Finite Group Databasebeta

← #11921029

Subgroups — #11921029

Order 1152.

400 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#10596586C211yesmaximal, characteristic
2C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
3#10593657C211yesmaximal, characteristic, complemented
4#73073—33nomaximal
5#71645—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64267C411yescharacteristic, complemented
8#64266—21no—
9#64265C411yescharacteristic, complemented
10#64264—21no—
11C3×C4×SL(2,𝔽3)—21no—
12C3⋊GU(2,𝔽3)—21no—
13#63632—41nomaximal
14#5923—33no—
15C3×C4×#41D311yescharacteristic, complemented
16#5822—31no—
17C4×#41⋊C3D313yescomplemented
18#5423—33no—
19#5236—31no—
20#5006—31no—
21C2×#805—31no—
22#4533—31no—
23#4523—31no—
24#3828—41no—
25C3×#41⋊C3C2×C411yescharacteristic
26C3×#41⋊C3D411yescharacteristic
27C2×C3×SL(2,𝔽3)D411yescharacteristic
28C3⋊GL(2,𝔽3)—21no—
29C3⋊#226—21no—
30C32×C42—41no—
31#3748—41no—
32#1906—91noSylow
33C2×C3×#41C2×D311yescharacteristic
34C2×#235—31no—
35C2×#41⋊C3C2×D313yes—
36#986—33no—
37#985—63no—
38#984—33no—
39#983—63no—
40C3×C4×Q8—21no—
41C3×C4×D4—61no—
42C3×#117—31no—
43C2×C3×C42—31no—
44#951—31no—
45#951—31no—
46#950—61no—
47#950—61no—
48#949—31no—
49#949—31no—
50#942—61no—
51#932—61no—
52#926—31no—
53C2×#208—31no—
54C2×#208—31no—
55C4×SL(2,𝔽3)—23no—
56GU(2,𝔽3)—63no—
57#837—61no—
58#837—61no—
59#806—62no—
60#805—61no—
61#805—61no—
62#805—123no—
63C2×C32×C4—41no—
64C2×C32×C4—81no—
65#638—81no—
66C4⋊(C3⋊D3)—41no—
67C4×C3⋊D3—81no—
68#634—41no—
69C3×SL(2,𝔽3)C22⋊C411yescharacteristic
70C3⋊(C3⋊C8)—81no—
71#575—91no—
72C4×#41C3⋊D311yescharacteristic, complemented
73#421—91no—
74C2×#104—91no—
75#410—91no—
76#344—91no—
77#339—91no—
78C3×#41—31no—
79C3×#41—31no—
80C3×#41C4×D311yescharacteristic
81C3×#41D1211yescharacteristic
82C2×C3×Q8#6711yescharacteristic
83C2×C3×D4—31no—
84C22×C3×C4—31no—
85C22×C3×C4—61no—
86C2×#67—61no—
87#235—61no—
88#235—61no—
89#235—61no—
90#235—61no—
91#235—123no—
92C2×D12—31no—
93C2×C4×D3—61no—
94C2×Dic6—31no—
95#41⋊C3C4×D313yes—
96#41⋊C3D1213yes—
97C2×SL(2,𝔽3)#6713yes—
98GL(2,𝔽3)—63no—
99#226—63no—
100C3×C4⋊C4—61no—
101C3×C22⋊C4—32no—
102C3×C42—31no—
103C3×C42—43no—
104C3×C42—61no—
105C3×C42S411yescharacteristic
106#217—61no—
107#216—61no—
108#216—61no—
109#215—61no—
110#215—61no—
111#214—61no—
112#214—61no—
113#213—61no—
114#213—61no—
115C4⋊Dic3—61no—
116C4×Dic3—61no—
117#208—31no—
118#208—31no—
119#208—61no—
120#208—61no—
121#208—61no—
122#208—123no—
123C2×C3⋊C8—61no—
124C2×C3⋊C8—61no—
125C22×C32—41no—
126C2×C3⋊D3—81no—
127C32×C4—41no—
128C32×C4—41no—
129C32×C4—82no—
130C3⋊Dic3—81no—
131C2×#41—91no—
132C2×#41C2×C3⋊D311yescharacteristic
133#137—91no—
134#137—91no—
135#137—181no—
136AGL(1,ℤ/8)—91no—
137AGL(1,ℤ/8)—91no—
138AGL(1,ℤ/8)—181no—
139#135—181no—
140#135—181no—
141C2×M16—91no—
142C2×M16—91no—
143C4×Q8—21no—
144C4×D4—61no—
145#117—31no—
146#117—91no—
147C2×C42—31no—
148#104—181no—
149#104—181no—
150#104—181no—
151#104—181no—
152#99—182no—
153C23×C3—31no—
154C22×D3—61no—
155C3×Q8—31no—
156C3×Q8(C2×D3)⋊C411yescharacteristic
157C3×D4—31no—
158C3×D4—31no—
159C3×D4—61no—
160C2×C3×C4—21no—
161C2×C3×C4—31no—
162C2×C3×C4—31no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—43no—
167C2×C3×C4—61no—
168C2×C3×C4—83no—
169C2×C3×C4—122no—
170C2×C3×C4C2×S411yescharacteristic
171#67—121no—
172#67—121no—
173#67—243no—
174C2×Dic3—61no—
175C2×Dic3—121no—
176D12—61no—
177D12—61no—
178D12—123no—
179C4×D3—121no—
180C4×D3—121no—
181C4×D3—243no—
182Dic6—61no—
183Dic6—61no—
184Dic6—123no—
185SL(2,𝔽3)(C2×D3)⋊C413yes—
186C3⋊C8—61no—
187C3⋊C8—61no—
188C3⋊C8—121no—
189C3⋊C8—243no—
190C2×C32—41no—
191C2×C32—81no—
192C3⋊D3—161no—
193#41—31no—
194#41—31no—
195#41—181no—
196#41—181no—
197#41—181no—
198#41—181no—
199#41C4×C3⋊D311yescharacteristic
200#41C4⋊(C3⋊D3)11yescharacteristic
201C2×Q8—91no—
202C2×Q8#63811yescharacteristic
203C2×D4—31no—
204C2×D4—91no—
205C2×D4—181no—
206C22×C4—31no—
207C22×C4—61no—
208C22×C4—181no—
209Q16—181no—
210Q16—181no—
211SD16—181no—
212SD16—181no—
213SD16—181no—
214SD16—181no—
215D8—181no—
216D8—181no—
217M16—91no—
218M16—91no—
219M16—181no—
220M16—181no—
221M16—181no—
222C2×C8—181no—
223C2×C8—181no—
224C4⋊C4—61no—
225C4⋊C4—181no—
226C22⋊C4—32no—
227C22⋊C4—181no—
228C42—31no—
229C42—61no—
230C42—181no—
231C42C3⋊S411yescharacteristic
232C22×C3—31no—
233C22×C3—31no—
234C22×C3—43no—
235C22×C3—121no—
236C22×C3GL(2,ℤ/4)11yescharacteristic
237C2×D3—121no—
238C2×D3—243no—
239C2×D3—241no—
240C3×C4—22no—
241C3×C4—31no—
242C3×C4—31no—
243C3×C4—43no—
244C3×C4—43no—
245C3×C4—86no—
246C3×C4—121no—
247C3×C4C4×S411yescharacteristic
248C3×C4C4⋊S411yescharacteristic
249Dic3—121no—
250Dic3—243no—
251Dic3—241no—
252C32—41noSylow
253C23—31no—
254C23—181no—
255Q8—31no—
256Q8—181no—
257Q8—181no—
258Q8#375211yescharacteristic
259D4—31no—
260D4—31no—
261D4—61no—
262D4—181no—
263D4—181no—
264D4—361no—
265D4—361no—
266C2×C4—21no—
267C2×C4—31no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4—31no—
271C2×C4—31no—
272C2×C4—61no—
273C2×C4—122no—
274C2×C4—181no—
275C2×C4—361no—
276C2×C4—361no—
277C2×C4—361no—
278C2×C4C2×C3⋊S411yescharacteristic
279C8—181no—
280C8—181no—
281C8—361no—
282C2×C3—21no—
283C2×C3—43no—
284C2×C3—61no—
285C2×C3—61no—
286C2×C3—83no—
287C2×C3(C2×S4)⋊C411yescharacteristic
288D3—241no—
289D3—483no—
290C22—31no—
291C22—31no—
292C22—121no—
293C22—361no—
294C22—721no—
295C22#6426911yescharacteristic
296C4—22no—
297C4—31no—
298C4—31no—
299C4—121no—
300C4—361no—
301C4—721no—
302C4C4×C3⋊S411yescharacteristic
303C4C4⋊(C3⋊S4)11yescharacteristic
304C3—43no—
305C3#7307311yescharacteristic, complemented
306C2—21no—
307C2—61no—
308C2—61no—
309C2—721no—
310C2#1059364711yescharacteristic
subgroupG/H
centerC4C4⋊(C3⋊S4)
commutatorC3×#41⋊C3C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC3×C4×#41D3
socleC2×C3(C2×S4)⋊C4
prime radical#10596586C2
cosocleC2×C3×#41⋊C3C22
hypercenterC42C3⋊S4
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C4 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#41⋊C3C2semidirect
3. #10593657C2semidirect
7. #64267C4semidirect
9. #64265C4semidirect
15. C3×C4×#41D3semidirect
17. C4×#41⋊C3D3semidirect
72. C4×#41C3⋊D3semidirect
305. C3#73073semidirect

Maximal subgroups

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

subgroupindex
#105965862
C3×C4×#41⋊C32
#105936572
#730733
#716453
#636324