Finite Group Databasebeta

← #11921033

Subgroups — #11921033

Order 1152.

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

normal subgroups only

This group has 402 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×#64265C211yesmaximal, characteristic
2C3×#520⋊C3C211yesmaximal, characteristic
3C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic
4#73077—33nomaximal
5#71666—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64265—21no—
8#64265C412yescomplemented
9C2×C3⋊#226—21no—
10C3×C4×SL(2,𝔽3)—21no—
11C3⋊GU(2,𝔽3)—21no—
12#63637—41nomaximal
13C2×#984—33no—
14C3×#520D311yescharacteristic
15C2×#951—31no—
16#520⋊C3D313yes—
17C2×GU(2,𝔽3)—33no—
18C2×#837—31no—
19#5004—31no—
20#4973—31no—
21#4532—31no—
22#4530—31no—
23C2×#634—41no—
24C3×#41⋊C3C2×C411yescharacteristic
25C3×#41⋊C3D411yescharacteristic
26C2×C3×SL(2,𝔽3)D411yescharacteristic
27C3⋊#226—22no—
28C32×C4⋊C4—41no—
29C2×C3⋊(C3⋊C8)—41no—
30#1882—91noSylow
31C2×C3×#41C2×D311yescharacteristic
32C22×Dic6—31no—
33C2×#41⋊C3C2×D313yes—
34#984—36no—
35#984—63no—
36C2×#226—63no—
37C3×C4×Q8—21no—
38C3×C4×D4—61no—
39C3×#117—31no—
40C2×C3×C4⋊C4—31no—
41#951—32no—
42#951—32no—
43#951—61no—
44#951—61no—
45C2×#216—61no—
46C2×#214—61no—
47C2×C4×Dic3—31no—
48C2×#208—31no—
49C2×#208—31no—
50C4×SL(2,𝔽3)—23no—
51GU(2,𝔽3)—63no—
52#837—61no—
53#837—61no—
54C3⋊#95—62no—
55#810—61no—
56#810—61no—
57#810—123no—
58C2×C32×C4—41no—
59C2×C32×C4—81no—
60C2×C3⋊Dic3—81no—
61#634—42no—
62#634—81no—
63C3×SL(2,𝔽3)C22⋊C411yescharacteristic
64C3⋊(C3⋊C8)—81no—
65C2×#137—91no—
66#520C3⋊D311yescharacteristic
67C2×#104—91no—
68#419—91no—
69#391—91no—
70#343—91no—
71#339—91no—
72C3×#41—31no—
73C3×#41—31no—
74C3×#41C4×D311yescharacteristic
75C3×#41D1211yescharacteristic
76C2×C3×Q8#6711yescharacteristic
77C2×C3×D4—31no—
78C22×C3×C4—31no—
79C22×C3×C4—32no—
80C22×Dic3—61no—
81C22×Dic3—61no—
82C2×Dic6—32no—
83C2×Dic6—61no—
84C2×Dic6—61no—
85C2×Dic6—61no—
86C2×Dic6—61no—
87C2×Dic6—61no—
88C2×Dic6—123no—
89#41⋊C3C4×D313yes—
90#41⋊C3D1213yes—
91C2×SL(2,𝔽3)#6713yes—
92#226—66no—
93C3×C4⋊C4—31no—
94C3×C4⋊C4—43no—
95C3×C4⋊C4—61no—
96C3×C4⋊C4S411yescharacteristic
97C3×C22⋊C4—61no—
98C3×C42—61no—
99#216—62no—
100#216—62no—
101#214—62no—
102#214—62no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105#208—32no—
106#208—61no—
107#208—61no—
108#208—61no—
109C2×C3⋊C8—61no—
110C2×C3⋊C8—61no—
111C2×C3⋊C8—123no—
112C22×C32—41no—
113C32×C4—41no—
114C32×C4—41no—
115C32×C4—161no—
116C3⋊Dic3—82no—
117C2×#41C2×C3⋊D311yescharacteristic
118C22×Q8—91no—
119#137—92no—
120#137—92no—
121#137—181no—
122#137—181no—
123C2×Q16—181no—
124C2×SD16—181no—
125C2×M16—91no—
126C2×M16—91no—
127C4×Q8—21no—
128C4×D4—61no—
129#117—31no—
130C2×C4⋊C4—31no—
131C2×C42—91no—
132#104—181no—
133#104—181no—
134#103—181no—
135#103—181no—
136#95—182no—
137C23×C3—31no—
138C3×Q8—31no—
139C3×Q8(C2×D3)⋊C411yescharacteristic
140C3×D4—31no—
141C3×D4—31no—
142C3×D4—61no—
143C2×C3×C4—21no—
144C2×C3×C4—31no—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—31no—
148C2×C3×C4—31no—
149C2×C3×C4—43no—
150C2×C3×C4—61no—
151C2×C3×C4—83no—
152C2×C3×C4—122no—
153C2×C3×C4C2×S411yescharacteristic
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—121no—
157C2×Dic3—121no—
158C2×Dic3—121no—
159C2×Dic3—121no—
160C2×Dic3—243no—
161Dic6—62no—
162Dic6—62no—
163Dic6—126no—
164Dic6—121no—
165Dic6—121no—
166Dic6—243no—
167SL(2,𝔽3)(C2×D3)⋊C413yes—
168C3⋊C8—62no—
169C3⋊C8—121no—
170C3⋊C8—243no—
171C2×C32—41no—
172C2×C32—41no—
173C2×C32—41no—
174#41—31no—
175#41—31no—
176#41C4×C3⋊D311yescharacteristic
177#41C4⋊(C3⋊D3)11yescharacteristic
178C2×Q8—92no—
179C2×Q8—181no—
180C2×Q8—181no—
181C2×Q8—181no—
182C2×Q8—181no—
183C2×Q8—181no—
184C2×Q8#63811yescharacteristic
185C2×D4—31no—
186C22×C4—31no—
187C22×C4—32no—
188C22×C4—181no—
189C22×C4—181no—
190Q16—182no—
191Q16—182no—
192SD16—182no—
193SD16—182no—
194M16—92no—
195M16—181no—
196M16—181no—
197M16—181no—
198C2×C8—181no—
199C2×C8—181no—
200C4⋊C4—31no—
201C4⋊C4—61no—
202C4⋊C4C3⋊S411yescharacteristic
203C22⋊C4—61no—
204C42—61no—
205C42—181no—
206C42—181no—
207C22×C3—31no—
208C22×C3—31no—
209C22×C3—43no—
210C22×C3—61no—
211C22×C3—61no—
212C22×C3GL(2,ℤ/4)11yescharacteristic
213C3×C4—31no—
214C3×C4—31no—
215C3×C4—41no—
216C3×C4—43no—
217C3×C4—43no—
218C3×C4—121no—
219C3×C4—163no—
220C3×C4C4×S411yescharacteristic
221C3×C4C4⋊S411yescharacteristic
222Dic3—122no—
223Dic3—122no—
224Dic3—246no—
225C32—41noSylow
226C23—31no—
227Q8—31no—
228Q8—182no—
229Q8—182no—
230Q8—361no—
231Q8—361no—
232Q8#375211yescharacteristic
233D4—31no—
234D4—31no—
235D4—61no—
236C2×C4—21no—
237C2×C4—31no—
238C2×C4—31no—
239C2×C4—31no—
240C2×C4—31no—
241C2×C4—31no—
242C2×C4—61no—
243C2×C4—122no—
244C2×C4—182no—
245C2×C4—182no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4—361no—
250C2×C4C2×C3⋊S411yescharacteristic
251C8—182no—
252C8—361no—
253C2×C3—43no—
254C2×C3—43no—
255C2×C3—43no—
256C2×C3—61no—
257C2×C3—61no—
258C2×C3(C2×S4)⋊C411yescharacteristic
259C2×C3#542811yescharacteristic
260C2×C3#543011yescharacteristic
261C22—31no—
262C22—31no—
263C22—61no—
264C22—61no—
265C22#6426911yescharacteristic
266C4—31no—
267C4—31no—
268C4—41no—
269C4—121no—
270C4—362no—
271C4—362no—
272C4C4×C3⋊S411yescharacteristic
273C4C4⋊(C3⋊S4)11yescharacteristic
274C3—43no—
275C3#7307711yescharacteristic, complemented
276C2—61no—
277C2—61no—
278C2#1059364711yescharacteristic
279C2#1059366211yescharacteristic
280C2#1059366411yescharacteristic
subgroupG/H
centerC22#64269
commutatorC3×#41⋊C3C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC3×#520D3
socleC22×C3GL(2,ℤ/4)
prime radical, cosocleC2×C3×#41⋊C3C22
hypercenterC4⋊C4C3⋊S4
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
8. #64265C4semidirect
275. C3#73077semidirect

Maximal subgroups

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

subgroupindex
C2×#642652
C3×#520⋊C32
C2×C3⋊GU(2,𝔽3)2
#730773
#716663
#636374