Finite Group Databasebeta

← #11922338

Subgroups — #11922338

Order 1152.

657 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 657 conjugacy classes of subgroups — too many to draw. Only its 83 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×D3×#41⋊C3C211yesmaximal, characteristic
2#10593658C211yesmaximal, characteristic, complemented
3C3×#5424C211yesmaximal, characteristic, complemented
4#10593209C212yesmaximal, complemented
5#10593200C212yesmaximal, complemented
6#85519—31nomaximal
7#78830—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9D3×#41⋊C3C414yescomplemented
10C2×D3×SL(2,𝔽3)C2211yescharacteristic
11C2×C3⋊(#41⋊C3)C2211yescharacteristic
12#63855—41nomaximal
13C3⋊#859C2212yescomplemented
14C3×#859C2212yescomplemented
15C2×D3×#41D311yescharacteristic
16C22×#41⋊C3—31no—
17C22×ΓL(1,𝔽25)—31no—
18D3×#117—31no—
19#5426—32no—
20#5424—31no—
21#5424—61no—
22#5424D311yescharacteristic, complemented
23#5420—32no—
24C3×#416—31no—
25#5233—31no—
26#5113—31no—
27#5002—31no—
28#4803—32no—
29#4802—32no—
30#4771—32no—
31#4770—32no—
32C2×C3×C4×D3—41no—
33C3×#41⋊C3C2×C412yescomplemented
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35D3×SL(2,𝔽3)C2×C412yescomplemented
36C3⋊(#41⋊C3)C2×C412yes—
37C4×C3⋊Dic3—41no—
38C3×C4×Dic3—41no—
39Dic3⋊Dic3—42no—
40(C2×D3)⋊Dic3—42no—
41#2896—91noSylow
42C2×C3×#41C2×D311yescharacteristic
43D3×#41—34no—
44D3×#41Dic314yescomplemented
45C2×#239C2×D311yescharacteristic
46C2×D3×Q8C2×D311yescharacteristic
47C2×#237—31no—
48C2×D3×D4—31no—
49C2×#235—31no—
50C22×C4×D3—31no—
51C2×#41⋊C3—21no—
52C2×#41⋊C3—34no—
53C2×#41⋊C3—31no—
54C2×#41⋊C3C2×D311yescharacteristic
55C22×SL(2,𝔽3)—31no—
56C22×C3×C8—31no—
57C3×#117—31no—
58#926—31no—
59#926—121no—
60C22×C3⋊C8—31no—
61C2×ΓL(1,𝔽25)—32no—
62C2×ΓL(1,𝔽25)—32no—
63C2×ΓL(1,𝔽25)—64no—
64#892—32no—
65D3×C4⋊C4—32no—
66D3×C22⋊C4—61no—
67#877—61no—
68#872—61no—
69C42×D3—61no—
70#859—32no—
71#859—62no—
72#859C2×D312yescomplemented
73C3×#103—32no—
74C3×#102—32no—
75#835—32no—
76#832—32no—
77#821—32no—
78#816—32no—
79#810—32no—
80#809—32no—
81C22×C3×D3—41no—
82C2×C32×C4—41no—
83C2×C3⋊Dic3—42no—
84C2×C3×Dic3—42no—
85C2×C3×Dic3—41no—
86C3×C4×D3—44no—
87C3×SL(2,𝔽3)C22×C411yescharacteristic
88C22×#41—31no—
89C22×M16—91no—
90C2×#117—91no—
91#419—92no—
92#418—92no—
93#417—92no—
94#417—92no—
95#416—31no—
96#416—91no—
97#416—91no—
98#416—91no—
99C23×D3—31no—
100C3×#41—32no—
101C3×#41C2×Dic312yes—
102C2×C3×Q8C22×D311yescharacteristic
103C2×C3×D4—31no—
104C22×C3×C4—31no—
105C22×C3×C4—121no—
106C2×#67—61no—
107C22×Dic3—31no—
108#239—32no—
109#239C2×Dic312yes—
110D3×Q8—32no—
111D3×Q8C2×Dic312yes—
112#237—34no—
113#237—62no—
114D3×D4—34no—
115D3×D4—62no—
116#235—34no—
117#235—62no—
118C2×D12—31no—
119C2×C4×D3—31no—
120C2×C4×D3—31no—
121C2×C4×D3—31no—
122C2×C4×D3—34no—
123C2×C4×D3—34no—
124C2×C4×D3—62no—
125C2×C4×D3S411yescharacteristic
126C2×Dic6—31no—
127#41⋊C3—22no—
128#41⋊C3—32no—
129#41⋊C3C4×D312yescomplemented
130C2×SL(2,𝔽3)—21no—
131C2×SL(2,𝔽3)—32no—
132C2×SL(2,𝔽3)C22×D311yescharacteristic
133C2×C3×C8—32no—
134C2×C3×C8—62no—
135C3×C4⋊C4—32no—
136C3×C22⋊C4—61no—
137C3×C42—61no—
138#217—61no—
139#217—122no—
140(C2×D3)⋊C4—62no—
141C4⋊Dic3—32no—
142C4⋊Dic3—122no—
143Dic3⋊C4—62no—
144C4×Dic3—41no—
145C4×Dic3—62no—
146C4×Dic3—61no—
147C4×Dic3—121no—
148C4×Dic3—241no—
149C2×C3⋊C8—32no—
150C2×C3⋊C8—62no—
151ΓL(1,𝔽25)—64no—
152ΓL(1,𝔽25)—64no—
153C22×C32—41no—
154C2×C3×D3—42no—
155C2×C3×D3—82no—
156C32×C4—42no—
157C3⋊Dic3—82no—
158C3×Dic3—42no—
159C3×Dic3—82no—
160C2×#41—34no—
161C2×#41—31no—
162C2×#41—91no—
163C2×#41—91no—
164C2×#41—94no—
165C2×#41D3211yescharacteristic
166C22×Q8—31no—
167C22×D4—91no—
168C23×C4—91no—
169C2×M16—92no—
170C2×M16—92no—
171C2×M16—184no—
172C22×C8—31no—
173C22×C8—91no—
174#117—31no—
175#117—92no—
176#117—91no—
177#117—181no—
178#117—181no—
179C2×C4⋊C4—92no—
180C2×C22⋊C4—181no—
181C2×C42—181no—
182#103—32no—
183#103—92no—
184#103—92no—
185#103—92no—
186#102—32no—
187#102—92no—
188#102—92no—
189#102—92no—
190C23×C3—31no—
191C23×C3—121no—
192C22×D3—31no—
193C22×D3—34no—
194C22×D3—122no—
195C22×D3C2×S411yescharacteristic
196C3×Q8—31no—
197C3×Q8C22×Dic311yescharacteristic
198C3×D4—32no—
199C3×D4—61no—
200C2×C3×C4—31no—
201C2×C3×C4—32no—
202C2×C3×C4—32no—
203C2×C3×C4—41no—
204C2×C3×C4—62no—
205C2×C3×C4—81no—
206C2×C3×C4—124no—
207C2×C3×C4—121no—
208C2×C3×C4C2×S411yescharacteristic
209#67—64no—
210C2×Dic3—31no—
211C2×Dic3—34no—
212C2×Dic3—42no—
213C2×Dic3—62no—
214C2×Dic3—122no—
215C2×Dic3—242no—
216C2×Dic3C2×S411yescharacteristic
217D12—32no—
218D12—61no—
219C4×D3—32no—
220C4×D3—32no—
221C4×D3—34no—
222C4×D3—32no—
223C4×D3—32no—
224C4×D3—124no—
225C4×D3SL(2,ℤ/4)14yes—
226Dic6—32no—
227Dic6—61no—
228SL(2,𝔽3)—21no—
229SL(2,𝔽3)C2×C4×D311yescharacteristic
230C3×C8—62no—
231C3⋊C8—62no—
232C2×C32—42no—
233C2×C32—41no—
234C3×D3—82no—
235C24—91no—
236#41—32no—
237#41—32no—
238#41—94no—
239#41—94no—
240#41—92no—
241#41—182no—
242#41—182no—
243#41D3×Dic312yes—
244C2×Q8—32no—
245C2×Q8—91no—
246C2×Q8—92no—
247C2×Q8C2×D3211yescharacteristic
248C2×D4—31no—
249C2×D4—91no—
250C2×D4—94no—
251C2×D4—182no—
252C2×D4—181no—
253C22×C4—31no—
254C22×C4—31no—
255C22×C4—91no—
256C22×C4—94no—
257C22×C4—94no—
258C22×C4—91no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4—182no—
262M16—184no—
263M16—184no—
264C2×C8—32no—
265C2×C8—62no—
266C2×C8—92no—
267C2×C8—182no—
268C4⋊C4—32no—
269C4⋊C4—92no—
270C4⋊C4—182no—
271C22⋊C4—61no—
272C22⋊C4—182no—
273C22⋊C4—181no—
274C42—61no—
275C42—182no—
276C42—181no—
277C22×C3—32no—
278C22×C3—41no—
279C22×C3—62no—
280C22×C3—81no—
281C22×C3—122no—
282C22×C3—242no—
283C22×C3C22×S411yescharacteristic
284C2×D3—22no—
285C2×D3—32no—
286C2×D3—62no—
287C2×D3—124no—
288C2×D3C2×SL(2,ℤ/4)12yes—
289C3×C4—31no—
290C3×C4—31no—
291C3×C4—42no—
292C3×C4—82no—
293C3×C4—122no—
294C3×C4—122no—
295C3×C4C2×SL(2,ℤ/4)12yes—
296Dic3—32no—
297Dic3—82no—
298Dic3—122no—
299Dic3—242no—
300Dic3—244no—
301Dic3C2×SL(2,ℤ/4)12yes—
302C32—41noSylow
303C23—31no—
304C23—31no—
305C23—94no—
306C23—91no—
307C23—362no—
308Q8—31no—
309Q8—92no—
310Q8—181no—
311Q8C2×D3×Dic311yescharacteristic
312D4—32no—
313D4—61no—
314D4—92no—
315D4—181no—
316D4—184no—
317C2×C4—31no—
318C2×C4—31no—
319C2×C4—32no—
320C2×C4—32no—
321C2×C4—34no—
322C2×C4—62no—
323C2×C4—92no—
324C2×C4—92no—
325C2×C4—92no—
326C2×C4—92no—
327C2×C4—94no—
328C2×C4—91no—
329C2×C4—94no—
330C2×C4—182no—
331C2×C4—364no—
332C2×C4D3×S411yescharacteristic
333C8—62no—
334C8—182no—
335C2×C3—42no—
336C2×C3—41no—
337C2×C3—62no—
338C2×C3—82no—
339C2×C3—81no—
340C2×C3—242no—
341C2×C3#592312yes—
342C2×C3C22×SL(2,ℤ/4)11yescharacteristic
343D3—22no—
344D3—62no—
345C22—32no—
346C22—32no—
347C22—62no—
348C22—62no—
349C22—92no—
350C22—182no—
351C22—364no—
352C22C2×D3×S411yescharacteristic
353C4—31no—
354C4—31no—
355C4—32no—
356C4—92no—
357C4—122no—
358C4—362no—
359C4D3×SL(2,ℤ/4)12yes—
360C3—41no—
361C3—81no—
362C3#8551911yescharacteristic, complemented
363C2—62no—
364C2—62no—
365C2—182no—
366C2#1059645412yes—
367C2C2×D3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC22C2×D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
prime radicalC2×D3×#41⋊C3C2
cosocleC2×C3×SL(2,𝔽3)C23
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #10593658C2semidirect
3. C3×#5424C2semidirect
4. #10593209C2semidirect
5. #10593200C2semidirect
9. D3×#41⋊C3C4semidirect
13. C3⋊#859C22semidirect
14. C3×#859C22semidirect
22. #5424D3semidirect
33. C3×#41⋊C3C2×C4semidirect
35. D3×SL(2,𝔽3)C2×C4semidirect
44. D3×#41Dic3semidirect
72. #859C2×D3semidirect
129. #41⋊C3C4×D3semidirect
362. C3#85519semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#41⋊C32
#105936582
C3×#54242
#105932092
#105932002
#855193
#788303
#638554