Finite Group Databasebeta

← C3×#68125 #11773825

Subgroups — C3×#68125 #11773825

Order 1152.

535 conjugacy classes of subgroups.

The subgroup lattice has 355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic
2C3×#4718C212yesmaximal
3C32×#324C211yesmaximal, characteristic
4C3×#4528C211yesmaximal, characteristic
5C3×#4469C212yesmaximal
6C3×#1461—31nomaximal
7#68125C311yesmaximal, characteristic, direct product factor
8C22×C3×Dic6C411yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C3×Dic3⋊C4C411yescharacteristic
11C2×C3×Dic3⋊C4C2211yescharacteristic
12C2×C3×C4×Dic3C411yescharacteristic
13C2×C3×C4×Dic3C411yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C3×#887—22no—
16C3×#887—22no—
17C32×C22⋊C8C2212yes—
18C3×#830C2212yes—
19C3×Dic3⋊C8—22no—
20C3×C8×Dic3—22no—
21C2×C3×C4×Q8—31no—
22C2×#887C2×C311yescharacteristic
23C3×#431—32no—
24#4718C2×C312yes—
25C3×#324—21no—
26C3×#324—31no—
27C3×#324—32no—
28C3×#324D311yescharacteristic
29C3×#324C2×C311yescharacteristic
30#4528C2×C311yescharacteristic
31#4469C2×C312yes—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3×Dic3C2×C411yescharacteristic
36C22×C3×Dic3C2×C411yescharacteristic
37C22×C3×Dic3C2×C411yescharacteristic
38C22×C3×Dic3C2×C411yescharacteristic
39C2×C3×Dic6—22no—
40C2×C3×Dic6—22no—
41C2×C3×Dic6C814yescomplemented
42C2×C32×C8—22no—
43C32×C4⋊C4—22no—
44C3×Dic3⋊C4—22no—
45C3×Dic3⋊C4—22no—
46C3×C4×Dic3—21no—
47C3×C4×Dic3—21no—
48C3×C4×Dic3—21no—
49C3×C4×Dic3—21no—
50C3×C4×Dic3D412yes—
51C3×C4×Dic3D412yes—
52C2×C3×C3⋊C8—22no—
53#1461—31noSylow
54C22×C3×Q8—31no—
55C22×Dic6C3×C411yescharacteristic
56C3×C4×Q8—62no—
57C3×C4×Q8—62no—
58C2×C3×C4⋊C4—21no—
59C2×C3×C4⋊C4—31no—
60C2×C3×C4⋊C4—31no—
61C2×C3×C4⋊C4C2×D311yescharacteristic
62C2×C3×C4⋊C4C22×C311yescharacteristic
63C2×C3×C42—31no—
64C2×C3×C42—31no—
65C2×C3×C42—31no—
66C2×Dic3⋊C4C3×C411yescharacteristic
67C2×Dic3⋊C4C22×C311yescharacteristic
68C2×C4×Dic3C3×C411yescharacteristic
69C2×C4×Dic3C3×C411yescharacteristic
70C2×C4×Dic3C22×C311yescharacteristic
71#887—22no—
72#887—22no—
73C3×C4⋊C8—62no—
74C3×C22⋊C8—22no—
75C3×C22⋊C8—32no—
76C3×C22⋊C8C2×D312yes—
77C3×C22⋊C8C22×C312yes—
78C3×C4×C8—62no—
79#830C22×C312yes—
80Dic3⋊C8—22no—
81C8×Dic3—22no—
82C23×C32C22×C411yescharacteristic
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4C2×C812yes—
89C2×C32×C4C2×D412yes—
90C2×C3×Dic3—21no—
91C2×C3×Dic3—21no—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—21no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3C22⋊C411yescharacteristic
96C2×C3×Dic3C22⋊C412yes—
97C2×C3×Dic3C22⋊C411yescharacteristic
98C2×C3×Dic3C2×C812yes—
99C2×C3×Dic3C2×C812yes—
100C2×C3×Dic3M1612yes—
101C3×Dic6—28no—
102C32×C8—42no—
103C3×C3⋊C8—42no—
104C2×C4×Q8—31no—
105#431—32no—
106#324—31no—
107#324—32no—
108#324C3×D311yescharacteristic
109C2×C3×Q8—34no—
110C2×C3×Q8—62no—
111C2×C3×Q8—62no—
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—31no—
116C22×C3×C4—31no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C22×C3×C4C4×D311yescharacteristic
120C22×C3×C4C4×D311yescharacteristic
121C22×C3×C4C2×C3×C411yescharacteristic
122C22×C3×C4C2×C3×C411yescharacteristic
123C22×C3×C4C22×D311yescharacteristic
124C22×C3×C4C23×C311yescharacteristic
125C22×Dic3C2×C3×C411yescharacteristic
126C22×Dic3C2×C3×C411yescharacteristic
127C22×Dic3C2×C3×C411yescharacteristic
128C22×Dic3C2×C3×C411yescharacteristic
129C2×Dic6—22no—
130C2×Dic6—22no—
131C2×Dic6C3×C814yescomplemented
132C2×C3×C8—22no—
133C2×C3×C8—22no—
134C2×C3×C8—42no—
135C2×C3×C8—62no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—42no—
139C3×C4⋊C4—62no—
140C3×C4⋊C4—62no—
141C3×C42—32no—
142C3×C42—32no—
143C3×C42—61no—
144C3×C42—61no—
145C3×C42—61no—
146C3×C42—61no—
147Dic3⋊C4—22no—
148Dic3⋊C4—22no—
149C4×Dic3—21no—
150C4×Dic3—21no—
151C4×Dic3—21no—
152C4×Dic3—21no—
153C4×Dic3C3×D412yes—
154C4×Dic3C3×D412yes—
155C2×C3⋊C8—22no—
156C22×C32—21no—
157C22×C32—21no—
158C22×C32C2×C22⋊C411yescharacteristic
159C22×C32C22×C811yescharacteristic
160C22×C32C2×M1611yescharacteristic
161C32×C4—22no—
162C32×C4—22no—
163C32×C4—41no—
164C3×Dic3—22no—
165C3×Dic3—21no—
166C3×Dic3—41no—
167C3×Dic3C22⋊C814yes—
168C3×Dic3#10112yes—
169C22×Q8—31no—
170C4×Q8—62no—
171C4×Q8—62no—
172C2×C4⋊C4—31no—
173C2×C4⋊C4—31no—
174C2×C4⋊C4C2×C3×D311yescharacteristic
175C2×C42—31no—
176C2×C42—31no—
177C2×C42—31no—
178C4⋊C8—62no—
179C22⋊C8—32no—
180C22⋊C8C2×C3×D312yes—
181C4×C8—62no—
182C23×C3—21no—
183C23×C3C2×C4×D311yescharacteristic
184C23×C3C22×C3×C411yescharacteristic
185C3×Q8—68no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—31no—
195C2×C3×C4—32no—
196C2×C3×C4—32no—
197C2×C3×C4—32no—
198C2×C3×C4—31no—
199C2×C3×C4—32no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—62no—
208C2×C3×C4—61no—
209C2×C3×C4—61no—
210C2×C3×C4—61no—
211C2×C3×C4—81no—
212C2×C3×C4—81no—
213C2×C3×C4—121no—
214C2×C3×C4D3×C812yes—
215C2×C3×C4C2×C3×C812yes—
216C2×C3×C4D3×D412yes—
217C2×C3×C4C2×C3×D412yes—
218C2×Dic3—21no—
219C2×Dic3—21no—
220C2×Dic3—22no—
221C2×Dic3—21no—
222C2×Dic3—41no—
223C2×Dic3C3×C22⋊C411yescharacteristic
224C2×Dic3C3×C22⋊C412yes—
225C2×Dic3C3×C22⋊C411yescharacteristic
226C2×Dic3C2×C3×C812yes—
227C2×Dic3C2×C3×C812yes—
228C2×Dic3C3×M1612yes—
229Dic6—28no—
230C3×C8—42no—
231C3×C8—42no—
232C3×C8—82no—
233C3×C8—122no—
234C3⋊C8—42no—
235C2×C32—21no—
236C2×C32—21no—
237C2×C32C2×C22⋊C811yescharacteristic
238C2×C32#41011yescharacteristic
239C2×C32C2×#10111yescharacteristic
240C2×Q8—34no—
241C2×Q8—62no—
242C2×Q8—62no—
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—31no—
246C22×C4—31no—
247C22×C4C3×C4×D311yescharacteristic
248C22×C4C3×C4×D311yescharacteristic
249C22×C4C22×C3×D311yescharacteristic
250C2×C8—22no—
251C2×C8—62no—
252C4⋊C4—22no—
253C4⋊C4—62no—
254C4⋊C4—62no—
255C42—32no—
256C42—32no—
257C42—61no—
258C42—61no—
259C42—61no—
260C42—61no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3D3×C22⋊C411yescharacteristic
271C22×C3C2×D3×C811yescharacteristic
272C22×C3D3×M1611yescharacteristic
273C22×C3C2×C3×C22⋊C411yescharacteristic
274C22×C3C22×C3×C811yescharacteristic
275C22×C3C2×C3×M1611yescharacteristic
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—22no—
280C3×C4—34no—
281C3×C4—32no—
282C3×C4—42no—
283C3×C4—42no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—62no—
287C3×C4—61no—
288C3×C4—81no—
289C3×C4—121no—
290Dic3—22no—
291Dic3—21no—
292Dic3—41no—
293Dic3C3×C22⋊C814yes—
294Dic3C3×#10112yes—
295C32#146111yescharacteristic, complemented, Sylow
296C23C2×C3×C4×D311yescharacteristic
297Q8—68no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—31no—
302C2×C4—32no—
303C2×C4—32no—
304C2×C4—32no—
305C2×C4—31no—
306C2×C4—32no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—62no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—121no—
314C2×C4C3×D3×C812yes—
315C2×C4C3×D3×D412yes—
316C8—42no—
317C8—122no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—41no—
326C2×C3—41no—
327C2×C3D3×C22⋊C811yescharacteristic
328C2×C3#474011yescharacteristic
329C2×C3D3×#10111yescharacteristic
330C2×C3C2×C3×C22⋊C811yescharacteristic
331C2×C3C3×#41011yescharacteristic
332C2×C3C2×C3×#10111yescharacteristic
333C22—21no—
334C22—21no—
335C22C3×D3×C22⋊C411yescharacteristic
336C22C2×C3×D3×C811yescharacteristic
337C22C3×D3×M1611yescharacteristic
338C4—22no—
339C4—22no—
340C4—34no—
341C4—32no—
342C4—41no—
343C4—62no—
344C4—61no—
345C4—121no—
346C3—21no—
347C3#6812511yescharacteristic, direct product factor
348C3C3×#146111yescharacteristic, complemented
349C2—21no—
350C2—21no—
351C2C3×D3×C22⋊C811yescharacteristic
352C2C3×#474011yescharacteristic
353C2C3×D3×#10111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC32×#324C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#324D3
hypocenterC3C3×#1461
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
7. #68125C3direct (N × H)
41. C2×C3×Dic6C8semidirect
131. C2×Dic6C3×C8semidirect
295. C32#1461semidirect
347. C3#68125direct (N × H)
348. C3C3×#1461semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C3×#47182
C32×#3242
C3×#45282
C3×#44692
C3×#14613
#681253