Finite Group Databasebeta

← #25063804

Subgroups — #25063804

Order 11008.

1102 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148639C211yesmaximal, characteristic
2#19143632C211yesmaximal, characteristic, complemented
3#19136957C211yesmaximal, characteristic, complemented
4#19133121C211yesmaximal, characteristic, complemented
5#19133113C212yesmaximal, complemented
6#19133098C212yesmaximal, complemented
7#19133094C211yesmaximal, characteristic, complemented
8#19133085C212yesmaximal, complemented
9#19133079C211yesmaximal, characteristic, complemented
10#328×D43C212yesmaximal, complemented
11C43×#1506C211yesmaximal, characteristic, complemented
12#14583623C411yescharacteristic, complemented
13#14583607—21no—
14#14583590C412yescomplemented
15#14583573—22no—
16#14583564C411yescharacteristic, complemented
17#14583561C412yescomplemented
18#14583552C411yescharacteristic, complemented
19#14583552C411yescharacteristic, complemented
20#14583540—21no—
21#14583521—21no—
22#14583497—22no—
23#14583433C2211yescharacteristic
24#14583412C2212yes—
25C22⋊Q8×D43C2212yes—
26#14583381—21no—
27C2×C4×D172—21no—
28C2×C4×D172C2211yescharacteristic
29#14582976—21no—
30#14582972—22no—
31#14582964—21no—
32#14582952C2211yescharacteristic
33#14582861C2212yes—
34C22⋊C8×D43C2212yes—
35C4×C4⋊Dic43—21no—
36C4×C4⋊Dic43C2211yescharacteristic
37#14582746—22no—
38#14582746C2212yes—
39#95×D43C2212yes—
40#14582637C2212yes—
41#14582636C2212yes—
42#14582636C2212yes—
43#14582635C2211yescharacteristic
44#14582635C2211yescharacteristic
45#14582634C2212yes—
46#14582632C2211yescharacteristic
47#14582632C2211yescharacteristic
48C43×#533C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#376C2211yescharacteristic
51C43×#328C2212yes—
52C43×#328C2212yes—
53C2×#10621902—21no—
54C2×#10621902C2×C412yescomplemented
55C2×Q8×D43C2×C412yescomplemented
56C22×D172D411yescharacteristic
57C22×C4×D43—22no—
58C22×C4×D43C2312yes—
59C2×#10621872—22no—
60C2×C8×D43—22no—
61#13063324—21no—
62#13063320—22no—
63#13063319—21no—
64#13063319—22no—
65#13063317C2×C411yescharacteristic, complemented
66#13063315—22no—
67#13063314—21no—
68#13063313—22no—
69#13063313C2×C411yescharacteristic, complemented
70#13063310—22no—
71#13063310—22no—
72#13063310—22no—
73#13063310—22no—
74#13063308—21no—
75#13063305—22no—
76#13063305C2×C412yescomplemented
77#13063304C2311yescharacteristic
78#13063303—22no—
79#13063303—22no—
80#13063302—22no—
81#13063301—21no—
82#13063301C2×C412yescomplemented
83#13063301C2×C412yescomplemented
84#13063300—21no—
85#13063300—22no—
86#13063300C2×C412yescomplemented
87#13063299C2311yescharacteristic
88#13063295—22no—
89Q8×Dic43—21no—
90C4×Dic86C2×C411yescharacteristic, complemented
91C4×D172—28no—
92C4×D172—22no—
93C4×D172C2×C411yescharacteristic
94C4×D172C2×C411yescharacteristic
95C4×D172C2×C412yes—
96C4×D172C2×C411yescharacteristic, complemented
97C4×D172D411yescharacteristic
98C4×D172D412yes—
99C4×D172D411yescharacteristic
100#13063287—21no—
101#13063287—22no—
102C4×C22⋊D43—21no—
103(C22⋊D43)⋊C4—22no—
104#13063283C2×C412yescomplemented
105#13063282—21no—
106#13063282—22no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43D411yescharacteristic
109C4⋊C4×D43—22no—
110C4⋊C4×D43—21no—
111C4⋊C4×D43C2×C412yescomplemented
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4D412yes—
114C22⋊C4×D43—22no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43—22no—
117C4⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)C2311yescharacteristic
119C22⋊(C43⋊C8)C2311yescharacteristic
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122C4×C43⋊C8—21no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C4⋊Q8×C43C2×C411yescharacteristic, complemented
126C4⋊Q8×C43C2×C411yescharacteristic, complemented
127#125×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43C2312yes—
130C4×Q8×C43—21no—
131C4×Q8×C43C2×C412yescomplemented
132#117×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2312yes—
137#97×C43—21no—
138#95×C43—21no—
139#95×C43C2311yescharacteristic
140#95×C43C2311yescharacteristic
141C23×D43C2×D412yes—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C2×C22⋊D43—21no—
150C22×Dic43—22no—
151C22×Dic43C2×D412yes—
152#10621902—44no—
153#10621902—82no—
154Q8×D43—82no—
155C2×D172—24no—
156C2×D172—22no—
157C2×D172—22no—
158C2×D172C22⋊C412yes—
159C2×D172C22⋊C411yescharacteristic
160C2×D172C22⋊C411yescharacteristic
161C2×D172C22×C411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—28no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—82no—
168C2×C4×D43—82no—
169C2×C4×D43—82no—
170C2×C4×D43C22×C412yes—
171C2×C4×D43C22×C412yes—
172C2×C4×D43C2×D412yes—
173C2×C4×D43C2×D412yes—
174C2×Dic86—22no—
175C2×Dic86C22×C411yescharacteristic
176C2×C8×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43C22×C412yes—
183C22⋊C4×C43—22no—
184C42×C43—24no—
185C42×C43—22no—
186C42×C43C22×C411yescharacteristic
187C42×C43C22×C411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C22⋊Dic43—21no—
191(C2×D43)⋊C4—28no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4C22⋊C412yes—
202(C2×D43)⋊C4C22⋊C412yes—
203(C2×D43)⋊C4C22⋊C412yes—
204(C2×D43)⋊C4C22⋊C412yes—
205C4⋊Dic43—24no—
206C4⋊Dic43—22no—
207C4⋊Dic43C22⋊C411yescharacteristic
208C4⋊Dic43C22⋊C411yescharacteristic
209C4⋊Dic43C22⋊C412yes—
210C4⋊Dic43C22×C411yescharacteristic
211C4⋊Dic43C22×C411yescharacteristic
212Dic43⋊C4—21no—
213Dic43⋊C4—21no—
214Dic43⋊C4—21no—
215Dic43⋊C4—21no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219C4×Dic43—21no—
220C4×Dic43—22no—
221C4×Dic43—81no—
222C4×Dic43—82no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225#10621872—82no—
226C8×D43—82no—
227C23×C43C22×D411yescharacteristic
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—24no—
231C22×D43—21no—
232C22×D43—42no—
233C22×D43C2×C22⋊C412yes—
234C22×D43C2×C22⋊C412yes—
235Q8×C43—42no—
236Q8×C43—42no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C23×C411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C22⋊D43—41no—
256C22⋊D43—41no—
257C2×Dic43—24no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43C2×C22⋊C412yes—
265C2×Dic43C2×C22⋊C412yes—
266D172—24no—
267D172—22no—
268D172—41no—
269D172—44no—
270D172—82no—
271D172#10414yes—
272C4×D43—42no—
273C4×D43—42no—
274C4×D43—42no—
275C4×D43—42no—
276C4×D43—44no—
277C4×D43—42no—
278C4×D43—82no—
279C4×D43—82no—
280C4×D43—88no—
281Dic86—41no—
282Dic86—82no—
283C8×C43—42no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#17548—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43C22×C22⋊C411yescharacteristic
290C22×C43#57711yescharacteristic
291C22×C43#57811yescharacteristic
292C2×D43—22no—
293C2×D43—22no—
294C2×D43—22no—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—44no—
298C2×D43—44no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43C2×#10414yes—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—42no—
309C4×C43—42no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43C2×#10412yes—
313Dic43—22no—
314Dic43—22no—
315Dic43—44no—
316Dic43—41no—
317Dic43—41no—
318Dic43—41no—
319#3520—431no—
320#2974—431no—
321#2275—431no—
322#1509—431no—
323#1508—432no—
324#1506D4311yescharacteristic, complemented
325#1504—432no—
326#1503—431no—
327#1501—432no—
328#1500—431no—
329C2×#328—432no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43#288311yescharacteristic
333C2×C43#289811yescharacteristic
334C2×C43C22×#10411yescharacteristic
335D43—24no—
336D43—42no—
337D43—81no—
338#556—431no—
339#554—861no—
340#552—432no—
341#551—862no—
342D4×Q8—431no—
343#548—432no—
344#547—431no—
345#547—431no—
346#546—861no—
347#542—861no—
348#539—862no—
349#533C2×D4311yescharacteristic
350#529—431no—
351#525—432no—
352C2×C22⋊Q8—432no—
353#520—861no—
354C2×C4×D4—431no—
355C2×C4×D4—861no—
356#436—861no—
357#435—862no—
358C8×D4—861no—
359#432C2×D4311yescharacteristic
360#431—431no—
361#407—432no—
362C2×C22⋊C8—432no—
363C4×C4⋊C4—431no—
364C4×C4⋊C4—861no—
365C4×C22⋊C4—432no—
366C4×C22⋊C4—862no—
367#376C2×D4311yescharacteristic
368C2×#95—432no—
369#328—432no—
370#328—432no—
371#328—432no—
372#328—431no—
373#328—431no—
374#328C2×D4312yes—
375#328C2×D4312yes—
376#327—432no—
377#327—431no—
378#327—431no—
379C43#1754811yescharacteristic, complemented, Sylow
380C2×#41—432no—
381C2×#41—861no—
382C22×Q8—432no—
383C22×D4—431no—
384C23×C4—432no—
385C23×C4—862no—
386C2×M16—862no—
387C22×C8—862no—
388C4⋊Q8—861no—
389C4⋊Q8C4×D4311yescharacteristic, complemented
390C4⋊Q8C4×D4311yescharacteristic, complemented
391#126—862no—
392#126—862no—
393#126—861no—
394#125—21no—
395#125—431no—
396#125—862no—
397#124—431no—
398#124—862no—
399#124—861no—
400#123—862no—
401#123—862no—
402#123—862no—
403#123—862no—
404#123—861no—
405C22⋊Q8—21no—
406C22⋊Q8—432no—
407C22⋊Q8—432no—
408C22⋊Q8—431no—
409C22⋊Q8—432no—
410C22⋊Q8—862no—
411C22⋊Q8—862no—
412C22⋊Q8—862no—
413C22⋊Q8—862no—
414C22⋊Q8—861no—
415C22⋊Q8C22×D4312yes—
416#121—431no—
417#121—432no—
418#121—862no—
419#121—861no—
420#120—862no—
421C4×Q8—21no—
422C4×Q8—431no—
423C4×Q8—861no—
424C4×Q8C4×D4312yescomplemented
425C4×D4—431no—
426C4×D4—431no—
427C4×D4—432no—
428C4×D4—431no—
429C4×D4—431no—
430C4×D4—432no—
431C4×D4—431no—
432C4×D4—862no—
433C4×D4—868no—
434C4×D4—862no—
435C4×D4—862no—
436C4×D4—861no—
437C4×D4—861no—
438#117—21no—
439#117—432no—
440#117—862no—
441#117—861no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—432no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—862no—
446C2×C4⋊C4—861no—
447C2×C22⋊C4—432no—
448C2×C22⋊C4—862no—
449C2×C22⋊C4—862no—
450C2×C42—21no—
451C2×C42—862no—
452C2×C42—861no—
453C2×C42C22×D4311yescharacteristic
454C4⋊C8—21no—
455C4⋊C8—861no—
456C22⋊C8—431no—
457C22⋊C8—431no—
458C22⋊C8—862no—
459C22⋊C8—862no—
460C22⋊C8C22×D4312yes—
461#97—21no—
462C4×C8—861no—
463#95—21no—
464#95—432no—
465#95—862no—
466#95C22×D4311yescharacteristic
467#95C22×D4311yescharacteristic
468C24—432no—
469#41—3442no—
470#41—1724no—
471C2×Q8—21no—
472C2×Q8—431no—
473C2×Q8—862no—
474C2×Q8—3442no—
475C2×Q8C2×C4×D4312yes—
476C2×D4—431no—
477C2×D4—432no—
478C2×D4—431no—
479C2×D4—431no—
480C2×D4—864no—
481C2×D4—862no—
482C2×D4—862no—
483C2×D4—861no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—432no—
487C22×C4—432no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—868no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—861no—
497C22×C4—3442no—
498C22×C4—3442no—
499C22×C4—3442no—
500C22×C4D4×D4311yescharacteristic
501C22×C4D4×D4311yescharacteristic
502C22×C4C23×D4311yescharacteristic
503M16—3442no—
504C2×C8—22no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—3442no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—431no—
514C4⋊C4—432no—
515C4⋊C4—431no—
516C4⋊C4—431no—
517C4⋊C4—431no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—864no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4C2×C4×D4312yes—
528C22⋊C4—22no—
529C22⋊C4—432no—
530C22⋊C4—432no—
531C22⋊C4—432no—
532C22⋊C4—432no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—868no—
539C22⋊C4—861no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C22⋊C4—861no—
543C22⋊C4—861no—
544C42—24no—
545C42—22no—
546C42—862no—
547C42—861no—
548C42—3441no—
549C42—3442no—
550C42C2×C4×D4311yescharacteristic
551C42C2×C4×D4311yescharacteristic
552C42D4×D4311yescharacteristic
553C42D4×D4311yescharacteristic
554C23—432no—
555C23—432no—
556C23—864no—
557C23—862no—
558C23—862no—
559C23—861no—
560C23—1722no—
561C23C2×D4×D4311yescharacteristic
562Q8—42no—
563Q8—42no—
564Q8—3442no—
565Q8—1721no—
566D4—434no—
567D4—864no—
568D4—862no—
569D4—3442no—
570D4—1721no—
571D4—1724no—
572D4—1721no—
573D4—1721no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—864no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—3442no—
593C2×C4—3442no—
594C2×C4—3448no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1724no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4C22⋊C4×D4311yescharacteristic
605C2×C4C22⋊C4×D4311yescharacteristic
606C2×C4C22⋊C4×D4311yescharacteristic
607C2×C4C22⋊C4×D4311yescharacteristic
608C2×C4C22×C4×D4311yescharacteristic
609C2×C4C2×D4×D4311yescharacteristic
610C8—42no—
611C8—1721no—
612C8—1721no—
613C22—21no—
614C22—21no—
615C22—434no—
616C22—862no—
617C22—862no—
618C22—862no—
619C22—862no—
620C22—862no—
621C22—1724no—
622C22—1724no—
623C22—1721no—
624C22—1721no—
625C22—1721no—
626C22C2×C22⋊C4×D4311yescharacteristic
627C22#1458370811yescharacteristic
628C22#1458371511yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—42no—
638C4—862no—
639C4—862no—
640C4—1724no—
641C4—1721no—
642C4—1721no—
643C4—1721no—
644C4#104×D4312yes—
645C2—21no—
646C2—21no—
647C2—864no—
648C2—3441no—
649C2—1722no—
650C2#1914305411yescharacteristic
651C2#1914312711yescharacteristic
652C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1506C2
socleC22×C43C22×C22⋊C4
prime radical#19148639C2
cosocleC22×C4×C43C24
hypercenter#1506D43
hypocenterC43#17548
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
2. #19143632C2semidirect
3. #19136957C2semidirect
4. #19133121C2semidirect
5. #19133113C2semidirect
6. #19133098C2semidirect
7. #19133094C2semidirect
8. #19133085C2semidirect
9. #19133079C2semidirect
10. #328×D43C2semidirect
11. C43×#1506C2semidirect
12. #14583623C4semidirect
14. #14583590C4semidirect
16. #14583564C4semidirect
17. #14583561C4semidirect
18. #14583552C4semidirect
19. #14583552C4semidirect
54. C2×#10621902C2×C4semidirect
55. C2×Q8×D43C2×C4semidirect
65. #13063317C2×C4semidirect
69. #13063313C2×C4semidirect
76. #13063305C2×C4semidirect
82. #13063301C2×C4semidirect
83. #13063301C2×C4semidirect
86. #13063300C2×C4semidirect
90. C4×Dic86C2×C4semidirect
96. C4×D172C2×C4semidirect
104. #13063283C2×C4semidirect
111. C4⋊C4×D43C2×C4semidirect
125. C4⋊Q8×C43C2×C4semidirect
126. C4⋊Q8×C43C2×C4semidirect
131. C4×Q8×C43C2×C4semidirect
324. #1506D43semidirect
379. C43#17548semidirect
389. C4⋊Q8C4×D43semidirect
390. C4⋊Q8C4×D43semidirect
424. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486392
#191436322
#191369572
#191331212
#191331132
#191330982
#191330942
#191330852
#191330792
#328×D432
C43×#15062
#1754843