Finite Group Databasebeta

← #11876966

Subgroups — #11876966

Order 1152.

1338 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#10596019C212yesmaximal, complemented
2C32×#442C211yesmaximal, characteristic, complemented
3#10592858C211yesmaximal, characteristic, complemented
4#10592850C211yesmaximal, characteristic, complemented
5#10592713C212yesmaximal, complemented
6#10592564C211yesmaximal, characteristic, complemented
7#10592554C211yesmaximal, characteristic, complemented
8#10592481C212yesmaximal, complemented
9#10592459C212yesmaximal, complemented
10#10592410C211yesmaximal, characteristic, complemented
11#10592406C211yesmaximal, characteristic, complemented
12#79877—34nomaximal
13C2×#3828—22no—
14C2×C32×D8C2211yescharacteristic
15C32×C4×D4C2212yes—
16#64149C2212yes—
17#64147C2212yes—
18C2×#3753C2212yes—
19C4×#638—22no—
20C2×#3745C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23#64104C2212yes—
24#64097C2212yes—
25#64094—22no—
26#64093—22no—
27C4×C4⋊(C3⋊D3)C2212yes—
28C42×C3⋊D3C2211yescharacteristic
29C32×#106C2211yescharacteristic
30C32×#102C2212yes—
31C32×#97C2211yescharacteristic
32#63659C2212yes—
33#63648C2212yes—
34#63644C2211yescharacteristic
35C8×C3⋊Dic3C2211yescharacteristic
36C8×C3⋊Dic3C2211yescharacteristic
37#63636C2212yes—
38#63635C2212yes—
39#63630C2211yescharacteristic
40#5548—38no—
41C3×#442D314yescomplemented
42#5159—34no—
43#5151—34no—
44#5014—38no—
45#4865—34no—
46#4855—34no—
47#4782—38no—
48#4760—38no—
49#4711—34no—
50#4707—34no—
51C2×C32×D4C2312yes—
52C22×C32×C4—22no—
53C2×#638—22no—
54C2×#638—22no—
55C2×#638—22no—
56#3828—48no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3D412yes—
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×#634—22no—
63C32×D8—22no—
64C2×C32×C8C2311yescharacteristic
65C2×C32×C8C2311yescharacteristic
66C32×C4⋊C4C2312yes—
67C32×C22⋊C4—22no—
68C32×C42C2311yescharacteristic
69#3757—22no—
70#3753—24no—
71#3752—22no—
72#3752—22no—
73C4⋊(C3⋊Dic3)C2312yes—
74#3750—22no—
75C4×C3⋊Dic3D412yes—
76C4×C3⋊Dic3C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79#3745—22no—
80#3743—22no—
81#3743—22no—
82#3184—91noSylow
83C2×#235—68no—
84C2×C3×D8C2×D314yes—
85C3×C4×D4C2×D318yes—
86#940—38no—
87#938—38no—
88C2×#213—38no—
89C4×#67—68no—
90C2×D24—34no—
91C2×ΓL(1,𝔽25)—34no—
92C2×ΓL(1,𝔽25)—34no—
93#895—38no—
94#888—38no—
95#885—68no—
96#884—68no—
97C4×D12—38no—
98C42×D3—34no—
99C3×#106C2×D314yes—
100C3×#102C2×D318yes—
101C3×#97C2×D314yes—
102#832—38no—
103#821—38no—
104#817—34no—
105C8×Dic3—34no—
106C8×Dic3—34no—
107#809—38no—
108#808—38no—
109#803—34no—
110C23×C32—22no—
111C22×C3⋊D3—22no—
112C22×C3⋊D3C2×D411yescharacteristic
113C32×D4—22no—
114C32×D4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—44no—
117C2×C32×C4C2×D412yes—
118C2×C32×C4C2411yescharacteristic
119#638—44no—
120#638—44no—
121#638—44no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3C2×D411yescharacteristic
124C2×C3⋊Dic3C2×D412yes—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)—22no—
127C4⋊(C3⋊D3)—44no—
128C4×C3⋊D3—21no—
129C4×C3⋊D3—21no—
130C4×C3⋊D3—24no—
131C4×C3⋊D3—44no—
132#634—44no—
133C32×C8—21no—
134C32×C8#4112yescomplemented
135C3⋊(C3⋊C8)—21no—
136C3⋊(C3⋊C8)#4112yescomplemented
137#532—92no—
138#498—91no—
139#493—91no—
140#486—92no—
141#469—91no—
142#469—91no—
143#469—92no—
144#442—92no—
145#442—91no—
146#442C3⋊D311yescharacteristic, complemented
147C4×M16—91no—
148C2×C3×D4C22×D318yes—
149C22×C3×C4—28no—
150C2×#67—68no—
151C2×#67—68no—
152C2×#67—68no—
153#235—1232no—
154C2×D12—38no—
155C2×D12—68no—
156C2×C4×D3—38no—
157C2×C4×D3—34no—
158C2×C4×D3—68no—
159C2×Dic6—68no—
160C3×D8—28no—
161C2×C3×C8C22×D314yes—
162C2×C3×C8C22×D314yes—
163C3×C4⋊C4C22×D318yes—
164C3×C22⋊C4—28no—
165C3×C42C22×D314yes—
166#217—68no—
167#213—616no—
168(C2×D3)⋊C4—68no—
169(C2×D3)⋊C4—68no—
170C4⋊Dic3—38no—
171Dic3⋊C4—68no—
172C4×Dic3—38no—
173C4×Dic3—34no—
174C2×C3⋊C8—34no—
175C2×C3⋊C8—34no—
176D24—68no—
177ΓL(1,𝔽25)—68no—
178ΓL(1,𝔽25)—68no—
179C22×C32—42no—
180C22×C32—42no—
181C22×C32—42no—
182C22×C32C22×D411yescharacteristic
183C2×C3⋊D3—21no—
184C2×C3⋊D3—22no—
185C2×C3⋊D3—42no—
186C2×C3⋊D3—42no—
187C2×C3⋊D3—42no—
188C32×C4—22no—
189C32×C4—42no—
190C32×C4C2×#4111yescharacteristic
191C32×C4C2×#4111yescharacteristic
192C3⋊Dic3—21no—
193C3⋊Dic3—42no—
194C3⋊Dic3AGL(1,ℤ/8)14yes—
195C2×#41—182no—
196C2×D8—92no—
197C2×D8—91no—
198C2×D8C2×C3⋊D311yescharacteristic
199C2×M16—91no—
200C2×M16—91no—
201C4⋊Q8—92no—
202#127—92no—
203#124—182no—
204#121—92no—
205#121—92no—
206#121—182no—
207C4×D4—92no—
208C4×D4—182no—
209C4×D4C2×C3⋊D312yes—
210C2×C42—91no—
211#106—91no—
212#106—92no—
213#106C2×C3⋊D311yescharacteristic
214#102—92no—
215#102—92no—
216#102—92no—
217#102C2×C3⋊D312yes—
218#97—91no—
219#97C2×C3⋊D311yescharacteristic
220C4×C8—91no—
221C4×C8—91no—
222C23×C3—28no—
223C22×D3—34no—
224C22×D3—68no—
225C3×D4—28no—
226C3×D4—28no—
227C2×C3×C4—28no—
228C2×C3×C4—416no—
229C2×C3×C4D3×D418yes—
230C2×C3×C4C23×D314yes—
231#67—1216no—
232#67—1216no—
233#67—1216no—
234C2×Dic3—38no—
235C2×Dic3—34no—
236C2×Dic3—68no—
237D12—68no—
238D12—68no—
239D12—1216no—
240C4×D3—616no—
241C4×D3—64no—
242C4×D3—64no—
243C4×D3—1216no—
244Dic6—1216no—
245C3×C8—24no—
246C3×C8#23518yescomplemented
247C3⋊C8—38no—
248C3⋊C8—64no—
249C2×C32—82no—
250C2×C32#53211yescharacteristic
251C2×C32C2×AGL(1,ℤ/8)12yes—
252C3⋊D3—41no—
253C3⋊D3—82no—
254#41—368no—
255C2×Q8—182no—
256C2×D4—92no—
257C2×D4—182no—
258C2×D4—182no—
259C2×D4—182no—
260C2×D4—182no—
261C2×D4C22×C3⋊D312yes—
262C22×C4—22no—
263C22×C4—91no—
264C22×C4—92no—
265C22×C4—182no—
266D8—22no—
267D8—184no—
268D8—182no—
269M16—182no—
270M16—182no—
271C2×C8—91no—
272C2×C8—91no—
273C2×C8C22×C3⋊D311yescharacteristic
274C2×C8C22×C3⋊D311yescharacteristic
275C4⋊C4—92no—
276C4⋊C4—182no—
277C4⋊C4C22×C3⋊D312yes—
278C22⋊C4—22no—
279C22⋊C4—182no—
280C22⋊C4—182no—
281C22⋊C4—182no—
282C42—91no—
283C42—92no—
284C42C22×C3⋊D311yescharacteristic
285C22×C3—48no—
286C22×C3—48no—
287C22×C3—48no—
288C22×C3C2×D3×D414yes—
289C2×D3—68no—
290C2×D3—64no—
291C2×D3—128no—
292C2×D3—128no—
293C2×D3—128no—
294C3×C4—28no—
295C3×C4—48no—
296C3×C4C2×#23514yes—
297C3×C4D3×#4114yes—
298Dic3—316no—
299Dic3—64no—
300Dic3—128no—
301C32#318411yescharacteristic, complemented, Sylow
302C23—22no—
303C23—91no—
304C23—182no—
305Q8—364no—
306D4—22no—
307D4—22no—
308D4—182no—
309D4—182no—
310D4—364no—
311D4—364no—
312D4—364no—
313D4—364no—
314C2×C4—22no—
315C2×C4—44no—
316C2×C4—92no—
317C2×C4—91no—
318C2×C4—184no—
319C2×C4—181no—
320C2×C4—181no—
321C2×C4—182no—
322C2×C4—364no—
323C2×C4D4×C3⋊D312yes—
324C2×C4C23×C3⋊D311yescharacteristic
325C8—21no—
326C8—92no—
327C8—181no—
328C8#382812yescomplemented
329C2×C3—88no—
330C2×C3#554814yes—
331C2×C3D3×AGL(1,ℤ/8)18yes—
332D3—124no—
333D3—248no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—182no—
338C22—181no—
339C22—362no—
340C22—362no—
341C22—362no—
342C22C2×D4×C3⋊D311yescharacteristic
343C4—22no—
344C4—42no—
345C4—94no—
346C4—181no—
347C4—362no—
348C4C2×#382811yescharacteristic
349C4#41×C3⋊D311yescharacteristic
350C3#7987714yescomplemented
351C2—82no—
352C2—361no—
353C2—722no—
354C2#1059601911yescharacteristic
355C2C3⋊D3×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#442C2
socleC22×C32C22×D4
hypercenter#442C3⋊D3
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #10596019C2semidirect
2. C32×#442C2semidirect
3. #10592858C2semidirect
4. #10592850C2semidirect
5. #10592713C2semidirect
6. #10592564C2semidirect
7. #10592554C2semidirect
8. #10592481C2semidirect
9. #10592459C2semidirect
10. #10592410C2semidirect
11. #10592406C2semidirect
41. C3×#442D3semidirect
134. C32×C8#41semidirect
136. C3⋊(C3⋊C8)#41semidirect
146. #442C3⋊D3semidirect
246. C3×C8#235semidirect
301. C32#3184semidirect
328. C8#3828semidirect
350. C3#79877semidirect

Maximal subgroups

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

subgroupindex
#105960192
C32×#4422
#105928582
#105928502
#105927132
#105925642
#105925542
#105924812
#105924592
#105924102
#105924062
#798773