Finite Group Databasebeta

← #25021917

Subgroups — #25021917

Order 11008.

1758 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063290C211yesmaximal, characteristic
2C2×#14582819C211yesmaximal, characteristic
3C2×#14582781C212yesmaximal
4C2×C4⋊C4×Dic43C211yesmaximal, characteristic
5#19132865C211yesmaximal, characteristic
6#19132854C211yesmaximal, characteristic
7#19132829C212yesmaximal
8#19132826C212yesmaximal
9#19132826C212yesmaximal
10#19132820C211yesmaximal, characteristic
11C43×#1441C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13C2×#13063290—28no—
14C2×#13063290—24no—
15C22×C4⋊Dic43C2211yescharacteristic
16C22×Dic43⋊C4C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×C4×Dic43C2211yescharacteristic
19C22×C4×Dic43C2212yes—
20C22×C4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14582819C418yescomplemented
23#14582781—28no—
24C4⋊C4×Dic43—24no—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2212yes—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C22×Dic86—22no—
41C22×Dic86—22no—
42C22×Dic86—24no—
43C22×Dic86—24no—
44C22×Dic86C2×C414yes—
45C23×Dic43C2312yes—
46C23×Dic43C2311yescharacteristic
47C23×Dic43C2311yescharacteristic
48C23×Dic43C2312yes—
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2311yescharacteristic
51#13063290—232no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43Q814yescomplemented
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4C2×C418yes—
60C2×Dic43⋊C4D418yes—
61C2×C4×Dic43—24no—
62C2×C4×Dic43—22no—
63C2×C4×Dic43—24no—
64C2×C4×Dic43—24no—
65C2×C4×Dic43—24no—
66C2×C4×Dic43—22no—
67C2×C4×Dic43—22no—
68C2×C4×Dic43—22no—
69C2×C4×Dic43—24no—
70C2×C4×Dic43D414yes—
71C43⋊#95—22no—
72C43⋊#95—24no—
73C43⋊#95—22no—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95C2×C414yes—
80C43⋊#95C2×C418yes—
81C23×C4×C43C2312yes—
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2312yes—
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43—24no—
87C2×C4⋊C4×C43—22no—
88C2×C4⋊C4×C43—22no—
89C2×C4⋊C4×C43—22no—
90C2×C4⋊C4×C43C2×C414yes—
91#95×C43—24no—
92#95×C43—24no—
93#95×C43—22no—
94C24×C43C2411yescharacteristic
95C22×C4×C43—21no—
96C22×C4×C43—22no—
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—21no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43C22×C412yes—
119C22×C4×C43C22×C412yes—
120C22×C4×C43C22×C412yes—
121C22×C4×C43C2×D414yes—
122C22×C4×C43C2×D412yes—
123C22×C4×C43C2×Q812yes—
124C22×C4×C43#4112yes—
125C22×C4×C43#4112yes—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—21no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43C22×C414yes—
150C22×Dic43C22×C414yes—
151C22×Dic43C2×D414yes—
152C22×Dic43C2×D414yes—
153C22×Dic43C2×D412yes—
154C22×Dic43C2×D412yes—
155C22×Dic43C2×Q812yes—
156C22×Dic43C2×Q812yes—
157C22×Dic43#4112yes—
158C22×Dic43#4114yes—
159C22×Dic43#4112yes—
160C2×Dic86—28no—
161C2×Dic86—216no—
162C2×Dic86—28no—
163C2×Dic86—28no—
164C2×Dic86—216no—
165C4⋊C4×C43—28no—
166C4⋊C4×C43—28no—
167C4⋊Dic43—28no—
168Dic43⋊C4—216no—
169Dic43⋊C4—216no—
170C4×Dic43—28no—
171C4×Dic43—216no—
172C4×Dic43—28no—
173C4×Dic43—44no—
174C23×C43C23×C411yescharacteristic
175C23×C43C22×D411yescharacteristic
176C23×C43C22×D412yes—
177C23×C43C22×Q811yescharacteristic
178C23×C43C2×#4112yes—
179C23×C43C2×#4111yescharacteristic
180C23×C43C2×#4111yescharacteristic
181C23×C43C2×#4111yescharacteristic
182C23×C43C2×#4111yescharacteristic
183C23×C432−1+412yes—
184C23×C432−1+412yes—
185C2×C4×C43—22no—
186C2×C4×C43—24no—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—24no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—24no—
196C2×C4×C43—22no—
197C2×C4×C43—24no—
198C2×C4×C43—24no—
199C2×C4×C43—24no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43C4×D414yes—
215C2×C4×C43C4×Q814yescomplemented
216C2×Dic43—24no—
217C2×Dic43—24no—
218C2×Dic43—22no—
219C2×Dic43—24no—
220C2×Dic43—22no—
221C2×Dic43—24no—
222C2×Dic43—24no—
223C2×Dic43—24no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—24no—
227C2×Dic43—24no—
228C2×Dic43—24no—
229C2×Dic43—24no—
230C2×Dic43—24no—
231C2×Dic43—24no—
232C2×Dic43—24no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—24no—
236C2×Dic43—24no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43C4×D418yes—
248C2×Dic43#12014yes—
249C2×Dic43C22⋊Q814yes—
250Dic86—232no—
251#14174—431nomaximal, Sylow
252C22×C43C2×C4×D412yes—
253C22×C43C2×C4×D411yescharacteristic
254C22×C43C2×C4×Q811yescharacteristic
255C22×C43C4×#4111yescharacteristic
256C22×C43#51912yes—
257C22×C43C2×#12011yescharacteristic
258C22×C43C2×C22⋊Q811yescharacteristic
259C22×C43#52511yescharacteristic
260C22×C43#52511yescharacteristic
261C22×C43#52512yes—
262C22×C43#52911yescharacteristic
263C22×C43#53311yescharacteristic
264C22×C43#53611yescharacteristic
265C22×C43#53611yescharacteristic
266C22×C43#54112yes—
267C22×C43#54712yes—
268C22×C43#54712yes—
269C22×C43#54812yes—
270C22×C43D4×Q812yes—
271C22×C43#55212yes—
272C22×C43#55612yes—
273C22×C43#55612yes—
274C22×C43#55712yes—
275C4×C43—24no—
276C4×C43—24no—
277C4×C43—44no—
278C4×C43—42no—
279C4×C43—82no—
280Dic43—24no—
281Dic43—24no—
282Dic43—28no—
283Dic43—42no—
284Dic43—44no—
285Dic43—42no—
286C22×C4×Q8—431no—
287C2×#395—431no—
288C2×#387—432no—
289C2×C4×C4⋊C4—431no—
290#1446—431no—
291#1442—431no—
292#1441D4311yescharacteristic
293#1436—432no—
294#1436—432no—
295#1436—432no—
296#1434—431no—
297C2×C43C4×#12011yescharacteristic
298C2×C43C4×C22⋊Q811yescharacteristic
299C2×C43#232711yescharacteristic
300C2×C43#236212yes—
301C2×C43#236512yes—
302C2×C43#240611yescharacteristic
303C2×C43#240911yescharacteristic
304C2×C43#246212yes—
305C2×C43#246912yes—
306C2×C43#258111yescharacteristic
307C2×C43#259911yescharacteristic
308C23×Q8—431no—
309C2×C4×Q8—864no—
310C2×C4×Q8—868no—
311C22×C4⋊C4—432no—
312C22×C4⋊C4—432no—
313C22×C4⋊C4—431no—
314C22×C4⋊C4C2×D4311yescharacteristic
315C22×C4⋊C4C2×D4311yescharacteristic
316C22×C42—431no—
317C22×C42—432no—
318C22×C42—431no—
319C22×C42—431no—
320#395—438no—
321#387—868no—
322C4×C4⋊C4—864no—
323C2×#95—431no—
324C2×#95—432no—
325C2×#95—432no—
326C2×#95—432no—
327C2×#95—432no—
328C2×#95—432no—
329C2×#95—431no—
330C2×#95—432no—
331C2×#95—432no—
332C2×#95—431no—
333C2×#95C2×D4311yescharacteristic
334C2×#95C2×D4312yes—
335C2×#95C2×D4312yes—
336C43#1417411yescharacteristic, complemented, Sylow
337C22×Q8—434no—
338C22×Q8—864no—
339C22×Q8—864no—
340C22×Q8—862no—
341C22×Q8—862no—
342C23×C4—432no—
343C23×C4—431no—
344C23×C4—431no—
345C23×C4—432no—
346C23×C4—431no—
347C23×C4—431no—
348C23×C4C22×D4312yes—
349C23×C4C22×D4311yescharacteristic
350C23×C4C22×D4312yes—
351C23×C4C22×D4311yescharacteristic
352C23×C4C22×D4311yescharacteristic
353C4×Q8—8632no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—438no—
359C2×C4⋊C4—438no—
360C2×C4⋊C4—434no—
361C2×C4⋊C4—864no—
362C2×C4⋊C4—864no—
363C2×C4⋊C4—864no—
364C2×C4⋊C4—864no—
365C2×C4⋊C4—862no—
366C2×C4⋊C4—862no—
367C2×C4⋊C4C4×D4314yes—
368C2×C42—434no—
369C2×C42—864no—
370C2×C42—864no—
371C2×C42—864no—
372C2×C42—862no—
373C2×C42—862no—
374C2×C42—864no—
375C2×C42—862no—
376C2×C42—862no—
377C2×C42—864no—
378#95—24no—
379#95—24no—
380#95—22no—
381#95—438no—
382#95—434no—
383#95—864no—
384#95—864no—
385#95—864no—
386#95—862no—
387#95—864no—
388#95—864no—
389#95—862no—
390#95—864no—
391C24C23×D4311yescharacteristic
392C2×Q8—8616no—
393C2×Q8—868no—
394C2×Q8—868no—
395C2×Q8—8616no—
396C2×Q8—868no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—434no—
421C22×C4—432no—
422C22×C4—434no—
423C22×C4—434no—
424C22×C4—432no—
425C22×C4—432no—
426C22×C4—432no—
427C22×C4—434no—
428C22×C4—434no—
429C22×C4—432no—
430C22×C4—432no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—861no—
435C22×C4—862no—
436C22×C4—861no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—861no—
442C22×C4—862no—
443C22×C4—861no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4C2×C4×D4312yes—
455C22×C4C2×C4×D4312yes—
456C22×C4C2×C4×D4312yes—
457C22×C4D4×D4314yes—
458C22×C4D4×D4312yes—
459C22×C4#1062190012yes—
460C22×C4#1062190012yes—
461C22×C4Q8×D4312yes—
462C4⋊C4—28no—
463C4⋊C4—28no—
464C4⋊C4—8616no—
465C4⋊C4—8616no—
466C4⋊C4—868no—
467C42—868no—
468C42—8616no—
469C42—868no—
470C42—1724no—
471C23C22×C4×D4311yescharacteristic
472C23C2×D4×D4312yes—
473C23C2×D4×D4311yescharacteristic
474C23C2×Q8×D4311yescharacteristic
475C23#41×D4311yescharacteristic
476C23#41×D4311yescharacteristic
477C23#41×D4312yes—
478C23C2×#1062190011yescharacteristic
479C23C2×#1062190011yescharacteristic
480C23#1306337212yes—
481C23#1306337312yes—
482Q8—8632no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—438no—
513C2×C4—434no—
514C2×C4—434no—
515C2×C4—864no—
516C2×C4—864no—
517C2×C4—864no—
518C2×C4—864no—
519C2×C4—862no—
520C2×C4—864no—
521C2×C4—864no—
522C2×C4—862no—
523C2×C4—864no—
524C2×C4—864no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—864no—
528C2×C4—864no—
529C2×C4—864no—
530C2×C4—864no—
531C2×C4—864no—
532C2×C4—864no—
533C2×C4—864no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1722no—
546C2×C4(C22⋊D43)⋊C414yes—
547C2×C4#1306329014yescomplemented
548C22C4×D4×D4312yes—
549C22C2×(C22⋊D43)⋊C411yescharacteristic
550C22C2×#1306329011yescharacteristic
551C22#1458336711yescharacteristic
552C22#1458337512yes—
553C22#120×D4311yescharacteristic
554C22C22⋊Q8×D4311yescharacteristic
555C22#1458340711yescharacteristic
556C22#1458340912yes—
557C22#1458340911yescharacteristic
558C22#1458343011yescharacteristic
559C22#1458345111yescharacteristic
560C22#1458346911yescharacteristic
561C22#1458347411yescharacteristic
562C22#1458350912yes—
563C22#1458354712yes—
564C22#1458354912yes—
565C22#1458355912yes—
566C22#1458356412yes—
567C22#1458358112yes—
568C22#1458361612yes—
569C22#1458362012yes—
570C22#1458362612yes—
571C4—24no—
572C4—24no—
573C4—42no—
574C4—44no—
575C4—82no—
576C4—868no—
577C4—864no—
578C4—864no—
579C4—1722no—
580C4—1724no—
581C4—1722no—
582C2#1913710011yescharacteristic
583C2#1913712311yescharacteristic
584C2#1913731311yescharacteristic
585C2#1913761712yes—
586C2#1913764812yes—
587C2#1913792511yescharacteristic
588C2#1913795511yescharacteristic
589C2#1913857812yes—
590C2#1913867712yes—
591C2#1913995811yescharacteristic
592C2#1914017511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1441C2
socle, prime radical, cosocleC24×C43C24
hypercenter#1441D43
hypocenterC43#14174
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
22. #14582819C4semidirect
54. C2×C4⋊Dic43Q8semidirect
215. C2×C4×C43C4×Q8semidirect
336. C43#14174semidirect
547. C2×C4#13063290semidirect

Maximal subgroups

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

subgroupindex
C22×#130632902
C2×#145828192
C2×#145827812
C2×C4⋊C4×Dic432
#191328652
#191328542
#191328292
#191328262
#191328202
C43×#14412
#1417443