Finite Group Databasebeta

← #11923773

Subgroups — #11923773

Order 1152.

584 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 35 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×#5948C211yesmaximal, characteristic
2C3⋊#5930C212yesmaximal, complemented
3#87508—33nomaximal
4#84084—31nomaximal
5C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
6#64265—42nomaximal
7#64259—41nomaximal
8C22×C3×#41D311yescharacteristic
9#5948D313yes—
10#5930—36no—
11C2×#951—32no—
12C2×#924—31no—
13#5239—34no—
14#5232—32no—
15#5228—32no—
16#5218—32no—
17#5207—31no—
18C3×#41⋊C3—42no—
19C3×#41⋊C3—81no—
20C3×C4×A4—41no—
21C3⋊SL(2,ℤ/4)—42no—
22C3⋊#226—44no—
23#3007—91noSylow
24C2×C3×#41—32no—
25C2×C3×#41—32no—
26C2×C3×#41—61no—
27C2×C3×#41—61no—
28C22×C3×Q8C2×D311yescharacteristic
29C22×C3×D4—31no—
30C23×C3×C4—31no—
31C22×Dic6—31no—
32C22⋊SL(2,𝔽3)C2×D313yes—
33#984—126no—
34A4⋊Q8—123no—
35C2×#217—61no—
36#951—62no—
37#951—62no—
38#951—62no—
39#951—62no—
40C2×#216—34no—
41C2×#214—34no—
42C2×C4⋊Dic3—31no—
43#924—32no—
44#924—32no—
45#924—61no—
46#924—61no—
47C2×Dic3⋊C4—61no—
48C2×#208—32no—
49#835—34no—
50#832—34no—
51#830—32no—
52#830—32no—
53C2×C3×A4—41no—
54#634—161no—
55C3×SL(2,𝔽3)—42no—
56C3×SL(2,𝔽3)—81no—
57C22×#41C3⋊D311yescharacteristic
58C2×#137—92no—
59C2×C22⋊Q8—91no—
60#452—94no—
61#451—92no—
62#450—92no—
63#417—92no—
64#407—91no—
65C24×C3—31no—
66C3×#41—21no—
67C3×#41—32no—
68C3×#41—32no—
69C3×#41—32no—
70C3×#41—61no—
71C3×#41—62no—
72C3×#41—61no—
73C3×#41—61no—
74C3×#41—62no—
75C3×#41S412yes—
76C2×C3×Q8—32no—
77C2×C3×Q8—61no—
78C2×C3×D4—32no—
79C2×C3×D4—61no—
80C2×C3×D4—62no—
81C2×C3×D4—62no—
82C22×C3×C4—31no—
83C22×C3×C4—31no—
84C22×C3×C4—31no—
85C22×C3×C4—31no—
86C22×C3×C4—31no—
87C22×C3×C4—62no—
88C22×C3×C4—62no—
89C22×C3×C4S411yescharacteristic
90C22×Dic3—61no—
91C22×Dic3—61no—
92C2×Dic6—32no—
93C2×Dic6—62no—
94C2×Dic6—62no—
95C2×Dic6—61no—
96#41⋊C3—46no—
97#41⋊C3—83no—
98C4×A4—43no—
99SL(2,ℤ/4)—126no—
100#226—1212no—
101#217—62no—
102#217—62no—
103#216—64no—
104#216—64no—
105#214—64no—
106#214—64no—
107C4⋊Dic3—32no—
108C4⋊Dic3—61no—
109Dic3⋊C4—62no—
110Dic3⋊C4—62no—
111#208—62no—
112#208—62no—
113C2×C3⋊C8—34no—
114C3×A4—41no—
115C32×C4—161no—
116C3⋊Dic3—162no—
117C2×#41—32no—
118C2×#41—32no—
119C2×#41—61no—
120C2×#41—61no—
121C22×Q8—91no—
122C22×Q8C2×C3⋊D311yescharacteristic
123C22×D4—31no—
124C23×C4—31no—
125#137—182no—
126#137—182no—
127#137—182no—
128#137—182no—
129C2×Q16—94no—
130C2×SD16—94no—
131C2×M16—92no—
132C22⋊Q8—92no—
133C22⋊Q8—92no—
134C22⋊Q8—181no—
135C22⋊Q8—181no—
136C2×C4⋊C4—91no—
137C2×C4⋊C4—181no—
138C2×C22⋊C4—181no—
139#103—94no—
140#102—94no—
141C22⋊C8—92no—
142C22⋊C8—92no—
143C23×C3—31no—
144C23×C3—31no—
145C23×C3—62no—
146C23×C3—61no—
147C23×C3—61no—
148C23×C3—121no—
149C23×C3C2×S411yescharacteristic
150C2×A4—43no—
151C3×Q8—21no—
152C3×Q8—32no—
153C3×Q8—61no—
154C3×Q8C2×S412yes—
155C3×D4—32no—
156C3×D4—32no—
157C3×D4—62no—
158C3×D4—61no—
159C3×D4—62no—
160C3×D4—61no—
161C2×C3×C4—31no—
162C2×C3×C4—32no—
163C2×C3×C4—32no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—31no—
167C2×C3×C4—62no—
168C2×C3×C4—62no—
169C2×C3×C4—62no—
170C2×C3×C4—61no—
171C2×C3×C4—61no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—122no—
175C2×Dic3—122no—
176Dic6—64no—
177Dic6—121no—
178Dic6—121no—
179Dic6—483no—
180SL(2,𝔽3)—46no—
181SL(2,𝔽3)—83no—
182C3⋊C8—64no—
183C2×C32—161no—
184C24—31no—
185#41—21no—
186#41—32no—
187#41—32no—
188#41—32no—
189#41—61no—
190#41—62no—
191#41—61no—
192#41—61no—
193#41—62no—
194#41C3⋊S412yes—
195C2×Q8—32no—
196C2×Q8—61no—
197C2×Q8—92no—
198C2×Q8—181no—
199C2×Q8—182no—
200C2×Q8—182no—
201C2×D4—32no—
202C2×D4—61no—
203C2×D4—62no—
204C2×D4—62no—
205C22×C4—31no—
206C22×C4—31no—
207C22×C4—31no—
208C22×C4—31no—
209C22×C4—31no—
210C22×C4—62no—
211C22×C4—62no—
212C22×C4—181no—
213C22×C4—181no—
214C22×C4C3⋊S411yescharacteristic
215Q16—184no—
216Q16—184no—
217SD16—184no—
218SD16—184no—
219M16—182no—
220M16—182no—
221C2×C8—94no—
222C4⋊C4—92no—
223C4⋊C4—181no—
224C4⋊C4—182no—
225C4⋊C4—182no—
226C22⋊C4—182no—
227C22⋊C4—182no—
228C22×C3—31no—
229C22×C3—31no—
230C22×C3—32no—
231C22×C3—61no—
232C22×C3—61no—
233C22×C3—61no—
234C22×C3—61no—
235C22×C3—61no—
236C22×C3—122no—
237C22×C3—122no—
238C22×C3#98411yescharacteristic, complemented
239A4—43no—
240C3×C4—32no—
241C3×C4—31no—
242C3×C4—61no—
243C3×C4—163no—
244C3×C4#102011yescharacteristic
245Dic3—122no—
246Dic3—122no—
247Dic3—486no—
248C32—161noSylow
249C23—31no—
250C23—31no—
251C23—62no—
252C23—61no—
253C23—61no—
254C23—121no—
255C23C2×C3⋊S411yescharacteristic
256Q8—21no—
257Q8—32no—
258Q8—61no—
259Q8—184no—
260Q8—361no—
261Q8—361no—
262Q8C2×C3⋊S412yes—
263D4—32no—
264D4—32no—
265D4—62no—
266D4—61no—
267D4—62no—
268D4—61no—
269C2×C4—31no—
270C2×C4—32no—
271C2×C4—31no—
272C2×C4—32no—
273C2×C4—31no—
274C2×C4—31no—
275C2×C4—62no—
276C2×C4—62no—
277C2×C4—62no—
278C2×C4—61no—
279C2×C4—61no—
280C2×C4—182no—
281C2×C4—182no—
282C2×C4—362no—
283C2×C4—362no—
284C8—184no—
285C2×C3—31no—
286C2×C3—31no—
287C2×C3—62no—
288C2×C3—121no—
289C2×C3—163no—
290C2×C3C2×#102011yescharacteristic
291C22—31no—
292C22—31no—
293C22—32no—
294C22—61no—
295C22—61no—
296C22—61no—
297C22—61no—
298C22—61no—
299C22—122no—
300C22—122no—
301C22#6426511yescharacteristic, complemented
302C4—32no—
303C4—31no—
304C4—61no—
305C4—362no—
306C4—362no—
307C4C3⋊#102011yescharacteristic
308C3—163no—
309C3#8750811yescharacteristic, complemented
310C2—31no—
311C2—31no—
312C2—62no—
313C2—121no—
314C2C2×C3⋊#102011yescharacteristic
subgroupG/H
center, FrattiniC2C2×C3⋊#1020
commutator, cosocle, hypocenterC3×C22⋊SL(2,𝔽3)C22
FittingC22×C3×#41D3
socleC23×C3C2×S4
prime radicalC3×#5948C2
hypercenterC4C3⋊#1020
LCSG ▷ C3×C22⋊SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C3⋊#5930C2semidirect
238. C22×C3#984semidirect
301. C22#64265semidirect
309. C3#87508semidirect

Maximal subgroups

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

subgroupindex
C3×#59482
C3⋊#59302
#875083
#840843
#642654
#642594