Finite Group Databasebeta

← #74875

Subgroups — #74875

Order 384.

808 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#937C211yesmaximal, characteristic
2C2×D4×Dic3C211yesmaximal, characteristic, complemented
3C22×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C3×#386C211yesmaximal, characteristic, complemented
5#5210C211yesmaximal, characteristic, complemented
6#4958C212yesmaximal, complemented
7#4957C212yesmaximal, complemented
8#4955C211yesmaximal, characteristic, complemented
9Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
10#4670C212yesmaximal, complemented
11#4669C212yesmaximal, complemented
12#2321—31nomaximal, Sylow
13C24×D3C2211yescharacteristic
14C22×C3×D4C2211yescharacteristic
15C23×C3×C4C2211yescharacteristic
16C22×#67C2212yes—
17C23×Dic3C2211yescharacteristic
18C23×Dic3C2211yescharacteristic, complemented
19C2×C3×C22⋊C4C2211yescharacteristic
20C2×C3×C22⋊C4C2212yescomplemented
21C2×#217C2211yescharacteristic
22C2×#217C2211yescharacteristic
23C2×#217C2211yescharacteristic, complemented
24#937C418yescomplemented
25D4×Dic3—24no—
26C2×(C2×D3)⋊C4—24no—
27C2×(C2×D3)⋊C4C2212yes—
28C2×(C2×D3)⋊C4C2212yes—
29C2×(C2×D3)⋊C4C2212yes—
30C2×(C2×D3)⋊C4C2212yes—
31C2×(C2×D3)⋊C4C2212yes—
32C2×C4⋊Dic3C2211yescharacteristic, complemented
33C2×Dic3⋊C4C2212yescomplemented
34C2×C4×Dic3C2211yescharacteristic, complemented
35C2×C4×Dic3C2212yescomplemented
36C3×#95C2212yescomplemented
37C3⋊#95C2212yescomplemented
38C3⋊#95C2212yescomplemented
39C2×#120—31no—
40C2×C4×D4—31no—
41C22×C22⋊C4—31no—
42#390—32no—
43#388—32no—
44#388—32no—
45#386—32no—
46#386D311yescharacteristic, complemented
47#385—31no—
48#379—31no—
49C4×C22⋊C4—31no—
50C24×C3C2311yescharacteristic
51C24×C3C2311yescharacteristic
52C23×D3—22no—
53C23×D3—22no—
54C23×D3—42no—
55C23×D3—42no—
56C23×D3C2×C414yescomplemented
57C23×D3C2312yes—
58C2×C3×D4—22no—
59C2×C3×D4—22no—
60C2×C3×D4C2×C414yes—
61C22×C3×C4—22no—
62C22×C3×C4—42no—
63C22×C3×C4C2312yes—
64C22×C3×C4C2312yes—
65C22×C3×C4C2311yescharacteristic
66C2×#67—42no—
67C2×#67—42no—
68C2×#67C2×C418yescomplemented
69C22×Dic3—22no—
70C22×Dic3—42no—
71C22×Dic3—42no—
72C22×Dic3D414yescomplemented
73C22×Dic3C2311yescharacteristic
74C22×Dic3C2311yescharacteristic
75C22×Dic3C2312yes—
76C22×Dic3C2311yescharacteristic
77C22×Dic3C2311yescharacteristic
78C3×C22⋊C4—22no—
79C3×C22⋊C4—42no—
80#217—22no—
81#217—22no—
82#217C2×C414yescomplemented
83(C2×D3)⋊C4—24no—
84(C2×D3)⋊C4—24no—
85(C2×D3)⋊C4—42no—
86(C2×D3)⋊C4—42no—
87(C2×D3)⋊C4C2×C418yescomplemented
88C4⋊Dic3—22no—
89Dic3⋊C4—42no—
90C4×Dic3—22no—
91C4×Dic3—42no—
92C25—31no—
93C22×D4—32no—
94C22×D4C2×D311yescharacteristic
95C23×C4—31no—
96C23×C4—31no—
97C23×C4C2×D311yescharacteristic
98#120—38no—
99C4×D4—64no—
100C2×C4⋊C4—31no—
101C2×C4⋊C4—32no—
102C2×C22⋊C4—31no—
103C2×C22⋊C4—32no—
104C2×C22⋊C4—31no—
105C2×C22⋊C4—31no—
106C2×C22⋊C4—32no—
107C2×C22⋊C4—32no—
108C2×C22⋊C4—32no—
109C2×C22⋊C4—32no—
110C2×C22⋊C4—64no—
111C2×C22⋊C4C2×D311yescharacteristic
112C2×C22⋊C4C2×D312yescomplemented
113C2×C42—31no—
114C2×C42—32no—
115#95—32no—
116#95—32no—
117#95C2×D312yescomplemented
118C23×C3—22no—
119C23×C3—22no—
120C23×C3—21no—
121C23×C3—21no—
122C23×C3—22no—
123C23×C3—22no—
124C23×C3C22×C412yes—
125C23×C3C22×C412yes—
126C23×C3C2×D412yes—
127C23×C3#4112yes—
128C23×C3C2411yescharacteristic
129C22×D3—28no—
130C22×D3—22no—
131C22×D3—22no—
132C22×D3—22no—
133C22×D3—22no—
134C22×D3—22no—
135C22×D3—22no—
136C22×D3—48no—
137C22×D3—44no—
138C22×D3—44no—
139C22×D3—48no—
140C22×D3C22×C414yes—
141C3×D4—28no—
142C2×C3×C4—21no—
143C2×C3×C4—21no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—44no—
151C2×C3×C4C22×C412yes—
152#67—48no—
153C2×Dic3—22no—
154C2×Dic3—22no—
155C2×Dic3—22no—
156C2×Dic3—22no—
157C2×Dic3—21no—
158C2×Dic3—21no—
159C2×Dic3—22no—
160C2×Dic3—22no—
161C2×Dic3—44no—
162C2×Dic3—44no—
163C2×Dic3C22×C414yes—
164C2×Dic3C2×D412yes—
165C2×Dic3C2×D412yes—
166C24—32no—
167C24—34no—
168C24—62no—
169C24—62no—
170C24—122no—
171C24—122no—
172C24C22×D311yescharacteristic
173C24C22×D311yescharacteristic
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—38no—
177C2×D4—122no—
178C2×D4—122no—
179C2×D4C4×D314yes—
180C22×C4—22no—
181C22×C4—32no—
182C22×C4—31no—
183C22×C4—31no—
184C22×C4—34no—
185C22×C4—31no—
186C22×C4—31no—
187C22×C4—42no—
188C22×C4—62no—
189C22×C4—122no—
190C22×C4—122no—
191C22×C4C22×D312yes—
192C22×C4C22×D312yes—
193C22×C4C22×D311yescharacteristic
194C4⋊C4—62no—
195C4⋊C4—122no—
196C22⋊C4—22no—
197C22⋊C4—34no—
198C22⋊C4—38no—
199C22⋊C4—42no—
200C22⋊C4—64no—
201C22⋊C4—64no—
202C22⋊C4—62no—
203C22⋊C4—62no—
204C22⋊C4—122no—
205C22⋊C4—122no—
206C42—62no—
207C42—122no—
208C22×C3—24no—
209C22×C3—22no—
210C22×C3—22no—
211C22×C3—24no—
212C22×C3—22no—
213C22×C3—24no—
214C22×C3—41no—
215C22×C3—41no—
216C22×C3—42no—
217C22×C3C4×D414yes—
218C22×C3C23×C411yescharacteristic
219C22×C3C22×D411yescharacteristic
220C22×C3C2×#4111yescharacteristic
221C22×C3H(5,𝔽2)12yes—
222C22×C3H(5,𝔽2)12yes—
223C2×D3—24no—
224C2×D3—24no—
225C2×D3—24no—
226C2×D3—416no—
227C2×D3—42no—
228C2×D3—42no—
229C2×D3—42no—
230C2×D3—42no—
231C3×C4—22no—
232C3×C4—42no—
233C3×C4—42no—
234Dic3—24no—
235Dic3—22no—
236Dic3—22no—
237Dic3—41no—
238Dic3—41no—
239C23—22no—
240C23—22no—
241C23—21no—
242C23—21no—
243C23—22no—
244C23—22no—
245C23—34no—
246C23—68no—
247C23—62no—
248C23—62no—
249C23—62no—
250C23—62no—
251C23—62no—
252C23—62no—
253C23—128no—
254C23—124no—
255C23—124no—
256C23—128no—
257C23C2×C4×D312yes—
258C23C2×C4×D312yes—
259C23D3×D412yes—
260C23#23712yes—
261C23C23×D311yescharacteristic
262D4—28no—
263D4—128no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—34no—
273C2×C4—32no—
274C2×C4—32no—
275C2×C4—44no—
276C2×C4—62no—
277C2×C4—62no—
278C2×C4—62no—
279C2×C4—62no—
280C2×C4—61no—
281C2×C4—61no—
282C2×C4—62no—
283C2×C4—62no—
284C2×C4—124no—
285C2×C4—124no—
286C2×C4C2×C4×D312yes—
287C2×C3—24no—
288C2×C3—42no—
289C2×C3C2×C4×D411yescharacteristic
290C2×C3#51812yes—
291C2×C3#53411yescharacteristic
292C2×C3#53511yescharacteristic
293C2×C3#53812yes—
294D3—44no—
295C22—22no—
296C22—24no—
297C22—22no—
298C22—24no—
299C22—22no—
300C22—24no—
301C22—41no—
302C22—41no—
303C22—42no—
304C22—64no—
305C22—64no—
306C22—64no—
307C22—1216no—
308C22—122no—
309C22—122no—
310C22—122no—
311C22—122no—
312C22#67⋊C414yes—
313C22C22×C4×D311yescharacteristic
314C22C2×D3×D411yescharacteristic
315C22C2×#23711yescharacteristic
316C22#100412yes—
317C22#100912yes—
318C4—22no—
319C4—42no—
320C4—42no—
321C4—62no—
322C4—62no—
323C4—64no—
324C4—121no—
325C4—121no—
326C3#232111yescharacteristic, complemented, Sylow
327C2—24no—
328C2—42no—
329C2—124no—
330C2C2×#67⋊C411yescharacteristic
331C2#554512yes—
332C2#559211yescharacteristic
333C2#561712yes—
334C2#565311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#386C2
socle, cosocleC23×C3C24
prime radicalC2×#937C2
hypercenter#386D3
hypocenterC3#2321
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic3C2semidirect
3. C22×(C2×D3)⋊C4C2semidirect
4. C3×#386C2semidirect
5. #5210C2semidirect
6. #4958C2semidirect
7. #4957C2semidirect
8. #4955C2semidirect
9. Dic3×C22⋊C4C2semidirect
10. #4670C2semidirect
11. #4669C2semidirect
18. C23×Dic3C22semidirect
20. C2×C3×C22⋊C4C22semidirect
23. C2×#217C22semidirect
24. #937C4semidirect
32. C2×C4⋊Dic3C22semidirect
33. C2×Dic3⋊C4C22semidirect
34. C2×C4×Dic3C22semidirect
35. C2×C4×Dic3C22semidirect
36. C3×#95C22semidirect
37. C3⋊#95C22semidirect
38. C3⋊#95C22semidirect
46. #386D3semidirect
56. C23×D3C2×C4semidirect
68. C2×#67C2×C4semidirect
72. C22×Dic3D4semidirect
82. #217C2×C4semidirect
87. (C2×D3)⋊C4C2×C4semidirect
112. C2×C22⋊C4C2×D3semidirect
117. #95C2×D3semidirect
326. C3#2321semidirect

Maximal subgroups

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

subgroupindex
C2×#9372
C2×D4×Dic32
C22×(C2×D3)⋊C42
C3×#3862
#52102
#49582
#49572
#49552
Dic3×C22⋊C42
#46702
#46692
#23213