Finite Group Databasebeta

← #25064180

Subgroups — #25064180

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148680C211yesmaximal, characteristic
2#19143684C211yesmaximal, characteristic, complemented
3#19133170C212yesmaximal, complemented
4#19133154C212yesmaximal, complemented
5#19133141C212yesmaximal, complemented
6#19133131C212yesmaximal, complemented
7#19133118C211yesmaximal, characteristic, complemented
8#19133102C211yesmaximal, characteristic, complemented
9#19133089C211yesmaximal, characteristic, complemented
10#19133079C211yesmaximal, characteristic, complemented
11C43×#2320C211yesmaximal, characteristic, complemented
12#14583634C411yescharacteristic, complemented
13#14583634C412yescomplemented
14Q8×Dic86C411yescharacteristic, complemented
15#14583609C411yescharacteristic, complemented
16#14583609C412yescomplemented
17#14583571C411yescharacteristic, complemented
18#14583560—21no—
19#14583550—22no—
20#14583550—21no—
21#14583521—21no—
22#14583521—22no—
23#14583449C2211yescharacteristic
24#14583449C2212yes—
25#14583433C2211yescharacteristic
26#14583433C2212yes—
27#14583381—21no—
28#14583030—21no—
29#14583030—22no—
30Q8×C43⋊C8—21no—
31#14582956C2211yescharacteristic
32#14582956C2212yes—
33#14582952C2211yescharacteristic
34#14582952C2212yes—
35#14582635C2211yescharacteristic
36#14582635C2211yescharacteristic
37#14582635C2212yes—
38#14582632C2211yescharacteristic
39#14582632C2211yescharacteristic
40#14582632C2212yes—
41#14582632C2212yes—
42#14582632C2212yes—
43#14582632C2212yes—
44#14582632C2212yes—
45C2×C4×Q8×C43C2211yescharacteristic
46C43×#391—21no—
47C43×#389—21no—
48C43×#387—22no—
49C43×#383C2212yes—
50C43×#382C2212yes—
51C4×C4⋊C4×C43C2211yescharacteristic
52C43×#376C2211yescharacteristic
53C2×#10621902—21no—
54C2×#10621898—21no—
55C2×#10621898—22no—
56#13063325C2×C411yescharacteristic
57#13063325C2×C412yes—
58#13063324—22no—
59#13063324—21no—
60#13063322C2×C411yescharacteristic
61#13063322C2×C412yes—
62#13063319—22no—
63#13063319—21no—
64#13063317C2×C411yescharacteristic
65#13063317C2×C412yes—
66#13063314—21no—
67#13063314—22no—
68#13063313—22no—
69#13063313—21no—
70#13063313C2×C411yescharacteristic
71#13063313C2×C412yes—
72#13063310—22no—
73#13063310—22no—
74#13063310—22no—
75#13063308—21no—
76#13063308—22no—
77#13063304C2311yescharacteristic
78#13063303—22no—
79#13063303—22no—
80#13063303—22no—
81#13063301—21no—
82#13063301—22no—
83#13063300—22no—
84#13063300—21no—
85#13063299—21no—
86#13063299—22no—
87#13063299C2311yescharacteristic
88#13063299C2312yes—
89Q8×Dic43—21no—
90C4×Dic86C2×C411yescharacteristic
91C4×Dic86C2×C412yes—
92C4×D172—21no—
93C4×D172—22no—
94C4×D172C2×C411yescharacteristic
95C4×D172C2×C412yes—
96C4×D172C2×C412yes—
97C4×D172C2×C412yes—
98C4×D172C2×C412yes—
99#13063287—22no—
100#13063287—21no—
101C4×C22⋊D43—21no—
102C4×C22⋊D43—22no—
103#13063282—21no—
104#13063282—22no—
105C4⋊C4×D43—22no—
106C4⋊C4×D43—21no—
107C4⋊(C43⋊C8)—22no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)C2311yescharacteristic
112C22⋊(C43⋊C8)C2311yescharacteristic
113C22⋊(C43⋊C8)C2312yes—
114#13063236—22no—
115#13063236—21no—
116C4×C43⋊C8—21no—
117C4×C43⋊C8—22no—
118C22×Q8×C43D411yescharacteristic
119C4×Q8×C43C2×C411yescharacteristic
120C4×Q8×C43C2×C411yescharacteristic
121C4×Q8×C43C2×C412yes—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43D411yescharacteristic
124C4×Q8×C43D412yes—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—22no—
127C2×C4⋊C4×C43D412yes—
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2312yes—
133#95×C43—21no—
134#95×C43—22no—
135#95×C43—22no—
136#95×C43—22no—
137#95×C43C2311yescharacteristic
138#95×C43C2311yescharacteristic
139#95×C43C2312yes—
140C2×Q8×C43—42no—
141C2×Q8×C43C22⋊C411yescharacteristic
142C2×Q8×C43C22⋊C411yescharacteristic
143C2×Q8×C43C22⋊C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—21no—
153C2×C22⋊D43—22no—
154#10621902—44no—
155#10621898—81no—
156#10621898—82no—
157#10621898—81no—
158#10621898—82no—
159C2×D172—22no—
160C2×D172—21no—
161C2×D172—22no—
162C2×D172—21no—
163C2×D172C22×C411yescharacteristic
164C2×D172C22×C412yes—
165C2×C4×D43—22no—
166C2×C4×D43—21no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×Dic86—22no—
171C2×Dic86—21no—
172C2×Dic86C22×C411yescharacteristic
173C4⋊C4×C43—42no—
174C4⋊C4×C43—82no—
175C4⋊C4×C43C22⋊C412yes—
176C4⋊C4×C43C22⋊C411yescharacteristic
177C4⋊C4×C43C22⋊C412yes—
178C4⋊C4×C43C22⋊C411yescharacteristic
179C4⋊C4×C43C22⋊C412yes—
180C4⋊C4×C43C22⋊C412yes—
181C4⋊C4×C43C22⋊C412yes—
182C42×C43—42no—
183C42×C43—81no—
184C42×C43C22×C411yescharacteristic
185C42×C43C22×C412yes—
186C42×C43C22×C412yes—
187C42×C43C22×C411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D412yes—
190C42×C43C2×D412yes—
191C42×C43C2×D411yescharacteristic
192C22⋊Dic43—21no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—22no—
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)⋊C4—21no—
202(C2×D43)⋊C4—21no—
203(C2×D43)⋊C4—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43—21no—
206C4⋊Dic43C22×C411yescharacteristic
207C4⋊Dic43C22×C412yes—
208C4⋊Dic43C22×C411yescharacteristic
209Dic43⋊C4—21no—
210Dic43⋊C4—22no—
211Dic43⋊C4—21no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—21no—
215Dic43⋊C4—21no—
216C4×Dic43—22no—
217C4×Dic43—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—22no—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—21no—
224Q8×C43—22no—
225Q8×C43—22no—
226Q8×C43—42no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43C2×C22⋊C412yes—
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C412yes—
246C2×C4×C43C2×C22⋊C412yes—
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C412yes—
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C22⋊D43—42no—
254C22⋊D43—41no—
255C22⋊D43—42no—
256C22⋊D43—41no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261D172—41no—
262D172—42no—
263D172—44no—
264D172—42no—
265D172—81no—
266D172—82no—
267C4×D43—44no—
268C4×D43—42no—
269C4×D43—82no—
270C4×D43—82no—
271C4×D43—82no—
272Dic86—41no—
273Dic86—81no—
274Dic86—82no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8—42no—
278#17602—431nomaximal, Sylow
279C22×C43—21no—
280C22×C43—21no—
281C22×C43C22×C22⋊C411yescharacteristic
282C22×C43#57611yescharacteristic
283C22×C43#57711yescharacteristic
284C2×D43—42no—
285C2×D43—41no—
286C2×D43—42no—
287C2×D43—41no—
288C2×D43—42no—
289C2×D43—41no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—22no—
294C4×C43—21no—
295C4×C43—22no—
296C4×C43—22no—
297C4×C43—21no—
298C4×C43—22no—
299C4×C43—81no—
300C4×C43—82no—
301C4×C43—81no—
302C4×C43#42112yes—
303Dic43—41no—
304Dic43—42no—
305Dic43—41no—
306Dic43—41no—
307#3522—431no—
308#2984—431no—
309#2320D4311yescharacteristic, complemented
310#1521—432no—
311#1517—432no—
312#1514—432no—
313#1512—432no—
314#1509—431no—
315#1505—431no—
316#1502—431no—
317#1500—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43#288411yescharacteristic
321C2×C43#289711yescharacteristic
322C2×C43C2×#42111yescharacteristic
323D43—82no—
324D43—81no—
325#559—432no—
326#559—431no—
327Q82—431no—
328#554—431no—
329#554—432no—
330#550—431no—
331#548—861no—
332#547—862no—
333#547—861no—
334#542—861no—
335#542—862no—
336#532—431no—
337#532—432no—
338#529—431no—
339#529—432no—
340#520—861no—
341C2×C4×Q8C2×D4311yescharacteristic
342#446—861no—
343#446—862no—
344C8×Q8—861no—
345#432—431no—
346#432—432no—
347#431—431no—
348#431—432no—
349#391—21no—
350#389—21no—
351#387—22no—
352#383C2×D4312yes—
353#382C2×D4312yes—
354C4×C4⋊C4C2×D4311yescharacteristic
355#376C2×D4311yescharacteristic
356#328—431no—
357#328—431no—
358#328—432no—
359#327—431no—
360#327—431no—
361#327—432no—
362#327—432no—
363#327—432no—
364#327—432no—
365#327—432no—
366C43#1760211yescharacteristic, complemented, Sylow
367C2×#41—861no—
368C2×#41—861no—
369C2×#41—862no—
370C22×Q8C22⋊D4311yescharacteristic
371C4⋊Q8—431no—
372C4⋊Q8—432no—
373C4⋊Q8—862no—
374C4⋊Q8—861no—
375#127—431no—
376#127—432no—
377#126—862no—
378#126—861no—
379#125—431no—
380#125—432no—
381#124—431no—
382#124—432no—
383#124—861no—
384#124—862no—
385#124—862no—
386#124—861no—
387#123—861no—
388#123—862no—
389#123—862no—
390#123—862no—
391#123—862no—
392C22⋊Q8—431no—
393C22⋊Q8—861no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398#121—431no—
399#121—432no—
400#121—861no—
401#121—862no—
402#121—862no—
403#121—861no—
404C4×Q8—431no—
405C4×Q8—432no—
406C4×Q8—861no—
407C4×Q8C4×D4311yescharacteristic
408C4×Q8C4×D4311yescharacteristic
409C4×Q8C4×D4312yes—
410C4×Q8D17211yescharacteristic
411C4×Q8D17211yescharacteristic
412C4×Q8D17212yes—
413C4×D4—431no—
414C4×D4—432no—
415C4×D4—432no—
416C4×D4—432no—
417C4×D4—432no—
418C4×D4—861no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—861no—
422C4×D4—861no—
423C4×D4—862no—
424#117—861no—
425#117—862no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—862no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22⋊D4312yes—
431C2×C4⋊C4C22⋊D4311yescharacteristic
432C2×C42—21no—
433C2×C42—21no—
434C2×C42C22×D4311yescharacteristic
435C2×C42C22×D4312yes—
436C4⋊C8—862no—
437C4⋊C8—861no—
438C4⋊C8—861no—
439C4⋊C8—862no—
440C22⋊C8—431no—
441C22⋊C8—431no—
442C22⋊C8—432no—
443#97—862no—
444#97—861no—
445C4×C8—861no—
446C4×C8—862no—
447#95—21no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95C22×D4311yescharacteristic
452#95C22×D4311yescharacteristic
453#95C22×D4312yes—
454#41—3441no—
455#41—3442no—
456#41—3441no—
457#41—3442no—
458#41—1724no—
459C2×Q8—42no—
460C2×Q8—431no—
461C2×Q8—862no—
462C2×Q8—861no—
463C2×Q8(C2×D43)⋊C411yescharacteristic
464C2×Q8(C2×D43)⋊C411yescharacteristic
465C2×Q8(C2×D43)⋊C412yes—
466C2×D4—431no—
467C2×D4—432no—
468C2×D4—861no—
469C2×D4—862no—
470C2×D4—862no—
471C2×D4—861no—
472C2×D4—862no—
473C2×D4—861no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—861no—
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C2×C22⋊D4312yes—
484C22×C4C2×C22⋊D4311yescharacteristic
485C22×C4C2×C22⋊D4312yes—
486C22×C4C23×D4311yescharacteristic
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—862no—
490C4⋊C4—42no—
491C4⋊C4—82no—
492C4⋊C4—431no—
493C4⋊C4—432no—
494C4⋊C4—431no—
495C4⋊C4—861no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4(C2×D43)⋊C412yes—
505C4⋊C4(C2×D43)⋊C411yescharacteristic
506C4⋊C4(C2×D43)⋊C412yes—
507C4⋊C4(C2×D43)⋊C411yescharacteristic
508C4⋊C4(C2×D43)⋊C412yes—
509C4⋊C4(C2×D43)⋊C412yes—
510C4⋊C4(C2×D43)⋊C412yes—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C22⋊C4—862no—
514C22⋊C4—862no—
515C22⋊C4—861no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—861no—
520C22⋊C4—862no—
521C22⋊C4—861no—
522C22⋊C4—862no—
523C42—42no—
524C42—81no—
525C42—862no—
526C42—861no—
527C42C2×C4×D4311yescharacteristic
528C42C2×C4×D4312yes—
529C42C2×C4×D4312yes—
530C42C2×C4×D4311yescharacteristic
531C42C2×D17211yescharacteristic
532C42C2×D17212yes—
533C42C2×D17212yes—
534C42C2×D17211yescharacteristic
535C23—862no—
536C23—861no—
537C23C22×C22⋊D4311yescharacteristic
538Q8—22no—
539Q8—22no—
540Q8—42no—
541Q8—3441no—
542Q8—3442no—
543Q8—1721no—
544D4—3441no—
545D4—3442no—
546D4—1721no—
547D4—1722no—
548D4—1724no—
549D4—1722no—
550D4—1721no—
551D4—1721no—
552D4—1722no—
553D4—1722no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—3442no—
575C2×C4—3442no—
576C2×C4—3442no—
577C2×C4—1724no—
578C2×C4—1722no—
579C2×C4C2×(C2×D43)⋊C412yes—
580C2×C4C2×(C2×D43)⋊C411yescharacteristic
581C2×C4C2×(C2×D43)⋊C412yes—
582C2×C4C2×(C2×D43)⋊C411yescharacteristic
583C2×C4C2×(C2×D43)⋊C412yes—
584C2×C4C2×(C2×D43)⋊C412yes—
585C2×C4C2×(C2×D43)⋊C411yescharacteristic
586C2×C4C2×(C2×D43)⋊C411yescharacteristic
587C2×C4C22×C4×D4311yescharacteristic
588C2×C4C22×D17211yescharacteristic
589C8—1721no—
590C8—1721no—
591C8—1722no—
592C22—21no—
593C22—21no—
594C22—1722no—
595C22—1721no—
596C22—1722no—
597C22—1721no—
598C22—1722no—
599C22—1721no—
600C22C22×(C2×D43)⋊C411yescharacteristic
601C22#1458370211yescharacteristic
602C22#1458370711yescharacteristic
603C4—21no—
604C4—21no—
605C4—21no—
606C4—22no—
607C4—21no—
608C4—22no—
609C4—21no—
610C4—22no—
611C4—22no—
612C4—81no—
613C4—82no—
614C4—81no—
615C4—1721no—
616C4—1722no—
617C4—1721no—
618C4—1721no—
619C4#1458291712yes—
620C2—21no—
621C2—21no—
622C2—3442no—
623C2—3441no—
624C2#1914305811yescharacteristic
625C2#1914311811yescharacteristic
626C2C2×#1458291711yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2320C2
socleC22×C43C22×C22⋊C4
prime radical#19148680C2
cosocleC22×C4×C43C24
hypercenter#2320D43
hypocenterC43#17602
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #19143684C2semidirect
3. #19133170C2semidirect
4. #19133154C2semidirect
5. #19133141C2semidirect
6. #19133131C2semidirect
7. #19133118C2semidirect
8. #19133102C2semidirect
9. #19133089C2semidirect
10. #19133079C2semidirect
11. C43×#2320C2semidirect
12. #14583634C4semidirect
13. #14583634C4semidirect
14. Q8×Dic86C4semidirect
15. #14583609C4semidirect
16. #14583609C4semidirect
17. #14583571C4semidirect
309. #2320D43semidirect
366. C43#17602semidirect

Maximal subgroups

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

subgroupindex
#191486802
#191436842
#191331702
#191331542
#191331412
#191331312
#191331182
#191331022
#191330892
#191330792
C43×#23202
#1760243