Finite Group Databasebeta

← #11922887

Subgroups — #11922887

Order 1152.

490 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 69 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#10593659C212yesmaximal
3#10593625C211yesmaximal, characteristic, complemented
4C4⋊(C3⋊#226)C211yesmaximal, characteristic, complemented
5#10593622C212yesmaximal, complemented
6#85338—33nomaximal
7#82535—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9C2×C3⋊#226C2212yes—
10#64079—41nomaximal
11C3×C4×SL(2,𝔽3)C2211yescharacteristic
12C3×C4×SL(2,𝔽3)C2211yescharacteristic
13C3⋊#859C2212yes—
14C3×C4×#41D311yescharacteristic
15#5470—31no—
16C4×#41⋊C3D313yes—
17#5425—36no—
18#5391—33no—
19C4⋊#226—33no—
20#5388—36no—
21#5239—32no—
22#5031—31no—
23#5030—32no—
24#5021—31no—
25#5019—31no—
26#5018—32no—
27#5008—31no—
28#4996—32no—
29#4926—31no—
30C3×#41⋊C3—21no—
31C2×C3×SL(2,𝔽3)C2311yescharacteristic
32C3⋊#226—22no—
33C32×C42—41no—
34C4⋊(C3⋊Dic3)—41no—
35C4⋊(C3⋊Dic3)—41no—
36#3750—42no—
37#3750—42no—
38#3116—91noSylow
39C2×C3×#41C2×D311yescharacteristic
40C2×#41⋊C3C2×D313yes—
41C2×#226—36no—
42C3×C4×Q8C2×D311yescharacteristic
43C3×C4×Q8C2×D311yescharacteristic
44C3×C4×D4—31no—
45C3×C4×D4—31no—
46C3×#117—31no—
47C2×C3×C42—31no—
48C2×#216—32no—
49C2×#214—32no—
50#926—61no—
51#924—32no—
52#924—61no—
53#870—61no—
54#870—123no—
55#869—31no—
56#869—31no—
57C4×Dic6—32no—
58C4×Dic6—61no—
59C4×SL(2,𝔽3)C2×D313yes—
60C4×SL(2,𝔽3)C2×D313yes—
61#859—36no—
62#835—32no—
63#832—32no—
64#830—32no—
65#810—32no—
66#810—32no—
67#808—32no—
68#807—32no—
69C4⋊(C3⋊C8)—31no—
70C4⋊(C3⋊C8)—31no—
71#803—32no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C3⋊Dic3—42no—
76C2×C3⋊Dic3—42no—
77C3×SL(2,𝔽3)#4111yescharacteristic
78#533—91no—
79C4×#41C3⋊D311yescharacteristic
80#485—92no—
81#477—91no—
82#476—91no—
83#462—91no—
84#461—91no—
85#452—92no—
86#441—92no—
87#440—92no—
88#432—91no—
89C3×#41—21no—
90C3×#41—61no—
91C2×C3×Q8C22×D311yescharacteristic
92C2×C3×D4—31no—
93C22×C3×C4—31no—
94C22×C3×C4—31no—
95C22×C3×C4—31no—
96C2×Dic6—32no—
97C2×Dic6—61no—
98#41⋊C3—23no—
99C2×SL(2,𝔽3)C22×D313yes—
100#226—66no—
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—
110#216—62no—
111#216—62no—
112#214—64no—
113C4⋊Dic3—32no—
114C4⋊Dic3—61no—
115C4⋊Dic3—61no—
116C4⋊Dic3—61no—
117C4⋊Dic3—123no—
118C4⋊Dic3—123no—
119Dic3⋊C4—62no—
120Dic3⋊C4—62no—
121Dic3⋊C4—126no—
122Dic3⋊C4—126no—
123C4×Dic3—62no—
124C2×C3⋊C8—32no—
125C2×C3⋊C8—32no—
126C22×C32—41no—
127C32×C4—42no—
128C32×C4—81no—
129C32×C4—81no—
130C3⋊Dic3—82no—
131C3⋊Dic3—82no—
132C2×#41C2×C3⋊D311yescharacteristic
133C2×Q16—92no—
134C2×SD16—92no—
135C4⋊Q8—91no—
136C4⋊Q8—91no—
137#125—181no—
138C22⋊Q8—92no—
139C22⋊Q8—181no—
140C4×Q8—92no—
141C4×Q8—181no—
142C4×Q8C2×C3⋊D311yescharacteristic
143C4×Q8C2×C3⋊D311yescharacteristic
144C4×D4—31no—
145C4×D4—31no—
146#117—31no—
147#117—181no—
148C2×C42—31no—
149#107—92no—
150#106—92no—
151C4⋊C8—91no—
152C4⋊C8—91no—
153#103—92no—
154#103—92no—
155#103—92no—
156#102—92no—
157C22⋊C8—92no—
158#97—92no—
159C23×C3—31no—
160C3×Q8—31no—
161C3×Q8#23511yescharacteristic
162C3×D4—32no—
163C3×D4—61no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—31no—
167C2×C3×C4—43no—
168C2×C3×C4—43no—
169C2×C3×C4—43no—
170C2×C3×C4—61no—
171C2×C3×C4—61no—
172C2×C3×C4—62no—
173C2×C3×C4—121no—
174C2×C3×C4C2×S411yescharacteristic
175C2×C3×C4C2×S411yescharacteristic
176C2×C3×C4C2×S411yescharacteristic
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—126no—
180C2×Dic3—126no—
181Dic6—62no—
182Dic6—62no—
183Dic6—122no—
184SL(2,𝔽3)#23513yes—
185C3⋊C8—62no—
186C3⋊C8—62no—
187C2×C32—41no—
188C2×C32—41no—
189C2×C32—41no—
190#41—21no—
191#41—61no—
192C2×Q8—92no—
193C2×Q8—181no—
194C2×Q8C22×C3⋊D311yescharacteristic
195C2×D4—31no—
196C22×C4—31no—
197C22×C4—31no—
198C22×C4—31no—
199Q16—182no—
200Q16—182no—
201SD16—184no—
202C2×C8—92no—
203C2×C8—92no—
204C4⋊C4—31no—
205C4⋊C4—31no—
206C4⋊C4—92no—
207C4⋊C4—181no—
208C4⋊C4—181no—
209C4⋊C4—181no—
210C4⋊C4—182no—
211C4⋊C4—182no—
212C22⋊C4—61no—
213C22⋊C4—182no—
214C42—31no—
215C42—31no—
216C42—31no—
217C42—182no—
218C42C3⋊S411yescharacteristic
219C22×C3—43no—
220C22×C3—61no—
221C22×C3—61no—
222C22×C3—61no—
223C22×C3C22×S411yescharacteristic
224C3×C4—21no—
225C3×C4—21no—
226C3×C4—31no—
227C3×C4—31no—
228C3×C4—46no—
229C3×C4—61no—
230C3×C4—61no—
231C3×C4—83no—
232C3×C4—83no—
233C3×C4#98412yes—
234Dic3—122no—
235Dic3—122no—
236Dic3—246no—
237Dic3—246no—
238C32—41noSylow
239C23—31no—
240Q8—31no—
241Q8—182no—
242Q8—182no—
243Q8—362no—
244Q8#382811yescharacteristic
245D4—32no—
246D4—61no—
247C2×C4—31no—
248C2×C4—31no—
249C2×C4—31no—
250C2×C4—61no—
251C2×C4—61no—
252C2×C4—62no—
253C2×C4—121no—
254C2×C4—182no—
255C2×C4—182no—
256C2×C4C2×C3⋊S411yescharacteristic
257C2×C4C2×C3⋊S411yescharacteristic
258C2×C4C2×C3⋊S411yescharacteristic
259C8—182no—
260C8—182no—
261C2×C3—43no—
262C2×C3—43no—
263C2×C3—43no—
264C2×C3—121no—
265C2×C3#591211yescharacteristic
266C2×C3C2×#98411yescharacteristic
267C2×C3#592311yescharacteristic
268C22—61no—
269C22—61no—
270C22—61no—
271C22C22×C3⋊S411yescharacteristic
272C4—21no—
273C4—21no—
274C4—31no—
275C4—31no—
276C4—61no—
277C4—61no—
278C4—362no—
279C4—362no—
280C4#6426512yes—
281C3—43no—
282C3#8533811yescharacteristic, complemented
283C2—121no—
284C2#1059657511yescharacteristic
285C2C2×#6426511yescharacteristic
286C2#1059658611yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FittingC3×C4×#41D3
socleC22×C3C22×S4
prime radicalC2×C3×#41⋊C3C22
hypercenterC42C3⋊S4
hypocenterC3×SL(2,𝔽3)#41
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #10593625C2semidirect
4. C4⋊(C3⋊#226)C2semidirect
5. #10593622C2semidirect
282. C3#85338semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#41⋊C32
#105936592
#105936252
C4⋊(C3⋊#226)2
#105936222
#853383
#825353
#640794