Finite Group Databasebeta

← #11922279

Subgroups — #11922279

Order 1152.

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

normal subgroups only

This group has 647 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#10593660C211yesmaximal, characteristic, complemented
3C3×#5424C211yesmaximal, characteristic, complemented
4#10593200C212yesmaximal, complemented
5#10593191C212yesmaximal, complemented
6#85528—31nomaximal
7#78831—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9C3⋊#994C414yescomplemented
10C2×C3⋊(#41⋊C3)C2212yes—
11Dic3×Dic6—41nomaximal
12C3⋊#859C2212yescomplemented
13C3×#859C2211yescharacteristic, complemented
14C3×#859C2211yescharacteristic, complemented
15C2×#1009D311yescharacteristic
16C2×#994—31no—
17C2×#901—31no—
18#5523—31no—
19#5426—31no—
20#5426—32no—
21#5426—61no—
22#5424—32no—
23#5424D311yescharacteristic, complemented
24C3×#416—31no—
25#5232—31no—
26C2×#821—31no—
27#5001—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
52C22×C3×C8—31no—
53C3×#117—31no—
54Q8×Dic3—121no—
55C2×C4⋊Dic3—31no—
56C2×#208—31no—
57#901—64no—
58C2×ΓL(1,𝔽25)—32no—
59C2×D3×C8—32no—
60#892—32no—
61D3×C4⋊C4—32no—
62#67⋊C4—62no—
63C4×D12—61no—
64C4×Dic6—61no—
65#859—32no—
66#859—62no—
67#859C2×D311yescharacteristic, complemented
68#859C2×D311yescharacteristic, complemented
69C3×#103—31no—
70C3×#103—31no—
71C3×#102—31no—
72C3×#102—31no—
73#835—32no—
74#832—32no—
75#821—32no—
76#821—32no—
77#809—32no—
78#809—32no—
79C2×C32×C4—41no—
80C2×C3⋊Dic3—42no—
81C2×C3×Dic3—41no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—42no—
84C3×Dic6—44no—
85C3×SL(2,𝔽3)C22×C411yescharacteristic
86C2×H(5,𝔽2)—31no—
87C2×#131—91no—
88#520—91no—
89#418—92no—
90#418—91no—
91#417—92no—
92#417—91no—
93#416—31no—
94#416—92no—
95C2×#102—92no—
96C2×#102—91no—
97C23×D3—61no—
98C3×#41—32no—
99C3×#41C2×Dic312yes—
100C2×C3×Q8—121no—
101C2×C3×Q8C22×D311yescharacteristic
102C2×C3×D4—31no—
103C22×C3×C4—31no—
104C2×#67—32no—
105C22×Dic3—61no—
106#239—34no—
107#239C2×Dic314yes—
108D3×D4—38no—
109D3×D4—64no—
110#235—34no—
111#235—34no—
112C2×D12—31no—
113C2×D12—34no—
114C2×D12—32no—
115C2×D12—62no—
116C2×C4×D3—32no—
117C2×C4×D3—62no—
118C2×Dic6S411yescharacteristic
119#41⋊C3—22no—
120#41⋊C3—34no—
121#41⋊C3C4×D312yescomplemented
122C2×SL(2,𝔽3)—21no—
123C2×SL(2,𝔽3)C22×D311yescharacteristic
124C2×C3×C8—31no—
125C2×C3×C8—31no—
126C2×C3×C8—62no—
127C3×C4⋊C4—31no—
128C3×C4⋊C4—31no—
129C3×C22⋊C4—61no—
130C3×C42—61no—
131(C2×D3)⋊C4—62no—
132C4⋊Dic3—32no—
133C4⋊Dic3—61no—
134C4⋊Dic3—122no—
135C4⋊Dic3—121no—
136C4⋊Dic3—241no—
137Dic3⋊C4—62no—
138C4×Dic3—41no—
139C4×Dic3—62no—
140C4×Dic3—122no—
141#208—62no—
142C2×C3⋊C8—32no—
143ΓL(1,𝔽25)—64no—
144D3×C8—64no—
145C22×C32—41no—
146C32×C4—42no—
147C3⋊Dic3—82no—
148C3×Dic3—42no—
149C3×Dic3—44no—
150C3×Dic3—81no—
151H(5,𝔽2)—34no—
152H(5,𝔽2)—94no—
153C2×#41—32no—
154C2×#41—91no—
155C2×#41D3211yescharacteristic
156C22×D4—91no—
157C22×D4—92no—
158#131—184no—
159C2×M16—92no—
160C2×M16—91no—
161C22×C8—31no—
162C22×C8—92no—
163C4×Q8—181no—
164C4×D4—181no—
165C4×D4—182no—
166#117—31no—
167#117—92no—
168C2×C4⋊C4—92no—
169C2×C4⋊C4—91no—
170#103—31no—
171#103—31no—
172#103—92no—
173#102—31no—
174#102—31no—
175#102—92no—
176#102—92no—
177#102—92no—
178#102—92no—
179#102—92no—
180C23×C3—31no—
181C22×D3—32no—
182C22×D3—64no—
183C22×D3—241no—
184C22×D3—241no—
185C3×Q8—31no—
186C3×Q8—124no—
187C3×Q8C22×Dic311yescharacteristic
188C3×D4—32no—
189C3×D4—61no—
190C2×C3×C4—31no—
191C2×C3×C4—32no—
192C2×C3×C4—32no—
193C2×C3×C4—41no—
194C2×C3×C4—61no—
195C2×C3×C4—61no—
196C2×C3×C4—81no—
197C2×C3×C4—122no—
198C2×C3×C4C2×S411yescharacteristic
199#67—38no—
200C2×Dic3—41no—
201C2×Dic3—41no—
202C2×Dic3—62no—
203C2×Dic3—122no—
204C2×Dic3—242no—
205C2×Dic3—241no—
206C2×Dic3C2×S412yes—
207D12—34no—
208D12—34no—
209D12—62no—
210C4×D3—34no—
211C4×D3—34no—
212C4×D3—242no—
213Dic6SL(2,ℤ/4)14yes—
214SL(2,𝔽3)—21no—
215SL(2,𝔽3)C2×C4×D311yescharacteristic
216C3×C8—61no—
217C3×C8—61no—
218C3⋊C8—62no—
219C2×C32—41no—
220C2×C32—41no—
221C2×C32—41no—
222C24—181no—
223#41—32no—
224#41—34no—
225#41—94no—
226#41—94no—
227#41—94no—
228#41D3×Dic312yes—
229C2×Q8—31no—
230C2×Q8C2×D3211yescharacteristic
231C2×D4—31no—
232C2×D4—92no—
233C2×D4—94no—
234C2×D4—92no—
235C2×D4—98no—
236C2×D4—91no—
237C2×D4—182no—
238C2×D4—184no—
239C22×C4—31no—
240C22×C4—92no—
241C22×C4—182no—
242C22×C4—181no—
243M16—184no—
244M16—182no—
245C2×C8—31no—
246C2×C8—31no—
247C2×C8—62no—
248C2×C8—92no—
249C2×C8—184no—
250C4⋊C4—31no—
251C4⋊C4—31no—
252C4⋊C4—92no—
253C4⋊C4—182no—
254C4⋊C4—181no—
255C22⋊C4—61no—
256C22⋊C4—182no—
257C42—61no—
258C42—182no—
259C22×C3—32no—
260C22×C3—41no—
261C22×C3—61no—
262C22×C3—61no—
263C22×C3—81no—
264C22×C3C22×S411yescharacteristic
265C2×D3—34no—
266C2×D3—62no—
267C2×D3—62no—
268C2×D3—244no—
269C3×C4—31no—
270C3×C4—31no—
271C3×C4—42no—
272C3×C4—82no—
273C3×C4—124no—
274C3×C4—121no—
275C3×C4—121no—
276C3×C4C2×SL(2,ℤ/4)12yes—
277Dic3—42no—
278Dic3—81no—
279Dic3—122no—
280Dic3—242no—
281Dic3—482no—
282Dic3C2×SL(2,ℤ/4)14yes—
283C32—41noSylow
284C23—31no—
285C23—92no—
286C23—184no—
287C23—721no—
288C23—721no—
289Q8—31no—
290Q8—34no—
291Q8C2×D3×Dic311yescharacteristic
292D4—32no—
293D4—61no—
294D4—98no—
295D4—94no—
296D4—94no—
297D4—182no—
298C2×C4—32no—
299C2×C4—31no—
300C2×C4—32no—
301C2×C4—32no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—94no—
305C2×C4—94no—
306C2×C4—182no—
307C2×C4—722no—
308C2×C4—721no—
309C2×C4D3×S411yescharacteristic
310C8—61no—
311C8—61no—
312C8—182no—
313C2×C3—41no—
314C2×C3—41no—
315C2×C3—41no—
316C2×C3—62no—
317C2×C3—81no—
318C2×C3—81no—
319C2×C3—81no—
320C2×C3#592411yescharacteristic
321C2×C3#592511yescharacteristic
322C2×C3C22×SL(2,ℤ/4)11yescharacteristic
323D3—64no—
324C22—32no—
325C22—61no—
326C22—61no—
327C22—94no—
328C22—182no—
329C22—182no—
330C22—724no—
331C22C2×D3×S411yescharacteristic
332C4—31no—
333C4—31no—
334C4—34no—
335C4—121no—
336C4—121no—
337C4—362no—
338C4D3×SL(2,ℤ/4)12yes—
339C3—41no—
340C3—81no—
341C3#8552811yescharacteristic, complemented
342C2—62no—
343C2—184no—
344C2#1059644711yescharacteristic
345C2#1059644911yescharacteristic
346C2C2×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. #10593660C2semidirect
3. C3×#5424C2semidirect
4. #10593200C2semidirect
5. #10593191C2semidirect
9. C3⋊#994C4semidirect
12. C3⋊#859C22semidirect
13. C3×#859C22semidirect
14. C3×#859C22semidirect
23. #5424D3semidirect
33. C3×#41⋊C3C2×C4semidirect
35. C3⋊(#41⋊C3)C2×C4semidirect
43. #1009Dic3semidirect
67. #859C2×D3semidirect
68. #859C2×D3semidirect
121. #41⋊C3C4×D3semidirect
341. 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
#105936602
C3×#54242
#105932002
#105931912
#855283
#788313
Dic3×Dic64