Finite Group Databasebeta

← C3×#69837 #11790585

Subgroups — C3×#69837 #11790585

Order 1152.

841 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic
2C2×C32×#97C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C8C214yesmaximal, complemented
4C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C3×#1955—31nomaximal
6#69837C311yesmaximal, characteristic, direct product factor
7C22×C3×D12C411yescharacteristic
8C22×C3×C4×D3C2212yes—
9C22×C32×C8C2212yes—
10C2×C32×C42C2211yescharacteristic
11C2×C3×(C2×D3)⋊C4C412yes—
12C2×C3×C4⋊Dic3C411yescharacteristic
13C22×C3×C3⋊C8C2212yes—
14C3×C4×D12—22no—
15C3×C4×D12—22no—
16C32×#97—22no—
17C3×(C2×D3)⋊C8—28no—
18C3×C4⋊(C3⋊C8)—22no—
19C2×C3×C4×D4—31no—
20C2×C4×D12C2×C311yescharacteristic
21C2×C3×C4⋊C8—31no—
22C2×C3×C22⋊C8—34no—
23C2×C3×#97—21no—
24C2×C3×#97D311yescharacteristic, complemented
25C2×C3×#97C2×C311yescharacteristic, complemented
26C2×(C2×D3)⋊C8C2×C314yescomplemented
27C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
28C23×C3×D3C2×C412yes—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4C2311yescharacteristic
32C22×C3×Dic3C2×C412yes—
33C2×C3×D12—24no—
34C2×C3×D12—22no—
35C2×C3×C4×D3—24no—
36C2×C3×C4×D3—22no—
37C2×C3×C4×D3—22no—
38C2×C3×C4×D3—24no—
39C2×C32×C8—22no—
40C2×C32×C8—22no—
41C2×C32×C8D414yescomplemented
42C32×C42D412yes—
43C32×C42D412yes—
44C3×(C2×D3)⋊C4—24no—
45C3×C4⋊Dic3—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8—24no—
48#1955—31noSylow
49C22×C3×D4—31no—
50C23×C3×C4—32no—
51C22×D12C3×C411yescharacteristic
52C22×C4×D3C22×C312yes—
53C22×C3×C8—22no—
54C22×C3×C8—32no—
55C22×C3×C8C2×D312yes—
56C22×C3×C8C22×C312yes—
57C3×C4×D4—62no—
58C3×C4×D4—62no—
59C2×C3×C4⋊C4—31no—
60C2×C3×C22⋊C4—32no—
61C2×C3×C42—21no—
62C2×C3×C42C2×D311yescharacteristic
63C2×C3×C42C22×C311yescharacteristic
64C2×(C2×D3)⋊C4C3×C412yes—
65C2×C4⋊Dic3C3×C411yescharacteristic
66C22×C3⋊C8C22×C312yes—
67C4×D12—22no—
68C4×D12—22no—
69C3×C4⋊C8—62no—
70C3×C22⋊C8—68no—
71C3×#97—24no—
72C3×#97—22no—
73C3×#97—22no—
74(C2×D3)⋊C8—28no—
75C4⋊(C3⋊C8)—22no—
76C23×C32C22×C411yescharacteristic
77C22×C3×D3—22no—
78C22×C3×D3—24no—
79C22×C3×D3—22no—
80C22×C3×D3—24no—
81C22×C3×D3M1614yes—
82C2×C32×C4—22no—
83C2×C32×C4—22no—
84C2×C32×C4C22⋊C412yes—
85C2×C32×C4C22⋊C412yes—
86C2×C32×C4C2×D412yes—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4#4112yes—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—24no—
92C3×D12—28no—
93C3×C4×D3—44no—
94C3×C4×D3—42no—
95C3×C4×D3—42no—
96C32×C8—24no—
97C3×C3⋊C8—42no—
98C2×C4×D4—31no—
99C2×C4⋊C8—31no—
100C2×C22⋊C8—34no—
101C2×#97C3×D311yescharacteristic, complemented
102C24×C3—32no—
103C23×D3C2×C3×C412yes—
104C2×C3×D4—64no—
105C2×C3×D4—62no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×C3×C4—32no—
110C22×C3×C4—64no—
111C22×C3×C4—62no—
112C22×C3×C4—64no—
113C22×C3×C4—62no—
114C22×C3×C4C4×D311yescharacteristic
115C22×C3×C4C4×D311yescharacteristic
116C22×C3×C4C2×C3×C411yescharacteristic
117C22×C3×C4C2×C3×C411yescharacteristic
118C22×C3×C4C22×D311yescharacteristic
119C22×C3×C4C23×C311yescharacteristic
120C22×Dic3C2×C3×C412yes—
121C2×D12—24no—
122C2×D12—22no—
123C2×C4×D3—24no—
124C2×C4×D3—22no—
125C2×C4×D3—22no—
126C2×C4×D3—24no—
127C2×C3×C8—24no—
128C2×C3×C8—24no—
129C2×C3×C8—22no—
130C2×C3×C8—22no—
131C2×C3×C8—22no—
132C2×C3×C8—22no—
133C2×C3×C8—24no—
134C2×C3×C8—64no—
135C2×C3×C8—62no—
136C2×C3×C8D1214yescomplemented
137C2×C3×C8C3×D414yescomplemented
138C3×C4⋊C4—62no—
139C3×C22⋊C4—64no—
140C3×C42—22no—
141C3×C42—22no—
142C3×C42D1212yes—
143C3×C42#6712yes—
144C3×C42C3×D412yes—
145C3×C42C3×D412yes—
146(C2×D3)⋊C4—24no—
147C4⋊Dic3—22no—
148C2×C3⋊C8—22no—
149C2×C3⋊C8—24no—
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32C4×D412yes—
152C22×C32C2×M1612yes—
153C22×C32#13112yes—
154C2×C3×D3—24no—
155C2×C3×D3—28no—
156C2×C3×D3—42no—
157C2×C3×D3—42no—
158C2×C3×D3—44no—
159C32×C4—22no—
160C32×C4—22no—
161C32×C4#12112yes—
162C32×C4#12411yescharacteristic
163C32×C4#12711yescharacteristic
164C3×Dic3—42no—
165C22×D4—31no—
166C23×C4—32no—
167C22×C8—32no—
168C22×C8C2×C3×D312yes—
169C4×D4—62no—
170C4×D4—62no—
171C2×C4⋊C4—31no—
172C2×C22⋊C4—32no—
173C2×C42C2×C3×D311yescharacteristic
174C4⋊C8—62no—
175C22⋊C8—68no—
176#97—22no—
177C23×C3—21no—
178C23×C3—34no—
179C23×C3—64no—
180C23×C3—62no—
181C23×C3—64no—
182C23×C3—62no—
183C23×C3C2×C4×D311yescharacteristic
184C23×C3C22×C3×C411yescharacteristic
185C22×D3—22no—
186C22×D3—24no—
187C22×D3—22no—
188C22×D3—24no—
189C22×D3C3×M1614yes—
190C3×D4—68no—
191C2×C3×C4—22no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—21no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—64no—
204C2×C3×C4—62no—
205C2×C3×C4—122no—
206C2×C3×C4—122no—
207C2×C3×C4—124no—
208C2×C3×C4(C2×D3)⋊C412yes—
209C2×C3×C4(C2×D3)⋊C412yes—
210C2×C3×C4C3×C22⋊C412yes—
211C2×C3×C4C3×C22⋊C412yes—
212C2×C3×C4C2×D1211yescharacteristic
213C2×C3×C4C2×D1212yes—
214C2×C3×C4#23512yes—
215C2×C3×C4C2×#6711yescharacteristic
216C2×C3×C4C2×C3×D412yes—
217C2×C3×C4C2×C3×D411yescharacteristic
218C2×C3×C4C2×C3×D411yescharacteristic
219C2×C3×C4C3×#4112yes—
220C2×Dic3—22no—
221C2×Dic3—24no—
222D12—28no—
223C4×D3—44no—
224C4×D3—42no—
225C4×D3—42no—
226C3×C8—28no—
227C3×C8—24no—
228C3×C8—24no—
229C3×C8—122no—
230C3⋊C8—42no—
231C2×C32#39011yescharacteristic
232C2×C32#40711yescharacteristic
233C2×C32#40811yescharacteristic
234C2×C32#43514yes—
235C3×D3—44no—
236C24—32no—
237C2×D4—64no—
238C2×D4—62no—
239C22×C4—32no—
240C22×C4—64no—
241C22×C4—62no—
242C22×C4—64no—
243C22×C4—62no—
244C22×C4C3×C4×D311yescharacteristic
245C22×C4C3×C4×D311yescharacteristic
246C22×C4C22×C3×D311yescharacteristic
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—64no—
250C2×C8—62no—
251C2×C8C3×D1214yescomplemented
252C4⋊C4—62no—
253C22⋊C4—64no—
254C42C3×D1212yes—
255C42C3×#6712yes—
256C22×C3—22no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3—22no—
260C22×C3—64no—
261C22×C3—68no—
262C22×C3—122no—
263C22×C3—122no—
264C22×C3—124no—
265C22×C3C4×D1212yes—
266C22×C3D3×M1612yes—
267C22×C3#90712yes—
268C22×C3C2×(C2×D3)⋊C411yescharacteristic
269C22×C3C2×C3×C22⋊C411yescharacteristic
270C22×C3C3×C4×D412yes—
271C22×C3C2×C3×M1612yes—
272C22×C3C3×#13112yes—
273C2×D3—24no—
274C2×D3—28no—
275C2×D3—42no—
276C2×D3—42no—
277C2×D3—44no—
278C3×C4—22no—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—22no—
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—42no—
286C3×C4—42no—
287C3×C4—122no—
288C3×C4#87411yescharacteristic
289C3×C4#87511yescharacteristic
290C3×C4#93012yes—
291C3×C4C3×#12112yes—
292C3×C4C3×#12411yescharacteristic
293C3×C4C3×#12711yescharacteristic
294Dic3—42no—
295C32#195511yescharacteristic, complemented, Sylow
296C23—34no—
297C23—62no—
298C23—64no—
299C23—62no—
300C23—64no—
301C23C2×C3×C4×D311yescharacteristic
302D4—68no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—62no—
306C2×C4—64no—
307C2×C4—124no—
308C2×C4—122no—
309C2×C4—122no—
310C2×C4C3×(C2×D3)⋊C412yes—
311C2×C4C3×(C2×D3)⋊C412yes—
312C2×C4C2×C3×D1212yes—
313C2×C4C2×C3×D1211yescharacteristic
314C2×C4C3×#23512yes—
315C2×C4C2×C3×#6711yescharacteristic
316C8—24no—
317C8—122no—
318C2×C3—21no—
319C2×C3—24no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—124no—
323C2×C3#470614yes—
324C2×C3#493911yescharacteristic
325C2×C3#512611yescharacteristic
326C2×C3#512911yescharacteristic
327C2×C3C3×#39011yescharacteristic
328C2×C3C3×#40711yescharacteristic
329C2×C3C3×#40811yescharacteristic
330C2×C3C3×#43514yes—
331D3—44no—
332C22—68no—
333C22—64no—
334C22—122no—
335C22—124no—
336C22—122no—
337C22C3×C4×D1212yes—
338C22C3×D3×M1612yes—
339C22C3×#90712yes—
340C22C2×C3×(C2×D3)⋊C411yescharacteristic
341C4—22no—
342C4—22no—
343C4—122no—
344C4C3×#87411yescharacteristic
345C4C3×#87511yescharacteristic
346C4C3×#93012yes—
347C3—21no—
348C3#6983711yescharacteristic, direct product factor
349C3C3×#195511yescharacteristic, complemented
350C2—124no—
351C2C3×#470614yes—
352C2C3×#493911yescharacteristic
353C2C3×#512611yescharacteristic
354C2C3×#512911yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#97C2
socleC23×C32C22×C4
prime radicalC22×C3×D12C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#97D3
hypocenterC3C3×#1955
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×#97

Complements

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

NH ≅ G/Ntype
2. C2×C32×#97C2semidirect
3. C2×C3×(C2×D3)⋊C8C2semidirect
4. C2×C3×C4⋊(C3⋊C8)C2semidirect
6. #69837C3direct (N × H)
24. C2×C3×#97D3semidirect
25. C2×C3×#97C2×C3semidirect
26. C2×(C2×D3)⋊C8C2×C3semidirect
27. C2×C4⋊(C3⋊C8)C2×C3semidirect
41. C2×C32×C8D4semidirect
101. C2×#97C3×D3semidirect
136. C2×C3×C8D12semidirect
137. C2×C3×C8C3×D4semidirect
251. C2×C8C3×D12semidirect
295. C32#1955semidirect
348. C3#69837direct (N × H)
349. C3C3×#1955semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C2×C32×#972
C2×C3×(C2×D3)⋊C82
C2×C3×C4⋊(C3⋊C8)2
C3×#19553
#698373