Finite Group Databasebeta

← C3⋊C8×#217 #11783657

Subgroups — C3⋊C8×#217 #11783657

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C3⋊C8C211yesmaximal, characteristic
2C2×#63657C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic
4C2×Dic3×C3⋊C8C212yesmaximal, complemented
5#10589155C212yesmaximal, complemented
6C8×#217—31nomaximal
7C22⋊C4×C3⋊C8—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2212yes—
10C2×C3×#217C412yes—
11C2×C3×C4×Dic3C2212yes—
12C22×C3×C3⋊C8—24no—
13C22×C3×C3⋊C8C414yescomplemented
14C22×C3×C3⋊C8C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16#63657C414yescomplemented
17C3×C3⋊#95C412yes—
18Dic3×C3⋊C8—24no—
19C23×C3×C8—31no—
20C23×C3⋊C8D311yescharacteristic
21C3×C4×C22⋊C4—31no—
22C4×#217D311yescharacteristic
23C2×#830—31no—
24C2×#830—31no—
25C2×#830—61no—
26C2×C8×Dic3—32no—
27C2×C4×C3⋊C8—32no—
28#4550—32no—
29#4524—32no—
30C24×C32C2×C411yescharacteristic
31C22×C32×C4—22no—
32C22×C32×C4—22no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C412yes—
35C22×C32×C4C2×C412yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3×Dic3C2×C414yes—
38C2×C3⋊(C3⋊C8)—22no—
39C2×C3⋊(C3⋊C8)—22no—
40C2×C3⋊(C3⋊C8)C2×C414yes—
41C3×#217C818yescomplemented
42C3×C4×Dic3—22no—
43C3×C4×Dic3—22no—
44C2×C3×C3⋊C8—22no—
45C2×C3×C3⋊C8—28no—
46C2×C3×C3⋊C8C2×C412yes—
47C2×C3×C3⋊C8C2×C412yes—
48C2×C3×C3⋊C8D414yes—
49C8×C22⋊C4—91noSylow
50C23×C3×C4—21no—
51C23×C3×C4C2×D311yescharacteristic
52C23×C3×C4C2×D311yescharacteristic
53C22×C3×C8—31no—
54C22×C3×C8—34no—
55C22×C3×C8—31no—
56C22×C3×C8—64no—
57C2×C3×C22⋊C4—32no—
58C2×C3×C42—32no—
59C2×#217Dic312yes—
60C2×C4×Dic3C2×D312yes—
61C22×C3⋊C8—24no—
62C22×C3⋊C8—32no—
63C22×C3⋊C8—32no—
64C22×C3⋊C8—62no—
65C22×C3⋊C8Dic314yescomplemented
66C22×C3⋊C8C2×D311yescharacteristic
67C22×C3⋊C8C2×D311yescharacteristic
68C3×#95—32no—
69C3⋊#95Dic312yes—
70#830—34no—
71#830—34no—
72#830—64no—
73C8×Dic3—64no—
74C4×C3⋊C8—64no—
75C23×C32—22no—
76C23×C32—22no—
77C23×C32C4212yes—
78C23×C32C2×C814yes—
79C23×C32C22×C411yescharacteristic
80C2×C32×C4—22no—
81C2×C32×C4—22no—
82C2×C32×C4—22no—
83C2×C32×C4—24no—
84C2×C32×C4C4212yes—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C22×C411yescharacteristic
87C2×C32×C4C2×D412yes—
88C2×C32×C4#4112yes—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—24no—
91C2×C3×Dic3C2×C818yescomplemented
92C3⋊(C3⋊C8)—24no—
93C3×C3⋊C8—22no—
94C3×C3⋊C8C22⋊C414yescomplemented
95C23×C8—31no—
96C2×C22⋊C8—91no—
97C2×C4×C8—92no—
98C4×C22⋊C4—31no—
99#336—92no—
100C24×C3—21no—
101C24×C3C4×D311yescharacteristic
102C24×C3C2×Dic311yescharacteristic
103C22×C3×C4—22no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—22no—
107C22×C3×C4—21no—
108C22×C3×C4—22no—
109C22×C3×C4—22no—
110C22×C3×C4—21no—
111C22×C3×C4—34no—
112C22×C3×C4—42no—
113C22×C3×C4—42no—
114C22×C3×C4C4×D311yescharacteristic
115C22×C3×C4C4×D312yes—
116C22×C3×C4C4×D312yes—
117C22×C3×C4C4×D312yes—
118C22×C3×C4C2×Dic311yescharacteristic
119C22×C3×C4C2×Dic312yes—
120C22×C3×C4C22×D311yescharacteristic
121C22×C3×C4C22×D311yescharacteristic
122C22×Dic3C2×Dic314yes—
123C2×C3×C8—32no—
124C2×C3×C8—34no—
125C2×C3×C8—32no—
126C2×C3×C8—68no—
127C2×C3×C8—62no—
128C3×C22⋊C4—38no—
129C3×C42—62no—
130C3×C42—62no—
131#217C3⋊C818yesdirect product factor
132C4×Dic3—22no—
133C4×Dic3—22no—
134C2×C3⋊C8—22no—
135C2×C3⋊C8—28no—
136C2×C3⋊C8—34no—
137C2×C3⋊C8—34no—
138C2×C3⋊C8—64no—
139C2×C3⋊C8—62no—
140C2×C3⋊C8—62no—
141C2×C3⋊C8—62no—
142C2×C3⋊C8—62no—
143C2×C3⋊C8—122no—
144C2×C3⋊C8—122no—
145C2×C3⋊C8C2×Dic312yes—
146C2×C3⋊C8C2×Dic312yes—
147C2×C3⋊C8#6714yes—
148C22×C32—22no—
149C22×C32—22no—
150C22×C32—28no—
151C22×C32C4×C814yescomplemented
152C22×C32C2×C4211yescharacteristic
153C22×C32C4×D412yes—
154C22×C32C22×C812yes—
155C22×C32#13112yes—
156C32×C4—22no—
157C32×C4C2×C22⋊C411yescharacteristic
158C32×C4#11711yescharacteristic
159C32×C4C4×D412yes—
160C3×Dic3—28no—
161C23×C4D3211yescharacteristic
162C22×C8—31no—
163C22×C8—34no—
164C22×C8—31no—
165C22×C8—64no—
166C22×C8—92no—
167C2×C22⋊C4—32no—
168C2×C42—32no—
169C22⋊C8—94no—
170C4×C8—184no—
171#95—32no—
172C23×C3—22no—
173C23×C3—22no—
174C23×C3—22no—
175C23×C3—22no—
176C23×C3—24no—
177C23×C3—22no—
178C23×C3—21no—
179C23×C3—42no—
180C23×C3—42no—
181C23×C3D3×C814yes—
182C23×C3C2×C3⋊C814yes—
183C23×C3C4×Dic312yes—
184C23×C3C4×Dic312yes—
185C23×C3C2×C4×D311yescharacteristic
186C23×C3C22×Dic311yescharacteristic
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—24no—
192C2×C3×C4—22no—
193C2×C3×C4—24no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—21no—
197C2×C3×C4—22no—
198C2×C3×C4—21no—
199C2×C3×C4—22no—
200C2×C3×C4—38no—
201C2×C3×C4—44no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—42no—
205C2×C3×C4—64no—
206C2×C3×C4—64no—
207C2×C3×C4C4×Dic312yes—
208C2×C3×C4C4×Dic312yes—
209C2×C3×C4C2×C4×D311yescharacteristic
210C2×C3×C4C2×C4×D311yescharacteristic
211C2×C3×C4C2×C4×D311yescharacteristic
212C2×C3×C4#23512yes—
213C2×C3×C4D3×D412yes—
214C2×C3×C4#23712yes—
215C2×C3×C4C22×Dic311yescharacteristic
216C2×C3×C4C2×#6712yes—
217C2×Dic3—24no—
218C2×Dic3—24no—
219C2×Dic3C2×C3⋊C818yescomplemented
220C3×C8—34no—
221C3×C8—62no—
222C3⋊C8—22no—
223C3⋊C8—64no—
224C3⋊C8—64no—
225C3⋊C8—124no—
226C3⋊C8#21714yesdirect product factor
227C2×C32—24no—
228C2×C32C4×C22⋊C411yescharacteristic
229C2×C32C2×C4×C811yescharacteristic
230C2×C32#40511yescharacteristic
231C2×C32C8×D414yes—
232C24D3×Dic311yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—34no—
236C22×C4D3×Dic311yescharacteristic
237C22×C4D3×Dic312yes—
238C22×C4#62412yes—
239C22×C4C2×D3211yescharacteristic
240C2×C8—32no—
241C2×C8—34no—
242C2×C8—32no—
243C2×C8—68no—
244C2×C8—62no—
245C2×C8—94no—
246C2×C8—182no—
247C2×C8—182no—
248C22⋊C4—38no—
249C42—62no—
250C42—62no—
251C22×C3—22no—
252C22×C3—22no—
253C22×C3—22no—
254C22×C3—28no—
255C22×C3—22no—
256C22×C3—28no—
257C22×C3—24no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—22no—
262C22×C3—42no—
263C22×C3—42no—
264C22×C3—48no—
265C22×C3C4×C3⋊C814yescomplemented
266C22×C3C8×Dic314yescomplemented
267C22×C3C2×D3×C812yes—
268C22×C3#90112yes—
269C22×C3C22×C3⋊C812yes—
270C22×C3C2×C4×Dic311yescharacteristic
271C22×C3C2×C4×Dic311yescharacteristic
272C22×C3C4×#6712yes—
273C22×C3D4×Dic312yes—
274C22×C3#94812yes—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—42no—
281C3×C4—68no—
282C3×C4#87711yescharacteristic
283C3×C4D3×C22⋊C411yescharacteristic
284C3×C4#67⋊C412yes—
285C3×C4#92611yescharacteristic
286C3×C4C4×#6712yes—
287C3×C4C2×#21711yescharacteristic
288Dic3—28no—
289C32C8×C22⋊C411yescharacteristic, complemented, Sylow
290C23—22no—
291C23—22no—
292C23D3×C3⋊C814yes—
293C23Dic3212yes—
294C23C2×D3×Dic311yescharacteristic
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—38no—
300C2×C4—64no—
301C2×C4—64no—
302C2×C4Dic3212yes—
303C2×C4C2×D3×Dic311yescharacteristic
304C2×C4#380412yes—
305C2×C4C2×#62411yescharacteristic
306C2×C4D3×#6712yes—
307C8—34no—
308C8—62no—
309C8—184no—
310C2×C3—24no—
311C2×C3—24no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—24no—
315C2×C3—21no—
316C2×C3—44no—
317C2×C3C2×C4×C3⋊C811yescharacteristic
318C2×C3Dic3×C22⋊C411yescharacteristic
319C2×C3#499711yescharacteristic
320C2×C3D4×C3⋊C814yes—
321C2×C3C2×C8×Dic311yescharacteristic
322C2×C3#510111yescharacteristic
323C2×C3C8×#6714yes—
324C2×C3C4×#21711yescharacteristic
325C22—22no—
326C22—28no—
327C22—22no—
328C22Dic3×C3⋊C814yescomplemented
329C22C2×D3×C3⋊C812yes—
330C22#6381412yes—
331C22C2×Dic3211yescharacteristic
332C22Dic3×#6712yes—
333C4—22no—
334C4—68no—
335C4#6395212yes—
336C4#6395511yescharacteristic
337C4D3×#21711yescharacteristic
338C3—21no—
339C3C22⋊C4×C3⋊C811yescharacteristic, complemented
340C3C8×#21711yescharacteristic, complemented
341C2—24no—
342C2C2×Dic3×C3⋊C811yescharacteristic
343C2#1059105511yescharacteristic
344C2C3⋊C8×#6714yes—
345C2Dic3×#21711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC2×C32C2×C4×C8
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32C8×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×Dic3×C3⋊C8C2semidirect
5. #10589155C2semidirect
13. C22×C3×C3⋊C8C4semidirect
16. #63657C4semidirect
41. C3×#217C8semidirect
65. C22×C3⋊C8Dic3semidirect
91. C2×C3×Dic3C2×C8semidirect
94. C3×C3⋊C8C22⋊C4semidirect
131. #217C3⋊C8direct (N × H)
151. C22×C32C4×C8semidirect
219. C2×Dic3C2×C3⋊C8semidirect
226. C3⋊C8#217direct (N × H)
265. C22×C3C4×C3⋊C8semidirect
266. C22×C3C8×Dic3semidirect
289. C32C8×C22⋊C4semidirect
328. C22Dic3×C3⋊C8semidirect
339. C3C22⋊C4×C3⋊C8semidirect
340. C3C8×#217semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C3⋊C82
C2×#636572
C3×C4×#2172
C2×Dic3×C3⋊C82
#105891552
C8×#2173
C22⋊C4×C3⋊C83