Finite Group Databasebeta

← #25097688

Subgroups — #25097688

Order 11008.

1714 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583372C211yesmaximal, characteristic
2C22×#13063239C211yesmaximal, characteristic
3#19137207C211yesmaximal, characteristic, complemented
4#19137170C211yesmaximal, characteristic
5#19134874C218yesmaximal, complemented
6C2×#14582666C211yesmaximal, characteristic, complemented
7C2×#14582665C211yesmaximal, characteristic, complemented
8C43×#2315C211yesmaximal, characteristic, complemented
9C23×C22⋊D43C2211yescharacteristic
10#14583372—22no—
11#14583372—22no—
12#14583372—22no—
13#14583372C2214yes—
14C2×C4×C22⋊D43—22no—
15C2×(C22⋊D43)⋊C4—22no—
16C2×#13063281—21no—
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C22×C22⋊Dic43C2211yescharacteristic
20C2×C22⋊C4×D43—21no—
21C2×#13063239C418yescomplemented
22C2×#13063239C2214yes—
23#14582778C2214yes—
24#14582776—22no—
25#14582772C2214yescomplemented
26#14582771—22no—
27#14582760—21no—
28#14582757—22no—
29#14582754—21no—
30#14582666C2214yescomplemented
31#14582665C2214yescomplemented
32C22×C22⋊C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43C2211yescharacteristic
35C43×#385—22no—
36C43×#385C2214yescomplemented
37C43×#380—22no—
38C24×D43D411yescharacteristic
39C22×C22⋊D43—21no—
40C22×C22⋊D43—21no—
41C22×C22⋊D43—21no—
42C22×C22⋊D43—21no—
43C22×C22⋊D43—22no—
44C22×C22⋊D43—22no—
45C22×C22⋊D43C2×C414yes—
46C22×C22⋊D43D412yes—
47C22×C22⋊D43Q814yes—
48C22×C22⋊D43C2312yes—
49C23×Dic43—21no—
50C23×Dic43—21no—
51C23×Dic43D411yescharacteristic
52C23×Dic43D412yes—
53C22×C4×D43—22no—
54C4×C22⋊D43—28no—
55C4×C22⋊D43—28no—
56(C22⋊D43)⋊C4—28no—
57(C22⋊D43)⋊C4—28no—
58#13063281—24no—
59#13063281—24no—
60C2×Dic43⋊C4—22no—
61C2×Dic43⋊C4—24no—
62C2×C22⋊Dic43—21no—
63C2×C22⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—22no—
68C2×C22⋊Dic43—22no—
69C2×C22⋊Dic43—22no—
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43C2×C414yescomplemented
72C2×C22⋊Dic43D412yes—
73C2×C22⋊Dic43C2312yes—
74C2×C22⋊Dic43C2312yes—
75C2×C22⋊Dic43C2312yes—
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—24no—
78C22⋊C4×D43—24no—
79C22⋊C4×D43—24no—
80C2×C4×Dic43—22no—
81#13063239C2×C4116yescomplemented
82C43⋊#95—24no—
83C43⋊#95—24no—
84C25×C43C2311yescharacteristic
85C23×C4×C43—21no—
86C23×C4×C43D412yes—
87C23×C4×C43C2312yes—
88C2×C4⋊C4×C43—24no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—22no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43C2×C414yescomplemented
102C2×C22⋊C4×C43D412yes—
103C2×C22⋊C4×C43C2312yes—
104C2×C22⋊C4×C43C2312yes—
105#95×C43—24no—
106C24×C43—82no—
107C24×C43C22×C412yes—
108C24×C43C2×D411yescharacteristic
109C24×C43C2×D411yescharacteristic
110C24×C43C2×D411yescharacteristic
111C24×C43C2×D411yescharacteristic
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C24×C43C2×Q812yes—
115C24×C43#4112yes—
116C24×C43#4112yes—
117C24×C43C2411yescharacteristic
118C23×D43—21no—
119C23×D43—21no—
120C23×D43—22no—
121C23×D43—82no—
122C23×D43C4⋊C414yescomplemented
123C23×D43C2×D412yes—
124C22×C4×C43—24no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—82no—
132C22×C4×C43—82no—
133C22×C4×C43—82no—
134C22×C4×C43C2×D414yes—
135C2×C22⋊D43—24no—
136C2×C22⋊D43—24no—
137C2×C22⋊D43—24no—
138C2×C22⋊D43—24no—
139C2×C22⋊D43—22no—
140C2×C22⋊D43—22no—
141C2×C22⋊D43—24no—
142C2×C22⋊D43—24no—
143C2×C22⋊D43—24no—
144C2×C22⋊D43—24no—
145C2×C22⋊D43—24no—
146C2×C22⋊D43—22no—
147C2×C22⋊D43—22no—
148C2×C22⋊D43—22no—
149C2×C22⋊D43—22no—
150C2×C22⋊D43C4⋊C418yescomplemented
151C2×C22⋊D43C22×C414yes—
152C2×C22⋊D43C2×Q814yes—
153C22×Dic43—24no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—42no—
162C22×Dic43—82no—
163C22×Dic43—82no—
164C22×Dic43—82no—
165C22×Dic43C4⋊C414yescomplemented
166C22×Dic43C2×D412yes—
167C22×Dic43C2×D414yes—
168C2×C4×D43—28no—
169C2×C4×D43—84no—
170C4⋊C4×C43—84no—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43C22×C414yescomplemented
182C22⋊Dic43—24no—
183C22⋊Dic43—22no—
184C22⋊Dic43—22no—
185C22⋊Dic43—22no—
186C22⋊Dic43—22no—
187C22⋊Dic43—22no—
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—42no—
191C22⋊Dic43C22×C414yescomplemented
192(C2×D43)⋊C4—28no—
193(C2×D43)⋊C4—84no—
194Dic43⋊C4—28no—
195Dic43⋊C4—84no—
196C4×Dic43—28no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—82no—
205C23×C43—82no—
206C23×C43—82no—
207C23×C43—82no—
208C23×C43C2×C4⋊C412yes—
209C23×C43C2×C4⋊C412yes—
210C23×C43C4×D412yes—
211C23×C43C4×D412yes—
212C23×C43C4×D412yes—
213C23×C43C4×D412yes—
214C23×C43#12011yescharacteristic
215C23×C43#12011yescharacteristic
216C23×C43#12011yescharacteristic
217C23×C43#12011yescharacteristic
218C23×C43C22⋊Q812yes—
219C23×C43C22⋊Q812yes—
220C23×C43C22⋊Q812yes—
221C23×C43C22⋊Q812yes—
222C23×C43#12312yes—
223C23×C43#12312yes—
224C23×C43C23×C411yescharacteristic
225C23×C43C22×D411yescharacteristic
226C23×C43C22×D411yescharacteristic
227C23×C43C22×D411yescharacteristic
228C23×C43C22×Q811yescharacteristic
229C23×C43C2×#4111yescharacteristic
230C23×C43C2×#4111yescharacteristic
231C22×D43—22no—
232C22×D43—24no—
233C22×D43—22no—
234C22×D43—24no—
235C22×D43—44no—
236C22×D43—44no—
237C22×D43—84no—
238C22×D43—82no—
239C22×D43—84no—
240C22×D43C2×C4⋊C414yes—
241C2×C4×C43—24no—
242C2×C4×C43—24no—
243C2×C4×C43—44no—
244C2×C4×C43—44no—
245C2×C4×C43—44no—
246C2×C4×C43—44no—
247C2×C4×C43—44no—
248C2×C4×C43—44no—
249C2×C4×C43—42no—
250C2×C4×C43—82no—
251C2×C4×C43—84no—
252C22⋊D43—24no—
253C22⋊D43—24no—
254C22⋊D43—24no—
255C22⋊D43—24no—
256C22⋊D43—28no—
257C22⋊D43—28no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—24no—
263C2×Dic43—24no—
264C2×Dic43—44no—
265C2×Dic43—44no—
266C2×Dic43—44no—
267C2×Dic43—44no—
268C2×Dic43—42no—
269C2×Dic43—82no—
270C2×Dic43—84no—
271C2×Dic43—84no—
272C2×Dic43C2×C4⋊C414yes—
273C4×D43—88no—
274#20889—431nomaximal, Sylow
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43#38512yes—
299C22×C43#38512yes—
300C22×C43#38512yes—
301C22×C43#38512yes—
302C22×C43C22×C4⋊C411yescharacteristic
303C22×C43C2×C4×D411yescharacteristic
304C22×C43C2×C4×D411yescharacteristic
305C22×C43C2×#12011yescharacteristic
306C22×C43C2×C22⋊Q811yescharacteristic
307C22×C43C2×C22⋊Q811yescharacteristic
308C22×C43C2×#12311yescharacteristic
309C2×D43—24no—
310C2×D43—48no—
311C2×D43—44no—
312C2×D43—44no—
313C2×D43—82no—
314C2×D43—84no—
315C4×C43—44no—
316C4×C43—44no—
317C4×C43—82no—
318Dic43—24no—
319Dic43—44no—
320Dic43—44no—
321Dic43—82no—
322C2×#518—431no—
323C22×#99—431no—
324#2315—431no—
325#2315D4311yescharacteristic, complemented
326#2308—431no—
327#1867—438no—
328C2×#342—431no—
329C2×#342—431no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—21no—
333C2×C43—21no—
334C2×C43—22no—
335C2×C43—22no—
336C2×C43—21no—
337C2×C43—21no—
338C2×C43—22no—
339C2×C43—22no—
340C2×C43C2×#38511yescharacteristic
341C2×C43#302612yes—
342D43—44no—
343C23×D4—431no—
344#518—434no—
345#518—862no—
346#518—862no—
347#518—862no—
348C2×C4×D4—862no—
349C2×C4×D4—862no—
350C2×#117—861no—
351C22×C22⋊C4—431no—
352C22×C22⋊C4—431no—
353C22×C22⋊C4—431no—
354C22×C22⋊C4—861no—
355C22×C22⋊C4C2×D4311yescharacteristic
356C22×C22⋊C4C2×D4311yescharacteristic
357C22×C22⋊C4C2×D4311yescharacteristic
358C2×#99—434no—
359C2×#99—438no—
360#386—434no—
361#386—862no—
362#385—22no—
363#385—434no—
364#385—862no—
365#385C2×D4314yescomplemented
366#381—861no—
367#380—22no—
368#380—862no—
369#379—861no—
370#342—434no—
371#342—434no—
372C43#2088911yescharacteristic, complemented, Sylow
373C25—431no—
374C25C22×D4311yescharacteristic
375C22×D4—434no—
376C22×D4—432no—
377C22×D4—434no—
378C22×D4—432no—
379C22×D4—862no—
380C22×D4—861no—
381C22×D4—861no—
382C22×D4—862no—
383C22×D4—861no—
384C22×D4—861no—
385C23×C4—21no—
386C23×C4—431no—
387C23×C4—432no—
388C23×C4—862no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4C22⋊D4312yes—
392C23×C4C22×D4312yes—
393C4×D4—868no—
394C4×D4—868no—
395C4×D4—868no—
396C4×D4—868no—
397#117—864no—
398#117—864no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—864no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—434no—
415C2×C22⋊C4—432no—
416C2×C22⋊C4—432no—
417C2×C22⋊C4—432no—
418C2×C22⋊C4—432no—
419C2×C22⋊C4—864no—
420C2×C22⋊C4—864no—
421C2×C22⋊C4—862no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—862no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—862no—
429C2×C22⋊C4—862no—
430C2×C22⋊C4—864no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4C4×D4314yescomplemented
433C2×C22⋊C4C22⋊D4312yes—
434C2×C22⋊C4C22×D4312yes—
435C2×C22⋊C4C22×D4312yes—
436C2×C42—862no—
437#99—4316no—
438#95—24no—
439#95—864no—
440#95—864no—
441C24—82no—
442C24—434no—
443C24—432no—
444C24—861no—
445C24—862no—
446C24—861no—
447C24—3442no—
448C24C2×C4×D4312yes—
449C24#1062189812yes—
450C24D4×D4311yescharacteristic
451C24D4×D4311yescharacteristic
452C24D4×D4311yescharacteristic
453C24D4×D4311yescharacteristic
454C24Q8×D4312yes—
455C24#1062190212yes—
456C24C2×C22⋊D4311yescharacteristic
457C24C2×C22⋊D4311yescharacteristic
458C24C23×D4311yescharacteristic
459C2×D4—438no—
460C2×D4—434no—
461C2×D4—434no—
462C2×D4—864no—
463C2×D4—864no—
464C2×D4—864no—
465C2×D4—864no—
466C2×D4—862no—
467C2×D4—862no—
468C2×D4—864no—
469C2×D4—864no—
470C2×D4—864no—
471C2×D4—864no—
472C2×D4—864no—
473C2×D4—862no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—862no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—82no—
485C22×C4—82no—
486C22×C4—82no—
487C22×C4—434no—
488C22×C4—432no—
489C22×C4—434no—
490C22×C4—868no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—862no—
494C22×C4—864no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—3444no—
500C22×C4—3442no—
501C22×C4—3442no—
502C22×C4—3442no—
503C22×C4—1722no—
504C22×C4C2×C22⋊D4314yes—
505C4⋊C4—84no—
506C4⋊C4—868no—
507C4⋊C4—3444no—
508C22⋊C4—24no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—434no—
519C22⋊C4—868no—
520C22⋊C4—864no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—3444no—
529C22⋊C4—1722no—
530C22⋊C4C2×C4×D4314yescomplemented
531C42—868no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—82no—
540C23—82no—
541C23—82no—
542C23—82no—
543C23—434no—
544C23—862no—
545C23—864no—
546C23—862no—
547C23—864no—
548C23—3442no—
549C23—3444no—
550C23—3444no—
551C23—1724no—
552C23—1724no—
553C23C4⋊C4×D4312yes—
554C23C4⋊C4×D4312yes—
555C23C4×C22⋊D4312yes—
556C23C4×C22⋊D4312yes—
557C23#1306328712yes—
558C23#1306328712yes—
559C23#1306329311yescharacteristic
560C23#1306329311yescharacteristic
561C23#1306329311yescharacteristic
562C23#1306329311yescharacteristic
563C23#1306330112yes—
564C23#1306330112yes—
565C23#1306330312yes—
566C23#1306330312yes—
567C23#1306331012yes—
568C23#1306331012yes—
569C23C22×C4×D4311yescharacteristic
570C23C2×D4×D4311yescharacteristic
571C23C2×D4×D4311yescharacteristic
572C23C22×C22⋊D4311yescharacteristic
573C23C2×Q8×D4311yescharacteristic
574C23C2×#1062189811yescharacteristic
575C23C2×#1062190211yescharacteristic
576D4—864no—
577D4—864no—
578D4—864no—
579D4—864no—
580D4—868no—
581D4—868no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—42no—
591C2×C4—82no—
592C2×C4—84no—
593C2×C4—434no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—864no—
597C2×C4—864no—
598C2×C4—864no—
599C2×C4—864no—
600C2×C4—3448no—
601C2×C4—3444no—
602C2×C4—3442no—
603C2×C4—3444no—
604C2×C4—1724no—
605C2×C4—1722no—
606C2×C4—1724no—
607C2×C4—1724no—
608C2×C4—1724no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—864no—
633C22—3444no—
634C22—3442no—
635C22—1724no—
636C22—1728no—
637C22—1724no—
638C22#1458277012yes—
639C22#1458277012yes—
640C22#1458277012yes—
641C22#1458277012yes—
642C22C2×C4⋊C4×D4311yescharacteristic
643C22C2×C4×C22⋊D4311yescharacteristic
644C22C2×#1306328711yescharacteristic
645C22C2×#1306329311yescharacteristic
646C22C2×#1306330111yescharacteristic
647C22C2×#1306330311yescharacteristic
648C22C2×#1306331011yescharacteristic
649C4—44no—
650C4—44no—
651C4—82no—
652C4—864no—
653C4—3442no—
654C4—1724no—
655C4—1724no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—22no—
660C2—21no—
661C2—22no—
662C2—21no—
663C2—21no—
664C2—22no—
665C2—22no—
666C2—1724no—
667C2C2×#1458277011yescharacteristic
668C2#1914399112yes—
subgroupG/H
centerC22C2×#13063293
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#2315C2
socleC22×C43C2×#120
prime radicalC23×C22⋊D43C22
cosocleC24×C43C24
hypercenter#2315D43
hypocenterC43#20889
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #2315

Complements

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

NH ≅ G/Ntype
3. #19137207C2semidirect
5. #19134874C2semidirect
6. C2×#14582666C2semidirect
7. C2×#14582665C2semidirect
8. C43×#2315C2semidirect
21. C2×#13063239C4semidirect
25. #14582772C22semidirect
30. #14582666C22semidirect
31. #14582665C22semidirect
36. C43×#385C22semidirect
71. C2×C22⋊Dic43C2×C4semidirect
81. #13063239C2×C4semidirect
101. C2×C22⋊C4×C43C2×C4semidirect
122. C23×D43C4⋊C4semidirect
150. C2×C22⋊D43C4⋊C4semidirect
165. C22×Dic43C4⋊C4semidirect
181. C22⋊C4×C43C22×C4semidirect
191. C22⋊Dic43C22×C4semidirect
325. #2315D43semidirect
365. #385C2×D43semidirect
372. C43#20889semidirect
432. C2×C22⋊C4C4×D43semidirect
530. C22⋊C4C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833722
C22×#130632392
#191372072
#191371702
#191348742
C2×#145826662
C2×#145826652
C43×#23152
#2088943