Finite Group Databasebeta

← #11860177

Subgroups — #11860177

Order 1152.

1281 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 1281 conjugacy classes of subgroups — too many to draw. Only its 232 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×#63797C211yesmaximal, characteristic
2#10594605C212yesmaximal, complemented
3C3⋊D3×#106C211yesmaximal, characteristic, complemented
4C3×#4869C212yesmaximal, complemented
5#10590771C212yesmaximal, complemented
6#10590668C211yesmaximal, characteristic, complemented
7#10590593C212yesmaximal, complemented
8#10590455C214yesmaximal, complemented
9D3×#442—32nomaximal
10C2×#3802C2212yes—
11C2×C4×D32—22no—
12C2×C8×C3⋊D3C2211yescharacteristic
13C4⋊C4×C3⋊D3C2212yes—
14C2×C3×D24C2212yes—
15C3×#893C2214yescomplemented
16#63921—22no—
17Dic3×D12C2214yescomplemented
18C4×#624C2211yescharacteristic
19#63879—24no—
20C2×#3713C2212yes—
21C2×#3710C2211yescharacteristic
22#63797C418yescomplemented
23C32×#106C2211yescharacteristic, complemented
24#63644C2211yescharacteristic, complemented
25#63635C2212yescomplemented
26C3×#815C2212yescomplemented
27C3×#809C2214yescomplemented
28#63563C2214yescomplemented
29#63554C2212yescomplemented
30C2×D3×D8—32no—
31C4×D3×D4—34no—
32C3×#442—32no—
33#5152—32no—
34#5014—34no—
35#4869D312yescomplemented
36D3×#106—32no—
37D3×#106—61no—
38#4785—34no—
39D3×#102—34no—
40#4711—32no—
41D3×#97—32no—
42C22×D32—22no—
43C2×C4×C3⋊D3—22no—
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×C3×D12C2314yes—
46C2×C3×C4×D3—24no—
47C2×#625—22no—
48C2×#624D412yes—
49C2×D3×Dic3—24no—
50#3802—24no—
51#3802C2×C418yescomplemented
52C4×D32—48no—
53C2×C32×C8C2311yescharacteristic
54C32×C4⋊C4C2312yes—
55C4⋊(C3⋊Dic3)C2312yes—
56#3750—22no—
57C2×C3⋊(C3⋊C8)C2311yescharacteristic
58C8×C3⋊D3C2×C414yescomplemented
59C3×(C2×D3)⋊C4—24no—
60C3×C4×Dic3C2312yes—
61C2×C3×C3⋊C8C2312yes—
62C3×D24C2×C418yescomplemented
63(C2×D3)⋊Dic3—24no—
64Dic32D412yes—
65#3713C2×C418yescomplemented
66#3710—22no—
67C2×#442—91noSylow
68C2×D3×D4—34no—
69C22×C4×D3—64no—
70C2×C3×D8—32no—
71C3×C4×D4—34no—
72D4×Dic3—34no—
73C2×#213—34no—
74C4×#67—64no—
75D3×D8—316no—
76C2×D24C2×D312yes—
77C2×D3×C8—32no—
78C2×D3×C8—32no—
79C2×D3×C8—61no—
80#893C2×D314yescomplemented
81D3×C4⋊C4—34no—
82D3×C4⋊C4—62no—
83#67⋊C4—64no—
84D3×C22⋊C4—64no—
85C4×D12—34no—
86C42×D3—32no—
87C3×#106—21no—
88C3×#106C2×D312yescomplemented
89C3×#102—34no—
90C3×#97—32no—
91#832—34no—
92#821—34no—
93#817—32no—
94#817—61no—
95#815—32no—
96#815C2×D312yescomplemented
97#809C2×D314yescomplemented
98#808—34no—
99#808—62no—
100#803—32no—
101C22×C3⋊D3C2×D411yescharacteristic
102C22×C3×D3—24no—
103C2×D32—28no—
104C2×D32—44no—
105C2×D32—44no—
106C2×C32×C4—22no—
107C2×C32×C4C2411yescharacteristic
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3C2×D411yescharacteristic
110C4×C3⋊D3—44no—
111C4×C3⋊D3C22×C412yes—
112C4×C3⋊D3#4112yes—
113C2×C3×Dic3C2×D414yes—
114C3×D12—24no—
115C3×D12C22×C418yescomplemented
116C3×C4×D3—48no—
117#625—28no—
118#624—24no—
119D3×Dic3—48no—
120C32×C8C22×C412yescomplemented
121C3⋊(C3⋊C8)C22×C412yescomplemented
122C3×C3⋊C8—22no—
123C22×D8—91no—
124C2×C4×D4—92no—
125#442—32no—
126#442—92no—
127#442—94no—
128C2×#106—91no—
129C2×#102—92no—
130C2×#97—91no—
131C23×D3—64no—
132C2×C3×D4—34no—
133C22×C3×C4—64no—
134C2×#67—64no—
135C22×Dic3—64no—
136D3×D4—316no—
137D3×D4—68no—
138C2×D12C22×D314yes—
139C2×C4×D3—24no—
140C2×C4×D3—32no—
141C2×C4×D3—34no—
142C2×C4×D3—61no—
143C2×C4×D3—64no—
144C2×C4×D3—64no—
145C2×C4×D3—122no—
146C2×C4×D3—1216no—
147C3×D8—38no—
148C2×C3×C8—21no—
149C2×C3×C8—32no—
150C2×C3×C8C22×D312yes—
151C3×C4⋊C4—22no—
152C3×C4⋊C4C22×D314yes—
153C3×C22⋊C4—64no—
154C3×C42—32no—
155#217—64no—
156#213—316no—
157(C2×D3)⋊C4—24no—
158(C2×D3)⋊C4—64no—
159C4⋊Dic3—34no—
160C4⋊Dic3—62no—
161Dic3⋊C4—64no—
162Dic3⋊C4—122no—
163C4×Dic3—34no—
164C4×Dic3C22×D312yes—
165C2×C3⋊C8—32no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8C22×D312yes—
168D24C4×D318yescomplemented
169D3×C8—38no—
170D3×C8—64no—
171D3×C8—64no—
172C22×C32C22×D411yescharacteristic
173C2×C3⋊D3C4×D412yes—
174C2×C3⋊D3AGL(1,ℤ/8)14yes—
175C2×C3×D3—28no—
176C2×C3×D3—44no—
177C2×C3×D3—44no—
178D32—416no—
179C32×C4—42no—
180C32×C4C23×C411yescharacteristic
181C32×C4C2×#4111yescharacteristic
182C3⋊Dic3—42no—
183C3⋊Dic3C4×D412yes—
184C3×Dic3—24no—
185C22×D4—92no—
186C23×C4—182no—
187C2×D8—32no—
188C2×D8—98no—
189C2×D8—92no—
190C22×C8—91no—
191C22×C8—91no—
192C4×D4—34no—
193C4×D4—94no—
194C4×D4—184no—
195C2×C4⋊C4—92no—
196C2×C22⋊C4—182no—
197C2×C42—91no—
198#106—91no—
199#106—92no—
200#106D3211yescharacteristic, complemented
201#102—34no—
202#102—94no—
203#97—32no—
204#97—92no—
205C23×C3—64no—
206C22×D3—24no—
207C22×D3—32no—
208C22×D3—61no—
209C22×D3—616no—
210C22×D3—128no—
211C22×D3—128no—
212C3×D4—38no—
213C3×D4—64no—
214C2×C3×C4—24no—
215C2×C3×C4—21no—
216C2×C3×C4—34no—
217C2×C3×C4—42no—
218C2×C3×C4—128no—
219C2×C3×C4C23×D312yes—
220#67—616no—
221C2×Dic3—32no—
222C2×Dic3—61no—
223C2×Dic3—64no—
224C2×Dic3—122no—
225C2×Dic3—128no—
226C2×Dic3D3×D414yes—
227D12—24no—
228D12C2×C4×D318yescomplemented
229C4×D3—34no—
230C4×D3—34no—
231C4×D3—48no—
232C4×D3—62no—
233C4×D3—62no—
234C4×D3—68no—
235C4×D3—128no—
236C4×D3—128no—
237C4×D3—244no—
238C3×C8—22no—
239C3×C8—62no—
240C3×C8C2×C4×D314yescomplemented
241C3⋊C8—22no—
242C3⋊C8—34no—
243C3⋊C8—62no—
244C2×C32C2×C4×D411yescharacteristic
245C2×C32C2×AGL(1,ℤ/8)12yes—
246C3⋊D3#44214yescomplemented
247C3×D3—48no—
248C24—182no—
249C2×D4—34no—
250C2×D4—98no—
251C2×D4—184no—
252C2×D4—182no—
253C22×C4—64no—
254C22×C4—92no—
255C22×C4—91no—
256C22×C4—182no—
257C22×C4—184no—
258C22×C4—368no—
259D8—38no—
260D8—98no—
261C2×C8—32no—
262C2×C8—91no—
263C2×C8—94no—
264C2×C8—182no—
265C2×C8C2×D3211yescharacteristic
266C4⋊C4—92no—
267C4⋊C4—182no—
268C4⋊C4C2×D3212yes—
269C22⋊C4—64no—
270C22⋊C4—184no—
271C42—32no—
272C42—92no—
273C22×C3—21no—
274C22×C3—68no—
275C22×C3—124no—
276C22×C3—124no—
277C22×C3C2×D3×D412yes—
278C2×D3—28no—
279C2×D3—38no—
280C2×D3—34no—
281C2×D3—44no—
282C2×D3—44no—
283C2×D3—62no—
284C2×D3—64no—
285C2×D3—1232no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—44no—
289C3×C4—64no—
290C3×C4—82no—
291C3×C4C22×C4×D312yes—
292C3×C4D3×#4112yes—
293Dic3—24no—
294Dic3—34no—
295Dic3—62no—
296Dic3—124no—
297Dic3—242no—
298C32C2×#44211yescharacteristic, complemented, Sylow
299C23—64no—
300C23—91no—
301C23—188no—
302C23—364no—
303C23—364no—
304D4—38no—
305D4—64no—
306D4—188no—
307C2×C4—22no—
308C2×C4—34no—
309C2×C4—91no—
310C2×C4—92no—
311C2×C4—92no—
312C2×C4—128no—
313C2×C4—184no—
314C2×C4—182no—
315C2×C4—364no—
316C2×C4—368no—
317C2×C4C22×D3211yescharacteristic
318C8—62no—
319C8—92no—
320C8C4×D3212yescomplemented
321C2×C3—21no—
322C2×C3—22no—
323C2×C3—128no—
324C2×C3C4×D3×D412yes—
325C2×C3D3×AGL(1,ℤ/8)14yes—
326D3—38no—
327D3—48no—
328D3—64no—
329C22—68no—
330C22—92no—
331C22—94no—
332C22—124no—
333C22—124no—
334C22—3616no—
335C22D32×D411yescharacteristic
336C4—42no—
337C4—64no—
338C4—92no—
339C4—362no—
340C4C2×C4×D3211yescharacteristic
341C4#6431911yescharacteristic
342C3—21no—
343C3D3×#44212yescomplemented
344C2—94no—
345C2—128no—
346C2#1059460511yescharacteristic
347C2#1059474012yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63797C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32C2×#442
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594605C2semidirect
3. C3⋊D3×#106C2semidirect
4. C3×#4869C2semidirect
5. #10590771C2semidirect
6. #10590668C2semidirect
7. #10590593C2semidirect
8. #10590455C2semidirect
15. C3×#893C22semidirect
17. Dic3×D12C22semidirect
22. #63797C4semidirect
23. C32×#106C22semidirect
24. #63644C22semidirect
25. #63635C22semidirect
26. C3×#815C22semidirect
27. C3×#809C22semidirect
28. #63563C22semidirect
29. #63554C22semidirect
35. #4869D3semidirect
51. #3802C2×C4semidirect
58. C8×C3⋊D3C2×C4semidirect
62. C3×D24C2×C4semidirect
65. #3713C2×C4semidirect
80. #893C2×D3semidirect
88. C3×#106C2×D3semidirect
96. #815C2×D3semidirect
97. #809C2×D3semidirect
115. C3×D12C22×C4semidirect
120. C32×C8C22×C4semidirect
121. C3⋊(C3⋊C8)C22×C4semidirect
168. D24C4×D3semidirect
200. #106D32semidirect
228. D12C2×C4×D3semidirect
240. C3×C8C2×C4×D3semidirect
246. C3⋊D3#442semidirect
298. C32C2×#442semidirect
320. C8C4×D32semidirect
343. C3D3×#442semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
#105946052
C3⋊D3×#1062
C3×#48692
#105907712
#105906682
#105905932
#105904552
D3×#4423