Finite Group Databasebeta

← #11872107

Subgroups — #11872107

Order 1152.

1218 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596005C211yesmaximal, characteristic, complemented
2#10595992C211yesmaximal, characteristic, complemented
3C32×#433C211yesmaximal, characteristic, complemented
4#10592545C211yesmaximal, characteristic, complemented
5#10592543C211yesmaximal, characteristic, complemented
6#10592543C211yesmaximal, characteristic, complemented
7#10592541C211yesmaximal, characteristic, complemented
8#10592436C211yesmaximal, characteristic, complemented
9#10592431C211yesmaximal, characteristic
10#10592430C211yesmaximal, characteristic, complemented
11#10592422C211yesmaximal, characteristic, complemented
12#10592410C211yesmaximal, characteristic, complemented
13#10592409C211yesmaximal, characteristic, complemented
14C4×#3745C211yesmaximal, characteristic, complemented
15C4×#3744C211yesmaximal, characteristic, complemented
16#79383—34nomaximal
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C32×#117C2211yescharacteristic
19#64139C2211yescharacteristic
20#64135C2211yescharacteristic
21#64133C2211yescharacteristic
22C2×#3745C2211yescharacteristic
23C2×#3745C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25C2×#3744C2211yescharacteristic
26#64107—21no—
27#64105—21no—
28#64102—21no—
29#64102—21no—
30#64094—21no—
31#64092—21no—
32C22⋊C4×C3⋊D3—21no—
33C22⋊C4×C3⋊D3—21no—
34#64084C2211yescharacteristic, complemented
35C4×C4⋊(C3⋊D3)C2211yescharacteristic
36C4×C4⋊(C3⋊D3)C2211yescharacteristic
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38C4×C4⋊(C3⋊D3)C2211yescharacteristic
39C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
40#64078C2211yescharacteristic, complemented
41C4×#634C2211yescharacteristic, complemented
42C32×C4⋊C8C2211yescharacteristic, complemented
43C32×C4⋊C8C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×#97C2211yescharacteristic, complemented
47C32×C4×C8C2211yescharacteristic, complemented
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63648C2211yescharacteristic
52#63648C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63645C2211yescharacteristic, complemented
55#63645C2211yescharacteristic, complemented
56#63644C2211yescharacteristic, complemented
57#63644C2211yescharacteristic, complemented
58#63643C2211yescharacteristic, complemented
59#63643C2211yescharacteristic, complemented
60#5534—34no—
61#5521—34no—
62C3×#433D314yescomplemented
63#4846—34no—
64#4844—34no—
65#4844—34no—
66#4842—34no—
67#4737—34no—
68#4732—34no—
69#4731—34no—
70#4723—34no—
71#4711—34no—
72#4710—34no—
73C4×D24—34no—
74C4×#204—34no—
75C23×C3⋊D3—21no—
76C22×C32×C4C2311yescharacteristic
77C2×#638—21no—
78C2×C4⋊(C3⋊D3)—21no—
79C2×C4⋊(C3⋊D3)—22no—
80C2×C4⋊(C3⋊D3)—22no—
81C2×C4⋊(C3⋊D3)C2311yescharacteristic
82C2×C4⋊(C3⋊D3)C2311yescharacteristic
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×#634—21no—
90C2×#634C2311yescharacteristic
91C2×C32×C8C2311yescharacteristic
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C32×C4⋊C4D411yescharacteristic
96C32×C4⋊C4D411yescharacteristic
97C32×C22⋊C4D411yescharacteristic
98C32×C22⋊C4D411yescharacteristic
99C32×C42C2311yescharacteristic
100C32×C42C2311yescharacteristic
101#3757—21no—
102#3757—21no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120#3745—22no—
121#3745—22no—
122#3744—22no—
123#3744—22no—
124#3118—91noSylow
125C22×D12—34no—
126C3×#117C2×D314yes—
127#930—34no—
128#926—34no—
129#924—34no—
130C2×D24—34no—
131C2×D24—34no—
132C2×#204—34no—
133C2×#204—34no—
134#898—64no—
135#896—64no—
136#893—64no—
137#893—64no—
138#885—64no—
139#883—64no—
140D3×C22⋊C4—64no—
141D3×C22⋊C4—64no—
142#875—34no—
143C4×D12—34no—
144C4×D12—34no—
145C4×D12—34no—
146C4×D12—34no—
147C4×D12—34no—
148#869—34no—
149C4×Dic6—34no—
150C3×C4⋊C8C2×D314yescomplemented
151C3×C4⋊C8C2×D314yescomplemented
152C3×C22⋊C8C2×D314yes—
153C3×C22⋊C8C2×D314yes—
154C3×#97C2×D314yescomplemented
155C3×C4×C8C2×D314yescomplemented
156#821—34no—
157#821—34no—
158#821—34no—
159#821—34no—
160#821—34no—
161#821—34no—
162#818—34no—
163#818—34no—
164#817—34no—
165#817—34no—
166#816—34no—
167#816—34no—
168C23×C32C2×D411yescharacteristic
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3—24no—
172C22×C3⋊D3—21no—
173C22×C3⋊D3—81no—
174C22×C3⋊D3—81no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183#638—81no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C4⋊(C3⋊D3)—24no—
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)#4112yes—
195C4⋊(C3⋊D3)#4112yes—
196C4×C3⋊D3—81no—
197C4×C3⋊D3—81no—
198C4×C3⋊D3—81no—
199C4×C3⋊D3—81no—
200C4×C3⋊D3—81no—
201#634—21no—
202#634—21no—
203#634—81no—
204C32×C8—21no—
205C32×C8—21no—
206C32×C8—21no—
207C32×C8—21no—
208#542—91no—
209#518—91no—
210#485—91no—
211#482—91no—
212#476—91no—
213#474—91no—
214#463—91no—
215#463—91no—
216#450—91no—
217#447—91no—
218#442—91no—
219#440—91no—
220C4×SD16—91no—
221C4×D8—91no—
222#433C3⋊D311yescharacteristic, complemented
223C23×D3—64no—
224C22×C3×C4C22×D314yes—
225C2×#67—64no—
226C2×D12—34no—
227C2×D12—34no—
228C2×D12—34no—
229C2×D12—68no—
230C2×D12—68no—
231C2×D12—64no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×Dic6—34no—
238C2×Dic6—64no—
239C2×C3×C8C22×D314yes—
240C2×C3×C8C22×D314yes—
241C2×C3×C8C22×D314yes—
242C2×C3×C8C22×D314yes—
243C3×C4⋊C4D1214yes—
244C3×C4⋊C4D1214yes—
245C3×C22⋊C4D1214yes—
246C3×C22⋊C4D1214yes—
247C3×C42C22×D314yes—
248C3×C42C22×D314yes—
249#217—64no—
250#217—64no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262C4⋊Dic3—34no—
263C4⋊Dic3—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266C4×Dic3—64no—
267C4×Dic3—64no—
268D24—68no—
269D24—68no—
270#204—68no—
271#204—68no—
272C22×C32—21no—
273C22×C32—21no—
274C22×C32—21no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—22no—
277C2×C3⋊D3—22no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—84no—
286C32×C4—21no—
287C32×C4—21no—
288C32×C4—21no—
289C32×C4—21no—
290C32×C4—21no—
291C32×C4C2×#4111yescharacteristic
292C32×C4C2×#4111yescharacteristic
293C3⋊Dic3—41no—
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C22×D4—91no—
299C2×SD16—91no—
300C2×SD16—91no—
301C2×D8—91no—
302C2×D8—91no—
303C4⋊Q8—91no—
304#126—181no—
305#124—91no—
306#124—181no—
307#123—181no—
308C22⋊Q8—91no—
309C22⋊Q8—181no—
310#121—91no—
311C4×Q8—91no—
312C4×D4—91no—
313C4×D4—91no—
314C4×D4—91no—
315C4×D4—91no—
316C4×D4—91no—
317C4×D4—181no—
318C4×D4—181no—
319#117—91no—
320#117C2×C3⋊D311yescharacteristic
321C2×C22⋊C4—181no—
322C2×C22⋊C4—181no—
323#107—91no—
324#107—91no—
325#106—91no—
326#106—91no—
327C4⋊C8C2×C3⋊D311yescharacteristic, complemented
328C4⋊C8C2×C3⋊D311yescharacteristic, complemented
329#103—91no—
330#103—91no—
331#102—91no—
332#102—91no—
333#102—91no—
334#102—91no—
335#102—91no—
336#102—91no—
337C22⋊C8C2×C3⋊D311yescharacteristic
338C22⋊C8C2×C3⋊D311yescharacteristic
339#97C2×C3⋊D311yescharacteristic, complemented
340C4×C8C2×C3⋊D311yescharacteristic, complemented
341C23×C3C2×D1214yes—
342C22×D3—64no—
343C22×D3—64no—
344C22×D3—616no—
345C22×D3—64no—
346C22×D3—244no—
347C22×D3—244no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4C2×D1214yes—
351C2×C3×C4C2×D1214yes—
352C2×C3×C4C2×D1214yes—
353C2×C3×C4C2×D1214yes—
354C2×C3×C4C2×D1214yes—
355C2×C3×C4C23×D314yes—
356#67—244no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362D12—38no—
363D12—38no—
364D12—616no—
365D12—64no—
366D12—64no—
367D12—64no—
368D12—64no—
369C4×D3—244no—
370C4×D3—244no—
371C4×D3—244no—
372C4×D3—244no—
373C4×D3—244no—
374Dic6—64no—
375Dic6—64no—
376Dic6—244no—
377C3×C8—24no—
378C3×C8—24no—
379C3×C8—24no—
380C3×C8—24no—
381C2×C32—41no—
382C2×C32#52511yescharacteristic
383C2×C32#57611yescharacteristic
384C2×C32#57711yescharacteristic
385C3⋊D3—42no—
386C3⋊D3—42no—
387C3⋊D3—81no—
388C24—181no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×D4—91no—
392C2×D4—91no—
393C2×D4—91no—
394C2×D4—182no—
395C2×D4—182no—
396C2×D4—181no—
397C2×D4—181no—
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4C22×C3⋊D311yescharacteristic
404SD16—182no—
405SD16—182no—
406D8—182no—
407D8—182no—
408C2×C8C22×C3⋊D311yescharacteristic
409C2×C8C22×C3⋊D311yescharacteristic
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
420C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
421C22⋊C4—181no—
422C22⋊C4—181no—
423C22⋊C4—181no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
432C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
433C42—181no—
434C42—181no—
435C42C22×C3⋊D311yescharacteristic
436C42C22×C3⋊D311yescharacteristic
437C22×C3—24no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3C22×D1214yes—
441C2×D3—68no—
442C2×D3—68no—
443C2×D3—124no—
444C2×D3—124no—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—124no—
449C2×D3—124no—
450C2×D3—2416no—
451C3×C4—24no—
452C3×C4—24no—
453C3×C4—24no—
454C3×C4—24no—
455C3×C4—24no—
456C3×C4D3×#4114yes—
457C3×C4D3×#4114yes—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461Dic3—124no—
462Dic3—124no—
463C32#311811yescharacteristic, complemented, Sylow
464C23—184no—
465C23—181no—
466C23—181no—
467C23—181no—
468C23—721no—
469C23—721no—
470C23C2×C4⋊(C3⋊D3)11yescharacteristic
471Q8—181no—
472Q8—181no—
473Q8—721no—
474D4—92no—
475D4—92no—
476D4—184no—
477D4—181no—
478D4—181no—
479D4—181no—
480D4—181no—
481D4—721no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—721no—
490C2×C4—721no—
491C2×C4—721no—
492C2×C4—721no—
493C2×C4—721no—
494C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
495C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
496C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
497C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
498C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
499C2×C4C23×C3⋊D311yescharacteristic
500C8—21no—
501C8—21no—
502C8—21no—
503C8—21no—
504C2×C3—44no—
505C2×C3#552414yes—
506C2×C3#575114yes—
507C2×C3#575214yes—
508D3—128no—
509D3—128no—
510D3—244no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—182no—
515C22—182no—
516C22—361no—
517C22—361no—
518C22—361no—
519C22—361no—
520C22—361no—
521C22—361no—
522C22—361no—
523C22—724no—
524C22C22×C4⋊(C3⋊D3)11yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—361no—
531C4—361no—
532C4—361no—
533C4—361no—
534C4—361no—
535C4#41×C3⋊D311yescharacteristic
536C4#41×C3⋊D311yescharacteristic
537C3#7938314yescomplemented
538C2—41no—
539C2—362no—
540C2—362no—
541C2—721no—
542C2#1059599511yescharacteristic
543C2#1059622211yescharacteristic
544C2#1059622311yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#433C2
socleC22×C32C22×D4
prime radical#10592431C2
hypercenter#433C3⋊D3
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #10596005C2semidirect
2. #10595992C2semidirect
3. C32×#433C2semidirect
4. #10592545C2semidirect
5. #10592543C2semidirect
6. #10592543C2semidirect
7. #10592541C2semidirect
8. #10592436C2semidirect
10. #10592430C2semidirect
11. #10592422C2semidirect
12. #10592410C2semidirect
13. #10592409C2semidirect
14. C4×#3745C2semidirect
15. C4×#3744C2semidirect
34. #64084C22semidirect
39. C4×C4⋊(C3⋊D3)C22semidirect
40. #64078C22semidirect
41. C4×#634C22semidirect
42. C32×C4⋊C8C22semidirect
43. C32×C4⋊C8C22semidirect
46. C32×#97C22semidirect
47. C32×C4×C8C22semidirect
52. #63648C22semidirect
53. #63648C22semidirect
54. #63645C22semidirect
55. #63645C22semidirect
56. #63644C22semidirect
57. #63644C22semidirect
58. #63643C22semidirect
59. #63643C22semidirect
62. C3×#433D3semidirect
150. C3×C4⋊C8C2×D3semidirect
151. C3×C4⋊C8C2×D3semidirect
154. C3×#97C2×D3semidirect
155. C3×C4×C8C2×D3semidirect
222. #433C3⋊D3semidirect
327. C4⋊C8C2×C3⋊D3semidirect
328. C4⋊C8C2×C3⋊D3semidirect
339. #97C2×C3⋊D3semidirect
340. C4×C8C2×C3⋊D3semidirect
463. C32#3118semidirect
537. C3#79383semidirect

Maximal subgroups

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

subgroupindex
#105960052
#105959922
C32×#4332
#105925452
#105925432
#105925412
#105924362
#105924312
#105924302
#105924222
#105924102
#105924092
C4×#37452
C4×#37442
#793833