Finite Group Databasebeta

← #25064367

Subgroups — #25064367

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148391C211yesmaximal, characteristic
2#19143621C211yesmaximal, characteristic
3#19137537C211yesmaximal, characteristic
4#19133166C211yesmaximal, characteristic, complemented
5#19133144C212yesmaximal, complemented
6#19133126C212yesmaximal, complemented
7#19133113C212yesmaximal, complemented
8#19133105C212yesmaximal, complemented
9C2×#14582637C211yesmaximal, characteristic, complemented
10C2×#14582636C211yesmaximal, characteristic, complemented
11C43×#1520C211yesmaximal, characteristic, complemented
12#14583607C412yescomplemented
13#14583604—22no—
14#14583604C412yescomplemented
15#14583603—22no—
16Q8×C22⋊D43C412yescomplemented
17#14583562C412yescomplemented
18#14583528—21no—
19#14583525—21no—
20#14583524—21no—
21#14583451C2212yes—
22C2×#13063304C2211yescharacteristic
23C22⋊Q8×D43C2212yes—
24#14583372—21no—
25C2×C4×C22⋊D43C2211yescharacteristic
26#14582970—22no—
27#14582967—22no—
28#14582953C2212yes—
29#14582861C2212yes—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582789—21no—
32#14582780—21no—
33#14582776—21no—
34#14582766C2211yescharacteristic
35#14582761C2211yescharacteristic
36C22⋊C4×Dic43—21no—
37#14582746C2211yescharacteristic
38#14582744C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40#14582637C2212yes—
41#14582637C2212yes—
42#14582636C2212yes—
43#14582636C2212yes—
44#14582635C2212yes—
45#14582635C2212yes—
46C2×C22⋊Q8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C43×#380C2211yescharacteristic
49C43×#328C2212yes—
50C43×#328C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C2×Q8×D43C2×C412yescomplemented
53C22×C22⋊D43D411yescharacteristic
54C23×Dic43—21no—
55C22×C4×D43C2311yescharacteristic
56C2×#10621872—22no—
57C22×C43⋊C8—21no—
58#13063324—22no—
59#13063324C2×C412yescomplemented
60#13063323—22no—
61#13063323C2×C412yescomplemented
62#13063315—22no—
63#13063315—22no—
64#13063315—22no—
65#13063305—22no—
66#13063305C2×C412yescomplemented
67#13063304—21no—
68#13063304—21no—
69#13063304—22no—
70#13063304—22no—
71#13063304C2×C412yes—
72#13063304C2312yes—
73#13063303—22no—
74#13063303—22no—
75#13063303—22no—
76#13063302—22no—
77#13063302—22no—
78#13063302—22no—
79#13063302—22no—
80#13063301—22no—
81#13063301C2×C412yescomplemented
82Q8×Dic43C2×C412yescomplemented
83#13063290—22no—
84#13063290C2×C412yescomplemented
85C4×C22⋊D43—22no—
86C4×C22⋊D43—22no—
87C4×C22⋊D43C2×C412yes—
88C4×C22⋊D43C2×C412yes—
89C4×C22⋊D43D412yes—
90C4×C22⋊D43D412yes—
91(C22⋊D43)⋊C4—22no—
92(C22⋊D43)⋊C4—22no—
93#13063281—22no—
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4D411yescharacteristic
97C4⋊C4×D43—22no—
98C4⋊C4×D43C2×C412yescomplemented
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43D411yescharacteristic
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4D411yescharacteristic
104C22⋊C4×D43—22no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108Dic43⋊C8—22no—
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)C2312yes—
111(C2×D43)⋊C8—22no—
112#13063235—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95C2311yescharacteristic
119C43⋊#95C2311yescharacteristic
120C22×Q8×C43C2×C411yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C22×C8×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43C2×C412yes—
126C22⋊Q8×C43C2312yes—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2×C411yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C22⋊C8×C43—21no—
133C22⋊C8×C43C2312yes—
134#95×C43C2311yescharacteristic
135#95×C43C2311yescharacteristic
136C24×C43C2×D411yescharacteristic
137C23×D43C2×D411yescharacteristic
138C2×Q8×C43—21no—
139C2×Q8×C43—81no—
140C2×Q8×C43C22×C412yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—81no—
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43C22⋊C412yes—
155C2×C22⋊D43C22⋊C412yes—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43—81no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166Q8×D43—82no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—81no—
170C2×C4×D43C22×C412yes—
171C2×C4×D43C2×D412yes—
172C2×Dic86—21no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175C2×Dic86—81no—
176C2×Dic86C22×C412yes—
177C2×C8×C43—22no—
178C2×C8×C43—81no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—81no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—42no—
187C22⋊Dic43—22no—
188C22⋊Dic43—22no—
189C22⋊Dic43C22⋊C412yes—
190C22⋊Dic43C22⋊C412yes—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—81no—
195(C2×D43)⋊C4C22⋊C412yes—
196(C2×D43)⋊C4C22⋊C412yes—
197C4⋊Dic43—21no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43C22×C412yes—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4C22⋊C412yes—
210Dic43⋊C4C22⋊C412yes—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43—42no—
214C4×Dic43—81no—
215C4×Dic43C22×C412yes—
216C4×Dic43C2×D412yes—
217C2×C43⋊C8—22no—
218C2×C43⋊C8—81no—
219#10621872—82no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C2×C22⋊C411yescharacteristic
223C23×C43C2×C22⋊C411yescharacteristic
224C23×C43#13712yes—
225C23×C43#13712yes—
226C23×C43C22×D411yescharacteristic
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43C2×C22⋊C412yes—
232Q8×C43—42no—
233Q8×C43—81no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
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—41no—
248C2×C4×C43—81no—
249C2×C4×C43—81no—
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C22⋊D43—24no—
255C22⋊D43—24no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—81no—
269C2×Dic43—81no—
270C2×Dic43—84no—
271C2×Dic43C2×C22⋊C412yes—
272C2×Dic43C2×C22⋊C412yes—
273C2×Dic43C2×C22⋊C412yes—
274C4×D43—42no—
275C4×D43—42no—
276C4×D43—82no—
277C4×D43—82no—
278Dic86—42no—
279Dic86—82no—
280Dic86—82no—
281Dic86—81no—
282C8×C43—42no—
283C43⋊C8—42no—
284#17621—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43#41912yes—
294C22×C43#41912yes—
295C22×C43C22×C22⋊C411yescharacteristic
296C22×C43C2×#13711yescharacteristic
297C22×C43C2×#13711yescharacteristic
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—81no—
302C2×D43—81no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—42no—
308C4×C43—42no—
309C4×C43—81no—
310C4×C43—81no—
311Dic43—22no—
312Dic43—22no—
313Dic43—22no—
314Dic43—42no—
315Dic43—42no—
316Dic43—42no—
317Dic43—81no—
318#3501—431no—
319#2973—431no—
320#2353—431no—
321#1520—431no—
322#1520D4311yescharacteristic, complemented
323#1515—432no—
324#1511—432no—
325#1508—432no—
326#1506—432no—
327C2×#328—431no—
328C2×#328—431no—
329C2×C43—21no—
330C2×C43—21no—
331C2×C43—22no—
332C2×C43—22no—
333C2×C43#288311yescharacteristic
334C2×C43C2×#41911yescharacteristic
335C2×C43#290111yescharacteristic
336D43—42no—
337#554—432no—
338#554—432no—
339#554—862no—
340#554—862no—
341D4×Q8—432no—
342D4×Q8—432no—
343#544—861no—
344#543—861no—
345#543—861no—
346#533—432no—
347C2×C22⋊Q8—431no—
348C2×C22⋊Q8—432no—
349C2×C22⋊Q8C2×D4311yescharacteristic
350#518—861no—
351C2×C4×D4—431no—
352#435—862no—
353#435—862no—
354#432—432no—
355#407—432no—
356C2×C22⋊C8—431no—
357C2×C22⋊C8C2×D4311yescharacteristic
358#388—861no—
359#387—861no—
360#386—861no—
361#383—431no—
362#381—431no—
363#380C2×D4311yescharacteristic
364C4×C22⋊C4—431no—
365C4×C22⋊C4—861no—
366#376—431no—
367C2×#95—431no—
368#328—432no—
369#328—432no—
370#328—432no—
371#328—432no—
372#328—432no—
373#328—432no—
374#328C2×D4312yes—
375#328C2×D4312yes—
376C43#1762111yescharacteristic, complemented, Sylow
377C22×Q8—432no—
378C22×Q8—431no—
379C22×Q8C4×D4311yescharacteristic
380C22×D4—431no—
381C23×C4—431no—
382C23×C4—861no—
383C23×C4C22×D4311yescharacteristic
384C2×M16—862no—
385C22×C8—21no—
386C22×C8—861no—
387C4⋊Q8—432no—
388C4⋊Q8—432no—
389C4⋊Q8—862no—
390C4⋊Q8—862no—
391#125—862no—
392#125—862no—
393#125—862no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—432no—
397C22⋊Q8—432no—
398C22⋊Q8—432no—
399C22⋊Q8—432no—
400C22⋊Q8—862no—
401C22⋊Q8—862no—
402C22⋊Q8—862no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405C22⋊Q8—862no—
406C22⋊Q8—862no—
407C22⋊Q8—862no—
408C22⋊Q8—862no—
409C22⋊Q8—862no—
410C22⋊Q8—862no—
411C22⋊Q8—861no—
412C22⋊Q8—861no—
413C22⋊Q8C4×D4312yes—
414C22⋊Q8C22×D4312yes—
415C4×Q8—432no—
416C4×Q8—432no—
417C4×Q8—862no—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—432no—
421C4×D4—432no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426#117—862no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—432no—
432C2×C4⋊C4—862no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4C4×D4311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—431no—
438C2×C22⋊C4—431no—
439C2×C22⋊C4—862no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446C4⋊C8—862no—
447C22⋊C8—21no—
448C22⋊C8—432no—
449C22⋊C8—862no—
450C22⋊C8—861no—
451C22⋊C8C22×D4312yes—
452#97—862no—
453#95—431no—
454#95—431no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95C22×D4311yescharacteristic
461#95C22×D4311yescharacteristic
462C24—431no—
463C24D4×D4311yescharacteristic
464C2×Q8—21no—
465C2×Q8—81no—
466C2×Q8—432no—
467C2×Q8—862no—
468C2×Q8—862no—
469C2×Q8—861no—
470C2×Q8—3441no—
471C2×Q8—3442no—
472C2×Q8C2×C4×D4312yes—
473C2×D4—432no—
474C2×D4—432no—
475C2×D4—862no—
476C2×D4—862no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—81no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—432no—
486C22×C4—432no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—3441no—
494C22×C4—3441no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4C2×C4×D4311yescharacteristic
498C22×C4C2×C4×D4311yescharacteristic
499C22×C4D4×D4311yescharacteristic
500C22×C4D4×D4311yescharacteristic
501C22×C4D4×D4311yescharacteristic
502C22×C4C23×D4311yescharacteristic
503M16—3442no—
504C2×C8—22no—
505C2×C8—81no—
506C2×C8—862no—
507C2×C8—3441no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—81no—
512C4⋊C4—432no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—861no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4C2×C4×D4312yes—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—42no—
530C22⋊C4—432no—
531C22⋊C4—432no—
532C22⋊C4—432no—
533C22⋊C4—432no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—3441no—
539C22⋊C4—1722no—
540C42—432no—
541C42—432no—
542C42—862no—
543C42—862no—
544C42—3441no—
545C42—1722no—
546C23—41no—
547C23—41no—
548C23—432no—
549C23—861no—
550C23—861no—
551C23—1721no—
552C23—1721no—
553C23C22⋊C4×D4311yescharacteristic
554C23C22⋊C4×D4311yescharacteristic
555C23#1306335412yes—
556C23#1306335712yes—
557C23C2×D4×D4311yescharacteristic
558Q8—42no—
559Q8—81no—
560Q8—3441no—
561Q8—3442no—
562Q8—3442no—
563Q8—1722no—
564D4—864no—
565D4—864no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—3442no—
591C2×C4—3442no—
592C2×C4—3444no—
593C2×C4—3441no—
594C2×C4—3441no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4C22⋊C4×D4311yescharacteristic
605C2×C4C22⋊C4×D4311yescharacteristic
606C2×C4C22×C4×D4311yescharacteristic
607C2×C4C2×D4×D4311yescharacteristic
608C8—42no—
609C8—1722no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—42no—
617C22—42no—
618C22—862no—
619C22—862no—
620C22—862no—
621C22—3441no—
622C22—3441no—
623C22#1458290612yes—
624C22#1458290612yes—
625C22C2×C22⋊C4×D4311yescharacteristic
626C22C2×#1306335411yescharacteristic
627C22C2×#1306335711yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—42no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—862no—
637C4—862no—
638C4—862no—
639C4—3441no—
640C4—1722no—
641C4—1722no—
642C4—1722no—
643C2—21no—
644C2—21no—
645C2—22no—
646C2—22no—
647C2—1722no—
648C2#1914305311yescharacteristic
649C2C2×#1458290611yescharacteristic
650C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1520C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43D4
cosocleC22×C4×C43C24
hypercenter#1520D43
hypocenterC43#17621
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
4. #19133166C2semidirect
5. #19133144C2semidirect
6. #19133126C2semidirect
7. #19133113C2semidirect
8. #19133105C2semidirect
9. C2×#14582637C2semidirect
10. C2×#14582636C2semidirect
11. C43×#1520C2semidirect
12. #14583607C4semidirect
14. #14583604C4semidirect
16. Q8×C22⋊D43C4semidirect
17. #14583562C4semidirect
52. C2×Q8×D43C2×C4semidirect
59. #13063324C2×C4semidirect
61. #13063323C2×C4semidirect
66. #13063305C2×C4semidirect
81. #13063301C2×C4semidirect
82. Q8×Dic43C2×C4semidirect
84. #13063290C2×C4semidirect
98. C4⋊C4×D43C2×C4semidirect
322. #1520D43semidirect
376. C43#17621semidirect

Maximal subgroups

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

subgroupindex
#191483912
#191436212
#191375372
#191331662
#191331442
#191331262
#191331132
#191331052
C2×#145826372
C2×#145826362
C43×#15202
#1762143