Finite Group Databasebeta

← C3×#68973 #11783797

Subgroups — C3×#68973 #11783797

Order 1152.

641 conjugacy classes of subgroups.

The subgroup lattice has 335 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic
2C2×C3×#824C212yesmaximal
3C3×Dic3×M16C212yesmaximal
4C32×#343C211yesmaximal, characteristic
5C3×#4530C211yesmaximal, characteristic
6C3×C4×#101—31nomaximal
7#68973C311yesmaximal, characteristic, direct product factor
8C22×C3×Dic6C2211yescharacteristic
9C2×C32×M16C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C3×Dic3⋊C4C412yes—
12C2×C3×C4×Dic3C412yes—
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×#208C2212yes—
15C3×#887—22no—
16C3×#887—22no—
17C3×#824C418yescomplemented
18C3×#815—22no—
19C3×C8×Dic3—22no—
20C2×C3×C4×Q8—31no—
21C2×#887C2×C311yescharacteristic
22C2×C3×#101—32no—
23C3×C4×M16—32no—
24C2×#824C2×C312yes—
25Dic3×M16C2×C312yes—
26C3×#343—21no—
27C3×#343—31no—
28C3×#343D311yescharacteristic
29C3×#343C2×C311yescharacteristic
30#4530C2×C311yescharacteristic
31C22×C32×C4C2×C412yes—
32C22×C32×C4C2311yescharacteristic
33C22×C3×Dic3C2×C412yes—
34C22×C3×Dic3C2×C411yescharacteristic
35C22×C3×Dic3C2×C411yescharacteristic
36C2×C3×Dic6—22no—
37C2×C3×Dic6—21no—
38C2×C3×Dic6—21no—
39C2×C3×Dic6C2×C414yes—
40C32×M16—22no—
41C32×M16C2×C414yes—
42C2×C32×C8—22no—
43C32×C4⋊C4—22no—
44C3×Dic3⋊C4—24no—
45C3×C4×Dic3—22no—
46C3×C4×Dic3—22no—
47C3×C4×Dic3D412yes—
48C3×C4×Dic3D412yes—
49C3×#208—22no—
50C3×#208C2×C414yes—
51C2×C3×C3⋊C8—22no—
52C4×#101—31noSylow
53C22×C3×Q8—31no—
54C22×Dic6C22×C311yescharacteristic
55C2×C3×M16—22no—
56C2×C3×M16—32no—
57C2×C3×M16C2×D312yes—
58C2×C3×M16C22×C312yes—
59C3×C4×Q8—62no—
60C3×C4×Q8—62no—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4C2×D311yescharacteristic
64C2×C3×C4⋊C4C22×C311yescharacteristic
65C2×C3×C42—31no—
66C2×C3×C42—32no—
67C2×Dic3⋊C4C3×C412yes—
68C2×C4×Dic3C3×C412yes—
69C2×C4×Dic3C22×C311yescharacteristic
70C2×#208C22×C312yes—
71#887—22no—
72#887—22no—
73C3×#101—38no—
74C3×#97—62no—
75C3×C4×C8—62no—
76#824C3×C418yescomplemented
77#815—22no—
78C8×Dic3—22no—
79C23×C32C22×C411yescharacteristic
80C2×C32×C4—22no—
81C2×C32×C4—42no—
82C2×C32×C4C22×C412yes—
83C2×C32×C4C2×D412yes—
84C2×C32×C4#4111yescharacteristic
85C2×C32×C4#4111yescharacteristic
86C2×C3×Dic3—22no—
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3C4214yes—
91C2×C3×Dic3C22⋊C411yescharacteristic
92C2×C3×Dic3C22⋊C412yes—
93C2×C3×Dic3C22⋊C411yescharacteristic
94C3×Dic6—24no—
95C3×Dic6—24no—
96C32×C8—24no—
97C3×C3⋊C8—24no—
98C2×C4×Q8—31no—
99C2×#101—32no—
100C4×M16—32no—
101#343—31no—
102#343C3×D311yescharacteristic
103C2×C3×Q8—34no—
104C2×C3×Q8—62no—
105C2×C3×Q8—61no—
106C2×C3×Q8—61no—
107C22×C3×C4—22no—
108C22×C3×C4—21no—
109C22×C3×C4—31no—
110C22×C3×C4—32no—
111C22×C3×C4—31no—
112C22×C3×C4C4×D312yes—
113C22×C3×C4C2×C3×C412yes—
114C22×C3×C4C22×D311yescharacteristic
115C22×C3×C4C23×C311yescharacteristic
116C22×Dic3C2×C3×C412yes—
117C22×Dic3C2×C3×C411yescharacteristic
118C22×Dic3C2×C3×C411yescharacteristic
119C2×Dic6—22no—
120C2×Dic6—21no—
121C2×Dic6—21no—
122C2×Dic6C2×C3×C414yes—
123C3×M16—22no—
124C3×M16—22no—
125C3×M16—24no—
126C3×M16—34no—
127C3×M16—42no—
128C3×M16—62no—
129C3×M16C4×D314yes—
130C3×M16C2×C3×C414yes—
131C2×C3×C8—22no—
132C2×C3×C8—22no—
133C2×C3×C8—42no—
134C2×C3×C8—62no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—42no—
138C3×C4⋊C4—64no—
139C3×C42—32no—
140C3×C42—32no—
141C3×C42—62no—
142C3×C42—62no—
143Dic3⋊C4—24no—
144C4×Dic3—22no—
145C4×Dic3—22no—
146C4×Dic3C3×D412yes—
147C4×Dic3C3×D412yes—
148#208—22no—
149#208C2×C3×C414yes—
150C2×C3⋊C8—22no—
151C22×C32—21no—
152C22×C32—21no—
153C22×C32C2×C4211yescharacteristic
154C22×C32C2×C22⋊C411yescharacteristic
155C22×C32#11711yescharacteristic
156C32×C4—42no—
157C32×C4C4×D412yes—
158C32×C4C4×D412yes—
159C3×Dic3—24no—
160C3×Dic3—21no—
161C3×Dic3—22no—
162C3×Dic3#10112yescomplemented
163C22×Q8—31no—
164C2×M16—32no—
165C2×M16C2×C3×D312yes—
166C4×Q8—62no—
167C4×Q8—62no—
168C2×C4⋊C4—32no—
169C2×C4⋊C4C2×C3×D311yescharacteristic
170C2×C42—31no—
171C2×C42—32no—
172#101—38no—
173#97—62no—
174C4×C8—62no—
175C23×C3—21no—
176C23×C3C2×C4×D311yescharacteristic
177C23×C3C22×C3×C411yescharacteristic
178C3×Q8—64no—
179C3×Q8—64no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—31no—
187C2×C3×C4—34no—
188C2×C3×C4—31no—
189C2×C3×C4—32no—
190C2×C3×C4—42no—
191C2×C3×C4—42no—
192C2×C3×C4—42no—
193C2×C3×C4—62no—
194C2×C3×C4—62no—
195C2×C3×C4—62no—
196C2×C3×C4—82no—
197C2×C3×C4—121no—
198C2×C3×C4C2×C4×D312yes—
199C2×C3×C4D3×D412yes—
200C2×C3×C4#23711yescharacteristic
201C2×C3×C4#23911yescharacteristic
202C2×C3×C4C22×C3×C412yes—
203C2×C3×C4C2×C3×D412yes—
204C2×C3×C4C3×#4111yescharacteristic
205C2×C3×C4C3×#4111yescharacteristic
206C2×Dic3—22no—
207C2×Dic3—22no—
208C2×Dic3—22no—
209C2×Dic3—41no—
210C2×Dic3C3×C4214yes—
211C2×Dic3C3×C22⋊C411yescharacteristic
212C2×Dic3C3×C22⋊C412yes—
213C2×Dic3C3×C22⋊C411yescharacteristic
214Dic6—24no—
215Dic6—24no—
216C3×C8—24no—
217C3×C8—24no—
218C3×C8—44no—
219C3×C8—64no—
220C3⋊C8—24no—
221C2×C32—21no—
222C2×C32—21no—
223C2×C32C4×C22⋊C411yescharacteristic
224C2×C32C2×#10111yescharacteristic
225C2×C32#41311yescharacteristic
226C2×Q8—34no—
227C2×Q8—62no—
228C2×Q8—61no—
229C2×Q8—61no—
230C22×C4—31no—
231C22×C4—32no—
232C22×C4—31no—
233C22×C4C3×C4×D312yes—
234C22×C4C22×C3×D311yescharacteristic
235M16—22no—
236M16—34no—
237M16—62no—
238M16C3×C4×D314yes—
239C2×C8—22no—
240C2×C8—62no—
241C4⋊C4—22no—
242C4⋊C4—64no—
243C42—32no—
244C42—32no—
245C42—62no—
246C42—62no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3C42×D311yescharacteristic
257C22×C3D3×C22⋊C411yescharacteristic
258C22×C3#89211yescharacteristic
259C22×C3C2×C3×C4211yescharacteristic
260C22×C3C2×C3×C22⋊C411yescharacteristic
261C22×C3C3×#11711yescharacteristic
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—32no—
265C3×C4—42no—
266C3×C4—42no—
267C3×C4—64no—
268C3×C4—62no—
269C3×C4—61no—
270C3×C4—82no—
271C3×C4#67⋊C412yes—
272C3×C4#89312yes—
273C3×C4C3×C4×D412yes—
274C3×C4C3×C4×D412yes—
275Dic3—24no—
276Dic3—21no—
277Dic3—22no—
278Dic3C3×#10112yescomplemented
279C32C4×#10111yescharacteristic, complemented, Sylow
280C23C2×C3×C4×D311yescharacteristic
281Q8—64no—
282Q8—64no—
283C2×C4—22no—
284C2×C4—31no—
285C2×C4—31no—
286C2×C4—32no—
287C2×C4—34no—
288C2×C4—42no—
289C2×C4—62no—
290C2×C4—62no—
291C2×C4—62no—
292C2×C4—121no—
293C2×C4C2×C3×C4×D312yes—
294C2×C4C3×D3×D412yes—
295C2×C4C3×#23711yescharacteristic
296C2×C4C3×#23911yescharacteristic
297C8—24no—
298C8—64no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—41no—
307C2×C3—41no—
308C2×C3#466611yescharacteristic
309C2×C3#474511yescharacteristic
310C2×C3D3×#10111yescharacteristic
311C2×C3C3×C4×C22⋊C411yescharacteristic
312C2×C3C2×C3×#10111yescharacteristic
313C2×C3C3×#41311yescharacteristic
314C22—21no—
315C22—21no—
316C22C3×C42×D311yescharacteristic
317C22C3×D3×C22⋊C411yescharacteristic
318C22C3×#89211yescharacteristic
319C4—32no—
320C4—42no—
321C4—64no—
322C4—62no—
323C4—61no—
324C4C3×#67⋊C412yes—
325C4C3×#89312yes—
326C3—21no—
327C3#6897311yescharacteristic, direct product factor
328C3C3×C4×#10111yescharacteristic, complemented
329C2—21no—
330C2—21no—
331C2C3×#466611yescharacteristic
332C2C3×#474511yescharacteristic
333C2C3×D3×#10111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#343D3
hypocenterC3C3×C4×#101
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
7. #68973C3direct (N × H)
17. C3×#824C4semidirect
76. #824C3×C4semidirect
162. C3×Dic3#101semidirect
278. Dic3C3×#101semidirect
279. C32C4×#101semidirect
327. C3#68973direct (N × H)
328. C3C3×C4×#101semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C2×C3×#8242
C3×Dic3×M162
C32×#3432
C3×#45302
C3×C4×#1013
#689733