Finite Group Databasebeta

← #11921083

Subgroups — #11921083

Order 1152.

416 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 59 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
2C2×C3×#131⋊C3C211yesmaximal, characteristic, complemented
3C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic, complemented
4#73127—33nomaximal
5#72010—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64266—21no—
8#64266—21no—
9C2×C3⋊GL(2,𝔽3)C411yescharacteristic, complemented
10C2×C3⋊#226C411yescharacteristic, complemented
11C3×#131⋊C3—21no—
12C3⋊GU(2,𝔽3)—21no—
13#63647—41nomaximal
14C2×#985—33no—
15C2×C3×#131D311yescharacteristic, complemented
16C2×#950—31no—
17C2×#131⋊C3D313yescomplemented
18C2×GU(2,𝔽3)—33no—
19C2×#837—31no—
20C2×#825—31no—
21#5110—31no—
22#4558—31no—
23#4550—31no—
24C2×C4×C3⋊D3—41no—
25C3×#41⋊C3D411yescharacteristic
26C3×#41⋊C3D411yescharacteristic
27C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
28C3⋊GL(2,𝔽3)—21no—
29C3⋊#226—21no—
30C2×C32×C8—41no—
31C2×C3⋊(C3⋊C8)—41no—
32#1876—91noSylow
33C2×C3×#41C2×D311yescharacteristic
34C2×#235—31no—
35C2×#41⋊C3C2×D313yes—
36#985—63no—
37#985—63no—
38C2×GL(2,𝔽3)—33no—
39C2×#226—33no—
40C3×#131—21no—
41C3×#131—61no—
42C2×C3×M16—31no—
43C22×C3×C8—31no—
44#950—61no—
45#950—61no—
46#950—61no—
47#950—61no—
48C2×#216—31no—
49C2×#215—31no—
50C2×#214—31no—
51C2×#213—31no—
52C2×C4×Dic3—31no—
53C2×#208—31no—
54C22×C3⋊C8—31no—
55#131⋊C3—23no—
56GU(2,𝔽3)—63no—
57#837—61no—
58#837—61no—
59#825—62no—
60(C2×D3)⋊C8—61no—
61(C2×D3)⋊C8—61no—
62(C2×D3)⋊C8—123no—
63C22×C3⋊D3—41no—
64C2×C32×C4—41no—
65C2×C3⋊Dic3—41no—
66C4×C3⋊D3—81no—
67C4×C3⋊D3—81no—
68C3×SL(2,𝔽3)C22⋊C411yescharacteristic
69C32×C8—81no—
70C3⋊(C3⋊C8)—81no—
71C2×#135—91no—
72C2×#131C3⋊D311yescharacteristic, complemented
73C2×#104—91no—
74C2×#104—91no—
75#408—91no—
76#341—91no—
77#336—91no—
78C3×#41—31no—
79C3×#41—31no—
80C3×#41D1211yescharacteristic
81C3×#41#6711yescharacteristic
82C2×C3×Q8C4×D311yescharacteristic
83C2×C3×D4—31no—
84C22×C3×C4—31no—
85C2×#67—61no—
86C22×Dic3—61no—
87#235—61no—
88#235—61no—
89#235—61no—
90#235—61no—
91C2×D12—31no—
92C2×C4×D3—61no—
93C2×C4×D3—123no—
94C2×Dic6—31no—
95#41⋊C3D1213yes—
96#41⋊C3#6713yes—
97C2×SL(2,𝔽3)C4×D313yes—
98GL(2,𝔽3)—63no—
99#226—63no—
100C3×M16—32no—
101C3×M16—61no—
102C2×C3×C8—31no—
103C2×C3×C8—43no—
104C2×C3×C8—61no—
105C2×C3×C8—61no—
106C2×C3×C8S411yescharacteristic
107#216—61no—
108#216—61no—
109#215—61no—
110#215—61no—
111#214—61no—
112#214—61no—
113#213—61no—
114#213—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117#208—61no—
118#208—61no—
119C2×C3⋊C8—31no—
120C2×C3⋊C8—31no—
121C2×C3⋊C8—61no—
122C2×C3⋊C8—61no—
123C2×C3⋊C8—61no—
124C2×C3⋊C8—123no—
125C22×C32—41no—
126C2×C3⋊D3—42no—
127C2×C3⋊D3—81no—
128C2×C3⋊D3—81no—
129C32×C4—41no—
130C32×C4—41no—
131C3⋊Dic3—81no—
132C2×#41—91no—
133C2×#41C2×C3⋊D311yescharacteristic
134#135—181no—
135#135—181no—
136#135—181no—
137#135—181no—
138C2×Q16—91no—
139C2×SD16—91no—
140C2×SD16—91no—
141C2×D8—91no—
142#131—21no—
143#131—61no—
144C2×M16—31no—
145C2×M16—91no—
146C22×C8—31no—
147C22×C8—91no—
148C2×C42—91no—
149#104—182no—
150#104—181no—
151#104—181no—
152C22⋊C8—181no—
153C22⋊C8—181no—
154C23×C3—31no—
155C22×D3—61no—
156C22×D3—123no—
157C3×Q8—31no—
158C3×Q8(C2×D3)⋊C411yescharacteristic
159C3×D4—31no—
160C3×D4—31no—
161C3×D4—61no—
162C2×C3×C4—31no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—31no—
167C2×C3×C4—43no—
168C2×C3×C4C2×S411yescharacteristic
169#67—121no—
170#67—121no—
171C2×Dic3—62no—
172C2×Dic3—61no—
173C2×Dic3—123no—
174C2×Dic3—121no—
175C2×Dic3—121no—
176D12—61no—
177D12—61no—
178C4×D3—121no—
179C4×D3—121no—
180C4×D3—243no—
181C4×D3—243no—
182Dic6—61no—
183Dic6—61no—
184SL(2,𝔽3)(C2×D3)⋊C413yes—
185C3×C8—21no—
186C3×C8—61no—
187C3×C8—83no—
188C3⋊C8—61no—
189C3⋊C8—61no—
190C3⋊C8—121no—
191C3⋊C8—243no—
192C2×C32—41no—
193C2×C32—41no—
194C2×C32—41no—
195C3⋊D3—82no—
196#41—31no—
197#41—31no—
198#41—181no—
199#41—181no—
200#41—181no—
201#41—181no—
202#41C4⋊(C3⋊D3)11yescharacteristic
203#41#63811yescharacteristic
204C2×Q8—91no—
205C2×Q8C4×C3⋊D311yescharacteristic
206C2×D4—31no—
207C2×D4—91no—
208C2×D4—181no—
209C22×C4—31no—
210C22×C4—181no—
211C22×C4—181no—
212Q16—181no—
213Q16—181no—
214SD16—181no—
215SD16—181no—
216SD16—181no—
217SD16—181no—
218D8—181no—
219D8—181no—
220M16—32no—
221M16—61no—
222M16—181no—
223M16—181no—
224C2×C8—31no—
225C2×C8—61no—
226C2×C8—61no—
227C2×C8—91no—
228C2×C8—91no—
229C2×C8—181no—
230C2×C8—181no—
231C2×C8—181no—
232C2×C8C3⋊S411yescharacteristic
233C42—181no—
234C42—181no—
235C22×C3—31no—
236C22×C3—31no—
237C22×C3—43no—
238C22×C3—61no—
239C22×C3—61no—
240C22×C3C4×S411yescharacteristic
241C2×D3—126no—
242C2×D3—121no—
243C2×D3—121no—
244C2×D3—121no—
245C2×D3—243no—
246C2×D3—243no—
247C3×C4—31no—
248C3×C4—31no—
249C3×C4—43no—
250C3×C4—43no—
251C3×C4C4⋊S411yescharacteristic
252C3×C4GL(2,ℤ/4)11yescharacteristic
253Dic3—122no—
254Dic3—121no—
255Dic3—243no—
256C32—41noSylow
257C23—31no—
258C23—181no—
259Q8—31no—
260Q8—181no—
261Q8—181no—
262Q8#375211yescharacteristic
263D4—31no—
264D4—31no—
265D4—61no—
266D4—181no—
267D4—181no—
268D4—361no—
269D4—361no—
270C2×C4—31no—
271C2×C4—31no—
272C2×C4—31no—
273C2×C4—31no—
274C2×C4—31no—
275C2×C4—182no—
276C2×C4—181no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4—361no—
280C2×C4—361no—
281C2×C4C2×C3⋊S411yescharacteristic
282C8—21no—
283C8—61no—
284C8—181no—
285C8—181no—
286C8—361no—
287C2×C3—43no—
288C2×C3—43no—
289C2×C3—43no—
290C2×C3—61no—
291C2×C3—61no—
292C2×C3#540411yescharacteristic
293C2×C3#540511yescharacteristic
294C2×C3(C2×S4)⋊C411yescharacteristic
295D3—246no—
296D3—241no—
297C22—31no—
298C22—31no—
299C22—61no—
300C22—61no—
301C22—361no—
302C22—361no—
303C22—361no—
304C22C4×C3⋊S411yescharacteristic
305C4—31no—
306C4—31no—
307C4—362no—
308C4—361no—
309C4C4⋊(C3⋊S4)11yescharacteristic
310C4#6426911yescharacteristic
311C3—43no—
312C3#7312711yescharacteristic, complemented
313C2—61no—
314C2—61no—
315C2—721no—
316C2#1059363811yescharacteristic
317C2#1059363911yescharacteristic
318C2#1059364711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×C3⋊S4
commutatorC2×C3×SL(2,𝔽3)C2×C4
FittingC2×C3×#131D3
socleC22×C3C4×S4
prime radicalC2×#64266C2
cosocleC2×C3×#41⋊C3C22
hypercenterC2×C8C3⋊S4
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#131⋊C3C2semidirect
3. C2×C3⋊GU(2,𝔽3)C2semidirect
9. C2×C3⋊GL(2,𝔽3)C4semidirect
10. C2×C3⋊#226C4semidirect
15. C2×C3×#131D3semidirect
17. C2×#131⋊C3D3semidirect
72. C2×#131C3⋊D3semidirect
312. C3#73127semidirect

Maximal subgroups

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

subgroupindex
C2×#642662
C2×C3×#131⋊C32
C2×C3⋊GU(2,𝔽3)2
#731273
#720103
#636474