Finite Group Databasebeta

← #11860702

Subgroups — #11860702

Order 1152.

1151 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594996C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic
4#10592830C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic, complemented
6C3×#5122C211yesmaximal, characteristic, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10590746C214yesmaximal, complemented
9#10590745C214yesmaximal, complemented
10#78915—31nomaximal
11#78561—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15#64135C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19#63974—22no—
20D3×#217—22no—
21#63898—22no—
22#63894—22no—
23#63894C2214yescomplemented
24Dic3×D12C2214yescomplemented
25C2×#3714C418yescomplemented
26C2×#3714C2212yes—
27C2×#3714C2212yes—
28#63648C2214yescomplemented
29C3×#821C2214yescomplemented
30C3×#815C2212yescomplemented
31C3×C8×Dic3C2212yescomplemented
32#63575C2212yescomplemented
33#63573C2212yescomplemented
34#5798—31no—
35C22×#213—31no—
36C22×D24—31no—
37#5521—31no—
38#5521—31no—
39#5521—31no—
40C3×#418—31no—
41C3×#405—31no—
42#5131—31no—
43#5131—31no—
44#5131—61no—
45#5131D311yescharacteristic, complemented
46#5122D311yescharacteristic, complemented
47#5106—31no—
48#4998—31no—
49#4785—34no—
50#4756—34no—
51#4711—34no—
52C4×D24—34no—
53C23×C3⋊D3—21no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)C2×C414yescomplemented
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yescomplemented
63C2×C3×D12C2312yes—
64C2×#624—24no—
65C2×D3×Dic3—24no—
66C32×M16—22no—
67C2×C32×C8C2312yes—
68#3757—21no—
69C4⋊(C3⋊Dic3)C2312yes—
70C4×C3⋊Dic3—21no—
71C3×#217—21no—
72C3×#217D412yes—
73C3×C4⋊Dic3D412yes—
74C3×C4⋊Dic3C2312yes—
75C3×C4×Dic3—21no—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8C2×C414yescomplemented
78C2×C3×C3⋊C8C2311yescharacteristic
79C2×C3×C3⋊C8C2311yescharacteristic
80#3722—24no—
81(C2×D3)⋊Dic3—24no—
82#3714C2×C418yescomplemented
83#3714C2×C418yescomplemented
84#2948—91noSylow
85C22×C3×D4—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×D12C2×D311yescharacteristic
90C2×C3×M16—21no—
91C2×C3×M16C2×D311yescharacteristic
92C2×C3×M16C2×D311yescharacteristic
93C22×C3×C8—31no—
94C3×#117—31no—
95C3×#117—31no—
96C2×#217—62no—
97D4×Dic3—34no—
98D4×Dic3—62no—
99C2×#213—38no—
100C2×#213—32no—
101C2×#213—32no—
102#926—31no—
103#926—31no—
104#926—61no—
105#926C2×D311yescharacteristic
106#926C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108C2×D24—38no—
109C2×D24—32no—
110C2×D24—32no—
111#893—34no—
112#893—62no—
113#893—62no—
114D3×C22⋊C4—62no—
115D3×C22⋊C4—62no—
116D3×C22⋊C4—62no—
117C4×D12—34no—
118C4×D12—34no—
119C4×D12—62no—
120C3×#102—34no—
121C3×#97—32no—
122C3×C4×C8—32no—
123#821—34no—
124#821—34no—
125#821—64no—
126#821C2×D314yescomplemented
127#818—32no—
128#817—32no—
129#815C2×D312yescomplemented
130C8×Dic3C2×D312yescomplemented
131#808—32no—
132#807—32no—
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—22no—
135C22×C3⋊D3—24no—
136C22×C3⋊D3—82no—
137C22×C3×D3—22no—
138C22×C3×D3—24no—
139C22×C3×D3—82no—
140C2×C32×C4C22×C412yes—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144C2×C3⋊Dic3—22no—
145C4⋊(C3⋊D3)—24no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)C22×C414yes—
148C2×C3×Dic3—22no—
149C2×C3×Dic3C2×D414yes—
150C3×D12—24no—
151C3×D12—22no—
152C3×D12C22×C414yes—
153#624—84no—
154D3×Dic3—84no—
155C32×C8—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×D8—91no—
159#518—91no—
160#518—91no—
161#442—94no—
162C4×D8—94no—
163#427—91no—
164#418—31no—
165#418—91no—
166#405—31no—
167C24×C3—61no—
168C23×D3—21no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3—121no—
172C2×C3×D4—34no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—62no—
176C22×C3×C4—21no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×Dic3—64no—
180C2×D12—21no—
181C2×D12—22no—
182C2×D12—34no—
183C2×D12—34no—
184C2×D12—32no—
185C2×D12—32no—
186C2×D12—62no—
187C2×D12—64no—
188C2×D12—61no—
189C2×D12—62no—
190C2×D12—61no—
191C2×D12—62no—
192C2×D12—121no—
193C2×D12—122no—
194C2×D12C4×D314yescomplemented
195C2×D12C22×D312yes—
196C2×C4×D3—64no—
197C2×C4×D3—64no—
198C2×C4×D3—64no—
199C3×M16—22no—
200C3×M16—22no—
201C3×M16—42no—
202C2×C3×C8—22no—
203C2×C3×C8—34no—
204C2×C3×C8—31no—
205C2×C3×C8—31no—
206C2×C3×C8C22×D312yes—
207C2×C3×C8C22×D312yes—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—32no—
210C3×C22⋊C4—32no—
211C3×C22⋊C4—61no—
212C3×C42—32no—
213C3×C42—61no—
214#217—21no—
215#217—61no—
216#217—61no—
217#217—64no—
218#217—121no—
219#217D1212yes—
220#213—38no—
221#213—38no—
222(C2×D3)⋊C4—64no—
223(C2×D3)⋊C4—64no—
224(C2×D3)⋊C4—64no—
225C4⋊Dic3—32no—
226C4⋊Dic3—32no—
227C4⋊Dic3—62no—
228C4⋊Dic3D1212yes—
229C4⋊Dic3C22×D312yes—
230C4×Dic3—21no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233C4×Dic3—121no—
234C4×Dic3C22×D312yes—
235C2×C3⋊C8C4×D314yescomplemented
236C2×C3⋊C8C22×D311yescharacteristic
237C2×C3⋊C8C22×D311yescharacteristic
238D24—38no—
239D24—38no—
240C22×C32—22no—
241C22×C32C4×D412yes—
242C22×C32C22×D411yescharacteristic
243C2×C3⋊D3—24no—
244C2×C3⋊D3—44no—
245C2×C3⋊D3—84no—
246C2×C3×D3—24no—
247C2×C3×D3—44no—
248C2×C3×D3—84no—
249C32×C4C4×D412yes—
250C32×C4C23×C411yescharacteristic
251C32×C4C2×#4111yescharacteristic
252C3⋊Dic3—42no—
253C3×Dic3—24no—
254C3×Dic3—42no—
255C22×D4—31no—
256C22×D4—91no—
257C2×D8—98no—
258C2×D8—92no—
259C2×D8—92no—
260C2×M16D3211yescharacteristic
261C22×C8—31no—
262C4×D4—94no—
263C4×D4—94no—
264C4×D4—182no—
265C4×D4—182no—
266#117—31no—
267#117—31no—
268#117—91no—
269C2×C22⋊C4—182no—
270C2×C22⋊C4—182no—
271#107—92no—
272#106—92no—
273#102—34no—
274#102—94no—
275#97—32no—
276C4×C8—32no—
277C23×C3—21no—
278C23×C3—62no—
279C23×C3—64no—
280C23×C3—242no—
281C23×C3C2×D1211yescharacteristic
282C23×C3D3×D411yescharacteristic
283C22×D3—22no—
284C22×D3—24no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—64no—
288C22×D3—64no—
289C22×D3—82no—
290C22×D3—122no—
291C22×D3—124no—
292C22×D3—242no—
293C22×D3—242no—
294C22×D3—244no—
295C3×D4—34no—
296C3×D4—64no—
297C3×D4—62no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—34no—
303C2×C3×C4—62no—
304C2×C3×C4C2×C4×D312yes—
305C2×C3×C4C2×C4×D312yes—
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4#23512yes—
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23712yes—
310C2×C3×C4C23×D311yescharacteristic
311C2×C3×C4C23×D311yescharacteristic
312C2×Dic3—22no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—122no—
316C2×Dic3—244no—
317C2×Dic3C2×D1214yes—
318D12—24no—
319D12—22no—
320D12—34no—
321D12—34no—
322D12—64no—
323D12—64no—
324D12—64no—
325D12—62no—
326D12—62no—
327D12—122no—
328D12—124no—
329D12C2×C4×D314yes—
330C4×D3—244no—
331C4×D3—244no—
332C4×D3—244no—
333C3×C8—22no—
334C3×C8—22no—
335C3×C8—32no—
336C3×C8—32no—
337C3×C8—42no—
338C3⋊C8C2×C4×D312yes—
339C3⋊C8C2×C4×D312yes—
340C2×C32—22no—
341C2×C32C2×C4×D411yescharacteristic
342C2×C32#57612yes—
343C3⋊D3—44no—
344C3×D3—44no—
345C24—61no—
346C24—181no—
347C2×D4—32no—
348C2×D4—34no—
349C2×D4—61no—
350C2×D4—62no—
351C2×D4—92no—
352C2×D4—94no—
353C2×D4—181no—
354C2×D4—182no—
355C22×C4—184no—
356C22×C4—184no—
357C22×C4C2×D3211yescharacteristic
358D8—98no—
359D8—98no—
360M16—22no—
361C2×C8—31no—
362C2×C8—31no—
363C2×C8—34no—
364C2×C8C2×D3212yes—
365C4⋊C4—32no—
366C4⋊C4—32no—
367C4⋊C4—92no—
368C22⋊C4—32no—
369C22⋊C4—61no—
370C22⋊C4—184no—
371C22⋊C4—184no—
372C22⋊C4—181no—
373C42—32no—
374C42—61no—
375C42—181no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—42no—
381C22×C3—64no—
382C22×C3—124no—
383C22×C3—244no—
384C22×C3C4×D1212yes—
385C22×C3#67⋊C412yes—
386C22×C3C22×D1211yescharacteristic
387C22×C3C2×D3×D411yescharacteristic
388C2×D3—24no—
389C2×D3—44no—
390C2×D3—64no—
391C2×D3—64no—
392C2×D3—84no—
393C2×D3—124no—
394C2×D3—124no—
395C2×D3—124no—
396C2×D3—244no—
397C2×D3—244no—
398C2×D3—244no—
399C2×D3—248no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—22no—
403C3×C4—64no—
404C3×C4—122no—
405C3×C4C4×D1212yes—
406C3×C4#67⋊C412yes—
407C3×C4C22×C4×D311yescharacteristic
408C3×C4C22×C4×D311yescharacteristic
409C3×C4C2×#23511yescharacteristic
410C3×C4C2×#23711yescharacteristic
411Dic3—24no—
412Dic3—42no—
413Dic3—122no—
414Dic3—122no—
415Dic3—242no—
416C32#294811yescharacteristic, complemented, Sylow
417C23—62no—
418C23—64no—
419C23—182no—
420C23—184no—
421C23—242no—
422C23—722no—
423C23D3×D1211yescharacteristic
424D4—34no—
425D4—62no—
426D4—64no—
427D4—94no—
428D4—182no—
429D4—184no—
430C2×C4—34no—
431C2×C4—62no—
432C2×C4—182no—
433C2×C4—724no—
434C2×C4—724no—
435C2×C4C4×D3212yes—
436C2×C4D3×D1211yescharacteristic
437C2×C4#380412yes—
438C2×C4C22×D3211yescharacteristic
439C8—22no—
440C8—32no—
441C8—32no—
442C2×C3—22no—
443C2×C3—22no—
444C2×C3—21no—
445C2×C3—22no—
446C2×C3—42no—
447C2×C3—124no—
448C2×C3C2×C4×D1211yescharacteristic
449C2×C3C2×#67⋊C411yescharacteristic
450C2×C3#575212yes—
451C2×C3#577412yes—
452D3—44no—
453D3—124no—
454D3—124no—
455D3—244no—
456C22—22no—
457C22—64no—
458C22—124no—
459C22—184no—
460C22—244no—
461C22—364no—
462C22—724no—
463C22#6388012yes—
464C22C2×D3×D1211yescharacteristic
465C4—64no—
466C4—122no—
467C4—362no—
468C4#6388012yes—
469C4C2×C4×D3211yescharacteristic
470C4C2×#380411yescharacteristic
471C3—21no—
472C3#7856111yescharacteristic, complemented
473C3#7891511yescharacteristic, complemented
474C2—22no—
475C2—124no—
476C2—364no—
477C2#1059471412yes—
478C2C2×#6388011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×#3714C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2948
LCSG ▷ 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. #10594996C2semidirect
2. #10594982C2semidirect
4. #10592830C2semidirect
5. C3×#5131C2semidirect
6. C3×#5122C2semidirect
7. #10591122C2semidirect
8. #10590746C2semidirect
9. #10590745C2semidirect
23. #63894C22semidirect
24. Dic3×D12C22semidirect
25. C2×#3714C4semidirect
28. #63648C22semidirect
29. C3×#821C22semidirect
30. C3×#815C22semidirect
31. C3×C8×Dic3C22semidirect
32. #63575C22semidirect
33. #63573C22semidirect
45. #5131D3semidirect
46. #5122D3semidirect
58. C2×C4⋊(C3⋊D3)C2×C4semidirect
62. C2×C3×D12C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
82. #3714C2×C4semidirect
83. #3714C2×C4semidirect
126. #821C2×D3semidirect
129. #815C2×D3semidirect
130. C8×Dic3C2×D3semidirect
194. C2×D12C4×D3semidirect
235. C2×C3⋊C8C4×D3semidirect
416. C32#2948semidirect
472. C3#78561semidirect
473. C3#78915semidirect

Maximal subgroups

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

subgroupindex
#105949962
#105949822
C22×#37142
#105928302
C3×#51312
C3×#51222
#105911222
#105907462
#105907452
#789153
#785613