Finite Group Databasebeta

← C3×#68888 #11792011

Subgroups — C3×#68888 #11792011

Order 1152.

841 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic12C211yesmaximal, characteristic, complemented
2C2×C3×#897C212yesmaximal
3C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
4C2×C3×#810C212yesmaximal, complemented
5C32×#340C211yesmaximal, characteristic, complemented
6C3×#2001—31nomaximal
7#68888C311yesmaximal, characteristic, direct product factor
8C22×C3×C4×D3C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10C22×C32×C8C2211yescharacteristic
11C2×C32×C4⋊C4C2212yes—
12C2×C3×(C2×D3)⋊C4—22no—
13C2×C3×C4⋊Dic3—22no—
14C22×C3×C3⋊C8C2211yescharacteristic
15C2×C3×Dic12—24no—
16C2×C3×Dic12—22no—
17C3×#897—24no—
18C3×#897—24no—
19C3×(C2×D3)⋊C8—22no—
20C3×#810—24no—
21C22×C3×Q16—31no—
22C2×C3×C22⋊Q8—32no—
23C22×Dic12C2×C311yescharacteristic, complemented
24C2×#897C2×C312yes—
25C2×C3×#103—32no—
26C2×C3×C22⋊C8—31no—
27C2×(C2×D3)⋊C8C2×C311yescharacteristic
28C2×#810C2×C312yescomplemented
29C3×#340—21no—
30C3×#340D311yescharacteristic, complemented
31C3×#340C2×C311yescharacteristic, complemented
32C23×C3×D3D411yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4C2311yescharacteristic
35C22×C3×Dic3—22no—
36C22×C3×Dic3D411yescharacteristic
37C2×C3×C4×D3—22no—
38C2×C3×C4×D3—22no—
39C2×C3×C4×D3—21no—
40C2×C3×C4×D3—21no—
41C2×C3×Dic6—22no—
42C2×C3×Dic6—22no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6—22no—
45C2×C3×Dic6—22no—
46C2×C3×Dic6D414yes—
47C2×C32×C8—22no—
48C2×C32×C8D412yes—
49C32×C4⋊C4—22no—
50C32×C4⋊C4D414yes—
51C3×(C2×D3)⋊C4—28no—
52C3×C4⋊Dic3—28no—
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—21no—
55C3×Dic12—28no—
56#2001—31noSylow
57C22×C3×Q8—32no—
58C23×C3×C4—31no—
59C22×C4×D3C22×C311yescharacteristic
60C22×Dic6C22×C312yes—
61C2×C3×Q16—64no—
62C2×C3×Q16—62no—
63C22×C3×C8—21no—
64C22×C3×C8—31no—
65C22×C3×C8C2×D311yescharacteristic
66C22×C3×C8C22×C311yescharacteristic
67C3×C22⋊Q8—64no—
68C3×C22⋊Q8—64no—
69C2×C3×C4⋊C4—22no—
70C2×C3×C4⋊C4—62no—
71C2×C3×C4⋊C4C2×D312yes—
72C2×C3×C4⋊C4C22×C312yes—
73C2×C3×C22⋊C4—62no—
74C2×(C2×D3)⋊C4—22no—
75C2×C4⋊Dic3—22no—
76C22×C3⋊C8C22×C311yescharacteristic
77C2×Dic12—24no—
78C2×Dic12—22no—
79#897—24no—
80#897—24no—
81C3×#103—64no—
82C3×C22⋊C8—62no—
83(C2×D3)⋊C8—22no—
84#810—24no—
85C23×C32C2×D411yescharacteristic
86C22×C3×D3—22no—
87C22×C3×D3—21no—
88C22×C3×D3—21no—
89C22×C3×D3—22no—
90C22×C3×D3Q1612yescomplemented
91C2×C32×C4—24no—
92C2×C32×C4—42no—
93C2×C32×C4—42no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D412yes—
96C2×C32×C4C2×D412yes—
97C2×C32×C4#4111yescharacteristic
98C2×C3×Dic3—22no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—42no—
103C3×C4×D3—41no—
104C3×C4×D3—42no—
105C3×C4×D3—41no—
106C3×Dic6—24no—
107C3×Dic6—24no—
108C3×Dic6—42no—
109C3×Dic6—42no—
110C32×C8—22no—
111C3×C3⋊C8—41no—
112C22×Q16—31no—
113C2×C22⋊Q8—32no—
114C2×#103—32no—
115C2×C22⋊C8—31no—
116#340C3×D311yescharacteristic, complemented
117C24×C3—31no—
118C23×D3C3×D411yescharacteristic
119C2×C3×Q8—34no—
120C2×C3×Q8—62no—
121C2×C3×Q8—62no—
122C2×C3×Q8—62no—
123C2×C3×Q8—62no—
124C2×C3×Q8—62no—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C22×C3×C4—21no—
128C22×C3×C4—31no—
129C22×C3×C4—42no—
130C22×C3×C4—62no—
131C22×C3×C4—61no—
132C22×C3×C4—62no—
133C22×C3×C4—62no—
134C22×C3×C4—61no—
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C23×C311yescharacteristic
137C22×Dic3—22no—
138C22×Dic3C3×D411yescharacteristic
139C2×C4×D3—21no—
140C2×C4×D3—22no—
141C2×C4×D3—22no—
142C2×C4×D3—21no—
143C2×Dic6—22no—
144C2×Dic6—22no—
145C2×Dic6—22no—
146C2×Dic6—22no—
147C2×Dic6—22no—
148C2×Dic6C3×D414yes—
149C3×Q16—68no—
150C2×C3×C8—22no—
151C2×C3×C8—22no—
152C2×C3×C8—22no—
153C2×C3×C8—42no—
154C2×C3×C8—61no—
155C2×C3×C8—62no—
156C2×C3×C8D1212yes—
157C2×C3×C8C3×D412yes—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—24no—
161C3×C4⋊C4—42no—
162C3×C4⋊C4—68no—
163C3×C4⋊C4D1214yes—
164C3×C4⋊C4C3×D414yes—
165C3×C22⋊C4—68no—
166(C2×D3)⋊C4—28no—
167C4⋊Dic3—28no—
168C2×C3⋊C8—22no—
169C2×C3⋊C8—21no—
170Dic12—28no—
171C22×C32#12012yes—
172C22×C32#12111yescharacteristic
173C22×C32C2×Q1611yescharacteristic
174C22×C32#13511yescharacteristic
175C22×C32#13712yes—
176C2×C3×D3—24no—
177C2×C3×D3—22no—
178C2×C3×D3—41no—
179C2×C3×D3—42no—
180C2×C3×D3—41no—
181C32×C4—44no—
182C32×C4#12011yescharacteristic
183C32×C4#12112yes—
184C32×C4#12711yescharacteristic
185C3×Dic3—44no—
186C3×Dic3—41no—
187C22×Q8—32no—
188C23×C4—31no—
189C2×Q16—64no—
190C2×Q16—62no—
191C22×C8—31no—
192C22×C8C2×C3×D311yescharacteristic
193C22⋊Q8—64no—
194C22⋊Q8—64no—
195C2×C4⋊C4—62no—
196C2×C4⋊C4C2×C3×D312yes—
197C2×C22⋊C4—62no—
198#103—64no—
199C22⋊C8—62no—
200C23×C3—21no—
201C23×C3—32no—
202C23×C3—62no—
203C23×C3—61no—
204C23×C3—61no—
205C23×C3—62no—
206C23×C3D3×D411yescharacteristic
207C23×C3C2×C3×D411yescharacteristic
208C22×D3—22no—
209C22×D3—21no—
210C22×D3—21no—
211C22×D3—22no—
212C22×D3C3×Q1612yescomplemented
213C3×Q8—64no—
214C3×Q8—64no—
215C3×Q8—122no—
216C3×Q8—122no—
217C2×C3×C4—24no—
218C2×C3×C4—24no—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—22no—
222C2×C3×C4—21no—
223C2×C3×C4—44no—
224C2×C3×C4—42no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4—64no—
229C2×C3×C4—62no—
230C2×C3×C4—61no—
231C2×C3×C4—82no—
232C2×C3×C4—82no—
233C2×C3×C4—122no—
234C2×C3×C4—122no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×C3×C4—122no—
238C2×C3×C4C2×D1211yescharacteristic
239C2×C3×C4C2×D1212yes—
240C2×C3×C4D3×D412yes—
241C2×C3×C4#23911yescharacteristic
242C2×C3×C4C2×C3×D411yescharacteristic
243C2×C3×C4C2×C3×D412yes—
244C2×C3×C4C2×C3×D412yes—
245C2×C3×C4C3×#4111yescharacteristic
246C2×Dic3—22no—
247C2×Dic3—24no—
248C2×Dic3—21no—
249C2×Dic3—42no—
250C2×Dic3—42no—
251C4×D3—41no—
252C4×D3—42no—
253C4×D3—41no—
254Dic6—24no—
255Dic6—24no—
256Dic6—42no—
257Dic6—42no—
258C3×C8—22no—
259C3×C8—22no—
260C3×C8—42no—
261C3×C8—121no—
262C3⋊C8—41no—
263C2×C32#39211yescharacteristic
264C2×C32#45112yes—
265C2×C32#45212yes—
266C2×C32#46711yescharacteristic
267C2×C32#47011yescharacteristic
268C3×D3—42no—
269C24—31no—
270C2×Q8—34no—
271C2×Q8—62no—
272C2×Q8—62no—
273C2×Q8—62no—
274C2×Q8—62no—
275C2×Q8—62no—
276C22×C4—22no—
277C22×C4—31no—
278C22×C4—62no—
279C22×C4—61no—
280C22×C4—62no—
281C22×C4—62no—
282C22×C4—61no—
283C22×C4C22×C3×D311yescharacteristic
284Q16—68no—
285C2×C8—22no—
286C2×C8—61no—
287C2×C8—62no—
288C2×C8C3×D1212yes—
289C4⋊C4—22no—
290C4⋊C4—68no—
291C4⋊C4C3×D1214yes—
292C22⋊C4—68no—
293C22×C3—22no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—22no—
297C22×C3—21no—
298C22×C3—62no—
299C22×C3—64no—
300C22×C3—121no—
301C22×C3—121no—
302C22×C3—122no—
303C22×C3#88212yes—
304C22×C3#89511yescharacteristic
305C22×C3#91211yescharacteristic
306C22×C3#91512yes—
307C22×C3D3×Q1611yescharacteristic
308C22×C3C3×#12012yes—
309C22×C3C3×#12111yescharacteristic
310C22×C3C2×C3×Q1611yescharacteristic
311C22×C3C3×#13511yescharacteristic
312C22×C3C3×#13712yes—
313C2×D3—24no—
314C2×D3—22no—
315C2×D3—41no—
316C2×D3—42no—
317C2×D3—41no—
318C3×C4—21no—
319C3×C4—22no—
320C3×C4—21no—
321C3×C4—44no—
322C3×C4—44no—
323C3×C4—84no—
324C3×C4—121no—
325C3×C4—124no—
326C3×C4#87411yescharacteristic
327C3×C4#88211yescharacteristic
328C3×C4#89512yes—
329C3×C4C3×#12011yescharacteristic
330C3×C4C3×#12112yes—
331C3×C4C3×#12711yescharacteristic
332Dic3—44no—
333Dic3—41no—
334C32#200111yescharacteristic, complemented, Sylow
335C23—32no—
336C23—62no—
337C23—61no—
338C23—61no—
339C23—62no—
340C23C3×D3×D411yescharacteristic
341Q8—64no—
342Q8—64no—
343Q8—122no—
344Q8—122no—
345C2×C4—24no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—64no—
349C2×C4—62no—
350C2×C4—61no—
351C2×C4—122no—
352C2×C4—122no—
353C2×C4—121no—
354C2×C4—122no—
355C2×C4—121no—
356C2×C4C2×C3×D1211yescharacteristic
357C2×C4C2×C3×D1212yes—
358C2×C4C3×D3×D412yes—
359C2×C4C3×#23911yescharacteristic
360C8—22no—
361C8—121no—
362C2×C3—21no—
363C2×C3—22no—
364C2×C3—22no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—122no—
368C2×C3#467111yescharacteristic
369C2×C3#478312yes—
370C2×C3#480912yes—
371C2×C3#486711yescharacteristic
372C2×C3#488711yescharacteristic
373C2×C3C3×#39211yescharacteristic
374C2×C3C3×#45112yes—
375C2×C3C3×#45212yes—
376C2×C3C3×#46711yescharacteristic
377C2×C3C3×#47011yescharacteristic
378D3—42no—
379C22—64no—
380C22—62no—
381C22—121no—
382C22—122no—
383C22—121no—
384C22C3×#88212yes—
385C22C3×#89511yescharacteristic
386C22C3×#91211yescharacteristic
387C22C3×#91512yes—
388C22C3×D3×Q1611yescharacteristic
389C4—44no—
390C4—121no—
391C4—124no—
392C4C3×#87411yescharacteristic
393C4C3×#88211yescharacteristic
394C4C3×#89512yes—
395C3—21no—
396C3#6888811yescharacteristic, direct product factor
397C3C3×#200111yescharacteristic, complemented
398C2—122no—
399C2C3×#467111yescharacteristic
400C2C3×#478312yes—
401C2C3×#480912yes—
402C2C3×#486711yescharacteristic
403C2C3×#488711yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC3×#340D3
hypocenterC3C3×#2001
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C3×#340

Complements

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

NH ≅ G/Ntype
1. C22×C3×Dic12C2semidirect
4. C2×C3×#810C2semidirect
5. C32×#340C2semidirect
7. #68888C3direct (N × H)
23. C22×Dic12C2×C3semidirect
28. C2×#810C2×C3semidirect
30. C3×#340D3semidirect
31. C3×#340C2×C3semidirect
90. C22×C3×D3Q16semidirect
116. #340C3×D3semidirect
212. C22×D3C3×Q16semidirect
334. C32#2001semidirect
396. C3#68888direct (N × H)
397. C3C3×#2001semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic122
C2×C3×#8972
C2×C3×(C2×D3)⋊C82
C2×C3×#8102
C32×#3402
C3×#20013
#688883