Finite Group Databasebeta

← #11895322

Subgroups — #11895322

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#10596184C211yesmaximal, characteristic, complemented
2#10596014C211yesmaximal, characteristic, complemented
3C32×#459C211yesmaximal, characteristic
4#10592852C212yesmaximal, complemented
5D8×C3⋊Dic3C212yesmaximal, complemented
6#10592769C211yesmaximal, characteristic, complemented
7C4×#3754C211yesmaximal, characteristic, complemented
8#10592549C211yesmaximal, characteristic, complemented
9#10592529C211yesmaximal, characteristic, complemented
10#10592467C212yesmaximal, complemented
11#10592465C212yesmaximal, complemented
12#80319—34nomaximal
13C2×C32×D8C2212yes—
14C32×#127C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16#64145—21no—
17#64145C2212yes—
18#64144—22no—
19D4×C3⋊Dic3—21no—
20D4×C3⋊Dic3C2212yes—
21D4×C3⋊Dic3C2212yes—
22C2×#3754C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)—21no—
24#64133—21no—
25#64099C2212yes—
26#64087—22no—
27#64078C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31C32×#102C2212yes—
32#63659C2212yes—
33#63659C2212yes—
34#63659C2211yescharacteristic
35#63645C2212yes—
36#63643C2212yes—
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63637C2211yescharacteristic
40#63635C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5713—34no—
43#5543—34no—
44C3×#459D314yes—
45#5153—38no—
46Dic3×D8—38no—
47#5070—34no—
48C4×#214—34no—
49#4850—34no—
50#4830—34no—
51#4768—38no—
52#4766—38no—
53C2×C32×D4—21no—
54C2×C32×D4—21no—
55C2×C32×D4C2312yes—
56C2×C32×D4C2311yescharacteristic
57C22×C32×C4—21no—
58C22×C3⋊Dic3—22no—
59C22×C3⋊Dic3—22no—
60C2×#634—21no—
61C2×#634D411yescharacteristic
62C2×#634C2311yescharacteristic
63C32×D8—24no—
64C2×C32×C8C2312yes—
65C32×C4⋊C4C2311yescharacteristic
66C32×C22⋊C4—21no—
67C32×C42C2311yescharacteristic
68#3757—22no—
69#3757—22no—
70#3757—22no—
71#3757—22no—
72#3754—22no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)—22no—
75C4⋊(C3⋊Dic3)D411yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77C4⋊(C3⋊Dic3)C2312yes—
78#3750—21no—
79#3750—22no—
80#3750D412yes—
81C4×C3⋊Dic3—21no—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3361—91noSylow
86C2×C3×D8C2×D318yes—
87C3×#127C2×D314yes—
88C3×C4×D4C2×D314yes—
89#936—38no—
90#936—64no—
91#935—68no—
92D4×Dic3—38no—
93D4×Dic3—38no—
94D4×Dic3—64no—
95C2×#214—34no—
96C2×C4⋊Dic3—64no—
97#924—64no—
98#890—38no—
99#878—68no—
100#869—34no—
101C4×Dic6—34no—
102C4×Dic6—34no—
103C3×C4⋊C8C2×D314yes—
104C3×#102C2×D318yes—
105#832—34no—
106#832—38no—
107#832—38no—
108#818—38no—
109#816—38no—
110Dic3⋊C8—38no—
111C8×Dic3—38no—
112#810—34no—
113#808—34no—
114C4×C3⋊C8—34no—
115C23×C32—21no—
116C23×C32—22no—
117C32×D4—22no—
118C32×D4—21no—
119C32×D4—22no—
120C32×D4—42no—
121C32×D4—81no—
122C32×D4#4112yes—
123C2×C32×C4—21no—
124C2×C32×C4—42no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—82no—
132C2×C3⋊Dic3—82no—
133C2×C3⋊Dic3C2×D412yes—
134C2×C3⋊Dic3C2×D412yes—
135#634—22no—
136#634—21no—
137#634—21no—
138#634—81no—
139C32×C8—22no—
140C3⋊(C3⋊C8)—21no—
141C3⋊(C3⋊C8)—21no—
142#559—91no—
143#554—91no—
144#488—92no—
145#486—91no—
146#478—92no—
147#477—91no—
148#463—92no—
149#459C3⋊D311yescharacteristic
150C8×Q8—91no—
151C4×SD16—91no—
152C4×D8—92no—
153C2×C3×D4—24no—
154C2×C3×D4—24no—
155C2×C3×D4C22×D318yes—
156C2×C3×D4C22×D314yes—
157C22×C3×C4—24no—
158C22×Dic3—68no—
159C22×Dic3—68no—
160C2×Dic6—34no—
161C2×Dic6—34no—
162C2×Dic6—64no—
163C3×D8—216no—
164C2×C3×C8C22×D318yes—
165C3×C4⋊C4C22×D314yes—
166C3×C22⋊C4—24no—
167C3×C42C22×D314yes—
168#217—68no—
169#217—68no—
170#217—68no—
171#217—68no—
172#214—68no—
173C4⋊Dic3—34no—
174C4⋊Dic3—34no—
175C4⋊Dic3—38no—
176C4⋊Dic3—68no—
177C4⋊Dic3—64no—
178Dic3⋊C4—38no—
179Dic3⋊C4—68no—
180Dic3⋊C4—64no—
181C4×Dic3—38no—
182C4×Dic3—64no—
183C2×C3⋊C8—34no—
184C2×C3⋊C8—34no—
185C22×C32—22no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32—42no—
189C22×C32—42no—
190C22×C32—42no—
191C22×C32C22×D411yescharacteristic
192C32×C4—21no—
193C32×C4—41no—
194C32×C4#13512yes—
195C32×C4C2×#4111yescharacteristic
196C32×C42−1+411yescharacteristic
197C3⋊Dic3—22no—
198C3⋊Dic3—22no—
199C3⋊Dic3—41no—
200C3⋊Dic3—42no—
201C3⋊Dic3—41no—
202C2×SD16—91no—
203C2×D8C2×C3⋊D312yes—
204C4⋊Q8—91no—
205#127C2×C3⋊D311yescharacteristic
206#125—92no—
207#124—92no—
208#124—181no—
209#123—182no—
210C22⋊Q8—182no—
211C22⋊Q8—181no—
212C4×Q8—91no—
213C4×Q8—91no—
214C4×D4—92no—
215C4×D4—92no—
216C4×D4—181no—
217C4×D4C2×C3⋊D311yescharacteristic
218C2×C4⋊C4—181no—
219#107—92no—
220#106—91no—
221C4⋊C8—92no—
222C4⋊C8C2×C3⋊D311yescharacteristic
223#103—92no—
224#103—91no—
225#102—91no—
226#102—92no—
227#102—92no—
228#102C2×C3⋊D312yes—
229C4×C8—92no—
230C4×C8—91no—
231C23×C3—24no—
232C23×C3—28no—
233C3×D4—28no—
234C3×D4—24no—
235C3×D4—28no—
236C3×D4—48no—
237C3×D4—84no—
238C3×D4#23718yes—
239C2×C3×C4—24no—
240C2×C3×C4—48no—
241C2×C3×C4D3×D414yes—
242C2×C3×C4D3×D414yes—
243C2×C3×C4C23×D314yes—
244C2×Dic3—38no—
245C2×Dic3—38no—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—68no—
249C2×Dic3—248no—
250C2×Dic3—248no—
251Dic6—68no—
252Dic6—64no—
253Dic6—64no—
254Dic6—244no—
255C3×C8—28no—
256C3⋊C8—64no—
257C3⋊C8—64no—
258C2×C32—42no—
259C2×C32—82no—
260C2×C32#54811yescharacteristic
261C2×C32C2×#13511yescharacteristic
262C2×C32#57611yescharacteristic
263C2×Q8—91no—
264C2×Q8—91no—
265C2×Q8—181no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4C22×C3⋊D312yes—
269C2×D4C22×C3⋊D311yescharacteristic
270C22×C4—21no—
271C22×C4—182no—
272C22×C4—182no—
273SD16—182no—
274D8—24no—
275C2×C8—91no—
276C2×C8—91no—
277C2×C8C22×C3⋊D312yes—
278C4⋊C4—91no—
279C4⋊C4—92no—
280C4⋊C4—92no—
281C4⋊C4—91no—
282C4⋊C4—182no—
283C4⋊C4—182no—
284C4⋊C4—181no—
285C4⋊C4—181no—
286C4⋊C4C22×C3⋊D311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22⋊C4—182no—
292C42—92no—
293C42—181no—
294C42C22×C3⋊D311yescharacteristic
295C22×C3—28no—
296C22×C3—44no—
297C22×C3—44no—
298C22×C3—48no—
299C22×C3—48no—
300C22×C3—48no—
301C22×C3C2×D3×D414yes—
302C3×C4—24no—
303C3×C4—44no—
304C3×C4#91218yes—
305C3×C4C2×#23714yes—
306C3×C4#101014yes—
307Dic3—68no—
308Dic3—68no—
309Dic3—128no—
310Dic3—124no—
311Dic3—124no—
312C32#336111yescharacteristic, complemented, Sylow
313C23—21no—
314C23—22no—
315Q8—182no—
316Q8—181no—
317Q8—181no—
318Q8—721no—
319D4—22no—
320D4—21no—
321D4—22no—
322D4—42no—
323D4—81no—
324D4#383012yes—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—92no—
328C2×C4—92no—
329C2×C4—181no—
330C2×C4—181no—
331C2×C4—182no—
332C2×C4—722no—
333C2×C4—722no—
334C2×C4D4×C3⋊D311yescharacteristic
335C2×C4D4×C3⋊D311yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—22no—
338C8—181no—
339C8—181no—
340C2×C3—48no—
341C2×C3—88no—
342C2×C3#559814yes—
343C2×C3C2×#91214yes—
344C2×C3#577414yes—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—41no—
354C4—182no—
355C4—182no—
356C4—361no—
357C4—362no—
358C4—361no—
359C4#6412112yes—
360C4C2×#383011yescharacteristic
361C4#6436711yescharacteristic
362C3#8031914yescomplemented
363C2—42no—
364C2—82no—
365C2#1059606911yescharacteristic
366C2C2×#6412111yescharacteristic
367C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
Fitting, prime radicalC32×#459C2
socleC22×C32C22×D4
hypercenter#459C3⋊D3
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #10596184C2semidirect
2. #10596014C2semidirect
4. #10592852C2semidirect
5. D8×C3⋊Dic3C2semidirect
6. #10592769C2semidirect
7. C4×#3754C2semidirect
8. #10592549C2semidirect
9. #10592529C2semidirect
10. #10592467C2semidirect
11. #10592465C2semidirect
312. C32#3361semidirect
362. C3#80319semidirect

Maximal subgroups

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

subgroupindex
#105961842
#105960142
C32×#4592
#105928522
D8×C3⋊Dic32
#105927692
C4×#37542
#105925492
#105925292
#105924672
#105924652
#803193