Finite Group Databasebeta

← #11922283

Subgroups — #11922283

Order 1152.

555 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 555 conjugacy classes of subgroups — too many to draw. Only its 69 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
2Dic3×#41⋊C3C211yesmaximal, characteristic
3C3×#5426C211yesmaximal, characteristic
4#10593195C212yesmaximal, complemented
5#10593193C212yesmaximal, complemented
6C4×#984—31nomaximal
7#78867—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#64265C414yescomplemented
10C2×C3⋊#226C2212yes—
11#63844—41nomaximal
12Dic3×SL(2,𝔽3)C2211yescharacteristic
13Dic3×SL(2,𝔽3)C2211yescharacteristic
14C3×#859C2212yes—
15C2×#984—31no—
16C2×#984—61no—
17Dic3×#41D311yescharacteristic
18C2×#951—31no—
19C2×#887—31no—
20C4×#41⋊C3—31no—
21#5426D311yescharacteristic
22#5388—32no—
23C4×#226—32no—
24C3×#417—31no—
25#5120—31no—
26Dic3×M16—31no—
27#4964—31no—
28#4790—32no—
29#4789—32no—
30#4758—32no—
31#4757—32no—
32C2×#634—41no—
33C3×#41⋊C3C2×C412yes—
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C3⋊#226C2×C414yescomplemented
36C3×C4⋊Dic3—41no—
37C3×C4×Dic3—41no—
38#3724—42no—
39Dic32—42no—
40C4×#137—91noSylow
41C2×C3×#41C2×D311yescharacteristic
42C22×Dic6—31no—
43C2×#41⋊C3—21no—
44C2×#41⋊C3C2×D311yescharacteristic
45#984—34no—
46#984—64no—
47C2×#226—32no—
48C2×#226—62no—
49C2×C3×M16—31no—
50C2×C3×C4⋊C4—31no—
51#951—34no—
52#951—34no—
53Q8×Dic3C2×D311yescharacteristic
54Q8×Dic3C2×D311yescharacteristic
55C2×#216—32no—
56D4×Dic3—31no—
57D4×Dic3—31no—
58C2×#214—32no—
59#926—31no—
60C2×Dic3⋊C4—61no—
61C2×C4×Dic3—31no—
62C2×C4×Dic3—61no—
63C2×#208—31no—
64#887—32no—
65#887—32no—
66#887—61no—
67#887—61no—
68C4×Dic6—121no—
69C4×SL(2,𝔽3)—31no—
70C4×SL(2,𝔽3)—31no—
71#859C2×D312yes—
72C3×#103—32no—
73C3×#102—32no—
74#816—32no—
75#816—32no—
76#815—32no—
77C8×Dic3—32no—
78#808—32no—
79#807—32no—
80C2×C32×C4—41no—
81C2×C3⋊Dic3—42no—
82#634—44no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3—41no—
86C3×SL(2,𝔽3)C22×C411yescharacteristic
87C2×#137—91no—
88C4×#41—31no—
89C2×C4×Q8—91no—
90#441—92no—
91#440—92no—
92C4×Q16—92no—
93C4×SD16—92no—
94#428—91no—
95#419—91no—
96#417—31no—
97C4×M16—91no—
98C3×#41—32no—
99C3×#41C4×D312yes—
100C2×C3×Q8C22×D311yescharacteristic
101C2×C3×D4—31no—
102C22×C3×C4—31no—
103C22×C3×C4—61no—
104C22×Dic3—31no—
105C22×Dic3—31no—
106C22×Dic3—61no—
107C2×Dic6—32no—
108C2×Dic6—34no—
109C2×Dic6—62no—
110C2×Dic6—61no—
111C2×Dic6—121no—
112C2×Dic6—241no—
113#41⋊C3—22no—
114#41⋊C3C4×D312yes—
115C2×SL(2,𝔽3)—21no—
116C2×SL(2,𝔽3)C22×D311yescharacteristic
117#226—34no—
118#226—64no—
119C3×M16—62no—
120C2×C3×C8—32no—
121C3×C4⋊C4—32no—
122C3×C4⋊C4—61no—
123C3×C42—121no—
124#217—61no—
125#216—34no—
126#216—34no—
127#214—38no—
128C4⋊Dic3—31no—
129C4⋊Dic3—31no—
130C4⋊Dic3—41no—
131Dic3⋊C4—62no—
132Dic3⋊C4—62no—
133Dic3⋊C4—122no—
134C4×Dic3—31no—
135C4×Dic3—31no—
136C4×Dic3—31no—
137C4×Dic3—62no—
138C4×Dic3—62no—
139C4×Dic3—122no—
140C4×Dic3S411yescharacteristic
141#208—34no—
142C2×C3⋊C8—32no—
143C22×C32—41no—
144C32×C4—42no—
145C3⋊Dic3—44no—
146C3×Dic3—42no—
147C3×Dic3—81no—
148C3×Dic3—82no—
149C2×#41D3211yescharacteristic
150C22×Q8—91no—
151#137—94no—
152#137—94no—
153C2×Q16—92no—
154C2×SD16—92no—
155C2×M16—31no—
156C2×M16—91no—
157C4×Q8—31no—
158C4×Q8—31no—
159C4×Q8—92no—
160C4×Q8—92no—
161C4×Q8—181no—
162C4×Q8—181no—
163C4×D4—91no—
164C4×D4—91no—
165#117—91no—
166C2×C4⋊C4—31no—
167C2×C4⋊C4—181no—
168C2×C42—91no—
169C2×C42—181no—
170#107—92no—
171#106—92no—
172#103—32no—
173#103—92no—
174#103—92no—
175#102—32no—
176#97—92no—
177C4×C8—92no—
178C23×C3—31no—
179C3×Q8—31no—
180C3×Q8C2×C4×D311yescharacteristic
181C3×D4—32no—
182C3×D4—61no—
183C2×C3×C4—31no—
184C2×C3×C4—32no—
185C2×C3×C4—32no—
186C2×C3×C4—41no—
187C2×C3×C4—62no—
188C2×C3×C4—81no—
189C2×C3×C4—121no—
190C2×C3×C4—121no—
191C2×C3×C4—122no—
192C2×C3×C4C2×S411yescharacteristic
193C2×Dic3—31no—
194C2×Dic3—31no—
195C2×Dic3—42no—
196C2×Dic3—64no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—122no—
200C2×Dic3—121no—
201C2×Dic3—242no—
202C2×Dic3C2×S411yescharacteristic
203C2×Dic3C2×S411yescharacteristic
204Dic6—34no—
205Dic6—62no—
206Dic6—64no—
207Dic6—124no—
208Dic6—244no—
209SL(2,𝔽3)—21no—
210SL(2,𝔽3)C2×C4×D311yescharacteristic
211C3×C8—62no—
212C3⋊C8—34no—
213C2×C32—41no—
214C2×C32—41no—
215C2×C32—41no—
216#41—32no—
217#41#62412yes—
218C2×Q8—92no—
219C2×Q8—94no—
220C2×Q8—182no—
221C2×Q8—181no—
222C2×Q8C2×D3211yescharacteristic
223C2×D4—31no—
224C22×C4—31no—
225C22×C4—61no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—181no—
229Q16—94no—
230Q16—94no—
231SD16—98no—
232M16—62no—
233M16—94no—
234C2×C8—32no—
235C2×C8—92no—
236C4⋊C4—32no—
237C4⋊C4—61no—
238C4⋊C4—91no—
239C4⋊C4—91no—
240C4⋊C4—182no—
241C4⋊C4—182no—
242C22⋊C4—181no—
243C42—31no—
244C42—91no—
245C42—91no—
246C42—91no—
247C42—182no—
248C42—182no—
249C22×C3—32no—
250C22×C3—41no—
251C22×C3—61no—
252C22×C3—61no—
253C22×C3—81no—
254C22×C3C22×S411yescharacteristic
255C3×C4—31no—
256C3×C4—31no—
257C3×C4—42no—
258C3×C4—82no—
259C3×C4—122no—
260C3×C4—122no—
261C3×C4—241no—
262C3×C4C4×S412yes—
263Dic3—21no—
264Dic3—64no—
265Dic3—61no—
266Dic3—61no—
267Dic3—82no—
268Dic3—124no—
269Dic3—244no—
270Dic3#98412yescomplemented
271C32—41noSylow
272C23—31no—
273Q8—31no—
274Q8—94no—
275Q8—182no—
276Q8—184no—
277Q8C2×#62411yescharacteristic
278D4—32no—
279D4—61no—
280C2×C4—31no—
281C2×C4—31no—
282C2×C4—32no—
283C2×C4—32no—
284C2×C4—31no—
285C2×C4—62no—
286C2×C4—91no—
287C2×C4—91no—
288C2×C4—122no—
289C2×C4—182no—
290C2×C4—184no—
291C2×C4—182no—
292C2×C4—361no—
293C2×C4D3×S411yescharacteristic
294C8—62no—
295C8—94no—
296C2×C3—41no—
297C2×C3—41no—
298C2×C3—41no—
299C2×C3—62no—
300C2×C3—81no—
301C2×C3—81no—
302C2×C3—81no—
303C2×C3C2×C4×S411yescharacteristic
304C2×C3C2×#98411yescharacteristic
305C2×C3#592311yescharacteristic
306C22—32no—
307C22—61no—
308C22—61no—
309C22C2×D3×S411yescharacteristic
310C4—32no—
311C4—31no—
312C4—31no—
313C4—61no—
314C4—122no—
315C4—181no—
316C4—181no—
317C4—184no—
318C4(C3⋊S4)⋊C412yes—
319C3—41no—
320C3—81no—
321C3C4×#98411yescharacteristic, complemented
322C2—62no—
323C2D3×#98411yescharacteristic
324C2#1059645511yescharacteristic
325C2C2×(C3⋊S4)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
prime radicalC2×C3×#41⋊C3C22
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC2×C4D3×S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #10593195C2semidirect
5. #10593193C2semidirect
9. #64265C4semidirect
35. C3⋊#226C2×C4semidirect
270. Dic3#984semidirect
321. C3C4×#984semidirect

Maximal subgroups

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

subgroupindex
C2×#642652
Dic3×#41⋊C32
C3×#54262
#105931952
#105931932
C4×#9843
#788673
#638444