Finite Group Databasebeta

← #11775255

Subgroups — #11775255

Order 1152.

726 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 131 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#10596095C211yesmaximal, characteristic
2#10592418C211yesmaximal, characteristic, complemented
3#10592348C211yesmaximal, characteristic, complemented
4C32×#328C211yesmaximal, characteristic, complemented
5#10589404C211yesmaximal, characteristic, complemented
6#10589336C211yesmaximal, characteristic
7#10589317C211yesmaximal, characteristic
8#68311—34nomaximal
9C32×C22⋊Q8C2211yescharacteristic
10#64156C411yescharacteristic, complemented
11Q8×C3⋊Dic3C411yescharacteristic, complemented
12#64139C2211yescharacteristic
13C2×#3750—21no—
14C2×C4×C3⋊Dic3—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64107—21no—
17#64102C411yescharacteristic, complemented
18#64101—21no—
19#64099C411yescharacteristic, complemented
20#64095—21no—
21#64090—21no—
22C32×C22⋊C8C2211yescharacteristic
23C32×#95C2211yescharacteristic
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26#63642—21no—
27#63641—21no—
28#5624—34no—
29#4719—34no—
30#4649—34no—
31C3×#328D314yescomplemented
32#4538—34no—
33#4470—34no—
34#4451—34no—
35C2×C32×Q8C2×C411yescharacteristic
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C2×#638—21no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3⋊Dic3D411yescharacteristic
42C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C32×C8—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4C2×C411yescharacteristic
47C32×C22⋊C4—21no—
48#3752—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—24no—
56#3750—21no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—42no—
59C4×C3⋊Dic3C2×C411yescharacteristic
60C4×C3⋊Dic3C2×C411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62C4×C3⋊Dic3D411yescharacteristic
63C2×C3⋊(C3⋊C8)—21no—
64#1509—91noSylow
65C3×C22⋊Q8C2×D314yes—
66#947—34no—
67Q8×Dic3—34no—
68#930—34no—
69C2×Dic3⋊C4—64no—
70C2×C4×Dic3—34no—
71C2×C4×Dic3—64no—
72#898—64no—
73#893—34no—
74#892—64no—
75#890—34no—
76#886—64no—
77#67⋊C4—64no—
78C3×C22⋊C8C2×D314yes—
79C3×#95C2×D314yes—
80C3⋊#95—34no—
81#830—34no—
82#815—64no—
83Dic3⋊C8—64no—
84C23×C32C2×D411yescharacteristic
85C22×C3⋊D3—21no—
86C32×Q8—41no—
87C2×C32×C4—22no—
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95#638—41no—
96#638—41no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C4⋊(C3⋊D3)—41no—
109C4×C3⋊D3—42no—
110C32×C8—41no—
111C3⋊(C3⋊C8)—41no—
112#529—91no—
113#432—91no—
114C4×C4⋊C4—91no—
115#328—91no—
116#328C3⋊D311yescharacteristic, complemented
117#327—91no—
118#327—91no—
119C2×C3×Q8C4×D314yes—
120C22×C3×C4—24no—
121C22×C3×C4C22×D314yes—
122C2×#67—64no—
123C22×Dic3—34no—
124C22×Dic3—34no—
125C22×Dic3—64no—
126C2×D12—34no—
127C2×C4×D3—64no—
128C2×C3×C8—24no—
129C3×C4⋊C4—24no—
130C3×C4⋊C4C4×D314yes—
131C3×C22⋊C4—24no—
132(C2×D3)⋊C4—64no—
133(C2×D3)⋊C4—64no—
134(C2×D3)⋊C4—64no—
135(C2×D3)⋊C4—64no—
136C4⋊Dic3—34no—
137C4⋊Dic3—64no—
138C4⋊Dic3—64no—
139Dic3⋊C4—64no—
140Dic3⋊C4—616no—
141C4×Dic3—34no—
142C4×Dic3—34no—
143C4×Dic3—34no—
144C4×Dic3—34no—
145C4×Dic3—64no—
146C4×Dic3—128no—
147C2×C3⋊C8—64no—
148C22×C32—21no—
149C22×C32—21no—
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32AGL(1,ℤ/8)11yescharacteristic
152C22×C32#13711yescharacteristic
153C2×C3⋊D3—41no—
154C2×C3⋊D3—41no—
155C2×C3⋊D3—41no—
156C32×C4—21no—
157C32×C4—21no—
158C32×C4—42no—
159C32×C4—41no—
160C32×C4—41no—
161C3⋊Dic3—21no—
162C3⋊Dic3—21no—
163C3⋊Dic3—21no—
164C3⋊Dic3—42no—
165C3⋊Dic3—41no—
166C3⋊Dic3#10412yes—
167#126—181no—
168#125—91no—
169#124—91no—
170#123—181no—
171C22⋊Q8C2×C3⋊D311yescharacteristic
172#121—91no—
173C4×Q8—91no—
174C4×D4—91no—
175C4×D4—181no—
176#117—181no—
177C2×C4⋊C4—181no—
178C2×C42—91no—
179C2×C42—181no—
180C4⋊C8—181no—
181C22⋊C8—91no—
182C22⋊C8C2×C3⋊D311yescharacteristic
183#97—181no—
184#95—91no—
185#95C2×C3⋊D311yescharacteristic
186C23×C3D3×D414yes—
187C22×D3—64no—
188C3×Q8—44no—
189C2×C3×C4—28no—
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—44no—
193C2×C3×C4—44no—
194C2×C3×C4—44no—
195C2×C3×C4C2×C4×D314yes—
196C2×C3×C4D3×D414yes—
197#67—124no—
198#67—124no—
199C2×Dic3—34no—
200C2×Dic3—34no—
201C2×Dic3—34no—
202C2×Dic3—34no—
203C2×Dic3—68no—
204C2×Dic3—64no—
205C2×Dic3—64no—
206C2×Dic3—68no—
207C2×Dic3—64no—
208C2×Dic3—124no—
209C2×Dic3—124no—
210D12—124no—
211C4×D3—128no—
212C3×C8—44no—
213C3⋊C8—124no—
214C2×C32—21no—
215C2×C32—21no—
216C2×C32#41011yescharacteristic
217C2×C32#41711yescharacteristic
218C2×C32C2×#10411yescharacteristic
219C3⋊D3—81no—
220C2×Q8C4×C3⋊D311yescharacteristic
221C2×D4—91no—
222C2×D4—181no—
223C22×C4—21no—
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—181no—
227C22×C4—181no—
228C22×C4C22×C3⋊D311yescharacteristic
229C2×C8—21no—
230C2×C8—181no—
231C4⋊C4—21no—
232C4⋊C4—91no—
233C4⋊C4—181no—
234C4⋊C4—181no—
235C4⋊C4—181no—
236C4⋊C4—184no—
237C4⋊C4C4×C3⋊D311yescharacteristic
238C22⋊C4—21no—
239C22⋊C4—181no—
240C22⋊C4—181no—
241C22⋊C4—181no—
242C22⋊C4—181no—
243C42—91no—
244C42—91no—
245C42—91no—
246C42—91no—
247C42—181no—
248C42—362no—
249C22×C3—24no—
250C22×C3—24no—
251C22×C3D3×C22⋊C414yes—
252C22×C3#91414yes—
253C22×C3#91814yes—
254C2×D3—124no—
255C2×D3—124no—
256C2×D3—124no—
257C3×C4—24no—
258C3×C4—24no—
259C3×C4—48no—
260C3×C4—44no—
261C3×C4—44no—
262Dic3—38no—
263Dic3—64no—
264Dic3—64no—
265Dic3—64no—
266Dic3—128no—
267Dic3—124no—
268C32#150911yescharacteristic, complemented, Sylow
269C23—181no—
270C23D4×C3⋊D311yescharacteristic
271Q8—41no—
272D4—361no—
273D4—361no—
274D4—361no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—182no—
286C2×C4—181no—
287C2×C4—181no—
288C2×C4—182no—
289C2×C4—181no—
290C2×C4—362no—
291C2×C4—361no—
292C2×C4—361no—
293C2×C4C2×C4×C3⋊D311yescharacteristic
294C2×C4D4×C3⋊D311yescharacteristic
295C8—41no—
296C8—361no—
297C2×C3—24no—
298C2×C3—24no—
299C2×C3#474014yes—
300C2×C3#480314yes—
301C2×C3D3×#10414yes—
302D3—244no—
303C22—21no—
304C22—21no—
305C22—361no—
306C22—361no—
307C22—361no—
308C22C22⋊C4×C3⋊D311yescharacteristic
309C22#6412311yescharacteristic
310C22#6412711yescharacteristic
311C4—21no—
312C4—21no—
313C4—42no—
314C4—41no—
315C4—41no—
316C4—92no—
317C4—181no—
318C4—181no—
319C4—181no—
320C4—362no—
321C4—361no—
322C3#6831114yescomplemented
323C2—21no—
324C2—21no—
325C2—721no—
326C2#1059243911yescharacteristic
327C2#1059250211yescharacteristic
328C2C3⋊D3×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#328C2
socleC22×C32C2×C22⋊C4
prime radical#64139C22
cosocleC22×C32×C4C23
hypercenter#328C3⋊D3
hypocenterC32#1509
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #10592418C2semidirect
3. #10592348C2semidirect
4. C32×#328C2semidirect
5. #10589404C2semidirect
10. #64156C4semidirect
11. Q8×C3⋊Dic3C4semidirect
17. #64102C4semidirect
19. #64099C4semidirect
31. C3×#328D3semidirect
116. #328C3⋊D3semidirect
268. C32#1509semidirect
322. C3#68311semidirect

Maximal subgroups

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

subgroupindex
#105960952
#105924182
#105923482
C32×#3282
#105894042
#105893362
#105893172
#683113