Finite Group Databasebeta

← C3×#69987 #11795360

Subgroups — C3×#69987 #11795360

Order 1152.

539 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 539 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#407C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3C3×#5125C211yesmaximal, characteristic, complemented
4C3×#5124C212yesmaximal, complemented
5C3×C3⋊#338C211yesmaximal, characteristic, complemented
6C3×#2091—31nomaximal
7#69987C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C2×C32×M16C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C2×C3×#208C2212yes—
12C2×C3×#208C2212yes—
13C32×C22⋊C8—22no—
14C3×#830—24no—
15C3×#822—24no—
16C3×#819—22no—
17C3×#430—32no—
18C3×#430—31no—
19C3×#407—21no—
20C3×#407—32no—
21C3×#407D311yescharacteristic
22C3×#407C2×C311yescharacteristic
23#5207C2×C312yes—
24#5125C2×C311yescharacteristic, complemented
25#5124C2×C312yescomplemented
26C3×#338—31no—
27C3⋊#338C2×C311yescharacteristic, complemented
28C24×C32Q811yescharacteristic
29C22×C32×C4—21no—
30C22×C32×C4—22no—
31C22×C32×C4—21no—
32C22×C32×C4—22no—
33C22×C32×C4Q811yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C32×M16—22no—
36C32×M16—22no—
37C2×C32×C8—21no—
38C2×C32×C8D412yes—
39C3×#208—22no—
40C3×#208—22no—
41C3×#208—22no—
42C3×#208—22no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8D414yes—
45#2091—31noSylow
46C23×C3×C4—21no—
47C23×C3×C4C2×D311yescharacteristic
48C23×C3×C4C22×C311yescharacteristic
49C2×C3×M16—21no—
50C2×C3×M16—21no—
51C2×C3×M16—32no—
52C2×C3×M16—32no—
53C2×C3×M16C2×D311yescharacteristic
54C2×C3×M16C2×D311yescharacteristic
55C2×C3×M16C22×C311yescharacteristic
56C2×C3×M16C22×C311yescharacteristic
57C2×#208C22×C312yes—
58C2×#208C22×C312yes—
59C3×#108—64no—
60C3×#108—62no—
61C3×C22⋊C8—24no—
62C3×C22⋊C8—22no—
63C3×C22⋊C8—22no—
64C3×C22⋊C8—64no—
65#830—24no—
66#822—24no—
67#819—22no—
68C23×C32—21no—
69C23×C32—22no—
70C23×C32—42no—
71C23×C32C2×Q811yescharacteristic
72C2×C32×C4—21no—
73C2×C32×C4—22no—
74C2×C32×C4—42no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4C2×D412yes—
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4#4111yescharacteristic
80C2×C32×C4#4112yes—
81C32×C8—22no—
82C32×C8—41no—
83C3×C3⋊C8—24no—
84C3×C3⋊C8—42no—
85#430—32no—
86#430—31no—
87#407—32no—
88#407C3×D311yescharacteristic
89#338—31no—
90C24×C3—21no—
91C24×C3Dic611yescharacteristic
92C24×C3C3×Q811yescharacteristic
93C22×C3×C4—22no—
94C22×C3×C4—22no—
95C22×C3×C4—21no—
96C22×C3×C4—22no—
97C22×C3×C4—22no—
98C22×C3×C4—21no—
99C22×C3×C4—22no—
100C22×C3×C4—21no—
101C22×C3×C4—21no—
102C22×C3×C4—22no—
103C22×C3×C4—21no—
104C22×C3×C4—21no—
105C22×C3×C4—42no—
106C22×C3×C4—42no—
107C22×C3×C4Dic611yescharacteristic
108C22×C3×C4C3×Q811yescharacteristic
109C22×C3×C4C22×D311yescharacteristic
110C22×C3×C4C23×C311yescharacteristic
111C3×M16—22no—
112C3×M16—22no—
113C3×M16—22no—
114C3×M16—22no—
115C3×M16—42no—
116C3×M16—42no—
117C3×M16—62no—
118C3×M16—62no—
119C3×M16—62no—
120C3×M16—62no—
121C2×C3×C8—22no—
122C2×C3×C8—21no—
123C2×C3×C8—21no—
124C2×C3×C8—22no—
125C2×C3×C8—34no—
126C2×C3×C8—62no—
127C2×C3×C8#6712yes—
128C2×C3×C8C3×D412yes—
129#208—22no—
130#208—22no—
131#208—22no—
132#208—22no—
133C2×C3⋊C8—22no—
134C2×C3⋊C8C3×D414yes—
135C22×C32—22no—
136C22×C32—24no—
137C22×C32—41no—
138C22×C32—41no—
139C22×C32—42no—
140C22×C32—41no—
141C22×C32C22⋊Q812yes—
142C22×C32C22⋊Q811yescharacteristic
143C32×C4—41no—
144C32×C4#12312yes—
145C32×C4#12311yescharacteristic
146C32×C4#12711yescharacteristic
147C23×C4C2×C3×D311yescharacteristic
148C2×M16—32no—
149C2×M16—32no—
150C2×M16C2×C3×D311yescharacteristic
151C2×M16C2×C3×D311yescharacteristic
152#108—64no—
153#108—62no—
154C22⋊C8—22no—
155C22⋊C8—64no—
156C23×C3—22no—
157C23×C3—22no—
158C23×C3—21no—
159C23×C3—22no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—42no—
163C23×C3—42no—
164C23×C3—42no—
165C23×C3—44no—
166C23×C3C2×Dic611yescharacteristic
167C23×C3C2×C3×Q811yescharacteristic
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—21no—
171C2×C3×C4—22no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—21no—
177C2×C3×C4—42no—
178C2×C3×C4—44no—
179C2×C3×C4—42no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—42no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4#23511yescharacteristic
188C2×C3×C4D3×D412yes—
189C2×C3×C4#23712yes—
190C2×C3×C4C2×#6711yescharacteristic
191C2×C3×C4C2×C3×D412yes—
192C2×C3×C4C2×C3×D411yescharacteristic
193C2×C3×C4C3×#4111yescharacteristic
194C2×C3×C4C3×#4112yes—
195C3×C8—22no—
196C3×C8—22no—
197C3×C8—42no—
198C3×C8—42no—
199C3×C8—41no—
200C3×C8—41no—
201C3×C8—64no—
202C3×C8—122no—
203C3⋊C8—24no—
204C3⋊C8—42no—
205C2×C32—21no—
206C2×C32—22no—
207C2×C32—42no—
208C2×C32#39911yescharacteristic
209C24C3×Dic611yescharacteristic
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—21no—
214C22×C4C3×Dic611yescharacteristic
215C22×C4C22×C3×D311yescharacteristic
216M16—22no—
217M16—22no—
218M16—62no—
219M16—62no—
220M16—62no—
221M16—62no—
222C2×C8—21no—
223C2×C8—34no—
224C2×C8—62no—
225C2×C8C3×#6712yes—
226C22×C3—24no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3—24no—
230C22×C3—24no—
231C22×C3—22no—
232C22×C3—21no—
233C22×C3—44no—
234C22×C3—41no—
235C22×C3—41no—
236C22×C3—42no—
237C22×C3—42no—
238C22×C3—42no—
239C22×C3—42no—
240C22×C3—41no—
241C22×C3—42no—
242C22×C3—41no—
243C22×C3—44no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3#87812yes—
247C22×C3#92411yescharacteristic
248C22×C3C3×C22⋊Q812yes—
249C22×C3C3×C22⋊Q811yescharacteristic
250C3×C4—22no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—42no—
254C3×C4—41no—
255C3×C4—41no—
256C3×C4#88312yes—
257C3×C4#93511yescharacteristic
258C3×C4#94011yescharacteristic
259C3×C4C3×#12312yes—
260C3×C4C3×#12311yescharacteristic
261C3×C4C3×#12711yescharacteristic
262C32#209111yescharacteristic, complemented, Sylow
263C23—22no—
264C23—21no—
265C23—42no—
266C23C2×C3×Dic611yescharacteristic
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4C3×#23511yescharacteristic
273C2×C4C3×D3×D412yes—
274C2×C4C3×#23712yes—
275C2×C4C2×C3×#6711yescharacteristic
276C8—22no—
277C8—41no—
278C8—64no—
279C8—122no—
280C2×C3—22no—
281C2×C3—22no—
282C2×C3—21no—
283C2×C3—22no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—42no—
287C2×C3—44no—
288C2×C3—42no—
289C2×C3—42no—
290C2×C3#494911yescharacteristic
291C2×C3C3×#39911yescharacteristic
292C22—22no—
293C22—24no—
294C22—41no—
295C22—42no—
296C22—41no—
297C22—41no—
298C22C3×#87812yes—
299C22C3×#92411yescharacteristic
300C4—41no—
301C4C3×#88312yes—
302C4C3×#93511yescharacteristic
303C4C3×#94011yescharacteristic
304C3—21no—
305C3#6998711yescharacteristic, direct product factor
306C3C3×#209111yescharacteristic, complemented
307C2—22no—
308C2—21no—
309C2—42no—
310C2C3×#494911yescharacteristic
subgroupG/H
centerC3×C4#940
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#407C2
socleC2×C32#399
prime radicalC24×C32Q8
hypercenterC3×#407D3
hypocenterC3C3×#2091
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
3. C3×#5125C2semidirect
4. C3×#5124C2semidirect
5. C3×C3⋊#338C2semidirect
7. #69987C3direct (N × H)
24. #5125C2×C3semidirect
25. #5124C2×C3semidirect
27. C3⋊#338C2×C3semidirect
262. C32#2091semidirect
305. C3#69987direct (N × H)
306. C3C3×#2091semidirect

Maximal subgroups

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

subgroupindex
C32×#4072
C3×#52072
C3×#51252
C3×#51242
C3×C3⋊#3382
C3×#20913
#699873