Finite Group Databasebeta

← #11922894

Subgroups — #11922894

Order 1152.

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

normal subgroups only

This group has 614 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, complemented
2#10593661C212yesmaximal, complemented
3C4⋊(C3⋊GL(2,𝔽3))C211yesmaximal, characteristic, complemented
4C4×C3⋊GL(2,𝔽3)C212yesmaximal, complemented
5#10593625C211yesmaximal, characteristic, complemented
6#85345—33nomaximal
7#82529—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9C2×C3⋊GL(2,𝔽3)C2212yes—
10C4×C4⋊(C3⋊D3)—41nomaximal
11C3×C4×SL(2,𝔽3)C2211yescharacteristic
12C3×C4×SL(2,𝔽3)C2211yescharacteristic
13C3⋊#859C2212yes—
14C3×C4×#41D311yescharacteristic, complemented
15#5477—31no—
16C4×#41⋊C3D313yescomplemented
17#5427—36no—
18C4⋊GL(2,𝔽3)—33no—
19C4×GL(2,𝔽3)—36no—
20#5391—33no—
21#5238—32no—
22#5027—31no—
23C4×#215—32no—
24#5021—31no—
25#5015—31no—
26C4×#213—32no—
27#5008—31no—
28#5003—32no—
29#4925—31no—
30C2×C4⋊(C3⋊D3)—41no—
31C2×C4×C3⋊D3—42no—
32C3×#41⋊C3—21no—
33C2×C3×SL(2,𝔽3)C2311yescharacteristic
34C3⋊GL(2,𝔽3)—22no—
35C32×C42—41no—
36#3752—42no—
37C4⋊(C3⋊Dic3)—41no—
38#3106—91noSylow
39C2×C3×#41C2×D311yescharacteristic
40C2×#235—61no—
41C2×#41⋊C3C2×D313yes—
42C2×GL(2,𝔽3)—36no—
43C3×C4×Q8C2×D311yescharacteristic
44C3×C4×Q8C2×D311yescharacteristic
45C3×C4×D4—31no—
46C3×C4×D4—31no—
47C3×#117—31no—
48C2×C3×C42—31no—
49C2×#215—32no—
50C2×#213—32no—
51#930—32no—
52#930—61no—
53#875—61no—
54#874—31no—
55C4×D12—32no—
56C4×D12—61no—
57C4×D12—123no—
58#869—31no—
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#809—32no—
66#809—32no—
67#808—32no—
68#807—32no—
69C4⋊(C3⋊C8)—31no—
70C4⋊(C3⋊C8)—31no—
71C4×C3⋊C8—32no—
72C22×C3⋊D3—42no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C3⋊Dic3—42no—
77C4⋊(C3⋊D3)—44no—
78C4×C3⋊D3—84no—
79C3×SL(2,𝔽3)#4111yescharacteristic, complemented
80#532—91no—
81C4×#41C3⋊D311yescharacteristic, complemented
82#482—92no—
83#477—91no—
84#476—91no—
85#460—91no—
86#459—91no—
87#449—92no—
88C4×SD16—92no—
89C4×D8—92no—
90#431—91no—
91C3×#41—21no—
92C3×#41—61no—
93C2×C3×Q8C22×D311yescharacteristic
94C2×C3×D4—31no—
95C22×C3×C4—31no—
96C22×C3×C4—31no—
97C22×C3×C4—31no—
98C2×#67—62no—
99#235—124no—
100C2×D12—32no—
101C2×D12—61no—
102C2×D12—61no—
103C2×D12—123no—
104C2×C4×D3—62no—
105C2×C4×D3—126no—
106C2×Dic6—61no—
107#41⋊C3—23no—
108C2×SL(2,𝔽3)C22×D313yes—
109GL(2,𝔽3)—66no—
110C3×C4⋊C4—31no—
111C3×C4⋊C4—31no—
112C3×C22⋊C4—61no—
113C3×C42—31no—
114C3×C42—31no—
115C3×C42—31no—
116C3×C42—43no—
117C3×C42S411yescharacteristic
118#215—62no—
119#215—62no—
120#213—64no—
121(C2×D3)⋊C4—62no—
122(C2×D3)⋊C4—62no—
123(C2×D3)⋊C4—126no—
124C4⋊Dic3—32no—
125C4⋊Dic3—61no—
126C4⋊Dic3—123no—
127C2×C3⋊C8—32no—
128C2×C3⋊C8—32no—
129C22×C32—41no—
130C2×C3⋊D3—44no—
131C2×C3⋊D3—82no—
132C2×C3⋊D3—82no—
133C32×C4—42no—
134C32×C4—42no—
135C32×C4—81no—
136C3⋊Dic3—82no—
137C2×#41—181no—
138C2×#41C2×C3⋊D311yescharacteristic
139C2×SD16—92no—
140C2×D8—92no—
141C4⋊Q8—91no—
142#127—91no—
143#124—181no—
144#121—92no—
145#121—181no—
146C4×Q8C2×C3⋊D311yescharacteristic
147C4×Q8C2×C3⋊D311yescharacteristic
148C4×D4—31no—
149C4×D4—31no—
150C4×D4—92no—
151C4×D4—181no—
152#117—31no—
153C2×C42—31no—
154#107—92no—
155#106—92no—
156C4⋊C8—91no—
157C4⋊C8—91no—
158#103—92no—
159#102—92no—
160#102—92no—
161#102—92no—
162C22⋊C8—92no—
163C4×C8—92no—
164C23×C3—31no—
165C22×D3—62no—
166C22×D3—126no—
167C3×Q8—31no—
168C3×Q8#23511yescharacteristic
169C3×D4—32no—
170C3×D4—61no—
171C2×C3×C4—31no—
172C2×C3×C4—31no—
173C2×C3×C4—31no—
174C2×C3×C4—43no—
175C2×C3×C4—43no—
176C2×C3×C4—43no—
177C2×C3×C4—61no—
178C2×C3×C4—61no—
179C2×C3×C4—62no—
180C2×C3×C4—62no—
181C2×C3×C4C2×S411yescharacteristic
182C2×C3×C4C2×S411yescharacteristic
183C2×C3×C4C2×S411yescharacteristic
184#67—124no—
185C2×Dic3—62no—
186C2×Dic3—126no—
187D12—62no—
188D12—62no—
189D12—1212no—
190D12—122no—
191D12—122no—
192C4×D3—124no—
193C4×D3—2412no—
194Dic6—122no—
195SL(2,𝔽3)#23513yescomplemented
196C3⋊C8—62no—
197C3⋊C8—62no—
198C2×C32—41no—
199C2×C32—41no—
200C2×C32—41no—
201C3⋊D3—84no—
202#41—21no—
203#41—61no—
204#41—364no—
205C2×Q8—181no—
206C2×Q8C22×C3⋊D311yescharacteristic
207C2×D4—31no—
208C2×D4—92no—
209C2×D4—181no—
210C2×D4—182no—
211C2×D4—181no—
212C22×C4—31no—
213C22×C4—31no—
214C22×C4—31no—
215C22×C4—182no—
216SD16—182no—
217SD16—182no—
218D8—184no—
219C2×C8—92no—
220C2×C8—92no—
221C4⋊C4—31no—
222C4⋊C4—31no—
223C4⋊C4—92no—
224C4⋊C4—181no—
225C22⋊C4—61no—
226C22⋊C4—182no—
227C22⋊C4—182no—
228C42—31no—
229C42—31no—
230C42—31no—
231C42C3⋊S411yescharacteristic
232C22×C3—43no—
233C22×C3—61no—
234C22×C3—61no—
235C22×C3—61no—
236C22×C3C22×S411yescharacteristic
237C2×D3—1212no—
238C2×D3—122no—
239C2×D3—122no—
240C2×D3—122no—
241C2×D3—246no—
242C2×D3—246no—
243C3×C4—21no—
244C3×C4—31no—
245C3×C4—31no—
246C3×C4—46no—
247C3×C4—46no—
248C3×C4—61no—
249C3×C4—61no—
250C3×C4—83no—
251C3×C4#98512yes—
252C3×C4#98612yes—
253Dic3—122no—
254Dic3—246no—
255C32—41noSylow
256C23—31no—
257C23—182no—
258Q8—31no—
259Q8—362no—
260Q8#382811yescharacteristic
261D4—32no—
262D4—61no—
263D4—182no—
264D4—182no—
265D4—362no—
266D4—364no—
267D4—362no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4—31no—
271C2×C4—61no—
272C2×C4—61no—
273C2×C4—62no—
274C2×C4—62no—
275C2×C4—182no—
276C2×C4—364no—
277C2×C4C2×C3⋊S411yescharacteristic
278C2×C4C2×C3⋊S411yescharacteristic
279C2×C4C2×C3⋊S411yescharacteristic
280C8—182no—
281C8—182no—
282C2×C3—43no—
283C2×C3—43no—
284C2×C3—43no—
285C2×C3—121no—
286C2×C3#591211yescharacteristic
287C2×C3C2×#98511yescharacteristic
288C2×C3C2×#98611yescharacteristic
289D3—2412no—
290D3—242no—
291C22—61no—
292C22—61no—
293C22—61no—
294C22—362no—
295C22—362no—
296C22—362no—
297C22C22×C3⋊S411yescharacteristic
298C4—21no—
299C4—31no—
300C4—31no—
301C4—61no—
302C4—61no—
303C4—362no—
304C4#6426612yes—
305C4#6426712yes—
306C3—43no—
307C3#8534511yescharacteristic, complemented
308C2—121no—
309C2—722no—
310C2#1059657511yescharacteristic
311C2C2×#6426611yescharacteristic
312C2C2×#6426711yescharacteristic
subgroupG/H
centerC2×C4C2×C3⋊S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C22×C3⋊S4
FittingC3×C4×#41D3
socleC22×C3C22×S4
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
1. C3×C4×#41⋊C3C2semidirect
2. #10593661C2semidirect
3. C4⋊(C3⋊GL(2,𝔽3))C2semidirect
4. C4×C3⋊GL(2,𝔽3)C2semidirect
5. #10593625C2semidirect
14. C3×C4×#41D3semidirect
16. C4×#41⋊C3D3semidirect
79. C3×SL(2,𝔽3)#41semidirect
81. C4×#41C3⋊D3semidirect
195. SL(2,𝔽3)#235semidirect
307. C3#85345semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#41⋊C32
#105936612
C4⋊(C3⋊GL(2,𝔽3))2
C4×C3⋊GL(2,𝔽3)2
#105936252
#853453
#825293
C4×C4⋊(C3⋊D3)4