Finite Group Databasebeta

← #25067710

Subgroups — #25067710

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143615C211yesmaximal, characteristic, complemented
2#19143339C211yesmaximal, characteristic, complemented
3#19133509C211yesmaximal, characteristic, complemented
4#19133480C211yesmaximal, characteristic, complemented
5#19133474C211yesmaximal, characteristic, complemented
6#19133460C211yesmaximal, characteristic, complemented
7#19133439C211yesmaximal, characteristic, complemented
8#19133425C211yesmaximal, characteristic, complemented
9SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
10SD16×C43⋊C8C211yesmaximal, characteristic, complemented
11#19133380C211yesmaximal, characteristic, complemented
12#19133064C211yesmaximal, characteristic, complemented
13#19132982C211yesmaximal, characteristic, complemented
14#19132890C211yesmaximal, characteristic, complemented
15C43×#3106C211yesmaximal, characteristic
16C2×#13063332—21no—
17Q8×C43⋊C8C2211yescharacteristic
18Q8×C43⋊C8C2211yescharacteristic
19#14582977—21no—
20#14582977—21no—
21#14582977C2211yescharacteristic
22#14582977C2211yescharacteristic
23#14582977C2211yescharacteristic
24#14582977C2211yescharacteristic
25#14582971—21no—
26#14582971—21no—
27D4×C43⋊C8C2211yescharacteristic
28D4×C43⋊C8C2211yescharacteristic
29#14582956—21no—
30#14582956C2211yescharacteristic
31#14582952C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582866—21no—
34C4×#10621877—21no—
35C4×#10621877C2211yescharacteristic
36#14582652C2211yescharacteristic
37#14582652C2211yescharacteristic
38#14582650C2211yescharacteristic
39#14582650C2211yescharacteristic
40Q8⋊(C43⋊C8)C2211yescharacteristic
41Q8⋊(C43⋊C8)C2211yescharacteristic
42D4⋊(C43⋊C8)C2211yescharacteristic
43D4⋊(C43⋊C8)C2211yescharacteristic
44D4⋊(C43⋊C8)C2211yescharacteristic
45D4⋊(C43⋊C8)C2211yescharacteristic
46D4⋊(C43⋊C8)C2211yescharacteristic
47D4⋊(C43⋊C8)C2211yescharacteristic
48#14582621C2211yescharacteristic
49#14582621C2211yescharacteristic
50#14582620C2211yescharacteristic
51C8×C43⋊C8C2211yescharacteristic
52C43×#532C2211yescharacteristic
53C4×#41×C43C2211yescharacteristic
54C43×#482C411yescharacteristic
55C43×#482C411yescharacteristic
56C43×#477C411yescharacteristic
57C43×#476C411yescharacteristic
58C43×#460C411yescharacteristic
59C43×#459C411yescharacteristic
60C43×#449C411yescharacteristic
61C43×#449C411yescharacteristic
62C4×SD16×C43C2211yescharacteristic
63C4×SD16×C43C2211yescharacteristic
64C4×D8×C43C2211yescharacteristic
65C4×D8×C43C2211yescharacteristic
66C43×#431C2211yescharacteristic
67#13063332—44no—
68C2×#10621877—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C2×#10621877—21no—
72C2×#10621877D411yescharacteristic
73C2×#10621877D411yescharacteristic
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)—21no—
79C4⋊(C43⋊C8)—21no—
80C4⋊(C43⋊C8)—21no—
81C4⋊(C43⋊C8)C2311yescharacteristic
82C4⋊(C43⋊C8)C2311yescharacteristic
83C4⋊(C43⋊C8)C2311yescharacteristic
84C4⋊(C43⋊C8)C2311yescharacteristic
85C22⋊(C43⋊C8)—21no—
86C22⋊(C43⋊C8)—21no—
87C22⋊(C43⋊C8)—21no—
88C22⋊(C43⋊C8)—21no—
89C22⋊(C43⋊C8)—21no—
90C22⋊(C43⋊C8)—21no—
91C22⋊(C43⋊C8)—21no—
92C22⋊(C43⋊C8)—21no—
93#13063236—21no—
94#13063236D411yescharacteristic
95#13063236D411yescharacteristic
96C4×C43⋊C8—21no—
97C4×C43⋊C8—21no—
98C4×C43⋊C8C2311yescharacteristic
99C4×C43⋊C8C2311yescharacteristic
100C4×C43⋊C8C2311yescharacteristic
101C4×C43⋊C8C2311yescharacteristic
102C2×#41×C43—21no—
103C2×#41×C43C2×C411yescharacteristic
104C2×SD16×C43C2×C411yescharacteristic
105C2×SD16×C43C2×C411yescharacteristic
106C2×D8×C43C2×C411yescharacteristic
107C2×D8×C43C2×C411yescharacteristic
108C4⋊Q8×C43C2×C411yescharacteristic
109#127×C43C2×C411yescharacteristic
110#124×C43—21no—
111#121×C43—21no—
112#121×C43C2×C411yescharacteristic
113#121×C43C2×C411yescharacteristic
114C4×Q8×C43C2×C411yescharacteristic
115C4×Q8×C43C2311yescharacteristic
116C4×D4×C43—21no—
117C4×D4×C43—21no—
118C4×D4×C43—21no—
119C4×D4×C43C2×C411yescharacteristic
120C4×D4×C43C2311yescharacteristic
121C4×D4×C43C2311yescharacteristic
122C4×D4×C43C2311yescharacteristic
123#117×C43—21no—
124#117×C43C2×C411yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#107×C43C2×C411yescharacteristic
128#107×C43C2×C411yescharacteristic
129#106×C43C2×C411yescharacteristic
130#106×C43C2×C411yescharacteristic
131C4⋊C8×C43C2×C411yescharacteristic
132C4⋊C8×C43C2×C411yescharacteristic
133#103×C43C2×C411yescharacteristic
134#103×C43C2×C411yescharacteristic
135#102×C43C2×C411yescharacteristic
136#102×C43C2×C411yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140#102×C43C2×C411yescharacteristic
141C22⋊C8×C43C2×C411yescharacteristic
142C22⋊C8×C43C2×C411yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—22no—
146#41×C43—41no—
147#41×C43—42no—
148#41×C43—42no—
149C2×Q8×C43—21no—
150C2×Q8×C43C22×C411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43C22×C411yescharacteristic
157C2×D4×C43C22×C411yescharacteristic
158C2×D4×C43C22×C411yescharacteristic
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43C22×C411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43#4111yescharacteristic
167SD16×C43—22no—
168SD16×C43—22no—
169D8×C43—41no—
170D8×C43—41no—
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C22×C411yescharacteristic
173C2×C8×C43C22×C411yescharacteristic
174C2×C8×C43C22×C411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C22×C411yescharacteristic
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C4⋊C4×C43C22×C411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43C22×C411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43#4111yescharacteristic
195C42×C43C2411yescharacteristic
196#10621877—22no—
197#10621877—41no—
198#10621877—42no—
199#10621877—42no—
200#10621877—42no—
201#10621877—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—42no—
209C2×C43⋊C8—42no—
210C2×C43⋊C8—42no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43C4×D411yescharacteristic
219Q8×C43—21no—
220Q8×C43—42no—
221Q8×C43#13112yescomplemented
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—42no—
229D4×C43—42no—
230D4×C43—42no—
231D4×C43—42no—
232D4×C43—81no—
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—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—42no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—81no—
251C2×C4×C43C4×D411yescharacteristic
252C2×C4×C43C4×D411yescharacteristic
253C2×C4×C43C4×D411yescharacteristic
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—21no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8AGL(1,ℤ/8)12yes—
271#18011—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43C2×C4×D411yescharacteristic
285C4×C43—21no—
286C4×C43—22no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43C2×#13111yescharacteristic
295C4×C43#56811yescharacteristic
296C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
297C4×C43#57511yescharacteristic
298#3106D4311yescharacteristic
299#2971—431no—
300#2935—431no—
301#1594—431no—
302#1589—431no—
303#1588—431no—
304#1586—431no—
305#1583—431no—
306#1581—431no—
307SD16⋊C8—431no—
308C8×SD16—431no—
309#1573—431no—
310#1496—431no—
311#1477—431no—
312#1453—431no—
313C2×C43—41no—
314C2×C43—81no—
315C2×C43—81no—
316C2×C43—81no—
317C2×C43#293311yescharacteristic
318C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
319C2×C43#295711yescharacteristic
320C2×#131—861no—
321#532C2×D4311yescharacteristic
322C4×#41C2×D4311yescharacteristic
323#482Dic4311yescharacteristic
324#482Dic4311yescharacteristic
325#477Dic4311yescharacteristic
326#476Dic4311yescharacteristic
327#460Dic4311yescharacteristic
328#459Dic4311yescharacteristic
329#449Dic4311yescharacteristic
330#449Dic4311yescharacteristic
331C8×Q8—431no—
332C8×Q8—431no—
333C4×SD16C2×D4311yescharacteristic
334C4×SD16C2×D4311yescharacteristic
335C4×D8C2×D4311yescharacteristic
336C4×D8C2×D4311yescharacteristic
337#436—431no—
338#436—431no—
339#436—431no—
340#436—431no—
341#436—861no—
342#436—861no—
343#435—861no—
344#435—861no—
345C8×D4—431no—
346C8×D4—431no—
347#432—431no—
348#432—861no—
349#431—431no—
350#431C2×D4311yescharacteristic
351C2×C4⋊C8—431no—
352#408—861no—
353C4×M16—431no—
354C4×M16—861no—
355#335—431no—
356#335—431no—
357#334—431no—
358#334—431no—
359Q8⋊C8—431no—
360Q8⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366D4⋊C8—431no—
367#322—431no—
368#322—431no—
369#322—431no—
370C82—431no—
371C43#1801111yescharacteristic, complemented, Sylow
372C2×#41—21no—
373C2×#41C2×Dic4311yescharacteristic
374C2×SD16C2×Dic4311yescharacteristic
375C2×SD16C2×Dic4311yescharacteristic
376C2×D8C2×Dic4311yescharacteristic
377C2×D8C2×Dic4311yescharacteristic
378#131—1724no—
379C2×M16—431no—
380C2×M16—431no—
381C2×M16—861no—
382C2×M16—861no—
383C2×M16—861no—
384C2×M16—861no—
385C22×C8—861no—
386C22×C8—861no—
387C22×C8—861no—
388C4⋊Q8C2×Dic4311yescharacteristic
389#127C2×Dic4311yescharacteristic
390#124—21no—
391#121—21no—
392#121C2×Dic4311yescharacteristic
393#121C2×Dic4311yescharacteristic
394C4×Q8C2×Dic4311yescharacteristic
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4C2×Dic4311yescharacteristic
400C4×D4C22×D4311yescharacteristic
401C4×D4C22×D4311yescharacteristic
402C4×D4C22×D4311yescharacteristic
403#117—21no—
404#117C2×Dic4311yescharacteristic
405C2×C42—21no—
406C2×C42C22×D4311yescharacteristic
407#107C2×Dic4311yescharacteristic
408#107C2×Dic4311yescharacteristic
409#106C2×Dic4311yescharacteristic
410#106C2×Dic4311yescharacteristic
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419C4⋊C8C2×Dic4311yescharacteristic
420C4⋊C8C2×Dic4311yescharacteristic
421#103C2×Dic4311yescharacteristic
422#103C2×Dic4311yescharacteristic
423#102C2×Dic4311yescharacteristic
424#102C2×Dic4311yescharacteristic
425#102C2×Dic4311yescharacteristic
426#102C2×Dic4311yescharacteristic
427#102C2×Dic4311yescharacteristic
428#102C2×Dic4311yescharacteristic
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8C2×Dic4311yescharacteristic
438C22⋊C8C2×Dic4311yescharacteristic
439#97—431no—
440#97—431no—
441#97—861no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—861no—
447C4×C8—861no—
448C4×C8C22×D4311yescharacteristic
449C4×C8C22×D4311yescharacteristic
450#41—22no—
451#41—41no—
452#41—42no—
453#41—42no—
454C2×Q8—21no—
455C2×Q8C22×Dic4311yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4C22×Dic4311yescharacteristic
462C2×D4C22×Dic4311yescharacteristic
463C2×D4C22×Dic4311yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4D4×D4311yescharacteristic
470C22×C4#1062190011yescharacteristic
471C22×C4C22×Dic4311yescharacteristic
472SD16—22no—
473SD16—22no—
474D8—41no—
475D8—41no—
476M16—862no—
477M16—1722no—
478M16—1722no—
479M16—1721no—
480M16—1722no—
481M16—1722no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—1722no—
493C2×C8—1722no—
494C2×C8—1722no—
495C2×C8C22×Dic4311yescharacteristic
496C2×C8C22×Dic4311yescharacteristic
497C2×C8C22×Dic4311yescharacteristic
498C2×C8C22×Dic4311yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4C22×Dic4311yescharacteristic
503C4⋊C4C22×Dic4311yescharacteristic
504C4⋊C4C22×Dic4311yescharacteristic
505C4⋊C4C22×Dic4311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42D4×D4311yescharacteristic
517C42#1062190011yescharacteristic
518C42C22×Dic4311yescharacteristic
519C42C23×D4311yescharacteristic
520C23—21no—
521C23—21no—
522C23—21no—
523C23D4×Dic4311yescharacteristic
524Q8—21no—
525Q8—42no—
526Q8#1306333212yescomplemented
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—81no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—81no—
556C2×C4D4×Dic4311yescharacteristic
557C2×C4D4×Dic4311yescharacteristic
558C2×C4D4×Dic4311yescharacteristic
559C2×C4C23×Dic4311yescharacteristic
560C2×C4C2×D4×D4311yescharacteristic
561C2×C4C2×#1062190011yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—432no—
567C8—861no—
568C8—861no—
569C8—861no—
570C8—1721no—
571C8—1721no—
572C8—1721no—
573C8—1721no—
574C8—1721no—
575C8—1721no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22C2×D4×Dic4311yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—22no—
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4C2×#1306333211yescharacteristic
599C4#1458366611yescharacteristic
600C4AGL(1,ℤ/8)×D4311yescharacteristic
601C4#1458369511yescharacteristic
602C2—41no—
603C2—81no—
604C2—81no—
605C2—81no—
606C2#1914332211yescharacteristic
607C2AGL(1,ℤ/8)×Dic4311yescharacteristic
608C2#1914351211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
Fitting, prime radicalC43×#3106C2
socleC22×C43C2×C4×D4
cosocleC42×C43C24
hypercenter#3106D43
hypocenterC43#18011
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #19143615C2semidirect
2. #19143339C2semidirect
3. #19133509C2semidirect
4. #19133480C2semidirect
5. #19133474C2semidirect
6. #19133460C2semidirect
7. #19133439C2semidirect
8. #19133425C2semidirect
9. SD16⋊(C43⋊C8)C2semidirect
10. SD16×C43⋊C8C2semidirect
11. #19133380C2semidirect
12. #19133064C2semidirect
13. #19132982C2semidirect
14. #19132890C2semidirect
221. Q8×C43#131semidirect
371. C43#18011semidirect
526. Q8#13063332semidirect

Maximal subgroups

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

subgroupindex
#191436152
#191433392
#191335092
#191334802
#191334742
#191334602
#191334392
#191334252
SD16⋊(C43⋊C8)2
SD16×C43⋊C82
#191333802
#191330642
#191329822
#191328902
C43×#31062
#1801143