Finite Group Databasebeta

← #11898349

Subgroups — #11898349

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596039C212yesmaximal, complemented
2C32×C4×Q16C211yesmaximal, characteristic, complemented
3#10592890C211yesmaximal, characteristic
4#10592882C211yesmaximal, characteristic, complemented
5#10592727C212yesmaximal, complemented
6#10592572C211yesmaximal, characteristic, complemented
7#10592571C211yesmaximal, characteristic
8#10592517C212yesmaximal, complemented
9#10592497C212yesmaximal, complemented
10#10592395C211yesmaximal, characteristic
11C8×#634C211yesmaximal, characteristic, complemented
12#79710—34nomaximal
13C2×C32×Q16C2211yescharacteristic
14C32×C4×Q8C2212yes—
15#64156C2212yes—
16#64153C2212yes—
17C2×#3756C2212yes—
18C2×#3755C2212yes—
19C2×#3746C2211yescharacteristic
20C2×#3745C2211yescharacteristic
21C2×#3744C2212yes—
22#64107—22no—
23#64105—22no—
24#64102C2212yes—
25#64096C2212yes—
26#64085—22no—
27#64084C2212yes—
28#64081—22no—
29C4×#634C2211yescharacteristic
30C32×#107C2211yescharacteristic
31C32×#103C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63641C2211yescharacteristic
34#63641C2211yescharacteristic
35C8×C3⋊Dic3C2211yescharacteristic
36C8×C3⋊Dic3C2211yescharacteristic
37#63637C2212yes—
38#63636C2212yes—
39C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
40#5568—38no—
41C3×C4×Q16D314yescomplemented
42#5191—34no—
43#5183—34no—
44#5028—38no—
45#4873—34no—
46#4872—34no—
47#4818—38no—
48#4798—38no—
49#4696—34no—
50C8×Dic6—34no—
51C2×C32×Q8C2312yes—
52C2×C4⋊(C3⋊D3)C2312yes—
53C2×C4×C3⋊D3—22no—
54C2×#634D411yescharacteristic
55C2×#634C2312yes—
56C32×Q16—22no—
57C2×C32×C8C2311yescharacteristic
58C2×C32×C8C2311yescharacteristic
59C32×C4⋊C4—22no—
60C32×C4⋊C4C2312yes—
61C32×C42—22no—
62C32×C42C2311yescharacteristic
63#3756—42no—
64#3755—42no—
65#3752—22no—
66#3752—22no—
67#3752—22no—
68#3752—22no—
69#3752—22no—
70C4⋊(C3⋊Dic3)D411yescharacteristic
71#3750—22no—
72#3750—22no—
73#3750—22no—
74#3750D411yescharacteristic
75#3750D411yescharacteristic
76C4×C3⋊Dic3—22no—
77C4×C3⋊Dic3C2311yescharacteristic
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3746—22no—
82#3745—22no—
83#3744—42no—
84#3393—91noSylow
85C2×C3×Q16C2×D314yes—
86C3×C4×Q8C2×D318yes—
87#947—38no—
88#944—38no—
89C2×#216—38no—
90C2×#215—38no—
91C2×Dic12—34no—
92C2×D24—34no—
93C2×#204—38no—
94#898—68no—
95#896—68no—
96#893—38no—
97#887—38no—
98#876—68no—
99#875—38no—
100#872—68no—
101C4×Dic6—34no—
102C3×#107C2×D314yes—
103C3×#103C2×D318yes—
104C3×C4×C8C2×D314yes—
105Dic3⋊C8—34no—
106Dic3⋊C8—34no—
107C8×Dic3—34no—
108C8×Dic3—34no—
109#810—38no—
110#809—38no—
111C4⋊(C3⋊C8)—34no—
112C22×C3⋊D3—22no—
113C32×Q8—22no—
114C32×Q8—22no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2411yescharacteristic
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3C2×D411yescharacteristic
122C2×C3⋊Dic3C2×D411yescharacteristic
123C2×C3⋊Dic3C2×D411yescharacteristic
124C2×C3⋊Dic3C2×D411yescharacteristic
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)—22no—
127C4×C3⋊D3—44no—
128#634—22no—
129#634—22no—
130#634—22no—
131C32×C8—21no—
132C32×C8#4112yes—
133C3⋊(C3⋊C8)—21no—
134C3⋊(C3⋊C8)—21no—
135#556—92no—
136#495—91no—
137#495—91no—
138#494—91no—
139#464—92no—
140#464—92no—
141#461—92no—
142C8×Q8—91no—
143C4×Q16—91no—
144C4×Q16C3⋊D311yescharacteristic, complemented
145C4×D8—91no—
146C2×C3×Q8C22×D318yes—
147C2×D12—38no—
148C2×C4×D3—68no—
149C2×Dic6—34no—
150C2×Dic6—38no—
151C3×Q16—28no—
152C2×C3×C8C22×D314yes—
153C2×C3×C8C22×D314yes—
154C3×C4⋊C4—28no—
155C3×C4⋊C4C22×D318yes—
156C3×C42—28no—
157C3×C42C22×D314yes—
158#216—128no—
159#215—128no—
160(C2×D3)⋊C4—68no—
161(C2×D3)⋊C4—68no—
162(C2×D3)⋊C4—68no—
163(C2×D3)⋊C4—68no—
164(C2×D3)⋊C4—68no—
165C4⋊Dic3—34no—
166Dic3⋊C4—34no—
167Dic3⋊C4—34no—
168Dic3⋊C4—68no—
169Dic3⋊C4—68no—
170Dic3⋊C4—68no—
171C4×Dic3—34no—
172C4×Dic3—34no—
173C4×Dic3—68no—
174C2×C3⋊C8—34no—
175C2×C3⋊C8—34no—
176Dic12—68no—
177D24—68no—
178#204—128no—
179C22×C32C22×D411yescharacteristic
180C2×C3⋊D3—42no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3—42no—
183C32×C4—21no—
184C32×C4—21no—
185C32×C4—42no—
186C32×C4—42no—
187C32×C4C2×#4111yescharacteristic
188C32×C4H(5,𝔽2)11yescharacteristic
189C3⋊Dic3—21no—
190C3⋊Dic3—21no—
191C3⋊Dic3—21no—
192C3⋊Dic3—42no—
193C3⋊Dic3#13512yes—
194C2×Q16—92no—
195C2×Q16—91no—
196C2×Q16C2×C3⋊D311yescharacteristic
197C2×SD16—92no—
198C2×SD16—92no—
199C2×D8—91no—
200C4⋊Q8—92no—
201#126—182no—
202#126—182no—
203#124—92no—
204#124—92no—
205C22⋊Q8—182no—
206C4×Q8—91no—
207C4×Q8—92no—
208C4×Q8C2×C3⋊D312yes—
209C4×D4—92no—
210#117—182no—
211#107C2×C3⋊D311yescharacteristic
212C4⋊C8—91no—
213C4⋊C8—91no—
214C4⋊C8—91no—
215#103—92no—
216#103C2×C3⋊D312yes—
217#102—92no—
218C4×C8—91no—
219C4×C8—91no—
220C4×C8C2×C3⋊D311yescharacteristic
221C22×D3—68no—
222C3×Q8—28no—
223C3×Q8—28no—
224C2×C3×C4—28no—
225C2×C3×C4—28no—
226C2×C3×C4D3×D414yes—
227C2×C3×C4D3×D414yes—
228C2×C3×C4C23×D314yes—
229C2×Dic3—34no—
230C2×Dic3—34no—
231C2×Dic3—34no—
232C2×Dic3—34no—
233C2×Dic3—68no—
234D12—68no—
235D12—68no—
236C4×D3—1216no—
237Dic6—68no—
238Dic6—68no—
239Dic6—68no—
240C3×C8—24no—
241C3×C8#23518yes—
242C3⋊C8—64no—
243C3⋊C8—64no—
244C2×C32#55011yescharacteristic
245C2×C32C2×#13511yescharacteristic
246C2×C32#57811yescharacteristic
247C3⋊D3—82no—
248C2×Q8—91no—
249C2×Q8—92no—
250C2×Q8C22×C3⋊D312yes—
251C2×D4—92no—
252C22×C4—182no—
253Q16—22no—
254Q16—182no—
255Q16—362no—
256SD16—362no—
257SD16—362no—
258D8—182no—
259C2×C8—91no—
260C2×C8—91no—
261C2×C8C22×C3⋊D311yescharacteristic
262C2×C8C22×C3⋊D311yescharacteristic
263C4⋊C4—22no—
264C4⋊C4—91no—
265C4⋊C4—91no—
266C4⋊C4—91no—
267C4⋊C4—182no—
268C4⋊C4—182no—
269C4⋊C4—182no—
270C4⋊C4C22×C3⋊D312yes—
271C22⋊C4—182no—
272C22⋊C4—182no—
273C22⋊C4—182no—
274C22⋊C4—182no—
275C22⋊C4—182no—
276C42—22no—
277C42—91no—
278C42—91no—
279C42—182no—
280C42C22×C3⋊D311yescharacteristic
281C22×C3C2×D3×D414yes—
282C2×D3—128no—
283C2×D3—128no—
284C2×D3—128no—
285C3×C4—24no—
286C3×C4—24no—
287C3×C4—48no—
288C3×C4—48no—
289C3×C4C2×#23514yes—
290C3×C4#100914yes—
291Dic3—38no—
292Dic3—64no—
293Dic3—64no—
294Dic3—64no—
295Dic3—128no—
296C32#339311yescharacteristic, complemented, Sylow
297C23—182no—
298Q8—22no—
299Q8—22no—
300Q8—182no—
301Q8—182no—
302Q8—182no—
303D4—182no—
304D4—182no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—91no—
311C2×C4—182no—
312C2×C4—364no—
313C2×C4D4×C3⋊D311yescharacteristic
314C2×C4D4×C3⋊D311yescharacteristic
315C2×C4C23×C3⋊D311yescharacteristic
316C8—21no—
317C8—181no—
318C8—181no—
319C8#382812yes—
320C2×C3#555314yes—
321C2×C3#576614yes—
322C2×C3D3×#13514yes—
323D3—248no—
324C22—362no—
325C22—362no—
326C22—362no—
327C22C2×D4×C3⋊D311yescharacteristic
328C4—21no—
329C4—21no—
330C4—42no—
331C4—42no—
332C4—92no—
333C4—181no—
334C4—181no—
335C4—181no—
336C4—362no—
337C4C2×#382811yescharacteristic
338C4#6436611yescharacteristic
339C3#7971014yescomplemented
340C2—722no—
341C2#1059602411yescharacteristic
342C2#1059623711yescharacteristic
343C2C3⋊D3×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×Q16C2
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenterC4×Q16C3⋊D3
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #10596039C2semidirect
2. C32×C4×Q16C2semidirect
4. #10592882C2semidirect
5. #10592727C2semidirect
6. #10592572C2semidirect
8. #10592517C2semidirect
9. #10592497C2semidirect
11. C8×#634C2semidirect
41. C3×C4×Q16D3semidirect
144. C4×Q16C3⋊D3semidirect
296. C32#3393semidirect
339. C3#79710semidirect

Maximal subgroups

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

subgroupindex
#105960392
C32×C4×Q162
#105928902
#105928822
#105927272
#105925722
#105925712
#105925172
#105924972
#105923952
C8×#6342
#797103