Finite Group Databasebeta

← C3×#71813 #11775420

Subgroups — C3×#71813 #11775420

Order 1152.

659 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic
2C3×#4937C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4C3×#4537C214yesmaximal, complemented
5C3×#1514—31nomaximal
6#71813C311yesmaximal, characteristic, direct product factor
7C2×C32×#41—21no—
8C32×C4⋊Q8C411yescharacteristic, complemented
9C32×#127C411yescharacteristic, complemented
10C32×#124—21no—
11C32×#121—21no—
12C32×#121C2212yes—
13C32×C4×D4—21no—
14C32×C4×D4C412yescomplemented
15C2×C32×C42C2211yescharacteristic
16C3×C3⋊#95—21no—
17C3×C3⋊#95—21no—
18C3×C3⋊#95C2212yes—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×#803—21no—
22C3×#532—21no—
23C3×#532D311yescharacteristic
24C3×#532C2×C311yescharacteristic
25C3×#432—31no—
26C3×#383—31no—
27#4937C2×C311yescharacteristic, complemented
28#4926C2×C311yescharacteristic, complemented
29C3×#327—34no—
30#4537C2×C314yescomplemented
31C32×#41—44no—
32C2×C32×Q8—21no—
33C2×C32×D4—22no—
34C2×C32×D4—21no—
35C2×C32×D4—21no—
36C2×C32×D4C2×C412yes—
37C22×C32×C4—22no—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C22×C3×Dic3—22no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4C2×C412yes—
44C32×C22⋊C4—22no—
45C32×C22⋊C4—22no—
46C32×C42C2×C411yescharacteristic
47C32×C42C2×C411yescharacteristic
48C32×C42D411yescharacteristic
49C32×C42D411yescharacteristic
50C2×C3×C3⋊C8—22no—
51#1514—31noSylow
52C2×C3×#41—22no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C3×C4⋊Q8—21no—
56C3×C4⋊Q8Dic311yescharacteristic, complemented
57C3×C4⋊Q8C3×C411yescharacteristic, complemented
58C3×#127—21no—
59C3×#127Dic311yescharacteristic, complemented
60C3×#127C3×C411yescharacteristic, complemented
61C3×#124—22no—
62C3×#124—21no—
63C3×#124—21no—
64C3×#121—22no—
65C3×#121—21no—
66C3×#121—21no—
67C3×#121—22no—
68C3×#121C2×D312yes—
69C3×#121C22×C312yes—
70C3×C4×D4—22no—
71C3×C4×D4—21no—
72C3×C4×D4—21no—
73C3×C4×D4—22no—
74C3×C4×D4Dic312yescomplemented
75C3×C4×D4C3×C412yescomplemented
76C2×C3×C42—21no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C22×C311yescharacteristic
79C3×C4⋊C8—61no—
80C3×C22⋊C8—32no—
81C3×#97—61no—
82C3×#95—32no—
83C3×#95—61no—
84C3×#95—61no—
85C3⋊#95—21no—
86C3⋊#95—21no—
87C3⋊#95C22×C312yes—
88#830C22×C312yes—
89C4⋊(C3⋊C8)—21no—
90#803—21no—
91C23×C32—22no—
92C23×C32C2×D411yescharacteristic
93C32×Q8—42no—
94C32×D4—42no—
95C32×D4—42no—
96C32×D4—42no—
97C32×D4—44no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—44no—
103C2×C32×C4C22⋊C411yescharacteristic
104C2×C32×C4C22⋊C411yescharacteristic
105C2×C32×C4C22⋊C411yescharacteristic
106C2×C32×C4C22⋊C411yescharacteristic
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3×Dic3—42no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C3×C3⋊C8—42no—
113#532C3×D311yescharacteristic
114#432—31no—
115#383—31no—
116#327—34no—
117C3×#41—48no—
118C3×#41—44no—
119C3×#41—44no—
120C2×C3×Q8—22no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×D4—22no—
124C2×C3×D4—24no—
125C2×C3×D4—22no—
126C2×C3×D4—22no—
127C2×C3×D4—22no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—22no—
133C2×C3×D4C2×Dic312yes—
134C2×C3×D4C2×C3×C412yes—
135C22×C3×C4—24no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—62no—
142C22×C3×C4#6711yescharacteristic
143C22×C3×C4#6711yescharacteristic
144C22×C3×C4C3×D411yescharacteristic
145C22×C3×C4C3×D411yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C23×C311yescharacteristic
148C22×Dic3—22no—
149C2×C3×C8—62no—
150C3×C4⋊C4—22no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4C2×Dic312yes—
155C3×C4⋊C4C2×C3×C412yes—
156C3×C22⋊C4—24no—
157C3×C22⋊C4—24no—
158C3×C22⋊C4—22no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—22no—
161C3×C22⋊C4—22no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—21no—
166C3×C42C2×Dic311yescharacteristic
167C3×C42C2×Dic311yescharacteristic
168C3×C42#6711yescharacteristic
169C3×C42#6711yescharacteristic
170C3×C42C2×C3×C411yescharacteristic
171C3×C42C2×C3×C411yescharacteristic
172C3×C42C3×D411yescharacteristic
173C3×C42C3×D411yescharacteristic
174C2×C3⋊C8—22no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32—42no—
178C22×C32—42no—
179C22×C32—42no—
180C22×C32C2×C22⋊C411yescharacteristic
181C22×C32AGL(1,ℤ/8)12yes—
182C32×C4—21no—
183C32×C4—21no—
184C32×C4—21no—
185C32×C4—21no—
186C32×C4—21no—
187C32×C4—21no—
188C32×C4—42no—
189C3×Dic3—82no—
190C2×#41—21no—
191C4⋊Q8C3×Dic311yescharacteristic, complemented
192#127C3×Dic311yescharacteristic, complemented
193#124—21no—
194#121—21no—
195#121C2×C3×D312yes—
196C4×D4—21no—
197C4×D4C3×Dic312yescomplemented
198C2×C42C2×C3×D311yescharacteristic
199C4⋊C8—61no—
200C22⋊C8—32no—
201#97—61no—
202#95—32no—
203#95—61no—
204#95—61no—
205C23×C3—24no—
206C23×C3—22no—
207C23×C3—22no—
208C23×C3—21no—
209C23×C3C2×#6711yescharacteristic
210C23×C3C2×C3×D411yescharacteristic
211C3×Q8—44no—
212C3×Q8—42no—
213C3×Q8—42no—
214C3×D4—42no—
215C3×D4—42no—
216C3×D4—44no—
217C3×D4—44no—
218C3×D4—42no—
219C3×D4—42no—
220C3×D4—44no—
221C3×D4—42no—
222C3×D4—42no—
223C3×D4—48no—
224C3×D4—44no—
225C3×D4—44no—
226C2×C3×C4—24no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—24no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—48no—
245C2×C3×C4—44no—
246C2×C3×C4—44no—
247C2×C3×C4—122no—
248C2×C3×C4—122no—
249C2×C3×C4—122no—
250C2×C3×C4#21711yescharacteristic
251C2×C3×C4#21711yescharacteristic
252C2×C3×C4#21711yescharacteristic
253C2×C3×C4#21711yescharacteristic
254C2×C3×C4C3×C22⋊C411yescharacteristic
255C2×C3×C4C3×C22⋊C411yescharacteristic
256C2×C3×C4C3×C22⋊C411yescharacteristic
257C2×C3×C4C3×C22⋊C411yescharacteristic
258C2×C3×C4C22×Dic311yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260C2×C3×C4C22×C3×C411yescharacteristic
261C2×C3×C4C2×C3×D411yescharacteristic
262C2×Dic3—42no—
263C2×Dic3—42no—
264C2×Dic3—42no—
265C3×C8—122no—
266C3⋊C8—42no—
267C2×C32—22no—
268C2×C32—82no—
269C2×C32#41011yescharacteristic
270C2×C32#41811yescharacteristic
271C2×C32#42111yescharacteristic
272#41—44no—
273C2×Q8—21no—
274C2×D4—22no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C2×C3×Dic312yes—
278C22×C4—22no—
279C22×C4—62no—
280C22×C4C3×#6711yescharacteristic
281C22×C4C3×#6711yescharacteristic
282C22×C4C22×C3×D311yescharacteristic
283C2×C8—62no—
284C4⋊C4—21no—
285C4⋊C4C2×C3×Dic312yes—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C42C2×C3×Dic311yescharacteristic
289C42C2×C3×Dic311yescharacteristic
290C42C3×#6711yescharacteristic
291C42C3×#6711yescharacteristic
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—22no—
297C22×C3—21no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—44no—
301C22×C3—44no—
302C22×C3—44no—
303C22×C3—42no—
304C22×C3—42no—
305C22×C3—42no—
306C22×C3—42no—
307C22×C3—42no—
308C22×C3—42no—
309C22×C3#93212yes—
310C22×C3C2×#21711yescharacteristic
311C22×C3C2×C3×C22⋊C411yescharacteristic
312C22×C3C3×AGL(1,ℤ/8)12yes—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—22no—
316C3×C4—22no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—41no—
330C3×C4—41no—
331C3×C4—44no—
332C3×C4—42no—
333C3×C4—42no—
334C3×C4—242no—
335Dic3—82no—
336C32#151411yescharacteristic, complemented, Sylow
337C23—22no—
338C23C2×C3×#6711yescharacteristic
339Q8—42no—
340D4—42no—
341D4—42no—
342D4—42no—
343D4—44no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—44no—
349C2×C4—122no—
350C2×C4—122no—
351C2×C4—122no—
352C2×C4C3×#21711yescharacteristic
353C2×C4C3×#21711yescharacteristic
354C2×C4C3×#21711yescharacteristic
355C2×C4C3×#21711yescharacteristic
356C2×C4C22×C3×Dic311yescharacteristic
357C2×C4C2×C3×#6711yescharacteristic
358C8—122no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—42no—
365C2×C3—84no—
366C2×C3—82no—
367C2×C3—82no—
368C2×C3#521511yescharacteristic
369C2×C3#523611yescharacteristic
370C2×C3#524011yescharacteristic
371C2×C3C3×#41011yescharacteristic
372C2×C3C3×#41811yescharacteristic
373C2×C3C3×#42111yescharacteristic
374C22—21no—
375C22—21no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22C3×#93212yes—
380C22C2×C3×#21711yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—42no—
388C4—242no—
389C3—21no—
390C3#7181311yescharacteristic, direct product factor
391C3C3×#151411yescharacteristic, complemented
392C2—22no—
393C2—82no—
394C2C3×#521511yescharacteristic
395C2C3×#523611yescharacteristic
396C2C3×#524011yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
Fitting, prime radicalC32×#532C2
socleC22×C32C2×C22⋊C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#532D3
hypocenterC3C3×#1514
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#532

Complements

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

NH ≅ G/Ntype
2. C3×#4937C2semidirect
3. C3×#4926C2semidirect
4. C3×#4537C2semidirect
6. #71813C3direct (N × H)
8. C32×C4⋊Q8C4semidirect
9. C32×#127C4semidirect
14. C32×C4×D4C4semidirect
27. #4937C2×C3semidirect
28. #4926C2×C3semidirect
30. #4537C2×C3semidirect
56. C3×C4⋊Q8Dic3semidirect
57. C3×C4⋊Q8C3×C4semidirect
59. C3×#127Dic3semidirect
60. C3×#127C3×C4semidirect
74. C3×C4×D4Dic3semidirect
75. C3×C4×D4C3×C4semidirect
191. C4⋊Q8C3×Dic3semidirect
192. #127C3×Dic3semidirect
197. C4×D4C3×Dic3semidirect
336. C32#1514semidirect
390. C3#71813direct (N × H)
391. C3C3×#1514semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
C3×#49372
C3×#49262
C3×#45372
C3×#15143
#718133