Finite Group Databasebeta

← #11922909

Subgroups — #11922909

Order 1152.

634 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 89 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
3#10593658C211yesmaximal, characteristic
4#10593622C212yesmaximal, complemented
5C4×C3⋊#226C212yesmaximal, complemented
6#85360—33nomaximal
7#82571—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#64265C414yescomplemented
10C2×C3⋊#226C2212yes—
11#64096—41nomaximal
12C3×C4×SL(2,𝔽3)C2212yes—
13C3⋊#859C2211yescharacteristic
14C3⋊#859C2211yescharacteristic
15C2×#984—33no—
16C3×#520D311yescharacteristic
17C2×#951—31no—
18#5516—31no—
19#520⋊C3D313yes—
20#5424—33no—
21#5388—36no—
22C4×#226—36no—
23#5233—31no—
24#5030—32no—
25C4×#216—32no—
26#5018—32no—
27C4×#214—32no—
28#4997—31no—
29C2×#810—31no—
30#4964—31no—
31C2×#634—41no—
32C3×#41⋊C3C2×C412yes—
33C2×C3×SL(2,𝔽3)C2311yescharacteristic
34C3⋊#226C2×C414yescomplemented
35C32×C4⋊C4—41no—
36#3750—42no—
37C4×C3⋊Dic3—42no—
38C4×C3⋊Dic3—41no—
39#2947—91noSylow
40C2×C3×#41C2×D311yescharacteristic
41C22×Dic6—31no—
42C2×#41⋊C3C2×D313yes—
43#984—312no—
44C2×#226—36no—
45C3×C4×Q8C2×D312yes—
46C3×C4×D4—32no—
47C3×#117—31no—
48C2×C3×C4⋊C4—31no—
49#951—34no—
50#951—34no—
51C2×#216—32no—
52C2×#214—32no—
53#926—31no—
54C2×#208—31no—
55C22×C3⋊C8—31no—
56#887—61no—
57#887—61no—
58#887—123no—
59#877—62no—
60C4×Dic6—32no—
61C4×Dic6—32no—
62C4×SL(2,𝔽3)C2×D316yes—
63#859—33no—
64#859—33no—
65#835—31no—
66#835—31no—
67#832—31no—
68#832—31no—
69#810—32no—
70#810—32no—
71#808—32no—
72#807—32no—
73#803—32no—
74C4×C3⋊C8—32no—
75C2×C32×C4—41no—
76C2×C32×C4—42no—
77C2×C3⋊Dic3—42no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3—41no—
80#634—44no—
81C3×SL(2,𝔽3)C22×C411yescharacteristic
82C2×#137—91no—
83#520C3⋊D311yescharacteristic
84#519—91no—
85#441—92no—
86#440—92no—
87C4×Q16—92no—
88C4×SD16—92no—
89#428—91no—
90#416—91no—
91C2×#103—91no—
92#405—91no—
93C3×#41—32no—
94C3×#41C4×D312yes—
95C2×C3×Q8C22×D311yescharacteristic
96C2×C3×D4—31no—
97C22×C3×C4—31no—
98C22×C3×C4—61no—
99C22×Dic3—61no—
100C2×Dic6—32no—
101C2×Dic6—34no—
102C2×Dic6—62no—
103C2×Dic6—61no—
104C2×Dic6—123no—
105#41⋊C3C4×D316yes—
106C2×SL(2,𝔽3)C22×D313yes—
107#226—312no—
108C3×C4⋊C4—32no—
109C3×C4⋊C4—31no—
110C3×C4⋊C4—43no—
111C3×C4⋊C4S411yescharacteristic
112C3×C22⋊C4—32no—
113C3×C42—32no—
114#217—61no—
115#216—34no—
116#216—34no—
117#214—38no—
118C4⋊Dic3—31no—
119C4⋊Dic3—31no—
120Dic3⋊C4—62no—
121Dic3⋊C4—62no—
122Dic3⋊C4—126no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C4×Dic3—61no—
126C4×Dic3—126no—
127C4×Dic3—123no—
128#208—34no—
129C2×C3⋊C8—32no—
130C2×C3⋊C8—31no—
131C2×C3⋊C8—31no—
132C2×C3⋊C8—62no—
133C22×C32—41no—
134C32×C4—42no—
135C32×C4—82no—
136C3⋊Dic3—44no—
137C3⋊Dic3—42no—
138C3⋊Dic3—81no—
139C2×#41C2×C3⋊D311yescharacteristic
140C22×Q8—91no—
141#137—94no—
142#137—94no—
143C2×Q16—92no—
144C2×SD16—92no—
145C2×M16—91no—
146C22×C8—91no—
147C4×Q8—92no—
148C4×Q8—92no—
149C4×Q8—181no—
150C4×Q8—181no—
151C4×Q8C2×C3⋊D312yes—
152C4×D4—32no—
153#117—31no—
154#117—91no—
155#117—182no—
156C2×C4⋊C4—31no—
157#107—92no—
158#106—92no—
159#103—92no—
160#103—92no—
161#103—91no—
162#103—91no—
163#102—91no—
164#102—91no—
165#97—92no—
166C4×C8—92no—
167C23×C3—31no—
168C3×Q8—31no—
169C3×Q8C2×C4×D311yescharacteristic
170C3×D4—32no—
171C3×D4—61no—
172C2×C3×C4—31no—
173C2×C3×C4—32no—
174C2×C3×C4—32no—
175C2×C3×C4—32no—
176C2×C3×C4—43no—
177C2×C3×C4—46no—
178C2×C3×C4—241no—
179C2×C3×C4C2×S412yes—
180C2×C3×C4C2×S411yescharacteristic
181C2×Dic3—64no—
182C2×Dic3—62no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—123no—
186C2×Dic3—126no—
187C2×Dic3—123no—
188Dic6—34no—
189Dic6—62no—
190Dic6—64no—
191Dic6—1212no—
192SL(2,𝔽3)C2×C4×D313yes—
193C3⋊C8—34no—
194C3⋊C8—61no—
195C3⋊C8—61no—
196C2×C32—41no—
197C2×C32—41no—
198C2×C32—41no—
199#41—32no—
200#41C4×C3⋊D312yes—
201C2×Q8—92no—
202C2×Q8—94no—
203C2×Q8—182no—
204C2×Q8—181no—
205C2×Q8C22×C3⋊D311yescharacteristic
206C2×D4—31no—
207C22×C4—31no—
208C22×C4—61no—
209C22×C4—181no—
210Q16—94no—
211Q16—94no—
212SD16—98no—
213M16—94no—
214C2×C8—92no—
215C2×C8—91no—
216C2×C8—91no—
217C2×C8—182no—
218C4⋊C4—32no—
219C4⋊C4—31no—
220C4⋊C4—91no—
221C4⋊C4—91no—
222C4⋊C4—182no—
223C4⋊C4—182no—
224C4⋊C4C3⋊S411yescharacteristic
225C22⋊C4—32no—
226C22⋊C4—181no—
227C42—32no—
228C42—182no—
229C42—181no—
230C42—182no—
231C22×C3—32no—
232C22×C3—43no—
233C22×C3—61no—
234C22×C3—61no—
235C22×C3C22×S411yescharacteristic
236C3×C4—22no—
237C3×C4—31no—
238C3×C4—31no—
239C3×C4—46no—
240C3×C4—62no—
241C3×C4—86no—
242C3×C4C4×S412yes—
243Dic3—64no—
244Dic3—1212no—
245Dic3—126no—
246Dic3—121no—
247Dic3—121no—
248Dic3—243no—
249C32—41noSylow
250C23—31no—
251Q8—31no—
252Q8—94no—
253Q8—182no—
254Q8—184no—
255Q8C2×C4×C3⋊D311yescharacteristic
256D4—32no—
257D4—61no—
258C2×C4—31no—
259C2×C4—32no—
260C2×C4—32no—
261C2×C4—32no—
262C2×C4—184no—
263C2×C4—182no—
264C2×C4—181no—
265C2×C4—181no—
266C2×C4—241no—
267C2×C4C2×C3⋊S412yes—
268C2×C4C2×C3⋊S411yescharacteristic
269C8—94no—
270C8—181no—
271C8—181no—
272C2×C3—43no—
273C2×C3—43no—
274C2×C3—43no—
275C2×C3—62no—
276C2×C3C2×C4×S411yescharacteristic
277C2×C3#592411yescharacteristic
278C2×C3#592711yescharacteristic
279C22—32no—
280C22—61no—
281C22—61no—
282C22C22×C3⋊S411yescharacteristic
283C4—22no—
284C4—31no—
285C4—31no—
286C4—62no—
287C4—184no—
288C4—361no—
289C4—361no—
290C4C4×C3⋊S412yes—
291C3—43no—
292C3#8536011yescharacteristic, complemented
293C2—62no—
294C2C2×C4×C3⋊S411yescharacteristic
295C2#1059658711yescharacteristic
296C2#1059659011yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FittingC3×#520D3
socleC22×C3C22×S4
prime radicalC2×C3×#41⋊C3C22
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC4⋊C4C3⋊S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10593622C2semidirect
5. C4×C3⋊#226C2semidirect
9. #64265C4semidirect
34. C3⋊#226C2×C4semidirect
292. C3#85360semidirect

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
#105936582
#105936222
C4×C3⋊#2262
#853603
#825713
#640964