Finite Group Databasebeta

← #25098387

Subgroups — #25098387

Order 11008.

1994 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583406C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic, complemented
3C2×#14582873C211yesmaximal, characteristic, complemented
4#19136974C211yesmaximal, characteristic, complemented
5#19135050C214yesmaximal, complemented
6#19135045C214yesmaximal, complemented
7#19134327C211yesmaximal, characteristic, complemented
8#19134327C211yesmaximal, characteristic, complemented
9C2×C43×#410C211yesmaximal, characteristic, complemented
10C23×C4×D43C2211yescharacteristic
11#14583406—21no—
12#14583406—21no—
13#14583406—21no—
14#14583406—21no—
15#14583406—22no—
16#14583406—22no—
17C2×#13063306C2212yes—
18C2×#13063301C412yescomplemented
19C2×#13063296C412yescomplemented
20C2×#13063293C2212yes—
21C2×C4×C22⋊D43C414yescomplemented
22C2×#13063284C2211yescharacteristic
23C2×#13063284C2211yescharacteristic
24C2×#13063284C2211yescharacteristic
25C2×#13063283—21no—
26C2×#13063282—21no—
27C2×#13063281C2212yes—
28#117×D43—24no—
29#117×D43—24no—
30C2×C4⋊C4×D43—21no—
31C2×C22⋊C4×D43C2212yes—
32C2×C42×D43—21no—
33#14582873—24no—
34C2×#13063240C2214yes—
35#14582760C2212yes—
36#14582756—22no—
37#14582754C2212yes—
38C4×(C2×D43)⋊C4—22no—
39#14582665C2214yes—
40#14582665C2214yes—
41C22×#41×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C43×#410—24no—
45C2×#99×C43C2214yes—
46C24×D43C2311yescharacteristic
47C22×C22⋊D43C2×C414yes—
48C23×Dic43C2311yescharacteristic
49C22×C4×D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43—22no—
53C22×C4×D43—22no—
54C22×C4×D43C2×C412yes—
55C22×C4×D43C2×C412yes—
56C22×C4×D43D411yescharacteristic
57C22×C4×D43D411yescharacteristic
58C22×C4×D43D411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D412yes—
61C22×C4×D43D412yes—
62#13063306—24no—
63#13063306—22no—
64#13063306—22no—
65#13063301—22no—
66#13063301—22no—
67#13063301—22no—
68#13063301—22no—
69#13063296—22no—
70#13063296—22no—
71#13063296—22no—
72#13063296—22no—
73#13063293—22no—
74#13063293—24no—
75#13063293—22no—
76C4×C22⋊D43—24no—
77C4×C22⋊D43—24no—
78C4×C22⋊D43—24no—
79C4×C22⋊D43—24no—
80#13063284—22no—
81#13063284—21no—
82#13063284—21no—
83#13063284—21no—
84#13063284—21no—
85#13063284—22no—
86#13063284—22no—
87#13063284D414yescomplemented
88#13063283—28no—
89#13063282—28no—
90#13063281—24no—
91#13063281—24no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43C2×C412yescomplemented
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4C2×C414yescomplemented
97C4⋊C4×D43—28no—
98C2×C22⋊Dic43C2×C414yescomplemented
99C2×C22⋊Dic43C2312yes—
100C2×C22⋊Dic43C2312yes—
101C2×C22⋊Dic43C2312yes—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—24no—
104C2×(C2×D43)⋊C4C2×C414yes—
105C22⋊C4×D43—24no—
106C22⋊C4×D43—24no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2×C412yescomplemented
111C42×D43—28no—
112#13063240—28no—
113C43⋊#95—24no—
114C2×#41×C43—22no—
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117C2×#41×C43—21no—
118C2×#41×C43—21no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C22×Q8×C43C2×C411yescharacteristic, complemented
123C22×D4×C43C2×C411yescharacteristic, complemented
124C22×D4×C43C2312yes—
125C23×C4×C43C2×C412yescomplemented
126C23×C4×C43C2311yescharacteristic
127#117×C43—22no—
128#117×C43—22no—
129#117×C43—22no—
130#117×C43D414yescomplemented
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C22⋊C4×C43C2312yes—
134C2×C22⋊C4×C43C2312yes—
135C2×C42×C43—21no—
136C2×C42×C43—21no—
137#99×C43—28no—
138C24×C43C22×C412yes—
139C24×C43C2411yescharacteristic
140C23×D43—21no—
141C23×D43—21no—
142C23×D43—21no—
143C23×D43—21no—
144C23×D43—44no—
145C23×D43C22×C412yes—
146C23×D43C2×D411yescharacteristic
147C23×D43C2×D412yes—
148C23×D43C2×D411yescharacteristic
149#41×C43—42no—
150#41×C43—42no—
151#41×C43—42no—
152#41×C43—42no—
153#41×C43—42no—
154#41×C43—42no—
155#41×C43—42no—
156#41×C43—42no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—22no—
160C2×Q8×C43—22no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—22no—
164C2×D4×C43—22no—
165C2×D4×C43—22no—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—22no—
170C2×D4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—24no—
174C22×C4×C43—24no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43C22×C412yes—
178C22×C4×C43C22×C411yescharacteristic
179C22×C4×C43C22×C411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D412yes—
185C22×C4×C43C2×D412yes—
186C22×C4×C43#4112yes—
187C22×C4×C43#4112yes—
188C2×C22⋊D43—24no—
189C2×C22⋊D43—24no—
190C2×C22⋊D43—48no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43C22×C412yes—
198C22×Dic43C22×C414yes—
199C22×Dic43C2×D412yes—
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C2×C4×D43—24no—
203C2×C4×D43—24no—
204C2×C4×D43—24no—
205C2×C4×D43—24no—
206C2×C4×D43—22no—
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—24no—
211C2×C4×D43—24no—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—28no—
219C2×C4×D43—48no—
220C2×C4×D43C22⋊C412yes—
221C2×C4×D43C22⋊C412yes—
222C2×C4×D43C22⋊C412yes—
223C2×C4×D43C22⋊C412yes—
224C2×C4×D43C22⋊C412yes—
225C2×C4×D43C22⋊C412yes—
226C2×C4×D43C22⋊C412yes—
227C2×C4×D43C22⋊C412yes—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—42no—
230C22⋊C4×C43—22no—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—22no—
233C22⋊C4×C43C2×D414yes—
234C42×C43—24no—
235C42×C43—42no—
236C22⋊Dic43—24no—
237C22⋊Dic43—24no—
238C22⋊Dic43—22no—
239C22⋊Dic43—22no—
240C22⋊Dic43—22no—
241C22⋊Dic43—22no—
242C22⋊Dic43—22no—
243C22⋊Dic43C2×D414yes—
244(C2×D43)⋊C4—28no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—48no—
248C4⋊Dic43—22no—
249C4⋊Dic43—22no—
250C4⋊Dic43—24no—
251C4⋊Dic43—42no—
252Dic43⋊C4—28no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255C4×Dic43—28no—
256C4×Dic43—22no—
257C4×Dic43—22no—
258C4×Dic43—24no—
259C4×Dic43—42no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—42no—
264C23×C43—44no—
265C23×C43C23×C411yescharacteristic
266C23×C43C22×D411yescharacteristic
267C23×C43C22×D411yescharacteristic
268C23×C43C22×D411yescharacteristic
269C23×C43C22×D411yescharacteristic
270C23×C43C2×#4111yescharacteristic
271C23×C43C2×#4111yescharacteristic
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—24no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—21no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—21no—
281C22×D43—24no—
282C22×D43—24no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43—44no—
290C22×D43C2×C22⋊C412yes—
291C22×D43C2×C22⋊C412yes—
292Q8×C43—42no—
293Q8×C43—42no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—42no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—42no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—24no—
304C2×C4×C43—44no—
305C2×C4×C43—44no—
306C2×C4×C43—44no—
307C2×C4×C43—44no—
308C2×C4×C43—42no—
309C2×C4×C43C2×C22⋊C411yescharacteristic
310C2×C4×C43C2×C22⋊C411yescharacteristic
311C2×C4×C43C2×C22⋊C411yescharacteristic
312C2×C4×C43C2×C22⋊C411yescharacteristic
313C2×C4×C43C4×D412yes—
314C2×C4×C43C4×D412yes—
315C2×C4×C43C4×D412yes—
316C2×C4×C43C4×D412yes—
317C2×C4×C43#12012yes—
318C2×C4×C43#12012yes—
319C2×C4×C43#12112yes—
320C2×C4×C43#12112yes—
321C2×C4×C43#12112yes—
322C2×C4×C43#12112yes—
323C2×C4×C43#12312yes—
324C2×C4×C43#12312yes—
325C22⋊D43—48no—
326C22⋊D43—48no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—24no—
336C2×Dic43—24no—
337C2×Dic43—44no—
338C2×Dic43—44no—
339C2×Dic43—44no—
340C2×Dic43—42no—
341C2×Dic43C2×C22⋊C412yes—
342C2×Dic43C2×C22⋊C412yes—
343C4×D43—24no—
344C4×D43—24no—
345C4×D43—24no—
346C4×D43—24no—
347C4×D43—24no—
348C4×D43—24no—
349C4×D43—24no—
350C4×D43—24no—
351C4×D43—416no—
352#20983—431nomaximal, Sylow
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—44no—
361C22×C43—42no—
362C22×C43—82no—
363C22×C43—82no—
364C22×C43C22×C22⋊C411yescharacteristic
365C22×C43C2×C4×D411yescharacteristic
366C22×C43C2×C4×D411yescharacteristic
367C22×C43C2×#12011yescharacteristic
368C22×C43C2×#12111yescharacteristic
369C22×C43C2×#12111yescharacteristic
370C22×C43C2×#12311yescharacteristic
371C2×D43—24no—
372C2×D43—24no—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—44no—
379C2×D43—44no—
380C2×D43—44no—
381C2×D43—44no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43#41014yescomplemented
385C4×C43—44no—
386C4×C43—42no—
387C4×C43—82no—
388C4×C43#38612yes—
389C4×C43#38612yes—
390C4×C43#38612yes—
391C4×C43#38612yes—
392Dic43—22no—
393Dic43—22no—
394Dic43—44no—
395Dic43—44no—
396Dic43—82no—
397C2×#525—431no—
398C22×#117—431no—
399C2×#410—431no—
400C2×#410D4311yescharacteristic, complemented
401#2280—431no—
402#1899—434no—
403#1898—434no—
404#1740—431no—
405#1740—431no—
406C2×C43—21no—
407C2×C43—21no—
408C2×C43—21no—
409C2×C43—21no—
410C2×C43—21no—
411C2×C43—21no—
412C2×C43—82no—
413C2×C43C2×#38611yescharacteristic
414C2×C43C2×#41012yes—
415D43—24no—
416D43—42no—
417C22×#41C2×D4311yescharacteristic
418C24×C4—431no—
419#525—861no—
420#525—861no—
421#525—861no—
422#525—862no—
423#525—862no—
424#525—861no—
425C2×#123—432no—
426C2×C22⋊Q8—432no—
427C2×#121—432no—
428C2×#120—432no—
429C2×C4×D4—434no—
430C2×#117—431no—
431C2×#117—431no—
432C2×#117—431no—
433C2×#117—432no—
434C2×#117—861no—
435C2×#117—861no—
436C2×#117—864no—
437C2×#117—864no—
438C2×#117C2×D4311yescharacteristic
439C2×#117C2×D4311yescharacteristic
440C22×C4⋊C4—861no—
441C22×C22⋊C4—432no—
442C22×C42—861no—
443#410—24no—
444#410—864no—
445C2×#99—434no—
446C2×#99C2×D4314yes—
447#381—432no—
448#380—862no—
449#379—432no—
450C4×C22⋊C4—862no—
451#342—434no—
452#342—434no—
453C43#2098311yescharacteristic, complemented, Sylow
454C25—431no—
455C2×#41—22no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—22no—
461C2×#41—22no—
462C2×#41—22no—
463C22×Q8C4×D4311yescharacteristic, complemented
464C22×D4—434no—
465C22×D4C4×D4311yescharacteristic, complemented
466C22×D4C22×D4312yes—
467C23×C4—431no—
468C23×C4—432no—
469C23×C4—432no—
470C23×C4—431no—
471C23×C4—431no—
472C23×C4—431no—
473C23×C4—432no—
474C23×C4—432no—
475C23×C4—431no—
476C23×C4—862no—
477C23×C4—862no—
478C23×C4—862no—
479C23×C4—862no—
480C23×C4—862no—
481C23×C4C4×D4312yescomplemented
482C23×C4C22×D4311yescharacteristic
483#123—864no—
484#123—862no—
485#123—862no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489C22⋊Q8—862no—
490#121—862no—
491#121—862no—
492#121—862no—
493#121—862no—
494#120—862no—
495#120—864no—
496#120—862no—
497C4×D4—864no—
498C4×D4—864no—
499C4×D4—864no—
500C4×D4—864no—
501#117—22no—
502#117—22no—
503#117—22no—
504#117—434no—
505#117—868no—
506#117—864no—
507#117—868no—
508#117—861no—
509#117—861no—
510#117—861no—
511#117—861no—
512#117—862no—
513#117—864no—
514#117—862no—
515#117—862no—
516#117C22⋊D4314yescomplemented
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—432no—
520C2×C4⋊C4—434no—
521C2×C4⋊C4—868no—
522C2×C4⋊C4—862no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C22⋊C4—432no—
526C2×C22⋊C4—434no—
527C2×C22⋊C4—432no—
528C2×C22⋊C4—434no—
529C2×C22⋊C4—432no—
530C2×C22⋊C4—864no—
531C2×C22⋊C4—862no—
532C2×C22⋊C4—864no—
533C2×C22⋊C4—864no—
534C2×C22⋊C4C22×D4312yes—
535C2×C22⋊C4C22×D4312yes—
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—432no—
539C2×C42—868no—
540C2×C42—862no—
541C2×C42—861no—
542C2×C42—861no—
543#99—28no—
544#99—868no—
545#95—864no—
546C24—431no—
547C24—432no—
548C24—432no—
549C24—431no—
550C24—861no—
551C24—861no—
552C24—861no—
553C24—861no—
554C24—1724no—
555C24C2×C4×D4312yes—
556C24C23×D4311yescharacteristic
557#41—42no—
558#41—42no—
559#41—42no—
560#41—42no—
561#41—42no—
562#41—42no—
563#41—42no—
564#41—42no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—864no—
580C2×D4—864no—
581C2×D4—1728no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—431no—
591C22×C4—431no—
592C22×C4—432no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—434no—
601C22×C4—868no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—864no—
607C22×C4—864no—
608C22×C4—864no—
609C22×C4—864no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—864no—
615C22×C4—864no—
616C22×C4—864no—
617C22×C4—864no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—1728no—
625C22×C4C2×C4×D4312yes—
626C22×C4C2×C4×D4311yescharacteristic
627C22×C4C2×C4×D4311yescharacteristic
628C22×C4#1062189812yes—
629C22×C4D4×D4311yescharacteristic
630C22×C4D4×D4311yescharacteristic
631C22×C4D4×D4311yescharacteristic
632C22×C4D4×D4311yescharacteristic
633C22×C4D4×D4312yes—
634C22×C4#1062190012yes—
635C22×C4C2×C22⋊D4312yes—
636C4⋊C4—24no—
637C4⋊C4—42no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—868no—
641C4⋊C4—862no—
642C4⋊C4—862no—
643C4⋊C4—864no—
644C4⋊C4—1722no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—434no—
649C22⋊C4—864no—
650C22⋊C4—864no—
651C22⋊C4—868no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—862no—
658C22⋊C4—862no—
659C22⋊C4—1728no—
660C22⋊C4C2×C22⋊D4314yes—
661C42—24no—
662C42—42no—
663C42—868no—
664C42—862no—
665C42—862no—
666C42—864no—
667C42—1722no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—42no—
672C23—44no—
673C23—432no—
674C23—432no—
675C23—864no—
676C23—864no—
677C23—864no—
678C23—861no—
679C23—861no—
680C23—862no—
681C23—862no—
682C23—861no—
683C23—862no—
684C23—862no—
685C23—861no—
686C23—1722no—
687C23—1722no—
688C23—1722no—
689C23—1724no—
690C23—1724no—
691C23—1724no—
692C23—1724no—
693C23C22×C4×D4311yescharacteristic
694C23C2×D4×D4311yescharacteristic
695C23C2×D4×D4311yescharacteristic
696C23C2×D4×D4311yescharacteristic
697C23C22×C22⋊D4311yescharacteristic
698C23C2×#1062190011yescharacteristic
699C23C2×#1062189811yescharacteristic
700Q8—42no—
701Q8—42no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—1728no—
709D4—1728no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—861no—
724C2×C4—861no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—864no—
730C2×C4—864no—
731C2×C4—864no—
732C2×C4—864no—
733C2×C4—864no—
734C2×C4—864no—
735C2×C4—864no—
736C2×C4—864no—
737C2×C4—864no—
738C2×C4—864no—
739C2×C4—17216no—
740C2×C4—1724no—
741C2×C4—1722no—
742C2×C4—1724no—
743C2×C4—1724no—
744C2×C4C22⋊C4×D4311yescharacteristic
745C2×C4C22⋊C4×D4311yescharacteristic
746C2×C4C22⋊C4×D4311yescharacteristic
747C2×C4C22⋊C4×D4311yescharacteristic
748C2×C4(C22⋊D43)⋊C412yes—
749C2×C4(C22⋊D43)⋊C412yes—
750C2×C4C4×C22⋊D4312yes—
751C2×C4C4×C22⋊D4312yes—
752C2×C4#1306329312yes—
753C2×C4#1306329312yes—
754C2×C4#1306329612yes—
755C2×C4#1306329612yes—
756C2×C4#1306329812yes—
757C2×C4#1306329812yes—
758C2×C4#1306330712yes—
759C2×C4#1306330712yes—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—44no—
768C22—42no—
769C22—82no—
770C22—82no—
771C22—434no—
772C22—864no—
773C22—864no—
774C22—862no—
775C22—862no—
776C22—862no—
777C22—862no—
778C22—862no—
779C22—1724no—
780C22—1724no—
781C22—1724no—
782C22—1724no—
783C22—1722no—
784C22—1722no—
785C22C2×C22⋊C4×D4311yescharacteristic
786C22C2×(C22⋊D43)⋊C411yescharacteristic
787C22C2×C4×C22⋊D4311yescharacteristic
788C22C2×#1306329311yescharacteristic
789C22C2×#1306329611yescharacteristic
790C22C2×#1306329811yescharacteristic
791C22C2×#1306330711yescharacteristic
792C4—44no—
793C4—42no—
794C4—82no—
795C4—862no—
796C4—862no—
797C4—3442no—
798C4—1724no—
799C4—1724no—
800C4#1458277512yes—
801C4#1458277512yes—
802C4#1458277512yes—
803C4#1458277512yes—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—21no—
809C2—21no—
810C2—82no—
811C2—864no—
812C2—1722no—
813C2C2×#1458277511yescharacteristic
814C2#410×D4312yes—
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C43×#410C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583406C2
cosocleC24×C43C24
hypercenterC2×#410D43
hypocenterC43#20983
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#117×D43C2semidirect
3. C2×#14582873C2semidirect
4. #19136974C2semidirect
5. #19135050C2semidirect
6. #19135045C2semidirect
7. #19134327C2semidirect
8. #19134327C2semidirect
9. C2×C43×#410C2semidirect
18. C2×#13063301C4semidirect
19. C2×#13063296C4semidirect
21. C2×C4×C22⋊D43C4semidirect
87. #13063284D4semidirect
94. C2×C4⋊Dic43C2×C4semidirect
96. C2×Dic43⋊C4C2×C4semidirect
98. C2×C22⋊Dic43C2×C4semidirect
110. C2×C4×Dic43C2×C4semidirect
122. C22×Q8×C43C2×C4semidirect
123. C22×D4×C43C2×C4semidirect
125. C23×C4×C43C2×C4semidirect
130. #117×C43D4semidirect
384. C2×D43#410semidirect
400. C2×#410D43semidirect
453. C43#20983semidirect
463. C22×Q8C4×D43semidirect
465. C22×D4C4×D43semidirect
481. C23×C4C4×D43semidirect
516. #117C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
C2×#117×D432
C2×#145828732
#191369742
#191350502
#191350452
#191343272
C2×C43×#4102
#2098343