Finite Group Databasebeta

← C3×#70834 #11775354

Subgroups — C3×#70834 #11775354

Order 1152.

499 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic
2C32×#432C211yesmaximal, characteristic, complemented
3C3×#4936C211yesmaximal, characteristic, complemented
4C3×#4470C212yesmaximal
5C3×#4467C212yesmaximal, complemented
6C3×#1512—31nomaximal
7#70834C311yesmaximal, characteristic, direct product factor
8C2×C32×C42C2211yescharacteristic
9C3×#930C2211yescharacteristic
10C3×#929—21no—
11C3×C4×#67—21no—
12C2×C3×C4⋊Dic3—21no—
13C3×#924C2211yescharacteristic
14C3×#876—21no—
15C3×#875C411yescharacteristic, complemented
16C3×C4×D12C411yescharacteristic, complemented
17C3×#872—21no—
18C3×#870C411yescharacteristic, complemented
19C3×C4×Dic6C411yescharacteristic, complemented
20C32×C4⋊C8—21no—
21C32×C22⋊C8C2212yes—
22C32×#97—21no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95C2212yes—
25C3×#529—31no—
26#5479C2×C311yescharacteristic
27C3×#432—21no—
28C3×#432D311yescharacteristic, complemented
29C3×#432C2×C311yescharacteristic, complemented
30C3×#382—31no—
31#4936C2×C311yescharacteristic, complemented
32C3×#328—32no—
33C3×#327—32no—
34#4470C2×C312yes—
35#4467C2×C312yescomplemented
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C2×C3×#67—21no—
40C22×C3×Dic3—22no—
41C2×C3×D12C2×C411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×Dic6C2×C411yescharacteristic
44C2×C32×C8—22no—
45C32×C42C2×C411yescharacteristic
46C32×C42C2×C411yescharacteristic
47C32×C42D411yescharacteristic
48C32×C42D411yescharacteristic
49C3×#217—21no—
50C3×(C2×D3)⋊C4—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×(C2×D3)⋊C4—21no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3—42no—
55C3×C4⋊Dic3C2×C411yescharacteristic
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62#1512—31noSylow
63C3×#126—61no—
64C3×#125—31no—
65C3×#124—31no—
66C3×#123—61no—
67C3×C22⋊Q8—31no—
68C3×#121—31no—
69C3×C4×Q8—31no—
70C3×C4×D4—31no—
71C3×C4×D4—61no—
72C3×#117—61no—
73C2×C3×C4⋊C4—61no—
74C2×C3×C42—21no—
75C2×C3×C42C2×D311yescharacteristic
76C2×C3×C42C22×C311yescharacteristic
77#930C22×C311yescharacteristic
78#929—21no—
79C4×#67—21no—
80C2×C4⋊Dic3—21no—
81#924C22×C311yescharacteristic
82#876—21no—
83#875C3×C411yescharacteristic, complemented
84C4×D12C3×C411yescharacteristic, complemented
85#872—21no—
86#870C3×C411yescharacteristic, complemented
87C4×Dic6C3×C411yescharacteristic, complemented
88C3×C4⋊C8—22no—
89C3×C4⋊C8—21no—
90C3×C4⋊C8—21no—
91C3×C22⋊C8—22no—
92C3×C22⋊C8C2×D312yes—
93C3×C22⋊C8C22×C312yes—
94C3×#97—22no—
95C3×#97—21no—
96C3×#97—21no—
97C3×#95—32no—
98C3×#95—61no—
99C3⋊#95—21no—
100C3⋊#95C22×C312yes—
101C23×C32C2×D411yescharacteristic
102C22×C3×D3—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C3×#67—41no—
114C3×#67—41no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—42no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C3×D12—41no—
122C3×C4×D3—42no—
123C3×Dic6—41no—
124C32×C8—42no—
125#529—31no—
126#432C3×D311yescharacteristic, complemented
127#382—31no—
128#328—32no—
129#327—32no—
130C2×C3×Q8—31no—
131C2×C3×D4—31no—
132C2×C3×D4—61no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—61no—
137C22×C3×C4—62no—
138C22×C3×C4D1211yescharacteristic
139C22×C3×C4D1211yescharacteristic
140C22×C3×C4C3×D411yescharacteristic
141C22×C3×C4C3×D411yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C23×C311yescharacteristic
144C2×#67—21no—
145C22×Dic3—22no—
146C2×D12C2×C3×C411yescharacteristic
147C2×C4×D3—21no—
148C2×Dic6C2×C3×C411yescharacteristic
149C2×C3×C8—24no—
150C2×C3×C8—22no—
151C2×C3×C8—22no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—122no—
159C3×C22⋊C4—61no—
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C22⋊C4—61no—
164C3×C42—21no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—21no—
168C3×C42—61no—
169C3×C42C4×D311yescharacteristic
170C3×C42C4×D311yescharacteristic
171C3×C42#6711yescharacteristic
172C3×C42#6711yescharacteristic
173C3×C42C2×C3×C411yescharacteristic
174C3×C42C2×C3×C411yescharacteristic
175C3×C42C3×D411yescharacteristic
176C3×C42C3×D411yescharacteristic
177#217—21no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—21no—
181(C2×D3)⋊C4—21no—
182C4⋊Dic3—42no—
183C4⋊Dic3C2×C3×C411yescharacteristic
184C4⋊Dic3C2×C3×C411yescharacteristic
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187Dic3⋊C4—21no—
188Dic3⋊C4—21no—
189C4×Dic3—21no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32C2×C22⋊C411yescharacteristic
193C22×C32AGL(1,ℤ/8)11yescharacteristic
194C22×C32#13711yescharacteristic
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4—21no—
204C3×Dic3—41no—
205C3×Dic3—41no—
206C3×Dic3—41no—
207C3×Dic3—82no—
208#126—61no—
209#125—31no—
210#124—31no—
211#123—61no—
212C22⋊Q8—31no—
213#121—31no—
214C4×Q8—31no—
215C4×D4—31no—
216C4×D4—61no—
217#117—61no—
218C2×C4⋊C4—61no—
219C2×C42C2×C3×D311yescharacteristic
220C4⋊C8—21no—
221C22⋊C8C2×C3×D312yes—
222#97—21no—
223#95—32no—
224#95—61no—
225C23×C3—21no—
226C23×C3—61no—
227C23×C3C2×D1211yescharacteristic
228C23×C3C2×C3×D411yescharacteristic
229C22×D3—21no—
230C3×Q8—121no—
231C3×D4—121no—
232C3×D4—121no—
233C3×D4—121no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—122no—
256C2×C3×C4—122no—
257C2×C3×C4—122no—
258C2×C3×C4—122no—
259C2×C3×C4(C2×D3)⋊C411yescharacteristic
260C2×C3×C4(C2×D3)⋊C411yescharacteristic
261C2×C3×C4(C2×D3)⋊C411yescharacteristic
262C2×C3×C4(C2×D3)⋊C411yescharacteristic
263C2×C3×C4C3×C22⋊C411yescharacteristic
264C2×C3×C4C3×C22⋊C411yescharacteristic
265C2×C3×C4C3×C22⋊C411yescharacteristic
266C2×C3×C4C3×C22⋊C411yescharacteristic
267C2×C3×C4C2×C4×D311yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×C3×C4C22×C3×C411yescharacteristic
270C2×C3×C4C2×C3×D411yescharacteristic
271#67—41no—
272#67—41no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—42no—
277C2×Dic3—42no—
278C2×Dic3—42no—
279D12—41no—
280C4×D3—42no—
281Dic6—41no—
282C3×C8—44no—
283C3×C8—42no—
284C3×C8—42no—
285C2×C32—21no—
286C2×C32—21no—
287C2×C32#41011yescharacteristic
288C2×C32#41711yescharacteristic
289C2×C32#42111yescharacteristic
290C3×D3—81no—
291C2×Q8—31no—
292C2×D4—31no—
293C2×D4—61no—
294C22×C4—61no—
295C22×C4—62no—
296C22×C4C3×D1211yescharacteristic
297C22×C4C3×D1211yescharacteristic
298C22×C4C22×C3×D311yescharacteristic
299C2×C8—22no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—61no—
303C4⋊C4—61no—
304C4⋊C4—61no—
305C4⋊C4—61no—
306C4⋊C4—122no—
307C22⋊C4—61no—
308C22⋊C4—61no—
309C22⋊C4—61no—
310C22⋊C4—61no—
311C22⋊C4—61no—
312C42—61no—
313C42C3×C4×D311yescharacteristic
314C42C3×C4×D311yescharacteristic
315C42C3×#6711yescharacteristic
316C42C3×#6711yescharacteristic
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—121no—
327C22×C3—121no—
328C22×C3—121no—
329C22×C3#90811yescharacteristic
330C22×C3#90911yescharacteristic
331C22×C3C2×(C2×D3)⋊C411yescharacteristic
332C22×C3C2×C3×C22⋊C411yescharacteristic
333C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
334C22×C3C3×#13711yescharacteristic
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C3×C4—22no—
339C3×C4—22no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—121no—
357C3×C4—121no—
358C3×C4—121no—
359C3×C4—242no—
360Dic3—41no—
361Dic3—41no—
362Dic3—41no—
363Dic3—82no—
364C32#151211yescharacteristic, complemented, Sylow
365C23—61no—
366C23C2×C3×D1211yescharacteristic
367Q8—121no—
368D4—121no—
369D4—121no—
370D4—121no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—122no—
379C2×C4—122no—
380C2×C4—122no—
381C2×C4—122no—
382C2×C4C3×(C2×D3)⋊C411yescharacteristic
383C2×C4C3×(C2×D3)⋊C411yescharacteristic
384C2×C4C3×(C2×D3)⋊C411yescharacteristic
385C2×C4C3×(C2×D3)⋊C411yescharacteristic
386C2×C4C2×C3×C4×D311yescharacteristic
387C2×C4C2×C3×#6711yescharacteristic
388C8—42no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—41no—
397C2×C3—41no—
398C2×C3—241no—
399C2×C3#500611yescharacteristic
400C2×C3#513311yescharacteristic
401C2×C3#513911yescharacteristic
402C2×C3C3×#41011yescharacteristic
403C2×C3C3×#41711yescharacteristic
404C2×C3C3×#42111yescharacteristic
405D3—81no—
406C22—21no—
407C22—21no—
408C22—121no—
409C22—121no—
410C22—121no—
411C22C3×#90811yescharacteristic
412C22C3×#90911yescharacteristic
413C22C2×C3×(C2×D3)⋊C411yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—121no—
421C4—121no—
422C4—121no—
423C4—242no—
424C3—21no—
425C3#7083411yescharacteristic, direct product factor
426C3C3×#151211yescharacteristic, complemented
427C2—21no—
428C2—21no—
429C2—241no—
430C2C3×#500611yescharacteristic
431C2C3×#513311yescharacteristic
432C2C3×#513911yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#432C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#432D3
hypocenterC3C3×#1512
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#432

Complements

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

NH ≅ G/Ntype
2. C32×#432C2semidirect
3. C3×#4936C2semidirect
5. C3×#4467C2semidirect
7. #70834C3direct (N × H)
15. C3×#875C4semidirect
16. C3×C4×D12C4semidirect
18. C3×#870C4semidirect
19. C3×C4×Dic6C4semidirect
28. C3×#432D3semidirect
29. C3×#432C2×C3semidirect
31. #4936C2×C3semidirect
35. #4467C2×C3semidirect
83. #875C3×C4semidirect
84. C4×D12C3×C4semidirect
86. #870C3×C4semidirect
87. C4×Dic6C3×C4semidirect
126. #432C3×D3semidirect
364. C32#1512semidirect
425. C3#70834direct (N × H)
426. C3C3×#1512semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C32×#4322
C3×#49362
C3×#44702
C3×#44672
C3×#15123
#708343