Finite Group Databasebeta

← C3×#71943 #11778919

Subgroups — C3×#71943 #11778919

Order 1152.

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

normal subgroups only

This group has 598 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, complemented
2C3×#5073C211yesmaximal, characteristic
3C3×#5027C212yesmaximal, complemented
4C3×#4544C211yesmaximal, characteristic, complemented
5C3×#4535C212yesmaximal, complemented
6C3×#1620—31nomaximal
7#71943C311yesmaximal, characteristic, direct product factor
8C32×#127C2211yescharacteristic
9C32×#124—22no—
10C32×#123—22no—
11C32×C4×Q8C2212yes—
12C32×C4×D4—22no—
13C2×C3×#215—22no—
14C2×C3×#213—22no—
15C3×#874C2211yescharacteristic
16C3×#809—22no—
17C3×C4⋊(C3⋊C8)C2212yes—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×#559—21no—
20C3×#559D311yescharacteristic, complemented
21C3×#559C2×C311yescharacteristic, complemented
22C3×#493—31no—
23C3×#460—32no—
24#5073C2×C311yescharacteristic
25#5027C2×C312yescomplemented
26C3×#331—31no—
27C3×Q8⋊C8—32no—
28#4544C2×C311yescharacteristic, complemented
29#4535C2×C312yescomplemented
30C2×C32×Q8D412yes—
31C2×C32×D4—22no—
32C2×C32×D4D412yes—
33C22×C32×C4—22no—
34C2×C3×D12—21no—
35C2×C3×D12—22no—
36C32×C4⋊C4—22no—
37C32×C4⋊C4D412yes—
38C32×C22⋊C4—24no—
39C32×C22⋊C4—22no—
40C32×C42—22no—
41C32×C42C2311yescharacteristic
42C3×#215—44no—
43C3×#213—44no—
44C2×C3×C3⋊C8—21no—
45C2×C3×C3⋊C8—22no—
46#1620—31noSylow
47C2×C3×SD16—62no—
48C2×C3×D8—62no—
49C3×#127—21no—
50C3×#127—31no—
51C3×#127C2×D311yescharacteristic
52C3×#127C22×C311yescharacteristic
53C3×#124—24no—
54C3×#124—22no—
55C3×#124—22no—
56C3×#123—24no—
57C3×#123—22no—
58C3×#123—22no—
59C3×C4×Q8—22no—
60C3×C4×Q8C2×D312yes—
61C3×C4×Q8C22×C312yes—
62C3×C4×D4—24no—
63C3×C4×D4—22no—
64C3×C4×D4—22no—
65C2×#215—22no—
66C2×#213—22no—
67#874C22×C311yescharacteristic
68C3×C4⋊C8—32no—
69C3×#102—62no—
70C3×C4×C8—31no—
71#809—22no—
72C4⋊(C3⋊C8)C22×C312yes—
73C4×C3⋊C8C22×C311yescharacteristic
74C23×C32—22no—
75C22×C3×D3—41no—
76C32×Q8—22no—
77C32×Q8—22no—
78C32×D4—42no—
79C32×D4—42no—
80C32×D4—42no—
81C2×C32×C4—22no—
82C2×C32×C4—22no—
83C2×C32×C4—82no—
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D412yes—
86C3×D12—42no—
87C3×D12—42no—
88C3×D12—42no—
89C3×C3⋊C8—22no—
90C3×C3⋊C8—42no—
91#559C3×D311yescharacteristic, complemented
92#493—31no—
93#460—32no—
94#331—31no—
95Q8⋊C8—32no—
96C2×C3×Q8—22no—
97C2×C3×Q8#6712yes—
98C2×C3×Q8C3×D412yes—
99C2×C3×D4—24no—
100C2×C3×D4—22no—
101C2×C3×D4—22no—
102C2×C3×D4—22no—
103C2×C3×D4—62no—
104C2×C3×D4—61no—
105C2×C3×D4#6712yes—
106C2×C3×D4C3×D412yes—
107C22×C3×C4—24no—
108C22×C3×C4—22no—
109C22×C3×C4—22no—
110C2×D12—22no—
111C2×D12—21no—
112C3×SD16—124no—
113C3×D8—124no—
114C2×C3×C8—61no—
115C2×C3×C8—62no—
116C3×C4⋊C4—24no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—22no—
119C3×C4⋊C4—22no—
120C3×C4⋊C4#6712yes—
121C3×C4⋊C4C3×D412yes—
122C3×C22⋊C4—28no—
123C3×C22⋊C4—24no—
124C3×C22⋊C4—24no—
125C3×C22⋊C4—24no—
126C3×C22⋊C4—22no—
127C3×C22⋊C4—22no—
128C3×C42—24no—
129C3×C42—22no—
130C3×C42—22no—
131C3×C42—21no—
132C3×C42C22×D311yescharacteristic
133C3×C42C23×C311yescharacteristic
134#215—44no—
135#213—44no—
136C2×C3⋊C8—21no—
137C2×C3⋊C8—22no—
138C22×C32—44no—
139C22×C32—42no—
140C22×C32#12011yescharacteristic
141C2×C3×D3—82no—
142C2×C3×D3—81no—
143C32×C4—21no—
144C32×C4—42no—
145C32×C4—42no—
146C32×C4#13512yes—
147C32×C4AGL(1,ℤ/8)12yes—
148C2×SD16—62no—
149C2×D8—62no—
150#127—31no—
151#127C2×C3×D311yescharacteristic
152#124—22no—
153#123—22no—
154C4×Q8C2×C3×D312yes—
155C4×D4—22no—
156C4⋊C8—32no—
157#102—62no—
158C4×C8—31no—
159C23×C3—24no—
160C23×C3—22no—
161C23×C3—22no—
162C23×C3—121no—
163C22×D3—41no—
164C3×Q8—22no—
165C3×Q8—22no—
166C3×Q8—22no—
167C3×Q8—22no—
168C3×Q8—42no—
169C3×Q8—42no—
170C3×D4—42no—
171C3×D4—42no—
172C3×D4—44no—
173C3×D4—44no—
174C3×D4—42no—
175C3×D4—42no—
176C3×D4—42no—
177C3×D4—42no—
178C3×D4—82no—
179C3×D4—122no—
180C3×D4—122no—
181C3×D4—122no—
182C2×C3×C4—24no—
183C2×C3×C4—24no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—21no—
190C2×C3×C4—84no—
191C2×C3×C4—82no—
192C2×C3×C4—82no—
193C2×C3×C4C2×#6711yescharacteristic
194C2×C3×C4C2×#6712yes—
195C2×C3×C4C2×C3×D411yescharacteristic
196C2×C3×C4C2×C3×D412yes—
197D12—42no—
198D12—42no—
199D12—42no—
200C3×C8—62no—
201C3×C8—122no—
202C3⋊C8—22no—
203C3⋊C8—42no—
204C2×C32—82no—
205C2×C32#44912yes—
206C2×C32#45311yescharacteristic
207C3×D3—161no—
208C2×Q8C3×#6712yes—
209C2×D4—22no—
210C2×D4—62no—
211C2×D4—61no—
212C2×D4C3×#6712yes—
213C22×C4—22no—
214SD16—124no—
215D8—124no—
216C2×C8—61no—
217C2×C8—62no—
218C4⋊C4—22no—
219C4⋊C4C3×#6712yes—
220C22⋊C4—24no—
221C22⋊C4—22no—
222C42—22no—
223C42C22×C3×D311yescharacteristic
224C22×C3—21no—
225C22×C3—44no—
226C22×C3—48no—
227C22×C3—44no—
228C22×C3—42no—
229C22×C3—44no—
230C22×C3—42no—
231C22×C3—242no—
232C22×C3—241no—
233C22×C3#95311yescharacteristic
234C22×C3C3×#12011yescharacteristic
235C2×D3—82no—
236C2×D3—81no—
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—22no—
240C3×C4—22no—
241C3×C4—41no—
242C3×C4—44no—
243C3×C4—44no—
244C3×C4—42no—
245C3×C4—42no—
246C3×C4—42no—
247C3×C4—42no—
248C3×C4#94912yes—
249C3×C4#95012yes—
250C3×C4C3×#13512yes—
251C3×C4C3×AGL(1,ℤ/8)12yes—
252C32#162011yescharacteristic, complemented, Sylow
253C23—22no—
254C23—121no—
255Q8—22no—
256Q8—22no—
257D4—42no—
258D4—42no—
259D4—42no—
260D4—122no—
261D4—122no—
262D4—122no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—82no—
266C2×C4C2×C3×#6711yescharacteristic
267C2×C4C2×C3×#6712yes—
268C8—62no—
269C8—122no—
270C2×C3—22no—
271C2×C3—21no—
272C2×C3—84no—
273C2×C3—82no—
274C2×C3—82no—
275C2×C3—481no—
276C2×C3#523812yes—
277C2×C3#524111yescharacteristic
278C2×C3C3×#44912yes—
279C2×C3C3×#45311yescharacteristic
280D3—161no—
281C22—44no—
282C22—42no—
283C22—242no—
284C22—241no—
285C22C3×#95311yescharacteristic
286C4—21no—
287C4—42no—
288C4—42no—
289C4C3×#94912yes—
290C4C3×#95012yes—
291C3—21no—
292C3#7194311yescharacteristic, direct product factor
293C3C3×#162011yescharacteristic, complemented
294C2—82no—
295C2—481no—
296C2C3×#523812yes—
297C2C3×#524111yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#559C2
socleC22×C32#120
prime radicalC3×#5073C2
hypercenterC3×#559D3
hypocenterC3C3×#1620
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
1. C32×#559C2semidirect
3. C3×#5027C2semidirect
4. C3×#4544C2semidirect
5. C3×#4535C2semidirect
7. #71943C3direct (N × H)
20. C3×#559D3semidirect
21. C3×#559C2×C3semidirect
25. #5027C2×C3semidirect
28. #4544C2×C3semidirect
29. #4535C2×C3semidirect
91. #559C3×D3semidirect
252. C32#1620semidirect
292. C3#71943direct (N × H)
293. C3C3×#1620semidirect

Maximal subgroups

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

subgroupindex
C32×#5592
C3×#50732
C3×#50272
C3×#45442
C3×#45352
C3×#16203
#719433