Finite Group Databasebeta

← #11895936

Subgroups — #11895936

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#10596189C211yesmaximal, characteristic
2#10596041C211yesmaximal, characteristic, complemented
3C32×#460C211yesmaximal, characteristic, complemented
4#10592863C212yesmaximal, complemented
5#10592862C212yesmaximal, complemented
6#10592769C211yesmaximal, characteristic, complemented
7C4×#3755C211yesmaximal, characteristic, complemented
8#10592545C211yesmaximal, characteristic, complemented
9#10592530C211yesmaximal, characteristic, complemented
10#10592465C212yesmaximal, complemented
11#10592463C212yesmaximal, complemented
12#80371—34nomaximal
13C2×#3830—21no—
14C2×C32×SD16C2212yes—
15C32×#127C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17Q8×C3⋊Dic3C2212yes—
18C2×#3755C2211yescharacteristic
19#64149C2212yes—
20#64148—22no—
21#64147—21no—
22D4×C3⋊Dic3C2212yes—
23#64099—22no—
24#64099C2212yes—
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26#64078—21no—
27#64078C2211yescharacteristic
28C4×#634—21no—
29C4×#634C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31C32×#102C2212yes—
32#63662C2211yescharacteristic
33#63659C2212yes—
34#63659C2212yes—
35#63648C2212yes—
36#63645C2212yes—
37#63642C2212yes—
38#63641C2212yes—
39#63636C2211yescharacteristic
40#63635C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5718—34no—
43#5570—34no—
44C3×#460D314yescomplemented
45#5164—38no—
46#5163—38no—
47#5070—34no—
48C4×#215—34no—
49#4846—34no—
50#4831—34no—
51#4766—38no—
52#4764—38no—
53C2×C32×Q8C2311yescharacteristic
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—21no—
64C2×#634D411yescharacteristic
65C32×SD16—24no—
66C2×C32×C8C2312yes—
67C32×C4⋊C4—21no—
68C32×C4⋊C4C2311yescharacteristic
69C32×C42—21no—
70C32×C42C2311yescharacteristic
71#3757—22no—
72#3755—22no—
73#3752—21no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)—22no—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)D411yescharacteristic
78C4⋊(C3⋊Dic3)C2312yes—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—22no—
81#3750D412yes—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3368—91noSylow
87C2×#237—64no—
88C2×C3×SD16C2×D318yes—
89C3×#127C2×D314yes—
90C3×C4×Q8C2×D314yes—
91Q8×Dic3—38no—
92C2×#215—34no—
93#940—38no—
94#939—68no—
95#938—64no—
96D4×Dic3—38no—
97#890—38no—
98#890—68no—
99C4×D12—34no—
100#869—34no—
101#869—64no—
102C4×Dic6—34no—
103C4×Dic6—64no—
104C3×C4⋊C8C2×D314yes—
105C3×#102C2×D318yes—
106#835—34no—
107#832—38no—
108#832—38no—
109#821—38no—
110#818—38no—
111#815—38no—
112Dic3⋊C8—38no—
113#809—34no—
114#808—34no—
115C4×C3⋊C8—34no—
116C23×C32—22no—
117C22×C3⋊D3—21no—
118C32×Q8—21no—
119C32×Q8#4112yescomplemented
120C32×D4—22no—
121C32×D4—22no—
122C32×D4—42no—
123C32×D4—81no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2411yescharacteristic
129#638—44no—
130#638—82no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—44no—
134C2×C3⋊Dic3C2×D412yes—
135C2×C3⋊Dic3C2×D412yes—
136C4⋊(C3⋊D3)—21no—
137C4⋊(C3⋊D3)—21no—
138C4×C3⋊D3—42no—
139#634—22no—
140#634—42no—
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#474—91no—
150#460—92no—
151#460C3⋊D311yescharacteristic, complemented
152#446—91no—
153#440—92no—
154C4×SD16—91no—
155C2×C3×Q8C22×D314yes—
156C2×C3×D4—24no—
157C2×C3×D4—24no—
158C2×C3×D4C22×D318yes—
159C2×#67—68no—
160C2×#67—68no—
161C22×Dic3—68no—
162#237—1216no—
163C2×D12—34no—
164C2×C4×D3—64no—
165C2×Dic6—34no—
166C2×Dic6—64no—
167C3×SD16—216no—
168C2×C3×C8C22×D318yes—
169C3×C4⋊C4—24no—
170C3×C4⋊C4C22×D314yes—
171C3×C42—24no—
172C3×C42C22×D314yes—
173#217—68no—
174#215—68no—
175(C2×D3)⋊C4—64no—
176C4⋊Dic3—34no—
177C4⋊Dic3—34no—
178C4⋊Dic3—38no—
179C4⋊Dic3—68no—
180C4⋊Dic3—68no—
181C4⋊Dic3—64no—
182Dic3⋊C4—38no—
183Dic3⋊C4—68no—
184C4×Dic3—38no—
185C4×Dic3—68no—
186C2×C3⋊C8—34no—
187C2×C3⋊C8—34no—
188C22×C32—42no—
189C22×C32—42no—
190C22×C32—42no—
191C22×C32C22×D411yescharacteristic
192C2×C3⋊D3—41no—
193C2×C3⋊D3—41no—
194C2×C3⋊D3—41no—
195C32×C4—22no—
196C32×C4—21no—
197C32×C4—41no—
198C32×C4AGL(1,ℤ/8)12yes—
199C32×C4C2×#4111yescharacteristic
200C32×C42−1+411yescharacteristic
201C3⋊Dic3—22no—
202C3⋊Dic3—22no—
203C3⋊Dic3—42no—
204C3⋊Dic3—41no—
205C2×#41—181no—
206C2×SD16—91no—
207C2×SD16C2×C3⋊D312yes—
208C4⋊Q8—91no—
209C4⋊Q8—181no—
210#127—92no—
211#127C2×C3⋊D311yescharacteristic
212#125—92no—
213#125—182no—
214#121—181no—
215#121—182no—
216C4×Q8—91no—
217C4×Q8—92no—
218C4×Q8—181no—
219C4×Q8C2×C3⋊D311yescharacteristic
220C4×D4—92no—
221C4×D4—91no—
222#107—92no—
223#106—91no—
224C4⋊C8—92no—
225C4⋊C8C2×C3⋊D311yescharacteristic
226#103—91no—
227#102—92no—
228#102—92no—
229#102—92no—
230#102—91no—
231#102C2×C3⋊D312yes—
232#97—92no—
233C4×C8—91no—
234C23×C3—28no—
235C22×D3—64no—
236C3×Q8—24no—
237C3×Q8#23718yescomplemented
238C3×D4—28no—
239C3×D4—28no—
240C3×D4—48no—
241C3×D4—84no—
242C2×C3×C4—24no—
243C2×C3×C4—24no—
244C2×C3×C4D3×D414yes—
245C2×C3×C4D3×D414yes—
246C2×C3×C4C23×D314yes—
247#67—1216no—
248#67—248no—
249C2×Dic3—38no—
250C2×Dic3—38no—
251C2×Dic3—68no—
252C2×Dic3—64no—
253C2×Dic3—1216no—
254D12—64no—
255D12—64no—
256C4×D3—128no—
257Dic6—68no—
258Dic6—128no—
259C3×C8—28no—
260C3⋊C8—64no—
261C3⋊C8—64no—
262C2×C32—82no—
263C2×C32#54811yescharacteristic
264C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
265C2×C32#57711yescharacteristic
266C3⋊D3—81no—
267#41—364no—
268C2×Q8—91no—
269C2×Q8—181no—
270C2×Q8C22×C3⋊D311yescharacteristic
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—91no—
274C2×D4—182no—
275C2×D4—182no—
276C2×D4C22×C3⋊D312yes—
277C22×C4—182no—
278C22×C4—181no—
279SD16—24no—
280SD16—182no—
281C2×C8—91no—
282C2×C8—91no—
283C2×C8C22×C3⋊D312yes—
284C4⋊C4—21no—
285C4⋊C4—91no—
286C4⋊C4—92no—
287C4⋊C4—92no—
288C4⋊C4—91no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—182no—
292C4⋊C4—181no—
293C4⋊C4C22×C3⋊D311yescharacteristic
294C22⋊C4—182no—
295C22⋊C4—181no—
296C42—21no—
297C42—92no—
298C42—182no—
299C42C22×C3⋊D311yescharacteristic
300C22×C3—48no—
301C22×C3—48no—
302C22×C3—48no—
303C22×C3C2×D3×D414yes—
304C2×D3—124no—
305C2×D3—124no—
306C2×D3—124no—
307C3×C4—24no—
308C3×C4—28no—
309C3×C4—44no—
310C3×C4#91418yes—
311C3×C4C2×#23714yes—
312C3×C4#101014yes—
313Dic3—68no—
314Dic3—68no—
315Dic3—128no—
316Dic3—124no—
317C32#336811yescharacteristic, complemented, Sylow
318C23—22no—
319C23—181no—
320Q8—21no—
321Q8—182no—
322Q8—362no—
323Q8#383012yescomplemented
324D4—22no—
325D4—22no—
326D4—42no—
327D4—81no—
328D4—181no—
329D4—181no—
330D4—364no—
331D4—722no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—92no—
335C2×C4—92no—
336C2×C4—182no—
337C2×C4—181no—
338C2×C4—364no—
339C2×C4—362no—
340C2×C4D4×C3⋊D311yescharacteristic
341C2×C4D4×C3⋊D311yescharacteristic
342C2×C4C23×C3⋊D311yescharacteristic
343C8—22no—
344C8—181no—
345C8—181no—
346C2×C3—88no—
347C2×C3#559814yes—
348C2×C3C2×#91414yes—
349C2×C3#577514yes—
350D3—244no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—361no—
355C22—361no—
356C22—361no—
357C22C2×D4×C3⋊D311yescharacteristic
358C4—21no—
359C4—22no—
360C4—41no—
361C4—182no—
362C4—182no—
363C4—361no—
364C4—362no—
365C4#6412312yes—
366C4C2×#383011yescharacteristic
367C4#6436711yescharacteristic
368C3#8037114yescomplemented
369C2—82no—
370C2—721no—
371C2#1059606911yescharacteristic
372C2C2×#6412311yescharacteristic
373C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#460C2
socleC22×C32C22×D4
prime radical#10596189C2
hypercenter#460C3⋊D3
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #10596041C2semidirect
3. C32×#460C2semidirect
4. #10592863C2semidirect
5. #10592862C2semidirect
6. #10592769C2semidirect
7. C4×#3755C2semidirect
8. #10592545C2semidirect
9. #10592530C2semidirect
10. #10592465C2semidirect
11. #10592463C2semidirect
44. C3×#460D3semidirect
119. C32×Q8#41semidirect
151. #460C3⋊D3semidirect
237. C3×Q8#237semidirect
317. C32#3368semidirect
323. Q8#3830semidirect
368. C3#80371semidirect

Maximal subgroups

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

subgroupindex
#105961892
#105960412
C32×#4602
#105928632
#105928622
#105927692
C4×#37552
#105925452
#105925302
#105924652
#105924632
#803713