Finite Group Databasebeta

← #25067963

Subgroups — #25067963

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143684C211yesmaximal, characteristic, complemented
2#19143662C211yesmaximal, characteristic
3#19133498C211yesmaximal, characteristic, complemented
4#19133486C211yesmaximal, characteristic, complemented
5#19133474C211yesmaximal, characteristic, complemented
6#19133453C211yesmaximal, characteristic, complemented
7#19133439C211yesmaximal, characteristic, complemented
8#19133432C211yesmaximal, characteristic, complemented
9SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
10SD16×C43⋊C8C211yesmaximal, characteristic, complemented
11#19133375C211yesmaximal, characteristic, complemented
12#19133064C211yesmaximal, characteristic
13#19132990C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#3103C211yesmaximal, characteristic
16#14583030—21no—
17#14583030—21no—
18#14583030C2211yescharacteristic
19#14583030C2211yescharacteristic
20Q8×C43⋊C8C2211yescharacteristic
21Q8×C43⋊C8C2211yescharacteristic
22#14582977—21no—
23#14582977C2211yescharacteristic
24#14582977C2211yescharacteristic
25D4×C43⋊C8—21no—
26D4×C43⋊C8C2211yescharacteristic
27D4×C43⋊C8C2211yescharacteristic
28#14582956—21no—
29#14582956C2211yescharacteristic
30#14582952—21no—
31#14582952C2211yescharacteristic
32#14582952C2211yescharacteristic
33#14582952C2211yescharacteristic
34#14582866—21no—
35#14582866—21no—
36#14582652C2211yescharacteristic
37#14582652C2211yescharacteristic
38#14582650C2211yescharacteristic
39#14582650C2211yescharacteristic
40Q8⋊(C43⋊C8)C2211yescharacteristic
41Q8⋊(C43⋊C8)C2211yescharacteristic
42Q8⋊(C43⋊C8)C2211yescharacteristic
43Q8⋊(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
53C2×C4×Q8×C43C2211yescharacteristic
54C43×#481C411yescharacteristic
55C43×#481C411yescharacteristic
56C43×#475C411yescharacteristic
57C43×#475C411yescharacteristic
58C43×#460C411yescharacteristic
59C43×#460C411yescharacteristic
60C43×#448C411yescharacteristic
61C43×#448C411yescharacteristic
62C4×SD16×C43C2211yescharacteristic
63C4×SD16×C43C2211yescharacteristic
64C4×SD16×C43C2211yescharacteristic
65C4×SD16×C43C2211yescharacteristic
66C43×#431C2211yescharacteristic
67C2×#10621877—21no—
68C2×#10621877—21no—
69C22×C43⋊C8—21no—
70C22×C43⋊C8—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)—21no—
74C4⋊(C43⋊C8)—21no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)D411yescharacteristic
77C4⋊(C43⋊C8)D411yescharacteristic
78C4⋊(C43⋊C8)C2311yescharacteristic
79C4⋊(C43⋊C8)C2311yescharacteristic
80C4⋊(C43⋊C8)C2311yescharacteristic
81C4⋊(C43⋊C8)C2311yescharacteristic
82C22⋊(C43⋊C8)—21no—
83C22⋊(C43⋊C8)—21no—
84C22⋊(C43⋊C8)—21no—
85C22⋊(C43⋊C8)—21no—
86C22⋊(C43⋊C8)—21no—
87C22⋊(C43⋊C8)—21no—
88C22⋊(C43⋊C8)—21no—
89C22⋊(C43⋊C8)D411yescharacteristic
90C22⋊(C43⋊C8)D411yescharacteristic
91#13063236—21no—
92#13063236—21no—
93#13063236—21no—
94C4×C43⋊C8—21no—
95C4×C43⋊C8—21no—
96C4×C43⋊C8—21no—
97C4×C43⋊C8C2311yescharacteristic
98C4×C43⋊C8C2311yescharacteristic
99C4×C43⋊C8C2311yescharacteristic
100C4×C43⋊C8C2311yescharacteristic
101C2×#41×C43—21no—
102C22×Q8×C43C2×C411yescharacteristic
103C2×SD16×C43C2×C411yescharacteristic
104C2×SD16×C43C2×C411yescharacteristic
105C2×SD16×C43C2×C411yescharacteristic
106C2×SD16×C43C2×C411yescharacteristic
107C4⋊Q8×C43C2×C411yescharacteristic
108#127×C43C2×C411yescharacteristic
109#124×C43—21no—
110#121×C43—21no—
111#121×C43C2×C411yescharacteristic
112#121×C43C2×C411yescharacteristic
113C4×Q8×C43—21no—
114C4×Q8×C43—21no—
115C4×Q8×C43C2×C411yescharacteristic
116C4×Q8×C43C2×C411yescharacteristic
117C4×Q8×C43C2311yescharacteristic
118C4×Q8×C43C2311yescharacteristic
119C4×D4×C43—21no—
120C4×D4×C43C2311yescharacteristic
121C4×D4×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2×C411yescharacteristic
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#106×C43C2×C411yescharacteristic
127#106×C43C2×C411yescharacteristic
128#106×C43C2×C411yescharacteristic
129#106×C43C2×C411yescharacteristic
130C4⋊C8×C43C2×C411yescharacteristic
131C4⋊C8×C43C2×C411yescharacteristic
132#103×C43C2×C411yescharacteristic
133#103×C43C2×C411yescharacteristic
134#103×C43C2×C411yescharacteristic
135#103×C43C2×C411yescharacteristic
136#102×C43C2×C411yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43C2×C411yescharacteristic
141C22⋊C8×C43C2×C411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—22no—
149C2×Q8×C43—41no—
150C2×Q8×C43C22×C411yescharacteristic
151C2×Q8×C43C22×C411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43C22×C411yescharacteristic
157C2×D4×C43C22×C411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43#4111yescharacteristic
165SD16×C43—22no—
166SD16×C43—22no—
167SD16×C43—41no—
168SD16×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×C43—21no—
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C4⋊C4×C43C22×C411yescharacteristic
182C4⋊C4×C43C22×C411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43C22×C411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43#4111yescharacteristic
194C42×C43C2411yescharacteristic
195#10621877—81no—
196#10621877—81no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C23×C43—21no—
210C23×C43—21no—
211C23×C43C4×D411yescharacteristic
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—42no—
216Q8×C43—81no—
217Q8×C43#13112yes—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—42no—
223D4×C43—81no—
224D4×C43—81no—
225D4×C43—81no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43C4×D411yescharacteristic
244C2×C4×C43C4×D411yescharacteristic
245C2×C4×C43C4×D411yescharacteristic
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263#18030—431nomaximal, Sylow
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43C2×C4×D411yescharacteristic
274C4×C43—21no—
275C4×C43—22no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43C2×#13111yescharacteristic
285C4×C43#56811yescharacteristic
286C4×C43#57711yescharacteristic
287C4×C43#57711yescharacteristic
288#3103D4311yescharacteristic
289#2984—431no—
290#2979—431no—
291#1592—431no—
292#1590—431no—
293#1588—431no—
294#1585—431no—
295#1583—431no—
296#1582—431no—
297SD16⋊C8—431no—
298C8×SD16—431no—
299#1572—431no—
300#1496—431no—
301#1479—431no—
302#1454—431no—
303C2×C43—41no—
304C2×C43—81no—
305C2×C43—81no—
306C2×C43#293311yescharacteristic
307C2×C43#294911yescharacteristic
308C2×C43#295511yescharacteristic
309#532C2×D4311yescharacteristic
310C2×C4×Q8C2×D4311yescharacteristic
311#481Dic4311yescharacteristic
312#481Dic4311yescharacteristic
313#475Dic4311yescharacteristic
314#475Dic4311yescharacteristic
315#460Dic4311yescharacteristic
316#460Dic4311yescharacteristic
317#448Dic4311yescharacteristic
318#448Dic4311yescharacteristic
319#446—431no—
320#446—431no—
321#446—861no—
322#446—861no—
323C8×Q8—431no—
324C8×Q8—431no—
325C4×SD16C2×D4311yescharacteristic
326C4×SD16C2×D4311yescharacteristic
327C4×SD16C2×D4311yescharacteristic
328C4×SD16C2×D4311yescharacteristic
329#436—431no—
330#436—431no—
331#436—861no—
332C8×D4—431no—
333C8×D4—431no—
334C8×D4—861no—
335#432—431no—
336#432—861no—
337#431—431no—
338#431—431no—
339#431—431no—
340#431—861no—
341#431C2×D4311yescharacteristic
342#408—861no—
343#408—861no—
344#335—431no—
345#335—431no—
346#334—431no—
347#334—431no—
348Q8⋊C8—431no—
349Q8⋊C8—431no—
350Q8⋊C8—431no—
351Q8⋊C8—431no—
352D4⋊C8—431no—
353D4⋊C8—431no—
354D4⋊C8—431no—
355D4⋊C8—431no—
356#322—431no—
357#322—431no—
358#322—431no—
359C82—431no—
360C43#1803011yescharacteristic, complemented, Sylow
361C2×#41—21no—
362C22×Q8C2×Dic4311yescharacteristic
363C2×SD16C2×Dic4311yescharacteristic
364C2×SD16C2×Dic4311yescharacteristic
365C2×SD16C2×Dic4311yescharacteristic
366C2×SD16C2×Dic4311yescharacteristic
367C2×M16—861no—
368C2×M16—861no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8C2×Dic4311yescharacteristic
372#127C2×Dic4311yescharacteristic
373#124—21no—
374#121—21no—
375#121C2×Dic4311yescharacteristic
376#121C2×Dic4311yescharacteristic
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C2×Dic4311yescharacteristic
380C4×Q8C2×Dic4311yescharacteristic
381C4×Q8C22×D4311yescharacteristic
382C4×Q8C22×D4311yescharacteristic
383C4×D4—21no—
384C4×D4C22×D4311yescharacteristic
385C4×D4C22×D4311yescharacteristic
386C2×C4⋊C4—21no—
387C2×C4⋊C4C2×Dic4311yescharacteristic
388C2×C42—21no—
389C2×C42C22×D4311yescharacteristic
390#106C2×Dic4311yescharacteristic
391#106C2×Dic4311yescharacteristic
392#106C2×Dic4311yescharacteristic
393#106C2×Dic4311yescharacteristic
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C2×Dic4311yescharacteristic
406C4⋊C8C2×Dic4311yescharacteristic
407#103C2×Dic4311yescharacteristic
408#103C2×Dic4311yescharacteristic
409#103C2×Dic4311yescharacteristic
410#103C2×Dic4311yescharacteristic
411#102C2×Dic4311yescharacteristic
412#102C2×Dic4311yescharacteristic
413#102C2×Dic4311yescharacteristic
414#102C2×Dic4311yescharacteristic
415C22⋊C8—431no—
416C22⋊C8—431no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8C2×Dic4311yescharacteristic
425C22⋊C8C2×Dic4311yescharacteristic
426#97—861no—
427#97—861no—
428#97—861no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—861no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8C22×D4311yescharacteristic
437C4×C8C22×D4311yescharacteristic
438#41—81no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—22no—
443C2×Q8—41no—
444C2×Q8C22×Dic4311yescharacteristic
445C2×Q8C22×Dic4311yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C22×Dic4311yescharacteristic
451C2×D4C22×Dic4311yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4D4×D4311yescharacteristic
457C22×C4#1062190011yescharacteristic
458C22×C4C22×Dic4311yescharacteristic
459SD16—22no—
460SD16—22no—
461SD16—41no—
462SD16—41no—
463M16—3441no—
464M16—3441no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—3441no—
476C2×C8—3441no—
477C2×C8C22×Dic4311yescharacteristic
478C2×C8C22×Dic4311yescharacteristic
479C2×C8C22×Dic4311yescharacteristic
480C2×C8C22×Dic4311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4C22×Dic4311yescharacteristic
488C4⋊C4C22×Dic4311yescharacteristic
489C4⋊C4C22×Dic4311yescharacteristic
490C4⋊C4C22×Dic4311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42D4×D4311yescharacteristic
500C42#1062190011yescharacteristic
501C42C22×Dic4311yescharacteristic
502C42C23×D4311yescharacteristic
503C23—21no—
504C23—21no—
505C23D4×Dic4311yescharacteristic
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—42no—
510Q8—81no—
511Q8#1306333212yes—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—81no—
518D4—81no—
519D4—81no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4D4×Dic4311yescharacteristic
538C2×C4D4×Dic4311yescharacteristic
539C2×C4D4×Dic4311yescharacteristic
540C2×C4C23×Dic4311yescharacteristic
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4C2×#1062190011yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—861no—
548C8—861no—
549C8—861no—
550C8—861no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C8—1721no—
555C8—1721no—
556C8—1721no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×D4×Dic4311yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4C2×#1306333211yescharacteristic
578C4#1458366611yescharacteristic
579C4#1458370511yescharacteristic
580C4#1458370511yescharacteristic
581C2—41no—
582C2—81no—
583C2—81no—
584C2#1914332211yescharacteristic
585C2#1914345511yescharacteristic
586C2#1914349811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#3103C2
socleC22×C43C2×C4×D4
prime radicalC43×#532C22
cosocleC42×C43C24
hypercenter#3103D43
hypocenterC43#18030
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
1. #19143684C2semidirect
3. #19133498C2semidirect
4. #19133486C2semidirect
5. #19133474C2semidirect
6. #19133453C2semidirect
7. #19133439C2semidirect
8. #19133432C2semidirect
9. SD16⋊(C43⋊C8)C2semidirect
10. SD16×C43⋊C8C2semidirect
11. #19133375C2semidirect
13. #19132990C2semidirect
14. #19132895C2semidirect
360. C43#18030semidirect

Maximal subgroups

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

subgroupindex
#191436842
#191436622
#191334982
#191334862
#191334742
#191334532
#191334392
#191334322
SD16⋊(C43⋊C8)2
SD16×C43⋊C82
#191333752
#191330642
#191329902
#191328952
C43×#31032
#1803043