Finite Group Databasebeta

← C2×#14052 #514367

Subgroups — C2×#14052 #514367

Order 512.

8090 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C22×#391C211yesmaximal, characteristic, complemented
3C22×#385C211yesmaximal, characteristic
4C22×C4×C22⋊C4C211yesmaximal, characteristic
5C23×#95C211yesmaximal, characteristic
6#14052C2116yesmaximal, direct product factor
7C2×#1446C211yesmaximal, characteristic, complemented
8C2×#1445C211yesmaximal, characteristic, complemented
9C2×#1441C211yesmaximal, characteristic, complemented
10C2×#1441C211yesmaximal, characteristic, complemented
11C2×#1436C211yesmaximal, characteristic, complemented
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×C4⋊#95C211yesmaximal, characteristic, complemented
14C2×C22⋊#95C211yesmaximal, characteristic
15C2×C22⋊#95C211yesmaximal, characteristic
16C2×C22⋊#95C211yesmaximal, characteristic
17C24×Q8C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C25×C4C2211yescharacteristic
21C22×C22⋊Q8—28no—
22C22×C22⋊Q8—28no—
23C22×C22⋊Q8C4116yescomplemented
24C22×C22⋊Q8C2218yes—
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35C23×C42C2211yescharacteristic
36C2×#391—28no—
37C2×#391C2218yescomplemented
38C2×#385—28no—
39C2×#385C2218yes—
40C2×C4×C22⋊C4—28no—
41C2×C4×C22⋊C4C2218yes—
42C22×#95—28no—
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2218yes—
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64#1446C2218yescomplemented
65#1445C2218yescomplemented
66#1441C2218yescomplemented
67#1441C2218yescomplemented
68#1436C2218yescomplemented
69#1436C2218yescomplemented
70C4⋊#95C2218yescomplemented
71C22⋊#95C2218yes—
72C22⋊#95C2218yes—
73C22⋊#95C2218yes—
74C26C2311yescharacteristic
75C23×Q8—24no—
76C23×Q8—24no—
77C23×Q8—24no—
78C23×Q8—24no—
79C23×Q8—42no—
80C23×Q8—42no—
81C23×Q8C2×C418yescomplemented
82C23×Q8C2314yes—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—24no—
92C24×C4—24no—
93C24×C4—24no—
94C24×C4—24no—
95C24×C4—24no—
96C24×C4—42no—
97C24×C4—42no—
98C24×C4—42no—
99C24×C4—42no—
100C24×C4—42no—
101C24×C4—42no—
102C24×C4C2×C418yes—
103C24×C4Q818yescomplemented
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2314yes—
115C24×C4C2314yes—
116C24×C4C2314yes—
117C24×C4C2311yescharacteristic
118C24×C4C2311yescharacteristic
119C24×C4C2311yescharacteristic
120C24×C4C2311yescharacteristic
121C2×C22⋊Q8—2128no—
122C2×C22⋊Q8—232no—
123C2×C22⋊Q8—232no—
124C2×C22⋊Q8C2×C4164yescomplemented
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—24no—
134C22×C4⋊C4—24no—
135C22×C4⋊C4—42no—
136C22×C4⋊C4—42no—
137C22×C4⋊C4C2×C418yescomplemented
138C22×C4⋊C4C2×C418yescomplemented
139C22×C4⋊C4C2×C418yescomplemented
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2314yes—
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⋊C4C2×C418yes—
153C22×C22⋊C4C2×C418yes—
154C22×C22⋊C4D418yes—
155C22×C22⋊C4D418yes—
156C22×C22⋊C4Q818yescomplemented
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C42—24no—
162C22×C42—24no—
163C22×C42—24no—
164C22×C42—24no—
165C22×C42—42no—
166C22×C42—42no—
167C22×C42C2314yes—
168C22×C42C2314yes—
169#391—232no—
170#385—232no—
171C4×C22⋊C4—232no—
172C2×#95—24no—
173C2×#95—24no—
174C2×#95—24no—
175C2×#95—24no—
176C2×#95—24no—
177C2×#95—24no—
178C2×#95—24no—
179C2×#95—24no—
180C2×#95—24no—
181C2×#95—24no—
182C2×#95—24no—
183C2×#95—24no—
184C2×#95—24no—
185C2×#95—232no—
186C2×#95—42no—
187C2×#95—42no—
188C2×#95—42no—
189C2×#95—42no—
190C2×#95—42no—
191C2×#95—42no—
192C2×#95D418yes—
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—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25C22×C414yes—
222C25C2×D414yes—
223C25C2×D414yes—
224C25C2×Q814yes—
225C25C2×Q814yes—
226C25#4114yes—
227C25#4114yes—
228C25C2412yes—
229C25C2411yescharacteristic
230C22×Q8—232no—
231C22×Q8—232no—
232C22×Q8—28no—
233C22×Q8—28no—
234C22×Q8—28no—
235C22×Q8—28no—
236C22×Q8—416no—
237C22×Q8—44no—
238C22×Q8—44no—
239C22×Q8—416no—
240C22×Q8—416no—
241C22×Q8—416no—
242C22×Q8—416no—
243C22×Q8C22×C4116yescomplemented
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—232no—
261C23×C4—232no—
262C23×C4—232no—
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—28no—
274C23×C4—28no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—28no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—28no—
285C23×C4—28no—
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—232no—
317C23×C4—232no—
318C23×C4—28no—
319C23×C4—28no—
320C23×C4—28no—
321C23×C4—28no—
322C23×C4—28no—
323C23×C4—28no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—28no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—28no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—416no—
341C23×C4—416no—
342C23×C4—44no—
343C23×C4—44no—
344C23×C4—44no—
345C23×C4—44no—
346C23×C4—44no—
347C23×C4—44no—
348C23×C4—416no—
349C23×C4—416no—
350C23×C4—416no—
351C23×C4—416no—
352C23×C4—416no—
353C23×C4—416no—
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×C4C22×C414yes—
363C23×C4C22×C414yes—
364C23×C4C22×C414yes—
365C23×C4C22×C4116yes—
366C23×C4C22×C414yes—
367C23×C4C22×C414yes—
368C23×C4C22×C414yes—
369C23×C4C2×D414yes—
370C23×C4C2×D414yes—
371C23×C4C2×D414yes—
372C23×C4C2×D414yes—
373C23×C4C2×D414yes—
374C23×C4C2×D414yes—
375C23×C4C2×D414yes—
376C23×C4C2×Q814yes—
377C23×C4C2×Q814yes—
378C23×C4C2×Q814yes—
379C23×C4C2×Q814yes—
380C23×C4C2×Q8116yescomplemented
381C23×C4#4114yes—
382C23×C4#4114yes—
383C23×C4#4114yes—
384C23×C4C2412yes—
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—
398C22⋊Q8—2256no—
399C2×C4⋊C4—232no—
400C2×C4⋊C4—232no—
401C2×C4⋊C4—232no—
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—416no—
415C2×C4⋊C4—416no—
416C2×C4⋊C4C22×C4116yescomplemented
417C2×C4⋊C4C22×C4116yescomplemented
418C2×C4⋊C4C22×C4116yescomplemented
419C2×C22⋊C4—232no—
420C2×C22⋊C4—232no—
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—416no—
429C2×C22⋊C4C22⋊C4164yes—
430C2×C22⋊C4C22×C4116yes—
431C2×C22⋊C4C22×C4116yes—
432C2×C22⋊C4C2×D4116yes—
433C2×C22⋊C4C2×D4116yes—
434C2×C22⋊C4C2×Q8116yescomplemented
435C2×C42—28no—
436C2×C42—28no—
437C2×C42—28no—
438C2×C42—28no—
439C2×C42—44no—
440C2×C42—44no—
441C2×C42—416no—
442C2×C42—416no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—28no—
454#95—28no—
455#95—28no—
456#95—44no—
457#95—44no—
458#95—44no—
459#95—44no—
460#95—44no—
461#95—44no—
462#95C2×D4116yes—
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—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—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24C2×C22⋊C4116yes—
500C24C4×Q8116yes—
501C24C4×Q8116yes—
502C24C22⋊Q8116yes—
503C24C22⋊Q8116yes—
504C24#124116yes—
505C24C4⋊Q8116yes—
506C24C23×C414yes—
507C24C23×C412yes—
508C24C22×D414yes—
509C24C22×D414yes—
510C24C22×D412yes—
511C24C22×D412yes—
512C24C22×D412yes—
513C24C22×Q814yes—
514C24C22×Q814yes—
515C24C22×Q812yes—
516C24C22×Q812yes—
517C24C2×#4114yes—
518C24C2×#4114yes—
519C24C2×#4112yes—
520C24C2×#4112yes—
521C24C2×#4112yes—
522C24C2×#4112yes—
523C24C2×#4112yes—
524C24H(5,𝔽2)12yes—
525C24H(5,𝔽2)12yes—
526C24H(5,𝔽2)12yes—
527C242−1+412yes—
528C24C2511yescharacteristic
529C2×Q8—232no—
530C2×Q8—232no—
531C2×Q8—416no—
532C2×Q8—4128no—
533C2×Q8—416no—
534C2×Q8—416no—
535C2×Q8—416no—
536C2×Q8—416no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—232no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—232no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—232no—
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—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
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—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—232no—
653C22×C4—232no—
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—416no—
669C22×C4—416no—
670C22×C4—4128no—
671C22×C4—4128no—
672C22×C4—416no—
673C22×C4—416no—
674C22×C4—416no—
675C22×C4—416no—
676C22×C4—416no—
677C22×C4—416no—
678C22×C4—416no—
679C22×C4—416no—
680C22×C4—416no—
681C22×C4—416no—
682C22×C4—416no—
683C22×C4—416no—
684C22×C4—416no—
685C22×C4—4128no—
686C22×C4—44no—
687C22×C4—416no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
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×C4C2×C22⋊C4116yes—
734C22×C4C2×C22⋊C4116yes—
735C22×C4C4×D4116yes—
736C22×C4C22⋊Q8116yescomplemented
737C22×C4C23×C414yes—
738C22×C4C23×C414yes—
739C22×C4C23×C414yes—
740C22×C4C23×C414yes—
741C22×C4C23×C414yes—
742C22×C4C23×C414yes—
743C22×C4C22×D414yes—
744C22×C4C22×D414yes—
745C22×C4C22×D414yes—
746C22×C4C22×D414yes—
747C22×C4C22×D414yes—
748C22×C4C22×D414yes—
749C22×C4C22×D414yes—
750C22×C4C22×Q814yes—
751C22×C4C22×Q814yes—
752C22×C4C22×Q814yes—
753C22×C4C22×Q814yes—
754C22×C4C2×#4114yes—
755C22×C4C2×#4114yes—
756C22×C4C2×#4114yes—
757C4⋊C4—232no—
758C4⋊C4—232no—
759C4⋊C4—232no—
760C4⋊C4—416no—
761C4⋊C4—416no—
762C22⋊C4—232no—
763C22⋊C4—232no—
764C22⋊C4—416no—
765C22⋊C4C2×C22⋊C4164yes—
766C42—416no—
767C42—416no—
768C23—232no—
769C23—232no—
770C23—232no—
771C23—232no—
772C23—232no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—232no—
786C23—232no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—232no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—232no—
805C23—232no—
806C23—232no—
807C23—232no—
808C23—232no—
809C23—232no—
810C23#391164yescomplemented
811C23C22×C22⋊C418yes—
812C23C22×C22⋊C414yes—
813C23C2×C4×D414yes—
814C23C2×C4×Q818yes—
815C23C2×C4×Q818yes—
816C23C2×C4×Q814yes—
817C23C2×C4×Q814yes—
818C23C4×#4114yes—
819C23#51814yes—
820C23#52014yes—
821C23C2×C22⋊Q818yes—
822C23C2×C22⋊Q818yes—
823C23C2×C22⋊Q814yes—
824C23C2×C22⋊Q814yes—
825C23C2×C22⋊Q814yes—
826C23#52514yes—
827C23C2×#12418yes—
828C23C2×#12414yes—
829C23#52914yes—
830C23C2×C4⋊Q818yes—
831C23C2×C4⋊Q814yes—
832C23#53314yes—
833C23#53814yes—
834C23#53914yes—
835C23#54314yes—
836C23#54414yes—
837C23D4214yes—
838C23D4214yes—
839C23#54614yes—
840C23#54614yes—
841C23#54614yes—
842C23#54614yes—
843C23#54614yes—
844C23#54714yes—
845C23#54714yes—
846C23D4×Q814yes—
847C23#55114yes—
848C23#55114yes—
849C23#55214yes—
850C23#55414yes—
851C23#55414yes—
852C23#55414yes—
853C23C24×C411yescharacteristic
854C23C23×D411yescharacteristic
855C23C23×D411yescharacteristic
856C23C23×D411yescharacteristic
857C23C23×Q811yescharacteristic
858C23C23×Q811yescharacteristic
859C23C22×#4111yescharacteristic
860C23C22×#4111yescharacteristic
861C23C22×#4111yescharacteristic
862C23C22×#4111yescharacteristic
863C23C22×#4111yescharacteristic
864C23C2×H(5,𝔽2)11yescharacteristic
865C23C2×H(5,𝔽2)11yescharacteristic
866C23C2×H(5,𝔽2)11yescharacteristic
867C23C2×2−1+411yescharacteristic
868Q8—464no—
869C2×C4—232no—
870C2×C4—232no—
871C2×C4—232no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—232no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—464no—
922C2×C4—464no—
923C2×C4—464no—
924C2×C4—416no—
925C2×C4—416no—
926C2×C4—416no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—416no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—416no—
961C2×C4—416no—
962C2×C4—416no—
963C2×C4—416no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—88no—
979C2×C4—88no—
980C2×C4C22×C22⋊C418yes—
981C2×C4C22×C22⋊C418yes—
982C2×C4C2×C4×D418yes—
983C2×C4C2×C22⋊Q818yescomplemented
984C22—28no—
985C22—28no—
986C22—28no—
987C22—28no—
988C22—28no—
989C22—28no—
990C22—28no—
991C22—28no—
992C22—28no—
993C22—28no—
994C22—28no—
995C22—28no—
996C22—28no—
997C22—2128no—
998C22—28no—
999C22C2×#39118yes—
1000C22C2×#391116yescomplemented
1001C22C4×C22⋊Q818yes—
1002C22#232918yes—
1003C22D4×C22⋊C418yes—
1004C22#233918yes—
1005C22#236018yes—
1006C22#236818yes—
1007C22#243718yes—
1008C22#243818yes—
1009C22#244018yes—
1010C22#244918yes—
1011C22#245018yes—
1012C22#247218yes—
1013C22#248818yes—
1014C22#254918yes—
1015C22C23×C22⋊C411yescharacteristic
1016C22C22×C4×D411yescharacteristic
1017C22C22×C4×Q811yescharacteristic
1018C22C22×C4×Q811yescharacteristic
1019C22C2×C4×#4111yescharacteristic
1020C22C2×#51811yescharacteristic
1021C22C2×#52011yescharacteristic
1022C22C22×C22⋊Q811yescharacteristic
1023C22C22×C22⋊Q811yescharacteristic
1024C22C22×C22⋊Q811yescharacteristic
1025C22C2×#52511yescharacteristic
1026C22C22×#12411yescharacteristic
1027C22C2×#52911yescharacteristic
1028C22C22×C4⋊Q811yescharacteristic
1029C22C2×#53311yescharacteristic
1030C22C2×#53811yescharacteristic
1031C22C2×#53911yescharacteristic
1032C22C2×#54311yescharacteristic
1033C22C2×#54411yescharacteristic
1034C22C2×D4211yescharacteristic
1035C22C2×D4211yescharacteristic
1036C22C2×#54611yescharacteristic
1037C22C2×#54611yescharacteristic
1038C22C2×#54611yescharacteristic
1039C22C2×#54611yescharacteristic
1040C22C2×#54611yescharacteristic
1041C22C2×#54711yescharacteristic
1042C22C2×#54711yescharacteristic
1043C22C2×D4×Q811yescharacteristic
1044C22C2×#55111yescharacteristic
1045C22C2×#55111yescharacteristic
1046C22C2×#55211yescharacteristic
1047C22C2×#55411yescharacteristic
1048C22C2×#55411yescharacteristic
1049C22C2×#55411yescharacteristic
1050C4—28no—
1051C4—28no—
1052C4—28no—
1053C4—28no—
1054C4—44no—
1055C4—44no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4—44no—
1060C4—44no—
1061C4—44no—
1062C4—82no—
1063C4—82no—
1064C2—216no—
1065C2#14052116yesdirect product factor
1066C2C22×#39111yescharacteristic
1067C2C2×C4×C22⋊Q811yescharacteristic
1068C2C2×#232911yescharacteristic
1069C2C2×D4×C22⋊C411yescharacteristic
1070C2C2×#233911yescharacteristic
1071C2C2×#236011yescharacteristic
1072C2C2×#236811yescharacteristic
1073C2C2×#243711yescharacteristic
1074C2C2×#244911yescharacteristic
1075C2C2×#247211yescharacteristic
1076C2C2×#245011yescharacteristic
1077C2C2×#244011yescharacteristic
1078C2C2×#243811yescharacteristic
1079C2C2×#248811yescharacteristic
1080C2C2×#254911yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC26C23
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×#391C2semidirect
6. #14052C2direct (N × H)
7. C2×#1446C2semidirect
8. C2×#1445C2semidirect
9. C2×#1441C2semidirect
10. C2×#1441C2semidirect
11. C2×#1436C2semidirect
12. C2×#1436C2semidirect
13. C2×C4⋊#95C2semidirect
23. C22×C22⋊Q8C4semidirect
37. C2×#391C22semidirect
64. #1446C22semidirect
65. #1445C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1436C22semidirect
69. #1436C22semidirect
70. C4⋊#95C22semidirect
81. C23×Q8C2×C4semidirect
103. C24×C4Q8semidirect
124. C2×C22⋊Q8C2×C4semidirect
137. C22×C4⋊C4C2×C4semidirect
138. C22×C4⋊C4C2×C4semidirect
139. C22×C4⋊C4C2×C4semidirect
156. C22×C22⋊C4Q8semidirect
243. C22×Q8C22×C4semidirect
380. C23×C4C2×Q8semidirect
416. C2×C4⋊C4C22×C4semidirect
417. C2×C4⋊C4C22×C4semidirect
418. C2×C4⋊C4C22×C4semidirect
434. C2×C22⋊C4C2×Q8semidirect
736. C22×C4C22⋊Q8semidirect
810. C23#391semidirect
983. C2×C4C2×C22⋊Q8semidirect
1000. C22C2×#391semidirect
1065. C2#14052direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C22×#3912
C22×#3852
C22×C4×C22⋊C42
C23×#952
#140522
C2×#14462
C2×#14452
C2×#14412
C2×#14362
C2×C4⋊#952
C2×C22⋊#952