Finite Group Databasebeta

← C2×#4825 #78985

Subgroups — C2×#4825 #78985

Order 384.

760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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×#1009C211yesmaximal, characteristic
2C2×#951C211yesmaximal, characteristic, complemented
3C2×#909C211yesmaximal, characteristic, complemented
4C2×#875C211yesmaximal, characteristic, complemented
5C2×C3×#104C211yesmaximal, characteristic, complemented
6C2×#823C211yesmaximal, characteristic, complemented
7C2×#805C211yesmaximal, characteristic, complemented
8#4825C218yesmaximal, direct product factor
9C2×#455—31nomaximal, Sylow
10C2×C3×#41C2211yescharacteristic
11#1009—22no—
12#1009—22no—
13#1009—22no—
14#1009C2214yes—
15C2×#239—21no—
16C2×D3×D4—22no—
17C2×D3×D4—21no—
18C2×#235—21no—
19C2×#235C2211yescharacteristic
20C22×D12—21no—
21C22×D12C2211yescharacteristic
22C22×Dic6C2211yescharacteristic, complemented
23C2×C3×M16C2211yescharacteristic, complemented
24C2×C3×C42C2211yescharacteristic, complemented
25#951—22no—
26#951C2214yescomplemented
27C2×#216—21no—
28C2×#214—21no—
29C2×(C2×D3)⋊C4—22no—
30C2×#208C2211yescharacteristic, complemented
31#909—22no—
32#909C2214yescomplemented
33C2×Dic12—21no—
34C2×#204—21no—
35#875—22no—
36#875C2214yescomplemented
37C3×#104C2214yescomplemented
38#823C2214yescomplemented
39#805C2214yescomplemented
40C2×H(5,𝔽2)—31no—
41C2×#137—31no—
42C2×#137—31no—
43C2×#124—31no—
44#455—38no—
45C2×#104—31no—
46C2×#104D311yescharacteristic, complemented
47C2×#100—31no—
48C23×D3—22no—
49C23×D3D412yes—
50C3×#41—21no—
51C3×#41—21no—
52C3×#41D412yes—
53C3×#41C2312yes—
54C2×C3×Q8D411yescharacteristic
55C2×C3×D4—21no—
56C2×C3×D4D411yescharacteristic
57C22×C3×C4—21no—
58C22×C3×C4—21no—
59C22×C3×C4C2311yescharacteristic
60C2×#67—22no—
61C2×#67—21no—
62C22×Dic3—21no—
63#239—24no—
64#239—24no—
65D3×D4—28no—
66D3×D4—24no—
67D3×D4—28no—
68D3×D4—24no—
69#235—24no—
70#235—21no—
71#235—21no—
72#235—24no—
73#235D412yes—
74#235C2312yes—
75C2×D12—22no—
76C2×D12—24no—
77C2×D12—21no—
78C2×D12—21no—
79C2×D12—21no—
80C2×D12—21no—
81C2×D12—24no—
82C2×D12D412yes—
83C2×D12D411yescharacteristic
84C2×D12C2312yes—
85C2×C4×D3—22no—
86C2×C4×D3—21no—
87C2×Dic6—21no—
88C2×Dic6—21no—
89C2×Dic6—21no—
90C2×Dic6—21no—
91C2×Dic6—21no—
92C2×Dic6D411yescharacteristic
93C2×Dic6C2312yescomplemented
94C3×M16—21no—
95C3×M16C2312yescomplemented
96C2×C3×C8—21no—
97C3×C42—21no—
98C3×C42C2312yescomplemented
99#216—24no—
100#214—24no—
101(C2×D3)⋊C4—28no—
102#208—21no—
103#208C2312yescomplemented
104C2×C3⋊C8—21no—
105Dic12—24no—
106#204—24no—
107H(5,𝔽2)—34no—
108H(5,𝔽2)—62no—
109H(5,𝔽2)—62no—
110H(5,𝔽2)—62no—
111C2×#41—31no—
112C2×#41—61no—
113C2×#41—61no—
114C2×#41C2×D311yescharacteristic
115C22×Q8—31no—
116C22×D4—31no—
117C22×D4—61no—
118C22×D4—62no—
119C22×D4—61no—
120#137—34no—
121#137—34no—
122#137—62no—
123#137—62no—
124C2×Q16—61no—
125C2×Q16—61no—
126C2×SD16—61no—
127C2×SD16—61no—
128C2×M16—31no—
129C2×M16C2×D311yescharacteristic, complemented
130#124—34no—
131#124—62no—
132C2×C22⋊C4—62no—
133C2×C42C2×D311yescharacteristic, complemented
134#104—34no—
135#104C2×D314yescomplemented
136#100—34no—
137C23×C3—21no—
138C23×C3C2×D411yescharacteristic
139C22×D3—22no—
140C22×D3—21no—
141C22×D3—28no—
142C22×D3—22no—
143C22×D3—44no—
144C22×D3—84no—
145C22×D3C2×D414yes—
146C3×Q8—21no—
147C3×Q8C2×D412yes—
148C3×D4—22no—
149C3×D4—22no—
150C3×D4—21no—
151C3×D4C2×D412yes—
152C2×C3×C4—21no—
153C2×C3×C4—22no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—42no—
157C2×C3×C4C2×D411yescharacteristic
158C2×C3×C4C2×D411yescharacteristic
159C2×C3×C4C2×D411yescharacteristic
160C2×C3×C4C2×D411yescharacteristic
161C2×C3×C4C2×D411yescharacteristic
162C2×C3×C4C2411yescharacteristic
163#67—28no—
164#67—22no—
165#67—22no—
166C2×Dic3—21no—
167C2×Dic3—22no—
168C2×Dic3—41no—
169C2×Dic3—41no—
170D12—28no—
171D12—22no—
172D12—21no—
173D12—22no—
174D12—22no—
175D12—22no—
176D12C2×D412yes—
177C4×D3—28no—
178C4×D3—22no—
179C4×D3—22no—
180Dic6—21no—
181Dic6—22no—
182Dic6—22no—
183Dic6—41no—
184Dic6—41no—
185Dic6C2×D412yes—
186C3×C8—22no—
187C3⋊C8—22no—
188C24—32no—
189C24—62no—
190#41—21no—
191#41—21no—
192#41—32no—
193#41—32no—
194#41—64no—
195#41—64no—
196#41—64no—
197#41—64no—
198#41—61no—
199#41—61no—
200#41D1212yes—
201#41C22×D312yes—
202C2×Q8—31no—
203C2×Q8—32no—
204C2×Q8—61no—
205C2×Q8—61no—
206C2×Q8—61no—
207C2×Q8—61no—
208C2×Q8—61no—
209C2×Q8D1211yescharacteristic
210C2×D4—21no—
211C2×D4—31no—
212C2×D4—32no—
213C2×D4—32no—
214C2×D4—64no—
215C2×D4—62no—
216C2×D4—64no—
217C2×D4—68no—
218C2×D4—68no—
219C2×D4—64no—
220C2×D4—62no—
221C2×D4—61no—
222C2×D4—64no—
223C2×D4—61no—
224C2×D4—61no—
225C2×D4—61no—
226C2×D4—61no—
227C2×D4D1211yescharacteristic
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—62no—
231C22×C4—61no—
232C22×C4—61no—
233C22×C4C22×D311yescharacteristic
234Q16—64no—
235Q16—64no—
236SD16—64no—
237SD16—64no—
238M16—21no—
239M16—32no—
240M16—61no—
241M16C22×D312yescomplemented
242C2×C8—21no—
243C2×C8—61no—
244C22⋊C4—68no—
245C42—21no—
246C42C22×D312yescomplemented
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—42no—
250C22×C3#12011yescharacteristic
251C22×C3#12011yescharacteristic
252C22×C3C22×D411yescharacteristic
253C2×D3—24no—
254C2×D3—22no—
255C2×D3—44no—
256C2×D3—42no—
257C2×D3—44no—
258C2×D3—82no—
259C2×D3—88no—
260C3×C4—22no—
261C3×C4—42no—
262C3×C4#12011yescharacteristic
263C3×C4#12011yescharacteristic
264C3×C4C22×D411yescharacteristic
265C3×C4C22×D411yescharacteristic
266Dic3—22no—
267Dic3—42no—
268C23—21no—
269C23—34no—
270C23—68no—
271C23—61no—
272C23—62no—
273C23—62no—
274C23—124no—
275C23—244no—
276C23D3×D411yescharacteristic
277Q8—21no—
278Q8—32no—
279Q8—61no—
280Q8—62no—
281Q8—62no—
282Q8—121no—
283Q8—121no—
284Q8C2×D1212yes—
285D4—22no—
286D4—22no—
287D4—21no—
288D4—32no—
289D4—68no—
290D4—68no—
291D4—62no—
292D4—62no—
293D4—61no—
294D4—62no—
295D4—62no—
296D4—62no—
297D4—62no—
298D4C2×D1212yes—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—42no—
304C2×C4—68no—
305C2×C4—61no—
306C2×C4—62no—
307C2×C4—62no—
308C2×C4—62no—
309C2×C4—121no—
310C2×C4—121no—
311C2×C4C2×D1211yescharacteristic
312C2×C4C2×D1211yescharacteristic
313C2×C4D3×D411yescharacteristic
314C2×C4D3×D411yescharacteristic
315C2×C4D3×D411yescharacteristic
316C2×C4C23×D311yescharacteristic
317C8—22no—
318C8—62no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—42no—
322C2×C3#45512yescomplemented
323C2×C3C2×#12011yescharacteristic
324D3—44no—
325D3—42no—
326C22—22no—
327C22—22no—
328C22—42no—
329C22—62no—
330C22—64no—
331C22—124no—
332C22—124no—
333C22—122no—
334C22—242no—
335C22—248no—
336C22#88211yescharacteristic
337C22#88211yescharacteristic
338C22C2×D3×D411yescharacteristic
339C4—22no—
340C4—42no—
341C4—62no—
342C4—122no—
343C4#88211yescharacteristic
344C4#88211yescharacteristic
345C4C22×D1211yescharacteristic
346C4C2×D3×D411yescharacteristic
347C3C2×#45511yescharacteristic, complemented, Sylow
348C2—21no—
349C2—21no—
350C2—42no—
351C2—124no—
352C2—122no—
353C2#482512yesdirect product factor
354C2C2×#88211yescharacteristic
subgroupG/H
centerC22#882
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC2×C3×#104C2
socleC22×C3#120
prime radicalC2×#1009C2
hypercenterC2×#104D3
hypocenterC3C2×#455
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#951C2semidirect
3. C2×#909C2semidirect
4. C2×#875C2semidirect
5. C2×C3×#104C2semidirect
6. C2×#823C2semidirect
7. C2×#805C2semidirect
8. #4825C2direct (N × H)
22. C22×Dic6C22semidirect
23. C2×C3×M16C22semidirect
24. C2×C3×C42C22semidirect
26. #951C22semidirect
30. C2×#208C22semidirect
32. #909C22semidirect
36. #875C22semidirect
37. C3×#104C22semidirect
38. #823C22semidirect
39. #805C22semidirect
46. C2×#104D3semidirect
93. C2×Dic6C23semidirect
95. C3×M16C23semidirect
98. C3×C42C23semidirect
103. #208C23semidirect
129. C2×M16C2×D3semidirect
133. C2×C42C2×D3semidirect
135. #104C2×D3semidirect
241. M16C22×D3semidirect
246. C42C22×D3semidirect
322. C2×C3#455semidirect
347. C3C2×#455semidirect
353. C2#4825direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#10092
C2×#9512
C2×#9092
C2×#8752
C2×C3×#1042
C2×#8232
C2×#8052
#48252
C2×#4553