Finite Group Databasebeta

← #11775601

Subgroups — #11775601

Order 1152.

864 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 229 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×#64133C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic
3#10592911C211yesmaximal, characteristic
4#10589333C214yesmaximal, complemented
5#69946—34nomaximal
6C23×C32×C4C2211yescharacteristic
7C22×#634C411yescharacteristic, complemented
8C22×C32×C8—21no—
9C2×#3757—21no—
10C2×#3757—21no—
11C2×C4⋊(C3⋊Dic3)—21no—
12C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
13#64133—21no—
14#64133—21no—
15#64133C412yescomplemented
16#64133C2212yes—
17C2×#3750—21no—
18C32×C22⋊C8—21no—
19C32×C22⋊C8C2212yes—
20#63658C2212yes—
21C2×#924—34no—
22C2×C3×C22⋊C8D314yes—
23#5212—34no—
24#4467—316no—
25C24×C32D411yescharacteristic
26C22×C32×C4—42no—
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—22no—
36C2×#634—21no—
37C2×#634—42no—
38C2×#634C2×C412yes—
39C2×C32×C8—22no—
40C2×C32×C8—42no—
41#3757—22no—
42#3757—22no—
43#3757—42no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—42no—
46C4⋊(C3⋊Dic3)C2×C412yes—
47#3750—22no—
48#3750—22no—
49#1520—91noSylow
50C23×C3×C4C2×D314yes—
51C22×Dic6—34no—
52C22×C3×C8—24no—
53C2×#217—64no—
54C2×#217—64no—
55C2×C4⋊Dic3—34no—
56C2×C4⋊Dic3—64no—
57#924—38no—
58#924—38no—
59#924—64no—
60#924—64no—
61C2×Dic3⋊C4—64no—
62C3×C22⋊C8—24no—
63C3×C22⋊C8C2×D318yes—
64C3⋊#95—38no—
65C23×C32—41no—
66C23×C32—41no—
67C23×C32C22⋊C411yescharacteristic
68C23×C32C22⋊C411yescharacteristic
69C23×C32SD1612yes—
70C23×C32Q1612yes—
71C23×C32C2×D411yescharacteristic
72C2×C32×C4—22no—
73C2×C32×C4—22no—
74C2×C32×C4—22no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3—42no—
86C2×C3⋊Dic3—42no—
87C2×C3⋊Dic3—42no—
88C2×C3⋊Dic3—42no—
89#634—42no—
90#634—42no—
91C32×C8—42no—
92C2×C22⋊Q8—91no—
93C2×C22⋊C8C3⋊D311yescharacteristic
94#380—91no—
95#328—94no—
96C24×C3D1214yes—
97C22×C3×C4—48no—
98C22×C3×C4C4×D314yes—
99C22×C3×C4C4×D314yes—
100C22×C3×C4D1214yes—
101C22×C3×C4#6714yes—
102C22×C3×C4#6714yes—
103C22×C3×C4C22×D314yes—
104C22×Dic3—64no—
105C22×Dic3—64no—
106C22×Dic3—68no—
107C2×Dic6—38no—
108C2×Dic6—64no—
109C2×Dic6—128no—
110C2×C3×C8—28no—
111C2×C3×C8—48no—
112#217—68no—
113#217—68no—
114#217—128no—
115C4⋊Dic3—38no—
116C4⋊Dic3—64no—
117C4⋊Dic3—128no—
118Dic3⋊C4—68no—
119Dic3⋊C4—68no—
120C22×C32—21no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—42no—
127C22×C32—42no—
128C22×C32#10312yes—
129C22×C32#10312yes—
130C22×C32C2×C22⋊C411yescharacteristic
131C22×C32C2×SD1611yescharacteristic
132C22×C32C2×Q1611yescharacteristic
133C32×C4—21no—
134C32×C4—21no—
135C32×C4—21no—
136C32×C4#9912yes—
137C3⋊Dic3—42no—
138C3⋊Dic3—42no—
139C3⋊Dic3—82no—
140C22×Q8—91no—
141C23×C4C2×C3⋊D311yescharacteristic
142C22×C8—21no—
143C22⋊Q8—92no—
144C22⋊Q8—92no—
145C22⋊Q8—181no—
146C22⋊Q8—181no—
147C2×C4⋊C4—91no—
148C2×C4⋊C4—181no—
149C2×C4⋊C4—181no—
150C2×C22⋊C4—181no—
151C2×C22⋊C4—181no—
152C22⋊C8—21no—
153C22⋊C8C2×C3⋊D312yes—
154#95—92no—
155C23×C3—44no—
156C23×C3—44no—
157C23×C3#20418yes—
158C23×C3Dic1218yes—
159C23×C3(C2×D3)⋊C414yes—
160C23×C3(C2×D3)⋊C414yes—
161C23×C3C2×D1214yes—
162C2×C3×C4—28no—
163C2×C3×C4—28no—
164C2×C3×C4—28no—
165C2×C3×C4—44no—
166C2×C3×C4—44no—
167C2×C3×C4—44no—
168C2×C3×C4(C2×D3)⋊C414yes—
169C2×C3×C4(C2×D3)⋊C414yes—
170C2×C3×C4C2×C4×D314yes—
171C2×C3×C4C2×#6714yes—
172C2×Dic3—68no—
173C2×Dic3—68no—
174C2×Dic3—128no—
175C2×Dic3—128no—
176C2×Dic3—128no—
177C2×Dic3—128no—
178C2×Dic3—128no—
179Dic6—128no—
180Dic6—128no—
181C3×C8—48no—
182C2×C32—21no—
183C2×C32—22no—
184C2×C32—22no—
185C2×C32—21no—
186C2×C32C2×#9911yescharacteristic
187C2×C32C2×#10311yescharacteristic
188C2×C32#42111yescharacteristic
189C24C4⋊(C3⋊D3)11yescharacteristic
190C2×Q8—92no—
191C2×Q8—181no—
192C2×Q8—362no—
193C22×C4—42no—
194C22×C4—181no—
195C22×C4—181no—
196C22×C4—182no—
197C22×C4C4×C3⋊D311yescharacteristic
198C22×C4C4×C3⋊D311yescharacteristic
199C22×C4C4⋊(C3⋊D3)11yescharacteristic
200C22×C4#63811yescharacteristic
201C22×C4#63811yescharacteristic
202C22×C4C22×C3⋊D311yescharacteristic
203C2×C8—22no—
204C2×C8—42no—
205C4⋊C4—92no—
206C4⋊C4—181no—
207C4⋊C4—182no—
208C4⋊C4—182no—
209C4⋊C4—362no—
210C22⋊C4—182no—
211C22⋊C4—182no—
212C22⋊C4—362no—
213C22×C3—24no—
214C22×C3—24no—
215C22×C3—24no—
216C22×C3—24no—
217C22×C3—24no—
218C22×C3—24no—
219C22×C3—48no—
220C22×C3—48no—
221C22×C3#81618yes—
222C22×C3#81618yes—
223C22×C3C2×#20414yes—
224C22×C3C2×Dic1214yes—
225C22×C3C2×(C2×D3)⋊C414yes—
226C3×C4—24no—
227C3×C4—24no—
228C3×C4—24no—
229C3×C4#80618yes—
230Dic3—128no—
231Dic3—128no—
232Dic3—248no—
233C32#152011yescharacteristic, complemented, Sylow
234C23—41no—
235C23—41no—
236C23#374412yes—
237C23#374612yes—
238C23#375211yescharacteristic
239C23#375211yescharacteristic
240C23C2×C4⋊(C3⋊D3)11yescharacteristic
241Q8—362no—
242Q8—362no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—182no—
250C2×C4—182no—
251C2×C4—362no—
252C2×C4—362no—
253C2×C4—362no—
254C2×C4—362no—
255C2×C4—362no—
256C2×C4#375211yescharacteristic
257C2×C4#375211yescharacteristic
258C2×C4C2×C4×C3⋊D311yescharacteristic
259C2×C4C2×#63811yescharacteristic
260C8—42no—
261C2×C3—24no—
262C2×C3—28no—
263C2×C3—28no—
264C2×C3—24no—
265C2×C3C2×#80614yes—
266C2×C3C2×#81614yes—
267C2×C3#513914yes—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—42no—
275C22—42no—
276C22#6364312yes—
277C22#6364312yes—
278C22C2×#374411yescharacteristic
279C22C2×#374611yescharacteristic
280C22C2×#375211yescharacteristic
281C4—21no—
282C4—21no—
283C4—21no—
284C4—362no—
285C4—362no—
286C4—722no—
287C4#6363312yes—
288C3#6994614yescomplemented
289C2—21no—
290C2—21no—
291C2—22no—
292C2—22no—
293C2C2×#6363311yescharacteristic
294C2C2×#6364311yescharacteristic
295C2#1059283811yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C22⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊C8C3⋊D3
hypocenterC32#1520
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #10589333C2semidirect
7. C22×#634C4semidirect
12. C2×C4⋊(C3⋊Dic3)C4semidirect
15. #64133C4semidirect
233. C32#1520semidirect
288. C3#69946semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C32×C22⋊C82
#105929112
#105893332
#699463