Finite Group Databasebeta

← C4×#63690 #11920232

Subgroups — C4×#63690 #11920232

Order 1152.

458 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 69 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×#63690C211yesmaximal, characteristic
2C4×#41⋊C9C211yesmaximal, characteristic
3#10589528C211yesmaximal, characteristic
4#10589490C212yesmaximal, complemented
5C4×#3688C212yesmaximal, complemented
6C4×#951—31nomaximal
7C2×#41⋊C9C2211yescharacteristic
8#63690C414yesdirect product factor
9C2×#3688C2212yes—
10C4×Dic18—41nomaximal
11C4×Q8⋊C9C2211yescharacteristic
12C4×Q8⋊C9C2211yescharacteristic
13#63421C2212yes—
14C3×C4×#41D311yescharacteristic
15C2×#951—31no—
16C2×C4×Dic6—31no—
17#5232—31no—
18#5030—32no—
19C4×#216—32no—
20#5018—32no—
21C4×#214—32no—
22#5004—31no—
23#4995—31no—
24C4×#208—31no—
25C2×Dic18—41no—
26#41⋊C9C2×C412yes—
27C2×Q8⋊C9C2311yescharacteristic
28#3688C2×C414yescomplemented
29C42×C9—41no—
30C4⋊Dic9—41no—
31Dic9⋊C4—42no—
32C4×Dic9—42no—
33C4×#137—91noSylow
34C2×C3×#41C2×D311yescharacteristic
35C22×Dic6—31no—
36C3×C4×Q8C2×D311yescharacteristic
37C3×C4×Q8C2×D311yescharacteristic
38C3×C4×D4—31no—
39C3×C4×D4—31no—
40C3×#117—31no—
41C2×C3×C42—31no—
42#951—34no—
43#951—34no—
44C2×#216—32no—
45C2×#214—32no—
46C2×C4⋊Dic3—31no—
47C2×Dic3⋊C4—61no—
48C2×C4×Dic3—61no—
49C2×#208—31no—
50C2×#208—31no—
51C4×Dic6—32no—
52C4×Dic6—32no—
53C4×Dic6—61no—
54C4×Dic6—61no—
55#835—32no—
56#832—32no—
57#810—32no—
58#810—32no—
59#808—32no—
60#807—32no—
61#803—32no—
62C4×C3⋊C8—32no—
63C2×C4×C9—41no—
64C2×C4×C9—41no—
65C2×C4×C9—41no—
66C2×Dic9—42no—
67C2×Dic9—42no—
68Dic18—44no—
69Q8⋊C9C22×C411yescharacteristic
70C2×#137—91no—
71C4×#41D911yescharacteristic
72C2×C4×Q8—91no—
73#441—92no—
74#440—92no—
75C4×Q16—92no—
76C4×SD16—92no—
77#428—91no—
78#419—91no—
79#417—91no—
80C4×M16—91no—
81C3×#41—32no—
82C3×#41C4×D312yes—
83C2×C3×Q8C22×D311yescharacteristic
84C2×C3×D4—31no—
85C22×C3×C4—31no—
86C22×C3×C4—31no—
87C22×C3×C4—31no—
88C22×Dic3—61no—
89C22×Dic3—61no—
90C2×Dic6—32no—
91C2×Dic6—34no—
92C2×Dic6—62no—
93C2×Dic6—61no—
94C3×C4⋊C4—31no—
95C3×C4⋊C4—31no—
96C3×C22⋊C4—61no—
97C3×C42—31no—
98C3×C42—31no—
99C3×C42—31no—
100C3×C42S411yescharacteristic
101#216—34no—
102#216—34no—
103#214—38no—
104C4⋊Dic3—32no—
105C4⋊Dic3—61no—
106Dic3⋊C4—62no—
107Dic3⋊C4—62no—
108C4×Dic3—62no—
109C4×Dic3—62no—
110#208—34no—
111#208—62no—
112C2×C3⋊C8—32no—
113C2×C3⋊C8—32no—
114C22×C9—41no—
115C4×C9—42no—
116C4×C9—42no—
117C4×C9—81no—
118Dic9—44no—
119Dic9—82no—
120C2×#41C2×D911yescharacteristic
121C22×Q8—91no—
122#137—94no—
123#137—94no—
124C2×Q16—92no—
125C2×SD16—92no—
126C2×M16—91no—
127C2×M16—91no—
128C4×Q8—92no—
129C4×Q8—92no—
130C4×Q8—181no—
131C4×Q8—181no—
132C4×Q8C2×D911yescharacteristic
133C4×Q8C2×D911yescharacteristic
134C4×D4—31no—
135C4×D4—31no—
136#117—31no—
137C2×C4⋊C4—91no—
138C2×C4⋊C4—181no—
139C2×C42—31no—
140C2×C42—181no—
141#107—92no—
142#106—92no—
143#103—92no—
144#103—92no—
145#103—92no—
146#102—92no—
147#97—92no—
148C4×C8—92no—
149C23×C3—31no—
150C3×Q8—31no—
151C3×Q8C2×C4×D311yescharacteristic
152C3×D4—32no—
153C3×D4—61no—
154C2×C3×C4—31no—
155C2×C3×C4—32no—
156C2×C3×C4—32no—
157C2×C3×C4—31no—
158C2×C3×C4—31no—
159C2×C3×C4—62no—
160C2×C3×C4—121no—
161C2×C3×C4C2×S411yescharacteristic
162C2×C3×C4C2×S411yescharacteristic
163C2×C3×C4C2×S411yescharacteristic
164C2×Dic3—64no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—122no—
168Dic6—34no—
169Dic6—62no—
170Dic6—64no—
171C3⋊C8—34no—
172C3⋊C8—62no—
173C2×C9—41no—
174C2×C9—41no—
175C2×C9—41no—
176#41—32no—
177#41C4×D912yes—
178C2×Q8—92no—
179C2×Q8—94no—
180C2×Q8—182no—
181C2×Q8—181no—
182C2×Q8C22×D911yescharacteristic
183C2×D4—31no—
184C22×C4—31no—
185C22×C4—31no—
186C22×C4—31no—
187C22×C4—181no—
188C22×C4—181no—
189Q16—94no—
190Q16—94no—
191SD16—98no—
192M16—94no—
193M16—182no—
194C2×C8—92no—
195C2×C8—92no—
196C4⋊C4—31no—
197C4⋊C4—31no—
198C4⋊C4—92no—
199C4⋊C4—182no—
200C4⋊C4—181no—
201C4⋊C4—182no—
202C22⋊C4—61no—
203C42—31no—
204C42—31no—
205C42—31no—
206C42—182no—
207C42—182no—
208C42(C22⋊C9)⋊C211yescharacteristic
209C22×C3—32no—
210C22×C3—61no—
211C22×C3—61no—
212C22×C3C22×S411yescharacteristic
213C3×C4—21no—
214C3×C4—31no—
215C3×C4—31no—
216C3×C4—61no—
217C3×C4—61no—
218C3×C4C4×S412yes—
219C3×C4#98412yes—
220Dic3—64no—
221Dic3—122no—
222C9—41noSylow
223C23—31no—
224Q8—31no—
225Q8—94no—
226Q8—182no—
227Q8—184no—
228Q8C2×C4×D911yescharacteristic
229D4—32no—
230D4—61no—
231C2×C4—31no—
232C2×C4—32no—
233C2×C4—32no—
234C2×C4—31no—
235C2×C4—31no—
236C2×C4—62no—
237C2×C4—121no—
238C2×C4—184no—
239C2×C4—182no—
240C2×C4—182no—
241C2×C4—362no—
242C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
243C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
244C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
245C8—94no—
246C8—182no—
247C2×C3—62no—
248C2×C3C2×C4×S411yescharacteristic
249C2×C3C2×#98411yescharacteristic
250C2×C3#592311yescharacteristic
251C22—32no—
252C22—61no—
253C22—61no—
254C22C22×(C22⋊C9)⋊C211yescharacteristic
255C4—21no—
256C4—31no—
257C4—31no—
258C4—61no—
259C4—61no—
260C4—184no—
261C4—362no—
262C4C4×(C22⋊C9)⋊C212yes—
263C4#6369012yesdirect product factor
264C3C4×#98411yescharacteristic
265C2—62no—
266C2C2×C4×(C22⋊C9)⋊C211yescharacteristic
267C2C2×#6369011yescharacteristic
268C2#1059309811yescharacteristic
subgroupG/H
centerC2×C4C2×(C22⋊C9)⋊C2
commutator, hypocenterQ8⋊C9C22×C4
Frattini, socleC22×C3C22×S4
FittingC3×C4×#41D3
prime radicalC2×C3×#41C2×D3
cosocleC2×Q8⋊C9C23
hypercenterC42(C22⋊C9)⋊C2
LCSG ▷ Q8⋊C9
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10589490C2semidirect
5. C4×#3688C2semidirect
8. #63690C4direct (N × H)
28. #3688C2×C4semidirect
263. C4#63690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#636902
C4×#41⋊C92
#105895282
#105894902
C4×#36882
C4×#9513
C4×Dic184