Finite Group Databasebeta

← #11895325

Subgroups — #11895325

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2#10596184C211yesmaximal, characteristic, complemented
3C32×#486C211yesmaximal, characteristic, complemented
4#10592790C211yesmaximal, characteristic, complemented
5#10592771C211yesmaximal, characteristic
6#10592486C212yesmaximal, complemented
7#10592467C212yesmaximal, complemented
8#10592462C212yesmaximal, complemented
9#10592455C212yesmaximal, complemented
10C4×#3744C211yesmaximal, characteristic, complemented
11C8×#634C211yesmaximal, characteristic, complemented
12#81585—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×#127C2211yescharacteristic
15#64155—22no—
16#64145—21no—
17#64145C2212yes—
18#64144—22no—
19D4×C3⋊Dic3—21no—
20D4×C3⋊Dic3C2212yes—
21C2×#3753C2212yes—
22C2×#3744C2211yescharacteristic
23#64106—21no—
24#64102C2212yes—
25C4⋊C4×C3⋊D3—21no—
26#64099C2212yes—
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#63637C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5730—34no—
43#5713—34no—
44C3×#486D314yescomplemented
45#5091—34no—
46#5072—34no—
47#4787—38no—
48#4768—38no—
49#4763—38no—
50#4756—38no—
51C4×#204—34no—
52C8×Dic6—34no—
53C2×C32×Q8—21no—
54C2×C32×D4—21no—
55C2×C32×D4—21no—
56C2×C32×D4C2312yes—
57C22×C3⋊Dic3—22no—
58C2×C4⋊(C3⋊D3)C2311yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—22no—
61C2×#634D411yescharacteristic
62C2×#634C2311yescharacteristic
63C2×C32×C8C2311yescharacteristic
64C2×C32×C8C2311yescharacteristic
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C32×C42C2311yescharacteristic
68#3757—22no—
69#3757—22no—
70#3757—22no—
71#3753—24no—
72#3752—21no—
73#3752—22no—
74C4⋊(C3⋊Dic3)—22no—
75C4⋊(C3⋊Dic3)D411yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78#3750—21no—
79#3750—22no—
80#3750D412yes—
81C4×C3⋊Dic3—21no—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84#3744—22no—
85#3361—91noSylow
86C3×C4⋊Q8C2×D314yes—
87C3×#127C2×D314yes—
88#946—68no—
89#936—38no—
90#936—64no—
91#935—68no—
92D4×Dic3—38no—
93D4×Dic3—64no—
94C2×#213—38no—
95C2×#204—34no—
96#897—64no—
97#893—38no—
98D3×C4⋊C4—64no—
99#890—38no—
100C4×D12—34no—
101C4×Dic6—34no—
102C4×Dic6—34no—
103C3×#102C2×D318yes—
104C3×#102C2×D318yes—
105C3×C4×C8C2×D314yes—
106#832—38no—
107#821—34no—
108#817—34no—
109#816—34no—
110Dic3⋊C8—38no—
111C8×Dic3—38no—
112#810—38no—
113#807—38no—
114C4⋊(C3⋊C8)—34no—
115C23×C32—22no—
116C22×C3⋊D3—21no—
117C32×Q8—81no—
118C32×D4—22no—
119C32×D4—22no—
120C32×D4—42no—
121C32×D4—81no—
122C2×C32×C4—22no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—82no—
130C2×C3⋊Dic3C2×D412yes—
131C2×C3⋊Dic3C2×D412yes—
132C4⋊(C3⋊D3)—21no—
133C4⋊(C3⋊D3)#4112yes—
134C4×C3⋊D3—42no—
135C4×C3⋊D3—82no—
136#634—22no—
137#634—21no—
138#634—21no—
139C32×C8—21no—
140C32×C8—21no—
141C3⋊(C3⋊C8)—22no—
142#559—91no—
143#554—91no—
144#488—92no—
145#486C3⋊D311yescharacteristic, complemented
146#478—92no—
147#477—91no—
148#463—92no—
149#459—91no—
150C8×Q8—91no—
151C4×SD16—91no—
152C4×D8—92no—
153C2×C3×Q8—24no—
154C2×C3×D4—24no—
155C2×C3×D4—24no—
156C2×C3×D4C22×D318yes—
157C22×Dic3—68no—
158C2×D12—34no—
159C2×C4×D3—64no—
160C2×C4×D3—68no—
161C2×Dic6—34no—
162C2×Dic6—34no—
163C2×C3×C8C22×D314yes—
164C2×C3×C8C22×D314yes—
165C3×C4⋊C4—24no—
166C3×C4⋊C4C22×D318yes—
167C3×C42C22×D314yes—
168#217—68no—
169#217—68no—
170#217—68no—
171#213—616no—
172(C2×D3)⋊C4—68no—
173(C2×D3)⋊C4—64no—
174C4⋊Dic3—34no—
175C4⋊Dic3—34no—
176C4⋊Dic3—34no—
177C4⋊Dic3—68no—
178Dic3⋊C4—38no—
179Dic3⋊C4—68no—
180Dic3⋊C4—64no—
181C4×Dic3—38no—
182C4×Dic3—64no—
183C2×C3⋊C8—38no—
184#204—68no—
185C22×C32—42no—
186C22×C32—42no—
187C22×C32—42no—
188C22×C32C22×D411yescharacteristic
189C2×C3⋊D3—22no—
190C2×C3⋊D3—41no—
191C2×C3⋊D3—41no—
192C32×C4—21no—
193C32×C4—42no—
194C32×C4#13512yes—
195C32×C4C2×#4111yescharacteristic
196C32×C42−1+411yescharacteristic
197C3⋊Dic3—22no—
198C3⋊Dic3—22no—
199C3⋊Dic3—41no—
200C3⋊Dic3—41no—
201C3⋊Dic3—41no—
202C2×SD16—91no—
203C2×D8—92no—
204C4⋊Q8C2×C3⋊D311yescharacteristic
205#127C2×C3⋊D311yescharacteristic
206#125—92no—
207#124—92no—
208#124—181no—
209#123—182no—
210C22⋊Q8—181no—
211C22⋊Q8—182no—
212C4×Q8—91no—
213C4×Q8—91no—
214C4×D4—92no—
215C4×D4—92no—
216C4×D4—91no—
217C4×D4—181no—
218C2×C4⋊C4—181no—
219#107—92no—
220#106—91no—
221C4⋊C8—92no—
222C4⋊C8—91no—
223#103—91no—
224#103—92no—
225#102—92no—
226#102—91no—
227#102C2×C3⋊D312yes—
228#102C2×C3⋊D312yes—
229C4×C8—92no—
230C4×C8C2×C3⋊D311yescharacteristic
231C23×C3—28no—
232C22×D3—64no—
233C3×Q8—84no—
234C3×D4—28no—
235C3×D4—28no—
236C3×D4—48no—
237C3×D4—84no—
238C2×C3×C4—28no—
239C2×C3×C4D3×D414yes—
240C2×C3×C4D3×D414yes—
241C2×C3×C4C23×D314yes—
242C2×Dic3—38no—
243C2×Dic3—38no—
244C2×Dic3—64no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—248no—
248D12—38no—
249D12—64no—
250C4×D3—128no—
251C4×D3—248no—
252Dic6—68no—
253Dic6—64no—
254Dic6—64no—
255C3×C8—24no—
256C3×C8—24no—
257C3⋊C8—68no—
258C2×C32—82no—
259C2×C32#54811yescharacteristic
260C2×C32C2×#13511yescharacteristic
261C2×C32#57611yescharacteristic
262C3⋊D3—42no—
263C2×Q8—21no—
264C2×Q8—91no—
265C2×Q8—91no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—91no—
269C2×D4C22×C3⋊D312yes—
270C22×C4—182no—
271C22×C4—182no—
272C22×C4—181no—
273SD16—182no—
274D8—184no—
275C2×C8—92no—
276C2×C8C22×C3⋊D311yescharacteristic
277C2×C8C22×C3⋊D311yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—91no—
280C4⋊C4—92no—
281C4⋊C4—91no—
282C4⋊C4—91no—
283C4⋊C4—182no—
284C4⋊C4—182no—
285C4⋊C4—181no—
286C4⋊C4C22×C3⋊D312yes—
287C22⋊C4—182no—
288C22⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22⋊C4—181no—
292C42—92no—
293C42—181no—
294C42C22×C3⋊D311yescharacteristic
295C22×C3—48no—
296C22×C3—48no—
297C22×C3—48no—
298C22×C3C2×D3×D414yes—
299C2×D3—68no—
300C2×D3—124no—
301C2×D3—124no—
302C3×C4—24no—
303C3×C4—48no—
304C3×C4#91618yes—
305C3×C4D3×#4114yes—
306C3×C4#101014yes—
307Dic3—68no—
308Dic3—68no—
309Dic3—124no—
310Dic3—124no—
311Dic3—124no—
312C32#336111yescharacteristic, complemented, Sylow
313C23—22no—
314C23—181no—
315Q8—81no—
316Q8—182no—
317Q8—181no—
318Q8—181no—
319D4—22no—
320D4—22no—
321D4—42no—
322D4—81no—
323D4—92no—
324D4—181no—
325C2×C4—22no—
326C2×C4—92no—
327C2×C4—92no—
328C2×C4—181no—
329C2×C4—181no—
330C2×C4—181no—
331C2×C4—362no—
332C2×C4—722no—
333C2×C4—722no—
334C2×C4D4×C3⋊D311yescharacteristic
335C2×C4D4×C3⋊D311yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—21no—
338C8—21no—
339C8—182no—
340C2×C3—88no—
341C2×C3#567714yes—
342C2×C3#575714yes—
343C2×C3C2×#91614yes—
344D3—128no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—182no—
349C22—361no—
350C22—361no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—42no—
354C4—182no—
355C4—182no—
356C4—361no—
357C4—361no—
358C4—361no—
359C4#6412512yes—
360C4#41×C3⋊D311yescharacteristic
361C4#6436711yescharacteristic
362C3#8158514yescomplemented
363C2—82no—
364C2—362no—
365C2#1059614811yescharacteristic
366C2#1059622811yescharacteristic
367C2C2×#6412511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#486C2
socleC22×C32C22×D4
prime radical#10592771C2
hypercenter#486C3⋊D3
hypocenterC32#3361
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. #10596201C2semidirect
2. #10596184C2semidirect
3. C32×#486C2semidirect
4. #10592790C2semidirect
6. #10592486C2semidirect
7. #10592467C2semidirect
8. #10592462C2semidirect
9. #10592455C2semidirect
10. C4×#3744C2semidirect
11. C8×#634C2semidirect
44. C3×#486D3semidirect
145. #486C3⋊D3semidirect
312. C32#3361semidirect
362. C3#81585semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105961842
C32×#4862
#105927902
#105927712
#105924862
#105924672
#105924622
#105924552
C4×#37442
C8×#6342
#815853