Finite Group Databasebeta

← #25119054

Subgroups — #25119054

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583101C211yesmaximal, characteristic
2C2×#14582997C211yesmaximal, characteristic
3C2×C4×#10621884C211yesmaximal, characteristic
4#19137506C211yesmaximal, characteristic
5#19135416C211yesmaximal, characteristic, complemented
6#19135363C211yesmaximal, characteristic, complemented
7#19135288C211yesmaximal, characteristic, complemented
8#19135274C211yesmaximal, characteristic, complemented
9#19134932C211yesmaximal, characteristic
10#19134932C211yesmaximal, characteristic
11#19134863C211yesmaximal, characteristic, complemented
12#19134849C211yesmaximal, characteristic, complemented
13#19134470C211yesmaximal, characteristic, complemented
14#19134423C211yesmaximal, characteristic
15C43×#2365C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583101C418yescomplemented
22#14582997—24no—
23C4×#10621884—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063236C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582770—21no—
41#14582770—21no—
42#14582765C2211yescharacteristic
43#14582758—21no—
44#95×D43—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C2×C4⋊Q8×C43C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C43×#391C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#389—21no—
57C43×#387—21no—
58C43×#387—21no—
59C4×C4⋊C4×C43—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884C2×C414yes—
71C2×#10621884C2×C414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C4×D172—22no—
77C4×D172—22no—
78C4×D172—22no—
79C4×D172—41no—
80C4×D172—41no—
81C4×D172C2×C414yes—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90#13063258—22no—
91#13063256—22no—
92C4⋊(C43⋊C8)C2×C414yescomplemented
93#13063249—22no—
94#13063249—22no—
95#13063249—41no—
96#13063249—41no—
97#13063249C2×C414yescomplemented
98#13063249C2×C414yescomplemented
99#13063245—22no—
100#13063245D414yes—
101#13063236—22no—
102#13063236—22no—
103C4×C43⋊C8—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C4⋊Q8×C43—22no—
111C4⋊Q8×C43C2×C414yescomplemented
112C4×Q8×C43—22no—
113C4×Q8×C43—22no—
114C4×Q8×C43—41no—
115C4×Q8×C43—41no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C42×C43—21no—
125C2×C42×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43C2311yescharacteristic
128C2×C42×C43C2311yescharacteristic
129C2×C42×C43C2311yescharacteristic
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43D411yescharacteristic
136#95×C43D411yescharacteristic
137C23×D43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C22×C412yes—
149C2×Q8×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172C22×C412yes—
168C2×D172C2×D412yes—
169C2×D172#4112yes—
170C2×C4×D43—24no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—81no—
176C2×C4×D43—81no—
177C2×C4×D43—81no—
178C2×C4×D43—81no—
179C4⋊C4×C43—24no—
180C4⋊C4×C43—24no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—42no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43C2×D412yes—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—42no—
194C42×C43—42no—
195C42×C43—42no—
196C42×C43C22×C412yes—
197C42×C43#4112yes—
198#10621884—28no—
199#10621884—28no—
200(C2×D43)⋊C4—24no—
201(C2×D43)⋊C4—42no—
202(C2×D43)⋊C4—42no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43C22×C412yes—
209Dic43⋊C4—81no—
210Dic43⋊C4—81no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8C22×C412yes—
221C2×C43⋊C8C22×C412yes—
222C2×C43⋊C8C2×D412yes—
223C23×C43C22×D411yescharacteristic
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—22no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—22no—
234Q8×C43—22no—
235Q8×C43—41no—
236Q8×C43—41no—
237Q8×C43—41no—
238Q8×C43—41no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43C4×D412yes—
267C2×C4×C43C4×D412yes—
268C2×C4×C43#13712yes—
269C2×C4×C43C23×C411yescharacteristic
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43H(5,𝔽2)11yescharacteristic
274C2×C4×C432−1+411yescharacteristic
275C2×Dic43—22no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284D172—22no—
285D172—22no—
286D172—22no—
287D172C4×D414yes—
288C4×D43—84no—
289C4×D43—84no—
290C4×D43—84no—
291C43⋊C8—22no—
292C43⋊C8—22no—
293C43⋊C8—22no—
294C43⋊C8—41no—
295#23012—431nomaximal, Sylow
296C22×C43C2×C4×D411yescharacteristic
297C22×C43D4211yescharacteristic
298C22×C43#54811yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57711yescharacteristic
303C2×D43—24no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C4×C43—22no—
311C4×C43—22no—
312C4×C43—22no—
313C4×C43—42no—
314C4×C43—42no—
315C4×C43—41no—
316C4×C43—41no—
317C4×C43—41no—
318C4×C43—42no—
319C4×C43—81no—
320C4×C43C2×C4×D411yescharacteristic
321C4×C43#52011yescharacteristic
322C4×C43#54711yescharacteristic
323C4×C43#55311yescharacteristic
324Dic43—42no—
325Dic43—81no—
326Dic43—81no—
327C2×#461—431no—
328C2×#440—431no—
329C2×C4×SD16—431no—
330#2365D4311yescharacteristic, complemented
331#2349—431no—
332#1960—431no—
333#1949—431no—
334#1935—431no—
335#1933—431no—
336#1877—431no—
337#1877—431no—
338#1865—431no—
339#1863—431no—
340#1771—431no—
341#1762—431no—
342C2×C43#236111yescharacteristic
343C2×C43C4×#13711yescharacteristic
344C2×C43#294911yescharacteristic
345C2×C43#326611yescharacteristic
346C2×C43#326711yescharacteristic
347C2×C43#337211yescharacteristic
348C2×C43#337611yescharacteristic
349D43—44no—
350C22×SD16—431no—
351C22×SD16—431no—
352C2×C4⋊Q8C2×D4311yescharacteristic
353C2×C4×Q8C2×D4311yescharacteristic
354C2×C4×Q8C2×D4311yescharacteristic
355C2×C4×D4—431no—
356C2×C4×D4—431no—
357C2×C4×D4—431no—
358#461—438no—
359#440—864no—
360C4×SD16—864no—
361C2×#107—431no—
362C2×#106—431no—
363C2×C4⋊C8—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#102—431no—
371C2×#102—431no—
372C2×#97—431no—
373C2×#97—431no—
374C2×C4×C8—431no—
375#391C2×D4311yescharacteristic
376#391C2×D4311yescharacteristic
377#389—21no—
378#389—431no—
379#389—431no—
380#387—21no—
381#387—21no—
382#385—861no—
383#385—861no—
384#382—431no—
385#380—861no—
386C4×C4⋊C4—21no—
387C4×C4⋊C4C2×D4311yescharacteristic
388C4×C4⋊C4C2×D4311yescharacteristic
389C2×#95—861no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#336—431no—
395#336—431no—
396C43#2301211yescharacteristic, complemented, Sylow
397C22×Q8C22×D4311yescharacteristic
398C22×Q8C22×D4311yescharacteristic
399C22×D4—431no—
400C23×C4—861no—
401C23×C4—861no—
402C23×C4—861no—
403C2×SD16—434no—
404C2×SD16—434no—
405C2×SD16—862no—
406C2×SD16—862no—
407C2×SD16—862no—
408C2×SD16—862no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8—431no—
413C4⋊Q8—22no—
414C4⋊Q8C4×D4314yescomplemented
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—41no—
418C4×Q8—41no—
419C4×D4—434no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4—1721no—
424C4×D4—1721no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4C22⋊D4311yescharacteristic
435C2×C4⋊C4C22⋊D4311yescharacteristic
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C22×D4311yescharacteristic
445C2×C42C22×D4311yescharacteristic
446C2×C42C22×D4311yescharacteristic
447#107—862no—
448#106—862no—
449C4⋊C8—434no—
450#103—434no—
451#103—434no—
452#103—862no—
453#103—862no—
454#103—1721no—
455#103—1721no—
456#102—434no—
457#102—862no—
458#97—862no—
459#97—862no—
460C4×C8—862no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95C22⋊D4311yescharacteristic
471#95C22⋊D4311yescharacteristic
472C24—861no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8C2×C4×D4312yes—
484C2×Q8C2×C4×D4312yes—
485C2×D4—432no—
486C2×D4—432no—
487C2×D4—432no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—861no—
496C22×C4—864no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—3441no—
500C22×C4—3441no—
501C22×C4—3441no—
502C22×C4—3441no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4C2×C22⋊D4311yescharacteristic
508C22×C4C2×C22⋊D4311yescharacteristic
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C2×C22⋊D4311yescharacteristic
511C22×C4C2×C22⋊D4311yescharacteristic
512C22×C4C2×C22⋊D4311yescharacteristic
513C22×C4C23×D4311yescharacteristic
514SD16—868no—
515SD16—868no—
516C2×C8—432no—
517C2×C8—432no—
518C2×C8—432no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—41no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—432no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—3441no—
544C4⋊C4—3441no—
545C4⋊C4D4×D4312yes—
546C22⋊C4—864no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—42no—
555C42—42no—
556C42C2×C4×D4312yes—
557C42#1062189812yes—
558C23—862no—
559C23—862no—
560C23—862no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23C22×C22⋊D4311yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—41no—
574D4—434no—
575D4—862no—
576D4—862no—
577D4—862no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—862no—
606C2×C4—3444no—
607C2×C4—3444no—
608C2×C4—3444no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4C4×C22⋊D4312yes—
618C2×C4C4×C22⋊D4312yes—
619C2×C4#1306335612yes—
620C2×C4C22×C4×D4311yescharacteristic
621C2×C4C2×D4×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4C2×#1062189811yescharacteristic
624C2×C4#1306337011yescharacteristic
625C2×C4#1306337211yescharacteristic
626C8—862no—
627C8—862no—
628C8—862no—
629C8—1721no—
630C22—864no—
631C22—1722no—
632C22—1722no—
633C22—1722no—
634C22—1722no—
635C22—1722no—
636C22—1722no—
637C22C2×C4×C22⋊D4311yescharacteristic
638C22D4×C22⋊D4311yescharacteristic
639C22#1458355611yescharacteristic
640C22C2×#1306335611yescharacteristic
641C22#1458369711yescharacteristic
642C22#1458370711yescharacteristic
643C22#1458370711yescharacteristic
644C4—22no—
645C4—22no—
646C4—22no—
647C4—42no—
648C4—42no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—42no—
653C4—81no—
654C4—3441no—
655C4—3441no—
656C4—1722no—
657C4C4×D4×D4311yescharacteristic
658C4#1458337811yescharacteristic
659C4#1458355411yescharacteristic
660C4#1458359911yescharacteristic
661C2—1724no—
662C2#1913760711yescharacteristic
663C2C4×#1306335611yescharacteristic
664C2#1914345411yescharacteristic
665C2#1914610611yescharacteristic
666C2#1914612111yescharacteristic
667C2#1914737211yescharacteristic
668C2#1914741611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2365C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#2365D43
hypocenterC43#23012
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
5. #19135416C2semidirect
6. #19135363C2semidirect
7. #19135288C2semidirect
8. #19135274C2semidirect
11. #19134863C2semidirect
12. #19134849C2semidirect
13. #19134470C2semidirect
15. C43×#2365C2semidirect
21. #14583101C4semidirect
92. C4⋊(C43⋊C8)C2×C4semidirect
97. #13063249C2×C4semidirect
98. #13063249C2×C4semidirect
111. C4⋊Q8×C43C2×C4semidirect
330. #2365D43semidirect
396. C43#23012semidirect
414. C4⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831012
C2×#145829972
C2×C4×#106218842
#191375062
#191354162
#191353632
#191352882
#191352742
#191349322
#191348632
#191348492
#191344702
#191344232
C43×#23652
#2301243