Finite Group Databasebeta

← C4⋊C4×#622 #11784258

Subgroups — C4⋊C4×#622 #11784258

Order 1152.

490 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 146 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⋊#622C211yesmaximal, characteristic
2C2×C4×#622C212yesmaximal
3C2×C4×#622C211yesmaximal, characteristic
4C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
5#10590207C212yesmaximal
6C22×#622C2212yes—
7C22×#622C2211yescharacteristic
8C22×#622C2211yescharacteristic
9C2×C32×C4⋊C4C411yescharacteristic
10C2×C4⋊(C3⋊Dic3)C411yescharacteristic
11C2×C4×C3⋊Dic3C2212yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C4⋊#622C414yescomplemented
14C4×#622—24no—
15C4×#622C414yescomplemented
16#63658C412yes—
17Dic3×C4⋊C4—62no—
18C22×C32×C4C2×C412yes—
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C412yes—
22C22×C3⋊Dic3C2311yescharacteristic
23C2×#622—22no—
24C2×#622—21no—
25C2×#622—21no—
26C2×#622—22no—
27C2×#622C2×C412yes—
28C2×#622C2×C414yes—
29C2×#622C2×C412yes—
30C2×#622D412yes—
31C2×#622Q812yes—
32C32×C4⋊C4C814yescomplemented
33C4⋊(C3⋊Dic3)C814yescomplemented
34C4×C3⋊Dic3—22no—
35C4×C3⋊Dic3—22no—
36C4×C3⋊Dic3C2×C412yes—
37C4×C3⋊Dic3C2×C412yes—
38C8×C4⋊C4—91nomaximal, Sylow
39C2×C3×C4⋊C4—22no—
40C2×C4⋊Dic3—62no—
41C2×C4×Dic3—62no—
42C2×C4×Dic3—64no—
43C3⋊#95—64no—
44C23×C32C22×C411yescharacteristic
45C2×C32×C4—22no—
46C2×C32×C4—22no—
47C2×C32×C4C4212yes—
48C2×C32×C4C2×C814yes—
49C2×C32×C4C2×C812yes—
50C2×C32×C4C2×C812yes—
51C2×C3⋊Dic3—22no—
52C2×C3⋊Dic3—21no—
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3—22no—
55C2×C3⋊Dic3C4212yes—
56C2×C3⋊Dic3C2×C814yes—
57C2×C3⋊Dic3C22×C411yescharacteristic
58C2×C3⋊Dic3C22×C411yescharacteristic
59C2×C3⋊Dic3C2×D411yescharacteristic
60C2×C3⋊Dic3C2×Q811yescharacteristic
61C2×C3⋊Dic3#4111yescharacteristic
62C2×C3⋊Dic3#4111yescharacteristic
63#622—22no—
64#622—24no—
65#622C4⋊C414yesdirect product factor
66C2×C4⋊C8—91no—
67C2×C4×C8—91no—
68C2×C4×C8—92no—
69C4×C4⋊C4—91no—
70#336—92no—
71C22×C3×C4—22no—
72C22×C3×C4—24no—
73C22×Dic3—62no—
74C22×Dic3—62no—
75C22×Dic3—64no—
76C3×C4⋊C4—28no—
77C4⋊Dic3—68no—
78C4×Dic3—64no—
79C4×Dic3—64no—
80C4×Dic3—124no—
81C4×Dic3—124no—
82C22×C32C2×C4211yescharacteristic
83C22×C32C4×D411yescharacteristic
84C22×C32C4×Q811yescharacteristic
85C22×C32C22×C811yescharacteristic
86C22×C32C22×C811yescharacteristic
87C22×C32#13111yescharacteristic
88C22×C32#13111yescharacteristic
89C32×C4—24no—
90C32×C4C4×C814yescomplemented
91C3⋊Dic3—22no—
92C3⋊Dic3—24no—
93C3⋊Dic3C2×C4⋊C411yescharacteristic
94C3⋊Dic3#11711yescharacteristic
95C3⋊Dic3C4×D411yescharacteristic
96C3⋊Dic3C4×Q811yescharacteristic
97C22×C8—91no—
98C22×C8—91no—
99C22×C8—92no—
100C2×C4⋊C4—91no—
101C2×C4⋊C4#15711yescharacteristic
102C2×C42—91no—
103C2×C42—92no—
104C4⋊C8—94no—
105C4×C8—94no—
106C4×C8—184no—
107#95—92no—
108C23×C3—22no—
109C2×C3×C4—24no—
110C2×C3×C4—24no—
111C2×C3×C4—24no—
112C2×C3×C4—28no—
113C2×C3×C4—44no—
114C2×C3×C4—44no—
115C2×Dic3—62no—
116C2×Dic3—62no—
117C2×Dic3—62no—
118C2×Dic3—62no—
119C2×Dic3—62no—
120C2×Dic3—62no—
121C2×Dic3—64no—
122C2×Dic3—68no—
123C2×Dic3—124no—
124C2×Dic3—122no—
125C2×Dic3—122no—
126C2×Dic3—124no—
127C2×C32C4×C4⋊C411yescharacteristic
128C2×C32C2×C4×C811yescharacteristic
129C2×C32#40511yescharacteristic
130C2×C32C8×D411yescharacteristic
131C2×C32C8×D411yescharacteristic
132C2×C32C8×Q811yescharacteristic
133C2×C32C8×Q811yescharacteristic
134C22×C4—91no—
135C22×C4—91no—
136C22×C4—92no—
137C22×C4C2×#15712yes—
138C22×C4C2×#15711yescharacteristic
139C2×C8—92no—
140C2×C8—92no—
141C2×C8—92no—
142C2×C8—92no—
143C2×C8—94no—
144C2×C8—182no—
145C2×C8—181no—
146C2×C8—181no—
147C2×C8—182no—
148C4⋊C4—94no—
149C4⋊C4#62214yesdirect product factor
150C42—92no—
151C42—92no—
152C42—182no—
153C42—182no—
154C22×C3—22no—
155C22×C3—22no—
156C22×C3—22no—
157C22×C3—22no—
158C22×C3—22no—
159C22×C3—22no—
160C22×C3—22no—
161C3×C4—28no—
162C3×C4—48no—
163Dic3—62no—
164Dic3—62no—
165Dic3—62no—
166Dic3—62no—
167Dic3—124no—
168Dic3—128no—
169C32C8×C4⋊C411yescharacteristic, complemented, Sylow
170C23C22×#15711yescharacteristic
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—91no—
179C2×C4—94no—
180C2×C4—92no—
181C2×C4—181no—
182C2×C4—182no—
183C2×C4—181no—
184C2×C4—182no—
185C2×C4#378712yes—
186C2×C4C4×#15712yes—
187C2×C4C2×#62214yes—
188C2×C4C2×#62212yes—
189C8—94no—
190C8—184no—
191C8—182no—
192C2×C3—22no—
193C2×C3—22no—
194C2×C3—22no—
195C2×C3—22no—
196C2×C3—22no—
197C2×C3—22no—
198C2×C3—22no—
199C22C2×#378711yescharacteristic
200C22C2×C4×#15711yescharacteristic
201C22#6428711yescharacteristic
202C22D4×#15711yescharacteristic
203C22#6428911yescharacteristic
204C22Q8×#15711yescharacteristic
205C22C22×#62211yescharacteristic
206C4—24no—
207C4—91no—
208C4—91no—
209C4—91no—
210C4—91no—
211C4—182no—
212C4—184no—
213C4C4×#62214yescomplemented
214C3—22no—
215C2#1059374811yescharacteristic
216C2#1059374911yescharacteristic
217C2#1059375011yescharacteristic
218C2C4⋊C4×#15711yescharacteristic
219C2C2×C4×#62211yescharacteristic
220C2D4×#62211yescharacteristic
221C2Q8×#62211yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC2×C32C2×C4×C8
FittingC2×C32×C4⋊C4C4
socle, prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32C8×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. C4⋊#622C4semidirect
15. C4×#622C4semidirect
32. C32×C4⋊C4C8semidirect
33. C4⋊(C3⋊Dic3)C8semidirect
65. #622C4⋊C4direct (N × H)
90. C32×C4C4×C8semidirect
149. C4⋊C4#622direct (N × H)
169. C32C8×C4⋊C4semidirect
213. C4C4×#622semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#6222
C2×C4×#6222
C4⋊C4×C3⋊Dic32
#105902072
C8×C4⋊C49