Finite Group Databasebeta

← #11799000

Subgroups — #11799000

Order 1152.

302 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 43 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×#63735C211yesmaximal, characteristic, complemented
2C2×#63734C211yesmaximal, characteristic
3#10590353C211yesmaximal, characteristic, complemented
4C4×#3713C211yesmaximal, characteristic, complemented
5C4⋊#3708C211yesmaximal, characteristic, complemented
6#10590062C211yesmaximal, characteristic, complemented
7#10590061C211yesmaximal, characteristic, complemented
8C3×#875—21no—
9C3×C4×D12—21no—
10C2×#3718C2211yescharacteristic
11C2×#3715—21no—
12C2×#3713C2211yescharacteristic
13C2×#3713C2211yescharacteristic
14C2×#3708C2211yescharacteristic
15C2×#3708C2211yescharacteristic
16#63735—22no—
17#63734—22no—
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19#63576C2211yescharacteristic
20#63562—21no—
21#5059—61no—
22C4×#213—61no—
23C2×C3×D12—21no—
24C2×C3×D12—21no—
25C2×C3×C4×D3—41no—
26C2×C3×Dic6—21no—
27C32×C42D411yescharacteristic
28C2×C3⋊(C3⋊C8)D411yescharacteristic
29C2×C3⋊(C3⋊C8)C2311yescharacteristic
30C3×(C2×D3)⋊C4—41no—
31C3×(C2×D3)⋊C4—41no—
32C3×(C2×D3)⋊C4—41no—
33C3×C4⋊Dic3—21no—
34#3718—21no—
35#3718—21no—
36#3715—42no—
37#3713—21no—
38#3713—21no—
39#3713—21no—
40#3713D412yes—
41#3708—21no—
42#3708—21no—
43#2210—91nomaximal, Sylow
44C3×#124—61no—
45C3×C4×D4—61no—
46C2×#216—61no—
47C2×#215—61no—
48C2×#214—61no—
49C2×#213—61no—
50C2×#213—61no—
51#875—21no—
52C4×D12—21no—
53#832—61no—
54#809—61no—
55#807—61no—
56C4×C3⋊C8—61no—
57C4×C3⋊C8—61no—
58C22×C3×D3—41no—
59C22×C3×D3—41no—
60C2×C32×C4D811yescharacteristic
61C2×C32×C4D811yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C3×Dic3—41no—
64C2×C3×Dic3—41no—
65C3×D12—22no—
66C3×D12—41no—
67C3×D12—41no—
68C3×D12—41no—
69C3×C4×D3—82no—
70C3×Dic6—41no—
71C3×Dic6—41no—
72C3⋊(C3⋊C8)—21no—
73C3⋊(C3⋊C8)C2×D411yescharacteristic
74C3⋊(C3⋊C8)#4111yescharacteristic
75C2×SD32—91no—
76C2×D16—91no—
77#495—91no—
78C4×D8—91no—
79C4⋊C16—91no—
80#358—91no—
81#357—91no—
82C2×C3×Q8—61no—
83C2×C3×D4—61no—
84C2×C3×D4—61no—
85C22×C3×C4—121no—
86C2×D12—21no—
87C2×D12—21no—
88C2×C4×D3—41no—
89C2×Dic6—21no—
90C3×C4⋊C4—61no—
91C3×C22⋊C4—121no—
92C3×C22⋊C4—121no—
93C3×C22⋊C4—121no—
94C3×C42—21no—
95C3×C42—21no—
96#216—121no—
97#216—121no—
98#215—122no—
99#214—122no—
100#213—62no—
101#213—62no—
102#213—121no—
103#213—121no—
104(C2×D3)⋊C4—41no—
105(C2×D3)⋊C4—41no—
106(C2×D3)⋊C4—41no—
107C4⋊Dic3—21no—
108C2×C3⋊C8—61no—
109C2×C3⋊C8—61no—
110C2×C3⋊C8—61no—
111C2×C3⋊C8—61no—
112C22×C32C2×D811yescharacteristic
113C2×C3×D3—42no—
114C2×C3×D3—81no—
115C2×C3×D3—81no—
116C2×C3×D3—81no—
117C2×C3×D3—81no—
118C2×C3×D3—81no—
119C32×C4—21no—
120C32×C4—21no—
121C32×C4#12111yescharacteristic
122C32×C4AGL(1,ℤ/8)11yescharacteristic
123C3×Dic3—81no—
124C3×Dic3—81no—
125C2×Q16—91no—
126C2×SD16—181no—
127C2×D8—91no—
128C2×D8—91no—
129#124—61no—
130C4×D4—61no—
131SD32—182no—
132D16—182no—
133C2×C16—91no—
134C2×C16—91no—
135#107—91no—
136#102—181no—
137C4×C8—91no—
138C23×C3—121no—
139C23×C3—121no—
140C22×D3—41no—
141C22×D3—41no—
142C3×Q8—121no—
143C3×Q8—121no—
144C3×D4—62no—
145C3×D4—121no—
146C3×D4—121no—
147C3×D4—121no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—121no—
155C2×C3×C4—121no—
156C2×C3×C4—242no—
157C2×Dic3—41no—
158C2×Dic3—41no—
159D12—22no—
160D12—41no—
161D12—41no—
162D12—41no—
163C4×D3—82no—
164Dic6—41no—
165Dic6—41no—
166C3⋊C8—61no—
167C3⋊C8—61no—
168C3⋊C8—61no—
169C3⋊C8—61no—
170C3⋊C8—62no—
171C3⋊C8—121no—
172C2×C32#45911yescharacteristic
173C2×C32#50811yescharacteristic
174C2×C32#50911yescharacteristic
175C3×D3—82no—
176C3×D3—161no—
177C2×Q8—61no—
178C2×D4—61no—
179C2×D4—61no—
180C22×C4—121no—
181Q16—181no—
182Q16—181no—
183SD16—362no—
184D8—92no—
185D8—181no—
186D8—181no—
187D8—181no—
188C2×C8—91no—
189C2×C8—91no—
190C4⋊C4—61no—
191C22⋊C4—121no—
192C22⋊C4—121no—
193C22⋊C4—121no—
194C42GO+(4,𝔽2)11yescharacteristic
195C16—181no—
196C16—181no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—122no—
200C22×C3—241no—
201C22×C3—241no—
202C22×C3—241no—
203C22×C3—241no—
204C22×C3—241no—
205C2×D3—42no—
206C2×D3—81no—
207C2×D3—81no—
208C2×D3—81no—
209C2×D3—81no—
210C2×D3—81no—
211C3×C4—22no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—41no—
217C3×C4—41no—
218C3×C4—41no—
219C3×C4—241no—
220C3×C4—241no—
221Dic3—81no—
222Dic3—81no—
223C32#221011yescharacteristic, complemented, Sylow
224C23—121no—
225C23—121no—
226Q8—121no—
227Q8—121no—
228D4—62no—
229D4—121no—
230D4—121no—
231D4—121no—
232C2×C4—121no—
233C2×C4—121no—
234C2×C4—242no—
235C2×C4#377411yescharacteristic
236C2×C4#377411yescharacteristic
237C2×C4C2×GO+(4,𝔽2)11yescharacteristic
238C8—91no—
239C8—91no—
240C8—181no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—242no—
248C2×C3—481no—
249D3—82no—
250D3—161no—
251C22—122no—
252C22—241no—
253C22—241no—
254C22—241no—
255C22—241no—
256C22—241no—
257C22C2×#377411yescharacteristic
258C4—21no—
259C4—21no—
260C4—241no—
261C4—241no—
262C4#6422411yescharacteristic
263C4#6423011yescharacteristic
264C3—21no—
265C3—21no—
266C2—242no—
267C2—481no—
268C2#1059333311yescharacteristic
269C2#1059333411yescharacteristic
270C2#1059341711yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×D8
prime radicalC2×#63734C2
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2210
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×#63735C2semidirect
3. #10590353C2semidirect
4. C4×#3713C2semidirect
5. C4⋊#3708C2semidirect
6. #10590062C2semidirect
7. #10590061C2semidirect
223. C32#2210semidirect

Maximal subgroups

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

subgroupindex
C2×#637352
C2×#637342
#105903532
C4×#37132
C4⋊#37082
#105900622
#105900612
#22109