Finite Group Databasebeta

← #25067244

Subgroups — #25067244

Order 11008.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143744C211yesmaximal, characteristic
2#19143690C211yesmaximal, characteristic, complemented
3#19133504C211yesmaximal, characteristic, complemented
4#19133498C211yesmaximal, characteristic, complemented
5#19133492C211yesmaximal, characteristic, complemented
6#19133486C211yesmaximal, characteristic, complemented
7#19133414C211yesmaximal, characteristic, complemented
8SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
9Q16×C43⋊C8C211yesmaximal, characteristic, complemented
10SD16×C43⋊C8C211yesmaximal, characteristic, complemented
11#19133362C211yesmaximal, characteristic, complemented
12#19133055C211yesmaximal, characteristic
13#19133050C211yesmaximal, characteristic, complemented
14M16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3172C211yesmaximal, characteristic
16#14583030—21no—
17#14583030—21no—
18#14583030C2211yescharacteristic
19#14583030C2211yescharacteristic
20#14583030C2211yescharacteristic
21Q8×C43⋊C8C2211yescharacteristic
22Q8×C43⋊C8C2211yescharacteristic
23Q8×C43⋊C8C2211yescharacteristic
24#14582977—21no—
25#14582977C2211yescharacteristic
26#14582971—21no—
27D4×C43⋊C8C2211yescharacteristic
28#14582960—21no—
29#14582960—21no—
30#14582960—21no—
31#14582956C2211yescharacteristic
32#14582952C2211yescharacteristic
33#14582926—21no—
34#14582923C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36#14582652C2211yescharacteristic
37#14582652C2211yescharacteristic
38#14582650C2211yescharacteristic
39#14582650C2211yescharacteristic
40Q8⋊(C43⋊C8)C2211yescharacteristic
41Q8⋊(C43⋊C8)C2211yescharacteristic
42Q8⋊(C43⋊C8)C2211yescharacteristic
43Q8⋊(C43⋊C8)C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46D4⋊(C43⋊C8)C2211yescharacteristic
47D4⋊(C43⋊C8)C2211yescharacteristic
48#14582620C2211yescharacteristic
49#14582620C2211yescharacteristic
50C8×C43⋊C8C2211yescharacteristic
51C8×C43⋊C8C2211yescharacteristic
52C43×#533C2211yescharacteristic
53C43×#529C2211yescharacteristic
54C43×#501C411yescharacteristic
55C43×#497C411yescharacteristic
56C43×#491C411yescharacteristic
57C43×#489C411yescharacteristic
58C43×#470C411yescharacteristic
59C43×#470C411yescharacteristic
60C43×#468C411yescharacteristic
61C43×#468C411yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C4×Q16×C43C2211yescharacteristic
64C4×SD16×C43C2211yescharacteristic
65C4×SD16×C43C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
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)—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)D411yescharacteristic
79C4⋊(C43⋊C8)D411yescharacteristic
80C4⋊(C43⋊C8)C2311yescharacteristic
81C4⋊(C43⋊C8)C2311yescharacteristic
82C4⋊(C43⋊C8)C2311yescharacteristic
83C4⋊(C43⋊C8)C2311yescharacteristic
84C22⋊(C43⋊C8)—21no—
85C22⋊(C43⋊C8)—21no—
86C22⋊(C43⋊C8)—21no—
87C22⋊(C43⋊C8)D411yescharacteristic
88C22⋊(C43⋊C8)D411yescharacteristic
89#13063236—21no—
90#13063236—21no—
91#13063236—21no—
92#13063236—21no—
93C4×C43⋊C8—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×Q16×C43C2×C411yescharacteristic
102C2×Q16×C43C2×C411yescharacteristic
103C2×SD16×C43C2×C411yescharacteristic
104C2×SD16×C43C2×C411yescharacteristic
105C2×M16×C43C2×C411yescharacteristic
106C2×M16×C43C2×C411yescharacteristic
107C4⋊Q8×C43C2×C411yescharacteristic
108C4⋊Q8×C43C2×C411yescharacteristic
109#126×C43—21no—
110#125×C43—21no—
111#125×C43C2×C411yescharacteristic
112#124×C43C2×C411yescharacteristic
113#123×C43—21no—
114C22⋊Q8×C43—21no—
115C22⋊Q8×C43C2×C411yescharacteristic
116C22⋊Q8×C43C2×C411yescharacteristic
117C22⋊Q8×C43C2×C411yescharacteristic
118#121×C43C2×C411yescharacteristic
119C4×Q8×C43—21no—
120C4×Q8×C43C2311yescharacteristic
121C4×Q8×C43C2311yescharacteristic
122C4×Q8×C43C2311yescharacteristic
123C4×D4×C43—21no—
124C4×D4×C43C2311yescharacteristic
125#117×C43—21no—
126#117×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#107×C43C2×C411yescharacteristic
129#107×C43C2×C411yescharacteristic
130#106×C43C2×C411yescharacteristic
131#106×C43C2×C411yescharacteristic
132#103×C43C2×C411yescharacteristic
133#103×C43C2×C411yescharacteristic
134#103×C43C2×C411yescharacteristic
135#103×C43C2×C411yescharacteristic
136#103×C43C2×C411yescharacteristic
137#103×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140#97×C43C2×C411yescharacteristic
141#97×C43C2×C411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C22×C411yescharacteristic
146C2×Q8×C43C22×C411yescharacteristic
147C2×Q8×C43C22×C411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43C22×C411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154Q16×C43—22no—
155Q16×C43—22no—
156SD16×C43—22no—
157SD16×C43—22no—
158M16×C43—22no—
159M16×C43—22no—
160C2×C8×C43C22×C411yescharacteristic
161C2×C8×C43C22×C411yescharacteristic
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C22×C411yescharacteristic
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C411yescharacteristic
176C4⋊C4×C43C22×C411yescharacteristic
177C4⋊C4×C43C22×C411yescharacteristic
178C4⋊C4×C43C22×C411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43C22×C411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43#4111yescharacteristic
192C42×C43C2411yescharacteristic
193#10621877—81no—
194#10621877—81no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—42no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43C4×D411yescharacteristic
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—81no—
216D4×C43—21no—
217D4×C43—21no—
218D4×C43—81no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C4×D411yescharacteristic
234C2×C4×C43C4×D411yescharacteristic
235C2×C4×C43C4×D411yescharacteristic
236C2×C4×C43C23×C411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C8×C43—21no—
240C8×C43—21no—
241C8×C43#13112yes—
242C8×C43#13112yes—
243C43⋊C8—22no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253#17969—431nomaximal, Sylow
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43C2×C4×D411yescharacteristic
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43C2×#13111yescharacteristic
273C4×C43C2×#13111yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57811yescharacteristic
276#3172D4311yescharacteristic
277#2993—431no—
278#2985—431no—
279#1593—431no—
280#1592—431no—
281#1591—431no—
282#1590—431no—
283#1579—431no—
284SD16⋊C8—431no—
285C8×Q16—431no—
286C8×SD16—431no—
287#1569—431no—
288#1494—431no—
289#1493—431no—
290C8×M16—431no—
291C2×C43—41no—
292C2×C43—81no—
293C2×C43#293111yescharacteristic
294C2×C43#294711yescharacteristic
295C2×C43#295611yescharacteristic
296#533C2×D4311yescharacteristic
297#529C2×D4311yescharacteristic
298#501Dic4311yescharacteristic
299#497Dic4311yescharacteristic
300#491Dic4311yescharacteristic
301#489Dic4311yescharacteristic
302#470Dic4311yescharacteristic
303#470Dic4311yescharacteristic
304#468Dic4311yescharacteristic
305#468Dic4311yescharacteristic
306#446—431no—
307#446—431no—
308#446—431no—
309#446—861no—
310#446—861no—
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—431no—
314C4×Q16C2×D4311yescharacteristic
315C4×Q16C2×D4311yescharacteristic
316C4×SD16C2×D4311yescharacteristic
317C4×SD16C2×D4311yescharacteristic
318#436—431no—
319#436—861no—
320#435—861no—
321C8×D4—431no—
322#433—861no—
323#433—861no—
324#433—861no—
325#432—431no—
326#431—431no—
327#424—861no—
328#423—431no—
329C4×M16C2×D4311yescharacteristic
330C2×C4×C8—431no—
331#335—431no—
332#335—431no—
333#334—431no—
334#334—431no—
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341D4⋊C8—431no—
342D4⋊C8—431no—
343#322—431no—
344#322—431no—
345C82—431no—
346C82—431no—
347C43#1796911yescharacteristic, complemented, Sylow
348C2×Q16C2×Dic4311yescharacteristic
349C2×Q16C2×Dic4311yescharacteristic
350C2×SD16C2×Dic4311yescharacteristic
351C2×SD16C2×Dic4311yescharacteristic
352C2×M16—861no—
353C2×M16—861no—
354C2×M16C2×Dic4311yescharacteristic
355C2×M16C2×Dic4311yescharacteristic
356C22×C8—861no—
357C22×C8—861no—
358C4⋊Q8C2×Dic4311yescharacteristic
359C4⋊Q8C2×Dic4311yescharacteristic
360#126—21no—
361#125—21no—
362#125C2×Dic4311yescharacteristic
363#124C2×Dic4311yescharacteristic
364#123—21no—
365C22⋊Q8—21no—
366C22⋊Q8C2×Dic4311yescharacteristic
367C22⋊Q8C2×Dic4311yescharacteristic
368C22⋊Q8C2×Dic4311yescharacteristic
369#121C2×Dic4311yescharacteristic
370C4×Q8—21no—
371C4×Q8C22×D4311yescharacteristic
372C4×Q8C22×D4311yescharacteristic
373C4×Q8C22×D4311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D4311yescharacteristic
376#117—21no—
377#117—21no—
378C2×C42C22×D4311yescharacteristic
379#107C2×Dic4311yescharacteristic
380#107C2×Dic4311yescharacteristic
381#106C2×Dic4311yescharacteristic
382#106C2×Dic4311yescharacteristic
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396#103C2×Dic4311yescharacteristic
397#103C2×Dic4311yescharacteristic
398#103C2×Dic4311yescharacteristic
399#103C2×Dic4311yescharacteristic
400#103C2×Dic4311yescharacteristic
401#103C2×Dic4311yescharacteristic
402#102C2×Dic4311yescharacteristic
403#102C2×Dic4311yescharacteristic
404C22⋊C8—431no—
405C22⋊C8—431no—
406C22⋊C8—861no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409#97—861no—
410#97—861no—
411#97—861no—
412#97—861no—
413#97C2×Dic4311yescharacteristic
414#97C2×Dic4311yescharacteristic
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C4×C8C22×D4311yescharacteristic
425C2×Q8—21no—
426C2×Q8C22×Dic4311yescharacteristic
427C2×Q8C22×Dic4311yescharacteristic
428C2×Q8C22×Dic4311yescharacteristic
429C2×D4—21no—
430C2×D4C22×Dic4311yescharacteristic
431C22×C4—21no—
432C22×C4D4×D4311yescharacteristic
433C22×C4#1062190011yescharacteristic
434C22×C4C22×Dic4311yescharacteristic
435Q16—22no—
436Q16—22no—
437SD16—22no—
438SD16—22no—
439M16—22no—
440M16—22no—
441M16—3441no—
442M16—3441no—
443C2×C8—431no—
444C2×C8—431no—
445C2×C8—431no—
446C2×C8—431no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—3441no—
454C2×C8—1722no—
455C2×C8C22×Dic4311yescharacteristic
456C2×C8C22×Dic4311yescharacteristic
457C2×C8C22×Dic4311yescharacteristic
458C2×C8C22×Dic4311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4C22×Dic4311yescharacteristic
471C4⋊C4C22×Dic4311yescharacteristic
472C4⋊C4C22×Dic4311yescharacteristic
473C4⋊C4C22×Dic4311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42D4×D4311yescharacteristic
485C42#1062190011yescharacteristic
486C42C22×Dic4311yescharacteristic
487C42C23×D4311yescharacteristic
488C23—21no—
489C23D4×Dic4311yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—81no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4D4×Dic4311yescharacteristic
515C2×C4D4×Dic4311yescharacteristic
516C2×C4D4×Dic4311yescharacteristic
517C2×C4C23×Dic4311yescharacteristic
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4C2×#1062190011yescharacteristic
520C8—21no—
521C8—21no—
522C8—862no—
523C8—861no—
524C8—861no—
525C8—861no—
526C8—861no—
527C8—1721no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C8#1306333212yes—
533C8#1306333212yes—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×D4×Dic4311yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4C2×#1306333211yescharacteristic
553C4C2×#1306333211yescharacteristic
554C4#1458370811yescharacteristic
555C4#1458371511yescharacteristic
556C2—41no—
557C2—81no—
558C2#1914330711yescharacteristic
559C2#1914343911yescharacteristic
560C2#1914350511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#3172C2
socleC22×C43C2×C4×D4
prime radical#121×C43C2×C4
cosocleC42×C43C24
hypercenter#3172D43
hypocenterC43#17969
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3172

Complements

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

NH ≅ G/Ntype
2. #19143690C2semidirect
3. #19133504C2semidirect
4. #19133498C2semidirect
5. #19133492C2semidirect
6. #19133486C2semidirect
7. #19133414C2semidirect
8. SD16⋊(C43⋊C8)C2semidirect
9. Q16×C43⋊C8C2semidirect
10. SD16×C43⋊C8C2semidirect
11. #19133362C2semidirect
13. #19133050C2semidirect
14. M16×C43⋊C8C2semidirect
347. C43#17969semidirect

Maximal subgroups

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

subgroupindex
#191437442
#191436902
#191335042
#191334982
#191334922
#191334862
#191334142
SD16⋊(C43⋊C8)2
Q16×C43⋊C82
SD16×C43⋊C82
#191333622
#191330552
#191330502
M16×C43⋊C82
C43×#31722
#1796943