Finite Group Databasebeta

← #11873576

Subgroups — #11873576

Order 1152.

1077 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595300C211yesmaximal, characteristic
2#10594482C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic, complemented
4C3×#4764C212yesmaximal, complemented
5#10591477C212yesmaximal, complemented
6#10591416C211yesmaximal, characteristic, complemented
7#10590940C211yesmaximal, characteristic, complemented
8#10590882C212yesmaximal, complemented
9#10590668C211yesmaximal, characteristic, complemented
10#10590593C211yesmaximal, characteristic, complemented
11#10590550C212yesmaximal, complemented
12D3×#490—32nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C2×#3811—21no—
15C2×#3811—21no—
16C2×#3802C2211yescharacteristic
17C2×C8×C3⋊D3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C3×#940C2212yes—
20C3×#890C2212yescomplemented
21#63979—22no—
22#63911C2212yes—
23#63900—21no—
24#63900C2211yescharacteristic
25#63883—21no—
26C4×#624C2211yescharacteristic
27#63869C2212yescomplemented
28#63847—22no—
29C2×#3710C2211yescharacteristic
30C32×#102C2211yescharacteristic, complemented
31#63659C2211yescharacteristic, complemented
32#63648C2211yescharacteristic, complemented
33#63636C2211yescharacteristic, complemented
34C3×#832C2212yescomplemented
35C3×#821C2212yescomplemented
36C3×#815C2212yescomplemented
37C3×#809C2212yescomplemented
38#63564C2212yescomplemented
39#63563C2212yescomplemented
40#63562C2212yescomplemented
41#63554C2212yescomplemented
42D3×#127—32no—
43D3×#125—32no—
44C3×#490—32no—
45#5071—32no—
46#5067—32no—
47D3×#102—32no—
48D3×#102—32no—
49D3×#102—32no—
50D3×#102—32no—
51D3×#102—61no—
52#4764—32no—
53#4764—32no—
54#4764—32no—
55#4764D312yescomplemented
56#4713—32no—
57D3×#97—32no—
58C23×C3⋊D3—21no—
59C22×D32—21no—
60C2×C32×D4C2311yescharacteristic
61C2×#638—21no—
62D4×C3⋊D3—22no—
63D4×C3⋊D3—22no—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C2×C3×D12C2312yes—
70#3811—44no—
71#3811—44no—
72C2×#626—22no—
73C2×#626—22no—
74C2×#625—21no—
75C2×#624—21no—
76C2×#624D411yescharacteristic
77C2×#624D411yescharacteristic
78#3802—22no—
79#3802—22no—
80C2×C32×C8C2311yescharacteristic
81C32×C4⋊C4C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C8×C3⋊D3—22no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4—22no—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2312yes—
91#3724—21no—
92#3724—22no—
93Dic3⋊Dic3—22no—
94Dic32D412yes—
95#3710—22no—
96C2×#490—91noSylow
97C2×D3×D4—32no—
98C2×D3×D4—32no—
99C2×D3×D4—61no—
100C2×D3×D4—62no—
101C2×D3×D4—62no—
102C3×#127—32no—
103C3×#125—32no—
104#940—32no—
105#940—62no—
106#940—62no—
107#940C2×D312yes—
108C2×D3×C8—32no—
109C2×D3×C8—32no—
110C2×D3×C8—61no—
111D3×C4⋊C4—32no—
112D3×C4⋊C4—32no—
113D3×C4⋊C4—61no—
114D3×C4⋊C4—62no—
115D3×C4⋊C4—62no—
116#890—32no—
117#890C2×D312yescomplemented
118#889—62no—
119#889—62no—
120#874—32no—
121C42×D3—32no—
122#870—32no—
123C3×#102—21no—
124C3×#102—32no—
125C3×#102—32no—
126C3×#102—32no—
127C3×#102C2×D312yescomplemented
128C3×#97—32no—
129#832—32no—
130#832—32no—
131#832—32no—
132#832—61no—
133#832C2×D312yescomplemented
134#821—32no—
135#821—32no—
136#821—32no—
137#821—61no—
138#821C2×D312yescomplemented
139#815—32no—
140#815C2×D312yescomplemented
141#809—32no—
142#809—32no—
143#809—32no—
144#809—61no—
145#809C2×D312yescomplemented
146#803—32no—
147C23×C32—21no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3—42no—
151C22×C3⋊D3—42no—
152C22×C3⋊D3C2×D411yescharacteristic
153C22×C3×D3—22no—
154C2×D32—42no—
155C2×D32—42no—
156C2×D32—42no—
157C32×D4—21no—
158C32×D4—21no—
159C2×C32×C4—21no—
160C2×C32×C4C2411yescharacteristic
161#638—42no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3C2×D411yescharacteristic
164C4⋊(C3⋊D3)—21no—
165C4⋊(C3⋊D3)—21no—
166C4×C3⋊D3—42no—
167C4×C3⋊D3#4112yes—
168C4×C3⋊D3#4112yes—
169C3×#67—44no—
170C3×#67—44no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C2×D412yes—
173C2×C3×Dic3C2×D412yes—
174C3×D12—22no—
175C3×D12—22no—
176#626—44no—
177#626—44no—
178#625—42no—
179#624—22no—
180#624—22no—
181#624—42no—
182C32×C8—21no—
183C3⋊(C3⋊C8)—21no—
184C3×C3⋊C8—22no—
185C2×#127—91no—
186C2×#125—91no—
187#490—32no—
188#490—92no—
189#490—92no—
190#490—92no—
191C2×#102—91no—
192C2×#102—91no—
193C2×#102—91no—
194C2×#102—91no—
195C2×#97—91no—
196C23×D3—62no—
197C23×D3—62no—
198C23×D3—121no—
199C2×C3×D4—21no—
200C2×C3×D4—32no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C2×C3×D4C22×D312yes—
204C2×#67—22no—
205C2×#67—22no—
206C2×#67—62no—
207C2×#67—62no—
208C2×#67—62no—
209C2×#67—62no—
210C2×#67—121no—
211D3×D4—64no—
212D3×D4—64no—
213D3×D4—64no—
214D3×D4—64no—
215D3×D4—64no—
216D3×D4—122no—
217D3×D4—128no—
218D3×D4—128no—
219C2×D12—32no—
220C2×D12—61no—
221C2×D12—62no—
222C2×D12—62no—
223C2×D12C22×D312yes—
224C2×C4×D3—32no—
225C2×C4×D3—32no—
226C2×C4×D3—32no—
227C2×C4×D3—61no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—121no—
231C2×C3×C8—21no—
232C2×C3×C8—32no—
233C2×C3×C8C22×D312yes—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4C22×D312yes—
239C3×C42—32no—
240C4⋊Dic3—22no—
241C4⋊Dic3—32no—
242C4⋊Dic3—61no—
243C4⋊Dic3—62no—
244C4⋊Dic3C22×D312yes—
245Dic3⋊C4—22no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—121no—
252C4×Dic3—32no—
253C4×Dic3—32no—
254C4×Dic3C22×D312yes—
255C2×C3⋊C8—32no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8C22×D312yes—
258D3×C8—64no—
259D3×C8—64no—
260D3×C8—122no—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32C22×D411yescharacteristic
265C2×C3⋊D3—41no—
266C2×C3⋊D3—41no—
267C2×C3⋊D3—41no—
268C2×C3⋊D3—84no—
269C2×C3⋊D3#12412yes—
270C2×C3⋊D3AGL(1,ℤ/8)12yes—
271C2×C3⋊D3AGL(1,ℤ/8)12yes—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275D32—84no—
276C32×C4—41no—
277C32×C4C2×#4111yescharacteristic
278C32×C4C2×#4111yescharacteristic
279C3⋊Dic3—41no—
280C3⋊Dic3#12412yes—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—42no—
284C22×D4—91no—
285C22×D4—91no—
286C22×D4—181no—
287C22×D4—181no—
288C22×C8—91no—
289C22×C8—91no—
290#127—32no—
291#127—92no—
292#127—182no—
293#125—32no—
294#125—92no—
295#125—182no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—181no—
299C2×C4⋊C4—181no—
300C2×C42—91no—
301#102—32no—
302#102—32no—
303#102—32no—
304#102—92no—
305#102—92no—
306#102—92no—
307#102—91no—
308#102—91no—
309#102—91no—
310#102D3211yescharacteristic, complemented
311#97—32no—
312#97—92no—
313C23×C3—22no—
314C23×C3—41no—
315C23×C3—62no—
316C22×D3—22no—
317C22×D3—32no—
318C22×D3—61no—
319C22×D3—62no—
320C22×D3—121no—
321C22×D3—124no—
322C22×D3—124no—
323C22×D3—124no—
324C22×D3—124no—
325C22×D3—124no—
326C22×D3—124no—
327C22×D3—124no—
328C22×D3—242no—
329C22×D3—242no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—41no—
334C3×D4—62no—
335C3×D4—62no—
336C3×D4—124no—
337C3×D4—124no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—41no—
343C2×C3×C4—62no—
344C2×C3×C4C23×D312yes—
345#67—44no—
346#67—44no—
347#67—124no—
348#67—124no—
349#67—124no—
350#67—124no—
351#67—124no—
352C2×Dic3—22no—
353C2×Dic3—32no—
354C2×Dic3—61no—
355C2×Dic3—62no—
356C2×Dic3—121no—
357C2×Dic3D3×D412yes—
358C2×Dic3D3×D412yes—
359D12—22no—
360D12—22no—
361D12—62no—
362D12—62no—
363D12—62no—
364D12—121no—
365D12—124no—
366D12—124no—
367C4×D3—34no—
368C4×D3—34no—
369C4×D3—62no—
370C4×D3—62no—
371C4×D3—64no—
372C4×D3—64no—
373C4×D3—124no—
374C4×D3—124no—
375C4×D3—242no—
376C3×C8—22no—
377C3×C8—41no—
378C3×C8—62no—
379C3⋊C8—22no—
380C3⋊C8—62no—
381C3⋊C8—121no—
382C2×C32—81no—
383C2×C32C2×#12411yescharacteristic
384C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
385C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
386C3⋊D3—81no—
387C3⋊D3#49014yescomplemented
388C3×D3—82no—
389C24—181no—
390C24—181no—
391C2×D4—32no—
392C2×D4—62no—
393C2×D4—62no—
394C2×D4—91no—
395C2×D4—182no—
396C2×D4—182no—
397C2×D4—182no—
398C2×D4—182no—
399C2×D4—182no—
400C2×D4—182no—
401C2×D4—181no—
402C2×D4—181no—
403C2×D4—364no—
404C2×D4—364no—
405C2×D4C2×D3211yescharacteristic
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—181no—
410C22×C4—181no—
411C2×C8—32no—
412C2×C8—91no—
413C2×C8—182no—
414C2×C8—182no—
415C2×C8C2×D3211yescharacteristic
416C4⋊C4—32no—
417C4⋊C4—62no—
418C4⋊C4—62no—
419C4⋊C4—91no—
420C4⋊C4—181no—
421C4⋊C4—182no—
422C4⋊C4—182no—
423C4⋊C4—181no—
424C4⋊C4C2×D3211yescharacteristic
425C42—32no—
426C42—92no—
427C22×C3—21no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3—122no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3C2×D3×D412yes—
438C2×D3—34no—
439C2×D3—34no—
440C2×D3—34no—
441C2×D3—42no—
442C2×D3—42no—
443C2×D3—42no—
444C2×D3—62no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—241no—
452C2×D3—241no—
453C2×D3—248no—
454C2×D3—248no—
455C2×D3—248no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—42no—
459C3×C4—62no—
460C3×C4—62no—
461C3×C4—81no—
462C3×C4—122no—
463C3×C4D3×#4112yes—
464C3×C4D3×#4112yes—
465Dic3—22no—
466Dic3—22no—
467Dic3—34no—
468Dic3—42no—
469Dic3—62no—
470Dic3—122no—
471Dic3—241no—
472C32C2×#49011yescharacteristic, complemented, Sylow
473C23—21no—
474C23—62no—
475C23—91no—
476C23—181no—
477C23—362no—
478C23—362no—
479C23—362no—
480C23—362no—
481C23—362no—
482C23—362no—
483D4—21no—
484D4—21no—
485D4—62no—
486D4—62no—
487D4—124no—
488D4—124no—
489D4—181no—
490D4—181no—
491D4—364no—
492D4—364no—
493D4—362no—
494D4—362no—
495C2×C4—21no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—62no—
499C2×C4—91no—
500C2×C4—92no—
501C2×C4—92no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—181no—
505C2×C4—362no—
506C2×C4—362no—
507C2×C4C22×D3211yescharacteristic
508C8—21no—
509C8—62no—
510C8—181no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—82no—
515C2×C3—82no—
516C2×C3—242no—
517C2×C3D3×#12412yes—
518C2×C3D3×AGL(1,ℤ/8)12yes—
519C2×C3D3×AGL(1,ℤ/8)12yes—
520D3—38no—
521D3—64no—
522D3—82no—
523D3—242no—
524D3—242no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—92no—
529C22—92no—
530C22—92no—
531C22—122no—
532C22—122no—
533C22—122no—
534C22—361no—
535C22—361no—
536C22—361no—
537C22—724no—
538C22—724no—
539C22D32×D411yescharacteristic
540C4—41no—
541C4—62no—
542C4—62no—
543C4—92no—
544C4—122no—
545C4—361no—
546C4#6430611yescharacteristic
547C4#6431211yescharacteristic
548C3—21no—
549C3D3×#49012yescomplemented
550C2—81no—
551C2—94no—
552C2—242no—
553C2—721no—
554C2#1059428811yescharacteristic
555C2#1059472611yescharacteristic
556C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595300C2
hypercenter#102D32
hypocenterC32C2×#490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594482C2semidirect
3. C3⋊D3×#102C2semidirect
4. C3×#4764C2semidirect
5. #10591477C2semidirect
6. #10591416C2semidirect
7. #10590940C2semidirect
8. #10590882C2semidirect
9. #10590668C2semidirect
10. #10590593C2semidirect
11. #10590550C2semidirect
20. C3×#890C22semidirect
27. #63869C22semidirect
30. C32×#102C22semidirect
31. #63659C22semidirect
32. #63648C22semidirect
33. #63636C22semidirect
34. C3×#832C22semidirect
35. C3×#821C22semidirect
36. C3×#815C22semidirect
37. C3×#809C22semidirect
38. #63564C22semidirect
39. #63563C22semidirect
40. #63562C22semidirect
41. #63554C22semidirect
55. #4764D3semidirect
117. #890C2×D3semidirect
127. C3×#102C2×D3semidirect
133. #832C2×D3semidirect
138. #821C2×D3semidirect
140. #815C2×D3semidirect
145. #809C2×D3semidirect
310. #102D32semidirect
387. C3⋊D3#490semidirect
472. C32C2×#490semidirect
549. C3D3×#490semidirect

Maximal subgroups

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

subgroupindex
#105953002
#105944822
C3⋊D3×#1022
C3×#47642
#105914772
#105914162
#105909402
#105908822
#105906682
#105905932
#105905502
D3×#4903