Finite Group Databasebeta

← #11895930

Subgroups — #11895930

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#10596048C211yesmaximal, characteristic
2#10596038C211yesmaximal, characteristic, complemented
3C32×#446C211yesmaximal, characteristic, complemented
4#10592547C211yesmaximal, characteristic, complemented
5#10592547C212yesmaximal, complemented
6#10592546C212yesmaximal, complemented
7#10592545C211yesmaximal, characteristic, complemented
8#10592412C212yesmaximal, complemented
9#10592409C212yesmaximal, complemented
10#10592393C211yesmaximal, characteristic, complemented
11C4×#3744C211yesmaximal, characteristic, complemented
12#79980—34nomaximal
13C2×#3832—21no—
14C32×C4×Q8C2211yescharacteristic
15#64153—21no—
16C2×#3744C2211yescharacteristic
17C2×#3744C2212yes—
18#64104—21no—
19#64104—22no—
20#64098—22no—
21#64096—21no—
22#64083C2211yescharacteristic
23#64083C2212yes—
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C4×C4⋊(C3⋊D3)C2212yes—
26#64079C2212yes—
27#64078C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C4×#634C2212yes—
30C32×C4⋊C8C2211yescharacteristic
31C32×C4⋊C8C2212yes—
32C32×#97C2212yes—
33C32×C4×C8C2211yescharacteristic
34#63648C2212yes—
35#63648C2212yes—
36#63648C2212yes—
37#63648C2211yescharacteristic
38#63648C2212yes—
39#63645C2212yes—
40#63644C2211yescharacteristic
41#63643C2211yescharacteristic
42#5577—34no—
43#5567—34no—
44C3×#446D314yescomplemented
45#4848—38no—
46#4848—34no—
47#4847—38no—
48#4846—34no—
49#4713—38no—
50#4710—38no—
51#4694—34no—
52C4×#204—34no—
53C2×C32×Q8D411yescharacteristic
54#3832—44no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2311yescharacteristic
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—21no—
63C2×#634—21no—
64C2×#634C2311yescharacteristic
65C2×C32×C8C2311yescharacteristic
66C2×C32×C8C2312yes—
67C2×C32×C8C2311yescharacteristic
68C32×C4⋊C4D411yescharacteristic
69C32×C4⋊C4D412yes—
70C32×C42C2311yescharacteristic
71C32×C42C2312yes—
72#3752—22no—
73#3752—21no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)C2312yes—
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78#3750—21no—
79#3750—22no—
80#3750—22no—
81#3750—22no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3—21no—
84#3744—22no—
85#3744—24no—
86#3368—91noSylow
87C2×#239—64no—
88C3×C4×Q8C2×D314yes—
89#944—64no—
90C2×#204—34no—
91C2×#204—38no—
92#895—64no—
93#895—68no—
94#889—68no—
95#887—64no—
96#874—34no—
97#874—38no—
98C4×D12—34no—
99C4×D12—38no—
100#870—38no—
101#869—34no—
102C4×Dic6—34no—
103C4×Dic6—38no—
104C3×C4⋊C8C2×D314yes—
105C3×C4⋊C8C2×D318yes—
106C3×#97C2×D318yes—
107C3×C4×C8C2×D314yes—
108#821—34no—
109#821—38no—
110#821—38no—
111#821—38no—
112#821—38no—
113#818—38no—
114#817—34no—
115#816—34no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—21no—
118C32×Q8—22no—
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—44no—
133C4⋊(C3⋊D3)—42no—
134C4⋊(C3⋊D3)—82no—
135C4⋊(C3⋊D3)—81no—
136C4×C3⋊D3—44no—
137C4×C3⋊D3—42no—
138#634—21no—
139#634—42no—
140#634#4112yescomplemented
141C32×C8—21no—
142C32×C8—22no—
143C32×C8—21no—
144#557—91no—
145#550—91no—
146#490—92no—
147#486—91no—
148#478—92no—
149#474—91no—
150#460—92no—
151#460—91no—
152#446C3⋊D311yescharacteristic, complemented
153#440—92no—
154C4×SD16—91no—
155C2×C3×Q8D1214yes—
156#239—1216no—
157C2×D12—34no—
158C2×D12—38no—
159C2×D12—68no—
160C2×D12—64no—
161C2×D12—68no—
162C2×D12—64no—
163C2×C4×D3—68no—
164C2×C4×D3—64no—
165C2×Dic6—34no—
166C2×Dic6—64no—
167C2×C3×C8C22×D314yes—
168C2×C3×C8C22×D314yes—
169C2×C3×C8C22×D318yes—
170C3×C4⋊C4D1214yes—
171C3×C4⋊C4D1218yes—
172C3×C42C22×D314yes—
173C3×C42C22×D318yes—
174(C2×D3)⋊C4—68no—
175(C2×D3)⋊C4—64no—
176C4⋊Dic3—34no—
177C4⋊Dic3—34no—
178C4⋊Dic3—38no—
179C4⋊Dic3—64no—
180Dic3⋊C4—64no—
181Dic3⋊C4—68no—
182Dic3⋊C4—68no—
183Dic3⋊C4—68no—
184C4×Dic3—68no—
185C4×Dic3—64no—
186#204—68no—
187#204—616no—
188C22×C32C22×D411yescharacteristic
189C2×C3⋊D3—42no—
190C2×C3⋊D3—41no—
191C2×C3⋊D3—42no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—41no—
195C32×C4—22no—
196C32×C4—22no—
197C32×C4—21no—
198C32×C4AGL(1,ℤ/8)12yes—
199C32×C4C2×#4111yescharacteristic
200C32×C42−1+411yescharacteristic
201C3⋊Dic3—22no—
202C3⋊Dic3—42no—
203C3⋊Dic3—41no—
204C3⋊Dic3—41no—
205C2×#41—181no—
206C2×SD16—91no—
207C2×SD16—92no—
208C4⋊Q8—91no—
209C4⋊Q8—181no—
210#127—91no—
211#127—92no—
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—91no—
221C4×D4—92no—
222#107—92no—
223#106—91no—
224C4⋊C8C2×C3⋊D311yescharacteristic
225C4⋊C8C2×C3⋊D312yes—
226#103—91no—
227#102—91no—
228#102—92no—
229#102—92no—
230#102—92no—
231#102—92no—
232#97C2×C3⋊D312yes—
233C4×C8C2×C3⋊D311yescharacteristic
234C22×D3—68no—
235C22×D3—64no—
236C3×Q8—28no—
237C2×C3×C4C2×D1218yes—
238C2×C3×C4C2×D1218yes—
239C2×C3×C4C2×D1214yes—
240C2×C3×C4C2×D1214yes—
241C2×C3×C4C23×D314yes—
242C2×Dic3—64no—
243C2×Dic3—64no—
244C2×Dic3—68no—
245C2×Dic3—64no—
246D12—64no—
247D12—68no—
248D12—64no—
249D12—68no—
250D12—1216no—
251D12—128no—
252D12—248no—
253D12—244no—
254C4×D3—1216no—
255C4×D3—128no—
256Dic6—38no—
257Dic6—64no—
258Dic6—128no—
259C3×C8—24no—
260C3×C8—24no—
261C3×C8—28no—
262C2×C32#54811yescharacteristic
263C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
264C2×C32#57711yescharacteristic
265C3⋊D3—82no—
266C3⋊D3—81no—
267#41—364no—
268C2×Q8—91no—
269C2×Q8—181no—
270C2×Q8C4⋊(C3⋊D3)11yescharacteristic
271C2×D4—91no—
272C2×D4—92no—
273C2×D4—182no—
274C2×D4—181no—
275C2×D4—182no—
276C2×D4—181no—
277C22×C4—182no—
278C22×C4—181no—
279SD16—182no—
280SD16—184no—
281C2×C8C22×C3⋊D311yescharacteristic
282C2×C8C22×C3⋊D311yescharacteristic
283C2×C8C22×C3⋊D312yes—
284C4⋊C4—91no—
285C4⋊C4—92no—
286C4⋊C4—91no—
287C4⋊C4—181no—
288C4⋊C4—182no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
293C4⋊C4C4⋊(C3⋊D3)12yes—
294C22⋊C4—182no—
295C22⋊C4—181no—
296C42—182no—
297C42—181no—
298C42C22×C3⋊D311yescharacteristic
299C42C22×C3⋊D312yes—
300C22×C3C22×D1214yes—
301C2×D3—128no—
302C2×D3—124no—
303C2×D3—128no—
304C2×D3—124no—
305C2×D3—128no—
306C2×D3—124no—
307C3×C4—28no—
308C3×C4—28no—
309C3×C4—24no—
310C3×C4#90818yes—
311C3×C4#100714yes—
312C3×C4D3×#4114yes—
313Dic3—68no—
314Dic3—128no—
315Dic3—124no—
316Dic3—124no—
317C32#336811yescharacteristic, complemented, Sylow
318C23—182no—
319C23—181no—
320Q8—22no—
321Q8—92no—
322Q8—181no—
323Q8—362no—
324D4—181no—
325D4—182no—
326D4—181no—
327D4—182no—
328D4—364no—
329D4—362no—
330D4—722no—
331D4—721no—
332C2×C4—181no—
333C2×C4—181no—
334C2×C4—182no—
335C2×C4—181no—
336C2×C4—364no—
337C2×C4—362no—
338C2×C4C2×C4⋊(C3⋊D3)12yes—
339C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
340C2×C4C2×C4⋊(C3⋊D3)12yes—
341C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
342C2×C4C23×C3⋊D311yescharacteristic
343C8—21no—
344C8—21no—
345C8—22no—
346C2×C3#557614yes—
347C2×C3C2×#90814yes—
348C2×C3#575114yes—
349D3—248no—
350D3—244no—
351C22—362no—
352C22—361no—
353C22—362no—
354C22—361no—
355C22—362no—
356C22—361no—
357C22C22×C4⋊(C3⋊D3)11yescharacteristic
358C4—22no—
359C4—22no—
360C4—21no—
361C4—182no—
362C4—361no—
363C4—362no—
364C4—361no—
365C4#6411712yes—
366C4#6436411yescharacteristic
367C4#41×C3⋊D311yescharacteristic
368C3#7998014yescomplemented
369C2—722no—
370C2—721no—
371C2#1059604711yescharacteristic
372C2C2×#6411711yescharacteristic
373C2#1059622211yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#446C2
socleC22×C32C22×D4
prime radical#10596048C2
hypercenter#446C3⋊D3
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #10596038C2semidirect
3. C32×#446C2semidirect
4. #10592547C2semidirect
5. #10592547C2semidirect
6. #10592546C2semidirect
7. #10592545C2semidirect
8. #10592412C2semidirect
9. #10592409C2semidirect
10. #10592393C2semidirect
11. C4×#3744C2semidirect
44. C3×#446D3semidirect
140. #634#41semidirect
152. #446C3⋊D3semidirect
317. C32#3368semidirect
368. C3#79980semidirect

Maximal subgroups

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

subgroupindex
#105960482
#105960382
C32×#4462
#105925472
#105925462
#105925452
#105924122
#105924092
#105923932
C4×#37442
#799803