Finite Group Databasebeta

← #25067792

Subgroups — #25067792

Order 11008.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143755C211yesmaximal, characteristic
2#19143684C211yesmaximal, characteristic, complemented
3#19133492C211yesmaximal, characteristic, complemented
4#19133486C211yesmaximal, characteristic, complemented
5#19133474C211yesmaximal, characteristic, complemented
6#19133467C211yesmaximal, characteristic, complemented
7#19133467C211yesmaximal, characteristic, complemented
8#19133453C211yesmaximal, characteristic, complemented
9Q16×C43⋊C8C211yesmaximal, characteristic, complemented
10SD16×C43⋊C8C211yesmaximal, characteristic, complemented
11#19133380C211yesmaximal, characteristic, complemented
12#19133055C211yesmaximal, characteristic
13C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
14#19132879C211yesmaximal, characteristic, complemented
15C43×#3108C211yesmaximal, characteristic
16#14583030—21no—
17#14583030—21no—
18#14583030C2211yescharacteristic
19#14583030C2211yescharacteristic
20#14583030C2211yescharacteristic
21Q8×C43⋊C8C2211yescharacteristic
22Q8×C43⋊C8C2211yescharacteristic
23Q8×C43⋊C8C2211yescharacteristic
24#14582977C2211yescharacteristic
25#14582971—21no—
26D4×C43⋊C8—21no—
27D4×C43⋊C8C2211yescharacteristic
28#14582960—21no—
29#14582956—21no—
30#14582956C2211yescharacteristic
31#14582952—21no—
32#14582952C2211yescharacteristic
33#14582926—21no—
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
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#14582621C2211yescharacteristic
49#14582621C2211yescharacteristic
50C8×C43⋊C8C2211yescharacteristic
51C8×C43⋊C8C2211yescharacteristic
52C43×#529C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C43×#483C411yescharacteristic
55C43×#480C411yescharacteristic
56C43×#479C411yescharacteristic
57C43×#479C411yescharacteristic
58C43×#464C411yescharacteristic
59C43×#464C411yescharacteristic
60C43×#451C411yescharacteristic
61C43×#448C411yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C4×Q16×C43C2211yescharacteristic
64C4×SD16×C43C2211yescharacteristic
65C4×SD16×C43C2211yescharacteristic
66C43×#431C2211yescharacteristic
67C2×#10621877—21no—
68C22×C43⋊C8—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
101C22×Q8×C43C2×C411yescharacteristic
102C2×Q16×C43C2×C411yescharacteristic
103C2×Q16×C43C2×C411yescharacteristic
104C2×SD16×C43C2×C411yescharacteristic
105C2×SD16×C43C2×C411yescharacteristic
106#126×C43—21no—
107#125×C43C2×C411yescharacteristic
108#124×C43C2×C411yescharacteristic
109#123×C43—21no—
110C22⋊Q8×C43C2×C411yescharacteristic
111#121×C43C2×C411yescharacteristic
112C4×Q8×C43—21no—
113C4×Q8×C43—21no—
114C4×Q8×C43C2×C411yescharacteristic
115C4×Q8×C43C2×C411yescharacteristic
116C4×Q8×C43C2311yescharacteristic
117C4×Q8×C43C2311yescharacteristic
118C4×Q8×C43C2311yescharacteristic
119C4×D4×C43—21no—
120C4×D4×C43C2311yescharacteristic
121#117×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2×C411yescharacteristic
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#107×C43C2×C411yescharacteristic
127#107×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#103×C43C2×C411yescharacteristic
137#103×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43C2×C411yescharacteristic
141C22⋊C8×C43C2×C411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—22no—
146C2×Q8×C43—41no—
147C2×Q8×C43C22×C411yescharacteristic
148C2×Q8×C43C22×C411yescharacteristic
149C2×Q8×C43C22×C411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43C22×C411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158Q16×C43—22no—
159Q16×C43—41no—
160SD16×C43—22no—
161SD16×C43—41no—
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C22×C411yescharacteristic
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—
184C42×C43—21no—
185C42×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—
194C2×C43⋊C8—24no—
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—81no—
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—42no—
215Q8×C43#13112yes—
216D4×C43—21no—
217D4×C43—21no—
218D4×C43—42no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
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—21no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43C4×D411yescharacteristic
236C2×C4×C43C4×D411yescharacteristic
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C43⋊C8—22no—
246C43⋊C8—22no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#18017—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43#44312yes—
262C22×C43C2×C4×D411yescharacteristic
263C4×C43—21no—
264C4×C43—22no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43C2×#13111yescharacteristic
275C4×C43#56811yescharacteristic
276C4×C43#57711yescharacteristic
277C4×C43#57811yescharacteristic
278#3108D4311yescharacteristic
279#2994—431no—
280#2984—431no—
281#1591—431no—
282#1590—431no—
283#1588—431no—
284#1587—431no—
285#1587—431no—
286#1585—431no—
287C8×Q16—431no—
288C8×SD16—431no—
289#1573—431no—
290#1494—431no—
291C2×Q8⋊C8—431no—
292#1450—431no—
293C2×C43—22no—
294C2×C43—81no—
295C2×C43#293311yescharacteristic
296C2×C43#294711yescharacteristic
297C2×C43C2×#44311yescharacteristic
298#529C2×D4311yescharacteristic
299C2×C4×Q8C2×D4311yescharacteristic
300#483Dic4311yescharacteristic
301#480Dic4311yescharacteristic
302#479Dic4311yescharacteristic
303#479Dic4311yescharacteristic
304#464Dic4311yescharacteristic
305#464Dic4311yescharacteristic
306#451Dic4311yescharacteristic
307#448Dic4311yescharacteristic
308#446—431no—
309#446—431no—
310#446—431no—
311#446—861no—
312#446—861no—
313C8×Q8—431no—
314C8×Q8—431no—
315C8×Q8—431no—
316C4×Q16C2×D4311yescharacteristic
317C4×Q16C2×D4311yescharacteristic
318C4×SD16C2×D4311yescharacteristic
319C4×SD16C2×D4311yescharacteristic
320#436—431no—
321#435—861no—
322C8×D4—431no—
323C8×D4—861no—
324#433—861no—
325#432—431no—
326#432—861no—
327#431—431no—
328#431—861no—
329#431C2×D4311yescharacteristic
330#424—861no—
331C2×C4⋊C8—431no—
332C2×C4×C8—431no—
333#335—431no—
334#335—431no—
335#334—431no—
336#334—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342Q8⋊C8—431no—
343D4⋊C8—431no—
344D4⋊C8—431no—
345#322—431no—
346#322—431no—
347C82—431no—
348C82—431no—
349C43#1801711yescharacteristic, complemented, Sylow
350C22×Q8C2×Dic4311yescharacteristic
351C2×Q16C2×Dic4311yescharacteristic
352C2×Q16C2×Dic4311yescharacteristic
353C2×SD16C2×Dic4311yescharacteristic
354C2×SD16C2×Dic4311yescharacteristic
355C2×M16—861no—
356C22×C8—861no—
357C22×C8—861no—
358C22×C8—861no—
359#126—21no—
360#125C2×Dic4311yescharacteristic
361#124C2×Dic4311yescharacteristic
362#123—21no—
363C22⋊Q8C2×Dic4311yescharacteristic
364#121C2×Dic4311yescharacteristic
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C2×Dic4311yescharacteristic
368C4×Q8C2×Dic4311yescharacteristic
369C4×Q8C22×D4311yescharacteristic
370C4×Q8C22×D4311yescharacteristic
371C4×Q8C22×D4311yescharacteristic
372C4×D4—21no—
373C4×D4C22×D4311yescharacteristic
374#117—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C2×Dic4311yescharacteristic
377C2×C42—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—
396C4⋊C8C2×Dic4311yescharacteristic
397C4⋊C8C2×Dic4311yescharacteristic
398#103C2×Dic4311yescharacteristic
399#103C2×Dic4311yescharacteristic
400#103C2×Dic4311yescharacteristic
401#103C2×Dic4311yescharacteristic
402#103C2×Dic4311yescharacteristic
403#103C2×Dic4311yescharacteristic
404#102C2×Dic4311yescharacteristic
405#102C2×Dic4311yescharacteristic
406C22⋊C8—431no—
407C22⋊C8—431no—
408C22⋊C8—861no—
409C22⋊C8—861no—
410C22⋊C8—861no—
411C22⋊C8C2×Dic4311yescharacteristic
412C22⋊C8C2×Dic4311yescharacteristic
413#97—861no—
414#97—861no—
415#97—861no—
416#97—861no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8—861no—
425C4×C8C22×D4311yescharacteristic
426C4×C8C22×D4311yescharacteristic
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8C22×Dic4311yescharacteristic
431C2×Q8C22×Dic4311yescharacteristic
432C2×Q8C22×Dic4311yescharacteristic
433C2×D4—21no—
434C2×D4C22×Dic4311yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4D4×D4311yescharacteristic
439C22×C4#1062190011yescharacteristic
440C22×C4C22×Dic4311yescharacteristic
441Q16—22no—
442Q16—41no—
443SD16—22no—
444SD16—41no—
445M16—3441no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—864no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—3441no—
458C2×C8—3441no—
459C2×C8C22×Dic4311yescharacteristic
460C2×C8C22×Dic4311yescharacteristic
461C2×C8C22×Dic4311yescharacteristic
462C2×C8C22×Dic4311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4C22×Dic4311yescharacteristic
473C4⋊C4C22×Dic4311yescharacteristic
474C4⋊C4C22×Dic4311yescharacteristic
475C4⋊C4C22×Dic4311yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42D4×D4311yescharacteristic
487C42#1062190011yescharacteristic
488C42C22×Dic4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—21no—
491C23D4×Dic4311yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—42no—
498Q8#1306333212yes—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4D4×Dic4311yescharacteristic
519C2×C4D4×Dic4311yescharacteristic
520C2×C4D4×Dic4311yescharacteristic
521C2×C4C23×Dic4311yescharacteristic
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C2×#1062190011yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—862no—
529C8—862no—
530C8—861no—
531C8—861no—
532C8—861no—
533C8—861no—
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1458301612yes—
544C22C2×D4×Dic4311yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—22no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4C2×#1306333211yescharacteristic
557C4#1458366611yescharacteristic
558C4#1458370811yescharacteristic
559C4#1458371511yescharacteristic
560C2—22no—
561C2—81no—
562C2#1914332211yescharacteristic
563C2#1914343911yescharacteristic
564C2C2×#1458301611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#3108C2
socleC22×C43C2×C4×D4
prime radical#121×C43C2×C4
cosocleC42×C43C24
hypercenter#3108D43
hypocenterC43#18017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3108

Complements

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

NH ≅ G/Ntype
2. #19143684C2semidirect
3. #19133492C2semidirect
4. #19133486C2semidirect
5. #19133474C2semidirect
6. #19133467C2semidirect
7. #19133467C2semidirect
8. #19133453C2semidirect
9. Q16×C43⋊C8C2semidirect
10. SD16×C43⋊C8C2semidirect
11. #19133380C2semidirect
13. C2×Q8⋊(C43⋊C8)C2semidirect
14. #19132879C2semidirect
349. C43#18017semidirect

Maximal subgroups

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

subgroupindex
#191437552
#191436842
#191334922
#191334862
#191334742
#191334672
#191334532
Q16×C43⋊C82
SD16×C43⋊C82
#191333802
#191330552
C2×Q8⋊(C43⋊C8)2
#191328792
C43×#31082
#1801743