Finite Group Databasebeta

← C2×#13975 #514256

Subgroups — C2×#13975 #514256

Order 512.

9874 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D4C211yesmaximal, characteristic
2C22×#386C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5C22×#385C211yesmaximal, characteristic, complemented
6C22×#380C211yesmaximal, characteristic, complemented
7C23×#95C211yesmaximal, characteristic, complemented
8#13975C2116yesmaximal, direct product factor
9C2×#1444C211yesmaximal, characteristic, complemented
10C2×#1442C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C25×C4C2211yescharacteristic
21C25×C4C2211yescharacteristic
22C22×C4×D4—28no—
23C22×C4×D4—28no—
24C22×C4×D4—28no—
25C22×C4×D4C2218yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C42C2211yescharacteristic
40C2×#386—28no—
41C2×#386C4116yescomplemented
42C2×#386C2218yes—
43C2×#386C2218yes—
44C2×#385—28no—
45C2×#385—28no—
46C2×#385C2218yescomplemented
47C2×#385C2218yescomplemented
48C2×#380—28no—
49C2×#380C2218yescomplemented
50C22×#95—28no—
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
66C22×#95C2211yescharacteristic
67C22×#95C2218yescomplemented
68#1444C2218yescomplemented
69#1442C2218yescomplemented
70#1439C2218yescomplemented
71#1439C2218yescomplemented
72#1436C2218yescomplemented
73#1436C2218yescomplemented
74C22⋊#95C2218yescomplemented
75C22⋊#95C2218yescomplemented
76C26C2311yescharacteristic
77C26C2311yescharacteristic
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—24no—
82C23×D4C2×C418yes—
83C23×D4D418yes—
84C23×D4Q818yes—
85C23×D4C2314yes—
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—24no—
97C24×C4—24no—
98C24×C4—24no—
99C24×C4—24no—
100C24×C4—24no—
101C24×C4—24no—
102C24×C4—24no—
103C24×C4—24no—
104C24×C4—42no—
105C24×C4—42no—
106C24×C4—42no—
107C24×C4—42no—
108C24×C4—42no—
109C24×C4—42no—
110C24×C4—42no—
111C24×C4—42no—
112C24×C4C2×C418yescomplemented
113C24×C4D418yes—
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C24×C4C2311yescharacteristic
118C24×C4C2311yescharacteristic
119C24×C4C2311yescharacteristic
120C24×C4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C24×C4C2311yescharacteristic
123C24×C4C2311yescharacteristic
124C24×C4C2314yes—
125C24×C4C2314yes—
126C24×C4C2314yes—
127C24×C4C2314yes—
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—24no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4—24no—
143C22×C4⋊C4—24no—
144C22×C4⋊C4—24no—
145C22×C4⋊C4—24no—
146C22×C4⋊C4—42no—
147C22×C4⋊C4—42no—
148C22×C4⋊C4—42no—
149C22×C4⋊C4—42no—
150C22×C4⋊C4C2314yes—
151C22×C4⋊C4C2314yes—
152C22×C4⋊C4C2314yes—
153C22×C4⋊C4C2314yes—
154C22×C4⋊C4C2314yes—
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—24no—
171C22×C22⋊C4—42no—
172C22×C22⋊C4—42no—
173C22×C22⋊C4—42no—
174C22×C22⋊C4—42no—
175C22×C22⋊C4C2×C418yescomplemented
176C22×C22⋊C4C2×C418yescomplemented
177C22×C22⋊C4C2×C418yescomplemented
178C22×C22⋊C4D418yes—
179C22×C22⋊C4C2314yes—
180C22×C22⋊C4C2314yes—
181C22×C22⋊C4C2314yes—
182C22×C22⋊C4C2314yes—
183C22×C22⋊C4C2314yes—
184C22×C22⋊C4C2314yes—
185C22×C22⋊C4C2314yes—
186C22×C22⋊C4C2314yes—
187C22×C42—24no—
188C22×C42—24no—
189C22×C42—24no—
190C22×C42C2314yes—
191#386—232no—
192#386C2×C4164yescomplemented
193#385—232no—
194#385—232no—
195#380—232no—
196C2×#95—24no—
197C2×#95—24no—
198C2×#95—24no—
199C2×#95—24no—
200C2×#95—24no—
201C2×#95—24no—
202C2×#95—24no—
203C2×#95—24no—
204C2×#95—24no—
205C2×#95—24no—
206C2×#95—24no—
207C2×#95—232no—
208C2×#95—42no—
209C2×#95—42no—
210C2×#95C2×C418yescomplemented
211C2×#95C2×C418yescomplemented
212C2×#95D418yescomplemented
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C25—22no—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—22no—
234C25—22no—
235C25—22no—
236C25—22no—
237C25—22no—
238C25—22no—
239C25—22no—
240C25—22no—
241C25—22no—
242C25—22no—
243C25—22no—
244C25—22no—
245C25—22no—
246C25—22no—
247C25—22no—
248C25—22no—
249C25C22×C414yes—
250C25C22×C414yes—
251C25C2×D414yes—
252C25C2×D414yes—
253C25C2×D414yes—
254C25C2×D414yes—
255C25C2×Q814yes—
256C25C2×Q814yes—
257C25#4114yes—
258C25#4114yes—
259C25C2412yes—
260C25C2412yes—
261C25C2411yescharacteristic
262C22×D4—232no—
263C22×D4—232no—
264C22×D4—232no—
265C22×D4—232no—
266C22×D4—232no—
267C22×D4—232no—
268C22×D4—28no—
269C22×D4—28no—
270C22×D4—28no—
271C22×D4—28no—
272C22×D4C4⋊C4164yescomplemented
273C22×D4C22×C4116yes—
274C22×D4C2×D4116yes—
275C22×D4C2×Q8116yes—
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—232no—
289C23×C4—232no—
290C23×C4—232no—
291C23×C4—232no—
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—28no—
305C23×C4—28no—
306C23×C4—28no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—28no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—28no—
318C23×C4—28no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
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—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—232no—
347C23×C4—232no—
348C23×C4—28no—
349C23×C4—28no—
350C23×C4—28no—
351C23×C4—28no—
352C23×C4—28no—
353C23×C4—28no—
354C23×C4—28no—
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—28no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—28no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—28no—
373C23×C4—28no—
374C23×C4—416no—
375C23×C4—416no—
376C23×C4—44no—
377C23×C4—44no—
378C23×C4—44no—
379C23×C4—44no—
380C23×C4—44no—
381C23×C4—44no—
382C23×C4—44no—
383C23×C4—44no—
384C23×C4—416no—
385C23×C4—416no—
386C23×C4—416no—
387C23×C4—416no—
388C23×C4—416no—
389C23×C4—416no—
390C23×C4—416no—
391C23×C4—416no—
392C23×C4—416no—
393C23×C4—416no—
394C23×C4—416no—
395C23×C4—416no—
396C23×C4—416no—
397C23×C4—416no—
398C23×C4—416no—
399C23×C4—416no—
400C23×C4—416no—
401C23×C4—416no—
402C23×C4—416no—
403C23×C4—416no—
404C23×C4C22×C414yes—
405C23×C4C22×C414yes—
406C23×C4C22×C414yes—
407C23×C4C22×C414yes—
408C23×C4C22×C414yes—
409C23×C4C22×C4116yescomplemented
410C23×C4C2×D414yes—
411C23×C4C2×D414yes—
412C23×C4C2×D414yes—
413C23×C4C2×D414yes—
414C23×C4C2×D4116yes—
415C23×C4C2×D414yes—
416C23×C4C2×D414yes—
417C23×C4C2×D414yes—
418C23×C4C2×D414yes—
419C23×C4C2×Q814yes—
420C23×C4#4114yes—
421C23×C4#4114yes—
422C23×C4#4114yes—
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2412yes—
436C4×D4—2256no—
437C2×C4⋊C4—232no—
438C2×C4⋊C4—28no—
439C2×C4⋊C4—28no—
440C2×C4⋊C4—28no—
441C2×C4⋊C4—28no—
442C2×C4⋊C4—28no—
443C2×C4⋊C4—28no—
444C2×C4⋊C4—28no—
445C2×C4⋊C4—28no—
446C2×C4⋊C4—28no—
447C2×C4⋊C4—28no—
448C2×C4⋊C4—28no—
449C2×C4⋊C4—44no—
450C2×C4⋊C4—44no—
451C2×C4⋊C4—44no—
452C2×C4⋊C4—44no—
453C2×C4⋊C4—416no—
454C2×C4⋊C4—416no—
455C2×C4⋊C4—416no—
456C2×C4⋊C4—416no—
457C2×C22⋊C4—232no—
458C2×C22⋊C4—232no—
459C2×C22⋊C4—232no—
460C2×C22⋊C4—28no—
461C2×C22⋊C4—28no—
462C2×C22⋊C4—28no—
463C2×C22⋊C4—28no—
464C2×C22⋊C4—28no—
465C2×C22⋊C4—232no—
466C2×C22⋊C4—28no—
467C2×C22⋊C4—28no—
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—416no—
478C2×C22⋊C4—44no—
479C2×C22⋊C4—44no—
480C2×C22⋊C4—44no—
481C2×C22⋊C4—44no—
482C2×C22⋊C4—416no—
483C2×C22⋊C4—416no—
484C2×C22⋊C4—416no—
485C2×C22⋊C4C22×C4116yescomplemented
486C2×C22⋊C4C22×C4116yescomplemented
487C2×C22⋊C4C22×C4116yescomplemented
488C2×C22⋊C4C2×D4116yes—
489C2×C42—232no—
490C2×C42—28no—
491C2×C42—28no—
492C2×C42—28no—
493#95—28no—
494#95—28no—
495#95—28no—
496#95—28no—
497#95—28no—
498#95—28no—
499#95—28no—
500#95—28no—
501#95—28no—
502#95—28no—
503#95—28no—
504#95—44no—
505#95—44no—
506#95C22×C4116yescomplemented
507#95C22×C4116yescomplemented
508#95C2×D4116yescomplemented
509C24—28no—
510C24—28no—
511C24—28no—
512C24—28no—
513C24—28no—
514C24—28no—
515C24—28no—
516C24—28no—
517C24—28no—
518C24—28no—
519C24—28no—
520C24—28no—
521C24—28no—
522C24—28no—
523C24—28no—
524C24—28no—
525C24—28no—
526C24—28no—
527C24—28no—
528C24—28no—
529C24—28no—
530C24—28no—
531C24—28no—
532C24—28no—
533C24—28no—
534C24—28no—
535C24—28no—
536C24—28no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
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—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—44no—
576C24—44no—
577C24—44no—
578C24—44no—
579C24—44no—
580C24—44no—
581C24—44no—
582C24—44no—
583C24—44no—
584C24—44no—
585C24—44no—
586C24—44no—
587C24—44no—
588C24—44no—
589C24—44no—
590C24—44no—
591C24C2×C4⋊C4116yes—
592C24C2×C4⋊C4116yes—
593C24C4×D4116yes—
594C24C4×D4116yes—
595C24#120116yes—
596C24C22⋊Q8116yes—
597C24C22⋊Q8116yes—
598C24#123116yes—
599C24C23×C414yes—
600C24C23×C414yes—
601C24C23×C412yes—
602C24C22×D414yes—
603C24C22×D414yes—
604C24C22×D414yes—
605C24C22×D414yes—
606C24C22×D412yes—
607C24C22×D412yes—
608C24C22×D412yes—
609C24C22×D412yes—
610C24C22×Q814yes—
611C24C22×Q814yes—
612C24C22×Q812yes—
613C24C2×#4114yes—
614C24C2×#4114yes—
615C24C2×#4112yes—
616C24C2×#4112yes—
617C24C2×#4112yes—
618C24C2×#4112yes—
619C24C2×#4112yes—
620C24H(5,𝔽2)12yes—
621C24H(5,𝔽2)12yes—
622C24H(5,𝔽2)12yes—
623C242−1+412yes—
624C24C2511yescharacteristic
625C2×D4—232no—
626C2×D4—232no—
627C2×D4—232no—
628C2×D4—232no—
629C2×D4—232no—
630C2×D4—232no—
631C2×D4—2256no—
632C2×D4C2×C4⋊C4164yescomplemented
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—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—232no—
664C22×C4—232no—
665C22×C4—28no—
666C22×C4—28no—
667C22×C4—28no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—232no—
671C22×C4—28no—
672C22×C4—28no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—232no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—28no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—232no—
740C22×C4—232no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—416no—
756C22×C4—416no—
757C22×C4—416no—
758C22×C4—416no—
759C22×C4—4128no—
760C22×C4—4128no—
761C22×C4—416no—
762C22×C4—416no—
763C22×C4—416no—
764C22×C4—416no—
765C22×C4—416no—
766C22×C4—416no—
767C22×C4—416no—
768C22×C4—416no—
769C22×C4—416no—
770C22×C4—416no—
771C22×C4—416no—
772C22×C4—416no—
773C22×C4—416no—
774C22×C4—416no—
775C22×C4—4128no—
776C22×C4—416no—
777C22×C4—4128no—
778C22×C4—416no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—416no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—416no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4C2×C4⋊C4116yes—
828C22×C4C4×D4116yescomplemented
829C22×C4#121116yes—
830C22×C4C23×C414yes—
831C22×C4C23×C414yes—
832C22×C4C23×C414yes—
833C22×C4C23×C414yes—
834C22×C4C23×C414yes—
835C22×C4C22×D414yes—
836C22×C4C22×D414yes—
837C22×C4C22×D414yes—
838C22×C4C22×D414yes—
839C22×C4C22×D414yes—
840C22×C4C22×D414yes—
841C22×C4C22×D414yes—
842C22×C4C22×D414yes—
843C22×C4C22×Q814yes—
844C22×C4C2×#4114yes—
845C22×C4C2×#4114yes—
846C22×C4C2×#4114yes—
847C4⋊C4—232no—
848C4⋊C4—416no—
849C4⋊C4—416no—
850C4⋊C4—416no—
851C4⋊C4—416no—
852C22⋊C4—232no—
853C22⋊C4—232no—
854C22⋊C4—232no—
855C22⋊C4—232no—
856C22⋊C4—416no—
857C22⋊C4—416no—
858C22⋊C4—416no—
859C22⋊C4—416no—
860C42—232no—
861C23—232no—
862C23—232no—
863C23—232no—
864C23—232no—
865C23—232no—
866C23—232no—
867C23—24no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—24no—
872C23—232no—
873C23—24no—
874C23—24no—
875C23—232no—
876C23—232no—
877C23—24no—
878C23—232no—
879C23—24no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23—232no—
884C23—24no—
885C23—24no—
886C23—24no—
887C23—24no—
888C23—24no—
889C23—24no—
890C23—24no—
891C23—24no—
892C23—24no—
893C23—24no—
894C23—24no—
895C23—24no—
896C23—24no—
897C23—24no—
898C23—24no—
899C23—24no—
900C23—232no—
901C23—232no—
902C23—232no—
903C23—232no—
904C23—232no—
905C23—24no—
906C23—24no—
907C23—24no—
908C23—24no—
909C23—24no—
910C23—24no—
911C23—24no—
912C23—24no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—232no—
924C23—416no—
925C23—416no—
926C23—416no—
927C23—416no—
928C23—42no—
929C23—416no—
930C23—42no—
931C23—42no—
932C23—416no—
933C23—416no—
934C23—42no—
935C23—416no—
936C23—42no—
937C23—42no—
938C23—42no—
939C23—42no—
940C23—416no—
941C23—42no—
942C23—42no—
943C23—42no—
944C23—42no—
945C23—42no—
946C23—42no—
947C23—42no—
948C23—42no—
949C23—416no—
950C23—416no—
951C23—416no—
952C23#385164yescomplemented
953C23C22×C4⋊C418yes—
954C23C22×C4⋊C418yes—
955C23C22×C4⋊C414yes—
956C23C2×C4×D418yes—
957C23C2×C4×D418yes—
958C23C2×C4×D414yes—
959C23C2×C4×D414yes—
960C23C2×C4×D414yes—
961C23C4×#4114yes—
962C23#51814yes—
963C23#52014yes—
964C23C2×#12018yes—
965C23C2×#12014yes—
966C23C2×#12114yes—
967C23C2×C22⋊Q818yes—
968C23C2×C22⋊Q818yes—
969C23C2×C22⋊Q814yes—
970C23C2×C22⋊Q814yes—
971C23C2×#12318yes—
972C23C2×#12314yes—
973C23#52514yes—
974C23#52914yes—
975C23#53214yes—
976C23#53414yes—
977C23#53714yes—
978C23#53814yes—
979C23#53914yes—
980C23D4214yes—
981C23D4214yes—
982C23#54614yes—
983C23#54614yes—
984C23#54614yes—
985C23#54614yes—
986C23#54614yes—
987C23#54714yes—
988C23#54714yes—
989C23D4×Q814yes—
990C23#55114yes—
991C23#55114yes—
992C23#55214yes—
993C23#55414yes—
994C23#55414yes—
995C23#55414yes—
996C23C24×C411yescharacteristic
997C23C23×D411yescharacteristic
998C23C23×D411yescharacteristic
999C23C23×D411yescharacteristic
1000C23C23×D411yescharacteristic
1001C23C23×Q811yescharacteristic
1002C23C22×#4111yescharacteristic
1003C23C22×#4111yescharacteristic
1004C23C22×#4111yescharacteristic
1005C23C22×#4111yescharacteristic
1006C23C22×#4111yescharacteristic
1007C23C2×H(5,𝔽2)11yescharacteristic
1008C23C2×H(5,𝔽2)11yescharacteristic
1009C23C2×H(5,𝔽2)11yescharacteristic
1010C23C2×2−1+411yescharacteristic
1011D4—2128no—
1012C2×C4—232no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—232no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—232no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—464no—
1058C2×C4—464no—
1059C2×C4—464no—
1060C2×C4—464no—
1061C2×C4—416no—
1062C2×C4—416no—
1063C2×C4—42no—
1064C2×C4—42no—
1065C2×C4—416no—
1066C2×C4—416no—
1067C2×C4—42no—
1068C2×C4—42no—
1069C2×C4—42no—
1070C2×C4—42no—
1071C2×C4—416no—
1072C2×C4—416no—
1073C2×C4—42no—
1074C2×C4—42no—
1075C2×C4—42no—
1076C2×C4—42no—
1077C2×C4—42no—
1078C2×C4—42no—
1079C2×C4—42no—
1080C2×C4—42no—
1081C2×C4—42no—
1082C2×C4—42no—
1083C2×C4—416no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—42no—
1089C2×C4—42no—
1090C2×C4—42no—
1091C2×C4—42no—
1092C2×C4—42no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—42no—
1100C2×C4—416no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—88no—
1116C2×C4—88no—
1117C2×C4C22×C4⋊C418yes—
1118C2×C4C2×C4×D418yescomplemented
1119C2×C4C2×#12118yes—
1120C22—28no—
1121C22—28no—
1122C22—28no—
1123C22—28no—
1124C22—28no—
1125C22—28no—
1126C22—28no—
1127C22—28no—
1128C22—28no—
1129C22—28no—
1130C22—28no—
1131C22—28no—
1132C22—2128no—
1133C22—28no—
1134C22—28no—
1135C22—28no—
1136C22—28no—
1137C22—28no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—44no—
1144C22—44no—
1145C22—44no—
1146C22—44no—
1147C22—44no—
1148C22—464no—
1149C22—44no—
1150C22—44no—
1151C22C2×#38518yes—
1152C22C2×#385116yescomplemented
1153C22C4×#12118yes—
1154C22#232518yes—
1155C22D4×C4⋊C418yes—
1156C22#234918yes—
1157C22#235818yes—
1158C22#235918yes—
1159C22#241018yes—
1160C22#241718yes—
1161C22#241818yes—
1162C22#241918yes—
1163C22#243018yes—
1164C22#244918yes—
1165C22#245018yes—
1166C22#256418yes—
1167C22C23×C4⋊C411yescharacteristic
1168C22C22×C4×D411yescharacteristic
1169C22C22×C4×D411yescharacteristic
1170C22C22×C4×D411yescharacteristic
1171C22C2×C4×#4111yescharacteristic
1172C22C2×#51811yescharacteristic
1173C22C2×#52011yescharacteristic
1174C22C22×#12011yescharacteristic
1175C22C22×#12111yescharacteristic
1176C22C22×C22⋊Q811yescharacteristic
1177C22C22×C22⋊Q811yescharacteristic
1178C22C22×#12311yescharacteristic
1179C22C2×#52511yescharacteristic
1180C22C2×#52911yescharacteristic
1181C22C2×#53211yescharacteristic
1182C22C2×#53411yescharacteristic
1183C22C2×#53711yescharacteristic
1184C22C2×#53811yescharacteristic
1185C22C2×#53911yescharacteristic
1186C22C2×D4211yescharacteristic
1187C22C2×D4211yescharacteristic
1188C22C2×#54611yescharacteristic
1189C22C2×#54611yescharacteristic
1190C22C2×#54611yescharacteristic
1191C22C2×#54611yescharacteristic
1192C22C2×#54611yescharacteristic
1193C22C2×#54711yescharacteristic
1194C22C2×#54711yescharacteristic
1195C22C2×D4×Q811yescharacteristic
1196C22C2×#55111yescharacteristic
1197C22C2×#55111yescharacteristic
1198C22C2×#55211yescharacteristic
1199C22C2×#55411yescharacteristic
1200C22C2×#55411yescharacteristic
1201C22C2×#55411yescharacteristic
1202C4—28no—
1203C4—28no—
1204C4—28no—
1205C4—44no—
1206C4—44no—
1207C4—44no—
1208C4—44no—
1209C4—44no—
1210C4—44no—
1211C4—44no—
1212C4—44no—
1213C4—82no—
1214C4—82no—
1215C2—216no—
1216C2—48no—
1217C2#13975116yesdirect product factor
1218C2C22×#38511yescharacteristic
1219C2C2×C4×#12111yescharacteristic
1220C2C2×#232511yescharacteristic
1221C2C2×D4×C4⋊C411yescharacteristic
1222C2C2×#234911yescharacteristic
1223C2C2×#235811yescharacteristic
1224C2C2×#235911yescharacteristic
1225C2C2×#241011yescharacteristic
1226C2C2×#241811yescharacteristic
1227C2C2×#244911yescharacteristic
1228C2C2×#241911yescharacteristic
1229C2C2×#245011yescharacteristic
1230C2C2×#241711yescharacteristic
1231C2C2×#243011yescharacteristic
1232C2C2×#256411yescharacteristic
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
4. C22×#385C2semidirect
5. C22×#385C2semidirect
6. C22×#380C2semidirect
7. C23×#95C2semidirect
8. #13975C2direct (N × H)
9. C2×#1444C2semidirect
10. C2×#1442C2semidirect
11. C2×#1439C2semidirect
12. C2×#1439C2semidirect
13. C2×#1436C2semidirect
14. C2×#1436C2semidirect
15. C2×C22⋊#95C2semidirect
16. C2×C22⋊#95C2semidirect
41. C2×#386C4semidirect
46. C2×#385C22semidirect
47. C2×#385C22semidirect
49. C2×#380C22semidirect
67. C22×#95C22semidirect
68. #1444C22semidirect
69. #1442C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1436C22semidirect
73. #1436C22semidirect
74. C22⋊#95C22semidirect
75. C22⋊#95C22semidirect
112. C24×C4C2×C4semidirect
175. C22×C22⋊C4C2×C4semidirect
176. C22×C22⋊C4C2×C4semidirect
177. C22×C22⋊C4C2×C4semidirect
192. #386C2×C4semidirect
210. C2×#95C2×C4semidirect
211. C2×#95C2×C4semidirect
212. C2×#95D4semidirect
272. C22×D4C4⋊C4semidirect
409. C23×C4C22×C4semidirect
485. C2×C22⋊C4C22×C4semidirect
486. C2×C22⋊C4C22×C4semidirect
487. C2×C22⋊C4C22×C4semidirect
506. #95C22×C4semidirect
507. #95C22×C4semidirect
508. #95C2×D4semidirect
632. C2×D4C2×C4⋊C4semidirect
828. C22×C4C4×D4semidirect
952. C23#385semidirect
1118. C2×C4C2×C4×D4semidirect
1152. C22C2×#385semidirect
1217. C2#13975direct (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×#3862
C22×#3852
C22×#3802
C23×#952
#139752
C2×#14442
C2×#14422
C2×#14392
C2×#14362
C2×C22⋊#952