Finite Group Databasebeta

← #11799370

Subgroups — #11799370

Order 1152.

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

normal subgroups only

This group has 284 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×#63773C211yesmaximal, characteristic, complemented
2C2×#63735C211yesmaximal, characteristic, complemented
3#10591188C211yesmaximal, characteristic, complemented
4#10591166C211yesmaximal, characteristic
5#10590068C211yesmaximal, characteristic, complemented
6#10590062C211yesmaximal, characteristic, complemented
7#10590061C211yesmaximal, characteristic, complemented
8C22×C3⋊(C3⋊C8)C2211yescharacteristic
9C3×#930—21no—
10C3×#924—21no—
11C2×#3718C2211yescharacteristic
12C2×#3713C2211yescharacteristic
13#63773—22no—
14C2×#3708C2211yescharacteristic
15C2×#3708C2211yescharacteristic
16#63735—22no—
17#63576C2211yescharacteristic
18#63576C2211yescharacteristic
19#63565—21no—
20#63562—21no—
21#5051—61no—
22#5038—61no—
23C22×C32×C4D411yescharacteristic
24C2×C3×#67—41no—
25C2×C3×D12—21no—
26C2×C3×Dic6—21no—
27C2×C3⋊(C3⋊C8)—21no—
28C2×C3⋊(C3⋊C8)—21no—
29C2×C3⋊(C3⋊C8)D411yescharacteristic
30C2×C3⋊(C3⋊C8)C2311yescharacteristic
31C3×#217—41no—
32C3×(C2×D3)⋊C4—41no—
33C3×C4⋊Dic3—21no—
34C3×C4⋊Dic3—21no—
35C3×Dic3⋊C4—41no—
36#3718—21no—
37#3718—21no—
38#3713—21no—
39#3713—21no—
40#3708—21no—
41#3708D412yescomplemented
42#2220—91nomaximal, Sylow
43C3×C22⋊Q8—61no—
44C3×#121—61no—
45C2×#216—61no—
46C2×#213—61no—
47#930—21no—
48#924—21no—
49C22×C3⋊C8—61no—
50C22×C3⋊C8—61no—
51#835—61no—
52#832—61no—
53#810—61no—
54#809—61no—
55#807—61no—
56#807—61no—
57C23×C32D811yescharacteristic
58C22×C3×D3—41no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4D811yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C3×#67—82no—
64C2×C3×Dic3—41no—
65C2×C3×Dic3—41no—
66C2×C3×Dic3—41no—
67C3×D12—41no—
68C3×D12—41no—
69C3×Dic6—41no—
70C3×Dic6—41no—
71C3⋊(C3⋊C8)—21no—
72C3⋊(C3⋊C8)C2×D411yescharacteristic
73C3⋊(C3⋊C8)#4111yescharacteristic
74C2×SD32—91no—
75C2×M32—91no—
76#467—91no—
77#466—91no—
78#366—91no—
79#358—91no—
80#357—91no—
81C2×C3×Q8—61no—
82C2×C3×D4—61no—
83C2×C3×D4—121no—
84C22×C3×C4—21no—
85C22×C3×C4—21no—
86C2×#67—41no—
87C2×D12—21no—
88C2×Dic6—21no—
89C3×C4⋊C4—61no—
90C3×C4⋊C4—61no—
91C3×C4⋊C4—121no—
92C3×C22⋊C4—121no—
93C3×C22⋊C4—121no—
94#217—41no—
95#216—121no—
96#216—121no—
97#213—121no—
98#213—121no—
99(C2×D3)⋊C4—41no—
100C4⋊Dic3—21no—
101C4⋊Dic3—21no—
102Dic3⋊C4—41no—
103C2×C3⋊C8—61no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8—61no—
107C2×C3⋊C8—121no—
108C2×C3⋊C8—121no—
109C2×C3⋊C8—121no—
110C2×C3⋊C8—121no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32C2×D811yescharacteristic
115C2×C3×D3—81no—
116C2×C3×D3—81no—
117C2×C3×D3—81no—
118C32×C4—21no—
119C32×C4#12111yescharacteristic
120C32×C4#13511yescharacteristic
121C3×Dic3—81no—
122C3×Dic3—81no—
123C3×Dic3—81no—
124C2×Q16—91no—
125C2×D8—91no—
126C22×C8—91no—
127C22⋊Q8—61no—
128#121—61no—
129SD32—182no—
130M32—182no—
131C2×C16—91no—
132C2×C16—91no—
133#107—91no—
134#107—91no—
135#103—181no—
136#102—181no—
137C23×C3—21no—
138C23×C3—21no—
139C23×C3—121no—
140C22×D3—41no—
141C3×Q8—121no—
142C3×Q8—121no—
143C3×D4—121no—
144C3×D4—121no—
145C3×D4—242no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—41no—
151C2×C3×C4—41no—
152C2×C3×C4—41no—
153C2×C3×C4—41no—
154C2×C3×C4—121no—
155C2×C3×C4—121no—
156C2×C3×C4—121no—
157#67—82no—
158C2×Dic3—41no—
159C2×Dic3—41no—
160C2×Dic3—41no—
161D12—41no—
162D12—41no—
163Dic6—41no—
164Dic6—41no—
165C3⋊C8—61no—
166C3⋊C8—61no—
167C3⋊C8—61no—
168C3⋊C8—61no—
169C3⋊C8—121no—
170C3⋊C8—121no—
171C2×C32—41no—
172C2×C32#46611yescharacteristic
173C2×C32#50911yescharacteristic
174C2×C32#51011yescharacteristic
175C3×D3—161no—
176C2×Q8—61no—
177C2×D4—61no—
178C2×D4—121no—
179C22×C4GO+(4,𝔽2)11yescharacteristic
180Q16—181no—
181Q16—181no—
182D8—181no—
183D8—181no—
184C2×C8—91no—
185C2×C8—91no—
186C2×C8—181no—
187C2×C8—181no—
188C4⋊C4—61no—
189C4⋊C4—61no—
190C4⋊C4—121no—
191C22⋊C4—121no—
192C22⋊C4—121no—
193C16—92no—
194C16—181no—
195C22×C3—22no—
196C22×C3—22no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—41no—
200C22×C3—41no—
201C22×C3—41no—
202C22×C3—41no—
203C22×C3—241no—
204C22×C3—241no—
205C22×C3—241no—
206C2×D3—81no—
207C2×D3—81no—
208C2×D3—81no—
209C3×C4—21no—
210C3×C4—21no—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—41no—
214C3×C4—41no—
215C3×C4—241no—
216C3×C4—241no—
217C3×C4—241no—
218Dic3—81no—
219Dic3—81no—
220Dic3—81no—
221C32#222011yescharacteristic, complemented, Sylow
222C23—121no—
223C23#377411yescharacteristic
224Q8—121no—
225Q8—121no—
226D4—121no—
227D4—121no—
228D4—242no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—121no—
232C2×C4—121no—
233C2×C4—121no—
234C2×C4#377411yescharacteristic
235C2×C4C2×GO+(4,𝔽2)11yescharacteristic
236C8—91no—
237C8—91no—
238C8—181no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—42no—
246C2×C3—42no—
247C2×C3—481no—
248D3—161no—
249C22—21no—
250C22—21no—
251C22—21no—
252C22—241no—
253C22—241no—
254C22—241no—
255C22C2×#377411yescharacteristic
256C4—21no—
257C4—241no—
258C4—241no—
259C4—241no—
260C4#6423711yescharacteristic
261C4#6424211yescharacteristic
262C3—21no—
263C3—21no—
264C2—41no—
265C2—481no—
266C2#1059333411yescharacteristic
267C2#1059333611yescharacteristic
268C2#1059352011yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×D8
prime radical#10591166C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2220
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
1. C2×#63773C2semidirect
2. C2×#63735C2semidirect
3. #10591188C2semidirect
5. #10590068C2semidirect
6. #10590062C2semidirect
7. #10590061C2semidirect
41. #3708D4semidirect
221. C32#2220semidirect

Maximal subgroups

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

subgroupindex
C2×#637732
C2×#637352
#105911882
#105911662
#105900682
#105900622
#105900612
#22209