Finite Group Databasebeta

← C4×#63788 #11783781

Subgroups — C4×#63788 #11783781

Order 1152.

786 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 96 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×C4×#638C211yesmaximal, characteristic
2C2×#63788C212yesmaximal
3C4×#3792C212yesmaximal, complemented
4#10590208C212yesmaximal, complemented
5C23×C32×C4C411yescharacteristic
6C22×#638C2211yescharacteristic
7C22×C4×C3⋊D3C411yescharacteristic
8C2×#3792C2214yes—
9C2×#3757C411yescharacteristic
10C4×#638—22no—
11C4×#638—22no—
12C2×#3752C411yescharacteristic
13C2×#3750C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#63788C418yesdirect product factor
16#63777—22no—
17C4×#622—22no—
18C2×C4×#67—62no—
19C24×C32C2×C411yescharacteristic
20C23×C3⋊D3C2×C411yescharacteristic
21C22×C32×C4—21no—
22C22×C32×C4—21no—
23C22×C32×C4—42no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C2×#638—22no—
27C2×#638—22no—
28C2×#638C2×C414yes—
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2311yescharacteristic
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—42no—
35#3792—24no—
36#3792C2×C418yescomplemented
37C2×#622—24no—
38#3757—22no—
39#3752—22no—
40#3750—22no—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3D412yes—
43C4×#100—91nomaximal, Sylow
44C23×C3×C4—22no—
45C22×#67—62no—
46C22×C4×D3—62no—
47C2×#217—62no—
48C4×#67—68no—
49C4×#67—68no—
50C2×(C2×D3)⋊C4—62no—
51C2×Dic3⋊C4—62no—
52C2×C4×Dic3—62no—
53C23×C32—21no—
54C23×C32—21no—
55C23×C32—41no—
56C23×C32—41no—
57C23×C32C4212yes—
58C23×C32C22×C411yescharacteristic
59C22×C3⋊D3—21no—
60C22×C3⋊D3—21no—
61C22×C3⋊D3—41no—
62C22×C3⋊D3—41no—
63C22×C3⋊D3C4212yes—
64C2×C32×C4—22no—
65C2×C32×C4—21no—
66C2×C32×C4—42no—
67C2×C32×C4—42no—
68C2×C32×C4—41no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22⋊C411yescharacteristic
71#638—28no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3C22⋊C412yes—
76C2×C3⋊Dic3C22×C412yes—
77C2×C3⋊Dic3C2×D412yes—
78C2×C3⋊Dic3#4112yes—
79C4×C3⋊D3—42no—
80C4×C3⋊D3—42no—
81#622—28no—
82C2×C4×D4—91no—
83C2×#100—92no—
84C4×M16—92no—
85#343—92no—
86C24×C3—22no—
87C23×D3—62no—
88C22×C3×C4—24no—
89C22×C3×C4—24no—
90C22×C3×C4—22no—
91C22×C3×C4—22no—
92C22×C3×C4—48no—
93C2×#67—68no—
94C2×#67—68no—
95C2×#67—68no—
96C22×Dic3—62no—
97C22×Dic3—62no—
98C22×Dic3—62no—
99C2×C4×D3—64no—
100C2×C4×D3—64no—
101C2×C4×D3—128no—
102#217—68no—
103(C2×D3)⋊C4—68no—
104Dic3⋊C4—68no—
105C4×Dic3—64no—
106C4×Dic3—64no—
107C22×C32—21no—
108C22×C32—21no—
109C22×C32—22no—
110C22×C32—42no—
111C22×C32—42no—
112C22×C32—41no—
113C22×C32—41no—
114C22×C32C2×C4211yescharacteristic
115C22×C32C2×C22⋊C411yescharacteristic
116C22×C32#11711yescharacteristic
117C2×C3⋊D3—22no—
118C2×C3⋊D3—42no—
119C2×C3⋊D3—41no—
120C2×C3⋊D3—41no—
121C2×C3⋊D3—42no—
122C32×C4—21no—
123C32×C4—41no—
124C32×C4#10012yescomplemented
125C3⋊Dic3—22no—
126C3⋊Dic3—41no—
127C3⋊Dic3C4×D414yes—
128C22×D4—91no—
129C23×C4—91no—
130C23×C4#15711yescharacteristic
131C2×M16—94no—
132C4×D4—182no—
133C4×D4—182no—
134C2×C4⋊C4—91no—
135C2×C22⋊C4—91no—
136C2×C22⋊C4—91no—
137C2×C42—91no—
138#100—98no—
139#97—182no—
140C4×C8—182no—
141C23×C3—24no—
142C23×C3—24no—
143C23×C3—22no—
144C23×C3—24no—
145C23×C3—44no—
146C23×C3—44no—
147C22×D3—64no—
148C22×D3—64no—
149C22×D3—64no—
150C22×D3—124no—
151C22×D3—124no—
152C2×C3×C4—28no—
153C2×C3×C4—24no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—48no—
157C2×C3×C4—48no—
158C2×C3×C4—44no—
159#67—632no—
160C2×Dic3—64no—
161C2×Dic3—64no—
162C2×Dic3—64no—
163C2×Dic3—64no—
164C2×Dic3—64no—
165C2×Dic3—124no—
166C2×Dic3—124no—
167C4×D3—128no—
168C4×D3—128no—
169C2×C32—21no—
170C2×C32—21no—
171C2×C32—42no—
172C2×C32C4×C22⋊C411yescharacteristic
173C2×C32C2×#10011yescharacteristic
174C2×C32#41311yescharacteristic
175C3⋊D3—42no—
176C24—91no—
177C24C2×#15711yescharacteristic
178C2×D4—94no—
179C2×D4—182no—
180C2×D4—182no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—42no—
184C22×C4—91no—
185C22×C4—91no—
186C22×C4—91no—
187C22×C4—181no—
188C22×C4—181no—
189C22×C4—362no—
190C22×C4C2×#15711yescharacteristic
191C22×C4C2×#15711yescharacteristic
192M16—98no—
193M16—184no—
194C2×C8—184no—
195C4⋊C4—182no—
196C22⋊C4—182no—
197C22⋊C4—182no—
198C42—92no—
199C42—92no—
200C22×C3—24no—
201C22×C3—24no—
202C22×C3—28no—
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—44no—
207C22×C3—48no—
208C22×C3—48no—
209C22×C3—44no—
210C2×D3—68no—
211C2×D3—124no—
212C2×D3—128no—
213C2×D3—128no—
214C2×D3—124no—
215C3×C4—24no—
216C3×C4—24no—
217C3×C4—44no—
218Dic3—68no—
219Dic3—124no—
220Dic3—124no—
221C32C4×#10011yescharacteristic, complemented, Sylow
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23—92no—
227C23—181no—
228C23—181no—
229C23—361no—
230C23—361no—
231C23C4×#15712yes—
232C23C22×#15711yescharacteristic
233D4—188no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—92no—
240C2×C4—92no—
241C2×C4—92no—
242C2×C4—92no—
243C2×C4—181no—
244C2×C4—362no—
245C2×C4—361no—
246C2×C4—362no—
247C2×C4—361no—
248C2×C4C22⋊#15711yescharacteristic
249C2×C4C22⋊#15711yescharacteristic
250C8—188no—
251C2×C3—24no—
252C2×C3—24no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—22no—
256C2×C3—48no—
257D3—128no—
258C22—21no—
259C22—21no—
260C22—22no—
261C22—42no—
262C22—42no—
263C22—41no—
264C22—41no—
265C22—182no—
266C22—362no—
267C22—362no—
268C22—361no—
269C22—361no—
270C22C2×C4×#15711yescharacteristic
271C22#6428611yescharacteristic
272C22C2×C22⋊#15711yescharacteristic
273C4—21no—
274C4—41no—
275C4—94no—
276C4—182no—
277C4—361no—
278C4#6378812yesdirect product factor
279C3—22no—
280C2—21no—
281C2—21no—
282C2—42no—
283C2—362no—
284C2#1059380811yescharacteristic
285C2C4×C22⋊#15711yescharacteristic
286C2C2×#6378811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC23×C32×C4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C22
cosocleC22×C3⋊Dic3C23
hypercenterC23×C4#157
hypocenterC32C4×#100
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C4×#3792C2semidirect
4. #10590208C2semidirect
15. #63788C4direct (N × H)
36. #3792C2×C4semidirect
124. C32×C4#100semidirect
221. C32C4×#100semidirect
278. C4#63788direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×#637882
C4×#37922
#105902082
C4×#1009