Finite Group Databasebeta

← #11787761

Subgroups — #11787761

Order 1152.

996 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596303C211yesmaximal, characteristic
2#10596290C211yesmaximal, characteristic, complemented
3C32×#410C211yesmaximal, characteristic, complemented
4#10592704C212yesmaximal, complemented
5#10589398C212yesmaximal, complemented
6#70045—34nomaximal
7C2×C32×#41C2211yescharacteristic
8C2×#3828C2211yescharacteristic
9C32×#117C2212yes—
10#64157—24no—
11#64156C411yescharacteristic, complemented
12#64153C411yescharacteristic, complemented
13#64149C411yescharacteristic, complemented
14#64148—22no—
15#64145C411yescharacteristic, complemented
16C4×#638—22no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×#3748—22no—
19C2×#3748C2212yes—
20C32×#99—22no—
21#63632—24no—
22#5832—34no—
23#5819—34no—
24C3×#410D314yescomplemented
25#5005—38no—
26#4532—38no—
27C32×#41—22no—
28C32×#41—22no—
29C2×C32×Q8C2×C411yescharacteristic
30C2×C32×D4C2×C411yescharacteristic
31C2×C32×D4D412yes—
32C22×C32×C4D412yes—
33C22×C32×C4C2311yescharacteristic
34C2×#638—22no—
35C2×#638—21no—
36C22×C3⋊Dic3—21no—
37#3828—22no—
38#3828—22no—
39C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
40C2×C4×C3⋊D3—21no—
41C2×#634C2×C411yescharacteristic
42C32×C4⋊C4—22no—
43C32×C22⋊C4—22no—
44C32×C42—22no—
45#3757—22no—
46#3752—22no—
47#3750—22no—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3C2×C411yescharacteristic
50C4×C3⋊Dic3C2×C411yescharacteristic
51#3748—24no—
52#3748—22no—
53#3748D414yescomplemented
54C2×C3⋊(C3⋊C8)—24no—
55C2×C3⋊(C3⋊C8)—22no—
56#1884—91noSylow
57C2×C3×#41C2×D314yes—
58C2×#235—34no—
59C3×#117C2×D318yes—
60#948—616no—
61#947—34no—
62#944—34no—
63#940—34no—
64#939—68no—
65#936—34no—
66C4×#67—68no—
67C2×C4×Dic3—34no—
68C2×#208—38no—
69C2×#208—68no—
70C3×#99—28no—
71#805—616no—
72C23×C32C22⋊C412yes—
73C23×C32C2×D411yescharacteristic
74C22×C3⋊D3—21no—
75C32×Q8—22no—
76C32×D4—24no—
77C32×D4—22no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4—42no—
81C2×C32×C4C22⋊C412yes—
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D412yes—
85C2×C32×C4#4112yes—
86#638—44no—
87#638—42no—
88C2×C3⋊Dic3—21no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—42no—
92C4⋊(C3⋊D3)—22no—
93C4×C3⋊D3—41no—
94C4×C3⋊D3—41no—
95#634—22no—
96C3⋊(C3⋊C8)—24no—
97#568—91no—
98#532—91no—
99#421—92no—
100#410C3⋊D311yescharacteristic, complemented
101#339—92no—
102C3×#41—28no—
103C3×#41—28no—
104C2×C3×Q8C4×D314yes—
105C2×C3×D4C4×D314yes—
106C2×C3×D4#6718yes—
107C22×C3×C4D1218yes—
108C22×C3×C4C22×D314yes—
109C2×#67—68no—
110C2×#67—64no—
111C22×Dic3—64no—
112#235—68no—
113#235—68no—
114C2×D12—34no—
115C2×C4×D3—64no—
116C2×Dic6—34no—
117C3×C4⋊C4—28no—
118C3×C22⋊C4—28no—
119C3×C42—28no—
120#217—68no—
121(C2×D3)⋊C4—68no—
122Dic3⋊C4—68no—
123C4×Dic3—34no—
124C4×Dic3—34no—
125C4×Dic3—64no—
126#208—316no—
127#208—616no—
128#208—68no—
129C2×C3⋊C8—616no—
130C2×C3⋊C8—68no—
131C22×C32—22no—
132C22×C32—41no—
133C22×C32—42no—
134C22×C32C2×C22⋊C411yescharacteristic
135C22×C32#12112yes—
136C2×C3⋊D3—42no—
137C2×C3⋊D3—41no—
138C32×C4—22no—
139C32×C4—82no—
140C32×C4C4×D412yes—
141C32×C4#12011yescharacteristic
142C32×C4#12311yescharacteristic
143C3⋊Dic3—22no—
144C3⋊Dic3—41no—
145C3⋊Dic3—41no—
146C2×#41—91no—
147C2×#41C2×C3⋊D311yescharacteristic
148#131—184no—
149C2×M16—92no—
150C2×M16—182no—
151C4⋊Q8—91no—
152#127—91no—
153#124—91no—
154#124—91no—
155#121—182no—
156C4×D4—182no—
157#117C2×C3⋊D312yes—
158C2×C42—91no—
159#104—184no—
160#99—22no—
161C23×C3(C2×D3)⋊C418yes—
162C23×C3C2×#6714yes—
163C22×D3—64no—
164C3×Q8—28no—
165C3×D4—216no—
166C3×D4—28no—
167C2×C3×C4—28no—
168C2×C3×C4—28no—
169C2×C3×C4—48no—
170C2×C3×C4(C2×D3)⋊C418yes—
171C2×C3×C4C2×C4×D314yes—
172C2×C3×C4C2×D1214yes—
173C2×C3×C4D3×D418yes—
174C2×C3×C4#23718yes—
175#67—1216no—
176#67—128no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C2×Dic3—64no—
180C2×Dic3—128no—
181D12—68no—
182C4×D3—124no—
183C4×D3—124no—
184Dic6—68no—
185C3⋊C8—616no—
186C2×C32—21no—
187C2×C32—22no—
188C2×C32—42no—
189C2×C32#38611yescharacteristic
190C3⋊D3—81no—
191#41—22no—
192#41—22no—
193#41—182no—
194#41—182no—
195C2×Q8—91no—
196C2×Q8C4×C3⋊D311yescharacteristic
197C2×D4—91no—
198C2×D4—182no—
199C2×D4—181no—
200C2×D4C4×C3⋊D311yescharacteristic
201C2×D4#63812yes—
202C22×C4—181no—
203C22×C4—181no—
204C22×C4C4⋊(C3⋊D3)12yes—
205C22×C4C22×C3⋊D311yescharacteristic
206M16—94no—
207M16—184no—
208M16—182no—
209C2×C8—184no—
210C2×C8—182no—
211C4⋊C4—22no—
212C4⋊C4—182no—
213C22⋊C4—22no—
214C22⋊C4—182no—
215C22⋊C4—182no—
216C42—22no—
217C42—91no—
218C42—91no—
219C42—181no—
220C22×C3—28no—
221C22×C3—44no—
222C22×C3—48no—
223C22×C3C2×(C2×D3)⋊C414yes—
224C22×C3#93918yes—
225C2×D3—128no—
226C2×D3—124no—
227C3×C4—28no—
228C3×C4—88no—
229C3×C4#67⋊C418yes—
230C3×C4#88214yes—
231C3×C4#88614yes—
232Dic3—68no—
233Dic3—124no—
234Dic3—124no—
235C32#188411yescharacteristic, complemented, Sylow
236C23—181no—
237C23#375212yes—
238C23C2×#63811yescharacteristic
239Q8—22no—
240Q8—182no—
241D4—24no—
242D4—22no—
243D4—182no—
244D4—364no—
245D4—362no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—42no—
249C2×C4—181no—
250C2×C4—181no—
251C2×C4—181no—
252C2×C4—362no—
253C2×C4—361no—
254C2×C4—361no—
255C2×C4#375212yes—
256C2×C4C2×C4×C3⋊D311yescharacteristic
257C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
258C2×C4D4×C3⋊D312yes—
259C2×C4#383012yes—
260C8—184no—
261C2×C3—24no—
262C2×C3—28no—
263C2×C3—48no—
264C2×C3#495814yes—
265D3—244no—
266C22—22no—
267C22—41no—
268C22—42no—
269C22—362no—
270C22—361no—
271C22C2×#375211yescharacteristic
272C22#6414812yes—
273C4—22no—
274C4—82no—
275C4—182no—
276C4—361no—
277C4—361no—
278C4#6409012yes—
279C4#6409111yescharacteristic
280C4#6409511yescharacteristic
281C3#7004514yescomplemented
282C2—22no—
283C2—21no—
284C2—42no—
285C2—721no—
286C2#1059265711yescharacteristic
subgroupG/H
centerC4#64091
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#410C2
socleC2×C32#386
prime radical#10596303C2
cosocleC22×C32×C4C23
hypercenter#410C3⋊D3
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #10596290C2semidirect
3. C32×#410C2semidirect
4. #10592704C2semidirect
5. #10589398C2semidirect
11. #64156C4semidirect
12. #64153C4semidirect
13. #64149C4semidirect
15. #64145C4semidirect
24. C3×#410D3semidirect
53. #3748D4semidirect
100. #410C3⋊D3semidirect
235. C32#1884semidirect
281. C3#70045semidirect

Maximal subgroups

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

subgroupindex
#105963032
#105962902
C32×#4102
#105927042
#105893982
#700453