Finite Group Databasebeta

← #11798073

Subgroups — #11798073

Order 1152.

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

normal subgroups only

This group has 502 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, complemented
2C2×#63734C212yesmaximal, complemented
3#10591166C211yesmaximal, characteristic, complemented
4C22⋊#3708C211yesmaximal, characteristic, complemented
5#10590061C212yesmaximal, complemented
6C22×C3×D12—21no—
7C22×C3⋊(C3⋊C8)C2211yescharacteristic
8C3×#930—21no—
9C2×#3713—21no—
10C2×#3713—24no—
11C2×#3713C2212yes—
12C2×#3713C2211yescharacteristic, complemented
13C2×#3708C2212yescomplemented
14#63734—24no—
15#63576C2211yescharacteristic, complemented
16#63562—21no—
17C22×#213—61no—
18#5038—61no—
19C23×C3×D3—41no—
20C22×C32×C4D411yescharacteristic
21C2×C3×#67—41no—
22C2×C3×D12—24no—
23C2×C3×D12—22no—
24C2×C3×D12—21no—
25C2×C3×D12—42no—
26C2×C3×D12—41no—
27C2×C3⋊(C3⋊C8)—22no—
28C2×C3⋊(C3⋊C8)D411yescharacteristic
29C2×C3⋊(C3⋊C8)C2311yescharacteristic
30C3×(C2×D3)⋊C4—41no—
31C3×C4⋊Dic3—21no—
32#3713—24no—
33#3713—22no—
34#3713—22no—
35#3713D414yescomplemented
36#3708—22no—
37#2184—91nomaximal, Sylow
38C22×C3×D4—61no—
39C22×D12—21no—
40C3×#121—61no—
41C2×#213—62no—
42C2×#213—61no—
43C2×#213—62no—
44C2×#213—68no—
45#930—21no—
46C22×C3⋊C8—61no—
47C22×C3⋊C8—61no—
48#832—61no—
49#809—61no—
50#807—61no—
51C23×C32D811yescharacteristic
52C22×C3×D3—44no—
53C22×C3×D3—42no—
54C22×C3×D3—41no—
55C22×C3×D3—82no—
56C22×C3×D3—82no—
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4D811yescharacteristic
60C2×C32×C4C2×D411yescharacteristic
61C3×#67—82no—
62C2×C3×Dic3—41no—
63C3×D12—24no—
64C3×D12—44no—
65C3×D12—41no—
66C3×D12—42no—
67C3×D12—41no—
68C3⋊(C3⋊C8)—21no—
69C3⋊(C3⋊C8)C2×D412yes—
70C22×D8—91no—
71C2×D16—92no—
72#466—91no—
73#357—92no—
74C22⋊C16—91no—
75C24×C3—121no—
76C23×D3—41no—
77C2×C3×D4—64no—
78C2×C3×D4—62no—
79C2×C3×D4—61no—
80C2×C3×D4—122no—
81C2×C3×D4—121no—
82C2×C3×D4—121no—
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C2×#67—41no—
86C2×D12—24no—
87C2×D12—22no—
88C2×D12—21no—
89C2×D12—42no—
90C2×D12—41no—
91C3×C4⋊C4—61no—
92C3×C22⋊C4—121no—
93#213—64no—
94#213—64no—
95#213—68no—
96#213—122no—
97(C2×D3)⋊C4—41no—
98C4⋊Dic3—21no—
99C2×C3⋊C8—61no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—64no—
104C2×C3⋊C8—122no—
105C22×C32—21no—
106C22×C32—21no—
107C22×C32D1612yescomplemented
108C22×C32C2×D811yescharacteristic
109C2×C3×D3—44no—
110C2×C3×D3—88no—
111C2×C3×D3—82no—
112C2×C3×D3—82no—
113C2×C3×D3—81no—
114C2×C3×D3—81no—
115C2×C3×D3—81no—
116C32×C4—21no—
117C32×C4#12011yescharacteristic
118C32×C4AGL(1,ℤ/8)11yescharacteristic
119C3×Dic3—81no—
120C22×D4—61no—
121C2×D8—92no—
122C2×D8—91no—
123C2×D8—181no—
124C2×D8—184no—
125C22×C8—91no—
126#121—61no—
127D16—184no—
128C2×C16—92no—
129#107—91no—
130#102—181no—
131C23×C3—21no—
132C23×C3—21no—
133C23×C3—124no—
134C23×C3—122no—
135C23×C3—121no—
136C23×C3—242no—
137C23×C3—242no—
138C22×D3—44no—
139C22×D3—42no—
140C22×D3—41no—
141C22×D3—82no—
142C22×D3—82no—
143C3×D4—64no—
144C3×D4—124no—
145C3×D4—122no—
146C3×D4—121no—
147C3×D4—121no—
148C3×D4—242no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—41no—
156C2×C3×C4—41no—
157C2×C3×C4—121no—
158#67—82no—
159C2×Dic3—41no—
160D12—24no—
161D12—44no—
162D12—42no—
163D12—41no—
164D12—41no—
165C3⋊C8—62no—
166C3⋊C8—62no—
167C3⋊C8—62no—
168C3⋊C8—121no—
169C2×C32—22no—
170C2×C32#44711yescharacteristic
171C2×C32C2×D1611yescharacteristic
172C2×C32#50911yescharacteristic
173C3×D3—84no—
174C3×D3—161no—
175C24—121no—
176C2×D4—64no—
177C2×D4—62no—
178C2×D4—61no—
179C2×D4—122no—
180C2×D4—121no—
181C2×D4—121no—
182C22×C4GO+(4,𝔽2)11yescharacteristic
183D8—94no—
184D8—182no—
185D8—182no—
186D8—184no—
187C2×C8—91no—
188C2×C8—91no—
189C2×C8—182no—
190C4⋊C4—61no—
191C22⋊C4—121no—
192C16—182no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—41no—
200C22×C3—41no—
201C22×C3—124no—
202C22×C3—248no—
203C22×C3—242no—
204C22×C3—242no—
205C22×C3—241no—
206C22×C3—241no—
207C22×C3—241no—
208C2×D3—44no—
209C2×D3—88no—
210C2×D3—82no—
211C2×D3—82no—
212C2×D3—81no—
213C2×D3—81no—
214C2×D3—81no—
215C3×C4—22no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—21no—
220C3×C4—41no—
221C3×C4—241no—
222Dic3—81no—
223C32#218411yescharacteristic, complemented, Sylow
224C23—124no—
225C23—122no—
226C23—121no—
227C23—242no—
228C23—242no—
229C23#377411yescharacteristic
230D4—64no—
231D4—124no—
232D4—122no—
233D4—121no—
234D4—121no—
235D4—242no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—121no—
239C2×C4#377411yescharacteristic
240C2×C4C2×GO+(4,𝔽2)11yescharacteristic
241C8—92no—
242C8—181no—
243C2×C3—24no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—42no—
251C2×C3—244no—
252C2×C3—481no—
253D3—84no—
254D3—161no—
255C22—21no—
256C22—21no—
257C22—124no—
258C22—248no—
259C22—242no—
260C22—242no—
261C22—241no—
262C22—241no—
263C22—241no—
264C22#6373412yescomplemented
265C22C2×#377411yescharacteristic
266C4—21no—
267C4—241no—
268C4#6423611yescharacteristic
269C4#6424111yescharacteristic
270C3—21no—
271C3—21no—
272C2—22no—
273C2—244no—
274C2—481no—
275C2C2×#6373411yescharacteristic
276C2#1059333411yescharacteristic
277C2#1059351911yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×D8
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2184
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. C22×#3713C2semidirect
2. C2×#63734C2semidirect
3. #10591166C2semidirect
4. C22⋊#3708C2semidirect
5. #10590061C2semidirect
12. C2×#3713C22semidirect
13. C2×#3708C22semidirect
15. #63576C22semidirect
35. #3713D4semidirect
107. C22×C32D16semidirect
223. C32#2184semidirect
264. C22#63734semidirect

Maximal subgroups

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

subgroupindex
C22×#37132
C2×#637342
#105911662
C22⋊#37082
#105900612
#21849