Finite Group Databasebeta

← #11922890

Subgroups — #11922890

Order 1152.

664 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#64266C211yesmaximal, characteristic
2C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
3#10593658C211yesmaximal, characteristic, complemented
4#10593628C212yesmaximal, complemented
5#10593622C212yesmaximal, complemented
6#85341—33nomaximal
7#82506—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#64266C414yescomplemented
10C2×C3⋊GL(2,𝔽3)C2211yescharacteristic
11C2×C3⋊#226C2211yescharacteristic
12#64081—41nomaximal
13C3×C4×SL(2,𝔽3)C2212yes—
14C3⋊#859C2212yes—
15C2×#985—33no—
16C3×C4×#41D311yescharacteristic, complemented
17C2×#950—31no—
18C4×#235—31no—
19C4×#41⋊C3D313yescomplemented
20#5424—33no—
21#5394—36no—
22#5388—36no—
23#5233—31no—
24#5030—32no—
25#5026—32no—
26#5018—32no—
27#5014—32no—
28#5002—31no—
29#4998—31no—
30C2×#803—31no—
31C2×C4×C3⋊D3—41no—
32C3×#41⋊C3C2×C412yescomplemented
33C2×C3×SL(2,𝔽3)C2311yescharacteristic
34C3⋊GL(2,𝔽3)C2×C412yescomplemented
35C3⋊#226C2×C412yescomplemented
36C32×C42—41no—
37#3752—42no—
38#3750—42no—
39C4×C3⋊Dic3—41no—
40#2943—91noSylow
41C2×C3×#41C2×D311yescharacteristic
42C2×#235—31no—
43C2×#41⋊C3C2×D313yes—
44#985—312no—
45C2×GL(2,𝔽3)—33no—
46C2×#226—33no—
47C3×C4×Q8C2×D312yes—
48C3×C4×D4—32no—
49C3×#117—31no—
50C2×C3×C42—31no—
51#950—34no—
52#950—34no—
53C2×#216—31no—
54C2×#215—31no—
55C2×#214—31no—
56C2×#213—31no—
57C4×#67—62no—
58#926—31no—
59C22×C3⋊C8—31no—
60C22×C3⋊C8—31no—
61C4×D12—32no—
62#872—61no—
63#872—123no—
64C42×D3—61no—
65C4×Dic6—32no—
66C4×SL(2,𝔽3)C2×D316yes—
67#859—36no—
68#835—32no—
69#832—32no—
70#810—32no—
71#809—32no—
72#808—32no—
73#807—32no—
74#803—32no—
75#803—32no—
76C22×C3⋊D3—41no—
77C2×C32×C4—41no—
78C2×C32×C4—42no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3—42no—
81C4×C3⋊D3—44no—
82C3×SL(2,𝔽3)C22×C411yescharacteristic
83C2×#135—91no—
84C4×#41—91no—
85C4×#41C3⋊D311yescharacteristic, complemented
86#442—92no—
87#441—92no—
88#440—92no—
89#440—92no—
90#427—91no—
91#416—91no—
92#416—91no—
93C2×#97—91no—
94C3×#41—32no—
95C3×#41C4×D312yes—
96C2×C3×Q8C22×D311yescharacteristic
97C2×C3×D4—31no—
98C22×C3×C4—31no—
99C22×C3×C4—32no—
100C2×#67—61no—
101#235—34no—
102#235—62no—
103C2×D12—31no—
104C2×C4×D3—61no—
105C2×C4×D3—62no—
106C2×C4×D3—123no—
107C2×Dic6—31no—
108#41⋊C3C4×D316yescomplemented
109C2×SL(2,𝔽3)C22×D313yes—
110GL(2,𝔽3)—36no—
111#226—36no—
112C3×C4⋊C4—32no—
113C3×C22⋊C4—61no—
114C3×C42—32no—
115C3×C42—31no—
116C3×C42—43no—
117C3×C42S411yescharacteristic
118#217—61no—
119#216—32no—
120#216—32no—
121#215—32no—
122#215—32no—
123#214—34no—
124#213—34no—
125(C2×D3)⋊C4—62no—
126(C2×D3)⋊C4—126no—
127C4⋊Dic3—32no—
128Dic3⋊C4—62no—
129Dic3⋊C4—126no—
130C4×Dic3—62no—
131C4×Dic3—61no—
132C4×Dic3—123no—
133C2×C3⋊C8—31no—
134C2×C3⋊C8—31no—
135C2×C3⋊C8—34no—
136C2×C3⋊C8—32no—
137C2×C3⋊C8—62no—
138C22×C32—41no—
139C2×C3⋊D3—42no—
140C2×C3⋊D3—82no—
141C32×C4—42no—
142C32×C4—82no—
143C3⋊Dic3—42no—
144C3⋊Dic3—82no—
145C2×#41—91no—
146C2×#41C2×C3⋊D311yescharacteristic
147#135—94no—
148#135—94no—
149C2×Q16—91no—
150C2×SD16—91no—
151C2×SD16—91no—
152C2×D8—91no—
153C22×C8—91no—
154C22×C8—91no—
155C4×Q8—92no—
156C4×Q8C2×C3⋊D312yes—
157C4×D4—32no—
158C4×D4—92no—
159C4×D4—182no—
160#117—31no—
161#117—91no—
162#117—181no—
163C2×C42—31no—
164C2×C42—181no—
165#107—92no—
166#106—92no—
167#103—92no—
168#103—92no—
169#102—92no—
170#102—92no—
171#97—92no—
172#97—92no—
173C23×C3—31no—
174C22×D3—61no—
175C22×D3—123no—
176C3×Q8—31no—
177C3×Q8C2×C4×D311yescharacteristic
178C3×D4—32no—
179C3×D4—61no—
180C2×C3×C4—31no—
181C2×C3×C4—32no—
182C2×C3×C4—32no—
183C2×C3×C4—32no—
184C2×C3×C4—46no—
185C2×C3×C4—43no—
186C2×C3×C4—122no—
187C2×C3×C4C2×S412yes—
188C2×C3×C4C2×S411yescharacteristic
189#67—64no—
190C2×Dic3—61no—
191C2×Dic3—62no—
192C2×Dic3—123no—
193C2×Dic3—126no—
194D12—32no—
195D12—61no—
196C4×D3—64no—
197C4×D3—1212no—
198C4×D3—124no—
199Dic6—32no—
200Dic6—61no—
201SL(2,𝔽3)C2×C4×D313yes—
202C3⋊C8—32no—
203C3⋊C8—32no—
204C3⋊C8—62no—
205C2×C32—41no—
206C2×C32—42no—
207C3⋊D3—82no—
208#41—32no—
209#41—94no—
210#41—182no—
211#41C4×C3⋊D312yes—
212C2×Q8—91no—
213C2×Q8C22×C3⋊D311yescharacteristic
214C2×D4—31no—
215C2×D4—91no—
216C2×D4—181no—
217C22×C4—31no—
218C22×C4—32no—
219C22×C4—182no—
220C22×C4—181no—
221Q16—92no—
222Q16—92no—
223SD16—94no—
224SD16—92no—
225SD16—92no—
226D8—94no—
227C2×C8—91no—
228C2×C8—91no—
229C2×C8—94no—
230C2×C8—92no—
231C2×C8—182no—
232C4⋊C4—32no—
233C4⋊C4—92no—
234C4⋊C4—182no—
235C22⋊C4—61no—
236C22⋊C4—181no—
237C22⋊C4—182no—
238C42—32no—
239C42—31no—
240C42—182no—
241C42—181no—
242C42C3⋊S411yescharacteristic
243C22×C3—32no—
244C22×C3—43no—
245C22×C3—62no—
246C22×C3C22×S411yescharacteristic
247C2×D3—62no—
248C2×D3—126no—
249C2×D3—122no—
250C2×D3—246no—
251C3×C4—22no—
252C3×C4—31no—
253C3×C4—31no—
254C3×C4—46no—
255C3×C4—62no—
256C3×C4—86no—
257C3×C4C4×S412yes—
258Dic3—62no—
259Dic3—126no—
260Dic3—122no—
261Dic3—246no—
262C32—41noSylow
263C23—31no—
264C23—181no—
265Q8—31no—
266Q8—92no—
267Q8—181no—
268Q8C2×C4×C3⋊D311yescharacteristic
269D4—32no—
270D4—61no—
271D4—92no—
272D4—181no—
273D4—184no—
274C2×C4—31no—
275C2×C4—32no—
276C2×C4—32no—
277C2×C4—32no—
278C2×C4—122no—
279C2×C4—181no—
280C2×C4—184no—
281C2×C4—182no—
282C2×C4—364no—
283C2×C4C2×C3⋊S412yes—
284C2×C4C2×C3⋊S411yescharacteristic
285C8—92no—
286C8—92no—
287C8—182no—
288C2×C3—43no—
289C2×C3—46no—
290C2×C3—62no—
291C2×C3C2×C4×S411yescharacteristic
292C2×C3#592312yes—
293D3—122no—
294D3—246no—
295C22—32no—
296C22—62no—
297C22—182no—
298C22—362no—
299C22C22×C3⋊S411yescharacteristic
300C4—22no—
301C4—31no—
302C4—31no—
303C4—62no—
304C4—182no—
305C4—362no—
306C4C4×C3⋊S412yes—
307C3—43no—
308C3#8534111yescharacteristic, complemented
309C2—62no—
310C2—362no—
311C2C2×C4×C3⋊S411yescharacteristic
312C2#1059658612yes—
subgroupG/H
centerC2×C4C2×C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC22C22×C3⋊S4
FittingC3×C4×#41D3
socleC22×C3C22×S4
prime radicalC2×#64266C2
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC42C3⋊S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#41⋊C3C2semidirect
3. #10593658C2semidirect
4. #10593628C2semidirect
5. #10593622C2semidirect
9. #64266C4semidirect
16. C3×C4×#41D3semidirect
19. C4×#41⋊C3D3semidirect
32. C3×#41⋊C3C2×C4semidirect
34. C3⋊GL(2,𝔽3)C2×C4semidirect
35. C3⋊#226C2×C4semidirect
85. C4×#41C3⋊D3semidirect
108. #41⋊C3C4×D3semidirect
308. C3#85341semidirect

Maximal subgroups

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

subgroupindex
C2×#642662
C3×C4×#41⋊C32
#105936582
#105936282
#105936222
#853413
#825063
#640814