Finite Group Databasebeta

← #11922883

Subgroups — #11922883

Order 1152.

516 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C3×C4×#41⋊C3C211yesmaximal, characteristic
2#10593658C212yesmaximal
3#10593625C211yesmaximal, characteristic, complemented
4#10593623C212yesmaximal, complemented
5#10593620C211yesmaximal, characteristic, complemented
6#85334—33nomaximal
7#82507—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9C4×#634—41nomaximal
10C3×C4×SL(2,𝔽3)C2211yescharacteristic
11C3×C4×SL(2,𝔽3)C2211yescharacteristic
12C3⋊#859C2212yes—
13C3⋊#859C2212yes—
14C3×C4×#41D311yescharacteristic
15#5470—31no—
16C4×#41⋊C3D313yes—
17#5424—36no—
18#5391—33no—
19#5389—36no—
20#5386—33no—
21#5233—32no—
22#5022—32no—
23#5021—31no—
24#5020—31no—
25#5009—32no—
26#5008—31no—
27#5007—31no—
28#4998—32no—
29C2×C4⋊(C3⋊C8)—31no—
30C2×#634—41no—
31C3×#41⋊C3Q812yescomplemented
32C2×C3×SL(2,𝔽3)C2311yescharacteristic
33C32×C42—41no—
34C4⋊(C3⋊Dic3)—41no—
35#3750—42no—
36C4×C3⋊Dic3—42no—
37#3076—91noSylow
38C2×C3×#41C2×D311yescharacteristic
39C2×#41⋊C3C2×D313yes—
40C3×C4×Q8C2×D311yescharacteristic
41C3×C4×Q8C2×D311yescharacteristic
42C3×C4×D4—31no—
43C3×C4×D4—31no—
44C3×#117—31no—
45C2×C3×C42—31no—
46#926—32no—
47#924—61no—
48#924—61no—
49C22×C3⋊C8—32no—
50#870—32no—
51#869—31no—
52#869—31no—
53C4×Dic6—61no—
54C4×Dic6—61no—
55C4×Dic6—123no—
56C4×SL(2,𝔽3)C2×D313yes—
57C4×SL(2,𝔽3)C2×D313yes—
58#859—36no—
59#859—36no—
60#835—32no—
61#835—32no—
62#832—32no—
63#832—32no—
64#808—32no—
65#808—32no—
66#807—32no—
67#807—32no—
68C4⋊(C3⋊C8)—31no—
69C4⋊(C3⋊C8)—31no—
70C4⋊(C3⋊C8)—32no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C3⋊Dic3—42no—
75C2×C3⋊Dic3—42no—
76#634—44no—
77C3×SL(2,𝔽3)C2×Q811yescharacteristic
78#533—91no—
79C4×#41C3⋊D311yescharacteristic
80#479—92no—
81#478—92no—
82#477—91no—
83#476—91no—
84#475—91no—
85#474—91no—
86#427—92no—
87C2×C4⋊C8—91no—
88#416—92no—
89C3×#41—32no—
90C3×#41Dic612yescomplemented
91C2×C3×Q8C22×D311yescharacteristic
92C2×C3×D4—31no—
93C22×C3×C4—31no—
94C22×C3×C4—31no—
95C22×C3×C4—31no—
96C2×Dic6—61no—
97C2×Dic6—61no—
98C2×Dic6—123no—
99#41⋊C3Dic616yescomplemented
100C2×SL(2,𝔽3)C22×D313yes—
101C3×C4⋊C4—31no—
102C3×C4⋊C4—31no—
103C3×C22⋊C4—61no—
104C3×C42—31no—
105C3×C42—31no—
106C3×C42—31no—
107C3×C42—43no—
108C3×C42S411yescharacteristic
109#217—62no—
110C4⋊Dic3—32no—
111C4⋊Dic3—32no—
112C4⋊Dic3—61no—
113C4⋊Dic3—61no—
114C4⋊Dic3—123no—
115Dic3⋊C4—62no—
116Dic3⋊C4—62no—
117Dic3⋊C4—126no—
118C4×Dic3—62no—
119C4×Dic3—126no—
120C2×C3⋊C8—32no—
121C2×C3⋊C8—32no—
122C2×C3⋊C8—64no—
123C22×C32—41no—
124C32×C4—42no—
125C32×C4—42no—
126C32×C4—81no—
127C3⋊Dic3—44no—
128C3⋊Dic3—82no—
129C2×#41C2×C3⋊D311yescharacteristic
130C22×C8—92no—
131C4⋊Q8—91no—
132C4⋊Q8—91no—
133#125—92no—
134C22⋊Q8—181no—
135C22⋊Q8—181no—
136C4×Q8—181no—
137C4×Q8—181no—
138C4×Q8C2×C3⋊D311yescharacteristic
139C4×Q8C2×C3⋊D311yescharacteristic
140C4×D4—31no—
141C4×D4—31no—
142#117—31no—
143#117—92no—
144C2×C42—31no—
145#107—92no—
146#107—92no—
147#106—92no—
148#106—92no—
149C4⋊C8—91no—
150C4⋊C8—91no—
151C4⋊C8—92no—
152#103—92no—
153#103—92no—
154#102—92no—
155#102—92no—
156C23×C3—31no—
157C3×Q8—31no—
158C3×Q8C2×Dic611yescharacteristic
159C3×D4—32no—
160C3×D4—61no—
161C2×C3×C4—31no—
162C2×C3×C4—32no—
163C2×C3×C4—32no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—43no—
167C2×C3×C4—43no—
168C2×C3×C4—43no—
169C2×C3×C4—62no—
170C2×C3×C4—121no—
171C2×C3×C4C2×S411yescharacteristic
172C2×C3×C4C2×S411yescharacteristic
173C2×C3×C4C2×S411yescharacteristic
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—126no—
177C2×Dic3—126no—
178Dic6—1212no—
179Dic6—122no—
180Dic6—122no—
181SL(2,𝔽3)C2×Dic613yes—
182C3⋊C8—62no—
183C3⋊C8—62no—
184C2×C32—41no—
185C2×C32—41no—
186C2×C32—41no—
187#41—32no—
188#41#63412yescomplemented
189C2×Q8—181no—
190C2×Q8—181no—
191C2×Q8C22×C3⋊D311yescharacteristic
192C2×D4—31no—
193C22×C4—31no—
194C22×C4—31no—
195C22×C4—31no—
196C2×C8—92no—
197C2×C8—92no—
198C2×C8—184no—
199C4⋊C4—31no—
200C4⋊C4—31no—
201C4⋊C4—92no—
202C4⋊C4—92no—
203C4⋊C4—182no—
204C4⋊C4—181no—
205C4⋊C4—182no—
206C4⋊C4—181no—
207C22⋊C4—61no—
208C22⋊C4—182no—
209C42—31no—
210C42—31no—
211C42—31no—
212C42—182no—
213C42C3⋊S411yescharacteristic
214C22×C3—32no—
215C22×C3—43no—
216C22×C3—61no—
217C22×C3—61no—
218C22×C3C22×S411yescharacteristic
219C3×C4—21no—
220C3×C4—31no—
221C3×C4—31no—
222C3×C4—46no—
223C3×C4—46no—
224C3×C4—61no—
225C3×C4—61no—
226C3×C4—83no—
227C3×C4A4⋊Q812yes—
228C3×C4#98512yes—
229Dic3—1212no—
230Dic3—122no—
231Dic3—122no—
232Dic3—246no—
233C32—41noSylow
234C23—31no—
235Q8—31no—
236Q8—362no—
237Q8—362no—
238Q8C2×#63411yescharacteristic
239D4—32no—
240D4—61no—
241C2×C4—31no—
242C2×C4—32no—
243C2×C4—32no—
244C2×C4—31no—
245C2×C4—31no—
246C2×C4—62no—
247C2×C4—121no—
248C2×C4—182no—
249C2×C4—182no—
250C2×C4C2×C3⋊S411yescharacteristic
251C2×C4C2×C3⋊S411yescharacteristic
252C2×C4C2×C3⋊S411yescharacteristic
253C8—182no—
254C8—182no—
255C2×C3—43no—
256C2×C3—43no—
257C2×C3—43no—
258C2×C3—62no—
259C2×C3C2×A4⋊Q811yescharacteristic
260C2×C3C2×#98511yescharacteristic
261C2×C3#592311yescharacteristic
262C22—32no—
263C22—61no—
264C22—61no—
265C22C22×C3⋊S411yescharacteristic
266C4—21no—
267C4—31no—
268C4—31no—
269C4—61no—
270C4—61no—
271C4—362no—
272C4—362no—
273C4#6425912yes—
274C4#6426612yes—
275C3—43no—
276C3#8533411yescharacteristic, complemented
277C2—62no—
278C2C2×#6425911yescharacteristic
279C2C2×#6426611yescharacteristic
280C2#1059658611yescharacteristic
subgroupG/H
centerC2×C4C2×C3⋊S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C22×C3⋊S4
FittingC3×C4×#41D3
socleC22×C3C22×S4
prime radicalC2×C3×#41⋊C3C22
hypercenterC42C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #10593625C2semidirect
4. #10593623C2semidirect
5. #10593620C2semidirect
31. C3×#41⋊C3Q8semidirect
90. C3×#41Dic6semidirect
99. #41⋊C3Dic6semidirect
188. #41#634semidirect
276. C3#85334semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#41⋊C32
#105936582
#105936252
#105936232
#105936202
#853343
#825073
C4×#6344