Finite Group Databasebeta

← #11922289

Subgroups — #11922289

Order 1152.

545 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 545 conjugacy classes of subgroups — too many to draw. Only its 67 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×#64265C211yesmaximal, characteristic
2#5827⋊C3C211yesmaximal, characteristic
3C3×#5424C211yesmaximal, characteristic
4#10593195C212yesmaximal, complemented
5#10593193C212yesmaximal, complemented
6#85360—31nomaximal
7#78821—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#64265C414yescomplemented
10C2×C3⋊#226C2212yes—
11#63844—41nomaximal
12Dic3×SL(2,𝔽3)C2212yes—
13C3×#859C2211yescharacteristic
14C3×#859C2211yescharacteristic
15C2×#984—31no—
16C2×#984—61no—
17#5827D311yescharacteristic
18C2×#951—31no—
19#5516—31no—
20#520⋊C3—31no—
21#5424D311yescharacteristic
22#5388—32no—
23C4×#226—32no—
24C3×#416—31no—
25C2×#816—31no—
26#5101—31no—
27#4995—31no—
28#4790—32no—
29#4789—32no—
30#4758—32no—
31#4757—32no—
32C2×#634—41no—
33C3×#41⋊C3C2×C412yes—
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C3⋊#226C2×C414yescomplemented
36C3×C4⋊Dic3—41no—
37C3×C4×Dic3—41no—
38#3724—42no—
39Dic32—42no—
40#2947—91noSylow
41C2×C3×#41C2×D311yescharacteristic
42C22×Dic6—31no—
43C2×#41⋊C3—21no—
44C2×#41⋊C3C2×D311yescharacteristic
45#984—34no—
46#984—64no—
47C2×#226—32no—
48C2×#226—62no—
49C22×C3×C8—31no—
50C3×#117—31no—
51#951—34no—
52#951—34no—
53Q8×Dic3C2×D312yes—
54C2×#216—32no—
55D4×Dic3—32no—
56C2×#214—32no—
57#926—31no—
58C2×C4⋊Dic3—31no—
59C2×#208—31no—
60#887—32no—
61#887—32no—
62#887—121no—
63#877—62no—
64C4×Dic6—61no—
65C4×Dic6—61no—
66C4×SL(2,𝔽3)—32no—
67#859C2×D311yescharacteristic
68#859C2×D311yescharacteristic
69C3×#103—31no—
70C3×#103—31no—
71C3×#102—31no—
72C3×#102—31no—
73#816—32no—
74#816—32no—
75#815—32no—
76C8×Dic3—32no—
77#808—32no—
78#807—32no—
79C2×C32×C4—41no—
80C2×C3⋊Dic3—42no—
81#634—44no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—41no—
84C2×C3×Dic3—42no—
85C3×SL(2,𝔽3)C22×C411yescharacteristic
86C2×#137—91no—
87#520—31no—
88#519—91no—
89#441—92no—
90#440—92no—
91C4×Q16—92no—
92C4×SD16—92no—
93#428—91no—
94#416—31no—
95C2×#103—91no—
96#405—91no—
97C3×#41—32no—
98C3×#41C4×D312yes—
99C2×C3×Q8C22×D311yescharacteristic
100C2×C3×D4—31no—
101C22×C3×C4—31no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C2×Dic6—32no—
105C2×Dic6—34no—
106C2×Dic6—62no—
107C2×Dic6—61no—
108C2×Dic6—121no—
109C2×Dic6—241no—
110#41⋊C3—22no—
111#41⋊C3C4×D312yes—
112C2×SL(2,𝔽3)—21no—
113C2×SL(2,𝔽3)C22×D311yescharacteristic
114#226—34no—
115#226—64no—
116C2×C3×C8—31no—
117C2×C3×C8—31no—
118C2×C3×C8—62no—
119C3×C4⋊C4—31no—
120C3×C4⋊C4—31no—
121C3×C4⋊C4—121no—
122C3×C22⋊C4—61no—
123C3×C42—61no—
124#217—32no—
125#216—34no—
126#216—34no—
127#214—38no—
128C4⋊Dic3—31no—
129C4⋊Dic3—32no—
130C4⋊Dic3S411yescharacteristic
131Dic3⋊C4—62no—
132Dic3⋊C4—62no—
133Dic3⋊C4—122no—
134C4×Dic3—32no—
135C4×Dic3—41no—
136C4×Dic3—62no—
137C4×Dic3—62no—
138C4×Dic3—122no—
139#208—34no—
140C2×C3⋊C8—32no—
141C22×C32—41no—
142C32×C4—42no—
143C3⋊Dic3—44no—
144C3×Dic3—42no—
145C3×Dic3—82no—
146C3×Dic3—81no—
147C2×#41D3211yescharacteristic
148C22×Q8—91no—
149#137—94no—
150#137—94no—
151C2×Q16—92no—
152C2×SD16—92no—
153C2×M16—91no—
154C22×C8—31no—
155C4×Q8—32no—
156C4×Q8—92no—
157C4×Q8—92no—
158C4×Q8—181no—
159C4×Q8—181no—
160C4×D4—92no—
161#117—31no—
162#117—91no—
163#117—182no—
164C2×C4⋊C4—91no—
165#107—92no—
166#106—92no—
167#103—31no—
168#103—31no—
169#103—92no—
170#103—92no—
171#102—31no—
172#102—31no—
173#97—92no—
174C4×C8—92no—
175C23×C3—31no—
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—41no—
184C2×C3×C4—61no—
185C2×C3×C4—61no—
186C2×C3×C4—81no—
187C2×C3×C4—122no—
188C2×C3×C4C2×S411yescharacteristic
189C2×Dic3—32no—
190C2×Dic3—41no—
191C2×Dic3—41no—
192C2×Dic3—64no—
193C2×Dic3—62no—
194C2×Dic3—122no—
195C2×Dic3—242no—
196C2×Dic3—241no—
197C2×Dic3C2×S412yes—
198Dic6—34no—
199Dic6—62no—
200Dic6—64no—
201Dic6—124no—
202Dic6—244no—
203SL(2,𝔽3)—21no—
204SL(2,𝔽3)C2×C4×D311yescharacteristic
205C3×C8—61no—
206C3×C8—61no—
207C3⋊C8—34no—
208C2×C32—41no—
209C2×C32—41no—
210C2×C32—41no—
211#41—32no—
212#41#62412yes—
213C2×Q8—92no—
214C2×Q8—94no—
215C2×Q8—182no—
216C2×Q8—181no—
217C2×Q8C2×D3211yescharacteristic
218C2×D4—31no—
219C22×C4—31no—
220C22×C4—181no—
221C22×C4—181no—
222Q16—94no—
223Q16—94no—
224SD16—98no—
225M16—94no—
226C2×C8—31no—
227C2×C8—31no—
228C2×C8—62no—
229C2×C8—92no—
230C4⋊C4—31no—
231C4⋊C4—31no—
232C4⋊C4—31no—
233C4⋊C4—92no—
234C4⋊C4—91no—
235C4⋊C4—182no—
236C4⋊C4—182no—
237C22⋊C4—61no—
238C22⋊C4—92no—
239C42—61no—
240C42—92no—
241C42—182no—
242C42—182no—
243C22×C3—32no—
244C22×C3—41no—
245C22×C3—61no—
246C22×C3—61no—
247C22×C3—81no—
248C22×C3C22×S411yescharacteristic
249C3×C4—31no—
250C3×C4—31no—
251C3×C4—42no—
252C3×C4—82no—
253C3×C4—121no—
254C3×C4—121no—
255C3×C4—242no—
256C3×C4C4×S412yes—
257Dic3—22no—
258Dic3—42no—
259Dic3—64no—
260Dic3—62no—
261Dic3—81no—
262Dic3—124no—
263Dic3—244no—
264C32—41noSylow
265C23—31no—
266Q8—31no—
267Q8—94no—
268Q8—182no—
269Q8—184no—
270Q8C2×#62411yescharacteristic
271D4—32no—
272D4—61no—
273C2×C4—31no—
274C2×C4—32no—
275C2×C4—32no—
276C2×C4—32no—
277C2×C4—61no—
278C2×C4—61no—
279C2×C4—92no—
280C2×C4—184no—
281C2×C4—182no—
282C2×C4—721no—
283C2×C4D3×S411yescharacteristic
284C8—61no—
285C8—61no—
286C8—94no—
287C2×C3—41no—
288C2×C3—41no—
289C2×C3—41no—
290C2×C3—62no—
291C2×C3—81no—
292C2×C3—81no—
293C2×C3—81no—
294C2×C3C2×C4×S411yescharacteristic
295C2×C3#592411yescharacteristic
296C2×C3#592711yescharacteristic
297C22—32no—
298C22—61no—
299C22—61no—
300C22C2×D3×S411yescharacteristic
301C4—31no—
302C4—31no—
303C4—62no—
304C4—121no—
305C4—121no—
306C4—182no—
307C4—184no—
308C4(C3⋊S4)⋊C412yes—
309C3—41no—
310C3—81no—
311C3#8536011yescharacteristic, complemented
312C2—62no—
313C2#1059644711yescharacteristic
314C2#1059645211yescharacteristic
315C2C2×(C3⋊S4)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
prime radicalC2×C3×#41⋊C3C22
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC2×C4D3×S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #10593195C2semidirect
5. #10593193C2semidirect
9. #64265C4semidirect
35. C3⋊#226C2×C4semidirect
311. C3#85360semidirect

Maximal subgroups

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

subgroupindex
C2×#642652
#5827⋊C32
C3×#54242
#105931952
#105931932
#853603
#788213
#638444