Finite Group Databasebeta

← #11792263

Subgroups — #11792263

Order 1152.

1110 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C2×#64151C212yesmaximal, complemented
2#10595981C211yesmaximal, characteristic
3C32×#391C211yesmaximal, characteristic, complemented
4C2×#63632C212yesmaximal, complemented
5#10589396C211yesmaximal, characteristic, complemented
6#69694—34nomaximal
7C22×C32×Q8C2211yescharacteristic
8C2×#3828C2212yes—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C32×C42C2211yescharacteristic
11C2×#3756—22no—
12#64151—24no—
13#64151—24no—
14C2×#3755—22no—
15#64139—22no—
16C2×#3748C2212yes—
17#64106—22no—
18#64104—22no—
19C32×#95—22no—
20#63632—24no—
21C2×#942—38no—
22#5510—34no—
23C3×#391D314yescomplemented
24C2×#805—38no—
25#4530—34no—
26C2×C32×Q8—21no—
27C2×C32×Q8—22no—
28C2×C32×Q8—22no—
29C2×C32×Q8D412yescomplemented
30C22×C32×C4—21no—
31C22×C32×C4—21no—
32C22×C32×C4D412yes—
33C22×C32×C4C2311yescharacteristic
34C2×#638—22no—
35#3828—22no—
36#3828—22no—
37#3828—22no—
38#3828—22no—
39C2×C4⋊(C3⋊D3)—22no—
40C2×C4⋊(C3⋊D3)D412yes—
41C2×C4×C3⋊D3—22no—
42C2×#634D412yes—
43C32×C4⋊C4—22no—
44C32×C42—22no—
45#3756—28no—
46#3755—28no—
47#3752—24no—
48C4⋊(C3⋊Dic3)—22no—
49#3748—22no—
50#3748D414yescomplemented
51C2×C3⋊(C3⋊C8)—22no—
52#2007—91noSylow
53C22×C3×Q8C2×D314yes—
54C2×#235—38no—
55C2×C3×C4⋊C4C2×D314yes—
56C2×C3×C42C2×D314yes—
57C2×#216—68no—
58#942—616no—
59#942—616no—
60C2×#215—68no—
61#930—68no—
62C2×#208—38no—
63#897—68no—
64#895—68no—
65C3×#95—28no—
66#805—616no—
67C23×C32C2×D411yescharacteristic
68C22×C3⋊D3—22no—
69C32×Q8—24no—
70C32×Q8—42no—
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4—22no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4—42no—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D412yes—
81C2×C32×C4C2×D412yes—
82C2×C32×C4#4111yescharacteristic
83#638—42no—
84#638—42no—
85C2×C3⋊Dic3—22no—
86C4⋊(C3⋊D3)—22no—
87C4⋊(C3⋊D3)—22no—
88C4⋊(C3⋊D3)—82no—
89C4×C3⋊D3—42no—
90C4×C3⋊D3—42no—
91#634—22no—
92#634—22no—
93C3⋊(C3⋊C8)—24no—
94C2×#137—92no—
95#537—91no—
96C2×#104—92no—
97#391C3⋊D311yescharacteristic, complemented
98#343—91no—
99C2×C3×Q8—24no—
100C2×C3×Q8—28no—
101C2×C3×Q8—28no—
102C2×C3×Q8D1218yescomplemented
103C22×C3×C4—24no—
104C22×C3×C4—24no—
105C22×C3×C4#6718yes—
106C22×C3×C4C22×D314yes—
107C2×#67—68no—
108#235—68no—
109#235—68no—
110#235—68no—
111#235—68no—
112C2×D12—38no—
113C2×D12—68no—
114C2×C4×D3—68no—
115C2×Dic6—38no—
116C3×C4⋊C4—28no—
117C3×C42—28no—
118#216—632no—
119#215—632no—
120(C2×D3)⋊C4—616no—
121C4⋊Dic3—68no—
122#208—316no—
123#208—68no—
124C2×C3⋊C8—68no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32#12011yescharacteristic
128C22×C32#12111yescharacteristic
129C22×C32#12711yescharacteristic
130C2×C3⋊D3—42no—
131C2×C3⋊D3—42no—
132C2×C3⋊D3—42no—
133C32×C4—42no—
134C32×C4—42no—
135C32×C4—42no—
136C32×C4#12012yes—
137C32×C4#12112yes—
138C3⋊Dic3—42no—
139C2×#41—92no—
140C22×Q8C2×C3⋊D311yescharacteristic
141#137—184no—
142#137—184no—
143C2×Q16—182no—
144C2×SD16—182no—
145C2×M16—92no—
146C22⋊Q8—182no—
147#121—182no—
148#121—182no—
149C2×C4⋊C4C2×C3⋊D311yescharacteristic
150C2×C42C2×C3⋊D311yescharacteristic
151#104—184no—
152#95—22no—
153C23×C3C2×#6714yes—
154C22×D3—68no—
155C3×Q8—216no—
156C3×Q8—48no—
157C2×C3×C4—28no—
158C2×C3×C4—28no—
159C2×C3×C4—28no—
160C2×C3×C4—44no—
161C2×C3×C4—44no—
162C2×C3×C4—44no—
163C2×C3×C4—44no—
164C2×C3×C4—48no—
165C2×C3×C4C2×D1214yes—
166C2×C3×C4#23514yes—
167C2×C3×C4D3×D418yes—
168C2×C3×C4D3×D418yes—
169#67—128no—
170#67—128no—
171C2×Dic3—68no—
172D12—68no—
173D12—68no—
174D12—248no—
175C4×D3—128no—
176C4×D3—128no—
177Dic6—68no—
178Dic6—68no—
179C3⋊C8—616no—
180C2×C32—21no—
181C2×C32—21no—
182C2×C32#39211yescharacteristic
183C2×C32#45511yescharacteristic
184C2×C32#45611yescharacteristic
185C3⋊D3—82no—
186#41—182no—
187#41—182no—
188#41—182no—
189#41—182no—
190C2×Q8—21no—
191C2×Q8—22no—
192C2×Q8—22no—
193C2×Q8—92no—
194C2×Q8C4⋊(C3⋊D3)12yescomplemented
195C2×D4—92no—
196C2×D4—182no—
197C2×D4—182no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—182no—
201C22×C4#63812yes—
202C22×C4C22×C3⋊D311yescharacteristic
203Q16—188no—
204SD16—188no—
205M16—94no—
206M16—182no—
207C2×C8—182no—
208C4⋊C4—22no—
209C4⋊C4—182no—
210C22⋊C4—184no—
211C42—22no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3#93014yes—
215C22×C3#93714yes—
216C22×C3#94014yes—
217C2×D3—128no—
218C2×D3—128no—
219C2×D3—128no—
220C3×C4—48no—
221C3×C4—48no—
222C3×C4—48no—
223C3×C4#88218yes—
224C3×C4#88418yes—
225Dic3—128no—
226C32#200711yescharacteristic, complemented, Sylow
227C23—182no—
228C23C2×#63811yescharacteristic
229Q8—24no—
230Q8—42no—
231Q8—182no—
232Q8—182no—
233D4—182no—
234D4—182no—
235D4—362no—
236D4—362no—
237D4—722no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—182no—
247C2×C4—362no—
248C2×C4—362no—
249C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
250C2×C4#382811yescharacteristic
251C2×C4D4×C3⋊D312yes—
252C2×C4D4×C3⋊D312yes—
253C8—184no—
254C2×C3—24no—
255C2×C3—24no—
256C2×C3#496014yes—
257C2×C3#506114yes—
258C2×C3#509514yes—
259D3—248no—
260C22—21no—
261C22—21no—
262C22—362no—
263C22—362no—
264C22—362no—
265C22#6413911yescharacteristic
266C22#6414611yescharacteristic
267C22#6414911yescharacteristic
268C4—42no—
269C4—42no—
270C4—42no—
271C4—362no—
272C4#6409112yes—
273C4#6409312yes—
274C3#6969414yescomplemented
275C2—21no—
276C2—21no—
277C2—722no—
278C2#1059265911yescharacteristic
279C2#1059276011yescharacteristic
280C2#1059279411yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#391C2
socleC22×C32#120
prime radical#10595981C2
hypercenter#391C3⋊D3
hypocenterC32#2007
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#64151C2semidirect
3. C32×#391C2semidirect
4. C2×#63632C2semidirect
5. #10589396C2semidirect
23. C3×#391D3semidirect
29. C2×C32×Q8D4semidirect
50. #3748D4semidirect
97. #391C3⋊D3semidirect
102. C2×C3×Q8D12semidirect
194. C2×Q8C4⋊(C3⋊D3)semidirect
226. C32#2007semidirect
274. C3#69694semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
#105959812
C32×#3912
C2×#636322
#105893962
#696943