Finite Group Databasebeta

← #24987979

Subgroups — #24987979

Order 11008.

836 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2#19134572C211yesmaximal, characteristic
3C4×(C2×D43)⋊C8C211yesmaximal, characteristic
4C2×#14582631C211yesmaximal, characteristic, complemented
5C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6C2×#14582629C211yesmaximal, characteristic, complemented
7C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8#14583453—22no—
9#14583453—22no—
10#14583453—22no—
11#14583453—22no—
12C2×#13063324C411yescharacteristic
13C2×#13063323C411yescharacteristic
14C2×#13063315—21no—
15C2×#13063305C411yescharacteristic
16C2×#13063303—21no—
17C2×#13063301C411yescharacteristic
18C2×C4×Dic86—21no—
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063282—21no—
21C2×C42×D43C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×(C2×D43)⋊C8—21no—
24C2×(C2×D43)⋊C8—21no—
25C2×C4×C43⋊C8C2211yescharacteristic
26#14582653—21no—
27#14582653—21no—
28#14582631—22no—
29Q8⋊(C43⋊C8)—22no—
30#14582629—22no—
31C2×C4×Q8×C43C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic
33C2×C4×C8×C43C2211yescharacteristic
34C43×Q8⋊C8—22no—
35C22×Dic86—21no—
36C22×Dic86C2×C411yescharacteristic
37C22×C4×D43C2×C411yescharacteristic
38C22×C4×D43D411yescharacteristic
39C22×C4×D43D411yescharacteristic
40C22×C43⋊C8—21no—
41C22×C43⋊C8—21no—
42#13063324—22no—
43#13063324—22no—
44#13063323—22no—
45#13063323—22no—
46#13063315—24no—
47#13063315—24no—
48#13063305—22no—
49#13063305—22no—
50#13063303—24no—
51#13063303—24no—
52#13063301—22no—
53#13063301—22no—
54C4×Dic86—24no—
55C4×Dic86—24no—
56C4×Dic86—21no—
57C4×Dic86—21no—
58C4×Dic86D412yes—
59C4×Dic86D412yes—
60#13063282—24no—
61#13063282—24no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43C2×C411yescharacteristic
64C2×Dic43⋊C4—21no—
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×(C2×D43)⋊C4—21no—
70C2×(C2×D43)⋊C4—21no—
71C2×C4×Dic43—21no—
72C2×C4×Dic43C2×C411yescharacteristic
73C2×C4×Dic43D411yescharacteristic
74C2×C4×Dic43D411yescharacteristic
75C42×D43—21no—
76C42×D43—21no—
77C42×D43—21no—
78C42×D43—21no—
79C4⋊(C43⋊C8)—21no—
80C4⋊(C43⋊C8)—21no—
81(C2×D43)⋊C8—24no—
82(C2×D43)⋊C8—42no—
83C4×C43⋊C8—21no—
84C4×C43⋊C8—21no—
85C22×Q8×C43C2×C411yescharacteristic
86C22×C8×C43—21no—
87C22×C8×C43—21no—
88C4×Q8×C43—21no—
89C4×Q8×C43—21no—
90C4×Q8×C43D412yes—
91C4×Q8×C43D412yes—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43C2×C411yescharacteristic
94C2×C42×C43—21no—
95C2×C42×C43C2311yescharacteristic
96C4⋊C8×C43—21no—
97C4⋊C8×C43—21no—
98C4×C8×C43—21no—
99C4×C8×C43—21no—
100C23×D43C22⋊C411yescharacteristic
101C2×Q8×C43—21no—
102C2×Q8×C43—21no—
103C2×Q8×C43—21no—
104C2×Q8×C43—21no—
105C2×Q8×C43—21no—
106C2×Q8×C43C22⋊C412yes—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43C22×C411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×Dic43—21no—
113C22×Dic43—21no—
114C22×Dic43C22⋊C411yescharacteristic
115C22×Dic43C22⋊C411yescharacteristic
116C22×Dic43C22⋊C411yescharacteristic
117C2×C4×D43—21no—
118C2×C4×D43—21no—
119C2×C4×D43—21no—
120C2×C4×D43—21no—
121C2×C4×D43—21no—
122C2×C4×D43—21no—
123C2×C4×D43—21no—
124C2×C4×D43—21no—
125C2×C4×D43—21no—
126C2×C4×D43—21no—
127C2×C4×D43—21no—
128C2×C4×D43—21no—
129C2×C4×D43—22no—
130C2×C4×D43—41no—
131C2×C4×D43SD1612yes—
132C2×C4×D43Q1612yes—
133C2×Dic86—21no—
134C2×Dic86—21no—
135C2×Dic86—21no—
136C2×Dic86—21no—
137C2×Dic86—24no—
138C2×Dic86—21no—
139C2×Dic86—42no—
140C2×Dic86—42no—
141C2×Dic86C22⋊C412yes—
142C2×C8×C43—22no—
143C2×C8×C43—41no—
144C2×C8×C43—41no—
145C2×C8×C43—41no—
146C2×C8×C43—41no—
147C2×C8×C43—41no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43C22⋊C412yes—
152C42×C43—22no—
153C42×C43—22no—
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158(C2×D43)⋊C4—24no—
159(C2×D43)⋊C4—24no—
160C4⋊Dic43—24no—
161C4⋊Dic43—21no—
162C4⋊Dic43C22⋊C412yes—
163Dic43⋊C4—24no—
164Dic43⋊C4—24no—
165Dic43⋊C4—24no—
166Dic43⋊C4—24no—
167Dic43⋊C4—22no—
168Dic43⋊C4—22no—
169C4×Dic43—21no—
170C4×Dic43—21no—
171C4×Dic43—21no—
172C4×Dic43—21no—
173C4×Dic43—21no—
174C4×Dic43—21no—
175C4×Dic43—22no—
176C4×Dic43—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—41no—
179C2×C43⋊C8—41no—
180C2×C43⋊C8—41no—
181C2×C43⋊C8—41no—
182C2×C43⋊C8—41no—
183C23×C43C2×C22⋊C411yescharacteristic
184C22×D43—21no—
185C22×D43—21no—
186C22×D43—21no—
187C22×D43—21no—
188C22×D43—21no—
189C22×D43—21no—
190C22×D43#10312yes—
191Q8×C43—22no—
192Q8×C43—22no—
193Q8×C43—41no—
194Q8×C43—41no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43C2×C22⋊C411yescharacteristic
204C2×C4×C43C2×C22⋊C411yescharacteristic
205C2×C4×C43#12011yescharacteristic
206C2×C4×C43#12011yescharacteristic
207C2×C4×C43#12011yescharacteristic
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#13111yescharacteristic
210C2×C4×C43#13111yescharacteristic
211C2×C4×C43#13111yescharacteristic
212C2×C4×C43#13111yescharacteristic
213C2×C4×C43C2×SD1611yescharacteristic
214C2×C4×C43C2×Q1611yescharacteristic
215C2×C4×C43#13711yescharacteristic
216C2×C4×C43#13711yescharacteristic
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43#10312yes—
231C2×Dic43#10412yes—
232C4×D43—22no—
233C4×D43—22no—
234C4×D43—22no—
235C4×D43—22no—
236C4×D43—42no—
237C4×D43—42no—
238C4×D43—41no—
239C4×D43—41no—
240C4×D43—41no—
241C4×D43—41no—
242Dic86—22no—
243Dic86—22no—
244Dic86—48no—
245Dic86—41no—
246Dic86—41no—
247C8×C43—42no—
248C8×C43—81no—
249C43⋊C8—42no—
250C43⋊C8—81no—
251#8314—431nomaximal, Sylow
252C22×C43#37911yescharacteristic
253C22×C43#40811yescharacteristic
254C22×C43#40811yescharacteristic
255C22×C43C2×#10311yescharacteristic
256C22×C43#41911yescharacteristic
257C22×C43C2×#10411yescharacteristic
258C22×C43#42111yescharacteristic
259C2×D43—22no—
260C2×D43—22no—
261C2×D43—22no—
262C2×D43—41no—
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—41no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43#40811yescharacteristic
271C4×C43#40811yescharacteristic
272C4×C43#40811yescharacteristic
273C4×C43#40811yescharacteristic
274C4×C43#44811yescharacteristic
275C4×C43#44811yescharacteristic
276C4×C43#45111yescharacteristic
277C4×C43#45111yescharacteristic
278Dic43—22no—
279Dic43—22no—
280Dic43—42no—
281Dic43—41no—
282Dic43—42no—
283C2×#533—431no—
284#1797—431no—
285C4×C22⋊C8—431no—
286C2×Q8⋊C8—431no—
287C2×Q8⋊C8—431no—
288C2×Q8⋊C8—431no—
289C2×Q8⋊C8D4311yescharacteristic, complemented
290C2×C43#148111yescharacteristic
291C2×C43#148511yescharacteristic
292C2×C43#149311yescharacteristic
293C2×C43#149711yescharacteristic
294C2×C43#178011yescharacteristic
295C2×C43#178711yescharacteristic
296C2×C43#178911yescharacteristic
297D43—42no—
298#533—862no—
299#533—862no—
300#533—862no—
301#533—862no—
302C2×C4⋊Q8—431no—
303C2×C4⋊Q8—431no—
304C2×#125—861no—
305C2×C22⋊Q8—431no—
306C2×C22⋊Q8—431no—
307C2×C22⋊Q8—861no—
308C2×C4×Q8—431no—
309C2×C4×Q8—861no—
310C2×C4×Q8C2×D4311yescharacteristic
311C2×#117—861no—
312C22×C42—431no—
313C2×C4⋊C8—431no—
314C2×C4⋊C8C2×D4311yescharacteristic
315C2×C22⋊C8—861no—
316C2×C22⋊C8—861no—
317C2×C4×C8—431no—
318C2×C4×C8C2×D4311yescharacteristic
319#336—861no—
320#336—861no—
321Q8⋊C8—22no—
322Q8⋊C8—862no—
323Q8⋊C8—862no—
324Q8⋊C8—862no—
325C43#831411yescharacteristic, complemented, Sylow
326C22×Q8—431no—
327C22×Q8—861no—
328C22×Q8C4×D4311yescharacteristic
329C23×C4—431no—
330C23×C4—431no—
331C23×C4—431no—
332C22×C8—21no—
333C22×C8—21no—
334C22×C8—861no—
335C22×C8—861no—
336C4⋊Q8—862no—
337C4⋊Q8—862no—
338C4⋊Q8—862no—
339C4⋊Q8—862no—
340#125—864no—
341#125—864no—
342C22⋊Q8—862no—
343C22⋊Q8—864no—
344C22⋊Q8—864no—
345C22⋊Q8—862no—
346C22⋊Q8—862no—
347C22⋊Q8—862no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—432no—
351C4×Q8—432no—
352C4×Q8—864no—
353C4×Q8—864no—
354C4×Q8—861no—
355C4×Q8—861no—
356C4×Q8D17212yes—
357C4×Q8C22⋊D4312yes—
358#117—864no—
359#117—864no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—861no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4C4×D4311yescharacteristic
369C2×C22⋊C4—861no—
370C2×C22⋊C4—861no—
371C2×C42—21no—
372C2×C42—431no—
373C2×C42—431no—
374C2×C42—431no—
375C2×C42—861no—
376C2×C42—861no—
377C2×C42—861no—
378C2×C42—861no—
379C2×C42—861no—
380C2×C42C22×D4311yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—861no—
384C4⋊C8—861no—
385C22⋊C8—864no—
386C22⋊C8—1722no—
387C4×C8—21no—
388C4×C8—21no—
389C4×C8—861no—
390C4×C8—861no—
391C24—431no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—432no—
398C2×Q8—864no—
399C2×Q8—861no—
400C2×Q8—861no—
401C2×Q8—861no—
402C2×Q8—861no—
403C2×Q8—861no—
404C2×Q8—1722no—
405C2×Q8—1722no—
406C2×Q8(C2×D43)⋊C412yes—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—431no—
410C22×C4—431no—
411C22×C4—432no—
412C22×C4—432no—
413C22×C4—431no—
414C22×C4—862no—
415C22×C4—861no—
416C22×C4—861no—
417C22×C4—861no—
418C22×C4—861no—
419C22×C4—861no—
420C22×C4—861no—
421C22×C4—861no—
422C22×C4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—1721no—
430C22×C4C2×C4×D4311yescharacteristic
431C22×C4D4×D4311yescharacteristic
432C22×C4D4×D4311yescharacteristic
433C2×C8—22no—
434C2×C8—41no—
435C2×C8—41no—
436C2×C8—41no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—862no—
440C2×C8—1721no—
441C2×C8—1721no—
442C2×C8—1721no—
443C2×C8—1721no—
444C2×C8—1721no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—432no—
449C4⋊C4—864no—
450C4⋊C4—864no—
451C4⋊C4—864no—
452C4⋊C4—864no—
453C4⋊C4—864no—
454C4⋊C4—861no—
455C4⋊C4—862no—
456C4⋊C4—862no—
457C4⋊C4(C2×D43)⋊C412yes—
458C22⋊C4—864no—
459C22⋊C4—864no—
460C42—22no—
461C42—22no—
462C42—861no—
463C42—861no—
464C42—861no—
465C42—861no—
466C42—862no—
467C42—861no—
468C42—861no—
469C42—862no—
470C42C2×D17211yescharacteristic
471C42D4×D4311yescharacteristic
472C42D4×D4311yescharacteristic
473C42C2×C22⋊D4311yescharacteristic
474C23—432no—
475C23—861no—
476C23—861no—
477C23—861no—
478C23—861no—
479C23—861no—
480C23—861no—
481C23C22⋊C4×D4311yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—862no—
487Q8—862no—
488Q8—1728no—
489Q8—1721no—
490Q8—1721no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—432no—
500C2×C4—432no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—862no—
508C2×C4—862no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4C22⋊C4×D4311yescharacteristic
525C2×C4C2×(C2×D43)⋊C411yescharacteristic
526C2×C4#1306329311yescharacteristic
527C2×C4#1306329311yescharacteristic
528C2×C4#1306329511yescharacteristic
529C2×C4#1306329511yescharacteristic
530C2×C4#1306333111yescharacteristic
531C2×C4#1306333111yescharacteristic
532C2×C4#1306333311yescharacteristic
533C2×C4#1306333311yescharacteristic
534C2×C4SD16×D4311yescharacteristic
535C2×C4Q16×D4311yescharacteristic
536C2×C4#1306335411yescharacteristic
537C2×C4#1306335711yescharacteristic
538C8—42no—
539C8—81no—
540C8—3441no—
541C8—1722no—
542C22—862no—
543C22—862no—
544C22—862no—
545C22—1721no—
546C22—1721no—
547C22—1721no—
548C22—1721no—
549C22#1458275411yescharacteristic
550C22#1458286411yescharacteristic
551C22#1458286411yescharacteristic
552C22#103×D4311yescharacteristic
553C22#1458290611yescharacteristic
554C22#104×D4311yescharacteristic
555C22#1458291411yescharacteristic
556C4—21no—
557C4—21no—
558C4—42no—
559C4—42no—
560C4—862no—
561C4—862no—
562C4—1721no—
563C4—1722no—
564C4—1722no—
565C4#1458286411yescharacteristic
566C4#1458286411yescharacteristic
567C4#1458286511yescharacteristic
568C4#1458286711yescharacteristic
569C4#1458303611yescharacteristic
570C4#1458303911yescharacteristic
571C4#1458305311yescharacteristic
572C4#1458305611yescharacteristic
573C2—1722no—
574C2#1913299611yescharacteristic
575C2#1913301411yescharacteristic
576C2#1913304811yescharacteristic
577C2#1913306611yescharacteristic
578C2#1913450611yescharacteristic
579C2#1913452811yescharacteristic
580C2#1913453711yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×Q8⋊C8C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×Q8⋊C8D43
hypocenterC43#8314
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#14582631C2semidirect
5. C2×Q8⋊(C43⋊C8)C2semidirect
6. C2×#14582629C2semidirect
7. C2×C43×Q8⋊C8C2semidirect
289. C2×Q8⋊C8D43semidirect
325. C43#8314semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
#191345722
C4×(C2×D43)⋊C82
C2×#145826312
C2×Q8⋊(C43⋊C8)2
C2×#145826292
C2×C43×Q8⋊C82
#831443