Finite Group Databasebeta

← #25063782

Subgroups — #25063782

Order 11008.

1194 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#19133121C211yesmaximal, characteristic, complemented
5#19133120C211yesmaximal, characteristic, complemented
6#19133118C211yesmaximal, characteristic, complemented
7#19133098C212yesmaximal, complemented
8#19133096C212yesmaximal, complemented
9#19133092C212yesmaximal, complemented
10#19133088C212yesmaximal, complemented
11C43×#1509C211yesmaximal, characteristic, complemented
12#14583455C411yescharacteristic, complemented
13#14583453C411yescharacteristic, complemented
14#14583451C2211yescharacteristic
15#14583448C411yescharacteristic, complemented
16#14583446C411yescharacteristic, complemented
17#14583444C2211yescharacteristic
18#14583434C411yescharacteristic, complemented
19#14583433C2211yescharacteristic
20#14583432—21no—
21#14583432—21no—
22#14583428C411yescharacteristic, complemented
23#14583427—21no—
24#14583426—21no—
25#14583412C2211yescharacteristic
26#14583409C2211yescharacteristic
27#14583408—21no—
28#14583407—21no—
29C4×#10621902C411yescharacteristic, complemented
30#14583367—21no—
31C4×#10621900—21no—
32C4×#10621900C411yescharacteristic, complemented
33C2×C4⋊C4×D43—21no—
34C2×C42×D43—21no—
35C2×C42×D43C2211yescharacteristic
36#14582956C2211yescharacteristic
37#14582954—21no—
38#14582951—21no—
39#14582949C2212yes—
40#14582921—21no—
41#14582861C2212yes—
42#14582851—21no—
43C4⋊C4×Dic43—21no—
44C4×Dic43⋊C4—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46#14582750C2212yes—
47#95×D43C2212yes—
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#529C2211yescharacteristic
55C43×#432C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#328C2212yes—
58C43×#327C2212yes—
59C2×#10621902C2×C411yescharacteristic
60C2×#10621898—21no—
61C2×#10621900—21no—
62C2×#10621900C2×C411yescharacteristic
63C22×C4×D43—22no—
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C2×#10621872—22no—
68#13063324C2×C411yescharacteristic, complemented
69#13063324C2×C411yescharacteristic, complemented
70#13063323C2×C411yescharacteristic, complemented
71#13063321C2×C411yescharacteristic, complemented
72#13063320—21no—
73#13063319—21no—
74#13063318—21no—
75#13063317C2×C411yescharacteristic, complemented
76#13063315—21no—
77#13063315—21no—
78#13063313C2×C411yescharacteristic, complemented
79#13063311—21no—
80#13063311—21no—
81#13063310—21no—
82#13063310—21no—
83#13063308—21no—
84#13063307—21no—
85#13063307—21no—
86#13063305C2×C411yescharacteristic
87#13063304C2311yescharacteristic
88#13063303—21no—
89#13063303—21no—
90#13063303—21no—
91#13063302—21no—
92#13063301C2×C411yescharacteristic
93#13063300C2×C411yescharacteristic
94#13063299C2311yescharacteristic
95#13063298—21no—
96#13063298—21no—
97#13063298—21no—
98#13063297—21no—
99#13063296C2×C411yescharacteristic
100#13063295—21no—
101#13063293—21no—
102Q8×Dic43C2×C411yescharacteristic, complemented
103C4×Dic86—21no—
104C4×Dic86C2×C411yescharacteristic, complemented
105#13063290—21no—
106#13063290—21no—
107#13063290—21no—
108#13063290C2×C411yescharacteristic, complemented
109C4×D172—21no—
110C4×D172C2×C411yescharacteristic, complemented
111D4×Dic43—21no—
112D4×Dic43C2×C411yescharacteristic, complemented
113#13063287—21no—
114#13063287—21no—
115#13063287—21no—
116#13063287C2×C411yescharacteristic, complemented
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119C4×C22⋊D43—21no—
120(C22⋊D43)⋊C4—21no—
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126(C22⋊D43)⋊C4—21no—
127#13063283—21no—
128#13063283—21no—
129#13063283C2×C411yescharacteristic
130#13063283C2×C411yescharacteristic
131#13063282—21no—
132#13063282—21no—
133#13063281—21no—
134#13063281—21no—
135#13063281—21no—
136C2×C4⋊Dic43—21no—
137C2×Dic43⋊C4—22no—
138C4⋊C4×D43—28no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—22no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145C42×D43—21no—
146C42×D43—44no—
147C42×D43C2×C411yescharacteristic
148C42×D43C2×C411yescharacteristic
149C42×D43C2×C411yescharacteristic
150C42×D43C2×C411yescharacteristic
151C42×D43D411yescharacteristic
152C42×D43D411yescharacteristic
153C42×D43D411yescharacteristic
154C42×D43D411yescharacteristic
155C4⋊(C43⋊C8)—21no—
156Dic43⋊C8—22no—
157C22⋊(C43⋊C8)C2312yes—
158(C2×D43)⋊C8—22no—
159#13063236—21no—
160C8×Dic43—22no—
161C43⋊#95—22no—
162C43⋊#95C2312yes—
163#126×C43—21no—
164#125×C43C2×C411yescharacteristic, complemented
165#124×C43C2×C411yescharacteristic, complemented
166#123×C43—21no—
167C22⋊Q8×C43C2311yescharacteristic
168#121×C43C2311yescharacteristic
169C4×Q8×C43C2×C411yescharacteristic, complemented
170C4×D4×C43—21no—
171C4×D4×C43C2×C411yescharacteristic, complemented
172#117×C43—21no—
173C2×C4⋊C4×C43—21no—
174C2×C42×C43—21no—
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43—21no—
177C22⋊C8×C43C2312yes—
178#97×C43—21no—
179#95×C43C2312yes—
180C23×D43C2×D411yescharacteristic
181C2×Q8×C43C22×C411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43C22×C411yescharacteristic
184C22×C4×C43—21no—
185C22×C4×C43—22no—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—22no—
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200#10621902—42no—
201#10621900—42no—
202#10621900—42no—
203#10621900—42no—
204#10621898—44no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172C22×C411yescharacteristic
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—24no—
211C2×C4×D43—28no—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—21no—
215C2×C4×D43—42no—
216C2×C4×D43—44no—
217C2×C4×D43—44no—
218C2×C4×D43C22⋊C411yescharacteristic
219C2×C4×D43C22⋊C411yescharacteristic
220C2×C4×D43C22⋊C411yescharacteristic
221C2×C4×D43C22⋊C411yescharacteristic
222C2×C4×D43C22⋊C411yescharacteristic
223C2×C4×D43C22⋊C411yescharacteristic
224C2×C4×D43C22⋊C411yescharacteristic
225C2×C4×D43C22⋊C411yescharacteristic
226C2×C4×D43C22×C411yescharacteristic
227C2×C4×D43C22×C411yescharacteristic
228C2×C4×D43C2×D411yescharacteristic
229C2×C4×D43C2×D411yescharacteristic
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86C22×C411yescharacteristic
233C2×C8×C43—22no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43C22×C411yescharacteristic
240C4⋊C4×C43C22×C411yescharacteristic
241C22⋊C4×C43—21no—
242C22⋊C4×C43—21no—
243C22⋊C4×C43—21no—
244C22⋊C4×C43—21no—
245C22⋊C4×C43—21no—
246C42×C43—21no—
247C42×C43—42no—
248C42×C43C22×C411yescharacteristic
249C42×C43C22×C411yescharacteristic
250C42×C43C2×D411yescharacteristic
251C42×C43C2×D411yescharacteristic
252C22⋊Dic43—21no—
253C22⋊Dic43—21no—
254C22⋊Dic43—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259(C2×D43)⋊C4—21no—
260(C2×D43)⋊C4—21no—
261(C2×D43)⋊C4—21no—
262(C2×D43)⋊C4—21no—
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265C4⋊Dic43—24no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43C22×C411yescharacteristic
269C4⋊Dic43C22×C411yescharacteristic
270Dic43⋊C4—28no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—21no—
276Dic43⋊C4—21no—
277Dic43⋊C4—21no—
278Dic43⋊C4—21no—
279Dic43⋊C4—21no—
280Dic43⋊C4—21no—
281C4×Dic43—21no—
282C4×Dic43—21no—
283C4×Dic43—21no—
284C4×Dic43—21no—
285C4×Dic43—21no—
286C4×Dic43—42no—
287C4×Dic43—44no—
288C4×Dic43C22⋊C411yescharacteristic
289C4×Dic43C22⋊C411yescharacteristic
290C4×Dic43C22⋊C411yescharacteristic
291C4×Dic43C22⋊C411yescharacteristic
292C4×Dic43C22⋊C411yescharacteristic
293C4×Dic43C22⋊C411yescharacteristic
294C4×Dic43C22⋊C411yescharacteristic
295C4×Dic43C22⋊C411yescharacteristic
296C4×Dic43C22×C411yescharacteristic
297C4×Dic43C22×C411yescharacteristic
298C4×Dic43C2×D411yescharacteristic
299C4×Dic43C2×D411yescharacteristic
300C2×C43⋊C8—22no—
301#10621872—44no—
302C23×C43—21no—
303C23×C43C22×D411yescharacteristic
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—21no—
309C22×D43C2×C22⋊C411yescharacteristic
310C22×D43C2×C22⋊C411yescharacteristic
311Q8×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—41no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—24no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—41no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43C2×C22⋊C411yescharacteristic
327C2×C4×C43C2×C22⋊C411yescharacteristic
328C2×C4×C43C2×C22⋊C411yescharacteristic
329C2×C4×C43C2×C22⋊C411yescharacteristic
330C2×C4×C43C23×C411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C22⋊D43—41no—
333C22⋊D43—41no—
334C22⋊D43—42no—
335C22⋊D43—42no—
336C22⋊D43—42no—
337C22⋊D43—42no—
338C2×Dic43—22no—
339C2×Dic43—24no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—41no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43C2×C22⋊C411yescharacteristic
349C2×Dic43C2×C22⋊C411yescharacteristic
350C2×Dic43C2×C22⋊C411yescharacteristic
351C2×Dic43C2×C22⋊C411yescharacteristic
352C2×Dic43C2×C22⋊C411yescharacteristic
353C2×Dic43C2×C22⋊C411yescharacteristic
354C2×Dic43AGL(1,ℤ/8)12yes—
355C2×Dic43#13712yes—
356D172—41no—
357D172—42no—
358D172—42no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—22no—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—22no—
367C4×D43—22no—
368C4×D43—41no—
369C4×D43—41no—
370C4×D43—42no—
371C4×D43—416no—
372C4×D43—42no—
373C4×D43—42no—
374C4×D43#10414yes—
375Dic86—42no—
376Dic86—42no—
377Dic86—41no—
378C8×C43—42no—
379C43⋊C8—42no—
380#17546—431nomaximal, Sylow
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43C22×C22⋊C411yescharacteristic
387C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C43C2×#13711yescharacteristic
389C2×D43—24no—
390C2×D43—24no—
391C2×D43—21no—
392C2×D43—21no—
393C2×D43—21no—
394C2×D43—21no—
395C2×D43—41no—
396C2×D43—41no—
397C2×D43—41no—
398C2×D43#41012yes—
399C2×D43C2×#10412yes—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—21no—
404C4×C43—21no—
405C4×C43—44no—
406C4×C43—41no—
407C4×C43—41no—
408C4×C43—41no—
409C4×C43C2×#10412yes—
410Dic43—21no—
411Dic43—21no—
412Dic43—21no—
413Dic43—44no—
414Dic43—41no—
415Dic43—41no—
416Dic43—41no—
417Dic43#41712yes—
418Dic43#41712yes—
419Dic43C2×#10412yes—
420#3444—431no—
421#2920—431no—
422C2×C4×C4⋊C4—431no—
423#1509—431no—
424#1509—431no—
425#1509—431no—
426#1509D4311yescharacteristic, complemented
427#1504—432no—
428#1504—432no—
429#1503—432no—
430#1502—432no—
431C2×C43—21no—
432C2×C43—21no—
433C2×C43—81no—
434C2×C43C2×#41011yescharacteristic
435C2×C43C2×#41711yescharacteristic
436C2×C43C22×#10411yescharacteristic
437D43—22no—
438D43—22no—
439D43—81no—
440#533—431no—
441#533—431no—
442#533—431no—
443#532—431no—
444#532—431no—
445#532—431no—
446#529—431no—
447#529—431no—
448#529—431no—
449#529—861no—
450#529—861no—
451#529—861no—
452#529—861no—
453#529C2×D4311yescharacteristic
454#525—431no—
455#525—431no—
456#525—861no—
457#525—861no—
458C4×#41—431no—
459C4×#41—431no—
460C4×#41—861no—
461C4×#41—861no—
462C22×C4⋊C4—861no—
463C22×C42—431no—
464C22×C42—861no—
465#432—431no—
466#432—861no—
467#432C2×D4311yescharacteristic
468#431—432no—
469#431—861no—
470#423—861no—
471#407—432no—
472C4×M16—861no—
473C4×C4⋊C4—431no—
474C4×C4⋊C4—432no—
475C4×C4⋊C4—861no—
476C4×C4⋊C4—861no—
477C4×C4⋊C4C2×D4311yescharacteristic
478C2×#95—432no—
479#328—432no—
480#328—432no—
481#328—432no—
482#328C2×D4312yes—
483#327—432no—
484#327—432no—
485#327—432no—
486#327C2×D4312yes—
487C43#1754611yescharacteristic, complemented, Sylow
488C2×#41—431no—
489C2×#41—431no—
490C2×#41—861no—
491C2×#41—861no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—862no—
496C2×M16—862no—
497C4⋊Q8—431no—
498C4⋊Q8—431no—
499C4⋊Q8—431no—
500#127—431no—
501#126—21no—
502#126—861no—
503#126—861no—
504#126—861no—
505#125—431no—
506#125—861no—
507#125—861no—
508#125C4×D4311yescharacteristic, complemented
509#124—431no—
510#124—861no—
511#124—861no—
512#124C4×D4311yescharacteristic, complemented
513#123—21no—
514#123—861no—
515#123—861no—
516#123—861no—
517#123—861no—
518#123—861no—
519C22⋊Q8—431no—
520C22⋊Q8—431no—
521C22⋊Q8—431no—
522C22⋊Q8—861no—
523C22⋊Q8—861no—
524C22⋊Q8—861no—
525C22⋊Q8—861no—
526C22⋊Q8C22×D4311yescharacteristic
527#121—431no—
528#121—431no—
529#121—431no—
530#121—861no—
531#121—861no—
532#121—861no—
533#121—861no—
534#121C22×D4311yescharacteristic
535#120—861no—
536#120—861no—
537C4×Q8—431no—
538C4×Q8—431no—
539C4×Q8—431no—
540C4×Q8—861no—
541C4×Q8—861no—
542C4×Q8—861no—
543C4×Q8—861no—
544C4×Q8C4×D4311yescharacteristic, complemented
545C4×D4—21no—
546C4×D4—431no—
547C4×D4—431no—
548C4×D4—431no—
549C4×D4—861no—
550C4×D4—861no—
551C4×D4—861no—
552C4×D4—861no—
553C4×D4—861no—
554C4×D4—861no—
555C4×D4—861no—
556C4×D4—861no—
557C4×D4—861no—
558C4×D4—861no—
559C4×D4—861no—
560C4×D4—861no—
561C4×D4—861no—
562C4×D4—861no—
563C4×D4—861no—
564C4×D4C4×D4311yescharacteristic, complemented
565#117—21no—
566#117—431no—
567#117—431no—
568#117—861no—
569#117—861no—
570#117—861no—
571#117—861no—
572#117—861no—
573#117—861no—
574#117—861no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—868no—
577C2×C4⋊C4—862no—
578C2×C4⋊C4—861no—
579C2×C42—21no—
580C2×C42—431no—
581C2×C42—431no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—431no—
587C2×C42—431no—
588C2×C42—431no—
589C2×C42—431no—
590C2×C42—431no—
591C2×C42—861no—
592C2×C42—861no—
593C2×C42—862no—
594C2×C42—861no—
595C2×C42—1724no—
596C2×C42C22×D4311yescharacteristic
597C4⋊C8—21no—
598C4⋊C8—862no—
599C4⋊C8—861no—
600C22⋊C8—432no—
601C22⋊C8—862no—
602C22⋊C8C22×D4312yes—
603#97—21no—
604#97—861no—
605C4×C8—862no—
606#95—432no—
607#95—862no—
608#95C22×D4312yes—
609C24—431no—
610#41—1724no—
611#41—1722no—
612#41—1722no—
613#41—1722no—
614#41—1722no—
615C2×Q8—431no—
616C2×Q8—861no—
617C2×Q8—861no—
618C2×Q8C2×C4×D4311yescharacteristic
619C2×D4—21no—
620C2×D4—431no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4—861no—
625C2×D4—861no—
626C2×D4—861no—
627C2×D4—861no—
628C2×D4C2×C4×D4311yescharacteristic
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—862no—
647C22×C4—864no—
648C22×C4—862no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—868no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—862no—
655C22×C4—861no—
656C22×C4—1722no—
657C22×C4—1724no—
658C22×C4—1724no—
659C22×C4D4×D4311yescharacteristic
660C22×C4D4×D4311yescharacteristic
661C22×C4C23×D4311yescharacteristic
662M16—1724no—
663C2×C8—22no—
664C2×C8—862no—
665C4⋊C4—24no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—431no—
671C4⋊C4—431no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—868no—
681C4⋊C4—864no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4C2×C4×D4311yescharacteristic
687C4⋊C4C2×C4×D4311yescharacteristic
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—861no—
694C22⋊C4—861no—
695C22⋊C4—861no—
696C22⋊C4—861no—
697C22⋊C4—861no—
698C22⋊C4—861no—
699C22⋊C4—861no—
700C22⋊C4—861no—
701C22⋊C4—861no—
702C22⋊C4—861no—
703C22⋊C4—861no—
704C22⋊C4—861no—
705C22⋊C4—861no—
706C42—21no—
707C42—42no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—431no—
712C42—431no—
713C42—431no—
714C42—431no—
715C42—431no—
716C42—431no—
717C42—431no—
718C42—431no—
719C42—431no—
720C42—861no—
721C42—861no—
722C42—861no—
723C42—861no—
724C42—861no—
725C42—1722no—
726C42—1724no—
727C42C2×C4×D4311yescharacteristic
728C42C2×C4×D4311yescharacteristic
729C42D4×D4311yescharacteristic
730C42D4×D4311yescharacteristic
731C23—21no—
732C23—431no—
733C23—431no—
734C23—862no—
735C23—862no—
736C23—861no—
737C23—861no—
738C23—861no—
739C23C2×D4×D4311yescharacteristic
740Q8—41no—
741Q8—1721no—
742Q8—1722no—
743Q8—1722no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—1721no—
748D4—1722no—
749D4—1722no—
750D4—1722no—
751D4—1722no—
752D4—1722no—
753D4—1722no—
754D4—1721no—
755D4—1721no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—431no—
768C2×C4—431no—
769C2×C4—431no—
770C2×C4—432no—
771C2×C4—432no—
772C2×C4—434no—
773C2×C4—431no—
774C2×C4—431no—
775C2×C4—431no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—864no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1722no—
793C2×C4—1722no—
794C2×C4—17216no—
795C2×C4—1722no—
796C2×C4—1721no—
797C2×C4—1722no—
798C2×C4—1722no—
799C2×C4—1722no—
800C2×C4—1722no—
801C2×C4C22⋊C4×D4311yescharacteristic
802C2×C4C22⋊C4×D4311yescharacteristic
803C2×C4C22⋊C4×D4311yescharacteristic
804C2×C4C22⋊C4×D4311yescharacteristic
805C2×C4C22×C4×D4311yescharacteristic
806C2×C4C2×D4×D4311yescharacteristic
807C8—42no—
808C8—1722no—
809C22—21no—
810C22—21no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—432no—
815C22—432no—
816C22—864no—
817C22—864no—
818C22—861no—
819C22—861no—
820C22—861no—
821C22—861no—
822C22—1721no—
823C22—1721no—
824C22—1721no—
825C22C2×C22⋊C4×D4311yescharacteristic
826C22AGL(1,ℤ/8)×D4311yescharacteristic
827C22#137×D4311yescharacteristic
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—44no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—432no—
838C4—432no—
839C4—432no—
840C4—861no—
841C4—861no—
842C4—861no—
843C4—1724no—
844C4—1721no—
845C4—1721no—
846C4—1721no—
847C4#104×D4312yes—
848C2—21no—
849C2—21no—
850C2—81no—
851C2—862no—
852C2—862no—
853C2—3441no—
854C2#410×D4311yescharacteristic
855C2#417×D4311yescharacteristic
856C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#19147889C2
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43#17546
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. C4×C4⋊C4×D43C2semidirect
4. #19133121C2semidirect
5. #19133120C2semidirect
6. #19133118C2semidirect
7. #19133098C2semidirect
8. #19133096C2semidirect
9. #19133092C2semidirect
10. #19133088C2semidirect
11. C43×#1509C2semidirect
12. #14583455C4semidirect
13. #14583453C4semidirect
15. #14583448C4semidirect
16. #14583446C4semidirect
18. #14583434C4semidirect
22. #14583428C4semidirect
29. C4×#10621902C4semidirect
32. C4×#10621900C4semidirect
68. #13063324C2×C4semidirect
69. #13063324C2×C4semidirect
70. #13063323C2×C4semidirect
71. #13063321C2×C4semidirect
75. #13063317C2×C4semidirect
78. #13063313C2×C4semidirect
102. Q8×Dic43C2×C4semidirect
104. C4×Dic86C2×C4semidirect
108. #13063290C2×C4semidirect
110. C4×D172C2×C4semidirect
112. D4×Dic43C2×C4semidirect
116. #13063287C2×C4semidirect
164. #125×C43C2×C4semidirect
165. #124×C43C2×C4semidirect
169. C4×Q8×C43C2×C4semidirect
171. C4×D4×C43C2×C4semidirect
426. #1509D43semidirect
487. C43#17546semidirect
508. #125C4×D43semidirect
512. #124C4×D43semidirect
544. C4×Q8C4×D43semidirect
564. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191478892
#191432252
C4×C4⋊C4×D432
#191331212
#191331202
#191331182
#191330982
#191330962
#191330922
#191330882
C43×#15092
#1754643