22semidirect
45. C2×#385C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
67. #1437C22semidirect
68. #1437C22semidirect
69. #1436C22semidirect
70. C4⋊#95C22semidirect
71. C22⋊#95C22semidirect
114. C22×C4⋊C4C2×C4semidirect
149. C22×C22⋊C4C2×C4semidirect
150. C22×C22⋊C4C2×C4semidirect
171. #394C2×C4semidirect
190. C2×#95C2×C4semidirect
191. C2×#95D4semidirect
388. C2×C4⋊C4C22×C4semidirect
430. C2×C22⋊C4C22×C4semidirect
431. C2×C22⋊C4C22×C4semidirect
455. #95C22×C4semidirect
456. #95C2×D4semidirect
1141. C2#14540direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3942
C22×#3882
C22×#3862
C22×#3852
#145402
C2×#14422
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C4⋊#952
C2×C22⋊#952