Finite Group Databasebeta

← C3×#71862 #11796549

Subgroups — C3×#71862 #11796549

Order 1152.

691 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 691 conjugacy classes of subgroups — too many to draw. Only its 146 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×#535C211yesmaximal, characteristic
2C3×#5237C212yesmaximal, complemented
3C3×#4542C214yesmaximal, complemented
4C3×#2134—31nomaximal
5#71862C311yesmaximal, characteristic, direct product factor
6C2×C32×#41C2211yescharacteristic
7C22×C32×D4C411yescharacteristic
8C32×#127C412yes—
9C32×#124C2212yes—
10C32×#121—22no—
11C32×#120—22no—
12C32×#117C411yescharacteristic
13C2×C3×#208—22no—
14C3×#836C2214yescomplemented
15C3×#833—22no—
16C3×#535—21no—
17C3×#535D311yescharacteristic
18C3×#535C2×C311yescharacteristic
19C3×#413—32no—
20#5237C2×C312yescomplemented
21C3×#355—34no—
22#4542C2×C314yescomplemented
23C24×C32—21no—
24C32×#41—42no—
25C2×C32×Q8C2311yescharacteristic
26C2×C32×D4—24no—
27C2×C32×D4—21no—
28C2×C32×D4—42no—
29C2×C32×D4C2×C412yes—
30C2×C32×D4C2×C411yescharacteristic
31C2×C32×D4D412yes—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4D412yes—
34C32×C4⋊C4—21no—
35C32×C22⋊C4—21no—
36C32×C22⋊C4—24no—
37C32×C42C2×C412yes—
38C3×#208—24no—
39C3×#208—42no—
40C2×C3×C3⋊C8—42no—
41#2134—31noSylow
42C2×C3×#41—21no—
43C2×C3×#41C2×D311yescharacteristic
44C2×C3×#41C22×C311yescharacteristic
45C22×C3×D4—21no—
46C22×C3×D4Dic311yescharacteristic
47C22×C3×D4C3×C411yescharacteristic
48C2×C3×M16—62no—
49C3×#127—22no—
50C3×#127Dic312yes—
51C3×#127C3×C412yes—
52C3×#124—22no—
53C3×#124C2×D312yes—
54C3×#124C22×C312yes—
55C3×#121—24no—
56C3×#121—22no—
57C3×#121—22no—
58C3×#120—24no—
59C3×#120—22no—
60C3×#120—22no—
61C3×#117—21no—
62C3×#117Dic311yescharacteristic
63C3×#117C3×C411yescharacteristic
64C2×#208—22no—
65C3×#101—34no—
66C3×#100—62no—
67#836C22×C314yescomplemented
68#833—22no—
69C23×C32—22no—
70C23×C32—42no—
71C23×C32—82no—
72C23×C32C22⋊C411yescharacteristic
73C23×C32C22⋊C412yes—
74C32×Q8—41no—
75C32×D4—41no—
76C32×D4—42no—
77C32×D4—42no—
78C32×D4—42no—
79C32×D4—84no—
80C2×C32×C4—22no—
81C2×C32×C4—22no—
82C2×C32×C4—22no—
83C2×C32×C4—22no—
84C2×C32×C4C22⋊C411yescharacteristic
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D412yes—
87C3×C3⋊C8—44no—
88#535C3×D311yescharacteristic
89#413—32no—
90#355—34no—
91C24×C3—22no—
92C24×C3—21no—
93C24×C3—21no—
94C3×#41—42no—
95C3×#41—42no—
96C3×#41—44no—
97C2×C3×Q8—21no—
98C2×C3×Q8C22×D311yescharacteristic
99C2×C3×Q8C23×C311yescharacteristic
100C2×C3×D4—22no—
101C2×C3×D4—28no—
102C2×C3×D4—24no—
103C2×C3×D4—24no—
104C2×C3×D4—21no—
105C2×C3×D4—21no—
106C2×C3×D4—22no—
107C2×C3×D4—21no—
108C2×C3×D4—22no—
109C2×C3×D4—44no—
110C2×C3×D4—42no—
111C2×C3×D4—42no—
112C2×C3×D4C2×Dic312yes—
113C2×C3×D4C2×Dic311yescharacteristic
114C2×C3×D4#6712yes—
115C2×C3×D4C2×C3×C412yes—
116C2×C3×D4C2×C3×C411yescharacteristic
117C2×C3×D4C3×D412yes—
118C22×C3×C4—21no—
119C22×C3×C4—22no—
120C22×C3×C4C2×Dic311yescharacteristic
121C22×C3×C4#6712yes—
122C22×C3×C4C2×C3×C411yescharacteristic
123C22×C3×C4C3×D412yes—
124C3×M16—64no—
125C3×M16—122no—
126C2×C3×C8—122no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C22⋊C4—22no—
131C3×C22⋊C4—28no—
132C3×C22⋊C4—21no—
133C3×C22⋊C4—21no—
134C3×C22⋊C4—24no—
135C3×C22⋊C4—24no—
136C3×C42—22no—
137C3×C42C2×Dic312yes—
138C3×C42C2×C3×C412yes—
139#208—24no—
140#208—42no—
141C2×C3⋊C8—42no—
142C22×C32—21no—
143C22×C32—22no—
144C22×C32—42no—
145C22×C32—41no—
146C22×C32—44no—
147C22×C32—42no—
148C22×C32—84no—
149C22×C32C2×C22⋊C411yescharacteristic
150C32×C4—21no—
151C32×C4—22no—
152C32×C4—42no—
153C32×C4#9912yes—
154C2×#41C2×C3×D311yescharacteristic
155C22×D4C3×Dic311yescharacteristic
156C2×M16—62no—
157#127C3×Dic312yes—
158#124C2×C3×D312yes—
159#121—22no—
160#120—22no—
161#117C3×Dic311yescharacteristic
162#101—34no—
163#100—62no—
164C23×C3—24no—
165C23×C3—22no—
166C23×C3—22no—
167C23×C3—21no—
168C23×C3—22no—
169C23×C3—44no—
170C23×C3—42no—
171C23×C3—42no—
172C23×C3—82no—
173C23×C3—82no—
174C23×C3—84no—
175C23×C3#21711yescharacteristic
176C23×C3#21712yes—
177C23×C3C3×C22⋊C411yescharacteristic
178C23×C3C3×C22⋊C412yes—
179C3×Q8—41no—
180C3×Q8—41no—
181C3×Q8—42no—
182C3×D4—41no—
183C3×D4—42no—
184C3×D4—41no—
185C3×D4—42no—
186C3×D4—42no—
187C3×D4—42no—
188C3×D4—44no—
189C3×D4—44no—
190C3×D4—42no—
191C3×D4—44no—
192C3×D4—42no—
193C3×D4—42no—
194C3×D4—84no—
195C3×D4—84no—
196C3×D4—88no—
197C2×C3×C4—24no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—24no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—22no—
210C2×C3×C4—42no—
211C2×C3×C4—42no—
212C2×C3×C4#21711yescharacteristic
213C2×C3×C4C3×C22⋊C411yescharacteristic
214C2×C3×C4C22×Dic311yescharacteristic
215C2×C3×C4C2×#6712yes—
216C2×C3×C4C22×C3×C411yescharacteristic
217C2×C3×C4C2×C3×D412yes—
218C3×C8—124no—
219C3⋊C8—44no—
220C2×C32—21no—
221C2×C32—41no—
222C2×C32—42no—
223C2×C32—82no—
224C2×C32C2×#9911yescharacteristic
225C24—21no—
226#41—42no—
227C2×Q8C22×C3×D311yescharacteristic
228C2×D4—24no—
229C2×D4—21no—
230C2×D4—42no—
231C2×D4C2×C3×Dic312yes—
232C2×D4C2×C3×Dic311yescharacteristic
233C2×D4C3×#6712yes—
234C22×C4C2×C3×Dic311yescharacteristic
235C22×C4C3×#6712yes—
236M16—64no—
237M16—122no—
238C2×C8—122no—
239C4⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—24no—
242C42C2×C3×Dic312yes—
243C22×C3—22no—
244C22×C3—21no—
245C22×C3—22no—
246C22×C3—21no—
247C22×C3—22no—
248C22×C3—21no—
249C22×C3—42no—
250C22×C3—42no—
251C22×C3—42no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3—42no—
255C22×C3—44no—
256C22×C3—44no—
257C22×C3—48no—
258C22×C3—44no—
259C22×C3—44no—
260C22×C3—42no—
261C22×C3—42no—
262C22×C3—88no—
263C22×C3—84no—
264C22×C3—84no—
265C22×C3C2×#21711yescharacteristic
266C22×C3C2×C3×C22⋊C411yescharacteristic
267C3×C4—22no—
268C3×C4—22no—
269C3×C4—21no—
270C3×C4—22no—
271C3×C4—21no—
272C3×C4—22no—
273C3×C4—42no—
274C3×C4—44no—
275C3×C4—42no—
276C3×C4—42no—
277C3×C4#83412yes—
278C3×C4C3×#9912yes—
279C32#213411yescharacteristic, complemented, Sylow
280C23—22no—
281C23—42no—
282C23—82no—
283C23C3×#21711yescharacteristic
284C23C3×#21712yes—
285Q8—41no—
286D4—41no—
287D4—42no—
288D4—42no—
289D4—42no—
290D4—84no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4C3×#21711yescharacteristic
296C2×C4C22×C3×Dic311yescharacteristic
297C2×C4C2×C3×#6712yes—
298C8—124no—
299C2×C3—22no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—42no—
304C2×C3—41no—
305C2×C3—42no—
306C2×C3—41no—
307C2×C3—42no—
308C2×C3—82no—
309C2×C3—84no—
310C2×C3—82no—
311C2×C3—82no—
312C2×C3C2×#83411yescharacteristic
313C2×C3C2×C3×#9911yescharacteristic
314C22—21no—
315C22—22no—
316C22—42no—
317C22—41no—
318C22—44no—
319C22—42no—
320C22—84no—
321C22C2×C3×#21711yescharacteristic
322C4—22no—
323C4—21no—
324C4—42no—
325C4C3×#83412yes—
326C3—21no—
327C3#7186211yescharacteristic, direct product factor
328C3C3×#213411yescharacteristic, complemented
329C2—21no—
330C2—41no—
331C2—42no—
332C2—82no—
333C2C2×C3×#83411yescharacteristic
subgroupG/H
centerC2×C3C2×#834
commutatorC2×C3×C4C22×C3×C4
FrattiniC2×Q8C22×C3×D3
Fitting, prime radicalC32×#535C2
socleC2×C32C2×#99
cosocleC2×C3×Q8C23×C3
hypercenterC3×#535D3
hypocenterC3C3×#2134
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#535

Complements

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

NH ≅ G/Ntype
2. C3×#5237C2semidirect
3. C3×#4542C2semidirect
5. #71862C3direct (N × H)
14. C3×#836C22semidirect
20. #5237C2×C3semidirect
22. #4542C2×C3semidirect
67. #836C22×C3semidirect
279. C32#2134semidirect
327. C3#71862direct (N × H)
328. C3C3×#2134semidirect

Maximal subgroups

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

subgroupindex
C32×#5352
C3×#52372
C3×#45422
C3×#21343
#718623