Finite Group Databasebeta

← C4×#63778 #11783555

Subgroups — C4×#63778 #11783555

Order 1152.

934 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 154 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×C42×C3⋊D3C211yesmaximal, characteristic
2C2×#63778C212yesmaximal
3C2×C4×#622C212yesmaximal, complemented
4#10590207C212yesmaximal, complemented
5C22×C4×C3⋊D3C411yescharacteristic
6C22×C4×C3⋊D3C411yescharacteristic
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#622C2214yes—
9C2×C32×C42C411yescharacteristic
10C2×C4×C3⋊Dic3C411yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C42×C3⋊D3—24no—
14#63778C418yesdirect product factor
15C4×#622—24no—
16C2×C42×D3—62no—
17C23×C3⋊D3C2×C411yescharacteristic
18C22×C32×C4C2×C411yescharacteristic
19C22×C32×C4C2×C411yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C411yescharacteristic
22C22×C3⋊Dic3C2×C411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C2×C4×C3⋊D3—22no—
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3C814yescomplemented
31C2×C4×C3⋊D3C814yescomplemented
32C2×C4×C3⋊D3C2×C414yes—
33C2×#622—24no—
34C2×#622—24no—
35C2×#622C2×C418yescomplemented
36C32×C42—22no—
37C4×C3⋊Dic3—22no—
38C4×C3⋊Dic3—22no—
39C4×C3⋊Dic3D414yes—
40C4×C22⋊C8—91nomaximal, Sylow
41C22×C4×D3—62no—
42C22×C4×D3—62no—
43C22×C4×D3—62no—
44C2×C3×C42—22no—
45C2×C4×Dic3—62no—
46C2×C4×Dic3—62no—
47C2×C4×Dic3—62no—
48C42×D3—616no—
49C23×C32C22×C411yescharacteristic
50C22×C3⋊D3—21no—
51C22×C3⋊D3—21no—
52C22×C3⋊D3—21no—
53C22×C3⋊D3—21no—
54C22×C3⋊D3C4212yes—
55C22×C3⋊D3C2×C812yes—
56C22×C3⋊D3C2×C812yes—
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4C4212yes—
62C2×C32×C4C22⋊C412yes—
63C2×C32×C4C2×C812yes—
64C2×C32×C4C2×C812yes—
65C2×C32×C4M1612yes—
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3C22⋊C412yes—
69C2×C3⋊Dic3C2×C812yes—
70C2×C3⋊Dic3C2×C812yes—
71C2×C3⋊Dic3M1612yes—
72C2×C3⋊Dic3C22×C412yes—
73C2×C3⋊Dic3C2×D412yes—
74C2×C3⋊Dic3#4112yes—
75C4×C3⋊D3—28no—
76C4×C3⋊D3—28no—
77C4×C3⋊D3—28no—
78#622—28no—
79C22×C42—91no—
80C2×C22⋊C8—92no—
81C2×C4×C8—92no—
82#336—92no—
83C23×D3—62no—
84C22×C3×C4—22no—
85C22×C3×C4—22no—
86C22×C3×C4—22no—
87C22×Dic3—62no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C2×C4×D3—68no—
91C2×C4×D3—68no—
92C2×C4×D3—68no—
93C2×C4×D3—68no—
94C2×C4×D3—68no—
95C2×C4×D3—68no—
96C2×C4×D3—68no—
97C2×C4×D3—68no—
98C2×C4×D3—68no—
99C3×C42—28no—
100C4×Dic3—68no—
101C4×Dic3—68no—
102C4×Dic3—68no—
103C22×C32C2×C4211yescharacteristic
104C22×C32C2×C22⋊C411yescharacteristic
105C22×C32#11711yescharacteristic
106C22×C32C22×C811yescharacteristic
107C22×C32C22×C811yescharacteristic
108C22×C32C2×M1611yescharacteristic
109C22×C32C2×M1611yescharacteristic
110C2×C3⋊D3—22no—
111C2×C3⋊D3—22no—
112C2×C3⋊D3—22no—
113C2×C3⋊D3—22no—
114C2×C3⋊D3—22no—
115C2×C3⋊D3—22no—
116C2×C3⋊D3C4×C814yescomplemented
117C32×C4—22no—
118C32×C4—22no—
119C32×C4C22⋊C814yescomplemented
120C3⋊Dic3—22no—
121C3⋊Dic3C22⋊C814yescomplemented
122C3⋊Dic3C4×D414yes—
123C23×C4—91no—
124C23×C4—91no—
125C23×C4—91no—
126C22×C8—94no—
127C2×C42—91no—
128C2×C42—91no—
129C2×C42—91no—
130C2×C42—184no—
131C2×C42#15711yescharacteristic
132C22⋊C8—98no—
133C4×C8—184no—
134C23×C3—22no—
135C22×D3—64no—
136C22×D3—64no—
137C22×D3—64no—
138C22×D3—64no—
139C22×D3—64no—
140C22×D3—64no—
141C22×D3—64no—
142C2×C3×C4—24no—
143C2×C3×C4—24no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×C3×C4—24no—
150C2×C3×C4—24no—
151C2×Dic3—64no—
152C2×Dic3—64no—
153C2×Dic3—64no—
154C2×Dic3—64no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—64no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160C4×D3—632no—
161C4×D3—632no—
162C4×D3—632no—
163C2×C32C4×C22⋊C411yescharacteristic
164C2×C32C2×C4×C811yescharacteristic
165C2×C32C4×M1611yescharacteristic
166C2×C32C2×C22⋊C811yescharacteristic
167C2×C32C2×C22⋊C811yescharacteristic
168C2×C32#43111yescharacteristic
169C2×C32#43111yescharacteristic
170C3⋊D3—24no—
171C24—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—94no—
176C22×C4—94no—
177C22×C4—94no—
178C22×C4—182no—
179C22×C4—182no—
180C22×C4—182no—
181C22×C4—182no—
182C22×C4—182no—
183C22×C4—182no—
184C22×C4C2×#15711yescharacteristic
185C22×C4C2×#15711yescharacteristic
186C22×C4C2×#15711yescharacteristic
187C2×C8—98no—
188C2×C8—184no—
189C2×C8—184no—
190C42—22no—
191C42—94no—
192C42—182no—
193C42—182no—
194C22×C3—22no—
195C22×C3—22no—
196C22×C3—22no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—22no—
200C22×C3—22no—
201C2×D3—68no—
202C2×D3—68no—
203C2×D3—68no—
204C2×D3—68no—
205C2×D3—68no—
206C2×D3—68no—
207C2×D3—68no—
208C3×C4—28no—
209C3×C4—28no—
210C3×C4—28no—
211Dic3—68no—
212Dic3—68no—
213Dic3—68no—
214C32C4×C22⋊C811yescharacteristic, complemented, Sylow
215C23—92no—
216C23—92no—
217C23—92no—
218C23—181no—
219C23—181no—
220C23—181no—
221C23—181no—
222C23C22×#15711yescharacteristic
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—92no—
228C2×C4—92no—
229C2×C4—92no—
230C2×C4—92no—
231C2×C4—92no—
232C2×C4—92no—
233C2×C4—92no—
234C2×C4—188no—
235C2×C4—188no—
236C2×C4—181no—
237C2×C4—181no—
238C2×C4—188no—
239C2×C4#378712yes—
240C2×C4#378712yes—
241C2×C4#378812yes—
242C2×C4C4×#15712yes—
243C2×C4C22⋊#15712yes—
244C8—188no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—22no—
251C2×C3—22no—
252D3—616no—
253C22—94no—
254C22—182no—
255C22—182no—
256C22—182no—
257C22—182no—
258C22—182no—
259C22—182no—
260C22C2×#378711yescharacteristic
261C22C2×#378711yescharacteristic
262C22C2×#378811yescharacteristic
263C22#6428311yescharacteristic
264C22C2×C4×#15711yescharacteristic
265C22#6428611yescharacteristic
266C22C2×C22⋊#15711yescharacteristic
267C4—22no—
268C4—22no—
269C4—94no—
270C4—94no—
271C4—182no—
272C4#6377814yesdirect product factor
273C3—22no—
274C2—184no—
275C2C4×#378711yescharacteristic
276C2C4×#378811yescharacteristic
277C2#1059372511yescharacteristic
278C2#1059372711yescharacteristic
279C2C2×#6377811yescharacteristic
280C2#1059380011yescharacteristic
281C2C4×C22⋊#15711yescharacteristic
subgroupG/H
centerC22×C4C2×#157
commutatorC2×C32C2×C4×C8
FrattiniC23C22×#157
FittingC2×C32×C42C4
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C42#157
hypocenterC32C4×C22⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×C4×#622C2semidirect
4. #10590207C2semidirect
14. #63778C4direct (N × H)
30. C2×C4×C3⋊D3C8semidirect
31. C2×C4×C3⋊D3C8semidirect
35. C2×#622C2×C4semidirect
116. C2×C3⋊D3C4×C8semidirect
119. C32×C4C22⋊C8semidirect
121. C3⋊Dic3C22⋊C8semidirect
214. C32C4×C22⋊C8semidirect
272. C4#63778direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C2×#637782
C2×C4×#6222
#105902072
C4×C22⋊C89