Finite Group Databasebeta

← #25156751

Subgroups — #25156751

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583101C211yesmaximal, characteristic
2C2×C4×#10621884C211yesmaximal, characteristic
3#19137506C211yesmaximal, characteristic
4#19136143C211yesmaximal, characteristic, complemented
5#19136096C211yesmaximal, characteristic, complemented
6#19136013C211yesmaximal, characteristic, complemented
7#19135838C211yesmaximal, characteristic, complemented
8#19135274C211yesmaximal, characteristic, complemented
9#19135154C211yesmaximal, characteristic, complemented
10#19134932C211yesmaximal, characteristic
11#19134932C211yesmaximal, characteristic
12#19134932C211yesmaximal, characteristic
13#19134849C211yesmaximal, characteristic, complemented
14#19134841C211yesmaximal, characteristic
15C43×#2446C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583101—24no—
22C4×#10621884—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582770—21no—
38#14582770—21no—
39#14582765C2211yescharacteristic
40#14582758—21no—
41#95×D43—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C4⋊Q8×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C43×#400—21no—
53C43×#398—21no—
54C43×#391C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#387—21no—
59C43×#387—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884D414yes—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C4×D172—22no—
76C4×D172—22no—
77C4×D172—22no—
78C4×D172—22no—
79C4×D172—41no—
80C4×D172—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89#13063258—41no—
90#13063256—22no—
91C4⋊(C43⋊C8)—22no—
92#13063249—22no—
93#13063249—22no—
94#13063249—22no—
95#13063249—22no—
96#13063249—22no—
97#13063249—41no—
98#13063245—22no—
99#13063245—22no—
100C4×C43⋊C8—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C22×Q8×C43C2311yescharacteristic
106C22×Q8×C43C2311yescharacteristic
107C4⋊Q8×C43—22no—
108C4⋊Q8×C43—41no—
109C4×Q8×C43—22no—
110C4×Q8×C43—41no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43D411yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43D411yescharacteristic
131#95×C43D411yescharacteristic
132C23×D43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—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×C43C2×D412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172C2×D412yes—
163C2×D172#4112yes—
164C2×D172#4112yes—
165C2×C4×D43—24no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—81no—
171C2×C4×D43—81no—
172C2×C4×D43—81no—
173C2×C4×D43—81no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—42no—
183C4⋊C4×C43—42no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—42no—
191#10621884—28no—
192#10621884—44no—
193(C2×D43)⋊C4—24no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43#4112yes—
202Dic43⋊C4—81no—
203Dic43⋊C4—81no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8C2×D412yes—
216C23×C43C22×D411yescharacteristic
217C22×D43—22no—
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224Q8×C43—22no—
225Q8×C43—22no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—41no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43#13512yes—
261C2×C4×C43#13712yes—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×Dic43—22no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277D172—22no—
278D172—22no—
279D172—22no—
280D172#12314yes—
281C4×D43—84no—
282C4×D43—84no—
283C4×D43—84no—
284C43⋊C8—22no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288#26170—431nomaximal, Sylow
289C22×C43#52511yescharacteristic
290C22×C43D4211yescharacteristic
291C22×C43#54811yescharacteristic
292C22×C43C2×#13511yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57711yescharacteristic
296C2×D43—24no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C4×C43—22no—
304C4×C43—22no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—42no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43C2×#12311yescharacteristic
314C4×C43#53911yescharacteristic
315C4×C43#54711yescharacteristic
316C4×C43#55311yescharacteristic
317Dic43—42no—
318Dic43—81no—
319Dic43—81no—
320C2×#461—431no—
321C2×C4×SD16—431no—
322#2446D4311yescharacteristic, complemented
323#2349—431no—
324#2097—431no—
325#2088—431no—
326#2074—431no—
327#2043—431no—
328#1933—431no—
329#1916—431no—
330#1877—431no—
331#1877—431no—
332#1877—431no—
333#1863—431no—
334#1862—431no—
335C2×C43#244311yescharacteristic
336C2×C43#310711yescharacteristic
337C2×C43#312311yescharacteristic
338C2×C43#326611yescharacteristic
339C2×C43#328211yescharacteristic
340C2×C43#336011yescharacteristic
341C2×C43#337211yescharacteristic
342D43—44no—
343C22×SD16—431no—
344C22×SD16—431no—
345C2×C4⋊Q8C2×D4311yescharacteristic
346C2×C4×Q8C2×D4311yescharacteristic
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349C2×C4×D4—431no—
350#461—864no—
351C4×SD16—864no—
352C2×#107—431no—
353C2×#106—431no—
354C2×C4⋊C8—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×C4×C8—431no—
364#400—21no—
365#398—21no—
366#391C2×D4311yescharacteristic
367#391C2×D4311yescharacteristic
368#391C2×D4311yescharacteristic
369#389—431no—
370#389—431no—
371#389C2×D4311yescharacteristic
372#387—21no—
373#387—21no—
374#385—861no—
375#385—861no—
376#382—431no—
377#380—861no—
378C4×C4⋊C4C2×D4311yescharacteristic
379C2×#95—861no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#336—431no—
385#336—431no—
386#336—431no—
387#336—431no—
388C43#2617011yescharacteristic, complemented, Sylow
389C22×Q8C22×D4311yescharacteristic
390C22×Q8C22×D4311yescharacteristic
391C22×D4—431no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C2×SD16—434no—
396C2×SD16—862no—
397C2×SD16—862no—
398C2×SD16—862no—
399C2×SD16—862no—
400C2×SD16—862no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—431no—
405C4⋊Q8—22no—
406C4⋊Q8—41no—
407C4×Q8—22no—
408C4×Q8—41no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—862no—
412C4×D4—862no—
413C4×D4—1721no—
414C4×D4—1721no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4C22⋊D4311yescharacteristic
425C2×C4⋊C4C22⋊D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C42—21no—
432C2×C42C22×D4311yescharacteristic
433C2×C42C22×D4311yescharacteristic
434C2×C42C22×D4311yescharacteristic
435#107—1721no—
436#106—862no—
437C4⋊C8—862no—
438#103—862no—
439#103—862no—
440#103—862no—
441#103—862no—
442#103—862no—
443#103—1721no—
444#102—862no—
445#102—862no—
446C4×C8—862no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95C22⋊D4311yescharacteristic
459#95C22⋊D4311yescharacteristic
460C24—861no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8D4×D4312yes—
473C2×D4—432no—
474C2×D4—432no—
475C2×D4—432no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—864no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—3441no—
488C22×C4—3441no—
489C22×C4—3441no—
490C22×C4—3441no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C2×C22⋊D4311yescharacteristic
497C22×C4C2×C22⋊D4311yescharacteristic
498C22×C4C2×C22⋊D4311yescharacteristic
499C22×C4C2×C22⋊D4311yescharacteristic
500C22×C4C2×C22⋊D4311yescharacteristic
501C22×C4C23×D4311yescharacteristic
502SD16—868no—
503SD16—1724no—
504C2×C8—432no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—432no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—3441no—
533C4⋊C4—3441no—
534C22⋊C4—864no—
535C22⋊C4—1722no—
536C22⋊C4—1722no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—42no—
544C23—862no—
545C23—862no—
546C23—862no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23C22×C22⋊D4311yescharacteristic
552Q8—22no—
553Q8—22no—
554Q8—41no—
555Q8—41no—
556Q8—41no—
557Q8—41no—
558Q8—41no—
559Q8—41no—
560D4—434no—
561D4—862no—
562D4—862no—
563D4—862no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—862no—
593C2×C4—3444no—
594C2×C4—3444no—
595C2×C4—3444no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4#1306334512yes—
605C2×C4#1306335612yes—
606C2×C4C2×D4×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#1306337011yescharacteristic
611C2×C4#1306337211yescharacteristic
612C8—862no—
613C8—1721no—
614C8—1721no—
615C8—1721no—
616C22—864no—
617C22—1722no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22—1722no—
623C22#1458340611yescharacteristic
624C22D4×C22⋊D4311yescharacteristic
625C22#1458355611yescharacteristic
626C22C2×#1306334511yescharacteristic
627C22C2×#1306335611yescharacteristic
628C22#1458370711yescharacteristic
629C22#1458370711yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—81no—
640C4—3441no—
641C4—3441no—
642C4—1722no—
643C4#123×D4311yescharacteristic
644C4#1458349211yescharacteristic
645C4#1458354711yescharacteristic
646C4#1458359411yescharacteristic
647C2—1724no—
648C2#1913832711yescharacteristic
649C2#1914466011yescharacteristic
650C2#1914484211yescharacteristic
651C2#1914610611yescharacteristic
652C2#1914630311yescharacteristic
653C2#1914724011yescharacteristic
654C2#1914737211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2446C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2446D43
hypocenterC43#26170
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2446

Complements

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

NH ≅ G/Ntype
4. #19136143C2semidirect
5. #19136096C2semidirect
6. #19136013C2semidirect
7. #19135838C2semidirect
8. #19135274C2semidirect
9. #19135154C2semidirect
13. #19134849C2semidirect
15. C43×#2446C2semidirect
322. #2446D43semidirect
388. C43#26170semidirect

Maximal subgroups

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

subgroupindex
C2×#145831012
C2×C4×#106218842
#191375062
#191361432
#191360962
#191360132
#191358382
#191352742
#191351542
#191349322
#191348492
#191348412
C43×#24462
#2617043