Finite Group Databasebeta

← #11895627

Subgroups — #11895627

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596056C211yesmaximal, characteristic
2#10596038C211yesmaximal, characteristic, complemented
3C32×C8×Q8C211yesmaximal, characteristic, complemented
4#10592550C211yesmaximal, characteristic, complemented
5#10592547C211yesmaximal, characteristic
6#10592546C212yesmaximal, complemented
7#10592544C212yesmaximal, complemented
8C4×#3746C211yesmaximal, characteristic, complemented
9#10592396C212yesmaximal, complemented
10#10592393C211yesmaximal, characteristic
11C4×#3744C212yesmaximal, complemented
12#79935—34nomaximal
13C32×C4×Q8C2211yescharacteristic
14#64156—21no—
15#64153—21no—
16C2×#3746C2211yescharacteristic
17C2×#3744C2212yes—
18#64103—22no—
19#64102—21no—
20#64098—22no—
21#64096—21no—
22#64084C2212yes—
23#64083C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2212yes—
25#64079C2212yes—
26#64078C2211yescharacteristic
27C4×#634C2212yes—
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×C4⋊C8C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×C4×C8C2212yes—
33C32×C4×C8C2211yescharacteristic
34#63648C2212yes—
35#63648C2212yes—
36#63648C2212yes—
37#63645C2211yescharacteristic
38#63644C2212yes—
39#63643C2212yes—
40#63643C2211yescharacteristic
41#63643C2211yescharacteristic
42#5585—34no—
43#5567—34no—
44C3×C8×Q8D314yescomplemented
45#4851—34no—
46#4848—34no—
47#4847—38no—
48#4845—38no—
49C4×Dic12—34no—
50#4697—38no—
51#4694—34no—
52C4×#204—38no—
53C2×C32×Q8D411yescharacteristic
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)C2312yes—
57C2×C4×C3⋊D3—22no—
58C2×#634—21no—
59C2×#634C2311yescharacteristic
60C2×#634C2311yescharacteristic
61C2×C32×C8C2312yes—
62C2×C32×C8C2311yescharacteristic
63C2×C32×C8C2311yescharacteristic
64C32×C4⋊C4D411yescharacteristic
65C32×C4⋊C4D412yes—
66C32×C42C2311yescharacteristic
67C32×C42C2312yes—
68#3752—22no—
69#3752—22no—
70#3752—22no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C4⋊(C3⋊Dic3)C2311yescharacteristic
74C4⋊(C3⋊Dic3)C2311yescharacteristic
75#3750—21no—
76#3750—22no—
77#3750—21no—
78#3750—22no—
79#3750—22no—
80C4×C3⋊Dic3—22no—
81C4×C3⋊Dic3—21no—
82C4×C3⋊Dic3—21no—
83#3746—22no—
84#3744—24no—
85#3365—91noSylow
86C3×C4×Q8C2×D314yes—
87#947—64no—
88#944—64no—
89C2×Dic12—34no—
90C2×#204—38no—
91#894—68no—
92#893—64no—
93#889—68no—
94#887—64no—
95#875—38no—
96#874—34no—
97C4×D12—38no—
98#870—38no—
99#869—34no—
100C4×Dic6—38no—
101C4×Dic6—34no—
102C4×Dic6—34no—
103C3×C4⋊C8C2×D318yes—
104C3×C4⋊C8C2×D314yes—
105C3×C4×C8C2×D318yes—
106C3×C4×C8C2×D314yes—
107#821—38no—
108#821—38no—
109#821—38no—
110#818—34no—
111#817—38no—
112#816—34no—
113#816—34no—
114#816—38no—
115C22×C3⋊D3—22no—
116C32×Q8—22no—
117C2×C32×C4C2×D412yes—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2411yescharacteristic
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—42no—
130C4⋊(C3⋊D3)—81no—
131C4×C3⋊D3—82no—
132#634—21no—
133#634—21no—
134#634—21no—
135#634—42no—
136#634#4112yes—
137C32×C8—22no—
138C32×C8—21no—
139C32×C8—21no—
140#559—91no—
141#557—91no—
142#488—92no—
143#486—91no—
144#478—92no—
145#475—91no—
146#464—92no—
147#460—91no—
148C8×Q8C3⋊D311yescharacteristic, complemented
149C4×Q16—91no—
150C4×SD16—92no—
151C2×C3×Q8D1214yes—
152C2×D12—38no—
153C2×D12—64no—
154C2×D12—64no—
155C2×C4×D3—68no—
156C2×Dic6—34no—
157C2×Dic6—34no—
158C2×Dic6—64no—
159C2×C3×C8C22×D314yes—
160C2×C3×C8C22×D318yes—
161C2×C3×C8C22×D314yes—
162C3×C4⋊C4D1214yes—
163C3×C4⋊C4D1218yes—
164C3×C42C22×D314yes—
165C3×C42C22×D318yes—
166(C2×D3)⋊C4—68no—
167(C2×D3)⋊C4—68no—
168(C2×D3)⋊C4—68no—
169C4⋊Dic3—34no—
170C4⋊Dic3—38no—
171C4⋊Dic3—34no—
172C4⋊Dic3—64no—
173Dic3⋊C4—64no—
174Dic3⋊C4—68no—
175Dic3⋊C4—64no—
176Dic3⋊C4—68no—
177Dic3⋊C4—68no—
178C4×Dic3—68no—
179C4×Dic3—64no—
180C4×Dic3—64no—
181Dic12—68no—
182#204—616no—
183C22×C32C22×D411yescharacteristic
184C2×C3⋊D3—42no—
185C2×C3⋊D3—42no—
186C2×C3⋊D3—42no—
187C32×C4—22no—
188C32×C4—22no—
189C32×C4—21no—
190C32×C4#13512yes—
191C32×C4C2×#4111yescharacteristic
192C32×C42−1+411yescharacteristic
193C3⋊Dic3—22no—
194C3⋊Dic3—41no—
195C3⋊Dic3—42no—
196C3⋊Dic3—41no—
197C3⋊Dic3—41no—
198C2×Q16—91no—
199C2×SD16—92no—
200C4⋊Q8—91no—
201C4⋊Q8—181no—
202#127—91no—
203#125—92no—
204#125—182no—
205#124—92no—
206#124—181no—
207#123—182no—
208C4×Q8—92no—
209C4×Q8—91no—
210C4×Q8—91no—
211C4×Q8—181no—
212C4×Q8C2×C3⋊D311yescharacteristic
213C4×D4—92no—
214C4×D4—181no—
215#107—91no—
216#106—92no—
217C4⋊C8C2×C3⋊D311yescharacteristic
218C4⋊C8C2×C3⋊D312yes—
219#103—91no—
220#103—91no—
221#103—92no—
222#102—92no—
223#102—92no—
224#102—92no—
225C4×C8C2×C3⋊D312yes—
226C4×C8C2×C3⋊D311yescharacteristic
227C22×D3—68no—
228C3×Q8—28no—
229C2×C3×C4C2×D1218yes—
230C2×C3×C4C2×D1214yes—
231C2×C3×C4C2×D1218yes—
232C2×C3×C4C2×D1214yes—
233C2×C3×C4C23×D314yes—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—68no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239D12—68no—
240D12—68no—
241D12—128no—
242D12—244no—
243C4×D3—248no—
244Dic6—38no—
245Dic6—64no—
246Dic6—64no—
247Dic6—64no—
248Dic6—128no—
249C3×C8—24no—
250C3×C8—28no—
251C3×C8—24no—
252C2×C32#54811yescharacteristic
253C2×C32C2×#13511yescharacteristic
254C2×C32#57711yescharacteristic
255C3⋊D3—82no—
256C2×Q8—91no—
257C2×Q8—91no—
258C2×Q8—181no—
259C2×Q8C4⋊(C3⋊D3)11yescharacteristic
260C2×D4—92no—
261C2×D4—181no—
262C2×D4—181no—
263C22×C4—182no—
264Q16—182no—
265SD16—184no—
266C2×C8C22×C3⋊D311yescharacteristic
267C2×C8C22×C3⋊D311yescharacteristic
268C2×C8C22×C3⋊D312yes—
269C4⋊C4—92no—
270C4⋊C4—91no—
271C4⋊C4—91no—
272C4⋊C4—181no—
273C4⋊C4—181no—
274C4⋊C4—182no—
275C4⋊C4—182no—
276C4⋊C4—182no—
277C4⋊C4—181no—
278C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
279C4⋊C4C4⋊(C3⋊D3)12yes—
280C22⋊C4—182no—
281C22⋊C4—182no—
282C22⋊C4—182no—
283C42—181no—
284C42—182no—
285C42—181no—
286C42C22×C3⋊D312yes—
287C42C22×C3⋊D311yescharacteristic
288C22×C3C22×D1214yes—
289C2×D3—128no—
290C2×D3—128no—
291C2×D3—128no—
292C3×C4—28no—
293C3×C4—28no—
294C3×C4—24no—
295C3×C4#90418yes—
296C3×C4#100714yes—
297C3×C4D3×#4114yes—
298Dic3—68no—
299Dic3—128no—
300Dic3—124no—
301Dic3—124no—
302Dic3—124no—
303C32#336511yescharacteristic, complemented, Sylow
304C23—182no—
305Q8—22no—
306Q8—92no—
307Q8—181no—
308Q8—181no—
309Q8—181no—
310Q8—362no—
311D4—182no—
312D4—182no—
313D4—362no—
314D4—721no—
315C2×C4—181no—
316C2×C4—181no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C4—182no—
320C2×C4—722no—
321C2×C4C2×C4⋊(C3⋊D3)12yes—
322C2×C4C2×C4⋊(C3⋊D3)12yes—
323C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
324C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
325C2×C4C23×C3⋊D311yescharacteristic
326C8—21no—
327C8—22no—
328C8—21no—
329C2×C3#557614yes—
330C2×C3C2×#90414yes—
331C2×C3#575114yes—
332D3—248no—
333C22—362no—
334C22—362no—
335C22—362no—
336C22C22×C4⋊(C3⋊D3)11yescharacteristic
337C4—22no—
338C4—22no—
339C4—21no—
340C4—182no—
341C4—362no—
342C4—361no—
343C4—361no—
344C4—361no—
345C4#6411312yes—
346C4#6436411yescharacteristic
347C4#41×C3⋊D311yescharacteristic
348C3#7993514yescomplemented
349C2—722no—
350C2#1059604711yescharacteristic
351C2C2×#6411311yescharacteristic
352C2#1059622211yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C8×Q8C2
socleC22×C32C22×D4
prime radical#64083C22
hypercenterC8×Q8C3⋊D3
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
2. #10596038C2semidirect
3. C32×C8×Q8C2semidirect
4. #10592550C2semidirect
6. #10592546C2semidirect
7. #10592544C2semidirect
8. C4×#3746C2semidirect
9. #10592396C2semidirect
11. C4×#3744C2semidirect
44. C3×C8×Q8D3semidirect
148. C8×Q8C3⋊D3semidirect
303. C32#3365semidirect
348. C3#79935semidirect

Maximal subgroups

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

subgroupindex
#105960562
#105960382
C32×C8×Q82
#105925502
#105925472
#105925462
#105925442
C4×#37462
#105923962
#105923932
C4×#37442
#799353