Finite Group Databasebeta

← #11922884

Subgroups — #11922884

Order 1152.

522 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 73 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
3C4⋊(C3⋊#226)C211yesmaximal, characteristic, complemented
4C4×C3⋊#226C212yesmaximal, complemented
5#10593620C211yesmaximal, characteristic, complemented
6#85335—33nomaximal
7#82534—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9C2×C3⋊#226C2212yes—
10C4×#634—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—
18C4⋊#226—33no—
19C4×#226—36no—
20#5386—33no—
21#5239—32no—
22#5031—31no—
23C4×#216—32no—
24#5020—31no—
25#5019—31no—
26C4×#214—32no—
27#5007—31no—
28#4996—32no—
29#4925—31no—
30C2×#634—41no—
31C3×#41⋊C3—21no—
32C2×C3×SL(2,𝔽3)C2311yescharacteristic
33C3⋊#226—22no—
34C32×C42—41no—
35C4⋊(C3⋊Dic3)—41no—
36#3750—42no—
37C4×C3⋊Dic3—42no—
38#3107—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#869—31no—
55#869—31no—
56C4×Dic6—32no—
57C4×Dic6—61no—
58C4×Dic6—123no—
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—
71C4×C3⋊C8—32no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C3⋊Dic3—42no—
76C2×C3⋊Dic3—42no—
77#634—44no—
78C3×SL(2,𝔽3)#4111yescharacteristic
79#533—91no—
80C4×#41C3⋊D311yescharacteristic
81#485—92no—
82#475—91no—
83#474—91no—
84#462—91no—
85#461—91no—
86#452—92no—
87C4×Q16—92no—
88C4×SD16—92no—
89#431—91no—
90C3×#41—21no—
91C3×#41—61no—
92C2×C3×Q8C22×D311yescharacteristic
93C2×C3×D4—31no—
94C22×C3×C4—31no—
95C22×C3×C4—31no—
96C22×C3×C4—31no—
97C2×Dic6—32no—
98C2×Dic6—61no—
99C2×Dic6—123no—
100#41⋊C3—23no—
101C2×SL(2,𝔽3)C22×D313yes—
102#226—66no—
103C3×C4⋊C4—31no—
104C3×C4⋊C4—31no—
105C3×C22⋊C4—61no—
106C3×C42—31no—
107C3×C42—31no—
108C3×C42—31no—
109C3×C42—43no—
110C3×C42S411yescharacteristic
111#217—62no—
112#216—62no—
113#216—62no—
114#214—64no—
115C4⋊Dic3—32no—
116C4⋊Dic3—61no—
117C4⋊Dic3—61no—
118C4⋊Dic3—61no—
119C4⋊Dic3—123no—
120Dic3⋊C4—62no—
121Dic3⋊C4—62no—
122Dic3⋊C4—126no—
123C4×Dic3—62no—
124C4×Dic3—126no—
125C2×C3⋊C8—32no—
126C2×C3⋊C8—32no—
127C22×C32—41no—
128C32×C4—42no—
129C32×C4—42no—
130C32×C4—81no—
131C3⋊Dic3—44no—
132C3⋊Dic3—82no—
133C2×#41C2×C3⋊D311yescharacteristic
134C2×Q16—92no—
135C2×SD16—92no—
136C4⋊Q8—91no—
137C4⋊Q8—91no—
138#125—181no—
139C22⋊Q8—92no—
140C22⋊Q8—181no—
141C4×Q8—92no—
142C4×Q8—181no—
143C4×Q8C2×C3⋊D311yescharacteristic
144C4×Q8C2×C3⋊D311yescharacteristic
145C4×D4—31no—
146C4×D4—31no—
147#117—31no—
148#117—181no—
149C2×C42—31no—
150#107—92no—
151#106—92no—
152C4⋊C8—91no—
153C4⋊C8—91no—
154#103—92no—
155#103—92no—
156#103—92no—
157#102—92no—
158C22⋊C8—92no—
159C4×C8—92no—
160C23×C3—31no—
161C3×Q8—31no—
162C3×Q8#23511yescharacteristic
163C3×D4—32no—
164C3×D4—61no—
165C2×C3×C4—31no—
166C2×C3×C4—31no—
167C2×C3×C4—31no—
168C2×C3×C4—43no—
169C2×C3×C4—43no—
170C2×C3×C4—43no—
171C2×C3×C4—61no—
172C2×C3×C4—61no—
173C2×C3×C4—62no—
174C2×C3×C4—62no—
175C2×C3×C4C2×S411yescharacteristic
176C2×C3×C4C2×S411yescharacteristic
177C2×C3×C4C2×S411yescharacteristic
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—126no—
181C2×Dic3—126no—
182Dic6—62no—
183Dic6—62no—
184Dic6—1212no—
185Dic6—122no—
186SL(2,𝔽3)#23513yes—
187C3⋊C8—62no—
188C3⋊C8—62no—
189C2×C32—41no—
190C2×C32—41no—
191C2×C32—41no—
192#41—21no—
193#41—61no—
194C2×Q8—92no—
195C2×Q8—181no—
196C2×Q8C22×C3⋊D311yescharacteristic
197C2×D4—31no—
198C22×C4—31no—
199C22×C4—31no—
200C22×C4—31no—
201Q16—182no—
202Q16—182no—
203SD16—184no—
204C2×C8—92no—
205C2×C8—92no—
206C4⋊C4—31no—
207C4⋊C4—31no—
208C4⋊C4—92no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C4⋊C4—182no—
212C4⋊C4—182no—
213C4⋊C4—181no—
214C22⋊C4—61no—
215C22⋊C4—182no—
216C42—31no—
217C42—31no—
218C42—31no—
219C42—182no—
220C42C3⋊S411yescharacteristic
221C22×C3—43no—
222C22×C3—61no—
223C22×C3—61no—
224C22×C3—61no—
225C22×C3C22×S411yescharacteristic
226C3×C4—21no—
227C3×C4—31no—
228C3×C4—31no—
229C3×C4—46no—
230C3×C4—46no—
231C3×C4—61no—
232C3×C4—61no—
233C3×C4—83no—
234C3×C4#98412yes—
235C3×C4#98512yes—
236Dic3—1212no—
237Dic3—122no—
238Dic3—122no—
239Dic3—246no—
240C32—41noSylow
241C23—31no—
242Q8—31no—
243Q8—182no—
244Q8—182no—
245Q8—362no—
246Q8#382811yescharacteristic
247D4—32no—
248D4—61no—
249C2×C4—31no—
250C2×C4—31no—
251C2×C4—31no—
252C2×C4—61no—
253C2×C4—61no—
254C2×C4—62no—
255C2×C4—62no—
256C2×C4—182no—
257C2×C4—182no—
258C2×C4C2×C3⋊S411yescharacteristic
259C2×C4C2×C3⋊S411yescharacteristic
260C2×C4C2×C3⋊S411yescharacteristic
261C8—182no—
262C8—182no—
263C2×C3—43no—
264C2×C3—43no—
265C2×C3—43no—
266C2×C3—121no—
267C2×C3#591211yescharacteristic
268C2×C3C2×#98411yescharacteristic
269C2×C3C2×#98511yescharacteristic
270C22—61no—
271C22—61no—
272C22—61no—
273C22C22×C3⋊S411yescharacteristic
274C4—21no—
275C4—31no—
276C4—31no—
277C4—61no—
278C4—61no—
279C4—362no—
280C4—362no—
281C4#6426512yes—
282C4#6426612yes—
283C3—43no—
284C3#8533511yescharacteristic, complemented
285C2—121no—
286C2#1059657511yescharacteristic
287C2C2×#6426511yescharacteristic
288C2C2×#6426611yescharacteristic
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)#41
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. C4⋊(C3⋊#226)C2semidirect
4. C4×C3⋊#226C2semidirect
5. #10593620C2semidirect
284. C3#85335semidirect

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
C4⋊(C3⋊#226)2
C4×C3⋊#2262
#105936202
#853353
#825343
C4×#6344