Finite Group Databasebeta

← C3×#71901 #11794267

Subgroups — C3×#71901 #11794267

Order 1152.

563 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#544C211yesmaximal, characteristic
2C3×#4995C212yesmaximal
3C3×#4977C211yesmaximal, characteristic
4C3×#4532C212yesmaximal
5C3×#4530C211yesmaximal, characteristic
6C3×#2061—31nomaximal
7#71901C311yesmaximal, characteristic, direct product factor
8C32×C4⋊Q8—22no—
9C32×#125—22no—
10C32×C22⋊Q8—22no—
11C32×#117C2212yes—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2212yes—
16C3×C3⋊#95—22no—
17C3×#808—22no—
18C3×#807—22no—
19C3×#544—21no—
20C3×#544D311yescharacteristic
21C3×#544C2×C311yescharacteristic
22C3×#428—32no—
23C3×#382—31no—
24#4995C2×C312yes—
25#4977C2×C311yescharacteristic
26C3×#343—31no—
27C3×#339—32no—
28#4532C2×C312yes—
29#4530C2×C311yescharacteristic
30C2×C32×Q8—22no—
31C22×C32×C4D412yes—
32C22×C32×C4C2311yescharacteristic
33C22×C3×Dic3—21no—
34C22×C3×Dic3—21no—
35C32×C4⋊C4—22no—
36C32×C4⋊C4—24no—
37C32×C4⋊C4—22no—
38C32×C4⋊C4D412yes—
39C32×C4⋊C4D412yes—
40C32×C22⋊C4—22no—
41C32×C42—22no—
42C3×C4⋊Dic3—22no—
43C3×C4×Dic3—21no—
44C3×C4×Dic3Q812yescomplemented
45C3×#208—22no—
46C3×#208Q814yescomplemented
47C2×C3×C3⋊C8—22no—
48#2061—31noSylow
49C2×C3×M16—32no—
50C3×C4⋊Q8—24no—
51C3×C4⋊Q8—22no—
52C3×C4⋊Q8—22no—
53C3×#125—24no—
54C3×#125—22no—
55C3×#125—22no—
56C3×C22⋊Q8—24no—
57C3×C22⋊Q8—22no—
58C3×C22⋊Q8—22no—
59C3×#117—22no—
60C3×#117C2×D312yes—
61C3×#117C22×C312yes—
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4—31no—
64C2×C3×C4⋊C4C2×D311yescharacteristic
65C2×C3×C4⋊C4C22×C311yescharacteristic
66C2×C3×C42—31no—
67C2×C4⋊Dic3C22×C311yescharacteristic
68C2×C4×Dic3C22×C311yescharacteristic
69C2×#208C22×C312yes—
70C3×#107—62no—
71C3×#106—62no—
72C3×#95—62no—
73C3⋊#95—22no—
74#808—22no—
75#807—22no—
76C23×C32C2×D411yescharacteristic
77C32×Q8—82no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4—22no—
81C2×C32×C4—42no—
82C2×C32×C4C2×D412yes—
83C2×C32×C4C2×Q812yes—
84C2×C32×C4C2×Q811yescharacteristic
85C2×C32×C4#4111yescharacteristic
86C2×C3×Dic3—22no—
87C2×C3×Dic3—41no—
88C2×C3×Dic3—41no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—41no—
91C3×C3⋊C8—24no—
92#544C3×D311yescharacteristic
93#428—32no—
94#382—31no—
95#343—31no—
96#339—32no—
97C2×C3×Q8—24no—
98C2×C3×Q8—22no—
99C2×C3×Q8—22no—
100C22×C3×C4—22no—
101C22×C3×C4—21no—
102C22×C3×C4—61no—
103C22×C3×C4—61no—
104C22×C3×C4#6712yes—
105C22×C3×C4C3×D412yes—
106C22×C3×C4C22×D311yescharacteristic
107C22×C3×C4C23×C311yescharacteristic
108C22×Dic3—21no—
109C22×Dic3—21no—
110C3×M16—34no—
111C3×M16—62no—
112C2×C3×C8—62no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—24no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—28no—
118C3×C4⋊C4—24no—
119C3×C4⋊C4—24no—
120C3×C4⋊C4—22no—
121C3×C4⋊C4—22no—
122C3×C4⋊C4—22no—
123C3×C4⋊C4—22no—
124C3×C4⋊C4—62no—
125C3×C4⋊C4#6712yes—
126C3×C4⋊C4#6712yes—
127C3×C4⋊C4C3×D412yes—
128C3×C4⋊C4C3×D412yes—
129C3×C22⋊C4—24no—
130C3×C22⋊C4—22no—
131C3×C22⋊C4—22no—
132C3×C42—24no—
133C3×C42—22no—
134C3×C42—22no—
135C3×C42—32no—
136C3×C42—61no—
137C4⋊Dic3—22no—
138C4×Dic3—21no—
139C4×Dic3C3×Q812yescomplemented
140#208—22no—
141#208C3×Q814yescomplemented
142C2×C3⋊C8—22no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32#12011yescharacteristic
146C22×C32C22⋊Q811yescharacteristic
147C22×C32C4⋊Q811yescharacteristic
148C32×C4—42no—
149C32×C4—42no—
150C32×C4—42no—
151C32×C4C22⋊Q812yes—
152C32×C4C4⋊Q812yes—
153C3×Dic3—42no—
154C3×Dic3—81no—
155C2×M16—32no—
156C4⋊Q8—22no—
157#125—22no—
158C22⋊Q8—22no—
159#117C2×C3×D312yes—
160C2×C4⋊C4—31no—
161C2×C4⋊C4C2×C3×D311yescharacteristic
162C2×C42—31no—
163#107—62no—
164#106—62no—
165#95—62no—
166C23×C3—21no—
167C23×C3C2×#6711yescharacteristic
168C23×C3C2×C3×D411yescharacteristic
169C3×Q8—84no—
170C3×Q8—82no—
171C3×Q8—82no—
172C2×C3×C4—24no—
173C2×C3×C4—24no—
174C2×C3×C4—24no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—21no—
182C2×C3×C4—22no—
183C2×C3×C4—21no—
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4—42no—
187C2×C3×C4—62no—
188C2×C3×C4—82no—
189C2×C3×C4—121no—
190C2×C3×C4—121no—
191C2×C3×C4—122no—
192C2×C3×C4—121no—
193C2×C3×C4D3×Q811yescharacteristic
194C2×C3×C4D3×Q812yes—
195C2×C3×C4#23911yescharacteristic
196C2×C3×C4C2×#6712yes—
197C2×C3×C4C2×C3×D412yes—
198C2×C3×C4C2×C3×Q812yes—
199C2×C3×C4C2×C3×Q811yescharacteristic
200C2×C3×C4C3×#4111yescharacteristic
201C2×Dic3—22no—
202C2×Dic3—41no—
203C2×Dic3—41no—
204C2×Dic3—42no—
205C2×Dic3—41no—
206C3×C8—64no—
207C3⋊C8—24no—
208C2×C32—21no—
209C2×C32—21no—
210C2×C32#39511yescharacteristic
211C2×C32#45411yescharacteristic
212C2×C32#45511yescharacteristic
213C2×Q8—22no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4C3×#6712yes—
217C22×C4C22×C3×D311yescharacteristic
218M16—34no—
219M16—62no—
220C2×C8—62no—
221C4⋊C4—22no—
222C4⋊C4—24no—
223C4⋊C4—22no—
224C4⋊C4—62no—
225C4⋊C4C3×#6712yes—
226C4⋊C4C3×#6712yes—
227C22⋊C4—22no—
228C42—22no—
229C42—32no—
230C42—61no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—41no—
239C22×C3—41no—
240C22×C3#94411yescharacteristic
241C22×C3#94611yescharacteristic
242C22×C3#95311yescharacteristic
243C22×C3C3×#12011yescharacteristic
244C22×C3C3×C22⋊Q811yescharacteristic
245C22×C3C3×C4⋊Q811yescharacteristic
246C3×C4—22no—
247C3×C4—22no—
248C3×C4—44no—
249C3×C4—44no—
250C3×C4—44no—
251C3×C4—42no—
252C3×C4—42no—
253C3×C4—42no—
254C3×C4—42no—
255C3×C4—42no—
256C3×C4—42no—
257C3×C4—122no—
258C3×C4—241no—
259C3×C4#94412yes—
260C3×C4#94612yes—
261C3×C4C3×C22⋊Q812yes—
262C3×C4C3×C4⋊Q812yes—
263Dic3—42no—
264Dic3—81no—
265C32#206111yescharacteristic, complemented, Sylow
266C23C2×C3×#6711yescharacteristic
267Q8—82no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—42no—
272C2×C4—62no—
273C2×C4—121no—
274C2×C4—121no—
275C2×C4—122no—
276C2×C4—121no—
277C2×C4C3×D3×Q811yescharacteristic
278C2×C4C3×D3×Q812yes—
279C2×C4C3×#23911yescharacteristic
280C2×C4C2×C3×#6712yes—
281C8—64no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—41no—
290C2×C3—41no—
291C2×C3#523011yescharacteristic
292C2×C3#524211yescharacteristic
293C2×C3#524511yescharacteristic
294C2×C3C3×#39511yescharacteristic
295C2×C3C3×#45411yescharacteristic
296C2×C3C3×#45511yescharacteristic
297C22—21no—
298C22—21no—
299C22C3×#94411yescharacteristic
300C22C3×#94611yescharacteristic
301C22C3×#95311yescharacteristic
302C4—42no—
303C4—42no—
304C4—42no—
305C4—122no—
306C4—241no—
307C4C3×#94412yes—
308C4C3×#94612yes—
309C3—21no—
310C3#7190111yescharacteristic, direct product factor
311C3C3×#206111yescharacteristic, complemented
312C2—21no—
313C2—21no—
314C2C3×#523011yescharacteristic
315C2C3×#524211yescharacteristic
316C2C3×#524511yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#544C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC3×#544D3
hypocenterC3C3×#2061
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#544

Complements

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

NH ≅ G/Ntype
7. #71901C3direct (N × H)
44. C3×C4×Dic3Q8semidirect
46. C3×#208Q8semidirect
139. C4×Dic3C3×Q8semidirect
141. #208C3×Q8semidirect
265. C32#2061semidirect
310. C3#71901direct (N × H)
311. C3C3×#2061semidirect

Maximal subgroups

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

subgroupindex
C32×#5442
C3×#49952
C3×#49772
C3×#45322
C3×#45302
C3×#20613
#719013