Finite Group Databasebeta

← C3×#71737 #11774050

Subgroups — C3×#71737 #11774050

Order 1152.

521 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#125C211yesmaximal, characteristic
2C3×#4926C211yesmaximal, characteristic
3C3×#4925C211yesmaximal, characteristic
4C3×#4528C214yesmaximal
5C3×#1470—31nomaximal
6#71737C311yesmaximal, characteristic, direct product factor
7C32×#125—21no—
8C32×#125—21no—
9C32×#125—21no—
10C32×#125—21no—
11C2×C32×C4⋊C4C411yescharacteristic
12C2×C32×C4⋊C4C412yes—
13C2×C32×C4⋊C4C411yescharacteristic
14C2×C32×C4⋊C4C2212yes—
15C2×C32×C42C2211yescharacteristic
16C3×#830C2212yes—
17C3×#830C2212yes—
18C3×C4⋊(C3⋊C8)—21no—
19C3×C4⋊(C3⋊C8)—21no—
20C3×#803—21no—
21C3×C4×C3⋊C8—21no—
22C2×C3×#125—21no—
23C2×C3×#125D311yescharacteristic
24C2×C3×#125C2×C311yescharacteristic
25C3×#432—31no—
26C3×#431—31no—
27#4926C2×C311yescharacteristic
28#4925C2×C311yescharacteristic
29C3×#324—34no—
30#4528C2×C314yes—
31C22×C32×C4C2×C412yes—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C412yes—
35C22×C32×C4C2311yescharacteristic
36C32×C4⋊C4—21no—
37C32×C4⋊C4—22no—
38C32×C4⋊C4—22no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4—22no—
43C32×C4⋊C4—22no—
44C32×C42D411yescharacteristic
45C32×C42D411yescharacteristic
46C32×C42D411yescharacteristic
47C32×C42D411yescharacteristic
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50#1470—31noSylow
51C3×#125—22no—
52C3×#125—22no—
53C3×#125—22no—
54C3×#125—22no—
55C3×#125—21no—
56C3×#125—21no—
57C3×#125—21no—
58C3×#125—21no—
59C3×#125—21no—
60C3×#125—21no—
61C3×#125—21no—
62C3×#125—21no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4—22no—
66C2×C3×C4⋊C4—22no—
67C2×C3×C4⋊C4Dic311yescharacteristic
68C2×C3×C4⋊C4Dic312yes—
69C2×C3×C4⋊C4Dic311yescharacteristic
70C2×C3×C4⋊C4C3×C411yescharacteristic
71C2×C3×C4⋊C4C3×C412yes—
72C2×C3×C4⋊C4C3×C411yescharacteristic
73C2×C3×C4⋊C4C2×D312yes—
74C2×C3×C4⋊C4C22×C312yes—
75C2×C3×C42—21no—
76C2×C3×C42C2×D311yescharacteristic
77C2×C3×C42C22×C311yescharacteristic
78C3×C4⋊C8—61no—
79C3×C4⋊C8—61no—
80C3×C22⋊C8—32no—
81C3×C22⋊C8—32no—
82C3×#97—61no—
83C3×C4×C8—61no—
84#830C22×C312yes—
85#830C22×C312yes—
86C4⋊(C3⋊C8)—21no—
87C4⋊(C3⋊C8)—21no—
88#803—21no—
89C4×C3⋊C8—21no—
90C23×C32C22×C411yescharacteristic
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—24no—
96C2×C32×C4—41no—
97C2×C32×C4—42no—
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C3×C3⋊C8—42no—
105C3×C3⋊C8—42no—
106C2×#125C3×D311yescharacteristic
107#432—31no—
108#431—31no—
109#324—34no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—22no—
113C22×C3×C4—22no—
114C22×C3×C4—21no—
115C22×C3×C4C2×Dic312yes—
116C22×C3×C4C2×Dic311yescharacteristic
117C22×C3×C4C2×Dic311yescharacteristic
118C22×C3×C4C2×Dic312yes—
119C22×C3×C4C2×C3×C412yes—
120C22×C3×C4C2×C3×C411yescharacteristic
121C22×C3×C4C2×C3×C411yescharacteristic
122C22×C3×C4C2×C3×C412yes—
123C22×C3×C4C22×D311yescharacteristic
124C22×C3×C4C23×C311yescharacteristic
125C2×C3×C8—62no—
126C2×C3×C8—62no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—24no—
132C3×C4⋊C4—24no—
133C3×C4⋊C4—24no—
134C3×C4⋊C4—24no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—22no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—22no—
151C3×C42—21no—
152C3×C42—21no—
153C3×C42—21no—
154C3×C42—21no—
155C3×C42#6711yescharacteristic
156C3×C42#6711yescharacteristic
157C3×C42#6711yescharacteristic
158C3×C42#6711yescharacteristic
159C3×C42C3×D411yescharacteristic
160C3×C42C3×D411yescharacteristic
161C3×C42C3×D411yescharacteristic
162C3×C42C3×D411yescharacteristic
163C2×C3⋊C8—22no—
164C2×C3⋊C8—22no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32C2×C22⋊C411yescharacteristic
168C22×C32#13112yes—
169C32×C4—21no—
170C32×C4—21no—
171C32×C4—21no—
172C32×C4—21no—
173C32×C4—21no—
174C32×C4—42no—
175C32×C4—42no—
176C32×C4#10112yes—
177#125—21no—
178#125—21no—
179#125—21no—
180#125—21no—
181C2×C4⋊C4C3×Dic311yescharacteristic
182C2×C4⋊C4C3×Dic312yes—
183C2×C4⋊C4C3×Dic311yescharacteristic
184C2×C4⋊C4C2×C3×D312yes—
185C2×C42C2×C3×D311yescharacteristic
186C4⋊C8—61no—
187C4⋊C8—61no—
188C22⋊C8—32no—
189C22⋊C8—32no—
190#97—61no—
191C4×C8—61no—
192C23×C3—21no—
193C23×C3C22×Dic311yescharacteristic
194C23×C3C22×C3×C411yescharacteristic
195C2×C3×C4—24no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—24no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—24no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—42no—
215C2×C3×C4—44no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—42no—
219C2×C3×C4—44no—
220C2×C3×C4—42no—
221C2×C3×C4—42no—
222C2×C3×C4#21711yescharacteristic
223C2×C3×C4#21711yescharacteristic
224C2×C3×C4#21711yescharacteristic
225C2×C3×C4#21711yescharacteristic
226C2×C3×C4C3×C22⋊C411yescharacteristic
227C2×C3×C4C3×C22⋊C411yescharacteristic
228C2×C3×C4C3×C22⋊C411yescharacteristic
229C2×C3×C4C3×C22⋊C411yescharacteristic
230C2×C3×C4C2×#6711yescharacteristic
231C2×C3×C4C2×#6711yescharacteristic
232C2×C3×C4C2×C3×D411yescharacteristic
233C2×C3×C4C2×C3×D411yescharacteristic
234C3×C8—122no—
235C3×C8—122no—
236C3⋊C8—42no—
237C3⋊C8—42no—
238C2×C32—22no—
239C2×C32#40811yescharacteristic
240C2×C32#41011yescharacteristic
241C2×C32C2×#10111yescharacteristic
242C22×C4C2×C3×Dic312yes—
243C22×C4C2×C3×Dic311yescharacteristic
244C22×C4C2×C3×Dic311yescharacteristic
245C22×C4C2×C3×Dic312yes—
246C22×C4C22×C3×D311yescharacteristic
247C2×C8—62no—
248C2×C8—62no—
249C4⋊C4—21no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C42C3×#6711yescharacteristic
258C42C3×#6711yescharacteristic
259C42C3×#6711yescharacteristic
260C42C3×#6711yescharacteristic
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—22no—
268C22×C3—21no—
269C22×C3#94812yes—
270C22×C3C2×#21711yescharacteristic
271C22×C3C2×C3×C22⋊C411yescharacteristic
272C22×C3C3×#13112yes—
273C3×C4—22no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—22no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—44no—
290C3×C4—44no—
291C3×C4—42no—
292C3×C4—42no—
293C3×C4—42no—
294C3×C4—42no—
295C3×C4#83612yes—
296C3×C4C3×#10112yes—
297C32#147011yescharacteristic, complemented, Sylow
298C23C22×C3×Dic311yescharacteristic
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4C3×#21711yescharacteristic
307C2×C4C3×#21711yescharacteristic
308C2×C4C3×#21711yescharacteristic
309C2×C4C3×#21711yescharacteristic
310C2×C4C2×C3×#6711yescharacteristic
311C2×C4C2×C3×#6711yescharacteristic
312C8—122no—
313C8—122no—
314C2×C3—24no—
315C2×C3—22no—
316C2×C3—22no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3C2×#83611yescharacteristic
321C2×C3#523411yescharacteristic
322C2×C3#524011yescharacteristic
323C2×C3C3×#40811yescharacteristic
324C2×C3C3×#41011yescharacteristic
325C2×C3C2×C3×#10111yescharacteristic
326C22—21no—
327C22—21no—
328C22C3×#94812yes—
329C22C2×C3×#21711yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—42no—
336C4—42no—
337C4C3×#83612yes—
338C3—21no—
339C3#7173711yescharacteristic, direct product factor
340C3C3×#147011yescharacteristic, complemented
341C2—22no—
342C2C2×C3×#83611yescharacteristic
343C2C3×#523411yescharacteristic
344C2C3×#524011yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#125C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#125D3
hypocenterC3C3×#1470
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×#125

Complements

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

NH ≅ G/Ntype
6. #71737C3direct (N × H)
297. C32#1470semidirect
339. C3#71737direct (N × H)
340. C3C3×#1470semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1252
C3×#49262
C3×#49252
C3×#45282
C3×#14703
#717373