Finite Group Databasebeta

← #25106601

Subgroups — #25106601

Order 11008.

1242 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#19135540C211yesmaximal, characteristic, complemented
5#19135514C211yesmaximal, characteristic, complemented
6#19135513C211yesmaximal, characteristic, complemented
7#19135037C214yesmaximal, complemented
8#19134614C214yesmaximal, complemented
9C43×#1986C211yesmaximal, characteristic, complemented
10#14583454C411yescharacteristic, complemented
11#14583454C411yescharacteristic, complemented
12#14583450C411yescharacteristic, complemented
13#14583450C411yescharacteristic, complemented
14#14583449C2211yescharacteristic
15#14583436—21no—
16#14583436—21no—
17#14583435—21no—
18#14583435—21no—
19#14583434C412yescomplemented
20#14583434C412yescomplemented
21#14583412—21no—
22#14583412—21no—
23#14583411C2212yes—
24C4×#10621902—21no—
25C4×#10621902—21no—
26#14583367C2212yes—
27C2×C4⋊C4×D43—21no—
28C2×C42×D43C2212yes—
29C2×C42×D43C2211yescharacteristic
30#14582954—21no—
31#14582954—21no—
32#14582950—21no—
33#14582950—21no—
34#14582922C2212yes—
35C2×#13063253C2214yes—
36C2×#13063251C2214yes—
37#14582862C2212yes—
38C4×#10621877C2211yescharacteristic
39C4⋊C4×Dic43—21no—
40C4×Dic43⋊C4C2212yes—
41C4×C4⋊Dic43C2211yescharacteristic
42#14582750—21no—
43#95×D43—21no—
44#14582658C2214yes—
45C43×#533C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#339C2214yes—
49C2×#10621902—21no—
50C2×#10621902—21no—
51C2×#10621898C2312yes—
52C22×C4×D43—22no—
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C22×C4×D43C2311yescharacteristic
56C2×#10621877C2312yes—
57#13063325C2×C411yescharacteristic, complemented
58#13063322C2×C411yescharacteristic, complemented
59#13063320—22no—
60#13063320—22no—
61#13063316—21no—
62#13063316—21no—
63#13063314—21no—
64#13063314—21no—
65#13063313C2×C412yescomplemented
66#13063310—22no—
67#13063310—22no—
68#13063309—22no—
69#13063305C2×C412yes—
70#13063305C2×C412yes—
71#13063301—21no—
72#13063301—21no—
73#13063300—21no—
74#13063300—21no—
75#13063300C2×C412yes—
76#13063300C2×C412yes—
77#13063299—21no—
78#13063299—21no—
79#13063295—22no—
80Q8×Dic43—21no—
81Q8×Dic43—21no—
82#13063290C2×C412yescomplemented
83#13063290C2×C412yescomplemented
84C4×D172—22no—
85C4×D172—22no—
86C4×D172—21no—
87C4×D172—21no—
88#13063287—22no—
89#13063287—22no—
90#13063287—21no—
91#13063287—21no—
92#13063287C2×C412yescomplemented
93#13063287C2×C412yescomplemented
94(C22⋊D43)⋊C4—22no—
95(C22⋊D43)⋊C4—22no—
96#13063283—21no—
97#13063283—21no—
98#13063283—22no—
99#13063283—22no—
100#13063282—22no—
101C2×C4⋊Dic43—21no—
102C2×Dic43⋊C4—22no—
103C4⋊C4×D43—28no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43C2312yes—
108C2×C4×Dic43C2311yescharacteristic
109C42×D43—22no—
110C42×D43—44no—
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43C2×C411yescharacteristic
114C42×D43C2×C411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118C42×D43D411yescharacteristic
119Dic43⋊C8—22no—
120Dic43⋊C8—22no—
121#13063253—44no—
122#13063251—44no—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8—22no—
125#13063236—21no—
126C4×C43⋊C8—21no—
127C43⋊#95—21no—
128C43⋊#95—22no—
129C2×M16×C43C2312yes—
130C4⋊Q8×C43C2×C411yescharacteristic, complemented
131C4⋊Q8×C43C2×C411yescharacteristic, complemented
132#125×C43C2×C412yescomplemented
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C4×Q8×C43—21no—
136C4×Q8×C43—21no—
137#117×C43C2312yes—
138C2×C4⋊C4×C43—21no—
139C2×C42×C43C2312yes—
140C2×C42×C43C2311yescharacteristic
141#97×C43—21no—
142C4×C8×C43—21no—
143#95×C43—21no—
144C23×D43C2×D411yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—22no—
152C22×Dic43—22no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156#10621902—44no—
157#10621902—44no—
158#10621898—24no—
159#10621898—24no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—22no—
163C2×D172—22no—
164C2×D172C22×C412yes—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—24no—
168C2×C4×D43—28no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—42no—
173C2×C4×D43—44no—
174C2×C4×D43—44no—
175C2×C4×D43C22⋊C411yescharacteristic
176C2×C4×D43C22⋊C411yescharacteristic
177C2×C4×D43C22⋊C411yescharacteristic
178C2×C4×D43C22⋊C411yescharacteristic
179C2×C4×D43C22⋊C411yescharacteristic
180C2×C4×D43C22⋊C411yescharacteristic
181C2×C4×D43C22⋊C411yescharacteristic
182C2×C4×D43C22⋊C411yescharacteristic
183C2×C4×D43C22×C411yescharacteristic
184C2×C4×D43C22×C411yescharacteristic
185C2×C4×D43C2×D411yescharacteristic
186C2×C4×D43C2×D411yescharacteristic
187C2×Dic86C22×C412yes—
188M16×C43—22no—
189M16×C43—22no—
190C2×C8×C43—22no—
191C4⋊C4×C43—24no—
192C4⋊C4×C43—22no—
193C4⋊C4×C43—22no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43C22×C412yes—
197C4⋊C4×C43C22×C412yes—
198C22⋊C4×C43—22no—
199C42×C43—22no—
200C42×C43—24no—
201C42×C43C22×C411yescharacteristic
202C42×C43C22×C411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C42×C43C2×D411yescharacteristic
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211(C2×D43)⋊C4—22no—
212(C2×D43)⋊C4—22no—
213C4⋊Dic43—24no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—22no—
217C4⋊Dic43—22no—
218Dic43⋊C4—28no—
219Dic43⋊C4—22no—
220Dic43⋊C4—22no—
221C4×Dic43—22no—
222C4×Dic43—22no—
223C4×Dic43—24no—
224C4×Dic43—44no—
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C22⋊C411yescharacteristic
233C4×Dic43C22×C411yescharacteristic
234C4×Dic43C22×C411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237#10621877—22no—
238#10621877—22no—
239C2×C43⋊C8—22no—
240C23×C43C22×D411yescharacteristic
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—22no—
244C22×D43—22no—
245C22×D43—22no—
246C22×D43C2×C22⋊C411yescharacteristic
247C22×D43C2×C22⋊C411yescharacteristic
248Q8×C43—42no—
249Q8×C43—42no—
250C2×C4×C43—22no—
251C2×C4×C43—24no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—41no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C2×C22⋊C411yescharacteristic
261C2×C4×C43C23×C411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43H(5,𝔽2)12yes—
264C2×C4×C432−1+412yes—
265C22⋊D43—42no—
266C22⋊D43—42no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—24no—
271C2×Dic43—22no—
272C2×Dic43—41no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C411yescharacteristic
280C2×Dic43C2×C22⋊C411yescharacteristic
281D172—24no—
282D172—42no—
283D172—44no—
284D172—44no—
285D172—42no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—22no—
295C4×D43—41no—
296C4×D43—41no—
297C4×D43—44no—
298C4×D43—416no—
299C4×D43—44no—
300C4×D43—44no—
301C4×D43#10414yescomplemented
302Dic86—24no—
303C8×C43—42no—
304C43⋊C8—42no—
305#21899—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43C22×C22⋊C411yescharacteristic
309C22×C43#53511yescharacteristic
310C22×C43#53611yescharacteristic
311C2×D43—24no—
312C2×D43—24no—
313C2×D43—21no—
314C2×D43—21no—
315C2×D43—21no—
316C2×D43—21no—
317C2×D43—42no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43C2×#10412yes—
321C2×D43#42112yes—
322C4×C43—21no—
323C4×C43—21no—
324C4×C43—21no—
325C4×C43—44no—
326C4×C43—42no—
327C4×C43—42no—
328C4×C43C2×#10412yes—
329C4×C43#52012yes—
330C4×C43#53712yes—
331Dic43—21no—
332Dic43—21no—
333Dic43—21no—
334Dic43—21no—
335Dic43—21no—
336Dic43—44no—
337Dic43—42no—
338Dic43C2×#10412yes—
339#3444—431no—
340#2920—431no—
341C2×C4×C4⋊C4—431no—
342#1986—431no—
343#1986D4311yescharacteristic, complemented
344#1980—431no—
345#1980—431no—
346#1896—434no—
347#1806—434no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43#231111yescharacteristic
351C2×C43C22×#10411yescharacteristic
352C2×C43C2×#42111yescharacteristic
353D43—22no—
354D43—22no—
355D43—82no—
356#533—431no—
357#533—431no—
358#533C2×D4311yescharacteristic
359#532—431no—
360#532—431no—
361#532—431no—
362#529—432no—
363#529—432no—
364#529—861no—
365#529—861no—
366#529—861no—
367#529—861no—
368#525—432no—
369#525—861no—
370#525—861no—
371C4×#41—432no—
372C4×#41—861no—
373C4×#41—861no—
374C22×C4⋊C4—861no—
375C22×C42—431no—
376C22×C42—432no—
377#432—861no—
378#432—861no—
379#431—861no—
380#431—861no—
381#423—432no—
382C2×#104—434no—
383C2×#104—434no—
384#407—432no—
385C4×M16—431no—
386C4×M16C2×D4311yescharacteristic
387C4×C4⋊C4—432no—
388C4×C4⋊C4—431no—
389C4×C4⋊C4—861no—
390C4×C4⋊C4—861no—
391C4×C4⋊C4C2×D4311yescharacteristic
392C2×#95—861no—
393#339—434no—
394#339C2×D4314yes—
395C43#2189911yescharacteristic, complemented, Sylow
396C2×#41—432no—
397C2×#41—861no—
398C2×#41—861no—
399C23×C4—431no—
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—862no—
403C2×M16—432no—
404C2×M16C22×D4312yes—
405C4⋊Q8—431no—
406C4⋊Q8C4×D4311yescharacteristic, complemented
407C4⋊Q8C4×D4311yescharacteristic, complemented
408#127—431no—
409#126—862no—
410#126—862no—
411#125—861no—
412#125—861no—
413#125C4×D4312yescomplemented
414#124—432no—
415#124—861no—
416#124—861no—
417#123—862no—
418#123—862no—
419#123—862no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—432no—
423C22⋊Q8—432no—
424C22⋊Q8—861no—
425C22⋊Q8—861no—
426#121—432no—
427#121—432no—
428#121—861no—
429#121—861no—
430#121—861no—
431#121—861no—
432#120—862no—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×Q8—432no—
436C4×Q8—432no—
437C4×Q8—861no—
438C4×Q8—861no—
439C4×D4—432no—
440C4×D4—432no—
441C4×D4—862no—
442C4×D4—862no—
443C4×D4—861no—
444C4×D4—861no—
445C4×D4—862no—
446C4×D4—862no—
447C4×D4—862no—
448C4×D4—862no—
449C4×D4—861no—
450C4×D4—861no—
451#117—862no—
452#117—862no—
453#117—862no—
454#117—861no—
455#117—861no—
456#117C22×D4312yes—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—868no—
459C2×C4⋊C4—862no—
460C2×C4⋊C4—861no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—431no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42—431no—
472C2×C42—432no—
473C2×C42—862no—
474C2×C42—862no—
475C2×C42—1724no—
476C2×C42C22×D4312yes—
477C2×C42C22×D4311yescharacteristic
478C4⋊C8—862no—
479C4⋊C8—862no—
480#104—1724no—
481#104—1724no—
482C22⋊C8—862no—
483C22⋊C8—862no—
484#97—21no—
485#97—861no—
486C4×C8—21no—
487C4×C8—861no—
488#95—21no—
489#95—862no—
490#95—861no—
491C24—431no—
492#41—864no—
493#41—864no—
494#41—1724no—
495#41—1724no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—432no—
499C2×D4—432no—
500C2×D4—862no—
501C2×D4—862no—
502C2×D4—862no—
503C2×D4—861no—
504C2×D4—861no—
505C22×C4—22no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—864no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—868no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—1722no—
530C22×C4—1724no—
531C22×C4—1724no—
532C22×C4D4×D4311yescharacteristic
533C22×C4D4×D4311yescharacteristic
534C22×C4C23×D4311yescharacteristic
535M16—22no—
536M16—22no—
537M16—862no—
538M16—862no—
539C2×C8—22no—
540C2×C8—862no—
541C4⋊C4—24no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4—862no—
549C4⋊C4—862no—
550C4⋊C4—868no—
551C4⋊C4—864no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4C2×C4×D4312yes—
555C4⋊C4C2×C4×D4312yes—
556C22⋊C4—22no—
557C22⋊C4—862no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—862no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—862no—
564C22⋊C4—862no—
565C42—22no—
566C42—24no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42—431no—
572C42—431no—
573C42—431no—
574C42—431no—
575C42—431no—
576C42—431no—
577C42—431no—
578C42—431no—
579C42—862no—
580C42—862no—
581C42—864no—
582C42—1724no—
583C42C2×C4×D4311yescharacteristic
584C42C2×C4×D4311yescharacteristic
585C42D4×D4311yescharacteristic
586C42D4×D4311yescharacteristic
587C23—431no—
588C23—431no—
589C23—862no—
590C23—862no—
591C23—861no—
592C23—861no—
593C23—862no—
594C23C2×D4×D4311yescharacteristic
595Q8—42no—
596Q8—42no—
597Q8—864no—
598D4—864no—
599D4—1722no—
600D4—1724no—
601D4—1724no—
602D4—1722no—
603D4—1722no—
604D4—1722no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—431no—
613C2×C4—434no—
614C2×C4—431no—
615C2×C4—431no—
616C2×C4—431no—
617C2×C4—431no—
618C2×C4—431no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—864no—
632C2×C4—862no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1724no—
636C2×C4—1724no—
637C2×C4—17216no—
638C2×C4—1721no—
639C2×C4—1722no—
640C2×C4—1722no—
641C2×C4—1724no—
642C2×C4C22⋊C4×D4311yescharacteristic
643C2×C4C22⋊C4×D4311yescharacteristic
644C2×C4C22⋊C4×D4311yescharacteristic
645C2×C4C22⋊C4×D4311yescharacteristic
646C2×C4C22×C4×D4311yescharacteristic
647C2×C4C2×D4×D4311yescharacteristic
648C2×C4#1306337112yes—
649C2×C4#1306337312yes—
650C8—42no—
651C8—1722no—
652C22—21no—
653C22—21no—
654C22—432no—
655C22—432no—
656C22—864no—
657C22—864no—
658C22—861no—
659C22—861no—
660C22—861no—
661C22—861no—
662C22—1722no—
663C22—1722no—
664C22—1722no—
665C22C2×C22⋊C4×D4311yescharacteristic
666C22#1458346711yescharacteristic
667C22#1458347411yescharacteristic
668C4—21no—
669C4—21no—
670C4—21no—
671C4—44no—
672C4—42no—
673C4—42no—
674C4—432no—
675C4—861no—
676C4—861no—
677C4—861no—
678C4—861no—
679C4—861no—
680C4—1724no—
681C4—1722no—
682C4#104×D4312yes—
683C4#1458338112yes—
684C4#1458347912yes—
685C2—21no—
686C2—21no—
687C2—862no—
688C2—862no—
689C2—3442no—
690C2#1913718611yescharacteristic
691C2C2×#104×D4311yescharacteristic
692C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1986C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC22×C4×C43C24
hypercenter#1986D43
hypocenterC43#21899
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. C4×C4⋊C4×D43C2semidirect
4. #19135540C2semidirect
5. #19135514C2semidirect
6. #19135513C2semidirect
7. #19135037C2semidirect
8. #19134614C2semidirect
9. C43×#1986C2semidirect
10. #14583454C4semidirect
11. #14583454C4semidirect
12. #14583450C4semidirect
13. #14583450C4semidirect
19. #14583434C4semidirect
20. #14583434C4semidirect
57. #13063325C2×C4semidirect
58. #13063322C2×C4semidirect
65. #13063313C2×C4semidirect
82. #13063290C2×C4semidirect
83. #13063290C2×C4semidirect
92. #13063287C2×C4semidirect
93. #13063287C2×C4semidirect
130. C4⋊Q8×C43C2×C4semidirect
131. C4⋊Q8×C43C2×C4semidirect
132. #125×C43C2×C4semidirect
301. C4×D43#104semidirect
343. #1986D43semidirect
395. C43#21899semidirect
406. C4⋊Q8C4×D43semidirect
407. C4⋊Q8C4×D43semidirect
413. #125C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191478922
#191432262
C4×C4⋊C4×D432
#191355402
#191355142
#191355132
#191350372
#191346142
C43×#19862
#2189943