Finite Group Databasebeta

← #11774827

Subgroups — #11774827

Order 1152.

648 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 141 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#10596051C211yesmaximal, characteristic
2#10592536C211yesmaximal, characteristic, complemented
3#10592384C211yesmaximal, characteristic, complemented
4C32×Q8⋊C8C211yesmaximal, characteristic, complemented
5#10589401C211yesmaximal, characteristic, complemented
6#10589349C211yesmaximal, characteristic, complemented
7#10589325C211yesmaximal, characteristic, complemented
8#68242—34nomaximal
9C32×C4×Q8C2211yescharacteristic
10#64156C411yescharacteristic
11#64155C411yescharacteristic
12C2×#3743—21no—
13#64107—21no—
14#64104C411yescharacteristic
15#64103—21no—
16#64099C411yescharacteristic
17C4×C4⋊(C3⋊D3)—21no—
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19#64081—21no—
20C42×C3⋊D3C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C32×C4×C8C2211yescharacteristic
23#63647—21no—
24#63641—21no—
25#63641—21no—
26C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
27C4×C3⋊(C3⋊C8)C2211yescharacteristic
28#5580—34no—
29#4837—34no—
30#4685—34no—
31C3×Q8⋊C8D314yescomplemented
32#4535—34no—
33#4483—34no—
34#4459—34no—
35C2×C32×Q8C2×C411yescharacteristic
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C32×C8—21no—
43C2×C32×C8—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4C2×C411yescharacteristic
46C32×C42—21no—
47C32×C42C2311yescharacteristic
48#3752—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52#3752—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56#3750—21no—
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62#3743—42no—
63#1495—91noSylow
64C3×C4×Q8C2×D314yes—
65#947—34no—
66#946—34no—
67C2×ΓL(1,𝔽25)—64no—
68#898—64no—
69#895—34no—
70#894—64no—
71#890—34no—
72C4×D12—34no—
73C4×D12—64no—
74#872—64no—
75C42×D3—34no—
76C3×C4⋊C8C2×D314yes—
77C3×C4×C8C2×D314yes—
78(C2×D3)⋊C8—64no—
79Dic3⋊C8—64no—
80Dic3⋊C8—64no—
81C4⋊(C3⋊C8)—34no—
82C4×C3⋊C8—34no—
83C22×C3⋊D3—21no—
84C22×C3⋊D3C22⋊C411yescharacteristic
85C32×Q8—21no—
86C32×Q8—21no—
87C2×C32×C4—21no—
88C2×C32×C4—21no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3C22⋊C411yescharacteristic
94C2×C3⋊Dic3C22⋊C411yescharacteristic
95C2×C3⋊Dic3C22⋊C411yescharacteristic
96C4⋊(C3⋊D3)—21no—
97C4⋊(C3⋊D3)—21no—
98C4⋊(C3⋊D3)—42no—
99C4×C3⋊D3—21no—
100C4×C3⋊D3—21no—
101C4×C3⋊D3—21no—
102C4×C3⋊D3—21no—
103C4×C3⋊D3—41no—
104C4×C3⋊D3—41no—
105C4×C3⋊D3—41no—
106C32×C8—41no—
107C32×C8—41no—
108C3⋊(C3⋊C8)—41no—
109C3⋊(C3⋊C8)—41no—
110#529—91no—
111#431—91no—
112#423—91no—
113Q8⋊C8—91no—
114Q8⋊C8C3⋊D311yescharacteristic, complemented
115D4⋊C8—91no—
116D4⋊C8—91no—
117C2×C3×Q8C4×D314yes—
118C2×D12—34no—
119C2×D12—64no—
120C2×C4×D3—34no—
121C2×C4×D3—34no—
122C2×C4×D3—34no—
123C2×C4×D3—64no—
124C2×C3×C8—24no—
125C2×C3×C8—24no—
126C3×C4⋊C4—24no—
127C3×C4⋊C4C4×D314yes—
128C3×C42—24no—
129C3×C42C22×D314yes—
130(C2×D3)⋊C4—64no—
131(C2×D3)⋊C4—64no—
132(C2×D3)⋊C4—64no—
133(C2×D3)⋊C4—64no—
134(C2×D3)⋊C4—64no—
135C4⋊Dic3—34no—
136C4⋊Dic3—64no—
137Dic3⋊C4—64no—
138Dic3⋊C4—64no—
139C4×Dic3—34no—
140C4×Dic3—34no—
141C4×Dic3—34no—
142C2×C3⋊C8—64no—
143C2×C3⋊C8—64no—
144ΓL(1,𝔽25)—128no—
145C22×C32C2×C22⋊C411yescharacteristic
146C2×C3⋊D3—21no—
147C2×C3⋊D3—21no—
148C2×C3⋊D3—21no—
149C2×C3⋊D3—41no—
150C2×C3⋊D3—41no—
151C2×C3⋊D3—41no—
152C32×C4—21no—
153C32×C4—41no—
154C32×C4—41no—
155C32×C4#13111yescharacteristic
156C32×C4#13111yescharacteristic
157C32×C4AGL(1,ℤ/8)11yescharacteristic
158C32×C4#13711yescharacteristic
159C3⋊Dic3—21no—
160C3⋊Dic3—21no—
161C3⋊Dic3—21no—
162C3⋊Dic3—41no—
163C2×M16—181no—
164#126—181no—
165#125—91no—
166#124—91no—
167#123—181no—
168C22⋊Q8—91no—
169#121—91no—
170C4×Q8C2×C3⋊D311yescharacteristic
171C4×D4—91no—
172C4×D4—181no—
173#117—181no—
174C2×C42—91no—
175C4⋊C8—91no—
176C4⋊C8—181no—
177C4⋊C8—181no—
178C4⋊C8C2×C3⋊D311yescharacteristic
179C22⋊C8—181no—
180C4×C8—91no—
181C4×C8C2×C3⋊D311yescharacteristic
182C22×D3—34no—
183C22×D3—64no—
184C3×Q8—24no—
185C3×Q8—24no—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4C2×C4×D314yes—
189C2×C3×C4D3×D414yes—
190C2×C3×C4D3×D414yes—
191C2×Dic3—34no—
192C2×Dic3—34no—
193C2×Dic3—34no—
194C2×Dic3—64no—
195D12—64no—
196D12—64no—
197D12—128no—
198C4×D3—64no—
199C4×D3—64no—
200C4×D3—64no—
201C4×D3—64no—
202C4×D3—124no—
203C4×D3—124no—
204C4×D3—124no—
205C3×C8—44no—
206C3×C8—44no—
207C3⋊C8—124no—
208C3⋊C8—124no—
209C2×C32#40811yescharacteristic
210C2×C32#41711yescharacteristic
211C2×C32#42111yescharacteristic
212C3⋊D3—41no—
213C3⋊D3—81no—
214C2×Q8C4×C3⋊D311yescharacteristic
215C2×D4—91no—
216C2×D4—181no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—181no—
221M16—362no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—181no—
225C2×C8—181no—
226C4⋊C4—21no—
227C4⋊C4—91no—
228C4⋊C4—181no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C4⋊C4C4×C3⋊D311yescharacteristic
232C22⋊C4—181no—
233C22⋊C4—181no—
234C22⋊C4—181no—
235C22⋊C4—181no—
236C22⋊C4—181no—
237C42—21no—
238C42—91no—
239C42—91no—
240C42—91no—
241C42C22×C3⋊D311yescharacteristic
242C22×C3D3×C22⋊C414yes—
243C2×D3—64no—
244C2×D3—64no—
245C2×D3—64no—
246C2×D3—124no—
247C2×D3—124no—
248C2×D3—124no—
249C3×C4—24no—
250C3×C4—44no—
251C3×C4—44no—
252C3×C4#90114yes—
253C3×C4#90714yes—
254C3×C4#91414yes—
255C3×C4#91814yes—
256Dic3—64no—
257Dic3—64no—
258Dic3—64no—
259Dic3—124no—
260C32#149511yescharacteristic, complemented, Sylow
261C23—91no—
262C23—181no—
263Q8—21no—
264Q8—21no—
265D4—181no—
266D4—181no—
267D4—362no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—91no—
271C2×C4—91no—
272C2×C4—91no—
273C2×C4—181no—
274C2×C4—181no—
275C2×C4—181no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—361no—
279C2×C4—361no—
280C2×C4—361no—
281C2×C4C2×C4×C3⋊D311yescharacteristic
282C2×C4D4×C3⋊D311yescharacteristic
283C2×C4D4×C3⋊D311yescharacteristic
284C8—41no—
285C8—41no—
286C8—361no—
287C8—361no—
288C2×C3#472714yes—
289C2×C3#480314yes—
290C2×C3#482114yes—
291D3—124no—
292D3—244no—
293C22—181no—
294C22—181no—
295C22—181no—
296C22—361no—
297C22—361no—
298C22—361no—
299C22C22⋊C4×C3⋊D311yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—181no—
304C4—181no—
305C4—181no—
306C4—361no—
307C4#6411011yescharacteristic
308C4#6411611yescharacteristic
309C4#6412311yescharacteristic
310C4#6412711yescharacteristic
311C3#6824214yescomplemented
312C2—361no—
313C2—721no—
314C2#1059242611yescharacteristic
315C2#1059250211yescharacteristic
316C2#1059252011yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×Q8⋊C8C2
socleC22×C32C2×C22⋊C4
prime radical#64104C4
cosocleC32×C42C23
hypercenterQ8⋊C8C3⋊D3
hypocenterC32#1495
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592536C2semidirect
3. #10592384C2semidirect
4. C32×Q8⋊C8C2semidirect
5. #10589401C2semidirect
6. #10589349C2semidirect
7. #10589325C2semidirect
31. C3×Q8⋊C8D3semidirect
114. Q8⋊C8C3⋊D3semidirect
260. C32#1495semidirect
311. C3#68242semidirect

Maximal subgroups

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

subgroupindex
#105960512
#105925362
#105923842
C32×Q8⋊C82
#105894012
#105893492
#105893252
#682423