Finite Group Databasebeta

← #11798181

Subgroups — #11798181

Order 1152.

482 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 49 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
1C22×#3713C211yesmaximal, characteristic
2C2×#63735C212yesmaximal, complemented
3#10591188C211yesmaximal, characteristic, complemented
4C22⋊#3708C211yesmaximal, characteristic, complemented
5#10590061C212yesmaximal, complemented
6C22×C3×D12—21no—
7C22×C3⋊(C3⋊C8)C2211yescharacteristic
8C3×#924—21no—
9C2×#3718C2211yescharacteristic, complemented
10C2×#3713—21no—
11C2×#3713—24no—
12C2×#3713C2212yes—
13C2×#3708C2212yescomplemented
14#63735—24no—
15#63576C2211yescharacteristic, complemented
16#63565—21no—
17C22×#213—61no—
18#5051—61no—
19C23×C3×D3—41no—
20C22×C32×C4D411yescharacteristic
21C2×C3×D12—24no—
22C2×C3×D12—22no—
23C2×C3×D12—42no—
24C2×C3×D12—41no—
25C2×C3×Dic6—21no—
26C2×C3⋊(C3⋊C8)—22no—
27C2×C3⋊(C3⋊C8)D411yescharacteristic
28C2×C3⋊(C3⋊C8)C2311yescharacteristic
29C3×#217—41no—
30C3×C4⋊Dic3—21no—
31C3×Dic3⋊C4—41no—
32#3718—22no—
33#3713—24no—
34#3713—22no—
35#3713D414yes—
36#3708—22no—
37#2187—91nomaximal, Sylow
38C22×C3×D4—61no—
39C22×D12—21no—
40C3×C22⋊Q8—61no—
41C2×#216—61no—
42C2×#213—62no—
43C2×#213—62no—
44C2×#213—68no—
45#924—21no—
46C22×C3⋊C8—61no—
47C22×C3⋊C8—61no—
48#835—61no—
49#810—61no—
50#807—61no—
51C23×C32D811yescharacteristic
52C22×C3×D3—44no—
53C22×C3×D3—42no—
54C22×C3×D3—82no—
55C22×C3×D3—82no—
56C2×C32×C4—21no—
57C2×C32×C4—21no—
58C2×C32×C4D811yescharacteristic
59C2×C32×C4C2×D411yescharacteristic
60C2×C3×Dic3—41no—
61C2×C3×Dic3—41no—
62C3×D12—24no—
63C3×D12—44no—
64C3×D12—42no—
65C3×Dic6—41no—
66C3×Dic6—41no—
67C3⋊(C3⋊C8)—21no—
68C3⋊(C3⋊C8)C2×D412yes—
69C22×D8—91no—
70C2×SD32—92no—
71#467—91no—
72#357—92no—
73C22⋊C16—91no—
74C24×C3—121no—
75C23×D3—41no—
76C2×C3×Q8—61no—
77C2×C3×D4—64no—
78C2×C3×D4—62no—
79C2×C3×D4—122no—
80C2×C3×D4—121no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C2×D12—24no—
84C2×D12—22no—
85C2×D12—42no—
86C2×D12—41no—
87C2×Dic6—21no—
88C3×C4⋊C4—61no—
89C3×C4⋊C4—121no—
90C3×C22⋊C4—121no—
91#217—41no—
92#216—122no—
93#213—64no—
94#213—64no—
95#213—68no—
96C4⋊Dic3—21no—
97Dic3⋊C4—41no—
98C2×C3⋊C8—61no—
99C2×C3⋊C8—61no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—64no—
103C2×C3⋊C8—122no—
104C22×C32—21no—
105C22×C32—21no—
106C22×C32SD3212yescomplemented
107C22×C32C2×D811yescharacteristic
108C2×C3×D3—44no—
109C2×C3×D3—88no—
110C2×C3×D3—82no—
111C2×C3×D3—82no—
112C32×C4—21no—
113C32×C4#12011yescharacteristic
114C32×C4AGL(1,ℤ/8)11yescharacteristic
115C3×Dic3—81no—
116C3×Dic3—81no—
117C22×D4—61no—
118C2×Q16—91no—
119C2×D8—92no—
120C2×D8—181no—
121C2×D8—184no—
122C22×C8—91no—
123C22⋊Q8—61no—
124SD32—184no—
125C2×C16—92no—
126#107—91no—
127#103—181no—
128C23×C3—21no—
129C23×C3—21no—
130C23×C3—124no—
131C23×C3—122no—
132C23×C3—242no—
133C23×C3—242no—
134C22×D3—44no—
135C22×D3—42no—
136C22×D3—82no—
137C22×D3—82no—
138C3×Q8—121no—
139C3×Q8—121no—
140C3×D4—64no—
141C3×D4—124no—
142C3×D4—122no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—41no—
150C2×C3×C4—41no—
151C2×C3×C4—121no—
152C2×C3×C4—121no—
153C2×Dic3—41no—
154C2×Dic3—41no—
155D12—24no—
156D12—44no—
157D12—42no—
158Dic6—41no—
159Dic6—41no—
160C3⋊C8—62no—
161C3⋊C8—62no—
162C3⋊C8—62no—
163C3⋊C8—121no—
164C2×C32—22no—
165C2×C32#44711yescharacteristic
166C2×C32C2×SD3211yescharacteristic
167C2×C32#50911yescharacteristic
168C3×D3—84no—
169C24—121no—
170C2×Q8—61no—
171C2×D4—64no—
172C2×D4—62no—
173C2×D4—122no—
174C2×D4—121no—
175C22×C4GO+(4,𝔽2)11yescharacteristic
176Q16—182no—
177D8—94no—
178D8—182no—
179D8—184no—
180C2×C8—91no—
181C2×C8—91no—
182C2×C8—182no—
183C4⋊C4—61no—
184C4⋊C4—121no—
185C22⋊C4—121no—
186C16—182no—
187C22×C3—22no—
188C22×C3—22no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—22no—
192C22×C3—22no—
193C22×C3—41no—
194C22×C3—41no—
195C22×C3—124no—
196C22×C3—248no—
197C22×C3—242no—
198C22×C3—242no—
199C2×D3—44no—
200C2×D3—88no—
201C2×D3—82no—
202C2×D3—82no—
203C3×C4—22no—
204C3×C4—21no—
205C3×C4—21no—
206C3×C4—21no—
207C3×C4—21no—
208C3×C4—41no—
209C3×C4—241no—
210C3×C4—241no—
211Dic3—81no—
212Dic3—81no—
213C32#218711yescharacteristic, complemented, Sylow
214C23—124no—
215C23—122no—
216C23—242no—
217C23—242no—
218C23#377411yescharacteristic
219Q8—121no—
220Q8—121no—
221D4—64no—
222D4—124no—
223D4—122no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—121no—
227C2×C4—121no—
228C2×C4#377411yescharacteristic
229C2×C4C2×GO+(4,𝔽2)11yescharacteristic
230C8—92no—
231C8—181no—
232C2×C3—24no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—42no—
240C2×C3—244no—
241D3—84no—
242C22—21no—
243C22—21no—
244C22—124no—
245C22—248no—
246C22—242no—
247C22—242no—
248C22#6373512yescomplemented
249C22C2×#377411yescharacteristic
250C4—21no—
251C4—241no—
252C4—241no—
253C4#6423611yescharacteristic
254C4#6424111yescharacteristic
255C3—21no—
256C3—21no—
257C2—22no—
258C2—244no—
259C2#1059333411yescharacteristic
260C2C2×#6373511yescharacteristic
261C2#1059351911yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×D8
prime radicalC22×#3713C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2187
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63735C2semidirect
3. #10591188C2semidirect
4. C22⋊#3708C2semidirect
5. #10590061C2semidirect
9. C2×#3718C22semidirect
13. C2×#3708C22semidirect
15. #63576C22semidirect
106. C22×C32SD32semidirect
213. C32#2187semidirect
248. C22#63735semidirect

Maximal subgroups

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

subgroupindex
C22×#37132
C2×#637352
#105911882
C22⋊#37082
#105900612
#21879