Finite Group Databasebeta

← C2×#4821 #78982

Subgroups — C2×#4821 #78982

Order 384.

772 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#41C211yesmaximal, characteristic
2C2×D3×M16C211yesmaximal, characteristic, complemented
3C2×#872C211yesmaximal, characteristic, complemented
4C2×C3×#104C211yesmaximal, characteristic, complemented
5C2×#837C211yesmaximal, characteristic, complemented
6C2×#825C211yesmaximal, characteristic, complemented
7C2×#805C211yesmaximal, characteristic, complemented
8#4821C218yesmaximal, direct product factor
9C2×#421—31nomaximal, Sylow
10C2×C3×#41C2211yescharacteristic
11D3×#41—22no—
12D3×#41—22no—
13D3×#41C414yescomplemented
14D3×#41C2214yes—
15C2×#239C411yescharacteristic, complemented
16C2×D3×Q8C411yescharacteristic, complemented
17C2×#237—21no—
18C2×#237C411yescharacteristic, complemented
19C2×D3×D4—21no—
20C2×D3×D4C411yescharacteristic, complemented
21C2×#235—21no—
22C2×#235C2211yescharacteristic
23C22×C4×D3—21no—
24C22×C4×D3C2211yescharacteristic
25C2×C3×M16C2211yescharacteristic, complemented
26C2×C3×C42C2211yescharacteristic, complemented
27C2×(C2×D3)⋊C4—21no—
28C2×Dic3⋊C4—21no—
29C2×C4×Dic3C2211yescharacteristic, complemented
30C2×#208C2211yescharacteristic, complemented
31D3×M16—22no—
32D3×M16C2214yescomplemented
33C2×ΓL(1,𝔽25)—21no—
34C2×D3×C8—21no—
35#872—22no—
36#872C2214yescomplemented
37C3×#104C2214yescomplemented
38#837C2214yescomplemented
39#825C2214yescomplemented
40#805C2214yescomplemented
41C22×#41—31no—
42C22×M16—31no—
43C2×#117—31no—
44#421—38no—
45C2×#104—31no—
46C2×#104—31no—
47C2×#104—31no—
48C2×#104D311yescharacteristic, complemented
49C23×D3—21no—
50C23×D3D411yescharacteristic
51C3×#41—21no—
52C3×#41—21no—
53C3×#41C2×C412yes—
54C3×#41C2312yes—
55C2×C3×Q8C2×C411yescharacteristic
56C2×C3×D4—21no—
57C2×C3×D4C2×C411yescharacteristic
58C22×C3×C4—21no—
59C22×C3×C4—21no—
60C22×C3×C4C2311yescharacteristic
61C2×#67—21no—
62C2×#67—21no—
63C2×#67—21no—
64C22×Dic3—21no—
65C22×Dic3—21no—
66C22×Dic3D411yescharacteristic
67#239—22no—
68#239C2×C414yescomplemented
69D3×Q8—22no—
70D3×Q8C2×C414yescomplemented
71#237—24no—
72#237—24no—
73#237—22no—
74#237C2×C414yescomplemented
75D3×D4—24no—
76D3×D4—24no—
77D3×D4—22no—
78D3×D4C2×C414yescomplemented
79#235—21no—
80#235—21no—
81#235—24no—
82#235—24no—
83#235C2×C412yes—
84#235C2312yes—
85C2×D12—21no—
86C2×D12C2×C411yescharacteristic
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×C4×D3—24no—
91C2×C4×D3—24no—
92C2×C4×D3C2×C411yescharacteristic
93C2×C4×D3C2×C411yescharacteristic
94C2×C4×D3C2×C412yes—
95C2×C4×D3D412yes—
96C2×C4×D3D411yescharacteristic
97C2×C4×D3D411yescharacteristic
98C2×C4×D3D412yes—
99C2×C4×D3C2312yes—
100C2×Dic6—21no—
101C2×Dic6C2×C411yescharacteristic
102C3×M16—21no—
103C3×M16C2312yescomplemented
104C2×C3×C8—21no—
105C3×C42—21no—
106C3×C42C2312yescomplemented
107(C2×D3)⋊C4—24no—
108Dic3⋊C4—24no—
109C4×Dic3—21no—
110C4×Dic3C2312yescomplemented
111#208—21no—
112#208C2312yescomplemented
113C2×C3⋊C8—21no—
114ΓL(1,𝔽25)—24no—
115D3×C8—24no—
116C2×#41—34no—
117C2×#41—34no—
118C2×#41—31no—
119C2×#41—31no—
120C2×#41—31no—
121C2×#41—61no—
122C2×#41—61no—
123C2×#41—62no—
124C2×#41—62no—
125C2×#41C2×D311yescharacteristic
126C22×Q8—31no—
127C22×D4—31no—
128C22×D4—61no—
129C23×C4—31no—
130C23×C4—61no—
131C2×M16—31no—
132C2×M16—34no—
133C2×M16—61no—
134C2×M16—62no—
135C2×M16C2×D311yescharacteristic, complemented
136C22×C8—61no—
137#117—34no—
138#117—62no—
139C2×C4⋊C4—61no—
140C2×C22⋊C4—61no—
141C2×C42—31no—
142C2×C42C2×D311yescharacteristic, complemented
143#104—34no—
144#104—34no—
145#104—34no—
146#104C2×D314yescomplemented
147C23×C3—21no—
148C23×C3C2×D411yescharacteristic
149C22×D3—21no—
150C22×D3—24no—
151C22×D3—42no—
152C22×D3—44no—
153C22×D3C22⋊C411yescharacteristic
154C22×D3C22⋊C411yescharacteristic
155C22×D3C22⋊C412yes—
156C22×D3C2×D412yes—
157C3×Q8—21no—
158C3×Q8C22×C412yes—
159C3×D4—22no—
160C3×D4—22no—
161C3×D4—21no—
162C3×D4C22×C412yes—
163C2×C3×C4—21no—
164C2×C3×C4—22no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—42no—
168C2×C3×C4C22×C411yescharacteristic
169C2×C3×C4C22×C411yescharacteristic
170C2×C3×C4C2×D411yescharacteristic
171C2×C3×C4C2×D411yescharacteristic
172C2×C3×C4C2×D411yescharacteristic
173C2×C3×C4C2411yescharacteristic
174#67—22no—
175#67—22no—
176#67—24no—
177#67—24no—
178C2×Dic3—21no—
179C2×Dic3—24no—
180C2×Dic3—22no—
181C2×Dic3—42no—
182C2×Dic3C22⋊C411yescharacteristic
183C2×Dic3C22⋊C411yescharacteristic
184C2×Dic3C22⋊C412yes—
185C2×Dic3C2×D412yes—
186D12—24no—
187D12—21no—
188D12C22×C412yes—
189C4×D3—24no—
190C4×D3—22no—
191C4×D3—22no—
192C4×D3—24no—
193C4×D3C22⋊C412yes—
194C4×D3C22⋊C412yes—
195C4×D3C22⋊C412yes—
196C4×D3C22⋊C412yes—
197C4×D3C22×C412yes—
198C4×D3C22×C412yes—
199C4×D3C2×D412yes—
200C4×D3C2×D412yes—
201Dic6—21no—
202Dic6—24no—
203Dic6C22×C412yes—
204C3×C8—22no—
205C3⋊C8—22no—
206C24—31no—
207C24—61no—
208#41—21no—
209#41—21no—
210#41—34no—
211#41—34no—
212#41—32no—
213#41—32no—
214#41—64no—
215#41—64no—
216#41—64no—
217#41—64no—
218#41—62no—
219#41—62no—
220#41—61no—
221#41—61no—
222#41C4×D312yes—
223#41C22×D312yes—
224C2×Q8—34no—
225C2×Q8—31no—
226C2×Q8—61no—
227C2×Q8—62no—
228C2×Q8C4×D311yescharacteristic
229C2×D4—21no—
230C2×D4—34no—
231C2×D4—31no—
232C2×D4—61no—
233C2×D4—62no—
234C2×D4—61no—
235C2×D4—64no—
236C2×D4—64no—
237C2×D4—61no—
238C2×D4—61no—
239C2×D4C4×D311yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—31no—
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—32no—
246C22×C4—32no—
247C22×C4—32no—
248C22×C4—31no—
249C22×C4—31no—
250C22×C4—32no—
251C22×C4—61no—
252C22×C4—64no—
253C22×C4—64no—
254C22×C4—61no—
255C22×C4—61no—
256C22×C4—61no—
257C22×C4—61no—
258C22×C4C22×D311yescharacteristic
259M16—21no—
260M16—32no—
261M16—64no—
262M16—61no—
263M16C22×D312yescomplemented
264C2×C8—21no—
265C2×C8—64no—
266C2×C8—61no—
267C4⋊C4—64no—
268C22⋊C4—64no—
269C42—21no—
270C42—32no—
271C42—61no—
272C42C22×D312yescomplemented
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—42no—
276C22×C3C2×C22⋊C411yescharacteristic
277C22×C3C2×C22⋊C411yescharacteristic
278C22×C3C22×D411yescharacteristic
279C2×D3—22no—
280C2×D3—22no—
281C2×D3—22no—
282C2×D3—42no—
283C2×D3—42no—
284C2×D3—48no—
285C2×D3—42no—
286C2×D3C2×C22⋊C412yes—
287C2×D3C2×C22⋊C412yes—
288C3×C4—22no—
289C3×C4—42no—
290C3×C4C2×C22⋊C411yescharacteristic
291C3×C4C2×C22⋊C411yescharacteristic
292C3×C4C23×C411yescharacteristic
293C3×C4C22×D411yescharacteristic
294Dic3—22no—
295Dic3—42no—
296Dic3C2×C22⋊C412yes—
297Dic3C2×C22⋊C412yes—
298C23—21no—
299C23—31no—
300C23—31no—
301C23—32no—
302C23—32no—
303C23—64no—
304C23—61no—
305C23—122no—
306C23—124no—
307C23D3×D411yescharacteristic
308Q8—21no—
309Q8—32no—
310Q8—64no—
311Q8—61no—
312Q8C2×C4×D312yes—
313D4—22no—
314D4—22no—
315D4—21no—
316D4—32no—
317D4—64no—
318D4—64no—
319D4—64no—
320D4—62no—
321D4—62no—
322D4—61no—
323D4C2×C4×D312yes—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—31no—
329C2×C4—31no—
330C2×C4—32no—
331C2×C4—32no—
332C2×C4—32no—
333C2×C4—32no—
334C2×C4—32no—
335C2×C4—32no—
336C2×C4—32no—
337C2×C4—32no—
338C2×C4—32no—
339C2×C4—32no—
340C2×C4—42no—
341C2×C4—64no—
342C2×C4—64no—
343C2×C4—64no—
344C2×C4—61no—
345C2×C4—62no—
346C2×C4—62no—
347C2×C4—62no—
348C2×C4—122no—
349C2×C4C2×C4×D311yescharacteristic
350C2×C4C2×C4×D311yescharacteristic
351C2×C4D3×D411yescharacteristic
352C2×C4D3×D411yescharacteristic
353C2×C4D3×D411yescharacteristic
354C2×C4C23×D311yescharacteristic
355C8—22no—
356C8—62no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—42no—
360C2×C3#42112yescomplemented
361C2×C3C22×C22⋊C411yescharacteristic
362D3—22no—
363D3—22no—
364D3—42no—
365C22—22no—
366C22—22no—
367C22—32no—
368C22—32no—
369C22—42no—
370C22—62no—
371C22—62no—
372C22—62no—
373C22—122no—
374C22—122no—
375C22—128no—
376C22—122no—
377C22D3×C22⋊C411yescharacteristic
378C22D3×C22⋊C411yescharacteristic
379C22C2×D3×D411yescharacteristic
380C4—22no—
381C4—32no—
382C4—32no—
383C4—42no—
384C4—62no—
385C4—122no—
386C4D3×C22⋊C411yescharacteristic
387C4D3×C22⋊C411yescharacteristic
388C4C22×C4×D311yescharacteristic
389C4C2×D3×D411yescharacteristic
390C3C2×#42111yescharacteristic, complemented, Sylow
391C2—21no—
392C2—21no—
393C2—42no—
394C2—62no—
395C2—62no—
396C2—122no—
397C2#482112yesdirect product factor
398C2C2×D3×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C4D3×D4
commutatorC3×C4C23×C4
FrattiniC2×C4C23×D3
FittingC2×C3×#104C2
socleC22×C3C2×C22⋊C4
prime radicalC2×D3×#41C2
cosocleC2×C3×C4C24
hypercenterC2×#104D3
hypocenterC3C2×#421
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×D3×M16C2semidirect
3. C2×#872C2semidirect
4. C2×C3×#104C2semidirect
5. C2×#837C2semidirect
6. C2×#825C2semidirect
7. C2×#805C2semidirect
8. #4821C2direct (N × H)
13. D3×#41C4semidirect
15. C2×#239C4semidirect
16. C2×D3×Q8C4semidirect
18. C2×#237C4semidirect
20. C2×D3×D4C4semidirect
25. C2×C3×M16C22semidirect
26. C2×C3×C42C22semidirect
29. C2×C4×Dic3C22semidirect
30. C2×#208C22semidirect
32. D3×M16C22semidirect
36. #872C22semidirect
37. C3×#104C22semidirect
38. #837C22semidirect
39. #825C22semidirect
40. #805C22semidirect
48. C2×#104D3semidirect
68. #239C2×C4semidirect
70. D3×Q8C2×C4semidirect
74. #237C2×C4semidirect
78. D3×D4C2×C4semidirect
103. C3×M16C23semidirect
106. C3×C42C23semidirect
110. C4×Dic3C23semidirect
112. #208C23semidirect
135. C2×M16C2×D3semidirect
142. C2×C42C2×D3semidirect
146. #104C2×D3semidirect
263. M16C22×D3semidirect
272. C42C22×D3semidirect
360. C2×C3#421semidirect
390. C3C2×#421semidirect
397. C2#4821direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#412
C2×D3×M162
C2×#8722
C2×C3×#1042
C2×#8372
C2×#8252
C2×#8052
#48212
C2×#4213