Finite Group Databasebeta

← #11796842

Subgroups — #11796842

Order 1152.

672 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C3⋊D3×#135C211yesmaximal, characteristic
2C3⋊D3×M32C211yesmaximal, characteristic, complemented
3#10592559C211yesmaximal, characteristic, complemented
4C32×#360C211yesmaximal, characteristic, complemented
5#10589432C211yesmaximal, characteristic, complemented
6#10589384C211yesmaximal, characteristic, complemented
7#10589354C211yesmaximal, characteristic, complemented
8#69251—34nomaximal
9#41×C3⋊D3—21no—
10C32×#135C2211yescharacteristic
11#64159—21no—
12#64128C411yescharacteristic, complemented
13Q16×C3⋊D3C411yescharacteristic, complemented
14#64125—21no—
15SD16×C3⋊D3—21no—
16#64121C411yescharacteristic, complemented
17D8×C3⋊D3C411yescharacteristic, complemented
18#64113C2211yescharacteristic
19C2×C8×C3⋊D3C2211yescharacteristic
20#64101—21no—
21C32×M32C2211yescharacteristic, complemented
22C32×#106C2211yescharacteristic, complemented
23#63644C2211yescharacteristic, complemented
24#63639C2211yescharacteristic, complemented
25#63634—21no—
26#63625—21no—
27C16×C3⋊D3—21no—
28D3×#135—34no—
29D3×M32—34no—
30#4860—34no—
31C3×#360D314yescomplemented
32#4566—34no—
33#4518—34no—
34#4488—34no—
35C32×#41—21no—
36#3832—21no—
37Q8×C3⋊D3—21no—
38#3830—21no—
39#3830—41no—
40D4×C3⋊D3—21no—
41D4×C3⋊D3—41no—
42#3828—21no—
43#3828—41no—
44C2×C4×C3⋊D3—41no—
45C2×C4×C3⋊D3D411yescharacteristic
46C32×Q16C2×C411yescharacteristic
47C32×SD16—21no—
48C32×D8C2×C411yescharacteristic
49C2×C32×C8C2311yescharacteristic
50C32×C4⋊C4—21no—
51#3756—21no—
52#3755—21no—
53#3754—21no—
54#3753—21no—
55#3752—41no—
56C4⋊(C3⋊Dic3)—21no—
57C4×C3⋊Dic3—41no—
58C2×C3⋊(C3⋊C8)D411yescharacteristic
59#3746C2×C411yescharacteristic
60#3745C2×C411yescharacteristic
61#3744—21no—
62C8×C3⋊D3C2×C411yescharacteristic
63C8×C3⋊D3C2×C411yescharacteristic
64C8×C3⋊D3D411yescharacteristic
65C8×C3⋊D3D411yescharacteristic
66C32×C16—21no—
67C3⋊(C3⋊C16)—21no—
68#2145—91noSylow
69D3×#41—64no—
70C3×#135C2×D314yes—
71#950—64no—
72#919—34no—
73D3×Q16—34no—
74#916—64no—
75D3×SD16—64no—
76#912—34no—
77D3×D8—34no—
78#904—34no—
79C2×D3×C8—34no—
80#892—64no—
81C3×M32C2×D314yescomplemented
82C3×#106C2×D314yescomplemented
83#817—34no—
84#812—34no—
85#807—64no—
86#798—64no—
87D3×C16—64no—
88C22×C3⋊D3—41no—
89C22×C3⋊D3D811yescharacteristic
90C32×Q8—21no—
91C32×D4—21no—
92C32×D4—41no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4C2×D411yescharacteristic
96#638—41no—
97#638—41no—
98#638—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3D811yescharacteristic
102C4⋊(C3⋊D3)—21no—
103C4⋊(C3⋊D3)—41no—
104C4×C3⋊D3—41no—
105C4×C3⋊D3—41no—
106C4×C3⋊D3—41no—
107C4×C3⋊D3C22⋊C411yescharacteristic
108C4×C3⋊D3C22⋊C411yescharacteristic
109C4×C3⋊D3SD1611yescharacteristic
110C4×C3⋊D3SD1611yescharacteristic
111#634—21no—
112#634—41no—
113C32×C8C22×C411yescharacteristic
114C32×C8C2×D411yescharacteristic
115C3⋊(C3⋊C8)C22⋊C411yescharacteristic
116C3⋊(C3⋊C8)C22⋊C411yescharacteristic
117C2×#135—91no—
118C2×M32—91no—
119#427—91no—
120#360—91no—
121#360—91no—
122#360—91no—
123#360C3⋊D311yescharacteristic, complemented
124C3×#41—24no—
125#239—64no—
126D3×Q8—64no—
127#237—64no—
128#237—124no—
129D3×D4—64no—
130D3×D4—124no—
131#235—64no—
132#235—124no—
133C2×C4×D3—34no—
134C2×C4×D3—124no—
135C3×Q16C4×D314yes—
136C3×SD16—24no—
137C3×D8C4×D314yes—
138C2×C3×C8C22×D314yes—
139C3×C4⋊C4—24no—
140#216—64no—
141#215—64no—
142#214—64no—
143#213—64no—
144(C2×D3)⋊C4—124no—
145C4⋊Dic3—64no—
146C4×Dic3—124no—
147C2×C3⋊C8—34no—
148Dic12—34no—
149D24—34no—
150#204—64no—
151D3×C8—34no—
152D3×C8—34no—
153D3×C8—34no—
154D3×C8—34no—
155C3×C16—24no—
156C3⋊C16—64no—
157C22×C32—41no—
158C22×C32C2×D811yescharacteristic
159C2×C3⋊D3—41no—
160C2×C3⋊D3—41no—
161C2×C3⋊D3—82no—
162C2×C3⋊D3#10211yescharacteristic
163C2×C3⋊D3#10211yescharacteristic
164C32×C4—41no—
165C32×C4—81no—
166C32×C4C2×C22⋊C411yescharacteristic
167C32×C4C2×SD1611yescharacteristic
168C3⋊Dic3—41no—
169C3⋊Dic3—81no—
170C3⋊Dic3#10211yescharacteristic
171C3⋊Dic3#10211yescharacteristic
172C2×#41—181no—
173#135—91no—
174#135—91no—
175#135—91no—
176#135—181no—
177#135—181no—
178#135C2×C3⋊D311yescharacteristic
179C2×Q16—91no—
180C2×SD16—181no—
181C2×D8—91no—
182C22×C8—91no—
183#117—181no—
184M32—91no—
185M32—181no—
186M32C2×C3⋊D311yescharacteristic, complemented
187C2×C16—181no—
188#107—181no—
189#106—91no—
190#106C2×C3⋊D311yescharacteristic, complemented
191C22×D3—34no—
192C22×D3—124no—
193C3×Q8—24no—
194C3×D4—24no—
195C3×D4—44no—
196C2×C3×C4—44no—
197C2×C3×C4—44no—
198C2×C3×C4D3×D414yes—
199#67—124no—
200#67—124no—
201#67—124no—
202C2×Dic3—34no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205D12—64no—
206D12—124no—
207C4×D3—34no—
208C4×D3—34no—
209C4×D3—34no—
210C4×D3—34no—
211C4×D3—124no—
212C4×D3—124no—
213C4×D3—124no—
214Dic6—64no—
215Dic6—124no—
216C3×C8C2×C4×D314yes—
217C3×C8D3×D414yes—
218C3⋊C8—34no—
219C3⋊C8—34no—
220C2×C32—21no—
221C2×C32—81no—
222C2×C32C2×#10211yescharacteristic
223C3⋊D3—21no—
224C3⋊D3—21no—
225C3⋊D3—81no—
226#41—21no—
227#41—181no—
228#41—181no—
229#41—181no—
230#41—361no—
231#41—361no—
232C2×Q8—181no—
233C2×D4—181no—
234C2×D4—361no—
235C22×C4—91no—
236C22×C4—361no—
237Q16—91no—
238Q16—181no—
239Q16C4×C3⋊D311yescharacteristic
240SD16—21no—
241SD16—181no—
242SD16—181no—
243SD16—181no—
244D8—91no—
245D8—181no—
246D8C4×C3⋊D311yescharacteristic
247C2×C8—91no—
248C2×C8—91no—
249C2×C8—91no—
250C2×C8—91no—
251C2×C8—91no—
252C2×C8C22×C3⋊D311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—181no—
255C22⋊C4—361no—
256C42—361no—
257C16—21no—
258C16—181no—
259C22×C3—44no—
260C22×C3D3×D814yes—
261C2×D3—34no—
262C2×D3—34no—
263C2×D3—124no—
264C2×D3—124no—
265C2×D3—248no—
266C3×C4—44no—
267C3×C4—84no—
268C3×C4D3×C22⋊C414yes—
269C3×C4D3×SD1614yes—
270Dic3—34no—
271Dic3—34no—
272Dic3—124no—
273Dic3—244no—
274C32#214511yescharacteristic, complemented, Sylow
275C23—91no—
276C23—361no—
277Q8—21no—
278Q8—181no—
279Q8—361no—
280D4—21no—
281D4—41no—
282D4—181no—
283D4—361no—
284D4—361no—
285D4—361no—
286D4—361no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—91no—
290C2×C4—91no—
291C2×C4—91no—
292C2×C4—91no—
293C2×C4—91no—
294C2×C4—361no—
295C2×C4—361no—
296C2×C4—361no—
297C2×C4—361no—
298C2×C4—361no—
299C2×C4D4×C3⋊D311yescharacteristic
300C8—91no—
301C8—91no—
302C8C2×C4×C3⋊D311yescharacteristic
303C8D4×C3⋊D311yescharacteristic
304C2×C3—24no—
305C2×C3—84no—
306C2×C3D3×#10214yes—
307D3—64no—
308D3—64no—
309D3—244no—
310C22—41no—
311C22—91no—
312C22—91no—
313C22—361no—
314C22—361no—
315C22—722no—
316C22D8×C3⋊D311yescharacteristic
317C4—41no—
318C4—81no—
319C4—91no—
320C4—91no—
321C4—361no—
322C4—721no—
323C4C22⋊C4×C3⋊D311yescharacteristic
324C4SD16×C3⋊D311yescharacteristic
325C3#6925114yescomplemented
326C2—21no—
327C2—81no—
328C2—181no—
329C2—181no—
330C2—721no—
331C2C3⋊D3×#10211yescharacteristic
subgroupG/H
centerC2C3⋊D3×#102
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#360C2
socleC2×C32C2×#102
prime radicalC3⋊D3×#135C2
cosocleC2×C32×C8C23
hypercenter#360C3⋊D3
hypocenterC32#2145
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×M32C2semidirect
3. #10592559C2semidirect
4. C32×#360C2semidirect
5. #10589432C2semidirect
6. #10589384C2semidirect
7. #10589354C2semidirect
12. #64128C4semidirect
13. Q16×C3⋊D3C4semidirect
16. #64121C4semidirect
17. D8×C3⋊D3C4semidirect
21. C32×M32C22semidirect
22. C32×#106C22semidirect
23. #63644C22semidirect
24. #63639C22semidirect
31. C3×#360D3semidirect
81. C3×M32C2×D3semidirect
82. C3×#106C2×D3semidirect
123. #360C3⋊D3semidirect
186. M32C2×C3⋊D3semidirect
190. #106C2×C3⋊D3semidirect
274. C32#2145semidirect
325. C3#69251semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1352
C3⋊D3×M322
#105925592
C32×#3602
#105894322
#105893842
#105893542
#692513