Finite Group Databasebeta

← C3×#71928 #11779487

Subgroups — C3×#71928 #11779487

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×#555C211yesmaximal, characteristic
2C3×#5092C211yesmaximal, characteristic, complemented
3C3×#5008C212yesmaximal, complemented
4C3×#4546C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
6C3×#1634—31nomaximal
7#71928C311yesmaximal, characteristic, direct product factor
8C32×C4⋊Q8C2211yescharacteristic
9C32×#124—22no—
10C32×#121—22no—
11C32×C4×D4C2212yes—
12C32×#117—22no—
13C2×C3×#216—22no—
14C3×#869C2211yescharacteristic
15C3×#832—22no—
16C3×#808—22no—
17C3×C4⋊(C3⋊C8)C2212yes—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×#555—21no—
20C3×#555D311yescharacteristic
21C3×#555C2×C311yescharacteristic
22C3×#494—31no—
23C3×#476—32no—
24#5092C2×C311yescharacteristic, complemented
25#5008C2×C312yescomplemented
26C3×#333—31no—
27C3×D4⋊C8—32no—
28#4546C2×C311yescharacteristic, complemented
29D4⋊(C3⋊C8)C2×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×#216—44no—
42C3×C4⋊Dic3—22no—
43C2×C3×C3⋊C8—21no—
44C2×C3×C3⋊C8—22no—
45#1634—31noSylow
46C2×C3×Q16—62no—
47C3×C4⋊Q8—21no—
48C3×C4⋊Q8—31no—
49C3×C4⋊Q8C2×D311yescharacteristic
50C3×C4⋊Q8C22×C311yescharacteristic
51C3×#124—24no—
52C3×#124—22no—
53C3×#124—22no—
54C3×#121—24no—
55C3×#121—22no—
56C3×#121—22no—
57C3×C4×D4—22no—
58C3×C4×D4C2×D312yes—
59C3×C4×D4C22×C312yes—
60C3×#117—24no—
61C3×#117—22no—
62C3×#117—22no—
63C2×#216—22no—
64#869C22×C311yescharacteristic
65C3×#106—62no—
66C3×C4⋊C8—32no—
67C3×#102—62no—
68C3×C4×C8—31no—
69#832—22no—
70#808—22no—
71C4⋊(C3⋊C8)C22×C312yes—
72C4×C3⋊C8C22×C311yescharacteristic
73C23×C32—22no—
74C32×Q8—42no—
75C32×D4—22no—
76C32×D4—22no—
77C32×D4—82no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4—42no—
81C2×C32×C4—42no—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D412yes—
84C2×C3×Dic3—41no—
85C3×Dic6—42no—
86C3×C3⋊C8—22no—
87C3×C3⋊C8—42no—
88#555C3×D311yescharacteristic
89#494—31no—
90#476—32no—
91#333—31no—
92D4⋊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×Q16—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#216—44no—
130C4⋊Dic3—22no—
131C2×C3⋊C8—21no—
132C2×C3⋊C8—22no—
133C22×C32—42no—
134C22×C32—42no—
135C22×C32—42no—
136C22×C32#12011yescharacteristic
137C32×C4—21no—
138C32×C4—42no—
139C32×C4—42no—
140C32×C4#13512yes—
141C32×C4#13712yes—
142C3×Dic3—81no—
143C2×Q16—62no—
144C4⋊Q8—31no—
145C4⋊Q8C2×C3×D311yescharacteristic
146#124—22no—
147#121—22no—
148C4×D4C2×C3×D312yes—
149#117—22no—
150#106—62no—
151C4⋊C8—32no—
152#102—62no—
153C4×C8—31no—
154C23×C3—24no—
155C23×C3—22no—
156C23×C3—22no—
157C3×Q8—42no—
158C3×Q8—42no—
159C3×Q8—82no—
160C3×Q8—122no—
161C3×D4—22no—
162C3×D4—22no—
163C3×D4—22no—
164C3×D4—22no—
165C3×D4—42no—
166C3×D4—42no—
167C3×D4—84no—
168C3×D4—82no—
169C3×D4—82no—
170C2×C3×C4—24no—
171C2×C3×C4—24no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—21no—
178C2×C3×C4—44no—
179C2×C3×C4—44no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—121no—
185C2×C3×C4C2×#6711yescharacteristic
186C2×C3×C4C2×#6712yes—
187C2×C3×C4C2×C3×D411yescharacteristic
188C2×C3×C4C2×C3×D412yes—
189C2×Dic3—41no—
190Dic6—42no—
191C3×C8—62no—
192C3×C8—122no—
193C3⋊C8—22no—
194C3⋊C8—42no—
195C2×C32—82no—
196C2×C32#45212yes—
197C2×C32#45311yescharacteristic
198C2×Q8—61no—
199C2×Q8C3×#6712yes—
200C2×D4—22no—
201C2×D4C3×#6712yes—
202C22×C4—22no—
203Q16—124no—
204C2×C8—61no—
205C2×C8—62no—
206C4⋊C4—22no—
207C4⋊C4—62no—
208C4⋊C4C3×#6712yes—
209C22⋊C4—24no—
210C22⋊C4—22no—
211C42—22no—
212C42C22×C3×D311yescharacteristic
213C22×C3—21no—
214C22×C3—44no—
215C22×C3—44no—
216C22×C3—44no—
217C22×C3—42no—
218C22×C3—42no—
219C22×C3—42no—
220C22×C3—42no—
221C22×C3—42no—
222C22×C3—42no—
223C22×C3#95311yescharacteristic
224C22×C3C3×#12011yescharacteristic
225C3×C4—21no—
226C3×C4—21no—
227C3×C4—22no—
228C3×C4—22no—
229C3×C4—41no—
230C3×C4—44no—
231C3×C4—44no—
232C3×C4—42no—
233C3×C4—42no—
234C3×C4—42no—
235C3×C4—42no—
236C3×C4—241no—
237C3×C4#95012yes—
238C3×C4#95112yes—
239C3×C4C3×#13512yes—
240C3×C4C3×#13712yes—
241Dic3—81no—
242C32#163411yescharacteristic, complemented, Sylow
243C23—22no—
244Q8—42no—
245Q8—122no—
246D4—22no—
247D4—22no—
248D4—82no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—121no—
254C2×C4C2×C3×#6711yescharacteristic
255C2×C4C2×C3×#6712yes—
256C8—62no—
257C8—122no—
258C2×C3—22no—
259C2×C3—21no—
260C2×C3—84no—
261C2×C3—82no—
262C2×C3—82no—
263C2×C3#523912yes—
264C2×C3#524111yescharacteristic
265C2×C3C3×#45212yes—
266C2×C3C3×#45311yescharacteristic
267C22—42no—
268C22—42no—
269C22—42no—
270C22C3×#95311yescharacteristic
271C4—21no—
272C4—42no—
273C4—42no—
274C4—241no—
275C4C3×#95012yes—
276C4C3×#95112yes—
277C3—21no—
278C3#7192811yescharacteristic, direct product factor
279C3C3×#163411yescharacteristic, complemented
280C2—82no—
281C2C3×#523912yes—
282C2C3×#524111yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
Fitting, prime radicalC32×#555C2
socleC22×C32#120
hypercenterC3×#555D3
hypocenterC3C3×#1634
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#555

Complements

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

NH ≅ G/Ntype
2. C3×#5092C2semidirect
3. C3×#5008C2semidirect
4. C3×#4546C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
7. #71928C3direct (N × H)
24. #5092C2×C3semidirect
25. #5008C2×C3semidirect
28. #4546C2×C3semidirect
29. D4⋊(C3⋊C8)C2×C3semidirect
242. C32#1634semidirect
278. C3#71928direct (N × H)
279. C3C3×#1634semidirect

Maximal subgroups

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

subgroupindex
C32×#5552
C3×#50922
C3×#50082
C3×#45462
C3×D4⋊(C3⋊C8)2
C3×#16343
#719283