Finite Group Databasebeta

← C3×#71601 #11773810

Subgroups — C3×#71601 #11773810

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C3×#4925C212yesmaximal, complemented
3C3×#4525C214yesmaximal, complemented
4C3×#1460—31nomaximal
5#71601C311yesmaximal, characteristic, direct product factor
6C22×C32×D4C411yescharacteristic
7C23×C32×C4C412yes—
8C32×C4×D4—22no—
9C32×C4×D4—22no—
10C2×C32×C4⋊C4C411yescharacteristic
11C2×C32×C22⋊C4C2212yes—
12C2×C32×C42C2211yescharacteristic
13C3×#830C2214yes—
14C3×C4⋊(C3⋊C8)—22no—
15C3×C4×C3⋊C8—22no—
16C2×C3×C4×D4—21no—
17C2×C3×C4×D4D311yescharacteristic
18C2×C3×C4×D4C2×C311yescharacteristic
19C3×#431—32no—
20#4925C2×C312yescomplemented
21C3×#323—34no—
22#4525C2×C314yescomplemented
23C24×C32C2×C412yes—
24C2×C32×D4—22no—
25C2×C32×D4—22no—
26C2×C32×D4C814yescomplemented
27C22×C32×C4—22no—
28C22×C32×C4—22no—
29C22×C32×C4—44no—
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4C2×C412yes—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C32×C4⋊C4—22no—
35C32×C22⋊C4—24no—
36C32×C42D412yes—
37C32×C42D412yes—
38C2×C3×C3⋊C8—24no—
39#1460—31noSylow
40C22×C3×D4—21no—
41C22×C3×D4Dic311yescharacteristic
42C22×C3×D4C3×C411yescharacteristic
43C23×C3×C4—22no—
44C23×C3×C4Dic312yes—
45C23×C3×C4C3×C412yes—
46C3×C4×D4—24no—
47C3×C4×D4—24no—
48C3×C4×D4—22no—
49C3×C4×D4—22no—
50C3×C4×D4—22no—
51C3×C4×D4—22no—
52C2×C3×C4⋊C4—21no—
53C2×C3×C4⋊C4Dic311yescharacteristic
54C2×C3×C4⋊C4C3×C411yescharacteristic
55C2×C3×C22⋊C4—22no—
56C2×C3×C22⋊C4C2×D312yes—
57C2×C3×C22⋊C4C22×C312yes—
58C2×C3×C42—21no—
59C2×C3×C42C2×D311yescharacteristic
60C2×C3×C42C22×C311yescharacteristic
61C3×C4⋊C8—62no—
62C3×C22⋊C8—34no—
63C3×C4×C8—62no—
64#830C22×C314yes—
65C4⋊(C3⋊C8)—22no—
66C4×C3⋊C8—22no—
67C23×C32—22no—
68C23×C32—22no—
69C23×C32—42no—
70C23×C32—42no—
71C23×C32C2×C814yes—
72C23×C32C22×C411yescharacteristic
73C32×D4—28no—
74C2×C32×C4—22no—
75C2×C32×C4—22no—
76C2×C32×C4—41no—
77C2×C32×C4—44no—
78C2×C32×C4—44no—
79C2×C32×C4—42no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C412yes—
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C2×C812yes—
84C2×C32×C4M1612yes—
85C2×C32×C4C2×D412yes—
86C3×C3⋊C8—44no—
87C2×C4×D4C3×D311yescharacteristic
88#431—32no—
89#323—34no—
90C24×C3—22no—
91C24×C3C2×Dic312yes—
92C24×C3C2×C3×C412yes—
93C2×C3×D4—24no—
94C2×C3×D4—24no—
95C2×C3×D4—22no—
96C2×C3×D4—22no—
97C2×C3×D4—22no—
98C2×C3×D4—22no—
99C2×C3×D4—24no—
100C2×C3×D4C3⋊C814yescomplemented
101C2×C3×D4C3×C814yescomplemented
102C22×C3×C4—24no—
103C22×C3×C4—24no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—21no—
109C22×C3×C4—21no—
110C22×C3×C4—22no—
111C22×C3×C4—21no—
112C22×C3×C4—48no—
113C22×C3×C4—44no—
114C22×C3×C4—44no—
115C22×C3×C4C2×Dic311yescharacteristic
116C22×C3×C4C2×Dic312yes—
117C22×C3×C4C2×Dic311yescharacteristic
118C22×C3×C4C2×C3×C411yescharacteristic
119C22×C3×C4C2×C3×C412yes—
120C22×C3×C4C2×C3×C411yescharacteristic
121C22×C3×C4C22×D311yescharacteristic
122C22×C3×C4C23×C311yescharacteristic
123C2×C3×C8—64no—
124C3×C4⋊C4—24no—
125C3×C4⋊C4—22no—
126C3×C4⋊C4—22no—
127C3×C22⋊C4—28no—
128C3×C22⋊C4—24no—
129C3×C22⋊C4—24no—
130C3×C42—22no—
131C3×C42—22no—
132C3×C42#6712yes—
133C3×C42#6712yes—
134C3×C42C3×D412yes—
135C3×C42C3×D412yes—
136C2×C3⋊C8—24no—
137C22×C32—21no—
138C22×C32—21no—
139C22×C32—24no—
140C22×C32—44no—
141C22×C32—44no—
142C22×C32—42no—
143C22×C32—42no—
144C22×C32C2×C22⋊C411yescharacteristic
145C22×C32C22×C811yescharacteristic
146C22×C32C2×M1611yescharacteristic
147C32×C4—21no—
148C32×C4—22no—
149C32×C4—42no—
150C32×C4C22⋊C814yes—
151C32×C4#10012yes—
152C22×D4C3×Dic311yescharacteristic
153C23×C4C3×Dic312yes—
154C4×D4—22no—
155C4×D4—22no—
156C2×C4⋊C4C3×Dic311yescharacteristic
157C2×C22⋊C4C2×C3×D312yes—
158C2×C42C2×C3×D311yescharacteristic
159C4⋊C8—62no—
160C22⋊C8—34no—
161C4×C8—62no—
162C23×C3—24no—
163C23×C3—24no—
164C23×C3—22no—
165C23×C3—22no—
166C23×C3—22no—
167C23×C3—22no—
168C23×C3—24no—
169C23×C3—21no—
170C23×C3—42no—
171C23×C3—42no—
172C23×C3—42no—
173C23×C3—42no—
174C23×C3—44no—
175C23×C3—44no—
176C23×C3C2×C3⋊C814yes—
177C23×C3C2×C3×C814yes—
178C23×C3C22×Dic311yescharacteristic
179C23×C3C22×C3×C411yescharacteristic
180C3×D4—216no—
181C3×D4—28no—
182C3×D4—28no—
183C2×C3×C4—24no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—24no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—22no—
195C2×C3×C4—41no—
196C2×C3×C4—41no—
197C2×C3×C4—48no—
198C2×C3×C4—44no—
199C2×C3×C4—44no—
200C2×C3×C4—48no—
201C2×C3×C4—42no—
202C2×C3×C4—44no—
203C2×C3×C4—44no—
204C2×C3×C4—44no—
205C2×C3×C4—42no—
206C2×C3×C4—42no—
207C2×C3×C4C2×C3⋊C812yes—
208C2×C3×C4#20812yes—
209C2×C3×C4#21711yescharacteristic
210C2×C3×C4#21712yes—
211C2×C3×C4#21711yescharacteristic
212C2×C3×C4C3×C22⋊C411yescharacteristic
213C2×C3×C4C3×C22⋊C412yes—
214C2×C3×C4C3×C22⋊C411yescharacteristic
215C2×C3×C4C2×C3×C812yes—
216C2×C3×C4C3×M1612yes—
217C2×C3×C4C2×#6712yes—
218C2×C3×C4C2×C3×D412yes—
219C3×C8—124no—
220C3⋊C8—44no—
221C2×C32—21no—
222C2×C32—21no—
223C2×C32—44no—
224C2×C32C2×C22⋊C811yescharacteristic
225C2×C32#41011yescharacteristic
226C2×C32C2×#10011yescharacteristic
227C24C2×C3×Dic312yes—
228C2×D4—22no—
229C2×D4—22no—
230C2×D4C3×C3⋊C814yescomplemented
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—44no—
234C22×C4C2×C3×Dic311yescharacteristic
235C22×C4C2×C3×Dic312yes—
236C22×C4C2×C3×Dic311yescharacteristic
237C22×C4C22×C3×D311yescharacteristic
238C2×C8—64no—
239C4⋊C4—22no—
240C22⋊C4—24no—
241C42C3×#6712yes—
242C42C3×#6712yes—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—28no—
250C22×C3—24no—
251C22×C3—24no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—44no—
256C22×C3—44no—
257C22×C3—44no—
258C22×C3—48no—
259C22×C3—48no—
260C22×C3—44no—
261C22×C3—44no—
262C22×C3—44no—
263C22×C3—42no—
264C22×C3—42no—
265C22×C3—42no—
266C22×C3—42no—
267C22×C3C22×C3⋊C811yescharacteristic
268C22×C3C2×#20811yescharacteristic
269C22×C3C2×#21711yescharacteristic
270C22×C3C2×C3×C22⋊C411yescharacteristic
271C22×C3C22×C3×C811yescharacteristic
272C22×C3C2×C3×M1611yescharacteristic
273C3×C4—22no—
274C3×C4—21no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—21no—
278C3×C4—24no—
279C3×C4—22no—
280C3×C4—42no—
281C3×C4—44no—
282C3×C4—42no—
283C3×C4—42no—
284C3×C4#83014yes—
285C3×C4#83312yes—
286C3×C4C3×C22⋊C814yes—
287C3×C4C3×#10012yes—
288C32#146011yescharacteristic, complemented, Sylow
289C23—22no—
290C23—22no—
291C23—42no—
292C23—42no—
293C23C2×C3×C3⋊C814yes—
294C23C22×C3×Dic311yescharacteristic
295D4—28no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4C2×C3×C3⋊C812yes—
303C2×C4C3×#20812yes—
304C2×C4C3×#21711yescharacteristic
305C2×C4C3×#21712yes—
306C2×C4C3×#21711yescharacteristic
307C2×C4C2×C3×#6712yes—
308C8—124no—
309C2×C3—22no—
310C2×C3—22no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—48no—
319C2×C3—44no—
320C2×C3—44no—
321C2×C3C2×#83011yescharacteristic
322C2×C3C2×#83311yescharacteristic
323C2×C3#524011yescharacteristic
324C2×C3C2×C3×C22⋊C811yescharacteristic
325C2×C3C3×#41011yescharacteristic
326C2×C3C2×C3×#10011yescharacteristic
327C22—21no—
328C22—21no—
329C22—24no—
330C22—44no—
331C22—44no—
332C22—42no—
333C22—42no—
334C22C22×C3×C3⋊C811yescharacteristic
335C22C2×C3×#20811yescharacteristic
336C22C2×C3×#21711yescharacteristic
337C4—21no—
338C4—22no—
339C4—42no—
340C4C3×#83014yes—
341C4C3×#83312yes—
342C3—21no—
343C3#7160111yescharacteristic, direct product factor
344C3C3×#146011yescharacteristic, complemented
345C2—21no—
346C2—21no—
347C2—44no—
348C2C2×C3×#83011yescharacteristic
349C2C2×C3×#83311yescharacteristic
350C2C3×#524011yescharacteristic
subgroupG/H
centerC2×C3×C4#217
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4×D4C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C32×D4C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#1460
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. C3×#4525C2semidirect
5. #71601C3direct (N × H)
20. #4925C2×C3semidirect
22. #4525C2×C3semidirect
26. C2×C32×D4C8semidirect
100. C2×C3×D4C3⋊C8semidirect
101. C2×C3×D4C3×C8semidirect
230. C2×D4C3×C3⋊C8semidirect
288. C32#1460semidirect
343. C3#71601direct (N × H)
344. C3C3×#1460semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C3×#49252
C3×#45252
C3×#14603
#716013