Finite Group Databasebeta

← #25156619

Subgroups — #25156619

Order 11008.

840 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583121C211yesmaximal, characteristic
2C2×C4×#10621884C211yesmaximal, characteristic
3#19138382C211yesmaximal, characteristic
4#19136139C211yesmaximal, characteristic, complemented
5#19136096C211yesmaximal, characteristic, complemented
6#19135999C211yesmaximal, characteristic
7#19135836C211yesmaximal, characteristic
8#19135270C211yesmaximal, characteristic, complemented
9#19135154C211yesmaximal, characteristic, complemented
10#19134950C211yesmaximal, characteristic
11#19134936C211yesmaximal, characteristic, complemented
12#19134936C211yesmaximal, characteristic, complemented
13#19134863C211yesmaximal, characteristic, complemented
14#19134855C211yesmaximal, characteristic
15Q8×C4⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20#14583121—24no—
21C4×#10621884—24no—
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582828—21no—
35#14582825—21no—
36#14582805C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582770—21no—
41#14582761—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
52C2×C4×Q8×C43C2211yescharacteristic
53C43×#389—21no—
54C43×#389—21no—
55C43×#389C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#384—21no—
58C43×#384C2211yescharacteristic
59C4×C4⋊C4×C43—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885—22no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884D414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063313—22no—
75#13063313—41no—
76C4×D172—22no—
77C4×D172—41no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86#13063256—22no—
87#13063256—41no—
88C4⋊(C43⋊C8)—22no—
89#13063249—22no—
90#13063249—22no—
91#13063248—22no—
92#13063248—22no—
93#13063248—41no—
94#13063245—22no—
95#13063245—22no—
96#13063245—22no—
97C4×C43⋊C8—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×Q8×C43C2311yescharacteristic
104C4×Q8×C43—22no—
105C4×Q8×C43—22no—
106C4×Q8×C43—22no—
107C4×Q8×C43—22no—
108C4×Q8×C43—41no—
109C4×Q8×C43—41no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43D411yescharacteristic
118C2×C4⋊C4×C43D411yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43—21no—
123C2×C42×C43—21no—
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
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×C43C2×D412yes—
137C2×Q8×C43#4112yes—
138C2×Q8×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172C2×D412yes—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C4⋊C4×C43—24no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—81no—
180C4⋊C4×C43—81no—
181C4⋊C4×C43—81no—
182C4⋊C4×C43#4112yes—
183C42×C43—24no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—42no—
191C42×C43—42no—
192#10621885—44no—
193#10621884—28no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—81no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
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—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224Q8×C43—22no—
225Q8×C43—22no—
226Q8×C43—22no—
227Q8×C43#12314yes—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
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—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—41no—
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#13512yes—
257C2×C4×C43#13712yes—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273D172—22no—
274D172—22no—
275D172—41no—
276D172—41no—
277C4×D43—84no—
278Dic86—41no—
279Dic86—41no—
280Dic86—41no—
281Dic86—41no—
282C43⋊C8—22no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#26161—431nomaximal, Sylow
287C22×C43#52511yescharacteristic
288C22×C43D4211yescharacteristic
289C22×C43#54811yescharacteristic
290C22×C43C2×#13511yescharacteristic
291C22×C43C2×#13711yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57711yescharacteristic
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—22no—
302C4×C43—24no—
303C4×C43—22no—
304C4×C43—41no—
305C4×C43—42no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43C2×#12311yescharacteristic
312C4×C43#53911yescharacteristic
313C4×C43#54711yescharacteristic
314C4×C43#55311yescharacteristic
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318C2×#464—431no—
319C2×C4×SD16—431no—
320#2447—431no—
321Q8×C4⋊C4D4311yescharacteristic, complemented
322#2096—431no—
323#2088—431no—
324#2071—431no—
325#2042—431no—
326#1933—431no—
327#1916—431no—
328#1880—431no—
329#1878—431no—
330#1878—431no—
331#1865—431no—
332#1864—431no—
333C2×C43#244311yescharacteristic
334C2×C43#310811yescharacteristic
335C2×C43#312511yescharacteristic
336C2×C43#326611yescharacteristic
337C2×C43#328411yescharacteristic
338C2×C43#336511yescharacteristic
339C2×C43#336911yescharacteristic
340D43—82no—
341C22×Q16—431no—
342C22×SD16—431no—
343C2×#124—431no—
344C2×C4×Q8C2×D4311yescharacteristic
345C2×C4×Q8C2×D4311yescharacteristic
346C2×C4×Q8C2×D4311yescharacteristic
347C2×C4×D4—431no—
348#464—864no—
349C4×SD16—864no—
350C2×#106—431no—
351C2×#106—431no—
352C2×C4⋊C8—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×C4×C8—431no—
362#397—861no—
363#397—861no—
364#391—431no—
365#391—431no—
366#390—431no—
367#389—21no—
368#389—21no—
369#389—431no—
370#389C2×D4311yescharacteristic
371#389C2×D4311yescharacteristic
372#385—861no—
373#384—21no—
374#384C2×D4311yescharacteristic
375#381—861no—
376C4×C4⋊C4—21no—
377C4×C4⋊C4C2×D4311yescharacteristic
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#336—431no—
383#336—431no—
384#336—431no—
385#336—431no—
386C43#2616111yescharacteristic, complemented, Sylow
387C22×Q8—431no—
388C22×Q8C22×D4311yescharacteristic
389C22×D4—431no—
390C23×C4—861no—
391C2×Q16—862no—
392C2×Q16—862no—
393C2×Q16—862no—
394C2×SD16—434no—
395C2×SD16—862no—
396C2×SD16—862no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8—431no—
401#124—862no—
402#124—1721no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—22no—
407C4×Q8—41no—
408C4×Q8—41no—
409C4×D4—862no—
410C4×D4—1721no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4C22⋊D4311yescharacteristic
422C2×C4⋊C4C22⋊D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42C22×D4311yescharacteristic
435C2×C42C22×D4311yescharacteristic
436C2×C42C22×D4311yescharacteristic
437#106—862no—
438#106—1721no—
439C4⋊C8—862no—
440#103—862no—
441#103—862no—
442#103—862no—
443#103—862no—
444#103—1721no—
445#102—862no—
446#102—862no—
447#102—862no—
448C4×C8—862no—
449#95—21no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95C22⋊D4311yescharacteristic
457#95C22⋊D4311yescharacteristic
458C24—861no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8#1062189812yes—
469C2×Q8D4×D4312yes—
470C2×Q8#1062190212yes—
471C2×D4—432no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—3441no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4C2×C22⋊D4311yescharacteristic
488C22×C4C2×C22⋊D4311yescharacteristic
489C22×C4C2×C22⋊D4311yescharacteristic
490C22×C4C2×C22⋊D4311yescharacteristic
491C22×C4C2×C22⋊D4311yescharacteristic
492C22×C4C2×C22⋊D4311yescharacteristic
493C22×C4C23×D4311yescharacteristic
494Q16—1724no—
495SD16—868no—
496C2×C8—432no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—81no—
520C4⋊C4—81no—
521C4⋊C4—81no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—3441no—
527C4⋊C4#1062189812yes—
528C22⋊C4—3441no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C42—24no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—42no—
541C42—42no—
542C23—862no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23C22×C22⋊D4311yescharacteristic
550Q8—22no—
551Q8—22no—
552Q8—22no—
553Q8—1721no—
554Q8—1721no—
555Q8—1721no—
556Q8—1721no—
557Q8#1306331014yes—
558D4—862no—
559D4—862no—
560D4—1721no—
561D4—1721no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—22no—
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—21no—
581C2×C4—21no—
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—3444no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4#1306334512yes—
601C2×C4#1306335612yes—
602C2×C4C2×D4×D4311yescharacteristic
603C2×C4C2×#1062189811yescharacteristic
604C2×C4C2×#1062189811yescharacteristic
605C2×C4C2×#1062190211yescharacteristic
606C2×C4#1306337011yescharacteristic
607C2×C4#1306337311yescharacteristic
608C8—862no—
609C8—1721no—
610C8—1721no—
611C8—1721no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22#1458341011yescharacteristic
620C22D4×C22⋊D4311yescharacteristic
621C22#1458356011yescharacteristic
622C22C2×#1306334511yescharacteristic
623C22C2×#1306335611yescharacteristic
624C22#1458370711yescharacteristic
625C22#1458371011yescharacteristic
626C4—24no—
627C4—22no—
628C4—22no—
629C4—41no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—3441no—
637C4—3441no—
638C4—3441no—
639C4C2×#1306331011yescharacteristic
640C4#1458349611yescharacteristic
641C4#1458355011yescharacteristic
642C4#1458359711yescharacteristic
643C2—3442no—
644C2#1913833011yescharacteristic
645C2#1914467511yescharacteristic
646C2#1914487211yescharacteristic
647C2#1914610611yescharacteristic
648C2#1914632511yescharacteristic
649C2#1914729111yescharacteristic
650C2#1914733511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingQ8×C4⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterQ8×C4⋊C4D43
hypocenterC43#26161
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #19136139C2semidirect
5. #19136096C2semidirect
8. #19135270C2semidirect
9. #19135154C2semidirect
11. #19134936C2semidirect
12. #19134936C2semidirect
13. #19134863C2semidirect
15. Q8×C4⋊C4×C43C2semidirect
321. Q8×C4⋊C4D43semidirect
386. C43#26161semidirect

Maximal subgroups

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

subgroupindex
C2×#145831212
C2×C4×#106218842
#191383822
#191361392
#191360962
#191359992
#191358362
#191352702
#191351542
#191349502
#191349362
#191348632
#191348552
Q8×C4⋊C4×C432
#2616143