Finite Group Databasebeta

← C4×#63692 #11920241

Subgroups — C4×#63692 #11920241

Order 1152.

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

normal subgroups only

This group has 534 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×#63692C211yesmaximal, characteristic
2C4×#41⋊C9C211yesmaximal, characteristic, complemented
3#10589528C211yesmaximal, characteristic, complemented
4#10589496C212yesmaximal, complemented
5C4×#3689C212yesmaximal, complemented
6C4×#949—31nomaximal
7C2×#41⋊C9C2211yescharacteristic
8#63692C414yesdirect product factor
9C2×#3689C2212yes—
10C4×D36—41nomaximal
11C4×Q8⋊C9C2211yescharacteristic, complemented
12C4×Q8⋊C9C2211yescharacteristic, complemented
13#63421C2212yescomplemented
14C3×C4×#41D311yescharacteristic
15C2×#949—31no—
16C2×C4×D12—31no—
17#5232—31no—
18#5026—32no—
19C4×#215—32no—
20#5014—32no—
21C4×#213—32no—
22#5001—31no—
23#4995—31no—
24C4×#208—31no—
25C2×D36—41no—
26C2×C4×D9—42no—
27#41⋊C9C2×C412yescomplemented
28C2×Q8⋊C9C2311yescharacteristic
29#3689C2×C414yescomplemented
30C42×C9—41no—
31(C2×D9)⋊C4—42no—
32C4⋊Dic9—41no—
33C4×AGL(1,ℤ/8)—91noSylow
34C2×C3×#41C2×D311yescharacteristic
35C22×D12—31no—
36C22×C4×D3—61no—
37C3×C4×Q8C2×D311yescharacteristic
38C3×C4×Q8C2×D311yescharacteristic
39C3×C4×D4—31no—
40C3×C4×D4—31no—
41C3×#117—31no—
42C2×C3×C42—31no—
43#949—34no—
44#949—34no—
45C2×#215—32no—
46C2×#213—32no—
47C2×(C2×D3)⋊C4—61no—
48C2×C4⋊Dic3—31no—
49C2×#208—31no—
50C2×#208—31no—
51C4×D12—32no—
52C4×D12—32no—
53C4×D12—61no—
54C4×D12—61no—
55#835—32no—
56#832—32no—
57#809—32no—
58#809—32no—
59#808—32no—
60#807—32no—
61#803—32no—
62C4×C3⋊C8—32no—
63C22×D9—42no—
64C2×C4×C9—41no—
65C2×C4×C9—41no—
66C2×C4×C9—41no—
67C2×Dic9—42no—
68D36—44no—
69C4×D9—84no—
70Q8⋊C9C22×C411yescharacteristic, complemented
71C2×AGL(1,ℤ/8)—91no—
72C4×#41D911yescharacteristic, complemented
73C2×C4×D4—91no—
74#442—92no—
75#440—92no—
76C4×SD16—92no—
77C4×D8—92no—
78#428—91no—
79#418—91no—
80#417—91no—
81C4×M16—91no—
82C23×D3—61no—
83C3×#41—32no—
84C3×#41C4×D312yes—
85C2×C3×Q8C22×D311yescharacteristic
86C2×C3×D4—31no—
87C22×C3×C4—31no—
88C22×C3×C4—31no—
89C22×C3×C4—31no—
90C22×Dic3—61no—
91C2×D12—32no—
92C2×D12—34no—
93C2×D12—62no—
94C2×D12—61no—
95C2×C4×D3—62no—
96C2×C4×D3—62no—
97C2×C4×D3—124no—
98C3×C4⋊C4—31no—
99C3×C4⋊C4—31no—
100C3×C22⋊C4—61no—
101C3×C42—31no—
102C3×C42—31no—
103C3×C42—31no—
104C3×C42S411yescharacteristic
105#215—34no—
106#215—34no—
107#213—38no—
108(C2×D3)⋊C4—62no—
109(C2×D3)⋊C4—62no—
110C4⋊Dic3—32no—
111C4⋊Dic3—61no—
112#208—34no—
113#208—62no—
114C2×C3⋊C8—32no—
115C2×C3⋊C8—32no—
116C22×C9—41no—
117C2×D9—44no—
118C2×D9—82no—
119C2×D9—82no—
120C4×C9—42no—
121C4×C9—42no—
122C4×C9—81no—
123Dic9—82no—
124C2×#41C2×D911yescharacteristic
125C22×D4—91no—
126C23×C4—181no—
127AGL(1,ℤ/8)—94no—
128AGL(1,ℤ/8)—94no—
129C2×SD16—92no—
130C2×D8—92no—
131C2×M16—91no—
132C2×M16—91no—
133C4×Q8C2×D911yescharacteristic
134C4×Q8C2×D911yescharacteristic
135C4×D4—31no—
136C4×D4—31no—
137C4×D4—92no—
138C4×D4—92no—
139C4×D4—181no—
140C4×D4—181no—
141#117—31no—
142C2×C4⋊C4—91no—
143C2×C22⋊C4—181no—
144C2×C42—31no—
145#107—92no—
146#106—92no—
147#103—92no—
148#102—92no—
149#102—92no—
150#102—92no—
151#97—92no—
152C4×C8—92no—
153C23×C3—31no—
154C22×D3—64no—
155C22×D3—62no—
156C22×D3—122no—
157C22×D3—122no—
158C3×Q8—31no—
159C3×Q8C2×C4×D311yescharacteristic
160C3×D4—32no—
161C3×D4—61no—
162C2×C3×C4—31no—
163C2×C3×C4—32no—
164C2×C3×C4—32no—
165C2×C3×C4—31no—
166C2×C3×C4—31no—
167C2×C3×C4—62no—
168C2×C3×C4—121no—
169C2×C3×C4C2×S411yescharacteristic
170C2×C3×C4C2×S411yescharacteristic
171C2×C3×C4C2×S411yescharacteristic
172C2×Dic3—62no—
173C2×Dic3—122no—
174D12—34no—
175D12—62no—
176D12—64no—
177C4×D3—124no—
178C4×D3—124no—
179C3⋊C8—34no—
180C3⋊C8—62no—
181C2×C9—41no—
182C2×C9—41no—
183C2×C9—41no—
184D9—84no—
185C24—181no—
186#41—32no—
187#41C4×D912yescomplemented
188C2×Q8C22×D911yescharacteristic
189C2×D4—31no—
190C2×D4—92no—
191C2×D4—94no—
192C2×D4—182no—
193C2×D4—181no—
194C22×C4—31no—
195C22×C4—31no—
196C22×C4—31no—
197C22×C4—182no—
198C22×C4—181no—
199C22×C4—182no—
200C22×C4—364no—
201SD16—94no—
202SD16—94no—
203D8—98no—
204M16—94no—
205M16—182no—
206C2×C8—92no—
207C2×C8—92no—
208C4⋊C4—31no—
209C4⋊C4—31no—
210C4⋊C4—92no—
211C4⋊C4—181no—
212C22⋊C4—61no—
213C22⋊C4—182no—
214C22⋊C4—182no—
215C42—31no—
216C42—31no—
217C42—31no—
218C42(C22⋊C9)⋊C211yescharacteristic
219C22×C3—32no—
220C22×C3—61no—
221C22×C3—61no—
222C22×C3C22×S411yescharacteristic
223C2×D3—64no—
224C2×D3—128no—
225C2×D3—122no—
226C2×D3—122no—
227C3×C4—21no—
228C3×C4—31no—
229C3×C4—31no—
230C3×C4—61no—
231C3×C4—61no—
232C3×C4C4×S412yes—
233C3×C4#98612yes—
234Dic3—122no—
235C9—41noSylow
236C23—31no—
237C23—184no—
238C23—182no—
239C23—362no—
240C23—362no—
241Q8—31no—
242Q8C2×C4×D911yescharacteristic
243D4—32no—
244D4—61no—
245D4—94no—
246D4—182no—
247D4—184no—
248C2×C4—31no—
249C2×C4—32no—
250C2×C4—32no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—62no—
254C2×C4—121no—
255C2×C4—182no—
256C2×C4—364no—
257C2×C4—362no—
258C2×C4—364no—
259C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
260C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
261C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
262C8—94no—
263C8—182no—
264C2×C3—62no—
265C2×C3C2×C4×S411yescharacteristic
266C2×C3C2×#98611yescharacteristic
267C2×C3#592311yescharacteristic
268D3—124no—
269C22—32no—
270C22—61no—
271C22—61no—
272C22—184no—
273C22—368no—
274C22—362no—
275C22—362no—
276C22C22×(C22⋊C9)⋊C211yescharacteristic
277C4—21no—
278C4—31no—
279C4—31no—
280C4—61no—
281C4—61no—
282C4—362no—
283C4C4×(C22⋊C9)⋊C212yes—
284C4#6369212yesdirect product factor
285C3C4×#98611yescharacteristic
286C2—62no—
287C2—364no—
288C2C2×C4×(C22⋊C9)⋊C211yescharacteristic
289C2C2×#6369211yescharacteristic
290C2#1059309811yescharacteristic
subgroupG/H
centerC2×C4C2×(C22⋊C9)⋊C2
commutator, hypocenterQ8⋊C9C22×C4
Frattini, socleC22×C3C22×S4
FittingC3×C4×#41D3
prime radicalC2×#63692C2
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
2. C4×#41⋊C9C2semidirect
3. #10589528C2semidirect
4. #10589496C2semidirect
5. C4×#3689C2semidirect
8. #63692C4direct (N × H)
11. C4×Q8⋊C9C22semidirect
12. C4×Q8⋊C9C22semidirect
13. #63421C22semidirect
27. #41⋊C9C2×C4semidirect
29. #3689C2×C4semidirect
70. Q8⋊C9C22×C4semidirect
72. C4×#41D9semidirect
187. #41C4×D9semidirect
284. C4#63692direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#636922
C4×#41⋊C92
#105895282
#105894962
C4×#36892
C4×#9493
C4×D364