Finite Group Databasebeta

← C2×D3×#815 #11857127

Subgroups — C2×D3×#815 #11857127

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic
2C2×C4×D3×Dic3C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic
4C2×#63642C211yesmaximal, characteristic, complemented
5C2×C3×#815C211yesmaximal, characteristic, complemented
6C2×#63555C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8D3×#815C218yesmaximal, direct product factor
9C22×#815—31nomaximal
10C2×D3×#97—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×D3×Dic3C412yes—
13C22×C32×C8C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×D3×C8C418yescomplemented
20C2×C3×D3×C8C2214yes—
21C2×Dic32C412yes—
22C4×D3×Dic3C414yes—
23C4×D3×Dic3C2214yes—
24C2×D3×C3⋊C8C418yescomplemented
25C2×D3×C3⋊C8C2214yes—
26#63642C2214yescomplemented
27C3×#815C2214yescomplemented
28#63555C2214yescomplemented
29#63554C2214yescomplemented
30C23×C3×C8—31no—
31C22×C4×Dic3—31no—
32C23×C3⋊C8—31no—
33C22×D3×C8—31no—
34C22×D3×C8D311yescharacteristic
35C2×C42×D3—31no—
36C2×C3×#97—31no—
37C2×#815—31no—
38C2×#815—31no—
39C2×#815—31no—
40C2×#815—31no—
41C2×#815—31no—
42C2×#815—38no—
43C2×#815—61no—
44C2×#815D311yescharacteristic, direct product factor
45C2×#803—31no—
46D3×#97—38no—
47C23×C3×D3C2×C411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2×C412yes—
50C22×C3×Dic3C2×C412yes—
51C22×C3×Dic3C2×C411yescharacteristic
52C2×C3×C4×D3C2×C412yes—
53C2×C3×C4×D3C2×C414yes—
54C2×C3×C4×D3C2×C414yes—
55C2×C3×C4×D3C2312yes—
56C2×D3×Dic3—28no—
57C2×D3×Dic3C2×C418yes—
58C2×C32×C8C2×C414yescomplemented
59C2×C32×C8C2312yes—
60C4×C3⋊Dic3C2×C412yes—
61C4×C3⋊Dic3C2312yes—
62C2×C3⋊(C3⋊C8)C2×C414yescomplemented
63C2×C3⋊(C3⋊C8)C2312yes—
64C3×C4×Dic3C2×C412yes—
65C3×C4×Dic3C2312yes—
66C2×C3×C3⋊C8C2×C414yescomplemented
67C2×C3×C3⋊C8C2×C414yescomplemented
68C2×C3×C3⋊C8C2312yes—
69C2×C3×C3⋊C8C2312yes—
70C3×D3×C8C2×C4116yescomplemented
71Dic32C2×C418yes—
72D3×C3⋊C8C2×C4116yescomplemented
73C22×#97—91noSylow
74C23×C3×C4—31no—
75C23×Dic3—32no—
76C22×C4×D3—32no—
77C22×C4×D3C2×D311yescharacteristic
78C22×C3×C8—21no—
79C22×C3×C8—31no—
80C22×C3×C8—31no—
81C22×C3×C8—38no—
82C22×C3×C8—34no—
83C22×C3×C8C2×D311yescharacteristic
84C22×C3×C8C2×D311yescharacteristic
85C2×C3×C42—31no—
86C2×C4×Dic3—31no—
87C2×C4×Dic3—31no—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—34no—
91C2×C4×Dic3—34no—
92C2×C4×Dic3—61no—
93C2×C4×Dic3C2×D311yescharacteristic
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—38no—
97C22×C3⋊C8—34no—
98C22×C3⋊C8—61no—
99C22×C3⋊C8C2×D311yescharacteristic
100C22×C3⋊C8C2×D311yescharacteristic
101C2×D3×C8—38no—
102C2×D3×C8—34no—
103C2×D3×C8Dic318yescomplemented
104C2×D3×C8C2×D314yes—
105C42×D3—34no—
106C42×D3—34no—
107C3×#97—34no—
108#815—34no—
109#815—34no—
110#815—34no—
111#815—34no—
112#815—34no—
113#815—64no—
114#815C2×D314yesdirect product factor
115#803—34no—
116C23×C32C22×C411yescharacteristic
117C22×C3×D3C4214yes—
118C22×C3×D3M1618yes—
119C22×C3×D3C22×C412yes—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C22×C412yes—
122C2×C32×C4C22×C412yes—
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3—24no—
125C2×C3⋊Dic3C22×C414yes—
126C2×C3×Dic3—24no—
127C2×C3×Dic3C4214yes—
128C2×C3×Dic3C22×C414yes—
129C2×C3×Dic3C22×C412yes—
130C3×C4×D3C4218yes—
131C3×C4×D3C22×C414yes—
132C3×C4×D3C22×C414yes—
133D3×Dic3—216no—
134C32×C8C22×C414yescomplemented
135C3⋊(C3⋊C8)C22×C414yescomplemented
136C3×C3⋊C8C22×C414yescomplemented
137C3×C3⋊C8C22×C414yescomplemented
138C23×C8—31no—
139C23×C8—91no—
140C22×C42—91no—
141C2×#97—31no—
142C2×#97—98no—
143C2×#97—91no—
144C2×#97—91no—
145C2×#97—91no—
146C24×C3—31no—
147C23×D3C4×D311yescharacteristic
148C22×C3×C4—21no—
149C22×C3×C4—31no—
150C22×C3×C4—34no—
151C22×C3×C4—32no—
152C22×C3×C4—34no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×Dic3—32no—
158C22×Dic3—32no—
159C22×Dic3—38no—
160C22×Dic3—62no—
161C22×Dic3—68no—
162C22×Dic3C4×D312yes—
163C22×Dic3C4×D311yescharacteristic
164C2×C4×D3—38no—
165C2×C4×D3—68no—
166C2×C4×D3C4×D312yes—
167C2×C4×D3C4×D314yes—
168C2×C4×D3C2×Dic314yes—
169C2×C4×D3C22×D312yes—
170C2×C3×C8—24no—
171C2×C3×C8—22no—
172C2×C3×C8—34no—
173C2×C3×C8—34no—
174C2×C3×C8—32no—
175C2×C3×C8—32no—
176C2×C3×C8—316no—
177C2×C3×C8C4×D314yescomplemented
178C2×C3×C8C2×Dic314yescomplemented
179C2×C3×C8C22×D312yes—
180C2×C3×C8C22×D312yes—
181C3×C42—32no—
182C3×C42—32no—
183C4×Dic3—32no—
184C4×Dic3—32no—
185C4×Dic3—32no—
186C4×Dic3—32no—
187C4×Dic3—38no—
188C4×Dic3—38no—
189C4×Dic3—62no—
190C4×Dic3—62no—
191C4×Dic3C4×D312yes—
192C4×Dic3C22×D312yes—
193C2×C3⋊C8—34no—
194C2×C3⋊C8—34no—
195C2×C3⋊C8—32no—
196C2×C3⋊C8—32no—
197C2×C3⋊C8—316no—
198C2×C3⋊C8—62no—
199C2×C3⋊C8—64no—
200C2×C3⋊C8C4×D314yescomplemented
201C2×C3⋊C8C2×Dic314yescomplemented
202C2×C3⋊C8C22×D312yes—
203C2×C3⋊C8C22×D312yes—
204D3×C8—316no—
205D3×C8C2×Dic3116yescomplemented
206C22×C32C2×C4212yes—
207C22×C32C2×M1614yes—
208C22×C32C23×C411yescharacteristic
209C2×C3×D3#97116yescomplemented
210C2×C3×D3C2×C4214yes—
211C2×C3×D3C2×M1618yes—
212C32×C4C2×C4212yes—
213C32×C4C23×C411yescharacteristic
214C32×C4C23×C411yescharacteristic
215C3⋊Dic3—24no—
216C3×Dic3—24no—
217C3×Dic3C2×C4214yes—
218C23×C4—31no—
219C23×C4—92no—
220C22×C8—31no—
221C22×C8—31no—
222C22×C8—38no—
223C22×C8—34no—
224C22×C8—94no—
225C22×C8—98no—
226C22×C8—91no—
227C22×C8D3211yescharacteristic
228C2×C42—31no—
229C2×C42—94no—
230C2×C42—94no—
231C2×C42—92no—
232C2×C42—91no—
233#97—34no—
234#97—94no—
235#97—94no—
236#97—94no—
237C23×C3—21no—
238C23×C3—34no—
239C23×C3—38no—
240C23×C3—32no—
241C23×C3C2×C4×D311yescharacteristic
242C23×C3C2×C4×D311yescharacteristic
243C22×D3ΓL(1,𝔽25)18yes—
244C22×D3C4×Dic314yes—
245C22×D3C2×C4×D312yes—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—22no—
250C2×C3×C4—34no—
251C2×C3×C4—32no—
252C2×C3×C4—38no—
253C2×C3×C4—34no—
254C2×C3×C4—34no—
255C2×C3×C4—34no—
256C2×C3×C4—64no—
257C2×C3×C4C2×C4×D311yescharacteristic
258C2×C3×C4C2×C4×D312yes—
259C2×C3×C4C2×C4×D311yescharacteristic
260C2×C3×C4C2×C4×D312yes—
261C2×C3×C4C2×C4×D312yes—
262C2×C3×C4C22×Dic312yes—
263C2×C3×C4C23×D311yescharacteristic
264C2×C3×C4C23×D311yescharacteristic
265C2×Dic3—24no—
266C2×Dic3—34no—
267C2×Dic3—34no—
268C2×Dic3—64no—
269C2×Dic3—616no—
270C2×Dic3—64no—
271C2×Dic3—64no—
272C2×Dic3—124no—
273C2×Dic3C4×Dic314yes—
274C2×Dic3C2×C4×D314yes—
275C2×Dic3C2×C4×D312yes—
276C4×D3—616no—
277C4×D3C4×Dic318yes—
278C4×D3C2×C4×D314yes—
279C4×D3C22×Dic314yes—
280C3×C8—24no—
281C3×C8—34no—
282C3×C8—34no—
283C3×C8C2×C4×D314yescomplemented
284C3×C8C22×Dic314yescomplemented
285C3⋊C8—34no—
286C3⋊C8—34no—
287C3⋊C8—64no—
288C3⋊C8C2×C4×D314yescomplemented
289C3⋊C8C22×Dic314yescomplemented
290C2×C32C2×#9714yescomplemented
291C2×C32C22×C4211yescharacteristic
292C2×C32C22×M1612yes—
293C3×D3C2×#9718yescomplemented
294C24—31no—
295C22×C4—31no—
296C22×C4—32no—
297C22×C4—32no—
298C22×C4—34no—
299C22×C4—34no—
300C22×C4—32no—
301C22×C4—98no—
302C22×C4—92no—
303C22×C4—188no—
304C22×C4C2×D3211yescharacteristic
305C2×C8—32no—
306C2×C8—32no—
307C2×C8—34no—
308C2×C8—34no—
309C2×C8—316no—
310C2×C8—916no—
311C2×C8—92no—
312C2×C8—94no—
313C2×C8D3×Dic314yescomplemented
314C2×C8C2×D3212yes—
315C42—32no—
316C42—32no—
317C42—98no—
318C42—92no—
319C42—92no—
320C22×C3—24no—
321C22×C3—21no—
322C22×C3—22no—
323C22×C3—34no—
324C22×C3—316no—
325C22×C3—38no—
326C22×C3C42×D312yes—
327C22×C3C2×ΓL(1,𝔽25)14yes—
328C22×C3D3×M1614yes—
329C22×C3C2×C4×Dic312yes—
330C22×C3C22×C4×D311yescharacteristic
331C22×C3C22×C4×D311yescharacteristic
332C2×D3#815116yesdirect product factor
333C2×D3C2×ΓL(1,𝔽25)18yes—
334C2×D3C2×C4×Dic314yes—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—22no—
338C3×C4—34no—
339C3×C4—64no—
340C3×C4C42×D312yes—
341C3×C4C2×C4×Dic312yes—
342C3×C4C22×C4×D311yescharacteristic
343C3×C4C22×C4×D311yescharacteristic
344C3×C4C22×C4×D311yescharacteristic
345C3×C4C23×Dic311yescharacteristic
346Dic3—24no—
347Dic3—64no—
348Dic3—64no—
349Dic3—124no—
350Dic3C2×C4×Dic314yes—
351C32C22×#9711yescharacteristic, complemented, Sylow
352C23—38no—
353C23—32no—
354C23—34no—
355C23C4×D3211yescharacteristic
356C2×C4—32no—
357C2×C4—34no—
358C2×C4—34no—
359C2×C4—34no—
360C2×C4—38no—
361C2×C4—34no—
362C2×C4—64no—
363C2×C4—94no—
364C2×C4—1816no—
365C2×C4—184no—
366C2×C4C4×D3212yes—
367C2×C4C4×D3211yescharacteristic
368C2×C4C2×D3×Dic312yes—
369C2×C4C22×D3211yescharacteristic
370C8—34no—
371C8—34no—
372C8—94no—
373C8C2×D3×Dic314yescomplemented
374C2×C3—21no—
375C2×C3—22no—
376C2×C3—24no—
377C2×C3—38no—
378C2×C3D3×#9714yescomplemented
379C2×C3C2×#81514yescomplemented
380C2×C3C2×C42×D311yescharacteristic
381C2×C3C22×ΓL(1,𝔽25)12yes—
382C2×C3C2×D3×M1612yes—
383C2×C3C22×C4×Dic311yescharacteristic
384D3C2×#81518yesdirect product factor
385C22—34no—
386C22—38no—
387C22—316no—
388C22D3×ΓL(1,𝔽25)14yes—
389C22C4×D3×Dic312yes—
390C22C2×C4×D3211yescharacteristic
391C4—34no—
392C4—64no—
393C4—184no—
394C4C4×D3×Dic312yes—
395C4C2×C4×D3211yescharacteristic
396C4C22×D3×Dic311yescharacteristic
397C3—21no—
398C3C2×D3×#9711yescharacteristic, complemented
399C3C22×#81511yescharacteristic, complemented
400C2—38no—
401C2D3×#81514yesdirect product factor
402C2C2×D3×ΓL(1,𝔽25)12yes—
403C2C2×C4×D3×Dic311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C22×#97
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×#63642C2semidirect
5. C2×C3×#815C2semidirect
6. C2×#63555C2semidirect
7. C2×#63554C2semidirect
8. D3×#815C2direct (N × H)
19. C2×C3×D3×C8C4semidirect
24. C2×D3×C3⋊C8C4semidirect
26. #63642C22semidirect
27. C3×#815C22semidirect
28. #63555C22semidirect
29. #63554C22semidirect
44. C2×#815D3direct (N × H)
58. C2×C32×C8C2×C4semidirect
62. C2×C3⋊(C3⋊C8)C2×C4semidirect
66. C2×C3×C3⋊C8C2×C4semidirect
67. C2×C3×C3⋊C8C2×C4semidirect
70. C3×D3×C8C2×C4semidirect
72. D3×C3⋊C8C2×C4semidirect
103. C2×D3×C8Dic3semidirect
114. #815C2×D3direct (N × H)
134. C32×C8C22×C4semidirect
135. C3⋊(C3⋊C8)C22×C4semidirect
136. C3×C3⋊C8C22×C4semidirect
137. C3×C3⋊C8C22×C4semidirect
177. C2×C3×C8C4×D3semidirect
178. C2×C3×C8C2×Dic3semidirect
200. C2×C3⋊C8C4×D3semidirect
201. C2×C3⋊C8C2×Dic3semidirect
205. D3×C8C2×Dic3semidirect
209. C2×C3×D3#97semidirect
283. C3×C8C2×C4×D3semidirect
284. C3×C8C22×Dic3semidirect
288. C3⋊C8C2×C4×D3semidirect
289. C3⋊C8C22×Dic3semidirect
290. C2×C32C2×#97semidirect
293. C3×D3C2×#97semidirect
313. C2×C8D3×Dic3semidirect
332. C2×D3#815direct (N × H)
351. C32C22×#97semidirect
373. C8C2×D3×Dic3semidirect
378. C2×C3D3×#97semidirect
379. C2×C3C2×#815semidirect
384. D3C2×#815direct (N × H)
398. C3C2×D3×#97semidirect
399. C3C22×#815semidirect
401. C2D3×#815direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×C4×D3×Dic32
C22×D3×C3⋊C82
C2×#636422
C2×C3×#8152
C2×#635552
C2×#635542
D3×#8152
C22×#8153
C2×D3×#973