Finite Group Databasebeta

← #11895151

Subgroups — #11895151

Order 1152.

1110 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic
2#10596038C211yesmaximal, characteristic, complemented
3C32×#475C211yesmaximal, characteristic, complemented
4#10592792C211yesmaximal, characteristic, complemented
5C4×#3755C211yesmaximal, characteristic
6#10592553C212yesmaximal, complemented
7#10592551C212yesmaximal
8#10592540C211yesmaximal, characteristic
9#10592529C211yesmaximal, characteristic, complemented
10#10592517C212yesmaximal
11#10592491C212yesmaximal, complemented
12#81037—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16#64155—21no—
17#64153C2212yes—
18C2×#3755C2211yescharacteristic
19C2×#3744C2212yes—
20#64105—22no—
21#64102C2212yes—
22#64098—22no—
23#64097C2212yes—
24#64096C2212yes—
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26#64079—21no—
27#64078C2211yescharacteristic
28C4×#634—21no—
29C4×#634C2211yescharacteristic
30C32×#106C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×#103C2212yes—
33#63662C2211yescharacteristic
34#63643C2212yes—
35#63641C2212yes—
36C8×C3⋊Dic3C2212yes—
37#63637C2212yes—
38#63637C2212yes—
39#63636C2211yescharacteristic
40#63635C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5727—34no—
43#5567—34no—
44C3×#475D314yescomplemented
45#5093—34no—
46C4×#215—34no—
47#4854—38no—
48#4852—38no—
49#4841—34no—
50#4830—34no—
51#4818—38no—
52#4792—38no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2311yescharacteristic
55Q8×C3⋊D3—44no—
56C2×C4⋊(C3⋊D3)C2311yescharacteristic
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—22no—
59C2×#634—22no—
60C2×#634D411yescharacteristic
61C2×#634C2312yes—
62C2×C32×C8C2312yes—
63C32×C4⋊C4—21no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4C2311yescharacteristic
66C32×C4⋊C4C2312yes—
67C32×C42—21no—
68C32×C42C2311yescharacteristic
69#3755—22no—
70#3752—21no—
71#3752—22no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)D411yescharacteristic
75C4⋊(C3⋊Dic3)C2311yescharacteristic
76#3750—22no—
77#3750—22no—
78#3750—22no—
79#3750—22no—
80#3750D412yes—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3744—24no—
86#3359—91noSylow
87C2×D3×Q8—64no—
88C3×C4⋊Q8C2×D314yes—
89C3×C4×Q8C2×D314yes—
90#946—64no—
91#944—38no—
92C2×#215—34no—
93C2×#204—38no—
94#896—68no—
95#893—38no—
96#889—68no—
97#888—38no—
98#887—38no—
99C4×D12—34no—
100#870—64no—
101#869—34no—
102C4×Dic6—34no—
103C4×Dic6—64no—
104C3×#106C2×D318yes—
105C3×C4⋊C8C2×D314yes—
106C3×#103C2×D318yes—
107#835—34no—
108#816—38no—
109Dic3⋊C8—38no—
110C8×Dic3—38no—
111#810—38no—
112#810—38no—
113#809—34no—
114#808—34no—
115C4×C3⋊C8—34no—
116C22×C3⋊D3—21no—
117C32×Q8—21no—
118C32×Q8—21no—
119C32×Q8—42no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—22no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3C2×D412yes—
129C2×C3⋊Dic3C2×D412yes—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)#4112yes—
132C4×C3⋊D3—42no—
133C4×C3⋊D3—44no—
134#634—22no—
135#634—22no—
136#634—44no—
137#634SD1614yescomplemented
138C32×C8—22no—
139C3⋊(C3⋊C8)—21no—
140C3⋊(C3⋊C8)—21no—
141#557—91no—
142D4×Q8—91no—
143#487—91no—
144#487—92no—
145#475—92no—
146#475C3⋊D311yescharacteristic, complemented
147#461—91no—
148#461—92no—
149C8×Q8—91no—
150C4×SD16—91no—
151C4×SD16—92no—
152C2×C3×Q8—24no—
153C2×C3×Q8C22×D314yes—
154D3×Q8—1216no—
155C2×D12—34no—
156C2×C4×D3—68no—
157C2×C4×D3—64no—
158C2×Dic6—34no—
159C2×Dic6—38no—
160C2×Dic6—68no—
161C2×C3×C8C22×D318yes—
162C3×C4⋊C4—24no—
163C3×C4⋊C4—24no—
164C3×C4⋊C4C22×D314yes—
165C3×C4⋊C4C22×D318yes—
166C3×C42—24no—
167C3×C42C22×D314yes—
168#215—68no—
169(C2×D3)⋊C4—68no—
170(C2×D3)⋊C4—64no—
171C4⋊Dic3—34no—
172C4⋊Dic3—34no—
173C4⋊Dic3—64no—
174C4⋊Dic3—64no—
175Dic3⋊C4—38no—
176Dic3⋊C4—68no—
177Dic3⋊C4—68no—
178Dic3⋊C4—68no—
179Dic3⋊C4—68no—
180C4×Dic3—38no—
181C4×Dic3—68no—
182C2×C3⋊C8—34no—
183C2×C3⋊C8—34no—
184#204—616no—
185C22×C32C22×D411yescharacteristic
186C2×C3⋊D3—22no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C32×C4—21no—
190C32×C4—41no—
191C32×C4—42no—
192C32×C4—41no—
193C32×C4C2×SD1612yes—
194C32×C4C2×#4111yescharacteristic
195C32×C42−1+411yescharacteristic
196C3⋊Dic3—22no—
197C3⋊Dic3—42no—
198C3⋊Dic3—41no—
199C3⋊Dic3C2×SD1614yes—
200C22×Q8—181no—
201C2×SD16—91no—
202C2×SD16—92no—
203C4⋊Q8—92no—
204C4⋊Q8—92no—
205C4⋊Q8—91no—
206C4⋊Q8C2×C3⋊D311yescharacteristic
207#125—181no—
208#125—182no—
209C22⋊Q8—182no—
210C22⋊Q8—181no—
211C4×Q8—91no—
212C4×Q8—92no—
213C4×Q8—181no—
214C4×Q8C2×C3⋊D311yescharacteristic
215C4×D4—92no—
216C4×D4—91no—
217#106—91no—
218#106C2×C3⋊D312yes—
219C4⋊C8—92no—
220C4⋊C8C2×C3⋊D311yescharacteristic
221#103—91no—
222#103—92no—
223#103—92no—
224#103—92no—
225#103C2×C3⋊D312yes—
226#102—91no—
227C4×C8—92no—
228C4×C8—91no—
229C22×D3—64no—
230C3×Q8—24no—
231C3×Q8—24no—
232C3×Q8—48no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—28no—
236C2×C3×C4D3×D414yes—
237C2×C3×C4D3×D414yes—
238C2×C3×C4C23×D314yes—
239C2×Dic3—38no—
240C2×Dic3—38no—
241C2×Dic3—68no—
242C2×Dic3—64no—
243D12—38no—
244D12—64no—
245C4×D3—1216no—
246C4×D3—128no—
247Dic6—316no—
248Dic6—68no—
249Dic6—68no—
250Dic6—1216no—
251C3×C8—28no—
252C3⋊C8—64no—
253C3⋊C8—64no—
254C2×C32#54811yescharacteristic
255C2×C32C22×SD1611yescharacteristic
256C2×C32#57811yescharacteristic
257C3⋊D3—42no—
258C2×Q8—21no—
259C2×Q8—91no—
260C2×Q8—92no—
261C2×Q8—182no—
262C2×Q8—364no—
263C2×Q8C22×C3⋊D311yescharacteristic
264C2×D4—91no—
265C22×C4—182no—
266C22×C4—181no—
267SD16—184no—
268SD16—182no—
269C2×C8—91no—
270C2×C8—91no—
271C2×C8C22×C3⋊D312yes—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—92no—
275C4⋊C4—91no—
276C4⋊C4—91no—
277C4⋊C4—182no—
278C4⋊C4—182no—
279C4⋊C4—182no—
280C4⋊C4—182no—
281C4⋊C4—181no—
282C4⋊C4—181no—
283C4⋊C4C22×C3⋊D311yescharacteristic
284C4⋊C4C22×C3⋊D312yes—
285C22⋊C4—182no—
286C22⋊C4—181no—
287C42—21no—
288C42—92no—
289C42—182no—
290C42C22×C3⋊D311yescharacteristic
291C22×C3C2×D3×D414yes—
292C2×D3—68no—
293C2×D3—124no—
294C2×D3—124no—
295C3×C4—24no—
296C3×C4—44no—
297C3×C4—48no—
298C3×C4—44no—
299C3×C4D3×SD1618yes—
300C3×C4#100714yes—
301C3×C4D3×#4114yes—
302Dic3—316no—
303Dic3—68no—
304Dic3—128no—
305Dic3—124no—
306C32#335911yescharacteristic, complemented, Sylow
307C23—181no—
308Q8—21no—
309Q8—21no—
310Q8—42no—
311Q8—94no—
312Q8—182no—
313Q8—182no—
314Q8—364no—
315D4—92no—
316D4—181no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—182no—
323C2×C4—181no—
324C2×C4—364no—
325C2×C4—362no—
326C2×C4D4×C3⋊D311yescharacteristic
327C2×C4D4×C3⋊D311yescharacteristic
328C2×C4C23×C3⋊D311yescharacteristic
329C8—22no—
330C8—181no—
331C8—181no—
332C2×C3#563314yes—
333C2×C3C2×D3×SD1614yes—
334C2×C3#577914yes—
335D3—128no—
336C22—182no—
337C22—361no—
338C22—361no—
339C22C2×D4×C3⋊D311yescharacteristic
340C4—21no—
341C4—41no—
342C4—42no—
343C4—41no—
344C4—94no—
345C4—182no—
346C4—362no—
347C4—361no—
348C4SD16×C3⋊D312yes—
349C4#6436411yescharacteristic
350C4#41×C3⋊D311yescharacteristic
351C3#8103714yescomplemented
352C2—362no—
353C2#1059610411yescharacteristic
354C2C2×SD16×C3⋊D311yescharacteristic
355C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenter#475C3⋊D3
hypocenterC32#3359
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #10596038C2semidirect
3. C32×#475C2semidirect
4. #10592792C2semidirect
6. #10592553C2semidirect
9. #10592529C2semidirect
11. #10592491C2semidirect
44. C3×#475D3semidirect
137. #634SD16semidirect
146. #475C3⋊D3semidirect
306. C32#3359semidirect
351. C3#81037semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105960382
C32×#4752
#105927922
C4×#37552
#105925532
#105925512
#105925402
#105925292
#105925172
#105924912
#810373