Finite Group Databasebeta

← #11895921

Subgroups — #11895921

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596192C211yesmaximal, characteristic, complemented
2#10596024C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic, complemented
5C4×#3754C211yesmaximal, characteristic, complemented
6#10592590C212yesmaximal, complemented
7#10592588C212yesmaximal, complemented
8#10592547C211yesmaximal, characteristic, complemented
9#10592530C211yesmaximal, characteristic, complemented
10#10592463C212yesmaximal, complemented
11#10592461C212yesmaximal, complemented
12#80995—34nomaximal
13C2×#3828—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16Q8×C3⋊Dic3—21no—
17#64153—21no—
18#64149C2212yes—
19C2×#3754C2211yescharacteristic
20#64139—21no—
21C2×#3744C2212yes—
22#64102C2212yes—
23#64099C2212yes—
24#64098—22no—
25#64096C2212yes—
26#64093—22no—
27#64083C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#107C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×#102C2212yes—
33#63659C2211yescharacteristic
34#63648C2212yes—
35#63642C2212yes—
36#63641C2212yes—
37#63637C2211yescharacteristic
38#63636C2212yes—
39#63636C2212yes—
40#63635C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5721—34no—
43#5553—34no—
44C3×#474D314yescomplemented
45#5088—34no—
46C4×#214—34no—
47#4891—38no—
48#4889—38no—
49#4848—34no—
50#4831—34no—
51#4764—38no—
52#4762—38no—
53C2×C32×Q8—21no—
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C2×#638—22no—
57C2×#638—22no—
58#3828—44no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C4×C3⋊D3—22no—
63C2×#634D411yescharacteristic
64C2×#634C2311yescharacteristic
65C2×C32×C8C2312yes—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2312yes—
68C32×C4⋊C4C2311yescharacteristic
69C32×C22⋊C4—21no—
70C32×C42C2311yescharacteristic
71#3754—22no—
72#3752—22no—
73C4⋊(C3⋊Dic3)—22no—
74C4⋊(C3⋊Dic3)D411yescharacteristic
75C4⋊(C3⋊Dic3)C2311yescharacteristic
76#3750—21no—
77#3750—22no—
78#3750—22no—
79#3750D412yes—
80C4×C3⋊Dic3—21no—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3744—24no—
86#3368—91noSylow
87C2×#235—64no—
88C3×C4⋊Q8C2×D314yes—
89C3×C4×D4C2×D314yes—
90Q8×Dic3—64no—
91#944—64no—
92#940—38no—
93C2×#214—34no—
94#930—64no—
95C2×#204—38no—
96#893—38no—
97#890—38no—
98#889—68no—
99#887—38no—
100#884—68no—
101#874—34no—
102C4×Dic6—34no—
103C4×Dic6—34no—
104C3×#107C2×D318yes—
105C3×C4⋊C8C2×D314yes—
106C3×#102C2×D318yes—
107#832—34no—
108#821—38no—
109#815—38no—
110Dic3⋊C8—38no—
111#810—34no—
112#809—38no—
113#809—38no—
114#808—34no—
115C4×C3⋊C8—34no—
116C23×C32—21no—
117C22×C3⋊D3—22no—
118C32×Q8—42no—
119C32×D4—21no—
120C32×D4—21no—
121C2×C32×C4—22no—
122C2×C32×C4—21no—
123C2×C32×C4—42no—
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⋊Dic3C2×D412yes—
132C2×C3⋊Dic3C2×D412yes—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—42no—
136C4⋊(C3⋊D3)—81no—
137C4×C3⋊D3—44no—
138#634—22no—
139#634—21no—
140#634#4112yescomplemented
141C32×C8—22no—
142C3⋊(C3⋊C8)—21no—
143C3⋊(C3⋊C8)—21no—
144#557—91no—
145#550—91no—
146#490—92no—
147#486—91no—
148#478—92no—
149#474C3⋊D311yescharacteristic, complemented
150#460—91no—
151#460—92no—
152#446—91no—
153#440—92no—
154C4×SD16—91no—
155C2×C3×Q8—24no—
156C2×C3×D4C22×D314yes—
157C22×C3×C4—24no—
158C2×#67—68no—
159C2×#67—68no—
160#235—1216no—
161C2×D12—38no—
162C2×D12—64no—
163C2×D12—64no—
164C2×C4×D3—68no—
165C2×Dic6—34no—
166C2×Dic6—34no—
167C2×C3×C8C22×D318yes—
168C3×C4⋊C4—24no—
169C3×C4⋊C4C22×D314yes—
170C3×C4⋊C4C22×D318yes—
171C3×C22⋊C4—24no—
172C3×C42C22×D314yes—
173#214—68no—
174(C2×D3)⋊C4—68no—
175C4⋊Dic3—34no—
176C4⋊Dic3—34no—
177C4⋊Dic3—68no—
178Dic3⋊C4—38no—
179Dic3⋊C4—68no—
180Dic3⋊C4—68no—
181Dic3⋊C4—64no—
182C4×Dic3—38no—
183C4×Dic3—68no—
184C4×Dic3—64no—
185C2×C3⋊C8—34no—
186C2×C3⋊C8—34no—
187#204—616no—
188C22×C32—41no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32C22×D411yescharacteristic
192C2×C3⋊D3—42no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—42no—
195C32×C4—21no—
196C32×C4—41no—
197C32×C4—42no—
198C32×C4AGL(1,ℤ/8)12yes—
199C32×C4C2×#4111yescharacteristic
200C32×C42−1+411yescharacteristic
201C3⋊Dic3—22no—
202C3⋊Dic3—22no—
203C3⋊Dic3—22no—
204C3⋊Dic3—41no—
205C2×#41—181no—
206C2×SD16—91no—
207C2×SD16—92no—
208C4⋊Q8—181no—
209C4⋊Q8C2×C3⋊D311yescharacteristic
210#127—92no—
211#127—91no—
212#125—92no—
213#125—182no—
214#121—182no—
215#121—181no—
216C4×Q8—91no—
217C4×Q8—92no—
218C4×Q8—91no—
219C4×Q8—181no—
220C4×D4—92no—
221C4×D4C2×C3⋊D311yescharacteristic
222#107C2×C3⋊D312yes—
223#106—91no—
224C4⋊C8—92no—
225C4⋊C8C2×C3⋊D311yescharacteristic
226#103—91no—
227#102—91no—
228#102—92no—
229#102—92no—
230#102—92no—
231#102C2×C3⋊D312yes—
232#97—92no—
233C4×C8—91no—
234C23×C3—24no—
235C22×D3—68no—
236C3×Q8—48no—
237C3×D4—24no—
238C3×D4—24no—
239C2×C3×C4—28no—
240C2×C3×C4—24no—
241C2×C3×C4—48no—
242C2×C3×C4D3×D414yes—
243C2×C3×C4D3×D414yes—
244C2×C3×C4C23×D314yes—
245#67—1216no—
246#67—248no—
247C2×Dic3—38no—
248C2×Dic3—38no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251D12—68no—
252D12—68no—
253D12—128no—
254D12—244no—
255C4×D3—1216no—
256Dic6—38no—
257Dic6—68no—
258Dic6—64no—
259C3×C8—28no—
260C3⋊C8—64no—
261C3⋊C8—64no—
262C2×C32—81no—
263C2×C32#54811yescharacteristic
264C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
265C2×C32#57711yescharacteristic
266C3⋊D3—82no—
267#41—364no—
268C2×Q8—21no—
269C2×Q8—91no—
270C2×Q8—91no—
271C2×D4—92no—
272C2×D4—182no—
273C2×D4—182no—
274C2×D4—181no—
275C2×D4—181no—
276C2×D4C22×C3⋊D311yescharacteristic
277C22×C4—21no—
278C22×C4—182no—
279SD16—184no—
280SD16—182no—
281C2×C8—91no—
282C2×C8—91no—
283C2×C8C22×C3⋊D312yes—
284C4⋊C4—21no—
285C4⋊C4—91no—
286C4⋊C4—92no—
287C4⋊C4—91no—
288C4⋊C4—182no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C4⋊C4C22×C3⋊D312yes—
293C4⋊C4C22×C3⋊D311yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—182no—
296C42—92no—
297C42—182no—
298C42—181no—
299C42C22×C3⋊D311yescharacteristic
300C22×C3—44no—
301C22×C3—44no—
302C22×C3—44no—
303C22×C3C2×D3×D414yes—
304C2×D3—128no—
305C2×D3—128no—
306C2×D3—128no—
307C3×C4—24no—
308C3×C4—44no—
309C3×C4—48no—
310C3×C4#91118yes—
311C3×C4#100714yes—
312C3×C4D3×#4114yes—
313Dic3—68no—
314Dic3—68no—
315Dic3—68no—
316Dic3—124no—
317C32#336811yescharacteristic, complemented, Sylow
318C23—21no—
319C23—182no—
320Q8—42no—
321Q8—92no—
322Q8—181no—
323Q8—182no—
324D4—21no—
325D4—21no—
326D4—182no—
327D4—182no—
328D4—364no—
329D4—362no—
330D4—721no—
331D4—722no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—92no—
336C2×C4—92no—
337C2×C4—181no—
338C2×C4—181no—
339C2×C4—364no—
340C2×C4D4×C3⋊D311yescharacteristic
341C2×C4D4×C3⋊D311yescharacteristic
342C2×C4C23×C3⋊D311yescharacteristic
343C8—22no—
344C8—181no—
345C8—181no—
346C2×C3—84no—
347C2×C3#563314yes—
348C2×C3C2×#91114yes—
349C2×C3#577814yes—
350D3—248no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—362no—
355C22—362no—
356C22—362no—
357C22C2×D4×C3⋊D311yescharacteristic
358C4—21no—
359C4—41no—
360C4—42no—
361C4—182no—
362C4—182no—
363C4—182no—
364C4—361no—
365C4#6412012yes—
366C4#6436411yescharacteristic
367C4#41×C3⋊D311yescharacteristic
368C3#8099514yescomplemented
369C2—81no—
370C2—722no—
371C2#1059610411yescharacteristic
372C2C2×#6412011yescharacteristic
373C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radical#10596024C2
hypercenter#474C3⋊D3
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10596192C2semidirect
3. C32×#474C2semidirect
4. #10592787C2semidirect
5. C4×#3754C2semidirect
6. #10592590C2semidirect
7. #10592588C2semidirect
8. #10592547C2semidirect
9. #10592530C2semidirect
10. #10592463C2semidirect
11. #10592461C2semidirect
44. C3×#474D3semidirect
140. #634#41semidirect
149. #474C3⋊D3semidirect
317. C32#3368semidirect
368. C3#80995semidirect

Maximal subgroups

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

subgroupindex
#105961922
#105960242
C32×#4742
#105927872
C4×#37542
#105925902
#105925882
#105925472
#105925302
#105924632
#105924612
#809953