Finite Group Databasebeta

← #11895307

Subgroups — #11895307

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#10596056C211yesmaximal, characteristic, complemented
3C32×#477C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic, complemented
5C4×#3755C211yesmaximal, characteristic, complemented
6#10592590C212yesmaximal, complemented
7#10592571C212yesmaximal, complemented
8#10592542C211yesmaximal, characteristic
9#10592529C211yesmaximal, characteristic, complemented
10#10592518C212yesmaximal, complemented
11#10592499C212yesmaximal, complemented
12#81134—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4×Q8C2211yescharacteristic
15#64156C2212yes—
16#64155—22no—
17C2×#3755C2211yescharacteristic
18C2×#3745C2212yes—
19#64106—21no—
20#64103—22no—
21#64102C2212yes—
22#64102C2212yes—
23C4⋊C4×C3⋊D3—21no—
24#64099C2212yes—
25#64084—21no—
26#64083C2211yescharacteristic
27C4×C4⋊(C3⋊D3)—21no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#107C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×#103C2212yes—
33#63662C2211yescharacteristic
34#63648C2212yes—
35#63641C2212yes—
36C8×C3⋊Dic3C2212yes—
37#63636C2212yes—
38#63636C2212yes—
39#63636C2211yescharacteristic
40#63635C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5730—34no—
43#5585—34no—
44C3×#477D314yescomplemented
45#5088—34no—
46C4×#215—34no—
47#4891—38no—
48#4872—38no—
49#4843—34no—
50#4830—34no—
51#4819—38no—
52#4800—38no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×C4⋊(C3⋊D3)C2311yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×#634D411yescharacteristic
63C2×C32×C8C2312yes—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C32×C4⋊C4C2311yescharacteristic
68C32×C42—21no—
69C32×C42C2311yescharacteristic
70#3755—22no—
71#3752—21no—
72#3752—22no—
73#3752—22no—
74#3752—22no—
75#3752—22no—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)D411yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—22no—
80#3750D412yes—
81C4×C3⋊Dic3C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3745—24no—
85#3361—91noSylow
86C3×C4⋊Q8C2×D314yes—
87C3×C4×Q8C2×D314yes—
88#947—38no—
89#946—68no—
90C2×#215—34no—
91C2×D24—38no—
92#897—64no—
93#894—68no—
94#893—38no—
95#893—38no—
96D3×C4⋊C4—64no—
97#890—38no—
98#875—64no—
99#874—34no—
100C4×D12—34no—
101C4×D12—64no—
102C4×Dic6—34no—
103C3×#107C2×D318yes—
104C3×C4⋊C8C2×D314yes—
105C3×#103C2×D318yes—
106#835—34no—
107#821—38no—
108Dic3⋊C8—38no—
109C8×Dic3—38no—
110#809—34no—
111#809—38no—
112#809—38no—
113#808—34no—
114C4×C3⋊C8—34no—
115C22×C3⋊D3—21no—
116C22×C3⋊D3—22no—
117C32×Q8—21no—
118C32×Q8—21no—
119C32×Q8—81no—
120C2×C32×C4—22no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3C2×D412yes—
128C2×C3⋊Dic3C2×D412yes—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—42no—
133C4⋊(C3⋊D3)—81no—
134C4⋊(C3⋊D3)#4112yes—
135C4×C3⋊D3—42no—
136C4×C3⋊D3—82no—
137C4×C3⋊D3—82no—
138#634—22no—
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#477C3⋊D311yescharacteristic, complemented
148#463—92no—
149#459—91no—
150C8×Q8—91no—
151C4×SD16—91no—
152C4×D8—92no—
153C2×C3×Q8—24no—
154C2×C3×Q8C22×D314yes—
155C2×D12—34no—
156C2×D12—38no—
157C2×D12—64no—
158C2×D12—64no—
159C2×C4×D3—64no—
160C2×C4×D3—68no—
161C2×C4×D3—68no—
162C2×Dic6—34no—
163C2×C3×C8C22×D318yes—
164C3×C4⋊C4—24no—
165C3×C4⋊C4—24no—
166C3×C4⋊C4C22×D314yes—
167C3×C4⋊C4C22×D318yes—
168C3×C42—24no—
169C3×C42C22×D314yes—
170#215—68no—
171(C2×D3)⋊C4—68no—
172(C2×D3)⋊C4—68no—
173(C2×D3)⋊C4—68no—
174(C2×D3)⋊C4—68no—
175(C2×D3)⋊C4—64no—
176C4⋊Dic3—34no—
177C4⋊Dic3—34no—
178C4⋊Dic3—68no—
179Dic3⋊C4—38no—
180Dic3⋊C4—68no—
181C4×Dic3—38no—
182C2×C3⋊C8—34no—
183C2×C3⋊C8—34no—
184D24—616no—
185C22×C32C22×D411yescharacteristic
186C2×C3⋊D3—22no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—42no—
190C2×C3⋊D3—42no—
191C2×C3⋊D3—42no—
192C32×C4—21no—
193C32×C4—41no—
194C32×C4—41no—
195C32×C4—42no—
196C32×C4#13512yes—
197C32×C4C2×#4111yescharacteristic
198C32×C42−1+411yescharacteristic
199C3⋊Dic3—22no—
200C3⋊Dic3—22no—
201C3⋊Dic3—41no—
202C2×SD16—91no—
203C2×D8—92no—
204C4⋊Q8C2×C3⋊D311yescharacteristic
205#127—91no—
206#125—92no—
207#124—92no—
208#124—181no—
209#123—182no—
210C22⋊Q8—181no—
211C22⋊Q8—182no—
212C4×Q8—91no—
213C4×Q8C2×C3⋊D311yescharacteristic
214C4×D4—92no—
215C4×D4—92no—
216C4×D4—91no—
217C4×D4—181no—
218C2×C4⋊C4—181no—
219#107C2×C3⋊D312yes—
220#106—91no—
221C4⋊C8—92no—
222C4⋊C8C2×C3⋊D311yescharacteristic
223#103—91no—
224#103C2×C3⋊D312yes—
225#102—92no—
226#102—91no—
227#102—92no—
228#102—92no—
229C4×C8—92no—
230C4×C8—91no—
231C22×D3—64no—
232C22×D3—68no—
233C3×Q8—24no—
234C3×Q8—24no—
235C3×Q8—84no—
236C2×C3×C4—28no—
237C2×C3×C4—24no—
238C2×C3×C4—24no—
239C2×C3×C4D3×D414yes—
240C2×C3×C4D3×D414yes—
241C2×C3×C4C23×D314yes—
242C2×Dic3—38no—
243C2×Dic3—38no—
244C2×Dic3—64no—
245D12—38no—
246D12—64no—
247D12—68no—
248D12—68no—
249D12—128no—
250D12—244no—
251C4×D3—128no—
252C4×D3—248no—
253C4×D3—248no—
254Dic6—68no—
255C3×C8—28no—
256C3⋊C8—64no—
257C3⋊C8—64no—
258C2×C32#54811yescharacteristic
259C2×C32C2×#13511yescharacteristic
260C2×C32#57611yescharacteristic
261C3⋊D3—42no—
262C3⋊D3—82no—
263C2×Q8—21no—
264C2×Q8—91no—
265C2×Q8C22×C3⋊D311yescharacteristic
266C2×D4—91no—
267C2×D4—92no—
268C2×D4—181no—
269C2×D4—181no—
270C22×C4—182no—
271C22×C4—182no—
272C22×C4—181no—
273SD16—182no—
274D8—184no—
275C2×C8—91no—
276C2×C8—91no—
277C2×C8C22×C3⋊D312yes—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—91no—
281C4⋊C4—92no—
282C4⋊C4—91no—
283C4⋊C4—182no—
284C4⋊C4—182no—
285C4⋊C4C22×C3⋊D312yes—
286C4⋊C4C22×C3⋊D311yescharacteristic
287C22⋊C4—182no—
288C22⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22⋊C4—181no—
292C42—21no—
293C42—92no—
294C42C22×C3⋊D311yescharacteristic
295C22×C3C2×D3×D414yes—
296C2×D3—68no—
297C2×D3—124no—
298C2×D3—124no—
299C2×D3—128no—
300C2×D3—128no—
301C2×D3—128no—
302C3×C4—24no—
303C3×C4—44no—
304C3×C4—44no—
305C3×C4—48no—
306C3×C4#91918yes—
307C3×C4#100714yes—
308C3×C4D3×#4114yes—
309Dic3—68no—
310Dic3—68no—
311Dic3—124no—
312C32#336111yescharacteristic, complemented, Sylow
313C23—181no—
314C23—182no—
315Q8—21no—
316Q8—21no—
317Q8—81no—
318Q8—182no—
319D4—92no—
320D4—181no—
321D4—182no—
322D4—182no—
323D4—362no—
324D4—721no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—92no—
329C2×C4—92no—
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—22no—
338C8—181no—
339C8—181no—
340C2×C3#563314yes—
341C2×C3C2×#91914yes—
342C2×C3#577414yes—
343D3—128no—
344D3—248no—
345C22—182no—
346C22—361no—
347C22—361no—
348C22—362no—
349C22—362no—
350C22—362no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—42no—
356C4—182no—
357C4—182no—
358C4—361no—
359C4#6412812yes—
360C4#6436411yescharacteristic
361C4#41×C3⋊D311yescharacteristic
362C3#8113414yescomplemented
363C2—362no—
364C2—722no—
365C2#1059610411yescharacteristic
366C2C2×#6412811yescharacteristic
367C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#477C2
socleC22×C32C22×D4
prime radical#10592542C2
hypercenter#477C3⋊D3
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. #10596056C2semidirect
3. C32×#477C2semidirect
4. #10592787C2semidirect
5. C4×#3755C2semidirect
6. #10592590C2semidirect
7. #10592571C2semidirect
9. #10592529C2semidirect
10. #10592518C2semidirect
11. #10592499C2semidirect
44. C3×#477D3semidirect
147. #477C3⋊D3semidirect
312. C32#3361semidirect
362. C3#81134semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105960562
C32×#4772
#105927872
C4×#37552
#105925902
#105925712
#105925422
#105925292
#105925182
#105924992
#811343