Finite Group Databasebeta

← C3×#2884⋊C3 #11919530

Subgroups — C3×#2884⋊C3 #11919530

Order 1152.

468 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 90 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×C3×2−1+4⋊C3C211yesmaximal, characteristic
2C3×#519⋊C3C212yesmaximal, complemented
3C3×#2884C311yesmaximal, characteristic, complemented
4#2884⋊C3C313yesmaximal, direct product factor
5C3×2−1+4⋊C3—22no—
6C2×C3×#41⋊C3C411yescharacteristic, complemented
7C22×C3×SL(2,𝔽3)C411yescharacteristic, complemented
8C22×C3×SL(2,𝔽3)C2211yescharacteristic
9C3×C4×SL(2,𝔽3)—22no—
10C32×#99—41nomaximal
11C2×C3×2−1+4C2×C311yescharacteristic
12C2×2−1+4⋊C3C2×C313yes—
13C3×#519C2×C312yescomplemented
14#519⋊C3C2×C316yescomplemented
15C3×#410—31no—
16C3×#410—31no—
17C3×#410—32no—
18C2×C32×D4—41no—
19C3×#41⋊C3—21no—
20C2×C3×SL(2,𝔽3)—21no—
21C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
22C2×C3×SL(2,𝔽3)D412yes—
23C32×C22⋊C4—42no—
24#2884C3211yescharacteristic, complemented, Sylow
25C3×2−1+4—22no—
26C3×2−1+4—62no—
27C2×C3×#41—31no—
28C2×C3×#41—31no—
29C2×C3×#41—31no—
30C2×C3×#41C3×C411yescharacteristic, complemented
31C22×C3×Q8—31no—
32C22×C3×Q8C3×C411yescharacteristic, complemented
33C22×C3×Q8C22×C311yescharacteristic
342−1+4⋊C3—26no—
35C2×#41⋊C3C3×C413yescomplemented
36C22×SL(2,𝔽3)C3×C413yescomplemented
37C22×SL(2,𝔽3)C22×C313yes—
38C3×C4×Q8—22no—
39C3×C4×Q8—62no—
40C3×#117—32no—
41C3×#117—32no—
42C4×SL(2,𝔽3)—26no—
43C3×#99—32no—
44C3×#99—31no—
45C3×#99—32no—
46C3×#99—43no—
47C3×#99A411yescharacteristic
48C23×C32—41no—
49C23×C32—41no—
50C32×D4—82no—
51C2×C32×C4—41no—
52C2×C32×C4—82no—
53C3×SL(2,𝔽3)C22⋊C411yescharacteristic
54C2×2−1+4C2×C3211yescharacteristic
55#519C2×C3212yescomplemented
56#410—31no—
57#410—31no—
58#410—32no—
59C3×#41—21no—
60C3×#41—62no—
61C3×#41—62no—
62C3×#41—62no—
63C3×#41—62no—
64C3×#41—62no—
65C3×#41—62no—
66C3×#41—61no—
67C2×C3×Q8—21no—
68C2×C3×Q8—31no—
69C2×C3×Q8—32no—
70C2×C3×Q8—31no—
71C2×C3×Q8—31no—
72C2×C3×Q8—62no—
73C2×C3×Q8—62no—
74C2×C3×Q8—61no—
75C2×C3×Q8C2×C3×C411yescharacteristic
76C2×C3×Q8C3×D412yes—
77C2×C3×D4—31no—
78C2×C3×D4—31no—
79C2×C3×D4—31no—
80C2×C3×D4—43no—
81C2×C3×D4C2×A411yescharacteristic
82C22×C3×C4—31no—
83C22×C3×C4—32no—
84C22×C3×C4—31no—
85C22×C3×C4—31no—
86#41⋊C3—23no—
87C2×SL(2,𝔽3)—23no—
88C2×SL(2,𝔽3)C2×C3×C413yes—
89C2×SL(2,𝔽3)C3×D416yes—
90C3×C4⋊C4—62no—
91C3×C4⋊C4—62no—
92C3×C22⋊C4—32no—
93C3×C22⋊C4—46no—
94C3×C22⋊C4C2×A412yes—
95C3×C42—62no—
96C3×C42—62no—
97C22×C32—41no—
98C22×C32—42no—
99C22×C32—81no—
100C22×C32—161no—
101C22×C32—161no—
102C32×C4—81no—
103C32×C4—162no—
1042−1+4—22no—
1052−1+4—62no—
106C2×#41—31no—
107C2×#41—31no—
108C2×#41—31no—
109C2×#41C32×C411yescharacteristic, complemented
110C22×Q8—31no—
111C22×Q8C32×C411yescharacteristic, complemented
112C22×Q8C22×C3211yescharacteristic
113C4×Q8—22no—
114C4×Q8—62no—
115#117—32no—
116#117—32no—
117#99—32no—
118#99—31no—
119#99—32no—
120#99C3×A411yescharacteristic
121C23×C3—31no—
122C23×C3—43no—
123C23×C3—43no—
124C23×C3C4×A411yescharacteristic
125C23×C3C22×A411yescharacteristic
126C3×Q8—31no—
127C3×Q8—32no—
128C3×Q8—32no—
129C3×Q8—62no—
130C3×Q8—61no—
131C3×Q8—61no—
132C3×Q8C3×C22⋊C411yescharacteristic
133C3×D4—22no—
134C3×D4—62no—
135C3×D4—61no—
136C3×D4—61no—
137C3×D4—62no—
138C3×D4—86no—
139C2×C3×C4—22no—
140C2×C3×C4—31no—
141C2×C3×C4—31no—
142C2×C3×C4—32no—
143C2×C3×C4—32no—
144C2×C3×C4—31no—
145C2×C3×C4—43no—
146C2×C3×C4—61no—
147C2×C3×C4—61no—
148C2×C3×C4—61no—
149C2×C3×C4—61no—
150C2×C3×C4—64no—
151C2×C3×C4—62no—
152C2×C3×C4—86no—
153C2×C3×C4C4×A411yescharacteristic
154SL(2,𝔽3)C3×C22⋊C413yes—
155C2×C32—41no—
156C2×C32—82no—
157C2×C32—81no—
158C2×C32—161no—
159#41—21no—
160#41—62no—
161#41—62no—
162#41—62no—
163#41—62no—
164#41—62no—
165#41—62no—
166#41—61no—
167C2×Q8—21no—
168C2×Q8—31no—
169C2×Q8—32no—
170C2×Q8—31no—
171C2×Q8—31no—
172C2×Q8—62no—
173C2×Q8—62no—
174C2×Q8—61no—
175C2×Q8C2×C32×C411yescharacteristic
176C2×Q8C32×D412yes—
177C2×D4—31no—
178C2×D4—31no—
179C2×D4—31no—
180C2×D4C2×C3×A411yescharacteristic
181C22×C4—31no—
182C22×C4—32no—
183C22×C4—31no—
184C22×C4—31no—
185C4⋊C4—62no—
186C4⋊C4—62no—
187C22⋊C4—32no—
188C22⋊C4C2×C3×A412yes—
189C42—62no—
190C42—62no—
191C22×C3—21no—
192C22×C3—41no—
193C22×C3—41no—
194C22×C3—43no—
195C22×C3—46no—
196C22×C3—61no—
197C22×C3—83no—
198C22×C3—121no—
199C22×C3—163no—
200C22×C3—163no—
201C22×C3C2×C4×A411yescharacteristic
202C22×C3D4×A412yes—
203C3×C4—21no—
204C3×C4—32no—
205C3×C4—31no—
206C3×C4—31no—
207C3×C4—42no—
208C3×C4—61no—
209C3×C4—83no—
210C3×C4—122no—
211C3×C4—166no—
212C32—41noSylow
213C23—31no—
214C23C3×C4×A411yescharacteristic
215C23C22×C3×A411yescharacteristic
216Q8—31no—
217Q8—32no—
218Q8—32no—
219Q8—62no—
220Q8—61no—
221Q8—61no—
222Q8C32×C22⋊C411yescharacteristic
223D4—22no—
224D4—62no—
225D4—61no—
226D4—61no—
227D4—62no—
228C2×C4—22no—
229C2×C4—31no—
230C2×C4—31no—
231C2×C4—32no—
232C2×C4—32no—
233C2×C4—31no—
234C2×C4—61no—
235C2×C4—61no—
236C2×C4—61no—
237C2×C4—61no—
238C2×C4—64no—
239C2×C4—62no—
240C2×C4C3×C4×A411yescharacteristic
241C2×C3—22no—
242C2×C3—21no—
243C2×C3—41no—
244C2×C3—43no—
245C2×C3—86no—
246C2×C3—83no—
247C2×C3—121no—
248C2×C3—163no—
249C2×C3A4×C22⋊C411yescharacteristic
250C22—21no—
251C22—41no—
252C22—41no—
253C22—61no—
254C22—121no—
255C22C2×C3×C4×A411yescharacteristic
256C22C3×D4×A412yes—
257C4—21no—
258C4—31no—
259C4—31no—
260C4—32no—
261C4—42no—
262C4—61no—
263C4—122no—
264C3—43no—
265C3#2884⋊C311yescharacteristic, direct product factor
266C2—22no—
267C2—21no—
268C2—41no—
269C2—121no—
270C2C3×A4×C22⋊C411yescharacteristic
subgroupG/H
center, socleC2×C3A4×C22⋊C4
commutatorC2×Q8C2×C32×C4
FrattiniC23C22×C3×A4
FittingC3×#2884C3
prime radicalC2×C3×2−1+4⋊C3C2
cosocleC22×Q8C22×C32
hypercenterC3×#99A4
hypocenterQ8C32×C22⋊C4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#99

Complements

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

NH ≅ G/Ntype
2. C3×#519⋊C3C2semidirect
3. C3×#2884C3semidirect
4. #2884⋊C3C3direct (N × H)
6. C2×C3×#41⋊C3C4semidirect
7. C22×C3×SL(2,𝔽3)C4semidirect
13. C3×#519C2×C3semidirect
14. #519⋊C3C2×C3semidirect
24. #2884C32semidirect
30. C2×C3×#41C3×C4semidirect
32. C22×C3×Q8C3×C4semidirect
35. C2×#41⋊C3C3×C4semidirect
36. C22×SL(2,𝔽3)C3×C4semidirect
55. #519C2×C32semidirect
109. C2×#41C32×C4semidirect
111. C22×Q8C32×C4semidirect
265. C3#2884⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×2−1+4⋊C32
C3×#519⋊C32
C3×#28843
#2884⋊C33
C32×#994