Finite Group Databasebeta

← C4×#63785 #11783872

Subgroups — C4×#63785 #11783872

Order 1152.

670 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C4×#3832C211yesmaximal, characteristic
2C2×#63785C212yesmaximal
3C42×#157C211yesmaximal, characteristic, complemented
4C4×#3788C211yesmaximal, characteristic, complemented
5#10590164C212yesmaximal, complemented
6C2×#3832C2211yescharacteristic
7C2×C4×#157—21no—
8C2×C4×#157—21no—
9C2×C4×#157C2212yes—
10C2×#3788C2212yes—
11C32×C4×Q8C411yescharacteristic, complemented
12Q8×C3⋊Dic3C411yescharacteristic, complemented
13#64102—21no—
14#64102C411yescharacteristic, complemented
15#64101—21no—
16#64101C2211yescharacteristic
17C4×C4⋊(C3⋊D3)—21no—
18C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
19C42×C3⋊D3—21no—
20C42×C3⋊D3C2211yescharacteristic
21#63785C418yesdirect product factor
22#63777—21no—
23C4×#622—21no—
24C4×#239—62no—
25C22×#157—22no—
26C2×C32×Q8C2×C411yescharacteristic
27#3832—22no—
28#3832C2×C414yes—
29C2×C4⋊(C3⋊D3)—21no—
30C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×#622—22no—
38C4×#157—24no—
39C4×#157—24no—
40C4×#157—22no—
41C4×#157C2×C414yescomplemented
42#3788—22no—
43#3788C2×C414yescomplemented
44C32×C4⋊C4—21no—
45C32×C4⋊C4C2×C411yescharacteristic
46C32×C42—21no—
47C32×C42C2×C411yescharacteristic
48#3752—21no—
49#3752—21no—
50#3752—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3C2×C411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C4×#104—91nomaximal, Sylow
59C2×#239—62no—
60C3×C4×Q8—22no—
61Q8×Dic3—62no—
62#893—62no—
63#893—64no—
64#892—62no—
65#892—64no—
66C4×D12—62no—
67C4×D12—64no—
68C42×D3—62no—
69C42×D3—64no—
70C22×C3⋊D3—21no—
71C22×C3⋊D3C2×D411yescharacteristic
72C2×#157—24no—
73C2×#157—24no—
74C2×#157—24no—
75C32×Q8—21no—
76C32×Q8C4212yescomplemented
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22×C411yescharacteristic
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C2×D411yescharacteristic
86C4⋊(C3⋊D3)—24no—
87C4⋊(C3⋊D3)—21no—
88C4⋊(C3⋊D3)C4212yescomplemented
89C4×C3⋊D3—24no—
90C4×C3⋊D3—22no—
91C4×C3⋊D3—22no—
92C4×C3⋊D3—42no—
93C4×C3⋊D3—42no—
94C4×C3⋊D3C22×C412yes—
95C4×C3⋊D3#4112yes—
96#622—24no—
97C4×#41—91no—
98C2×#104—92no—
99C4×M16—91no—
100C43—91no—
101#339—92no—
102C2×C3×Q8—22no—
103#239—68no—
104#239—68no—
105C2×D12—62no—
106C2×D12—64no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×C4×D3—64no—
111C2×C4×D3—64no—
112C2×C4×D3—64no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—22no—
115C3×C42—24no—
116C3×C42—22no—
117(C2×D3)⋊C4—64no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—64no—
120C4⋊Dic3—62no—
121C4⋊Dic3—64no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C4×Dic3—64no—
126C4×Dic3—64no—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3⋊D3—22no—
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—41no—
132C2×C3⋊D3—41no—
133C2×C3⋊D3C4×D412yes—
134#157—28no—
135C32×C4—22no—
136C32×C4—21no—
137C32×C4—41no—
138C32×C4#10412yescomplemented
139C32×C4C2×C4211yescharacteristic
140C32×C4#11711yescharacteristic
141C3⋊Dic3—21no—
142C3⋊Dic3—41no—
143C3⋊Dic3#10412yescomplemented
144C3⋊Dic3C4×D412yes—
145C2×#41—91no—
146C2×M16—92no—
147C4×Q8—91no—
148C4×Q8#15711yescharacteristic, complemented
149C4×D4—91no—
150C4×D4—91no—
151C4×D4—181no—
152C4×D4—181no—
153#117—91no—
154#117—181no—
155C2×C42—91no—
156C2×C42—92no—
157C2×C42—181no—
158C2×C42—181no—
159C2×C42—181no—
160#104—98no—
161#97—181no—
162C4×C8—181no—
163C22×D3—62no—
164C22×D3—64no—
165C3×Q8—24no—
166C3×Q8—24no—
167C2×C3×C4—24no—
168C2×C3×C4—24no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—64no—
176D12—64no—
177D12—616no—
178D12—64no—
179C4×D3—64no—
180C4×D3—64no—
181C4×D3—616no—
182C4×D3—124no—
183C4×D3—124no—
184C4×D3—128no—
185C4×D3—128no—
186C2×C32C4×C22⋊C411yescharacteristic
187C2×C32C2×#10411yescharacteristic
188C2×C32C2×#10411yescharacteristic
189C3⋊D3—22no—
190C3⋊D3—42no—
191#41—94no—
192#41—182no—
193C2×Q8C2×#15711yescharacteristic
194C2×D4—91no—
195C2×D4—181no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—91no—
199C22×C4—181no—
200C22×C4—181no—
201C22×C4—182no—
202C22×C4—181no—
203M16—94no—
204M16—182no—
205C2×C8—182no—
206C4⋊C4—21no—
207C4⋊C4—91no—
208C4⋊C4—181no—
209C4⋊C4C2×#15711yescharacteristic
210C22⋊C4—181no—
211C22⋊C4—181no—
212C22⋊C4—181no—
213C42—21no—
214C42—91no—
215C42—91no—
216C42—91no—
217C42—94no—
218C42—181no—
219C42—181no—
220C42—182no—
221C42—184no—
222C42—184no—
223C42C2×#15711yescharacteristic
224C22×C3—22no—
225C2×D3—64no—
226C2×D3—68no—
227C2×D3—122no—
228C2×D3—122no—
229C2×D3—124no—
230C2×D3—124no—
231C3×C4—28no—
232C3×C4—22no—
233C3×C4—22no—
234C3×C4—24no—
235C3×C4—42no—
236C3×C4—44no—
237Dic3—64no—
238Dic3—64no—
239Dic3—122no—
240Dic3—124no—
241C32C4×#10411yescharacteristic, complemented, Sylow
242C23—91no—
243C23—181no—
244Q8—21no—
245Q8C4×#15712yescomplemented
246D4—92no—
247D4—184no—
248D4—181no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—92no—
254C2×C4—92no—
255C2×C4—91no—
256C2×C4—182no—
257C2×C4—184no—
258C2×C4—184no—
259C2×C4—184no—
260C2×C4—184no—
261C2×C4—182no—
262C2×C4—181no—
263C2×C4—362no—
264C2×C4—362no—
265C2×C4C22⋊#15711yescharacteristic
266C2×C4C22⋊#15711yescharacteristic
267C2×C4C22×#15711yescharacteristic
268C8—184no—
269C2×C3—22no—
270C2×C3—22no—
271C2×C3—22no—
272D3—124no—
273D3—128no—
274C22—92no—
275C22—181no—
276C22—181no—
277C22—182no—
278C22—361no—
279C22—361no—
280C22C2×C22⋊#15711yescharacteristic
281C4—22no—
282C4—21no—
283C4—41no—
284C4—92no—
285C4—92no—
286C4—188no—
287C4—181no—
288C4—361no—
289C4#6378512yesdirect product factor
290C4C2×C4×#15711yescharacteristic
291C4#6428611yescharacteristic
292C3—22no—
293C2—182no—
294C2—362no—
295C2C4×C22⋊#15711yescharacteristic
296C2C2×#6378511yescharacteristic
297C2#1059383911yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3832C22
cosocleC2×C4×C3⋊D3C23
hypercenterC4×Q8#157
hypocenterC32C4×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. C42×#157C2semidirect
4. C4×#3788C2semidirect
5. #10590164C2semidirect
11. C32×C4×Q8C4semidirect
12. Q8×C3⋊Dic3C4semidirect
14. #64102C4semidirect
18. C4×C4⋊(C3⋊D3)C4semidirect
21. #63785C4direct (N × H)
41. C4×#157C2×C4semidirect
43. #3788C2×C4semidirect
76. C32×Q8C42semidirect
88. C4⋊(C3⋊D3)C42semidirect
138. C32×C4#104semidirect
143. C3⋊Dic3#104semidirect
148. C4×Q8#157semidirect
241. C32C4×#104semidirect
245. Q8C4×#157semidirect
289. C4#63785direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#38322
C2×#637852
C42×#1572
C4×#37882
#105901642
C4×#1049