Finite Group Databasebeta

← #11920701

Subgroups — #11920701

Order 1152.

347 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 347 conjugacy classes of subgroups — too many to draw. Only its 45 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
2C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic
3C3×#5426C211yesmaximal, characteristic
4#73124—31nomaximal
5#70304—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64265—21no—
8#64265C412yescomplemented
9C2×C3⋊#226—21no—
10C3⋊(#131⋊C3)—21no—
11C3×#859—21no—
12#63567—41nomaximal
13C2×#984—31no—
14C2×#984—61no—
15C2×#951—31no—
16C2×#948D311yescharacteristic
17C2×#131⋊C3—31no—
18#5426D311yescharacteristic
19C3×#417—31no—
20C2×#824—31no—
21C2×#810—31no—
22#4558—31no—
23#4530—31no—
24C2×#634—41no—
25C3×#41⋊C3C2×C411yescharacteristic
26C3×#41⋊C3D411yescharacteristic
27C2×C3×SL(2,𝔽3)D411yescharacteristic
28C3⋊#226—22no—
29C3×C4⋊Dic3—41no—
30C2×C3×C3⋊C8—41no—
31#1908—91noSylow
32C2×C3×#41C2×D311yescharacteristic
33C22×Dic6—31no—
34C2×#41⋊C3—21no—
35C2×#41⋊C3C2×D311yescharacteristic
36#984—32no—
37#984—62no—
38#984—62no—
39#984—61no—
40C2×#226—62no—
41C2×#226—61no—
42C2×C3×M16—31no—
43C2×C3×C4⋊C4—31no—
44#951—32no—
45#951—32no—
46#951—61no—
47#951—61no—
48#948—21no—
49#948—61no—
50C2×#216—61no—
51C2×#214—61no—
52C2×#208—31no—
53C2×#208—31no—
54C22×C3⋊C8—31no—
55#131⋊C3—61no—
56#859—21no—
57C3×#103—61no—
58C3×#102—61no—
59#824—62no—
60#816—121no—
61#810—61no—
62#810—61no—
63C2×C32×C4—41no—
64C2×C3⋊Dic3—81no—
65#634—42no—
66#634—81no—
67C2×C3×Dic3—81no—
68C3×SL(2,𝔽3)C22⋊C411yescharacteristic
69C3×C3⋊C8—81no—
70C2×#137—91no—
71C2×#131—31no—
72#417—31no—
73C2×#103—91no—
74C2×#101—91no—
75#343—91no—
76#341—91no—
77C3×#41—31no—
78C3×#41—31no—
79C3×#41C4×D311yescharacteristic
80C3×#41#6711yescharacteristic
81C2×C3×Q8D1211yescharacteristic
82C2×C3×D4—31no—
83C22×C3×C4—31no—
84C22×C3×C4—61no—
85C22×Dic3—61no—
86C2×Dic6—32no—
87C2×Dic6—61no—
88C2×Dic6—61no—
89C2×Dic6—61no—
90C2×Dic6—61no—
91C2×Dic6—61no—
92C2×Dic6—121no—
93C2×Dic6—241no—
94#41⋊C3—21no—
95#41⋊C3—21no—
96#41⋊C3C4×D311yescharacteristic
97#41⋊C3D1211yescharacteristic
98C2×SL(2,𝔽3)—21no—
99C2×SL(2,𝔽3)#6711yescharacteristic
100#226—64no—
101#226—62no—
102C3×M16—61no—
103C3×M16—61no—
104C2×C3×C8—61no—
105C2×C3×C8—121no—
106C3×C4⋊C4—61no—
107C3×C4⋊C4—61no—
108#216—62no—
109#216—62no—
110#214—62no—
111#214—62no—
112C4⋊Dic3—41no—
113#208—32no—
114#208—32no—
115#208—61no—
116#208—61no—
117C2×C3⋊C8—31no—
118C2×C3⋊C8—61no—
119C2×C3⋊C8—61no—
120C2×C3⋊C8—61no—
121C2×C3⋊C8S411yescharacteristic
122C22×C32—41no—
123C32×C4—41no—
124C32×C4—41no—
125C3⋊Dic3—82no—
126C3×Dic3—161no—
127C2×#41D3211yescharacteristic
128C22×Q8—91no—
129#137—92no—
130#137—92no—
131#137—181no—
132#137—181no—
133C2×Q16—181no—
134C2×SD16—181no—
135#131—61no—
136#131—181no—
137C2×M16—31no—
138C2×M16—91no—
139C2×M16—91no—
140C22×C8—91no—
141C2×C4⋊C4—31no—
142#103—61no—
143#103—181no—
144#103—181no—
145#102—61no—
146#101—182no—
147C23×C3—31no—
148C3×Q8—31no—
149C3×Q8(C2×D3)⋊C411yescharacteristic
150C3×D4—31no—
151C3×D4—31no—
152C3×D4—61no—
153C2×C3×C4—31no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—31no—
157C2×C3×C4—31no—
158C2×C3×C4—41no—
159C2×C3×C4—81no—
160C2×C3×C4—121no—
161C2×C3×C4—241no—
162C2×C3×C4C2×S411yescharacteristic
163C2×Dic3—62no—
164C2×Dic3—81no—
165C2×Dic3—121no—
166C2×Dic3—121no—
167C2×Dic3—241no—
168C2×Dic3—242no—
169Dic6—62no—
170Dic6—62no—
171Dic6—122no—
172Dic6—121no—
173Dic6—121no—
174Dic6—242no—
175Dic6—241no—
176Dic6—242no—
177SL(2,𝔽3)—21no—
178SL(2,𝔽3)(C2×D3)⋊C411yescharacteristic
179C3×C8—121no—
180C3×C8—241no—
181C3⋊C8—21no—
182C3⋊C8—62no—
183C3⋊C8—61no—
184C2×C32—41no—
185C2×C32—41no—
186C2×C32—41no—
187#41—31no—
188#41—31no—
189#41#62411yescharacteristic
190#41#62611yescharacteristic
191C2×Q8—92no—
192C2×Q8—181no—
193C2×Q8—181no—
194C2×Q8—181no—
195C2×Q8—181no—
196C2×Q8—181no—
197C2×Q8#62611yescharacteristic
198C2×D4—31no—
199C22×C4—31no—
200C22×C4—61no—
201C22×C4—181no—
202Q16—182no—
203Q16—182no—
204SD16—182no—
205SD16—182no—
206M16—61no—
207M16—61no—
208M16—92no—
209M16—92no—
210M16—181no—
211M16—181no—
212C2×C8—31no—
213C2×C8—61no—
214C2×C8—91no—
215C2×C8—181no—
216C2×C8—181no—
217C2×C8—181no—
218C4⋊C4—61no—
219C4⋊C4—61no—
220C22×C3—31no—
221C22×C3—31no—
222C22×C3—41no—
223C22×C3—61no—
224C22×C3—61no—
225C22×C3—81no—
226C22×C3C4⋊S411yescharacteristic
227C3×C4—31no—
228C3×C4—31no—
229C3×C4—41no—
230C3×C4—41no—
231C3×C4—81no—
232C3×C4—81no—
233C3×C4—241no—
234C3×C4C4×S411yescharacteristic
235C3×C4GL(2,ℤ/4)11yescharacteristic
236Dic3—122no—
237Dic3—161no—
238Dic3—242no—
239Dic3—244no—
240C32—41noSylow
241C23—31no—
242Q8—31no—
243Q8—182no—
244Q8—182no—
245Q8—361no—
246Q8—361no—
247Q8#372211yescharacteristic
248D4—31no—
249D4—31no—
250D4—61no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—31no—
255C2×C4—31no—
256C2×C4—121no—
257C2×C4—182no—
258C2×C4—241no—
259C2×C4—361no—
260C2×C4—361no—
261C2×C4D3×S411yescharacteristic
262C8—61no—
263C8—121no—
264C8—182no—
265C8—181no—
266C2×C3—41no—
267C2×C3—41no—
268C2×C3—41no—
269C2×C3—61no—
270C2×C3—61no—
271C2×C3—81no—
272C2×C3—81no—
273C2×C3—81no—
274C2×C3#540311yescharacteristic
275C2×C3#540611yescharacteristic
276C2×C3(C2×S4)⋊C411yescharacteristic
277C22—31no—
278C22—31no—
279C22—61no—
280C22—61no—
281C22#6420711yescharacteristic
282C4—31no—
283C4—31no—
284C4—241no—
285C4—362no—
286C4(C3⋊S4)⋊C411yescharacteristic
287C4#6421011yescharacteristic
288C3—41no—
289C3—81no—
290C3#7312411yescharacteristic, complemented
291C2—61no—
292C2—61no—
293C2#1059322311yescharacteristic
294C2#1059322611yescharacteristic
295C2#1059324211yescharacteristic
subgroupG/H
centerC22#64207
commutatorC3×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C4⋊S4
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
8. #64265C4semidirect
290. C3#73124semidirect

Maximal subgroups

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

subgroupindex
C2×#642652
C2×C3⋊(#131⋊C3)2
C3×#54262
#731243
#703043
#635674