Finite Group Databasebeta

← #11895402

Subgroups — #11895402

Order 1152.

1176 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596193C211yesmaximal, characteristic, complemented
2#10596189C211yesmaximal, characteristic
3C32×#486C211yesmaximal, characteristic, complemented
4#10592783C211yesmaximal, characteristic, complemented
5#10592774C211yesmaximal, characteristic, complemented
6#10592461C212yesmaximal, complemented
7#10592460C212yesmaximal, complemented
8#10592459C212yesmaximal, complemented
9#10592457C212yesmaximal, complemented
10C4×#3744C211yesmaximal, characteristic, complemented
11C8×#634C211yesmaximal, characteristic, complemented
12#81588—34nomaximal
13C2×#3830—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#127C2211yescharacteristic
16#64153—22no—
17#64149C2212yes—
18#64148—22no—
19#64147—21no—
20D4×C3⋊Dic3C2212yes—
21C2×#3754C2212yes—
22C2×#3744C2211yescharacteristic
23#64097—21no—
24#64097C2212yes—
25#64096—21no—
26#64096C2212yes—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#102C2212yes—
31C32×#102C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63659C2212yes—
34#63648C2211yescharacteristic
35#63644C2211yescharacteristic
36#63643C2211yescharacteristic
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63636C2212yes—
40#63635C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5722—34no—
43#5718—34no—
44C3×#486D314yescomplemented
45#5084—34no—
46#5075—34no—
47#4762—38no—
48#4761—38no—
49#4760—38no—
50#4758—38no—
51C4×#204—34no—
52C8×Dic6—34no—
53C2×C32×Q8—21no—
54C2×C32×D4—21no—
55C2×C32×D4—21no—
56C2×C32×D4C2312yes—
57C2×#638—22no—
58C2×#638—22no—
59C22×C3⋊Dic3—22no—
60#3830—44no—
61C2×C4⋊(C3⋊D3)C2311yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×#634—22no—
64C2×#634D411yescharacteristic
65C2×#634C2311yescharacteristic
66C2×C32×C8C2311yescharacteristic
67C2×C32×C8C2311yescharacteristic
68C32×C4⋊C4—21no—
69C32×C4⋊C4C2312yes—
70C32×C42C2311yescharacteristic
71#3757—22no—
72#3754—24no—
73#3752—21no—
74C4⋊(C3⋊Dic3)D411yescharacteristic
75C4⋊(C3⋊Dic3)C2311yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77#3750—21no—
78#3750—22no—
79#3750—22no—
80#3750D412yes—
81C4×C3⋊Dic3—21no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2312yes—
85#3744—22no—
86#3362—91noSylow
87C2×#237—64no—
88C3×C4⋊Q8C2×D314yes—
89C3×#127C2×D314yes—
90#944—68no—
91#940—38no—
92#939—68no—
93#938—64no—
94D4×Dic3—38no—
95C2×#214—38no—
96C2×#204—34no—
97#888—38no—
98#888—64no—
99#887—38no—
100#887—64no—
101C4×D12—34no—
102C4×Dic6—34no—
103C4×Dic6—34no—
104C3×#102C2×D318yes—
105C3×#102C2×D318yes—
106C3×C4×C8C2×D314yes—
107#832—38no—
108#821—34no—
109#817—34no—
110#816—34no—
111Dic3⋊C8—38no—
112C8×Dic3—38no—
113#809—38no—
114#808—38no—
115C4⋊(C3⋊C8)—34no—
116C23×C32—22no—
117C22×C3⋊D3—21no—
118C32×Q8—81no—
119C32×D4—22no—
120C32×D4—22no—
121C32×D4—42no—
122C32×D4—81no—
123C2×C32×C4—22no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2411yescharacteristic
127#638—44no—
128#638—82no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—44no—
133C2×C3⋊Dic3C2×D412yes—
134C2×C3⋊Dic3C2×D412yes—
135C4⋊(C3⋊D3)—21no—
136C4⋊(C3⋊D3)—21no—
137C4×C3⋊D3—42no—
138#634—21no—
139#634—82no—
140#634SD1614yescomplemented
141#634#4112yescomplemented
142C32×C8—21no—
143C32×C8—21no—
144C3⋊(C3⋊C8)—22no—
145Q82—91no—
146#550—91no—
147#486—92no—
148#486C3⋊D311yescharacteristic, complemented
149#476—91no—
150#476—92no—
151#460—91no—
152#460—92no—
153C8×Q8—91no—
154C4×SD16—92no—
155C4×SD16—91no—
156C2×C3×Q8—24no—
157C2×C3×D4—24no—
158C2×C3×D4—24no—
159C2×C3×D4C22×D318yes—
160C2×#67—68no—
161C2×#67—68no—
162C22×Dic3—68no—
163#237—1216no—
164C2×D12—34no—
165C2×C4×D3—64no—
166C2×Dic6—34no—
167C2×Dic6—34no—
168C2×Dic6—68no—
169C2×C3×C8C22×D314yes—
170C2×C3×C8C22×D314yes—
171C3×C4⋊C4—24no—
172C3×C4⋊C4C22×D318yes—
173C3×C42C22×D314yes—
174#217—68no—
175#214—616no—
176(C2×D3)⋊C4—64no—
177C4⋊Dic3—34no—
178C4⋊Dic3—34no—
179C4⋊Dic3—34no—
180Dic3⋊C4—38no—
181Dic3⋊C4—68no—
182Dic3⋊C4—68no—
183Dic3⋊C4—64no—
184C4×Dic3—38no—
185C4×Dic3—68no—
186C4×Dic3—64no—
187C2×C3⋊C8—38no—
188#204—68no—
189C22×C32—42no—
190C22×C32—42no—
191C22×C32—42no—
192C22×C32C22×D411yescharacteristic
193C2×C3⋊D3—41no—
194C2×C3⋊D3—41no—
195C2×C3⋊D3—41no—
196C32×C4—21no—
197C32×C4—42no—
198C32×C4C2×SD1612yes—
199C32×C4C2×#4111yescharacteristic
200C32×C42−1+411yescharacteristic
201C3⋊Dic3—22no—
202C3⋊Dic3—22no—
203C3⋊Dic3—41no—
204C3⋊Dic3—41no—
205C3⋊Dic3C2×SD1614yes—
206C2×#41—181no—
207C2×SD16—92no—
208C2×SD16—91no—
209C4⋊Q8—92no—
210C4⋊Q8—181no—
211C4⋊Q8—182no—
212C4⋊Q8C2×C3⋊D311yescharacteristic
213#127—92no—
214#127C2×C3⋊D311yescharacteristic
215#121—181no—
216#121—182no—
217C4×Q8—91no—
218C4×Q8—92no—
219C4×Q8—91no—
220C4×Q8—181no—
221C4×D4—92no—
222C4×D4—91no—
223#106—91no—
224#106—92no—
225C4⋊C8—92no—
226C4⋊C8—91no—
227#103—91no—
228#102—92no—
229#102—91no—
230#102—92no—
231#102C2×C3⋊D312yes—
232#102C2×C3⋊D312yes—
233C4×C8—92no—
234C4×C8C2×C3⋊D311yescharacteristic
235C23×C3—28no—
236C22×D3—64no—
237C3×Q8—84no—
238C3×D4—28no—
239C3×D4—28no—
240C3×D4—48no—
241C3×D4—84no—
242C2×C3×C4—28no—
243C2×C3×C4D3×D414yes—
244C2×C3×C4D3×D414yes—
245C2×C3×C4C23×D314yes—
246#67—1216no—
247#67—248no—
248C2×Dic3—38no—
249C2×Dic3—38no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—1216no—
254D12—64no—
255D12—64no—
256C4×D3—128no—
257Dic6—316no—
258Dic6—38no—
259Dic6—64no—
260Dic6—248no—
261C3×C8—24no—
262C3×C8—24no—
263C3⋊C8—68no—
264C2×C32—82no—
265C2×C32#54811yescharacteristic
266C2×C32C22×SD1611yescharacteristic
267C2×C32#57611yescharacteristic
268C3⋊D3—81no—
269#41—364no—
270C2×Q8—21no—
271C2×Q8—91no—
272C2×Q8—91no—
273C2×Q8—182no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—91no—
277C2×D4—182no—
278C2×D4—182no—
279C2×D4C22×C3⋊D312yes—
280C22×C4—182no—
281C22×C4—181no—
282SD16—182no—
283SD16—184no—
284C2×C8—92no—
285C2×C8C22×C3⋊D311yescharacteristic
286C2×C8C22×C3⋊D311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—92no—
289C4⋊C4—91no—
290C4⋊C4—91no—
291C4⋊C4—91no—
292C4⋊C4—182no—
293C4⋊C4—182no—
294C4⋊C4—181no—
295C4⋊C4C22×C3⋊D312yes—
296C22⋊C4—182no—
297C22⋊C4—181no—
298C42—92no—
299C42—182no—
300C42—181no—
301C42C22×C3⋊D311yescharacteristic
302C22×C3—48no—
303C22×C3—48no—
304C22×C3—48no—
305C22×C3C2×D3×D414yes—
306C2×D3—124no—
307C2×D3—124no—
308C2×D3—124no—
309C3×C4—24no—
310C3×C4—48no—
311C3×C4D3×SD1618yes—
312C3×C4D3×#4114yes—
313C3×C4#101014yes—
314Dic3—316no—
315Dic3—68no—
316Dic3—68no—
317Dic3—124no—
318Dic3—124no—
319C32#336211yescharacteristic, complemented, Sylow
320C23—22no—
321C23—181no—
322Q8—81no—
323Q8—94no—
324Q8—92no—
325Q8—181no—
326Q8—722no—
327D4—22no—
328D4—22no—
329D4—42no—
330D4—81no—
331D4—181no—
332D4—181no—
333D4—364no—
334D4—722no—
335C2×C4—22no—
336C2×C4—92no—
337C2×C4—92no—
338C2×C4—181no—
339C2×C4—181no—
340C2×C4—181no—
341C2×C4—364no—
342C2×C4—362no—
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4C23×C3⋊D311yescharacteristic
346C8—21no—
347C8—21no—
348C8—182no—
349C2×C3—88no—
350C2×C3#567714yes—
351C2×C3#575714yes—
352C2×C3C2×D3×SD1614yes—
353D3—244no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—361no—
358C22—361no—
359C22—361no—
360C22C2×D4×C3⋊D311yescharacteristic
361C4—21no—
362C4—42no—
363C4—94no—
364C4—182no—
365C4—182no—
366C4—361no—
367C4—361no—
368C4SD16×C3⋊D312yes—
369C4#41×C3⋊D311yescharacteristic
370C4#6436711yescharacteristic
371C3#8158814yescomplemented
372C2—82no—
373C2—721no—
374C2#1059614811yescharacteristic
375C2#1059622811yescharacteristic
376C2C2×SD16×C3⋊D311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#486C2
socleC22×C32C22×D4
prime radical#10596189C2
hypercenter#486C3⋊D3
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10596193C2semidirect
3. C32×#486C2semidirect
4. #10592783C2semidirect
5. #10592774C2semidirect
6. #10592461C2semidirect
7. #10592460C2semidirect
8. #10592459C2semidirect
9. #10592457C2semidirect
10. C4×#3744C2semidirect
11. C8×#634C2semidirect
44. C3×#486D3semidirect
140. #634SD16semidirect
141. #634#41semidirect
148. #486C3⋊D3semidirect
319. C32#3362semidirect
371. C3#81588semidirect

Maximal subgroups

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

subgroupindex
#105961932
#105961892
C32×#4862
#105927832
#105927742
#105924612
#105924602
#105924592
#105924572
C4×#37442
C8×#6342
#815883