Finite Group Databasebeta

← C4×#64265 #11922882

Subgroups — C4×#64265 #11922882

Order 1152.

644 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 93 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
2C3×C4×#41⋊C3C211yesmaximal, characteristic
3#10593660C211yesmaximal, characteristic
4#10593622C212yesmaximal, complemented
5C4×C3⋊#226C212yesmaximal, complemented
6C4×#984—33nomaximal
7C4×#951—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#64265C414yesdirect product factor
10C2×C3⋊#226C2212yes—
11C4×#634—41nomaximal
12C3×C4×SL(2,𝔽3)C2211yescharacteristic
13C3×C4×SL(2,𝔽3)C2211yescharacteristic
14C3⋊#859C2212yes—
15C2×#984—33no—
16C3×C4×#41D311yescharacteristic
17C2×#951—31no—
18C2×C4×Dic6—31no—
19C4×#41⋊C3D313yes—
20#5426—33no—
21#5388—36no—
22C4×#226—36no—
23#5232—31no—
24#5030—32no—
25C4×#216—32no—
26#5018—32no—
27C4×#214—32no—
28#5004—31no—
29#4995—31no—
30C4×#208—31no—
31C2×#634—41no—
32C3×#41⋊C3C2×C412yes—
33C2×C3×SL(2,𝔽3)C2311yescharacteristic
34C3⋊#226C2×C414yescomplemented
35C32×C42—41no—
36C4⋊(C3⋊Dic3)—41no—
37#3750—42no—
38C4×C3⋊Dic3—42no—
39C4×#137—91noSylow
40C2×C3×#41C2×D311yescharacteristic
41C22×Dic6—31no—
42C2×#41⋊C3C2×D313yes—
43#984—312no—
44C2×#226—36no—
45C3×C4×Q8C2×D311yescharacteristic
46C3×C4×Q8C2×D311yescharacteristic
47C3×C4×D4—31no—
48C3×C4×D4—31no—
49C3×#117—31no—
50C2×C3×C42—31no—
51#951—34no—
52#951—34no—
53C2×#216—32no—
54C2×#214—32no—
55C2×C4⋊Dic3—31no—
56C2×Dic3⋊C4—61no—
57C2×C4×Dic3—61no—
58C2×#208—31no—
59C2×#208—31no—
60C4×Dic6—32no—
61C4×Dic6—32no—
62C4×Dic6—61no—
63C4×Dic6—61no—
64C4×Dic6—123no—
65C4×SL(2,𝔽3)C2×D313yes—
66C4×SL(2,𝔽3)C2×D313yes—
67#859—36no—
68#835—32no—
69#832—32no—
70#810—32no—
71#810—32no—
72#808—32no—
73#807—32no—
74#803—32no—
75C4×C3⋊C8—32no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C3⋊Dic3—42no—
80C2×C3⋊Dic3—42no—
81#634—44no—
82C3×SL(2,𝔽3)C22×C411yescharacteristic
83C2×#137—91no—
84C4×#41C3⋊D311yescharacteristic
85C2×C4×Q8—91no—
86#441—92no—
87#440—92no—
88C4×Q16—92no—
89C4×SD16—92no—
90#428—91no—
91#419—91no—
92#417—91no—
93C4×M16—91no—
94C3×#41—32no—
95C3×#41C4×D312yes—
96C2×C3×Q8C22×D311yescharacteristic
97C2×C3×D4—31no—
98C22×C3×C4—31no—
99C22×C3×C4—31no—
100C22×C3×C4—31no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C2×Dic6—32no—
104C2×Dic6—34no—
105C2×Dic6—62no—
106C2×Dic6—61no—
107C2×Dic6—123no—
108#41⋊C3C4×D316yes—
109C2×SL(2,𝔽3)C22×D313yes—
110#226—312no—
111C3×C4⋊C4—31no—
112C3×C4⋊C4—31no—
113C3×C22⋊C4—61no—
114C3×C42—31no—
115C3×C42—31no—
116C3×C42—31no—
117C3×C42—43no—
118C3×C42S411yescharacteristic
119#216—34no—
120#216—34no—
121#214—38no—
122C4⋊Dic3—32no—
123C4⋊Dic3—61no—
124C4⋊Dic3—123no—
125Dic3⋊C4—62no—
126Dic3⋊C4—62no—
127Dic3⋊C4—126no—
128C4×Dic3—62no—
129C4×Dic3—62no—
130C4×Dic3—126no—
131#208—34no—
132#208—62no—
133C2×C3⋊C8—32no—
134C2×C3⋊C8—32no—
135C22×C32—41no—
136C32×C4—42no—
137C32×C4—42no—
138C32×C4—81no—
139C3⋊Dic3—44no—
140C3⋊Dic3—82no—
141C2×#41C2×C3⋊D311yescharacteristic
142C22×Q8—91no—
143#137—94no—
144#137—94no—
145C2×Q16—92no—
146C2×SD16—92no—
147C2×M16—91no—
148C2×M16—91no—
149C4×Q8—92no—
150C4×Q8—92no—
151C4×Q8—181no—
152C4×Q8—181no—
153C4×Q8C2×C3⋊D311yescharacteristic
154C4×Q8C2×C3⋊D311yescharacteristic
155C4×D4—31no—
156C4×D4—31no—
157#117—31no—
158C2×C4⋊C4—91no—
159C2×C4⋊C4—181no—
160C2×C42—31no—
161C2×C42—181no—
162#107—92no—
163#106—92no—
164#103—92no—
165#103—92no—
166#103—92no—
167#102—92no—
168#97—92no—
169C4×C8—92no—
170C23×C3—31no—
171C3×Q8—31no—
172C3×Q8C2×C4×D311yescharacteristic
173C3×D4—32no—
174C3×D4—61no—
175C2×C3×C4—31no—
176C2×C3×C4—32no—
177C2×C3×C4—32no—
178C2×C3×C4—31no—
179C2×C3×C4—31no—
180C2×C3×C4—43no—
181C2×C3×C4—43no—
182C2×C3×C4—43no—
183C2×C3×C4—62no—
184C2×C3×C4—121no—
185C2×C3×C4C2×S411yescharacteristic
186C2×C3×C4C2×S411yescharacteristic
187C2×C3×C4C2×S411yescharacteristic
188C2×Dic3—64no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—126no—
192C2×Dic3—126no—
193C2×Dic3—122no—
194Dic6—34no—
195Dic6—62no—
196Dic6—64no—
197Dic6—1212no—
198SL(2,𝔽3)C2×C4×D313yes—
199C3⋊C8—34no—
200C3⋊C8—62no—
201C2×C32—41no—
202C2×C32—41no—
203C2×C32—41no—
204#41—32no—
205#41C4×C3⋊D312yes—
206C2×Q8—92no—
207C2×Q8—94no—
208C2×Q8—182no—
209C2×Q8—181no—
210C2×Q8C22×C3⋊D311yescharacteristic
211C2×D4—31no—
212C22×C4—31no—
213C22×C4—31no—
214C22×C4—31no—
215C22×C4—181no—
216C22×C4—181no—
217Q16—94no—
218Q16—94no—
219SD16—98no—
220M16—94no—
221M16—182no—
222C2×C8—92no—
223C2×C8—92no—
224C4⋊C4—31no—
225C4⋊C4—31no—
226C4⋊C4—92no—
227C4⋊C4—182no—
228C4⋊C4—181no—
229C4⋊C4—182no—
230C22⋊C4—61no—
231C42—31no—
232C42—31no—
233C42—31no—
234C42—182no—
235C42—182no—
236C42C3⋊S411yescharacteristic
237C22×C3—32no—
238C22×C3—43no—
239C22×C3—61no—
240C22×C3—61no—
241C22×C3C22×S411yescharacteristic
242C3×C4—21no—
243C3×C4—31no—
244C3×C4—31no—
245C3×C4—46no—
246C3×C4—46no—
247C3×C4—61no—
248C3×C4—61no—
249C3×C4—83no—
250C3×C4C4×S412yes—
251C3×C4#98412yescomplemented
252Dic3—64no—
253Dic3—1212no—
254Dic3—122no—
255Dic3—246no—
256C32—41noSylow
257C23—31no—
258Q8—31no—
259Q8—94no—
260Q8—182no—
261Q8—184no—
262Q8C2×C4×C3⋊D311yescharacteristic
263D4—32no—
264D4—61no—
265C2×C4—31no—
266C2×C4—32no—
267C2×C4—32no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4—62no—
271C2×C4—121no—
272C2×C4—184no—
273C2×C4—182no—
274C2×C4—182no—
275C2×C4—362no—
276C2×C4C2×C3⋊S411yescharacteristic
277C2×C4C2×C3⋊S411yescharacteristic
278C2×C4C2×C3⋊S411yescharacteristic
279C8—94no—
280C8—182no—
281C2×C3—43no—
282C2×C3—43no—
283C2×C3—43no—
284C2×C3—62no—
285C2×C3C2×C4×S411yescharacteristic
286C2×C3C2×#98411yescharacteristic
287C2×C3#592311yescharacteristic
288C22—32no—
289C22—61no—
290C22—61no—
291C22C22×C3⋊S411yescharacteristic
292C4—21no—
293C4—31no—
294C4—31no—
295C4—61no—
296C4—61no—
297C4—184no—
298C4—362no—
299C4C4×C3⋊S412yes—
300C4#6426512yesdirect product factor
301C3—43no—
302C3C4×#98411yescharacteristic, complemented
303C2—62no—
304C2C2×C4×C3⋊S411yescharacteristic
305C2C2×#6426511yescharacteristic
306C2#1059658611yescharacteristic
subgroupG/H
centerC2×C4C2×C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC22C22×C3⋊S4
FittingC3×C4×#41D3
socleC22×C3C22×S4
prime radicalC2×C3×#41⋊C3C22
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
4. #10593622C2semidirect
5. C4×C3⋊#226C2semidirect
9. #64265C4direct (N × H)
34. C3⋊#226C2×C4semidirect
251. C3×C4#984semidirect
300. C4#64265direct (N × H)
302. C3C4×#984semidirect

Maximal subgroups

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

subgroupindex
C2×#642652
C3×C4×#41⋊C32
#105936602
#105936222
C4×C3⋊#2262
C4×#9843
C4×#9513
C4×#6344