Finite Group Databasebeta

← C3×#71944 #11779330

Subgroups — C3×#71944 #11779330

Order 1152.

554 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C32×#559C211yesmaximal, characteristic
2C3×#5076C211yesmaximal, characteristic
3C3×#5021C212yesmaximal, complemented
4C3×#4544C211yesmaximal, characteristic
5C3×#4535C212yesmaximal, complemented
6C3×#1630—31nomaximal
7#71944C311yesmaximal, characteristic, direct product factor
8C32×#127C2211yescharacteristic
9C32×#124—22no—
10C32×#123—22no—
11C32×C4×Q8C2212yes—
12C32×C4×D4—22no—
13C2×C3×#214—22no—
14C3×#869C2211yescharacteristic
15C3×#835—22no—
16C3×#807—22no—
17C3×C4⋊(C3⋊C8)C2212yes—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×#559—21no—
20C3×#559D311yescharacteristic
21C3×#559C2×C311yescharacteristic
22C3×#492—31no—
23C3×#477—32no—
24#5076C2×C311yescharacteristic
25#5021C2×C312yescomplemented
26C3×#331—31no—
27C3×Q8⋊C8—32no—
28#4544C2×C311yescharacteristic
29#4535C2×C312yescomplemented
30C2×C32×Q8D412yes—
31C2×C32×D4—22no—
32C2×C32×D4D412yes—
33C22×C32×C4—22no—
34C2×C3×Dic6—21no—
35C32×C4⋊C4—22no—
36C32×C4⋊C4D412yes—
37C32×C22⋊C4—24no—
38C32×C22⋊C4—22no—
39C32×C42—22no—
40C32×C42C2311yescharacteristic
41C3×#214—44no—
42C3×C4⋊Dic3—22no—
43C2×C3×C3⋊C8—21no—
44C2×C3×C3⋊C8—22no—
45#1630—31noSylow
46C2×C3×SD16—62no—
47C3×C4⋊Q8—31no—
48C3×#127—21no—
49C3×#127C2×D311yescharacteristic
50C3×#127C22×C311yescharacteristic
51C3×#124—24no—
52C3×#124—22no—
53C3×#124—22no—
54C3×#123—24no—
55C3×#123—22no—
56C3×#123—22no—
57C3×C4×Q8—22no—
58C3×C4×Q8C2×D312yes—
59C3×C4×Q8C22×C312yes—
60C3×C4×D4—24no—
61C3×C4×D4—22no—
62C3×C4×D4—22no—
63C2×#214—22no—
64#869C22×C311yescharacteristic
65C3×#107—62no—
66C3×C4⋊C8—32no—
67C3×#103—62no—
68C3×C4×C8—31no—
69#835—22no—
70#807—22no—
71C4⋊(C3⋊C8)C22×C312yes—
72C4×C3⋊C8C22×C311yescharacteristic
73C23×C32—22no—
74C32×Q8—22no—
75C32×Q8—22no—
76C32×D4—42no—
77C32×D4—42no—
78C32×D4—42no—
79C2×C32×C4—22no—
80C2×C32×C4—22no—
81C2×C32×C4—82no—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D412yes—
84C2×C3×Dic3—41no—
85C3×Dic6—42no—
86C3×C3⋊C8—22no—
87C3×C3⋊C8—42no—
88#559C3×D311yescharacteristic
89#492—31no—
90#477—32no—
91#331—31no—
92Q8⋊C8—32no—
93C2×C3×Q8—22no—
94C2×C3×Q8—61no—
95C2×C3×Q8#6712yes—
96C2×C3×Q8C3×D412yes—
97C2×C3×D4—24no—
98C2×C3×D4—22no—
99C2×C3×D4—22no—
100C2×C3×D4—22no—
101C2×C3×D4#6712yes—
102C2×C3×D4C3×D412yes—
103C22×C3×C4—24no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C2×Dic6—21no—
107C3×SD16—124no—
108C2×C3×C8—61no—
109C2×C3×C8—62no—
110C3×C4⋊C4—24no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—62no—
115C3×C4⋊C4#6712yes—
116C3×C4⋊C4C3×D412yes—
117C3×C22⋊C4—28no—
118C3×C22⋊C4—24no—
119C3×C22⋊C4—24no—
120C3×C22⋊C4—24no—
121C3×C22⋊C4—22no—
122C3×C22⋊C4—22no—
123C3×C42—24no—
124C3×C42—22no—
125C3×C42—22no—
126C3×C42—21no—
127C3×C42C22×D311yescharacteristic
128C3×C42C23×C311yescharacteristic
129#214—44no—
130C4⋊Dic3—22no—
131C2×C3⋊C8—21no—
132C2×C3⋊C8—22no—
133C22×C32—44no—
134C22×C32—42no—
135C22×C32#12011yescharacteristic
136C32×C4—21no—
137C32×C4—42no—
138C32×C4—42no—
139C32×C4#13512yes—
140C32×C4#13712yes—
141C3×Dic3—81no—
142C2×SD16—62no—
143C4⋊Q8—31no—
144#127C2×C3×D311yescharacteristic
145#124—22no—
146#123—22no—
147C4×Q8C2×C3×D312yes—
148C4×D4—22no—
149#107—62no—
150C4⋊C8—32no—
151#103—62no—
152C4×C8—31no—
153C23×C3—24no—
154C23×C3—22no—
155C23×C3—22no—
156C3×Q8—22no—
157C3×Q8—22no—
158C3×Q8—22no—
159C3×Q8—22no—
160C3×Q8—42no—
161C3×Q8—42no—
162C3×Q8—122no—
163C3×D4—42no—
164C3×D4—42no—
165C3×D4—44no—
166C3×D4—44no—
167C3×D4—42no—
168C3×D4—42no—
169C3×D4—42no—
170C3×D4—42no—
171C3×D4—82no—
172C2×C3×C4—24no—
173C2×C3×C4—24no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—21no—
180C2×C3×C4—84no—
181C2×C3×C4—82no—
182C2×C3×C4—82no—
183C2×C3×C4—121no—
184C2×C3×C4C2×#6711yescharacteristic
185C2×C3×C4C2×#6712yes—
186C2×C3×C4C2×C3×D411yescharacteristic
187C2×C3×C4C2×C3×D412yes—
188C2×Dic3—41no—
189Dic6—42no—
190C3×C8—62no—
191C3×C8—122no—
192C3⋊C8—22no—
193C3⋊C8—42no—
194C2×C32—82no—
195C2×C32#45212yes—
196C2×C32#45311yescharacteristic
197C2×Q8—61no—
198C2×Q8C3×#6712yes—
199C2×D4—22no—
200C2×D4C3×#6712yes—
201C22×C4—22no—
202SD16—124no—
203C2×C8—61no—
204C2×C8—62no—
205C4⋊C4—22no—
206C4⋊C4—62no—
207C4⋊C4C3×#6712yes—
208C22⋊C4—24no—
209C22⋊C4—22no—
210C42—22no—
211C42C22×C3×D311yescharacteristic
212C22×C3—21no—
213C22×C3—44no—
214C22×C3—48no—
215C22×C3—44no—
216C22×C3—42no—
217C22×C3—44no—
218C22×C3—42no—
219C22×C3#95311yescharacteristic
220C22×C3C3×#12011yescharacteristic
221C3×C4—21no—
222C3×C4—21no—
223C3×C4—22no—
224C3×C4—22no—
225C3×C4—41no—
226C3×C4—44no—
227C3×C4—44no—
228C3×C4—42no—
229C3×C4—42no—
230C3×C4—42no—
231C3×C4—42no—
232C3×C4—241no—
233C3×C4#95012yes—
234C3×C4#95112yes—
235C3×C4C3×#13512yes—
236C3×C4C3×#13712yes—
237Dic3—81no—
238C32#163011yescharacteristic, complemented, Sylow
239C23—22no—
240Q8—22no—
241Q8—22no—
242Q8—122no—
243D4—42no—
244D4—42no—
245D4—42no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—82no—
249C2×C4—121no—
250C2×C4C2×C3×#6711yescharacteristic
251C2×C4C2×C3×#6712yes—
252C8—62no—
253C8—122no—
254C2×C3—22no—
255C2×C3—21no—
256C2×C3—84no—
257C2×C3—82no—
258C2×C3—82no—
259C2×C3#523912yes—
260C2×C3#524111yescharacteristic
261C2×C3C3×#45212yes—
262C2×C3C3×#45311yescharacteristic
263C22—44no—
264C22—42no—
265C22C3×#95311yescharacteristic
266C4—21no—
267C4—42no—
268C4—42no—
269C4—241no—
270C4C3×#95012yes—
271C4C3×#95112yes—
272C3—21no—
273C3#7194411yescharacteristic, direct product factor
274C3C3×#163011yescharacteristic, complemented
275C2—82no—
276C2C3×#523912yes—
277C2C3×#524111yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#559C2
socleC22×C32#120
prime radicalC32×#127C22
hypercenterC3×#559D3
hypocenterC3C3×#1630
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#559

Complements

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

NH ≅ G/Ntype
3. C3×#5021C2semidirect
5. C3×#4535C2semidirect
7. #71944C3direct (N × H)
25. #5021C2×C3semidirect
29. #4535C2×C3semidirect
238. C32#1630semidirect
273. C3#71944direct (N × H)
274. C3C3×#1630semidirect

Maximal subgroups

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

subgroupindex
C32×#5592
C3×#50762
C3×#50212
C3×#45442
C3×#45352
C3×#16303
#719443