Finite Group Databasebeta

← C2×#4959 #82124

Subgroups — C2×#4959 #82124

Order 384.

1252 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#67C211yesmaximal, characteristic
2C22×C3×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×#217C211yesmaximal, characteristic, complemented
4C22×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C22×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C22×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C2×C3⋊#95C211yesmaximal, characteristic, complemented
8#4959C218yesmaximal, direct product factor
9C2×#394—31nomaximal, Sylow
10C25×C3C2211yescharacteristic
11C24×D3C2211yescharacteristic
12C23×C3×C4C2211yescharacteristic
13C23×C3×C4C2211yescharacteristic
14C22×#67—24no—
15C22×#67—24no—
16C22×#67—24no—
17C22×#67C2214yes—
18C23×Dic3C2211yescharacteristic
19C23×Dic3C2211yescharacteristic
20C23×Dic3C2211yescharacteristic
21C2×C3×C22⋊C4—24no—
22C2×C3×C22⋊C4C2214yescomplemented
23C2×#217—24no—
24C2×#217C2214yescomplemented
25C2×(C2×D3)⋊C4—24no—
26C2×(C2×D3)⋊C4—24no—
27C2×(C2×D3)⋊C4C2214yescomplemented
28C2×(C2×D3)⋊C4C2214yescomplemented
29C2×Dic3⋊C4—24no—
30C2×Dic3⋊C4C2214yescomplemented
31C3⋊#95C2214yescomplemented
32C23×D4—31no—
33C22×C4⋊C4—31no—
34C22×C22⋊C4—31no—
35C22×C22⋊C4—31no—
36C22×C22⋊C4—31no—
37C22×C22⋊C4D311yescharacteristic, complemented
38#394—38no—
39C2×#95—31no—
40C24×C3—22no—
41C24×C3—22no—
42C24×C3—22no—
43C24×C3—22no—
44C24×C3—22no—
45C24×C3—22no—
46C24×C3D414yes—
47C24×C3C2312yes—
48C24×C3C2311yescharacteristic
49C23×D3—22no—
50C23×D3—22no—
51C23×D3—22no—
52C23×D3—22no—
53C23×D3—22no—
54C23×D3—22no—
55C23×D3D414yes—
56C23×D3C2312yes—
57C22×C3×C4—22no—
58C22×C3×C4—22no—
59C22×C3×C4—22no—
60C22×C3×C4—22no—
61C22×C3×C4—22no—
62C22×C3×C4—22no—
63C22×C3×C4C2312yes—
64C22×C3×C4C2312yes—
65C2×#67—232no—
66C2×#67—28no—
67C2×#67—28no—
68C2×#67—28no—
69C22×Dic3—22no—
70C22×Dic3—22no—
71C22×Dic3—22no—
72C22×Dic3—22no—
73C22×Dic3—22no—
74C22×Dic3—22no—
75C22×Dic3—22no—
76C22×Dic3D414yes—
77C22×Dic3D414yescomplemented
78C22×Dic3C2312yes—
79C22×Dic3C2312yes—
80C22×Dic3C2312yes—
81C3×C22⋊C4—28no—
82#217—28no—
83(C2×D3)⋊C4—28no—
84(C2×D3)⋊C4—28no—
85Dic3⋊C4—28no—
86C25—31no—
87C25C2×D311yescharacteristic
88C22×D4—34no—
89C22×D4—64no—
90C22×D4—64no—
91C22×D4—64no—
92C23×C4—31no—
93C23×C4—31no—
94C23×C4—31no—
95C23×C4C2×D311yescharacteristic
96C23×C4C2×D311yescharacteristic
97C2×C4⋊C4—34no—
98C2×C4⋊C4—64no—
99C2×C22⋊C4—24no—
100C2×C22⋊C4—34no—
101C2×C22⋊C4—34no—
102C2×C22⋊C4—34no—
103C2×C22⋊C4—64no—
104C2×C22⋊C4—64no—
105C2×C22⋊C4—64no—
106C2×C22⋊C4C2×D314yescomplemented
107#95—34no—
108C23×C3—28no—
109C23×C3—28no—
110C23×C3—28no—
111C23×C3—22no—
112C23×C3—22no—
113C23×C3—22no—
114C23×C3—22no—
115C23×C3—22no—
116C23×C3—22no—
117C23×C3—44no—
118C23×C3—44no—
119C23×C3—44no—
120C23×C3—44no—
121C23×C3C2×D412yes—
122C23×C3C2×D412yes—
123C23×C3C2×D412yes—
124C23×C3C2×D414yes—
125C23×C3C2×D412yes—
126C23×C3#4112yes—
127C23×C3#4112yes—
128C23×C3#4112yes—
129C23×C3C2411yescharacteristic
130C22×D3—28no—
131C22×D3—28no—
132C22×D3—28no—
133C22×D3—22no—
134C22×D3—22no—
135C22×D3—22no—
136C22×D3—22no—
137C22×D3—22no—
138C22×D3—22no—
139C22×D3—44no—
140C22×D3—44no—
141C22×D3—44no—
142C22×D3—44no—
143C22×D3C2×D414yes—
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×C4—44no—
152#67—232no—
153C2×Dic3—28no—
154C2×Dic3—28no—
155C2×Dic3—22no—
156C2×Dic3—22no—
157C2×Dic3—22no—
158C2×Dic3—22no—
159C2×Dic3—22no—
160C2×Dic3—22no—
161C2×Dic3—22no—
162C2×Dic3—44no—
163C2×Dic3C2×D414yes—
164C2×Dic3C2×D414yescomplemented
165C24—22no—
166C24—22no—
167C24—22no—
168C24—22no—
169C24—22no—
170C24—22no—
171C24—34no—
172C24—32no—
173C24—62no—
174C24—62no—
175C24—62no—
176C24—62no—
177C24—62no—
178C24—62no—
179C24#6714yes—
180C24C22×D312yes—
181C24C22×D311yescharacteristic
182C2×D4—68no—
183C2×D4—68no—
184C2×D4—632no—
185C2×D4—68no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—34no—
193C22×C4—34no—
194C22×C4—32no—
195C22×C4—32no—
196C22×C4—32no—
197C22×C4—62no—
198C22×C4—62no—
199C22×C4—62no—
200C22×C4—62no—
201C22×C4—62no—
202C22×C4—62no—
203C22×C4—62no—
204C22×C4C22×D312yes—
205C22×C4C22×D312yes—
206C4⋊C4—68no—
207C22⋊C4—28no—
208C22⋊C4—68no—
209C22⋊C4—68no—
210C22⋊C4—68no—
211C22×C3—24no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3—42no—
215C22×C3—42no—
216C22×C3—42no—
217C22×C3—42no—
218C22×C3—416no—
219C22×C3#12014yes—
220C22×C3#12114yes—
221C22×C3#12114yes—
222C22×C3#12114yes—
223C22×C3#12314yes—
224C22×C3#12314yes—
225C22×C3#12414yes—
226C22×C3C22×D411yescharacteristic
227C22×C3C22×D411yescharacteristic
228C22×C3C22×D411yescharacteristic
229C22×C3C22×D411yescharacteristic
230C22×C3C2×#4111yescharacteristic
231C22×C3C2×#4111yescharacteristic
232C22×C3C2×#4111yescharacteristic
233C2×D3—24no—
234C2×D3—24no—
235C2×D3—24no—
236C2×D3—42no—
237C2×D3—42no—
238C2×D3—42no—
239C2×D3—42no—
240C2×D3—416no—
241C3×C4—42no—
242C3×C4—42no—
243Dic3—24no—
244Dic3—24no—
245Dic3—42no—
246C23—28no—
247C23—28no—
248C23—28no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—34no—
256C23—44no—
257C23—44no—
258C23—44no—
259C23—44no—
260C23—68no—
261C23—68no—
262C23—68no—
263C23—62no—
264C23—62no—
265C23—62no—
266C23—62no—
267C23—62no—
268C23—62no—
269C23—124no—
270C23—124no—
271C23—124no—
272C23—124no—
273C23#23512yes—
274C23#23512yes—
275C23D3×D412yes—
276C23D3×D412yes—
277C23D3×D412yes—
278C23#23712yes—
279C23C2×#6714yes—
280C23C2×#6712yes—
281C23C23×D311yescharacteristic
282D4—632no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—34no—
290C2×C4—34no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—68no—
294C2×C4—68no—
295C2×C4—62no—
296C2×C4—62no—
297C2×C4—62no—
298C2×C4—62no—
299C2×C4—62no—
300C2×C4—62no—
301C2×C4—62no—
302C2×C4—124no—
303C2×C3—44no—
304C2×C3#39418yescomplemented
305C2×C3C2×#12011yescharacteristic
306C2×C3C2×#12111yescharacteristic
307C2×C3C2×#12111yescharacteristic
308C2×C3C2×#12111yescharacteristic
309C2×C3C2×#12311yescharacteristic
310C2×C3C2×#12311yescharacteristic
311C2×C3C2×#12411yescharacteristic
312D3—44no—
313C22—24no—
314C22—24no—
315C22—24no—
316C22—416no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—64no—
322C22—64no—
323C22—64no—
324C22—1216no—
325C22—122no—
326C22—122no—
327C22—122no—
328C22—122no—
329C22#88314yes—
330C22#88414yes—
331C22#88414yes—
332C22#88514yes—
333C22#92914yes—
334C22#93714yes—
335C22#93914yes—
336C22C2×#23511yescharacteristic
337C22C2×#23511yescharacteristic
338C22C2×D3×D411yescharacteristic
339C22C2×D3×D411yescharacteristic
340C22C2×D3×D411yescharacteristic
341C22C2×#23711yescharacteristic
342C22C22×#6711yescharacteristic
343C4—42no—
344C4—42no—
345C4—64no—
346C4—64no—
347C4—122no—
348C3C2×#39411yescharacteristic, complemented, Sylow
349C2—44no—
350C2—124no—
351C2#495918yesdirect product factor
352C2C2×#88311yescharacteristic
353C2C2×#88411yescharacteristic
354C2C2×#88411yescharacteristic
355C2C2×#88511yescharacteristic
356C2C2×#92911yescharacteristic
357C2C2×#93711yescharacteristic
358C2C2×#93911yescharacteristic
subgroupG/H
centerC24C22×D3
commutator, cosocleC23×C3C24
FrattiniC23C23×D3
FittingC22×C3×C22⋊C4C2
socleC24×C3C23
prime radicalC23×#67C2
hypercenterC22×C22⋊C4D3
hypocenterC3C2×#394
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C22⋊C4C2semidirect
3. C22×#217C2semidirect
4. C22×(C2×D3)⋊C4C2semidirect
5. C22×(C2×D3)⋊C4C2semidirect
6. C22×Dic3⋊C4C2semidirect
7. C2×C3⋊#95C2semidirect
8. #4959C2direct (N × H)
22. C2×C3×C22⋊C4C22semidirect
24. C2×#217C22semidirect
27. C2×(C2×D3)⋊C4C22semidirect
28. C2×(C2×D3)⋊C4C22semidirect
30. C2×Dic3⋊C4C22semidirect
31. C3⋊#95C22semidirect
37. C22×C22⋊C4D3semidirect
77. C22×Dic3D4semidirect
106. C2×C22⋊C4C2×D3semidirect
164. C2×Dic3C2×D4semidirect
304. C2×C3#394semidirect
348. C3C2×#394semidirect
351. C2#4959direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#672
C22×C3×C22⋊C42
C22×#2172
C22×(C2×D3)⋊C42
C22×Dic3⋊C42
C2×C3⋊#952
#49592
C2×#3943