Finite Group Databasebeta

← #11775438

Subgroups — #11775438

Order 1152.

462 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#10593972C211yesmaximal, characteristic
2#10593737C211yesmaximal, characteristic, complemented
3#10590299C211yesmaximal, characteristic, complemented
4#10590033C214yesmaximal, complemented
5C2×#3798—21no—
6C42×C3⋊D3C2211yescharacteristic
7C3×C4×D12—21no—
8#63919C411yescharacteristic, complemented
9#63916—21no—
10#63915—21no—
11#63914C411yescharacteristic, complemented
12#63912C2212yes—
13C4×#625C412yescomplemented
14#63781—21no—
15#63781—21no—
16#63781C2212yes—
17C3×#803—21no—
18#63572—21no—
19#63557C2212yes—
20#5548—61no—
21#4705—61no—
22C22×#157—22no—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×D12—21no—
27C2×C3×C4×D3—22no—
28C2×#627—21no—
29C2×#626—22no—
30C2×#625—21no—
31C2×#625C2×C412yes—
32#3798—44no—
33C32×C42D411yescharacteristic
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C3×(C2×D3)⋊C4—22no—
38C3×C4⋊Dic3—21no—
39C2×C3×C3⋊C8—22no—
40#3724C2×C412yes—
41(C2×D3)⋊Dic3—22no—
42#1514—91nomaximal, Sylow
43C2×#235—62no—
44C3×C4×D4—61no—
45#940—61no—
46#938—61no—
47C4×#67—62no—
48#895—61no—
49#888—61no—
50#885—62no—
51#884—62no—
52C4×D12—21no—
53C42×D3—61no—
54C42×D3—61no—
55C3×#97—61no—
56(C2×D3)⋊C8—62no—
57Dic3⋊C8—62no—
58#803—21no—
59C22×C3⋊D3C2×D411yescharacteristic
60C22×C3×D3—22no—
61C2×#157—42no—
62C2×#157—42no—
63C2×#157—42no—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22×C411yescharacteristic
70C4×C3⋊D3—22no—
71C4×C3⋊D3—41no—
72C4×C3⋊D3—41no—
73C2×C3×Dic3—22no—
74C3×D12—42no—
75C3×C4×D3—44no—
76#627—42no—
77#626—44no—
78#625—42no—
79#625—42no—
80C3×C3⋊C8—42no—
81#532—91no—
82#432—91no—
83#383—91no—
84#327—94no—
85C2×C3×D4—61no—
86C22×C3×C4—62no—
87C2×#67—62no—
88C2×#67—62no—
89C2×#67—62no—
90#235—128no—
91C2×D12—21no—
92C2×D12—62no—
93C2×C4×D3—22no—
94C2×C4×D3—61no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×Dic6—62no—
101C2×C3×C8—62no—
102C3×C4⋊C4—61no—
103C3×C22⋊C4—62no—
104C3×C42—21no—
105C3×C42—21no—
106#217—62no—
107(C2×D3)⋊C4—22no—
108(C2×D3)⋊C4—62no—
109C4⋊Dic3—21no—
110Dic3⋊C4—62no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C2×C3⋊C8—22no—
118C22×C32C2×C22⋊C411yescharacteristic
119C2×C3⋊D3—21no—
120C2×C3⋊D3—21no—
121C2×C3⋊D3AGL(1,ℤ/8)12yes—
122C2×C3×D3—42no—
123C2×C3×D3—42no—
124C2×C3×D3—42no—
125#157—82no—
126C32×C4—21no—
127C32×C4—21no—
128C32×C4—21no—
129C3⋊Dic3—21no—
130C3⋊Dic3—21no—
131C3⋊Dic3—21no—
132C3×Dic3—42no—
133C2×#41—181no—
134C4⋊Q8—91no—
135#127—91no—
136#124—181no—
137#121—92no—
138#121—181no—
139C4×D4—61no—
140C4×D4—92no—
141C2×C42—91no—
142C4⋊C8—181no—
143C22⋊C8—92no—
144#97—61no—
145#95—92no—
146#95—181no—
147#95—181no—
148C23×C3—62no—
149C22×D3—22no—
150C22×D3—61no—
151C22×D3—61no—
152C3×D4—122no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—62no—
160C2×C3×C4—124no—
161#67—124no—
162#67—124no—
163#67—124no—
164C2×Dic3—22no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171D12—42no—
172D12—124no—
173C4×D3—44no—
174C4×D3—64no—
175C4×D3—122no—
176C4×D3—122no—
177C4×D3—122no—
178C4×D3—122no—
179C4×D3—122no—
180Dic6—124no—
181C3×C8—122no—
182C3⋊C8—42no—
183C2×C32#41011yescharacteristic
184C2×C32#41811yescharacteristic
185C2×C32#42111yescharacteristic
186C3⋊D3—22no—
187C3×D3—82no—
188#41—364no—
189C2×Q8—181no—
190C2×D4—61no—
191C2×D4—92no—
192C2×D4—182no—
193C2×D4—181no—
194C22×C4—62no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—182no—
199C2×C8—62no—
200C4⋊C4—61no—
201C4⋊C4—92no—
202C22⋊C4—62no—
203C22⋊C4—182no—
204C42—91no—
205C42—91no—
206C42—91no—
207C42GO+(4,𝔽2)11yescharacteristic
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—122no—
211C22×C3—122no—
212C22×C3—122no—
213C2×D3—42no—
214C2×D3—42no—
215C2×D3—42no—
216C2×D3—62no—
217C2×D3—62no—
218C2×D3—121no—
219C2×D3—121no—
220C2×D3—121no—
221C2×D3—121no—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—22no—
225C3×C4—41no—
226C3×C4—41no—
227C3×C4—41no—
228C3×C4—122no—
229Dic3—42no—
230Dic3—62no—
231Dic3—62no—
232Dic3—62no—
233Dic3—121no—
234Dic3—121no—
235Dic3—121no—
236C32#151411yescharacteristic, complemented, Sylow
237C23—62no—
238C23—91no—
239Q8—362no—
240D4—122no—
241D4—364no—
242D4—362no—
243D4—362no—
244C2×C4—62no—
245C2×C4—91no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C4—124no—
249C2×C4—182no—
250C2×C4—361no—
251C2×C4—361no—
252C2×C4—362no—
253C2×C4—362no—
254C2×C4—362no—
255C2×C4D32⋊C411yescharacteristic
256C2×C4D32⋊C411yescharacteristic
257C2×C4C2×GO+(4,𝔽2)11yescharacteristic
258C8—122no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—242no—
266D3—82no—
267D3—122no—
268D3—122no—
269C22—92no—
270C22—122no—
271C22—122no—
272C22—122no—
273C22—181no—
274C22—181no—
275C22C2×D32⋊C411yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—122no—
280C4—181no—
281C4—181no—
282C4—181no—
283C4—722no—
284C3—21no—
285C3—21no—
286C2—182no—
287C2—242no—
288C2#1059331811yescharacteristic
289C2#1059332311yescharacteristic
290C2#1059334511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1514
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593737C2semidirect
3. #10590299C2semidirect
4. #10590033C2semidirect
8. #63919C4semidirect
11. #63914C4semidirect
13. C4×#625C4semidirect
236. C32#1514semidirect

Maximal subgroups

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

subgroupindex
#105939722
#105937372
#105902992
#105900332
#15149