Finite Group Databasebeta

← #11922280

Subgroups — #11922280

Order 1152.

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

normal subgroups only

This group has 649 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×C3⋊#994C211yesmaximal, characteristic
2#10593658C211yesmaximal, characteristic, complemented
3C3×#5426C211yesmaximal, characteristic, complemented
4#10593200C212yesmaximal, complemented
5#10593191C212yesmaximal, complemented
6#85528—31nomaximal
7#78882—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9C3⋊#994C414yescomplemented
10C2×C3⋊(#41⋊C3)C2212yes—
11#63843—41nomaximal
12C3⋊#859C2211yescharacteristic, complemented
13C3⋊#859C2211yescharacteristic, complemented
14C3×#859C2212yescomplemented
15C2×#1009D311yescharacteristic
16C2×#994—31no—
17C2×#907—31no—
18#5504—31no—
19#5426—32no—
20#5426D311yescharacteristic, complemented
21#5424—31no—
22#5424—32no—
23#5424—61no—
24C3×#417—31no—
25#5233—31no—
26#5131—31no—
27C2×#809—31no—
28#4804—32no—
29#4803—32no—
30#4770—32no—
31D3×#102—32no—
32C2×C3×Dic6—41no—
33C3×#41⋊C3C2×C412yescomplemented
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C3⋊(#41⋊C3)C2×C414yescomplemented
36C4×C3⋊Dic3—41no—
37C3×C4⋊Dic3—41no—
38Dic3⋊Dic3—42no—
39Dic32—42no—
40#2897—91noSylow
41C2×C3×#41C2×D311yescharacteristic
42#1009—34no—
43#1009Dic314yescomplemented
44C2×#239C2×D312yes—
45C2×D3×D4—32no—
46C2×#235—31no—
47C22×D12—31no—
48#994—34no—
49C2×#41⋊C3—21no—
50C2×#41⋊C3—32no—
51C2×#41⋊C3C2×D311yescharacteristic
52C2×C3×M16—31no—
53C2×C3×C4⋊C4—31no—
54Q8×Dic3—121no—
55C4×#67—62no—
56#926—31no—
57C22×C3⋊C8—31no—
58#907—64no—
59C2×ΓL(1,𝔽25)—32no—
60C2×D3×C8—32no—
61#893—61no—
62#892—32no—
63D3×C4⋊C4—32no—
64#887—61no—
65#859—31no—
66#859—31no—
67#859—61no—
68#859—61no—
69#859C2×D312yescomplemented
70C3×#103—32no—
71C3×#102—32no—
72#835—31no—
73#835—31no—
74#832—31no—
75#832—31no—
76#821—32no—
77#821—32no—
78#809—32no—
79#809—32no—
80C2×C32×C4—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—41no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—42no—
85C3×Dic6—44no—
86C3×SL(2,𝔽3)C22×C411yescharacteristic
87C2×H(5,𝔽2)—31no—
88C2×#131—91no—
89#520—91no—
90#418—92no—
91#418—91no—
92#417—31no—
93#417—92no—
94#416—92no—
95#416—91no—
96C2×#102—92no—
97C2×#102—91no—
98C23×D3—61no—
99C3×#41—32no—
100C3×#41C2×Dic312yes—
101C2×C3×Q8—121no—
102C2×C3×Q8C22×D311yescharacteristic
103C2×C3×D4—31no—
104C22×C3×C4—31no—
105C22×C3×C4—61no—
106C2×#67—32no—
107#239—34no—
108#239C2×Dic314yes—
109D3×D4—38no—
110D3×D4—64no—
111#235—34no—
112#235—34no—
113C2×D12—31no—
114C2×D12—34no—
115C2×D12—32no—
116C2×D12—62no—
117C2×C4×D3—32no—
118C2×C4×D3—62no—
119C2×Dic6S411yescharacteristic
120#41⋊C3—22no—
121#41⋊C3—34no—
122#41⋊C3C4×D312yescomplemented
123C2×SL(2,𝔽3)—21no—
124C2×SL(2,𝔽3)C22×D311yescharacteristic
125C3×M16—62no—
126C2×C3×C8—32no—
127C3×C4⋊C4—32no—
128C3×C4⋊C4—61no—
129#217—61no—
130(C2×D3)⋊C4—62no—
131C4⋊Dic3—31no—
132C4⋊Dic3—31no—
133C4⋊Dic3—41no—
134C4⋊Dic3—122no—
135Dic3⋊C4—62no—
136C4×Dic3—61no—
137C4×Dic3—62no—
138C4×Dic3—122no—
139C4×Dic3—121no—
140C4×Dic3—241no—
141C2×C3⋊C8—31no—
142C2×C3⋊C8—31no—
143C2×C3⋊C8—62no—
144ΓL(1,𝔽25)—64no—
145D3×C8—64no—
146C22×C32—41no—
147C32×C4—42no—
148C3⋊Dic3—42no—
149C3⋊Dic3—81no—
150C3×Dic3—44no—
151C3×Dic3—82no—
152H(5,𝔽2)—34no—
153H(5,𝔽2)—94no—
154C2×#41—32no—
155C2×#41—91no—
156C2×#41D3211yescharacteristic
157C22×D4—91no—
158C22×D4—92no—
159#131—184no—
160C2×M16—31no—
161C2×M16—92no—
162C22×C8—92no—
163C22×C8—91no—
164C4×Q8—181no—
165C4×D4—181no—
166C4×D4—182no—
167#117—92no—
168#117—91no—
169C2×C4⋊C4—31no—
170C2×C4⋊C4—92no—
171#103—32no—
172#103—91no—
173#103—91no—
174#102—32no—
175#102—92no—
176#102—92no—
177#102—92no—
178#102—92no—
179#102—91no—
180#102—91no—
181C23×C3—31no—
182C22×D3—32no—
183C22×D3—64no—
184C22×D3—241no—
185C22×D3—241no—
186C3×Q8—31no—
187C3×Q8—124no—
188C3×Q8C22×Dic311yescharacteristic
189C3×D4—32no—
190C3×D4—61no—
191C2×C3×C4—31no—
192C2×C3×C4—32no—
193C2×C3×C4—32no—
194C2×C3×C4—41no—
195C2×C3×C4—62no—
196C2×C3×C4—81no—
197C2×C3×C4—122no—
198C2×C3×C4—241no—
199C2×C3×C4C2×S411yescharacteristic
200#67—38no—
201C2×Dic3—42no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—121no—
205C2×Dic3—121no—
206C2×Dic3—241no—
207C2×Dic3—241no—
208C2×Dic3C2×S412yes—
209D12—34no—
210D12—34no—
211D12—62no—
212C4×D3—34no—
213C4×D3—34no—
214C4×D3—242no—
215Dic6SL(2,ℤ/4)14yes—
216SL(2,𝔽3)—21no—
217SL(2,𝔽3)C2×C4×D311yescharacteristic
218C3×C8—62no—
219C3⋊C8—61no—
220C3⋊C8—61no—
221C2×C32—41no—
222C2×C32—41no—
223C2×C32—41no—
224C24—181no—
225#41—32no—
226#41—34no—
227#41—94no—
228#41—94no—
229#41—94no—
230#41D3×Dic312yes—
231C2×Q8—31no—
232C2×Q8C2×D3211yescharacteristic
233C2×D4—31no—
234C2×D4—92no—
235C2×D4—94no—
236C2×D4—92no—
237C2×D4—98no—
238C2×D4—91no—
239C2×D4—182no—
240C2×D4—184no—
241C22×C4—31no—
242C22×C4—61no—
243C22×C4—92no—
244C22×C4—182no—
245M16—62no—
246M16—184no—
247C2×C8—32no—
248C2×C8—91no—
249C2×C8—91no—
250C2×C8—184no—
251C2×C8—182no—
252C4⋊C4—32no—
253C4⋊C4—61no—
254C4⋊C4—91no—
255C4⋊C4—91no—
256C4⋊C4—182no—
257C22⋊C4—182no—
258C22⋊C4—181no—
259C42—182no—
260C42—181no—
261C22×C3—32no—
262C22×C3—41no—
263C22×C3—61no—
264C22×C3—61no—
265C22×C3—81no—
266C22×C3C22×S411yescharacteristic
267C2×D3—34no—
268C2×D3—62no—
269C2×D3—62no—
270C2×D3—244no—
271C3×C4—31no—
272C3×C4—31no—
273C3×C4—42no—
274C3×C4—82no—
275C3×C4—124no—
276C3×C4—122no—
277C3×C4C2×SL(2,ℤ/4)12yes—
278Dic3—82no—
279Dic3—122no—
280Dic3—121no—
281Dic3—121no—
282Dic3—241no—
283Dic3—242no—
284Dic3—242no—
285Dic3C2×SL(2,ℤ/4)14yes—
286C32—41noSylow
287C23—31no—
288C23—92no—
289C23—184no—
290C23—721no—
291C23—721no—
292Q8—31no—
293Q8—34no—
294Q8C2×D3×Dic311yescharacteristic
295D4—32no—
296D4—61no—
297D4—98no—
298D4—94no—
299D4—94no—
300D4—182no—
301C2×C4—32no—
302C2×C4—31no—
303C2×C4—32no—
304C2×C4—32no—
305C2×C4—62no—
306C2×C4—94no—
307C2×C4—94no—
308C2×C4—181no—
309C2×C4—181no—
310C2×C4—241no—
311C2×C4—722no—
312C2×C4D3×S411yescharacteristic
313C8—62no—
314C8—181no—
315C8—181no—
316C2×C3—41no—
317C2×C3—41no—
318C2×C3—41no—
319C2×C3—62no—
320C2×C3—81no—
321C2×C3—81no—
322C2×C3—81no—
323C2×C3#592411yescharacteristic
324C2×C3#592511yescharacteristic
325C2×C3C22×SL(2,ℤ/4)11yescharacteristic
326D3—64no—
327C22—32no—
328C22—61no—
329C22—61no—
330C22—94no—
331C22—182no—
332C22—182no—
333C22—724no—
334C22C2×D3×S411yescharacteristic
335C4—31no—
336C4—31no—
337C4—34no—
338C4—122no—
339C4—361no—
340C4—361no—
341C4D3×SL(2,ℤ/4)12yes—
342C3—41no—
343C3—81no—
344C3#8552811yescharacteristic, complemented
345C2—62no—
346C2—184no—
347C2#1059644811yescharacteristic
348C2#1059645011yescharacteristic
349C2C2×D3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
prime radicalC2×C3⋊#994C2
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
2. #10593658C2semidirect
3. C3×#5426C2semidirect
4. #10593200C2semidirect
5. #10593191C2semidirect
9. C3⋊#994C4semidirect
12. C3⋊#859C22semidirect
13. C3⋊#859C22semidirect
14. C3×#859C22semidirect
20. #5426D3semidirect
33. C3×#41⋊C3C2×C4semidirect
35. C3⋊(#41⋊C3)C2×C4semidirect
43. #1009Dic3semidirect
69. #859C2×D3semidirect
122. #41⋊C3C4×D3semidirect
344. C3#85528semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#9942
#105936582
C3×#54262
#105932002
#105931912
#855283
#788823
#638434