Finite Group Databasebeta

← #25066689

Subgroups — #25066689

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143706C211yesmaximal, characteristic, complemented
2#19143671C211yesmaximal, characteristic, complemented
3#19133474C211yesmaximal, characteristic, complemented
4#19133460C211yesmaximal, characteristic, complemented
5#19133439C211yesmaximal, characteristic, complemented
6#19133425C211yesmaximal, characteristic, complemented
7#19133419C211yesmaximal, characteristic, complemented
8SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
9SD16×C43⋊C8C211yesmaximal, characteristic, complemented
10D8×C43⋊C8C211yesmaximal, characteristic, complemented
11#19133380C211yesmaximal, characteristic, complemented
12#19133029C211yesmaximal, characteristic, complemented
13#19132994C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#3106C211yesmaximal, characteristic
16Q8×C43⋊C8C2211yescharacteristic
17Q8×C43⋊C8C2211yescharacteristic
18#14582977C2211yescharacteristic
19#14582977C2211yescharacteristic
20#14582971—21no—
21#14582971—21no—
22D4×C43⋊C8—21no—
23D4×C43⋊C8—21no—
24D4×C43⋊C8C2211yescharacteristic
25D4×C43⋊C8C2211yescharacteristic
26D4×C43⋊C8C2211yescharacteristic
27D4×C43⋊C8C2211yescharacteristic
28#14582956C2211yescharacteristic
29#14582952—21no—
30#14582952C2211yescharacteristic
31#14582952C2211yescharacteristic
32C2×C4⋊(C43⋊C8)—21no—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic
34#14582866—21no—
35#14582866—21no—
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
67C2×#10621877—21no—
68C2×#10621877—21no—
69C22×C43⋊C8—21no—
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72C22×C43⋊C8—21no—
73C22×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)—21no—
88C22⋊(C43⋊C8)—21no—
89C22⋊(C43⋊C8)—21no—
90C22⋊(C43⋊C8)—21no—
91C22⋊(C43⋊C8)—21no—
92C22⋊(C43⋊C8)D411yescharacteristic
93C22⋊(C43⋊C8)D411yescharacteristic
94#13063236—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—
102C2×#41×C43C2×C411yescharacteristic
103C2×SD16×C43C2×C411yescharacteristic
104C2×SD16×C43C2×C411yescharacteristic
105C2×D8×C43C2×C411yescharacteristic
106C2×D8×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×C43C2×C411yescharacteristic
114C4×Q8×C43C2311yescharacteristic
115C4×D4×C43—21no—
116C4×D4×C43—21no—
117C4×D4×C43—21no—
118C4×D4×C43C2×C411yescharacteristic
119C4×D4×C43C2311yescharacteristic
120C4×D4×C43C2311yescharacteristic
121C4×D4×C43C2311yescharacteristic
122#117×C43—21no—
123#117×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#102×C43C2×C411yescharacteristic
135#102×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—22no—
145#41×C43—22no—
146#41×C43—81no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43C22×C411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43C22×C411yescharacteristic
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×C43—21no—
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43#4111yescharacteristic
166SD16×C43—22no—
167SD16×C43—22no—
168D8×C43—22no—
169D8×C43—22no—
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C22×C411yescharacteristic
173C2×C8×C43C22×C411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C22×C411yescharacteristic
178C4⋊C4×C43C22×C411yescharacteristic
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×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⋊C8—81no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43C4×D411yescharacteristic
216Q8×C43—21no—
217Q8×C43—81no—
218Q8×C43#13112yes—
219D4×C43—24no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—81no—
226D4×C43—81no—
227D4×C43—81no—
228D4×C43—81no—
229D4×C43#13112yes—
230C2×C4×C43—24no—
231C2×C4×C43—21no—
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—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—81no—
248C2×C4×C43C4×D411yescharacteristic
249C2×C4×C43C4×D411yescharacteristic
250C2×C4×C43C4×D411yescharacteristic
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#17920—431nomaximal, Sylow
269C22×C43—22no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43C2×C4×D411yescharacteristic
282C4×C43—21no—
283C4×C43—22no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43C2×#13111yescharacteristic
292C4×C43C2×#13111yescharacteristic
293C4×C43#57611yescharacteristic
294C4×C43#57711yescharacteristic
295#3106D4311yescharacteristic
296#2988—431no—
297#2981—431no—
298#1588—431no—
299#1586—431no—
300#1583—431no—
301#1581—431no—
302#1580—431no—
303SD16⋊C8—431no—
304C8×SD16—431no—
305C8×D8—431no—
306#1573—431no—
307#1488—431no—
308#1480—431no—
309#1454—431no—
310C2×C43—41no—
311C2×C43—42no—
312C2×C43—81no—
313C2×C43—81no—
314C2×C43#292911yescharacteristic
315C2×C43#294611yescharacteristic
316C2×C43#295711yescharacteristic
317#532C2×D4311yescharacteristic
318C4×#41C2×D4311yescharacteristic
319#482Dic4311yescharacteristic
320#482Dic4311yescharacteristic
321#477Dic4311yescharacteristic
322#476Dic4311yescharacteristic
323#460Dic4311yescharacteristic
324#459Dic4311yescharacteristic
325#449Dic4311yescharacteristic
326#449Dic4311yescharacteristic
327C8×Q8—431no—
328C8×Q8—431no—
329C4×SD16C2×D4311yescharacteristic
330C4×SD16C2×D4311yescharacteristic
331C4×D8C2×D4311yescharacteristic
332C4×D8C2×D4311yescharacteristic
333#436—431no—
334#436—431no—
335#435—861no—
336#435—861no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—861no—
342C8×D4—861no—
343#432—431no—
344#431—431no—
345#431—431no—
346#431—861no—
347#431C2×D4311yescharacteristic
348C2×C4⋊C8—431no—
349C2×C4⋊C8—861no—
350#408—861no—
351#408—861no—
352#335—431no—
353#335—431no—
354#334—431no—
355#334—431no—
356Q8⋊C8—431no—
357Q8⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364#322—431no—
365#322—431no—
366#322—431no—
367C82—431no—
368C43#1792011yescharacteristic, complemented, Sylow
369C2×#41—21no—
370C2×#41C2×Dic4311yescharacteristic
371C2×SD16C2×Dic4311yescharacteristic
372C2×SD16C2×Dic4311yescharacteristic
373C2×D8C2×Dic4311yescharacteristic
374C2×D8C2×Dic4311yescharacteristic
375C2×M16—861no—
376C2×M16—861no—
377C22×C8—861no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C4⋊Q8C2×Dic4311yescharacteristic
383#127C2×Dic4311yescharacteristic
384#124—21no—
385#121—21no—
386#121C2×Dic4311yescharacteristic
387#121C2×Dic4311yescharacteristic
388C4×Q8C2×Dic4311yescharacteristic
389C4×Q8C22×D4311yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C2×Dic4311yescharacteristic
394C4×D4C22×D4311yescharacteristic
395C4×D4C22×D4311yescharacteristic
396C4×D4C22×D4311yescharacteristic
397#117—21no—
398#117C2×Dic4311yescharacteristic
399C2×C42—21no—
400C2×C42C22×D4311yescharacteristic
401#107C2×Dic4311yescharacteristic
402#107C2×Dic4311yescharacteristic
403#106C2×Dic4311yescharacteristic
404#106C2×Dic4311yescharacteristic
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8C2×Dic4311yescharacteristic
416C4⋊C8C2×Dic4311yescharacteristic
417#103C2×Dic4311yescharacteristic
418#103C2×Dic4311yescharacteristic
419#102C2×Dic4311yescharacteristic
420#102C2×Dic4311yescharacteristic
421#102C2×Dic4311yescharacteristic
422#102C2×Dic4311yescharacteristic
423#102C2×Dic4311yescharacteristic
424#102C2×Dic4311yescharacteristic
425C22⋊C8—431no—
426C22⋊C8—431no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8C2×Dic4311yescharacteristic
436C22⋊C8C2×Dic4311yescharacteristic
437#97—861no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—861no—
443C4×C8—861no—
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446#41—22no—
447#41—22no—
448#41—81no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8C22×Dic4311yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
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×C4D4×D4311yescharacteristic
466C22×C4#1062190011yescharacteristic
467C22×C4C22×Dic4311yescharacteristic
468SD16—22no—
469SD16—22no—
470D8—22no—
471D8—22no—
472M16—3441no—
473M16—3441no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—431no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—3441no—
485C2×C8—3441no—
486C2×C8—3441no—
487C2×C8—3441no—
488C2×C8—3441no—
489C2×C8C22×Dic4311yescharacteristic
490C2×C8C22×Dic4311yescharacteristic
491C2×C8C22×Dic4311yescharacteristic
492C2×C8C22×Dic4311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4C22×Dic4311yescharacteristic
497C4⋊C4C22×Dic4311yescharacteristic
498C4⋊C4C22×Dic4311yescharacteristic
499C4⋊C4C22×Dic4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42D4×D4311yescharacteristic
511C42#1062190011yescharacteristic
512C42C22×Dic4311yescharacteristic
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23D4×Dic4311yescharacteristic
518Q8—21no—
519Q8—81no—
520Q8#1306333212yes—
521D4—24no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4#1306333212yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4D4×Dic4311yescharacteristic
551C2×C4D4×Dic4311yescharacteristic
552C2×C4D4×Dic4311yescharacteristic
553C2×C4C23×Dic4311yescharacteristic
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4C2×#1062190011yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—861no—
561C8—861no—
562C8—861no—
563C8—861no—
564C8—1721no—
565C8—1721no—
566C8—1721no—
567C8—1721no—
568C8—1721no—
569C8—1721no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22C2×D4×Dic4311yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4C2×#1306333211yescharacteristic
593C4C2×#1306333211yescharacteristic
594C4#1458370311yescharacteristic
595C4#1458370911yescharacteristic
596C2—41no—
597C2—42no—
598C2—81no—
599C2—81no—
600C2#1914329011yescharacteristic
601C2#1914342811yescharacteristic
602C2#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#17920
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. #19143706C2semidirect
2. #19143671C2semidirect
3. #19133474C2semidirect
4. #19133460C2semidirect
5. #19133439C2semidirect
6. #19133425C2semidirect
7. #19133419C2semidirect
8. SD16⋊(C43⋊C8)C2semidirect
9. SD16×C43⋊C8C2semidirect
10. D8×C43⋊C8C2semidirect
11. #19133380C2semidirect
12. #19133029C2semidirect
13. #19132994C2semidirect
14. #19132895C2semidirect
368. C43#17920semidirect

Maximal subgroups

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

subgroupindex
#191437062
#191436712
#191334742
#191334602
#191334392
#191334252
#191334192
SD16⋊(C43⋊C8)2
SD16×C43⋊C82
D8×C43⋊C82
#191333802
#191330292
#191329942
#191328952
C43×#31062
#1792043