Finite Group Databasebeta

← #74936

Subgroups — #74936

Order 384.

1102 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D3C211yesmaximal, characteristic, complemented
2C2×#937C211yesmaximal, characteristic
3C2×#883C212yesmaximal, complemented
4C3×#386C211yesmaximal, characteristic, complemented
5#5220C211yesmaximal, characteristic, complemented
6#5210C211yesmaximal, characteristic, complemented
7#4956C212yesmaximal, complemented
8#4955C211yesmaximal, characteristic, complemented
9#4950C211yesmaximal, characteristic, complemented
10#4668C212yesmaximal, complemented
11#4664C212yesmaximal, complemented
12#2849—31nomaximal, Sylow
13C24×D3C2211yescharacteristic
14C22×C3×D4C2211yescharacteristic
15C23×C3×C4C2211yescharacteristic
16C22×#67C2211yescharacteristic
17C22×#67C2211yescharacteristic
18C23×Dic3C2211yescharacteristic
19C22×C4×D3—24no—
20C22×C4×D3—28no—
21C22×C4×D3C2212yes—
22C22×C4×D3C2212yes—
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×C3×C22⋊C4C2212yescomplemented
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×#217C2212yescomplemented
28#937—24no—
29C2×(C2×D3)⋊C4C2211yescharacteristic
30C2×(C2×D3)⋊C4C2212yes—
31C2×(C2×D3)⋊C4C2211yescharacteristic
32C2×(C2×D3)⋊C4C2212yes—
33C2×C4⋊Dic3C2212yescomplemented
34C2×Dic3⋊C4C2212yescomplemented
35#883—28no—
36C3×#95C2212yescomplemented
37C3⋊#95C2212yescomplemented
38C3⋊#95C2212yescomplemented
39C3⋊#95C2212yescomplemented
40C24×C4—31no—
41C2×#123—32no—
42C2×#120—31no—
43#386—31no—
44#386—32no—
45#386D311yescharacteristic, complemented
46#385—31no—
47#385—31no—
48#385—32no—
49#381—32no—
50#379—31no—
51C24×C3C2311yescharacteristic
52C24×C3C2311yescharacteristic
53C23×D3—22no—
54C23×D3—22no—
55C23×D3—24no—
56C23×D3—24no—
57C23×D3D414yes—
58C23×D3C2311yescharacteristic
59C23×D3C2311yescharacteristic
60C2×C3×D4—22no—
61C2×C3×D4—22no—
62C2×C3×D4—22no—
63C22×C3×C4—22no—
64C22×C3×C4—24no—
65C22×C3×C4C2311yescharacteristic
66C22×C3×C4C2312yes—
67C22×C3×C4C2312yes—
68C2×#67—24no—
69C2×#67—22no—
70C2×#67—22no—
71C2×#67—24no—
72C22×Dic3—22no—
73C22×Dic3—24no—
74C22×Dic3C2311yescharacteristic
75C22×Dic3C2312yes—
76C22×Dic3C2311yescharacteristic
77C22×Dic3C2312yes—
78C2×C4×D3—232no—
79C2×C4×D3—24no—
80C2×C4×D3—24no—
81C2×C4×D3—24no—
82C2×C4×D3—24no—
83C2×C4×D3—24no—
84C2×C4×D3D418yescomplemented
85C3×C22⋊C4—22no—
86C3×C22⋊C4—24no—
87#217—22no—
88#217—22no—
89#217—24no—
90(C2×D3)⋊C4—24no—
91(C2×D3)⋊C4—22no—
92(C2×D3)⋊C4—22no—
93(C2×D3)⋊C4—24no—
94C4⋊Dic3—24no—
95Dic3⋊C4—24no—
96C25—31no—
97C22×D4—31no—
98C22×D4—31no—
99C22×D4C2×D311yescharacteristic
100C23×C4—32no—
101C23×C4—31no—
102C23×C4—32no—
103C23×C4—68no—
104C23×C4—64no—
105C23×C4C2×D311yescharacteristic
106#123—68no—
107#120—64no—
108C2×C4⋊C4—32no—
109C2×C4⋊C4—32no—
110C2×C22⋊C4—31no—
111C2×C22⋊C4—32no—
112C2×C22⋊C4—31no—
113C2×C22⋊C4—31no—
114C2×C22⋊C4—31no—
115C2×C22⋊C4—32no—
116C2×C22⋊C4—32no—
117C2×C22⋊C4C2×D311yescharacteristic
118C2×C22⋊C4C2×D312yescomplemented
119#95—32no—
120#95—32no—
121#95—32no—
122#95C2×D312yescomplemented
123C23×C3—22no—
124C23×C3—22no—
125C23×C3—22no—
126C23×C3—21no—
127C23×C3—22no—
128C23×C3—21no—
129C23×C3—21no—
130C23×C3C2×D412yes—
131C23×C3#4112yes—
132C23×C3#4112yes—
133C23×C3C2411yescharacteristic
134C22×D3—216no—
135C22×D3—216no—
136C22×D3—28no—
137C22×D3—22no—
138C22×D3—21no—
139C22×D3—21no—
140C22×D3—21no—
141C22×D3—21no—
142C22×D3—22no—
143C22×D3—28no—
144C22×D3—28no—
145C22×D3C2×D412yes—
146C22×D3C2×D414yes—
147C22×D3C2×D412yes—
148C22×D3#4114yes—
149C3×D4—44no—
150C2×C3×C4—28no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—22no—
154C2×C3×C4—21no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4C2×D414yes—
160#67—44no—
161#67—44no—
162C2×Dic3—28no—
163C2×Dic3—22no—
164C2×Dic3—22no—
165C2×Dic3—22no—
166C2×Dic3—22no—
167C2×Dic3—21no—
168C2×Dic3—21no—
169C2×Dic3—22no—
170C2×Dic3—22no—
171C2×Dic3—22no—
172C2×Dic3C2×D414yes—
173C4×D3—216no—
174C4×D3—216no—
175C24—31no—
176C24—31no—
177C24—34no—
178C24—64no—
179C24—64no—
180C24—62no—
181C24—62no—
182C24C22×D311yescharacteristic
183C24C22×D311yescharacteristic
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—62no—
188C2×D4—62no—
189C2×D4—64no—
190C2×D4—64no—
191C22×C4—22no—
192C22×C4—24no—
193C22×C4—32no—
194C22×C4—38no—
195C22×C4—31no—
196C22×C4—32no—
197C22×C4—31no—
198C22×C4—64no—
199C22×C4—64no—
200C22×C4—64no—
201C22×C4—64no—
202C22×C4—632no—
203C22×C4—64no—
204C22×C4—62no—
205C22×C4—64no—
206C22×C4C22×D311yescharacteristic
207C22×C4C22×D312yes—
208C22×C4C22×D312yes—
209C4⋊C4—64no—
210C4⋊C4—64no—
211C22⋊C4—22no—
212C22⋊C4—24no—
213C22⋊C4—62no—
214C22⋊C4—62no—
215C22⋊C4—64no—
216C22⋊C4—64no—
217C22⋊C4—64no—
218C22⋊C4—62no—
219C22⋊C4—62no—
220C22×C3—22no—
221C22×C3—22no—
222C22×C3—24no—
223C22×C3—24no—
224C22×C3—41no—
225C22×C3—41no—
226C22×C3—41no—
227C22×C3—42no—
228C22×C3—42no—
229C22×C3#12314yescomplemented
230C22×C3C22×D411yescharacteristic
231C22×C3C22×D412yes—
232C22×C3C2×#4111yescharacteristic
233C22×C3C2×#4111yescharacteristic
234C22×C3C2×#4112yes—
235C2×D3—232no—
236C2×D3—22no—
237C2×D3—22no—
238C2×D3—22no—
239C2×D3—22no—
240C2×D3—24no—
241C2×D3—24no—
242C2×D3—24no—
243C2×D3—24no—
244C2×D3#12014yes—
245C2×D3#12314yescomplemented
246C3×C4—24no—
247C3×C4—41no—
248C3×C4—42no—
249Dic3—24no—
250Dic3—41no—
251Dic3—41no—
252Dic3—42no—
253C23—22no—
254C23—22no—
255C23—21no—
256C23—22no—
257C23—21no—
258C23—21no—
259C23—22no—
260C23—34no—
261C23—32no—
262C23—32no—
263C23—34no—
264C23—68no—
265C23—68no—
266C23—616no—
267C23—616no—
268C23—68no—
269C23—61no—
270C23—61no—
271C23—62no—
272C23—61no—
273C23—61no—
274C23—62no—
275C23#23512yes—
276C23D3×D412yes—
277C23#23712yes—
278C23C23×D311yescharacteristic
279D4—44no—
280D4—124no—
281D4—124no—
282C2×C4—28no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—34no—
292C2×C4—616no—
293C2×C4—616no—
294C2×C4—68no—
295C2×C4—62no—
296C2×C4—62no—
297C2×C4—62no—
298C2×C4—62no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—62no—
302C2×C4—62no—
303C2×C4—62no—
304C2×C4D3×D414yes—
305C2×C3—24no—
306C2×C3—81no—
307C2×C3C2×#12011yescharacteristic
308C2×C3C2×#12311yescharacteristic
309C2×C3C2×#12311yescharacteristic
310C2×C3#52512yes—
311C2×C3#52512yes—
312D3—24no—
313D3—24no—
314C22—22no—
315C22—24no—
316C22—22no—
317C22—24no—
318C22—34no—
319C22—34no—
320C22—41no—
321C22—41no—
322C22—42no—
323C22—41no—
324C22—42no—
325C22—632no—
326C22—62no—
327C22—62no—
328C22—62no—
329C22—64no—
330C22—64no—
331C22—62no—
332C22—64no—
333C22—64no—
334C22#88314yescomplemented
335C22C2×#23511yescharacteristic
336C22C2×D3×D411yescharacteristic
337C22C2×D3×D412yes—
338C22C2×#23711yescharacteristic
339C22D3×#4112yes—
340C4—24no—
341C4—41no—
342C4—42no—
343C4—64no—
344C4—121no—
345C4—122no—
346C4—121no—
347C3#284911yescharacteristic, complemented, Sylow
348C2—24no—
349C2—64no—
350C2—64no—
351C2—81no—
352C2C2×#88311yescharacteristic
353C2#554712yes—
354C2D3×#12011yescharacteristic
355C2#560612yes—
356C2D3×#12311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
prime radicalC2×#937C2
hypercenter#386D3
hypocenterC3#2849
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C23×C4×D3C2semidirect
3. C2×#883C2semidirect
4. C3×#386C2semidirect
5. #5220C2semidirect
6. #5210C2semidirect
7. #4956C2semidirect
8. #4955C2semidirect
9. #4950C2semidirect
10. #4668C2semidirect
11. #4664C2semidirect
24. C2×C3×C22⋊C4C22semidirect
27. C2×#217C22semidirect
33. C2×C4⋊Dic3C22semidirect
34. C2×Dic3⋊C4C22semidirect
36. C3×#95C22semidirect
37. C3⋊#95C22semidirect
38. C3⋊#95C22semidirect
39. C3⋊#95C22semidirect
45. #386D3semidirect
84. C2×C4×D3D4semidirect
118. C2×C22⋊C4C2×D3semidirect
122. #95C2×D3semidirect
229. C22×C3#123semidirect
245. C2×D3#123semidirect
334. C22#883semidirect
347. C3#2849semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D32
C2×#9372
C2×#8832
C3×#3862
#52202
#52102
#49562
#49552
#49502
#46682
#46642
#28493