Finite Group Databasebeta

← #11896040

Subgroups — #11896040

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596203C211yesmaximal, characteristic
2#10596193C211yesmaximal, characteristic, complemented
3C32×#487C211yesmaximal, characteristic, complemented
4#10592789C211yesmaximal, characteristic, complemented
5#10592783C211yesmaximal, characteristic
6#10592497C212yesmaximal
7#10592493C212yesmaximal
8#10592490C212yesmaximal, complemented
9#10592488C212yesmaximal, complemented
10C4×#3744C211yesmaximal, characteristic
11#10592378C211yesmaximal, characteristic, complemented
12#81626—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15#64156C2212yes—
16Q8×C3⋊Dic3C2212yes—
17#64153—22no—
18C2×#3756C2212yes—
19C2×#3744C2211yescharacteristic
20#64107—22no—
21#64106—21no—
22#64101—21no—
23#64097—21no—
24#64097C2212yes—
25#64096—21no—
26#64096C2212yes—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#103C2212yes—
31C32×#103C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63662C2212yes—
34#63648C2211yescharacteristic
35#63644C2211yescharacteristic
36#63643C2211yescharacteristic
37#63642C2212yes—
38#63641C2212yes—
39#63636C2212yes—
40#63635C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5732—34no—
43#5722—34no—
44C3×#487D314yescomplemented
45#5090—34no—
46#5084—34no—
47#4798—38no—
48#4794—38no—
49#4791—38no—
50#4789—38no—
51C4×#204—34no—
52#4679—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2312yes—
55C2×C4⋊(C3⋊D3)C2311yescharacteristic
56C2×C4×C3⋊D3—21no—
57C2×#634—22no—
58C2×#634D411yescharacteristic
59C2×#634C2311yescharacteristic
60C2×C32×C8C2311yescharacteristic
61C2×C32×C8C2311yescharacteristic
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4C2312yes—
66C32×C42C2311yescharacteristic
67#3756—24no—
68#3752—21no—
69#3752—22no—
70#3752—22no—
71C4⋊(C3⋊Dic3)—22no—
72C4⋊(C3⋊Dic3)D411yescharacteristic
73C4⋊(C3⋊Dic3)C2311yescharacteristic
74C4⋊(C3⋊Dic3)C2311yescharacteristic
75#3750—21no—
76#3750—22no—
77#3750—22no—
78#3750D412yes—
79C4×C3⋊Dic3—21no—
80C4×C3⋊Dic3—22no—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84#3744—22no—
85#3369—91noSylow
86C3×C4⋊Q8C2×D314yes—
87C3×C4⋊Q8C2×D314yes—
88#947—38no—
89Q8×Dic3—38no—
90#944—68no—
91C2×#216—38no—
92C2×#204—34no—
93#898—68no—
94#897—64no—
95#892—64no—
96#888—38no—
97#888—64no—
98#887—38no—
99#887—64no—
100C4×D12—34no—
101C4×Dic6—34no—
102C4×Dic6—34no—
103C3×#103C2×D318yes—
104C3×#103C2×D318yes—
105C3×C4×C8C2×D314yes—
106#835—38no—
107#821—34no—
108#817—34no—
109#816—34no—
110#815—38no—
111Dic3⋊C8—38no—
112#809—38no—
113#808—38no—
114C4⋊(C3⋊C8)—34no—
115C22×C3⋊D3—21no—
116C32×Q8—22no—
117C32×Q8—22no—
118C32×Q8—81no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3C2×D412yes—
128C2×C3⋊Dic3C2×D412yes—
129C4⋊(C3⋊D3)—21no—
130C4⋊(C3⋊D3)—21no—
131C4×C3⋊D3—42no—
132#634—22no—
133#634—21no—
134#634—82no—
135#634#4112yes—
136C32×C8—21no—
137C32×C8—21no—
138C3⋊(C3⋊C8)—22no—
139Q82—91no—
140#556—91no—
141#489—92no—
142#487C3⋊D311yescharacteristic, complemented
143#476—91no—
144#475—92no—
145#464—92no—
146#462—91no—
147#446—91no—
148#441—92no—
149C4×SD16—91no—
150C2×C3×Q8—24no—
151C2×C3×Q8C22×D318yes—
152C2×D12—34no—
153C2×C4×D3—64no—
154C2×Dic6—34no—
155C2×Dic6—34no—
156C2×Dic6—68no—
157C2×C3×C8C22×D314yes—
158C2×C3×C8C22×D314yes—
159C3×C4⋊C4—24no—
160C3×C4⋊C4—24no—
161C3×C4⋊C4—24no—
162C3×C4⋊C4C22×D318yes—
163C3×C42C22×D314yes—
164#216—616no—
165(C2×D3)⋊C4—68no—
166(C2×D3)⋊C4—68no—
167(C2×D3)⋊C4—64no—
168C4⋊Dic3—34no—
169C4⋊Dic3—34no—
170C4⋊Dic3—34no—
171C4⋊Dic3—68no—
172Dic3⋊C4—38no—
173Dic3⋊C4—68no—
174Dic3⋊C4—68no—
175Dic3⋊C4—64no—
176C4×Dic3—38no—
177C4×Dic3—68no—
178C4×Dic3—68no—
179C4×Dic3—64no—
180C2×C3⋊C8—38no—
181#204—68no—
182C22×C32C22×D411yescharacteristic
183C2×C3⋊D3—41no—
184C2×C3⋊D3—41no—
185C2×C3⋊D3—41no—
186C32×C4—21no—
187C32×C4—42no—
188C32×C4—42no—
189C32×C4#13712yes—
190C32×C4C2×#4111yescharacteristic
191C32×C42−1+411yescharacteristic
192C3⋊Dic3—22no—
193C3⋊Dic3—22no—
194C3⋊Dic3—22no—
195C3⋊Dic3—41no—
196C3⋊Dic3—41no—
197C2×Q16—92no—
198C2×SD16—91no—
199C4⋊Q8—92no—
200C4⋊Q8—181no—
201C4⋊Q8—182no—
202C4⋊Q8C2×C3⋊D311yescharacteristic
203C4⋊Q8C2×C3⋊D311yescharacteristic
204#126—182no—
205#124—92no—
206C22⋊Q8—181no—
207C4×Q8—91no—
208C4×Q8—92no—
209C4×Q8—92no—
210C4×Q8—91no—
211C4×Q8—181no—
212C4×D4—91no—
213#117—181no—
214#106—91no—
215#106—92no—
216C4⋊C8—92no—
217C4⋊C8—91no—
218#103—92no—
219#103—91no—
220#103C2×C3⋊D312yes—
221#103C2×C3⋊D312yes—
222#102—91no—
223#102—92no—
224#97—92no—
225C4×C8C2×C3⋊D311yescharacteristic
226C22×D3—64no—
227C3×Q8—28no—
228C3×Q8—28no—
229C3×Q8—84no—
230C2×C3×C4—28no—
231C2×C3×C4—28no—
232C2×C3×C4D3×D414yes—
233C2×C3×C4D3×D414yes—
234C2×C3×C4C23×D314yes—
235C2×Dic3—38no—
236C2×Dic3—38no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240D12—64no—
241D12—64no—
242C4×D3—128no—
243Dic6—38no—
244Dic6—68no—
245Dic6—64no—
246Dic6—248no—
247C3×C8—24no—
248C3×C8—24no—
249C3⋊C8—68no—
250C2×C32#54811yescharacteristic
251C2×C32C2×#13711yescharacteristic
252C2×C32#57711yescharacteristic
253C3⋊D3—81no—
254C2×Q8—21no—
255C2×Q8—91no—
256C2×Q8—91no—
257C2×Q8—182no—
258C2×Q8C22×C3⋊D312yes—
259C2×D4—91no—
260C22×C4—181no—
261Q16—184no—
262SD16—182no—
263C2×C8—92no—
264C2×C8C22×C3⋊D311yescharacteristic
265C2×C8C22×C3⋊D311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—91no—
270C4⋊C4—92no—
271C4⋊C4—91no—
272C4⋊C4—91no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4—182no—
276C4⋊C4—181no—
277C4⋊C4C22×C3⋊D312yes—
278C22⋊C4—182no—
279C22⋊C4—182no—
280C22⋊C4—181no—
281C42—92no—
282C42—182no—
283C42—182no—
284C42—181no—
285C42C22×C3⋊D311yescharacteristic
286C22×C3C2×D3×D414yes—
287C2×D3—124no—
288C2×D3—124no—
289C2×D3—124no—
290C3×C4—24no—
291C3×C4—48no—
292C3×C4—48no—
293C3×C4#91818yes—
294C3×C4D3×#4114yes—
295C3×C4#101014yes—
296Dic3—68no—
297Dic3—68no—
298Dic3—68no—
299Dic3—124no—
300Dic3—124no—
301C32#336911yescharacteristic, complemented, Sylow
302C23—181no—
303Q8—22no—
304Q8—22no—
305Q8—81no—
306Q8—92no—
307Q8—181no—
308Q8—182no—
309Q8—722no—
310D4—181no—
311D4—181no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—92no—
315C2×C4—92no—
316C2×C4—181no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C4—362no—
320C2×C4D4×C3⋊D311yescharacteristic
321C2×C4D4×C3⋊D311yescharacteristic
322C2×C4C23×C3⋊D311yescharacteristic
323C8—21no—
324C8—21no—
325C8—182no—
326C2×C3#567714yes—
327C2×C3#576214yes—
328C2×C3C2×#91814yes—
329D3—244no—
330C22—361no—
331C22—361no—
332C22—361no—
333C22C2×D4×C3⋊D311yescharacteristic
334C4—21no—
335C4—42no—
336C4—42no—
337C4—182no—
338C4—182no—
339C4—182no—
340C4—361no—
341C4—361no—
342C4#6412712yes—
343C4#41×C3⋊D311yescharacteristic
344C4#6436711yescharacteristic
345C3#8162614yescomplemented
346C2—721no—
347C2#1059614811yescharacteristic
348C2#1059623311yescharacteristic
349C2C2×#6412711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenter#487C3⋊D3
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #10596193C2semidirect
3. C32×#487C2semidirect
4. #10592789C2semidirect
8. #10592490C2semidirect
9. #10592488C2semidirect
11. #10592378C2semidirect
44. C3×#487D3semidirect
142. #487C3⋊D3semidirect
301. C32#3369semidirect
345. C3#81626semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105961932
C32×#4872
#105927892
#105927832
#105924972
#105924932
#105924902
#105924882
C4×#37442
#105923782
#816263