Finite Group Databasebeta

← #25067665

Subgroups — #25067665

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143600C211yesmaximal, characteristic, complemented
2D4×#10621877C211yesmaximal, characteristic, complemented
3#19133498C211yesmaximal, characteristic, complemented
4#19133480C211yesmaximal, characteristic, complemented
5#19133460C211yesmaximal, characteristic, complemented
6#19133453C211yesmaximal, characteristic, complemented
7#19133439C211yesmaximal, characteristic, complemented
8#19133425C211yesmaximal, characteristic, complemented
9#19133419C211yesmaximal, characteristic, complemented
10SD16×C43⋊C8C211yesmaximal, characteristic, complemented
11#19133384C211yesmaximal, characteristic, complemented
12#19133060C211yesmaximal, characteristic, complemented
13#19132986C211yesmaximal, characteristic, complemented
14#19132890C211yesmaximal, characteristic, complemented
15C43×#3105C211yesmaximal, characteristic
16C22×#10621877—21no—
17#14583030C2211yescharacteristic, complemented
18Q8×C43⋊C8C2211yescharacteristic, complemented
19#14582977—21no—
20#14582977C2211yescharacteristic
21#14582977C2211yescharacteristic
22#14582977C2211yescharacteristic, complemented
23#14582971—21no—
24#14582971—21no—
25#14582971—21no—
26D4×C43⋊C8C2211yescharacteristic
27D4×C43⋊C8C2211yescharacteristic
28D4×C43⋊C8C2211yescharacteristic, complemented
29#14582960—21no—
30#14582952C2211yescharacteristic
31#14582952C2211yescharacteristic
32#14582923C2211yescharacteristic
33#14582863—21no—
34#14582855—21no—
35C4×#10621877C2211yescharacteristic
36#14582652C2211yescharacteristic, complemented
37#14582652C2211yescharacteristic, complemented
38#14582650C2211yescharacteristic, complemented
39#14582650C2211yescharacteristic, complemented
40Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
41Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
42D4⋊(C43⋊C8)C2211yescharacteristic
43D4⋊(C43⋊C8)C2211yescharacteristic
44D4⋊(C43⋊C8)C2211yescharacteristic
45D4⋊(C43⋊C8)C2211yescharacteristic
46D4⋊(C43⋊C8)C2211yescharacteristic, complemented
47D4⋊(C43⋊C8)C2211yescharacteristic, complemented
48#14582621C2211yescharacteristic, complemented
49#14582621C2211yescharacteristic, complemented
50#14582620C2211yescharacteristic, complemented
51C8×C43⋊C8C2211yescharacteristic, complemented
52C43×#529C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#484C411yescharacteristic
55C43×#481C411yescharacteristic
56C43×#478C411yescharacteristic
57C43×#478C411yescharacteristic
58C43×#463C411yescharacteristic
59C43×#463C411yescharacteristic
60C43×#450C411yescharacteristic
61C43×#447C411yescharacteristic
62C4×SD16×C43C2211yescharacteristic
63C4×SD16×C43C2211yescharacteristic
64C4×D8×C43C2211yescharacteristic
65C4×D8×C43C2211yescharacteristic
66C43×#431C2211yescharacteristic
67C2×#10621877—21no—
68C2×#10621877—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C2×#10621877—44no—
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
102C22×D4×C43C2×C411yescharacteristic
103C23×C4×C43—21no—
104C2×SD16×C43C2×C411yescharacteristic
105C2×SD16×C43C2×C411yescharacteristic
106C2×D8×C43C2×C411yescharacteristic
107C2×D8×C43C2×C411yescharacteristic
108#126×C43—21no—
109#125×C43C2×C411yescharacteristic
110#124×C43C2×C411yescharacteristic
111#123×C43—21no—
112C22⋊Q8×C43C2×C411yescharacteristic
113#121×C43C2×C411yescharacteristic
114C4×Q8×C43C2311yescharacteristic
115C4×D4×C43—21no—
116C4×D4×C43—21no—
117C4×D4×C43—21no—
118C4×D4×C43C2×C411yescharacteristic
119C4×D4×C43C2×C411yescharacteristic
120C4×D4×C43C2311yescharacteristic
121C4×D4×C43C2311yescharacteristic
122C4×D4×C43C2311yescharacteristic
123#117×C43—21no—
124C2×C4⋊C4×C43C2×C411yescharacteristic
125C2×C22⋊C4×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
145C24×C43—21no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—22no—
150C2×D4×C43—41no—
151C2×D4×C43C22×C411yescharacteristic
152C2×D4×C43C22×C411yescharacteristic
153C2×D4×C43C22×C411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43#4111yescharacteristic
165SD16×C43—22no—
166SD16×C43—41no—
167D8×C43—22no—
168D8×C43—41no—
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C22×C411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
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—
189C22⋊C4×C43—21no—
190C22⋊C4×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×C43—42no—
219C23×C43—42no—
220C23×C43—81no—
221C23×C43C4×D411yescharacteristic
222Q8×C43—21no—
223Q8×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—42no—
230D4×C43—81no—
231D4×C43#13112yes—
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—21no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
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#18008—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
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×C43—84no—
285C22×C43C2×C4×D411yescharacteristic
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43C2×#13111yescharacteristic
296C4×C43#56811yescharacteristic
297C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
298C4×C43#57511yescharacteristic
299#3105D4311yescharacteristic
300#2969—431no—
301D4×M16—431no—
302#1592—431no—
303#1589—431no—
304#1586—431no—
305#1585—431no—
306#1583—431no—
307#1581—431no—
308#1580—431no—
309C8×SD16—431no—
310#1574—431no—
311#1495—431no—
312#1478—431no—
313#1453—431no—
314C2×C43—41no—
315C2×C43—42no—
316C2×C43—81no—
317C2×C43—81no—
318C2×C43#293311yescharacteristic
319C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
320C2×C43#295711yescharacteristic
321C22×M16—861no—
322#529C2×D4311yescharacteristic
323C2×C4×D4C2×D4311yescharacteristic
324#484Dic4311yescharacteristic
325#481Dic4311yescharacteristic
326#478Dic4311yescharacteristic
327#478Dic4311yescharacteristic
328#463Dic4311yescharacteristic
329#463Dic4311yescharacteristic
330#450Dic4311yescharacteristic
331#447Dic4311yescharacteristic
332#446—431no—
333C8×Q8—431no—
334C4×SD16C2×D4311yescharacteristic
335C4×SD16C2×D4311yescharacteristic
336C4×D8C2×D4311yescharacteristic
337C4×D8C2×D4311yescharacteristic
338#436—431no—
339#436—431no—
340#436—431no—
341#436—861no—
342#435—861no—
343#435—861no—
344#435—861no—
345C8×D4—431no—
346C8×D4—431no—
347C8×D4—431no—
348#433—861no—
349#431—431no—
350#431—431no—
351#431C2×D4311yescharacteristic
352#423—431no—
353#407—861no—
354#405—861no—
355C4×M16—431no—
356#335—431no—
357#335—431no—
358#334—431no—
359#334—431no—
360Q8⋊C8—431no—
361Q8⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8—431no—
368#322—431no—
369#322—431no—
370#322—431no—
371C82—431no—
372C43#1800811yescharacteristic, complemented, Sylow
373C22×D4C2×Dic4311yescharacteristic
374C23×C4—21no—
375C2×SD16C2×Dic4311yescharacteristic
376C2×SD16C2×Dic4311yescharacteristic
377C2×D8C2×Dic4311yescharacteristic
378C2×D8C2×Dic4311yescharacteristic
379C2×M16—431no—
380C2×M16—431no—
381C2×M16—861no—
382C2×M16—861no—
383C2×M16—861no—
384C2×M16—861no—
385C2×M16—1724no—
386C22×C8—861no—
387C22×C8—861no—
388C22×C8—861no—
389#126—21no—
390#125C2×Dic4311yescharacteristic
391#124C2×Dic4311yescharacteristic
392#123—21no—
393C22⋊Q8C2×Dic4311yescharacteristic
394#121C2×Dic4311yescharacteristic
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4C2×Dic4311yescharacteristic
400C4×D4C2×Dic4311yescharacteristic
401C4×D4C22×D4311yescharacteristic
402C4×D4C22×D4311yescharacteristic
403C4×D4C22×D4311yescharacteristic
404#117—21no—
405C2×C4⋊C4C2×Dic4311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C42C22×D4311yescharacteristic
408#107C2×Dic4311yescharacteristic
409#107C2×Dic4311yescharacteristic
410#106C2×Dic4311yescharacteristic
411#106C2×Dic4311yescharacteristic
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8C2×Dic4311yescharacteristic
421C4⋊C8C2×Dic4311yescharacteristic
422#103C2×Dic4311yescharacteristic
423#103C2×Dic4311yescharacteristic
424#102C2×Dic4311yescharacteristic
425#102C2×Dic4311yescharacteristic
426#102C2×Dic4311yescharacteristic
427#102C2×Dic4311yescharacteristic
428#102C2×Dic4311yescharacteristic
429#102C2×Dic4311yescharacteristic
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8C2×Dic4311yescharacteristic
439C22⋊C8C2×Dic4311yescharacteristic
440#97—431no—
441#97—431no—
442#97—861no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8—861no—
448C4×C8—861no—
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451C24—21no—
452C2×Q8C22×Dic4311yescharacteristic
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—41no—
457C2×D4C22×Dic4311yescharacteristic
458C2×D4C22×Dic4311yescharacteristic
459C2×D4C22×Dic4311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4D4×D4311yescharacteristic
469C22×C4#1062190011yescharacteristic
470C22×C4C22×Dic4311yescharacteristic
471SD16—22no—
472SD16—41no—
473D8—22no—
474D8—41no—
475M16—862no—
476M16—1722no—
477M16—1722no—
478M16—1721no—
479M16—1722no—
480M16—1722no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—1722no—
492C2×C8—1722no—
493C2×C8—1722no—
494C2×C8C22×Dic4311yescharacteristic
495C2×C8C22×Dic4311yescharacteristic
496C2×C8C22×Dic4311yescharacteristic
497C2×C8C22×Dic4311yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4C22×Dic4311yescharacteristic
504C4⋊C4C22×Dic4311yescharacteristic
505C4⋊C4C22×Dic4311yescharacteristic
506C4⋊C4C22×Dic4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C42—21no—
517C42D4×D4311yescharacteristic
518C42#1062190011yescharacteristic
519C42C22×Dic4311yescharacteristic
520C42C23×D4311yescharacteristic
521C23—21no—
522C23—21no—
523C23—21no—
524C23—42no—
525C23—42no—
526C23—81no—
527C23D4×Dic4311yescharacteristic
528Q8—21no—
529Q8—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—42no—
536D4—81no—
537D4#1306333212yes—
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—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4D4×Dic4311yescharacteristic
558C2×C4D4×Dic4311yescharacteristic
559C2×C4D4×Dic4311yescharacteristic
560C2×C4C23×Dic4311yescharacteristic
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4C2×#1062190011yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—432no—
568C8—861no—
569C8—861no—
570C8—861no—
571C8—1721no—
572C8—1721no—
573C8—1721no—
574C8—1721no—
575C8—1721no—
576C8—1721no—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—84no—
590C22C2×D4×Dic4311yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4C2×#1306333211yescharacteristic
601C4#1458366611yescharacteristic
602C4AGL(1,ℤ/8)×D4311yescharacteristic
603C4#1458369511yescharacteristic
604C2—41no—
605C2—42no—
606C2—81no—
607C2—81no—
608C2#1914332211yescharacteristic
609C2AGL(1,ℤ/8)×Dic4311yescharacteristic
610C2#1914351211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#3105C2
socleC22×C43C2×C4×D4
prime radicalC43×#447C4
cosocleC42×C43C24
hypercenter#3105D43
hypocenterC43#18008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3105

Complements

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

NH ≅ G/Ntype
1. #19143600C2semidirect
2. D4×#10621877C2semidirect
3. #19133498C2semidirect
4. #19133480C2semidirect
5. #19133460C2semidirect
6. #19133453C2semidirect
7. #19133439C2semidirect
8. #19133425C2semidirect
9. #19133419C2semidirect
10. SD16×C43⋊C8C2semidirect
11. #19133384C2semidirect
12. #19133060C2semidirect
13. #19132986C2semidirect
14. #19132890C2semidirect
17. #14583030C22semidirect
18. Q8×C43⋊C8C22semidirect
22. #14582977C22semidirect
28. D4×C43⋊C8C22semidirect
36. #14582652C22semidirect
37. #14582652C22semidirect
38. #14582650C22semidirect
39. #14582650C22semidirect
40. Q8⋊(C43⋊C8)C22semidirect
41. Q8⋊(C43⋊C8)C22semidirect
46. D4⋊(C43⋊C8)C22semidirect
47. D4⋊(C43⋊C8)C22semidirect
48. #14582621C22semidirect
49. #14582621C22semidirect
50. #14582620C22semidirect
51. C8×C43⋊C8C22semidirect
372. C43#18008semidirect

Maximal subgroups

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

subgroupindex
#191436002
D4×#106218772
#191334982
#191334802
#191334602
#191334532
#191334392
#191334252
#191334192
SD16×C43⋊C82
#191333842
#191330602
#191329862
#191328902
C43×#31052
#1800843