Finite Group Databasebeta

← #25960419

Subgroups — #25960419

Order 11008.

2038 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147794C211yesmaximal, characteristic
2#19143263C213yesmaximal, complemented
3#19143260C213yesmaximal, complemented
4#19143252C213yesmaximal, complemented
5#19143252C213yesmaximal, complemented
6#19143245C213yesmaximal, complemented
7#19143238C213yesmaximal, complemented
8#19143232C213yesmaximal, complemented
9C2×#14582959C213yesmaximal, complemented
10#19143163C211yesmaximal, characteristic, complemented
11#19143042C211yesmaximal, characteristic
12#19143042C211yesmaximal, characteristic
13#19143021C211yesmaximal, characteristic, complemented
14#131×Dic43C211yesmaximal, characteristic, complemented
15C43×#2906C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19#14583381C411yescharacteristic
20#14583381C411yescharacteristic
21#14583378C413yes—
22#14583378C413yes—
23#14583375C411yescharacteristic
24#14583375C411yescharacteristic
25#14583371C413yes—
26#14583371C413yes—
27#41×Dic43C2211yescharacteristic
28C4×#10621898C2213yes—
29#14583367C2213yes—
30C2×#13063282C2213yes—
31#117×D43C2213yes—
32#14582959C2211yescharacteristic
33#14582959C2213yes—
34#14582959C2213yes—
35#14582959C2213yes—
36#14582959C2216yes—
37#14582959C2213yescomplemented
38#14582959C2213yescomplemented
39#14582959C2213yescomplemented
40#14582959C2213yescomplemented
41#14582959C2216yescomplemented
42#14582959C2216yescomplemented
43#14582955C2216yescomplemented
44#14582955C2216yescomplemented
45#14582951C2216yescomplemented
46#14582951C2216yescomplemented
47#14582926C2213yescomplemented
48#14582926C2213yescomplemented
49#14582923C2213yescomplemented
50C2×C4⋊(C43⋊C8)C2213yescomplemented
51#14582867C2213yes—
52#14582867C2213yes—
53#14582865C2213yes—
54#14582865C2213yes—
55#14582862C2213yes—
56#14582862C2213yes—
57C2×(C2×D43)⋊C8C2213yes—
58C2×(C2×D43)⋊C8C2213yes—
59#14582857C2213yescomplemented
60#14582857C2213yescomplemented
61#14582854C2213yescomplemented
62#14582854C2213yescomplemented
63M16×Dic43C2213yescomplemented
64M16×Dic43C2213yescomplemented
65C2×#13063235C2213yescomplemented
66C2×C8×Dic43C2213yescomplemented
67C2×#131×C43C2211yescharacteristic
68C2×#131×C43C2211yescharacteristic
69C4×#41×C43C2211yescharacteristic
70C43×#424C2213yescomplemented
71C43×#424C2213yescomplemented
72C43×#423C2213yescomplemented
73C2×C4⋊C8×C43C2213yescomplemented
74C2×#10621902C2×C411yescharacteristic
75C2×#10621898C2313yes—
76C2×#10621900C2×C413yes—
77#41×D43—24no—
78#41×D43—24no—
79C2×Q8×D43C2×C411yescharacteristic
80C2×D4×D43C2×C413yes—
81C22×C4×D43C2313yes—
82#13063332—24no—
83#13063332—24no—
84C2×#10621877C2313yes—
85C2×#10621877C2313yes—
86C22×C43⋊C8C2313yes—
87C22×C43⋊C8C2313yes—
88Q8×Dic43C2×C411yescharacteristic
89Q8×Dic43C2×C411yescharacteristic
90C4×Dic86C2×C413yes—
91C4×Dic86C2×C413yes—
92#13063290C2×C413yes—
93#13063290C2×C413yes—
94C4×D172C2×C413yes—
95C4×D172C2×C413yes—
96D4×Dic43C2×C413yes—
97D4×Dic43C2×C413yes—
98#13063287C2×C413yes—
99#13063287C2×C413yes—
100C4×C22⋊D43C2×C416yes—
101C4×C22⋊D43C2×C416yes—
102(C22⋊D43)⋊C4C2×C416yes—
103(C22⋊D43)⋊C4C2×C416yes—
104#13063284C2313yes—
105#13063283C2×C413yes—
106#13063283C2×C413yes—
107#13063282C2×C413yes—
108#13063282C2×C413yes—
109#13063282C2×C413yes—
110#13063282C2×C413yes—
111#13063282C2313yes—
112#13063282C2311yescharacteristic
113#13063282C2313yes—
114#13063282C2313yes—
115#13063281C2×C416yes—
116C2×Dic43⋊C4C2×C413yes—
117C2×Dic43⋊C4C2×C413yes—
118C4⋊C4×D43C2×C413yes—
119C4⋊C4×D43C2×C413yes—
120C2×(C2×D43)⋊C4C2×C413yes—
121C2×(C2×D43)⋊C4C2×C413yes—
122C22⋊C4×D43C2×C416yes—
123C2×C4×Dic43C2313yes—
124C42×D43C2316yes—
125C4⋊(C43⋊C8)C2311yescharacteristic
126C4⋊(C43⋊C8)C2313yes—
127C4⋊(C43⋊C8)C2313yes—
128C4⋊(C43⋊C8)C2313yes—
129C4⋊(C43⋊C8)C2316yes—
130(C2×D43)⋊C8C2311yescharacteristic
131(C2×D43)⋊C8C2311yescharacteristic
132(C2×D43)⋊C8C2313yes—
133(C2×D43)⋊C8C2313yes—
134(C2×D43)⋊C8C2313yes—
135(C2×D43)⋊C8C2313yes—
136(C2×D43)⋊C8C2313yes—
137(C2×D43)⋊C8C2313yes—
138(C2×D43)⋊C8C2316yes—
139(C2×D43)⋊C8C2316yes—
140#13063235C2311yescharacteristic
141#13063235C2313yes—
142#13063235C2313yes—
143#13063235C2313yes—
144#13063235C2316yes—
145C8×Dic43C2311yescharacteristic
146C8×Dic43C2313yes—
147C8×Dic43C2313yes—
148C8×Dic43C2313yes—
149C8×Dic43C2316yes—
150C2×#41×C43C2311yescharacteristic
151#131×C43—24no—
152#131×C43—24no—
153C2×M16×C43C2313yes—
154C2×M16×C43C2313yes—
155C22×C8×C43C2313yes—
156C22×C8×C43C2313yes—
157C4×Q8×C43C2×C411yescharacteristic
158C4×Q8×C43C2×C411yescharacteristic
159C4×D4×C43C2×C413yes—
160C4×D4×C43C2×C413yes—
161#117×C43C2313yes—
162C2×C42×C43C2313yes—
163C4⋊C8×C43C2313yes—
164C4⋊C8×C43C2316yes—
165C4⋊C8×C43C2313yes—
166C4⋊C8×C43C2311yescharacteristic
167C4⋊C8×C43C2313yes—
168C23×D43C22×C413yes—
169#41×C43#4114yes—
170#41×C43#4114yes—
171C2×Q8×C43C22×C411yescharacteristic
172C2×D4×C43C22×C413yes—
173C22×C4×C43C22×C413yes—
174C22×C4×C43C22×C413yes—
175C22×C4×C43C2413yes—
176C2×C22⋊D43C22×C416yes—
177C22×Dic43C22×C413yes—
178C22×Dic43C22×C413yes—
179C22×Dic43C22×C413yes—
180#10621902—24no—
181Q8×D43—24no—
182#10621900—212no—
183D4×D43—212no—
184#10621898—26no—
185#10621898—26no—
186C2×D172C22×C413yes—
187C2×C4×D43—26no—
188C2×C4×D43—26no—
189C2×C4×D43C22×C413yes—
190C2×C4×D43C22×C413yes—
191C2×C4×D43C22×C416yes—
192C2×C4×D43C22×C416yes—
193C2×C4×D43C2413yes—
194C2×C4×D43C2411yescharacteristic
195C2×Dic86C22×C413yes—
196M16×C43—26no—
197M16×C43—26no—
198C2×C8×C43—26no—
199C2×C8×C43—26no—
200C2×C8×C43C2411yescharacteristic
201C2×C8×C43C2411yescharacteristic
202C2×C8×C43C2413yes—
203C2×C8×C43C2413yes—
204C4⋊C4×C43C22×C413yes—
205C4⋊C4×C43C22×C413yes—
206C22⋊C4×C43C22×C416yes—
207C42×C43C22×C413yes—
208C42×C43C22×C413yes—
209C42×C43C2411yescharacteristic
210C42×C43C2413yes—
211C22⋊Dic43C22×C416yes—
212(C2×D43)⋊C4C22×C413yes—
213(C2×D43)⋊C4C22×C413yes—
214(C2×D43)⋊C4C22×C411yescharacteristic
215(C2×D43)⋊C4C22×C411yescharacteristic
216(C2×D43)⋊C4C22×C413yes—
217(C2×D43)⋊C4C22×C413yes—
218(C2×D43)⋊C4C22×C413yes—
219(C2×D43)⋊C4C22×C413yes—
220C4⋊Dic43C22×C413yes—
221C4⋊Dic43C22×C413yes—
222Dic43⋊C4C22×C413yes—
223Dic43⋊C4C22×C413yes—
224Dic43⋊C4C22×C411yescharacteristic
225Dic43⋊C4C22×C411yescharacteristic
226Dic43⋊C4C22×C413yes—
227Dic43⋊C4C22×C413yes—
228Dic43⋊C4C22×C413yes—
229Dic43⋊C4C22×C413yes—
230C4×Dic43C22×C416yes—
231C4×Dic43C22×C416yes—
232C4×Dic43C22×C413yes—
233C4×Dic43C22×C413yes—
234C4×Dic43C2413yes—
235C4×Dic43C2411yescharacteristic
236#10621877—26no—
237#10621877—26no—
238C2×C43⋊C8—26no—
239C2×C43⋊C8—26no—
240C2×C43⋊C8C2411yescharacteristic
241C2×C43⋊C8C2413yes—
242C2×C43⋊C8C2413yes—
243C2×C43⋊C8C2411yescharacteristic
244C23×C43C23×C413yes—
245C22×D43—26no—
246C22×D43—43no—
247C22×D43—43no—
248C22×D43C23×C411yescharacteristic
249C22×D43C23×C413yes—
250Q8×C43#11714yes—
251D4×C43#117112yes—
252C2×C4×C43—43no—
253C2×C4×C43—43no—
254C2×C4×C43C23×C413yes—
255C2×C4×C43C23×C413yes—
256C2×C4×C43C23×C411yescharacteristic
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C23×C413yes—
259C2×C4×C43C2×#4116yes—
260C2×C4×C43C2×#4116yes—
261C2×C4×C43C2511yescharacteristic
262C22⋊D43—212no—
263C2×Dic43—26no—
264C2×Dic43—43no—
265C2×Dic43—43no—
266C2×Dic43C23×C413yes—
267C2×Dic43C23×C411yescharacteristic
268C2×Dic43C23×C411yescharacteristic
269C2×Dic43C23×C413yes—
270C2×Dic43C23×C413yes—
271C2×Dic43C23×C411yescharacteristic
272D172—26no—
273C4×D43—26no—
274C4×D43—26no—
275C4×D43—21no—
276C4×D43—21no—
277C4×D43—23no—
278C4×D43—23no—
279C4×D43—46no—
280C4×D43—46no—
281Dic86—26no—
282C8×C43—21no—
283C8×C43—21no—
284C8×C43—23no—
285C8×C43—23no—
286C43⋊C8—21no—
287C43⋊C8—21no—
288C43⋊C8—23no—
289C43⋊C8—23no—
290#60129—431nomaximal, Sylow
291C22×C43—23no—
292C22×C43—23no—
293C22×C43C2×#11716yes—
294C22×C43C24×C411yescharacteristic
295C2×D43—21no—
296C2×D43—23no—
297C2×D43—21no—
298C2×D43—21no—
299C2×D43—23no—
300C2×D43—23no—
301C2×D43—86no—
302C4×C43—23no—
303C4×C43—23no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43C2×#11716yes—
307C4×C43C22×#4111yescharacteristic
308C4×C43C22×#4111yescharacteristic
309Dic43—23no—
310Dic43—21no—
311Dic43—23no—
312Dic43—23no—
313Dic43—21no—
314Dic43—21no—
315#3428—431no—
316#2925—433no—
317#2925—433no—
318#2924—433no—
319#2924—433no—
320#2923—433no—
321#2922—433no—
322#2921—433no—
323C2×#433—433no—
324#2906—431no—
325#2906D4311yescharacteristic, complemented
326#2880—431no—
327#2880—431no—
328#2875—431no—
329C4×#131—431no—
330C2×C43—26no—
331C2×C43C22×#11711yescharacteristic
332C2×C43#357311yescharacteristic
333C2×C43#357311yescharacteristic
334D43—43no—
335D43—41no—
336C22×#41—431no—
337C2×#131—431no—
338C2×#131—431no—
339C2×#131C2×D4311yescharacteristic
340C2×#131C2×D4311yescharacteristic
341#520—431no—
342#520—431no—
343#520—433no—
344#520—433no—
345#519—431no—
346#519—431no—
347#518—433no—
348#518—433no—
349C4×#41—431no—
350C4×#41—433no—
351C4×#41—433no—
352C4×#41C2×D4311yescharacteristic
353C2×#117—433no—
354C2×#117—433no—
355#433—431no—
356#433—433no—
357#433—433no—
358#433—433no—
359#433—433no—
360#433—433no—
361#433—433no—
362#433—433no—
363#433—436no—
364#433—436no—
365#433—436no—
366#432—436no—
367#432—436no—
368#431—436no—
369#431—436no—
370#424—433no—
371#424—433no—
372#424C2×D4313yescomplemented
373#424C2×D4313yescomplemented
374#423—433no—
375#423C2×D4313yescomplemented
376C2×C4⋊C8—433no—
377C2×C4⋊C8C2×D4313yescomplemented
378#408—433no—
379#408—433no—
380#408—433no—
381#408—433no—
382#407—433no—
383#407—433no—
384C2×C22⋊C8—433no—
385C2×C22⋊C8—433no—
386#405—433no—
387#405—433no—
388#405—433no—
389#405—433no—
390C4×M16—433no—
391C4×M16—433no—
392C2×#97—433no—
393C2×C4×C8—433no—
394C43#6012911yescharacteristic, complemented, Sylow
395C2×#41—431no—
396C2×#41—433no—
397C2×#41—433no—
398C2×#41—864no—
399C2×#41—864no—
400C2×#41C22×D4311yescharacteristic
401C22×Q8—431no—
402C22×D4—433no—
403C23×C4—433no—
404#131—24no—
405#131—24no—
406#131—864no—
407#131—864no—
408C2×M16—433no—
409C2×M16—433no—
410C2×M16C22×D4313yes—
411C2×M16C22×D4313yes—
412C22×C8—433no—
413C22×C8—433no—
414C22×C8C22×D4313yes—
415C22×C8C22×D4313yes—
416C4×Q8—431no—
417C4×Q8—431no—
418C4×Q8—433no—
419C4×Q8—433no—
420C4×Q8—433no—
421C4×Q8—433no—
422C4×Q8C4×D4311yescharacteristic
423C4×Q8C4×D4311yescharacteristic
424C4×D4—433no—
425C4×D4—433no—
426C4×D4—436no—
427C4×D4—436no—
428C4×D4—433no—
429C4×D4—433no—
430C4×D4—436no—
431C4×D4—436no—
432C4×D4—433no—
433C4×D4—433no—
434C4×D4C4×D4313yes—
435C4×D4C4×D4313yes—
436#117—433no—
437#117—433no—
438#117—433no—
439#117—436no—
440#117—433no—
441#117—433no—
442#117—433no—
443#117—433no—
444#117—433no—
445#117—431no—
446#117—433no—
447#117—433no—
448#117C22×D4313yes—
449C2×C4⋊C4—433no—
450C2×C4⋊C4—433no—
451C2×C4⋊C4—433no—
452C2×C4⋊C4—433no—
453C2×C22⋊C4—433no—
454C2×C22⋊C4—433no—
455C2×C22⋊C4—436no—
456C2×C42—433no—
457C2×C42—436no—
458C2×C42C22×D4313yes—
459C4⋊C8—431no—
460C4⋊C8—433no—
461C4⋊C8—433no—
462C4⋊C8—433no—
463C4⋊C8—436no—
464C4⋊C8C22×D4311yescharacteristic
465C4⋊C8C22×D4313yes—
466C4⋊C8C22×D4313yes—
467C4⋊C8C22×D4313yes—
468C4⋊C8C22×D4316yes—
469C22⋊C8—431no—
470C22⋊C8—431no—
471C22⋊C8—433no—
472C22⋊C8—433no—
473C22⋊C8—433no—
474C22⋊C8—433no—
475C22⋊C8—433no—
476C22⋊C8—433no—
477C22⋊C8—436no—
478C22⋊C8—436no—
479#97—431no—
480#97—433no—
481#97—433no—
482#97—433no—
483#97—436no—
484C4×C8—431no—
485C4×C8—433no—
486C4×C8—433no—
487C4×C8—433no—
488C4×C8—436no—
489C24—433no—
490#41—864no—
491#41—8612no—
492#41—866no—
493#41—866no—
494#41#1062190014yes—
495#41#1062190214yes—
496C2×Q8—433no—
497C2×Q8—864no—
498C2×Q8C2×C4×D4311yescharacteristic
499C2×D4—436no—
500C2×D4—433no—
501C2×D4—8612no—
502C2×D4C2×C4×D4313yes—
503C22×C4—433no—
504C22×C4—433no—
505C22×C4—433no—
506C22×C4—433no—
507C22×C4—433no—
508C22×C4—433no—
509C22×C4—431no—
510C22×C4—436no—
511C22×C4—436no—
512C22×C4—866no—
513C22×C4—866no—
514C22×C4C2×C4×D4313yes—
515C22×C4C2×C4×D4313yes—
516C22×C4C23×D4313yes—
517M16—26no—
518M16—26no—
519M16—866no—
520M16—866no—
521C2×C8—26no—
522C2×C8—26no—
523C2×C8—431no—
524C2×C8—433no—
525C2×C8—433no—
526C2×C8—431no—
527C2×C8—866no—
528C2×C8—866no—
529C2×C8C23×D4311yescharacteristic
530C2×C8C23×D4313yes—
531C2×C8C23×D4313yes—
532C2×C8C23×D4311yescharacteristic
533C4⋊C4—433no—
534C4⋊C4—433no—
535C4⋊C4—431no—
536C4⋊C4—431no—
537C4⋊C4—433no—
538C4⋊C4—433no—
539C4⋊C4—433no—
540C4⋊C4—433no—
541C4⋊C4—433no—
542C4⋊C4—433no—
543C4⋊C4C2×C4×D4313yes—
544C4⋊C4C2×C4×D4313yes—
545C22⋊C4—436no—
546C22⋊C4—433no—
547C22⋊C4—433no—
548C22⋊C4—431no—
549C22⋊C4—431no—
550C22⋊C4—433no—
551C22⋊C4—433no—
552C22⋊C4—433no—
553C22⋊C4—433no—
554C22⋊C4C2×C4×D4316yes—
555C42—433no—
556C42—433no—
557C42—436no—
558C42—436no—
559C42—431no—
560C42—433no—
561C42C2×C4×D4313yes—
562C42C2×C4×D4313yes—
563C42C23×D4313yes—
564C42C23×D4311yescharacteristic
565C23—431no—
566C23—433no—
567C23—866no—
568C23—1723no—
569C23—1723no—
570C23C22×C4×D4313yes—
571Q8—866no—
572Q8#1306328314yes—
573D4—8612no—
574D4—866no—
575D4#13063283112yes—
576C2×C4—43no—
577C2×C4—43no—
578C2×C4—433no—
579C2×C4—431no—
580C2×C4—433no—
581C2×C4—431no—
582C2×C4—433no—
583C2×C4—431no—
584C2×C4—866no—
585C2×C4—866no—
586C2×C4—866no—
587C2×C4—861no—
588C2×C4—863no—
589C2×C4—861no—
590C2×C4—863no—
591C2×C4—1726no—
592C2×C4—1726no—
593C2×C4—1723no—
594C2×C4—1723no—
595C2×C4C22×C4×D4313yes—
596C2×C4C22×C4×D4313yes—
597C2×C4C22×C4×D4311yescharacteristic
598C2×C4C22×C4×D4311yescharacteristic
599C2×C4C22×C4×D4313yes—
600C2×C4C2×#1062190016yes—
601C2×C4C2×#1062190216yes—
602C2×C4C24×D4311yescharacteristic
603C8—21no—
604C8—21no—
605C8—23no—
606C8—23no—
607C8—861no—
608C8—861no—
609C8—863no—
610C8—863no—
611C22—23no—
612C22—23no—
613C22—861no—
614C22—863no—
615C22—863no—
616C22—861no—
617C22—863no—
618C22—861no—
619C22—3446no—
620C22C2×#1306328316yes—
621C22C23×C4×D4311yescharacteristic
622C4—21no—
623C4—23no—
624C4—21no—
625C4—23no—
626C4—861no—
627C4—863no—
628C4—863no—
629C4—861no—
630C4—863no—
631C4—861no—
632C4C2×#1306328316yes—
633C4C22×#1062190011yescharacteristic
634C4C22×#1062190211yescharacteristic
635C2—26no—
636C2—1721no—
637C2—1723no—
638C2C22×#1306328311yescharacteristic
639C2#1914930611yescharacteristic
640C2#1914930811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC43×#2906C2
prime radicalC2×#41×D43C22
cosocleC2×C4×C43C25
hypercenter#2906D43
hypocenterC43#60129
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #19143263C2semidirect
3. #19143260C2semidirect
4. #19143252C2semidirect
5. #19143252C2semidirect
6. #19143245C2semidirect
7. #19143238C2semidirect
8. #19143232C2semidirect
9. C2×#14582959C2semidirect
10. #19143163C2semidirect
13. #19143021C2semidirect
14. #131×Dic43C2semidirect
15. C43×#2906C2semidirect
37. #14582959C22semidirect
38. #14582959C22semidirect
39. #14582959C22semidirect
40. #14582959C22semidirect
41. #14582959C22semidirect
42. #14582959C22semidirect
43. #14582955C22semidirect
44. #14582955C22semidirect
45. #14582951C22semidirect
46. #14582951C22semidirect
47. #14582926C22semidirect
48. #14582926C22semidirect
49. #14582923C22semidirect
50. C2×C4⋊(C43⋊C8)C22semidirect
59. #14582857C22semidirect
60. #14582857C22semidirect
61. #14582854C22semidirect
62. #14582854C22semidirect
63. M16×Dic43C22semidirect
64. M16×Dic43C22semidirect
65. C2×#13063235C22semidirect
66. C2×C8×Dic43C22semidirect
70. C43×#424C22semidirect
71. C43×#424C22semidirect
72. C43×#423C22semidirect
73. C2×C4⋊C8×C43C22semidirect
325. #2906D43semidirect
372. #424C2×D43semidirect
373. #424C2×D43semidirect
375. #423C2×D43semidirect
377. C2×C4⋊C8C2×D43semidirect
394. C43#60129semidirect

Maximal subgroups

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

subgroupindex
#191477942
#191432632
#191432602
#191432522
#191432452
#191432382
#191432322
C2×#145829592
#191431632
#191430422
#191430212
#131×Dic432
C43×#29062
#6012943