Finite Group Databasebeta

← #11868993

Subgroups — #11868993

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595051C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic
3#10592818C211yesmaximal, characteristic, complemented
4C3×#5131C211yesmaximal, characteristic
5C3×#5121C211yesmaximal, characteristic, complemented
6#10591138C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic
8#10590782C212yesmaximal, complemented
9#10590780C212yesmaximal, complemented
10#10590778C212yesmaximal, complemented
11#10590776C212yesmaximal, complemented
12#79242—31nomaximal
13#78918—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21D3×#217—22no—
22#63964—22no—
23#63919C2212yescomplemented
24#63918—21no—
25#63898C2212yes—
26#63898C2212yes—
27Dic3×D12—21no—
28Dic3×D12—21no—
29#63872C2212yescomplemented
30#63869—21no—
31#63641C2212yescomplemented
32#63641C2212yescomplemented
33C3×#821C2212yes—
34C3×#821C2212yes—
35C3×#818C2212yescomplemented
36C3×#817C2212yescomplemented
37#63576C2211yescharacteristic, complemented
38#63576C2211yescharacteristic, complemented
39#63574C2211yescharacteristic, complemented
40#63574C2211yescharacteristic, complemented
41#63562C2212yes—
42#63562C2212yes—
43#5798—31no—
44#5521—31no—
45#5519—31no—
46#5500—31no—
47C3×#428—31no—
48C3×#418—31no—
49C2×#832—31no—
50#5131D311yescharacteristic
51#5121D311yescharacteristic, complemented
52#5119—31no—
53#5119—31no—
54#5119—61no—
55#4998—31no—
56#4998—31no—
57C2×#809—31no—
58#4891—32no—
59#4890—32no—
60#4871—32no—
61#4870—32no—
62#4766—32no—
63#4763—32no—
64#4761—32no—
65#4759—32no—
66C23×C3×D3—21no—
67C22×C32×C4C2311yescharacteristic
68C22×C3×Dic3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12Q814yescomplemented
72C2×C3×D12C2312yes—
73C2×#627—22no—
74C2×D3×Dic3—22no—
75C2×D3×Dic3—22no—
76C32×M16—22no—
77C2×C32×C8C2312yes—
78#3757D412yes—
79C4⋊(C3⋊Dic3)D411yescharacteristic
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4×C3⋊Dic3C2312yes—
82C2×C3⋊(C3⋊C8)—22no—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×#217—21no—
86C3×#217—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4×Dic3—21no—
94C3×C4×Dic3—21no—
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3081—91noSylow
101C22×C3×D4—31no—
102C22×D12C2×D311yescharacteristic
103C2×C3×M16—21no—
104C2×C3×M16C2×D311yescharacteristic
105C2×C3×M16C2×D311yescharacteristic
106C3×#117—31no—
107C3×#117—31no—
108C2×C3×C4⋊C4—31no—
109C2×#217—62no—
110D4×Dic3—32no—
111D4×Dic3—32no—
112D4×Dic3—61no—
113D4×Dic3—61no—
114#926—31no—
115#926—31no—
116#926—61no—
117#926C2×D311yescharacteristic
118#926C2×D311yescharacteristic
119C2×C4⋊Dic3C2×D311yescharacteristic
120#924—62no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—61no—
124#893—32no—
125#893—32no—
126#890—32no—
127#890—32no—
128#890—61no—
129#888—32no—
130#888—32no—
131#888—61no—
132D3×C22⋊C4—62no—
133#878—62no—
134C4×D12—61no—
135C4×D12—61no—
136#870—61no—
137#869—61no—
138C3×#107—32no—
139C3×#106—32no—
140C3×#102—32no—
141C3×#102—32no—
142#832—32no—
143#832—32no—
144#821C2×D312yes—
145#821C2×D312yes—
146#818C2×D312yescomplemented
147#817C2×D312yescomplemented
148Dic3⋊C8—32no—
149Dic3⋊C8—32no—
150Dic3⋊C8—32no—
151Dic3⋊C8—32no—
152Dic3⋊C8—62no—
153Dic3⋊C8—62no—
154#809—32no—
155#809—32no—
156#808—31no—
157#808—31no—
158#808—31no—
159#808—31no—
160#807—31no—
161#807—31no—
162#807—31no—
163#807—31no—
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—22no—
166C22×C3×D3—24no—
167C22×C3×D3—81no—
168C22×C3×D3—81no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×Q812yes—
171C2×C32×C4#4112yes—
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—81no—
181C3×D12—24no—
182C3×D12—22no—
183C3×D12C2×Q814yes—
184#627—82no—
185D3×Dic3—82no—
186D3×Dic3—82no—
187C32×C8—22no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—21no—
190#544—91no—
191#518—91no—
192#478—92no—
193#478—92no—
194#476—92no—
195#474—92no—
196#428—31no—
197#427—91no—
198#424—91no—
199#418—31no—
200C2×#102—91no—
201C24×C3—61no—
202C23×D3—21no—
203C2×C3×D4—34no—
204C2×C3×D4—32no—
205C2×C3×D4—62no—
206C2×C3×D4—61no—
207C22×C3×C4—21no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×Dic3—21no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C2×D12—21no—
215C2×D12—22no—
216C2×D12Dic614yescomplemented
217C2×D12C22×D312yes—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C3×M16—22no—
223C3×M16—22no—
224C3×M16—42no—
225C2×C3×C8—22no—
226C2×C3×C8C22×D312yes—
227C2×C3×C8C22×D312yes—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—61no—
234C3×C22⋊C4—61no—
235C3×C22⋊C4—61no—
236C3×C42—61no—
237C3×C42—61no—
238#217—21no—
239#217—21no—
240#217—32no—
241#217—32no—
242#217—62no—
243#217—62no—
244#217—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247C4⋊Dic3—21no—
248C4⋊Dic3—31no—
249C4⋊Dic3—31no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3C22×D311yescharacteristic
257C4⋊Dic3C22×D311yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D311yescharacteristic
260C4⋊Dic3C22×D312yes—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265C4×Dic3—21no—
266C4×Dic3—21no—
267C4×Dic3—32no—
268C4×Dic3—32no—
269C4×Dic3—62no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—122no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32C22⋊Q812yes—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—24no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3—84no—
287C32×C4C22⋊Q812yes—
288C32×C4C22×Q811yescharacteristic
289C32×C4C2×#4111yescharacteristic
290C3⋊Dic3—22no—
291C3⋊Dic3—22no—
292C3×Dic3—41no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C22×D4—31no—
298C2×M16D3211yescharacteristic
299C22×C8—91no—
300C4⋊Q8—92no—
301C4⋊Q8—181no—
302#125—92no—
303#125—181no—
304C22⋊Q8—182no—
305C4×D4—92no—
306C4×D4—92no—
307C4×D4—181no—
308C4×D4—181no—
309#117—31no—
310#117—31no—
311#117—91no—
312C2×C4⋊C4—31no—
313C2×C22⋊C4—182no—
314#107—32no—
315#107—91no—
316#107—91no—
317#106—32no—
318#106—91no—
319#106—91no—
320C4⋊C8—92no—
321C4⋊C8—92no—
322#102—32no—
323#102—32no—
324#102—92no—
325#102—92no—
326C23×C3—21no—
327C23×C3—62no—
328C23×C3—64no—
329C23×C3—241no—
330C23×C3—241no—
331C23×C3D3×D411yescharacteristic
332C23×C3D3×D411yescharacteristic
333C22×D3—22no—
334C22×D3—24no—
335C22×D3—81no—
336C22×D3—81no—
337C3×D4—34no—
338C3×D4—64no—
339C3×D4—62no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—61no—
345C2×C3×C4—62no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—241no—
350C2×C3×C4C2×Dic612yes—
351C2×C3×C4#23512yes—
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23712yes—
355C2×C3×C4D3×Q812yes—
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—81no—
370C2×Dic3—242no—
371C2×Dic3—242no—
372D12—24no—
373D12—22no—
374D12C2×Dic614yes—
375C4×D3—242no—
376C4×D3—242no—
377Dic6—242no—
378Dic6—242no—
379C3×C8—22no—
380C3×C8—22no—
381C3×C8—42no—
382C3⋊C8—61no—
383C3⋊C8—61no—
384C3⋊C8—61no—
385C3⋊C8—61no—
386C3⋊C8—121no—
387C3⋊C8—121no—
388C2×C32—22no—
389C2×C32C2×C22⋊Q811yescharacteristic
390C2×C32#57611yescharacteristic
391C2×C32#57711yescharacteristic
392C3×D3—44no—
393C24—61no—
394C2×Q8—182no—
395C2×D4—32no—
396C2×D4—34no—
397C2×D4—61no—
398C2×D4—62no—
399C22×C4—61no—
400C22×C4—182no—
401C22×C4—182no—
402C22×C4C2×D3211yescharacteristic
403M16—22no—
404C2×C8—91no—
405C2×C8—91no—
406C2×C8—182no—
407C2×C8C2×D3212yes—
408C4⋊C4—31no—
409C4⋊C4—31no—
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—31no—
413C4⋊C4—61no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C22⋊C4—61no—
420C22⋊C4—61no—
421C22⋊C4—92no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C42—61no—
425C42—61no—
426C42—92no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—64no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—244no—
439C22×C3#87812yes—
440C22×C3#89612yes—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C2×D3×D411yescharacteristic
443C2×D3—24no—
444C2×D3—42no—
445C2×D3—42no—
446C2×D3—84no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—121no—
451C3×C4—122no—
452C3×C4—121no—
453C3×C4—121no—
454C3×C4—121no—
455C3×C4#87812yes—
456C3×C4#89612yes—
457C3×C4C22×Dic611yescharacteristic
458C3×C4C2×#23511yescharacteristic
459C3×C4C2×#23711yescharacteristic
460C3×C4C2×D3×Q811yescharacteristic
461Dic3—41no—
462Dic3—42no—
463Dic3—41no—
464Dic3—41no—
465Dic3—41no—
466Dic3—62no—
467Dic3—62no—
468Dic3—62no—
469Dic3—62no—
470Dic3—122no—
471Dic3—122no—
472C32#308111yescharacteristic, complemented, Sylow
473C23—62no—
474C23—64no—
475C23—241no—
476C23—241no—
477C23#380211yescharacteristic
478Q8—722no—
479D4—34no—
480D4—62no—
481D4—64no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—62no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—241no—
490C2×C4—722no—
491C2×C4—722no—
492C2×C4D3×Dic612yes—
493C2×C4#380211yescharacteristic
494C2×C4#380412yes—
495C2×C4C22×D3211yescharacteristic
496C8—22no—
497C8—181no—
498C8—181no—
499C2×C3—22no—
500C2×C3—22no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—42no—
505C2×C3—124no—
506C2×C3C2×#87811yescharacteristic
507C2×C3C2×#89611yescharacteristic
508C2×C3#577411yescharacteristic
509C2×C3#577411yescharacteristic
510C2×C3#577511yescharacteristic
511C2×C3#577811yescharacteristic
512D3—44no—
513C22—21no—
514C22—21no—
515C22—64no—
516C22—122no—
517C22—122no—
518C22—244no—
519C22#6389912yes—
520C22C2×#380211yescharacteristic
521C4—121no—
522C4—121no—
523C4—122no—
524C4—121no—
525C4—121no—
526C4—182no—
527C4—182no—
528C4#6389912yes—
529C4C2×D3×Dic611yescharacteristic
530C4C2×#380411yescharacteristic
531C3—21no—
532C3#7891811yescharacteristic, complemented
533C3#7924211yescharacteristic, complemented
534C2—22no—
535C2—124no—
536C2#1059471911yescharacteristic
537C2#1059472011yescharacteristic
538C2C2×#6389911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC2×M16D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10595051C2semidirect
3. #10592818C2semidirect
5. C3×#5121C2semidirect
6. #10591138C2semidirect
8. #10590782C2semidirect
9. #10590780C2semidirect
10. #10590778C2semidirect
11. #10590776C2semidirect
23. #63919C22semidirect
29. #63872C22semidirect
31. #63641C22semidirect
32. #63641C22semidirect
35. C3×#818C22semidirect
36. C3×#817C22semidirect
37. #63576C22semidirect
38. #63576C22semidirect
39. #63574C22semidirect
40. #63574C22semidirect
51. #5121D3semidirect
71. C2×C3×D12Q8semidirect
146. #818C2×D3semidirect
147. #817C2×D3semidirect
216. C2×D12Dic6semidirect
472. C32#3081semidirect
532. C3#78918semidirect
533. C3#79242semidirect

Maximal subgroups

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

subgroupindex
#105950512
#105949822
#105928182
C3×#51312
C3×#51212
#105911382
C2×#635622
#105907822
#105907802
#105907782
#105907762
#792423
#789183