Finite Group Databasebeta

← C3×#71035 #11779200

Subgroups — C3×#71035 #11779200

Order 1152.

564 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic, complemented
2C32×#460C211yesmaximal, characteristic, complemented
3C3×#5072C211yesmaximal, characteristic
4C3×#5070C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1627—31nomaximal
9#71035C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×Q8—21no—
11C2×C32×SD16—21no—
12C32×#127C2211yescharacteristic
13C32×C4×Q8C2211yescharacteristic
14C2×C3×#213—21no—
15C3×#897—21no—
16C3×#897—22no—
17C3×C4×D12—21no—
18C3×C4×D12C2211yescharacteristic
19C3×#869—21no—
20C3×#869C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C32×#102—21no—
23C3×#832—22no—
24C3×#832—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×D4×Q8—31no—
28Q8×D12C2×C311yescharacteristic, complemented
29C3×#486—31no—
30C3×#460—21no—
31C3×#460D311yescharacteristic, complemented
32C3×#460C2×C311yescharacteristic, complemented
33C3×#459—31no—
34#5072C2×C311yescharacteristic
35#5070C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39#4535C2×C311yescharacteristic, complemented
40#4483C2×C311yescharacteristic, complemented
41#4482C2×C311yescharacteristic, complemented
42C2×C32×Q8D411yescharacteristic
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C3×D3×Q8—42no—
47C3×D3×Q8—42no—
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—22no—
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—22no—
52C2×C3×Dic6—21no—
53C32×SD16—42no—
54C2×C32×C8—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C42—21no—
58C32×C42C2311yescharacteristic
59C3×#213—42no—
60C3×(C2×D3)⋊C4—22no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D412yes—
65C3×C4⋊Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1627—31noSylow
69C22×C3×Q8—61no—
70C2×D3×Q8—21no—
71C2×C3×SD16—22no—
72C2×C3×SD16—21no—
73C2×C3×SD16—21no—
74C2×C3×D8—61no—
75C3×C4⋊Q8—31no—
76C3×C4⋊Q8—61no—
77C3×#127—21no—
78C3×#127C2×D311yescharacteristic
79C3×#127C22×C311yescharacteristic
80C3×C22⋊Q8—62no—
81C3×C22⋊Q8—61no—
82C3×C4×Q8—21no—
83C3×C4×Q8C2×D311yescharacteristic
84C3×C4×Q8C22×C311yescharacteristic
85C3×C4×D4—31no—
86C3×C4×D4—61no—
87C2×#213—21no—
88#897—21no—
89#897—22no—
90C4×D12—21no—
91C4×D12C22×C311yescharacteristic
92#869—21no—
93#869C22×C311yescharacteristic
94C3×C4⋊C8—21no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8C2×D311yescharacteristic
97C3×C4⋊C8C22×C311yescharacteristic
98C3×#102—22no—
99C3×#102—21no—
100C3×#102—21no—
101C3×#102—61no—
102C3×#102—62no—
103C3×C4×C8—31no—
104#832—22no—
105#832—21no—
106C4⋊(C3⋊C8)C22×C311yescharacteristic
107C4×C3⋊C8C22×C311yescharacteristic
108C23×C32—41no—
109C22×C3×D3—21no—
110C32×Q8—21no—
111C32×Q8D812yescomplemented
112C32×D4—41no—
113C32×D4—41no—
114C32×D4—42no—
115C32×D4—41no—
116C32×D4—41no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3×Dic3—21no—
123C2×C3×Dic3—22no—
124C3×D12—21no—
125C3×D12SD1612yescomplemented
126C3×C4×D3—44no—
127C3×C4×D3—41no—
128C3×C4×D3—41no—
129C3×Dic6—44no—
130C3×Dic6—41no—
131C3×Dic6—41no—
132C32×C8—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135D4×Q8—31no—
136#486—31no—
137#460C3×D311yescharacteristic, complemented
138#459—31no—
139#332—31no—
140Q8⋊C8—31no—
141D4⋊C8—31no—
142C2×C3×Q8—21no—
143C2×C3×Q8—62no—
144C2×C3×Q8—61no—
145C2×C3×Q8—122no—
146C2×C3×Q8—122no—
147C2×C3×Q8#6711yescharacteristic
148C2×C3×Q8C3×D411yescharacteristic
149C2×C3×D4—22no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—31no—
157C2×C3×D4—41no—
158C2×C3×D4—41no—
159C22×C3×C4—62no—
160C22×C3×C4—61no—
161D3×Q8—42no—
162D3×Q8—42no—
163C2×D12C3×D411yescharacteristic
164C2×C4×D3—22no—
165C2×C4×D3—21no—
166C2×Dic6—22no—
167C2×Dic6—21no—
168C3×SD16—44no—
169C3×SD16—42no—
170C3×SD16—42no—
171C3×D8—122no—
172C2×C3×C8—22no—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—31no—
181C3×C4⋊C4—32no—
182C3×C4⋊C4—41no—
183C3×C4⋊C4—62no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4#6711yescharacteristic
186C3×C4⋊C4C3×D411yescharacteristic
187C3×C22⋊C4—62no—
188C3×C22⋊C4—61no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—21no—
192C3×C42—41no—
193C3×C42C22×D311yescharacteristic
194C3×C42C23×C311yescharacteristic
195#213—42no—
196(C2×D3)⋊C4—22no—
197(C2×D3)⋊C4—21no—
198C4⋊Dic3—22no—
199C4⋊Dic3—21no—
200C4⋊Dic3C3×D411yescharacteristic
201C4⋊Dic3C3×D412yes—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C22×C32—81no—
205C22×C32—81no—
206C22×C32—81no—
207C22×C32#12011yescharacteristic
208C2×C3×D3—22no—
209C2×C3×D3—41no—
210C2×C3×D3—41no—
211C32×C4—22no—
212C32×C4—21no—
213C32×C4—41no—
214C32×C4C2×D811yescharacteristic
215C32×C4C2×SD1611yescharacteristic
216C32×C4AGL(1,ℤ/8)11yescharacteristic
217C32×C4#13711yescharacteristic
218C3×Dic3—41no—
219C3×Dic3—42no—
220C22×Q8—61no—
221C2×SD16—21no—
222C2×D8—61no—
223C4⋊Q8—31no—
224C4⋊Q8—61no—
225#127C2×C3×D311yescharacteristic
226C22⋊Q8—62no—
227C22⋊Q8—61no—
228C4×Q8C2×C3×D311yescharacteristic
229C4×D4—31no—
230C4×D4—61no—
231C4⋊C8—31no—
232C4⋊C8C2×C3×D311yescharacteristic
233#102—21no—
234#102—61no—
235#102—62no—
236C4×C8—31no—
237C23×C3—42no—
238C23×C3—41no—
239C23×C3—41no—
240C23×C3—61no—
241C22×D3—21no—
242C3×Q8—21no—
243C3×Q8—21no—
244C3×Q8—22no—
245C3×Q8—41no—
246C3×Q8—124no—
247C3×Q8—121no—
248C3×Q8—121no—
249C3×Q8#21312yescomplemented
250C3×Q8C3×D812yescomplemented
251C3×D4—32no—
252C3×D4—42no—
253C3×D4—42no—
254C3×D4—42no—
255C3×D4—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—61no—
265C3×D4—81no—
266C3×D4—81no—
267C3×D4—82no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—62no—
278C2×C3×C4—61no—
279C2×C3×C4—124no—
280C2×C3×C4—121no—
281C2×C3×C4—121no—
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×C3×C4C2×C3×D411yescharacteristic
286C2×C3×C4C2×C3×D411yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288C2×Dic3—21no—
289C2×Dic3—22no—
290D12—21no—
291D12C3×SD1612yescomplemented
292C4×D3—44no—
293C4×D3—41no—
294C4×D3—41no—
295Dic6—44no—
296Dic6—41no—
297Dic6—41no—
298C3×C8—42no—
299C3×C8—41no—
300C3×C8—41no—
301C3×C8—121no—
302C3×C8—121no—
303C3⋊C8—41no—
304C3⋊C8—41no—
305C2×C32—161no—
306C2×C32#44711yescharacteristic
307C2×C32#44811yescharacteristic
308C2×C32#45411yescharacteristic
309C3×D3—42no—
310C2×Q8—62no—
311C2×Q8—61no—
312C2×Q8—122no—
313C2×Q8—122no—
314C2×Q8C3×#6711yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—31no—
319C22×C4—62no—
320C22×C4—61no—
321SD16—42no—
322D8—122no—
323C2×C8—21no—
324C2×C8—61no—
325C2×C8—61no—
326C4⋊C4—21no—
327C4⋊C4—31no—
328C4⋊C4—32no—
329C4⋊C4—62no—
330C4⋊C4—61no—
331C4⋊C4C3×#6711yescharacteristic
332C22⋊C4—62no—
333C22⋊C4—61no—
334C42—21no—
335C42C22×C3×D311yescharacteristic
336C22×C3—21no—
337C22×C3—62no—
338C22×C3—82no—
339C22×C3—82no—
340C22×C3—82no—
341C22×C3—81no—
342C22×C3—81no—
343C22×C3—81no—
344C22×C3—81no—
345C22×C3—81no—
346C22×C3—81no—
347C22×C3—121no—
348C22×C3—121no—
349C22×C3#93711yescharacteristic
350C22×C3C3×#12011yescharacteristic
351C2×D3—22no—
352C2×D3—41no—
353C2×D3—41no—
354C3×C4—21no—
355C3×C4—22no—
356C3×C4—22no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—41no—
363C3×C4—42no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—81no—
367C3×C4—122no—
368C3×C4—121no—
369C3×C4D3×SD1611yescharacteristic
370C3×C4#91511yescharacteristic
371C3×C4C2×#21311yescharacteristic
372C3×C4#94911yescharacteristic
373C3×C4C2×C3×D811yescharacteristic
374C3×C4C2×C3×SD1611yescharacteristic
375C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
376C3×C4C3×#13711yescharacteristic
377Dic3—41no—
378Dic3—42no—
379C32#162711yescharacteristic, complemented, Sylow
380C23—41no—
381C23—61no—
382Q8—21no—
383Q8—124no—
384Q8—121no—
385Q8—121no—
386Q8C3×#21312yescomplemented
387D4—32no—
388D4—42no—
389D4—41no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—61no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—62no—
397C2×C4—61no—
398C2×C4—124no—
399C2×C4—121no—
400C2×C4—121no—
401C2×C4C3×D3×D411yescharacteristic
402C2×C4C3×D3×D411yescharacteristic
403C2×C4C2×C3×#6711yescharacteristic
404C8—41no—
405C8—121no—
406C8—121no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—122no—
411C2×C3—162no—
412C2×C3—161no—
413C2×C3—161no—
414C2×C3#503611yescharacteristic
415C2×C3#517011yescharacteristic
416C2×C3#520111yescharacteristic
417C2×C3C3×#44711yescharacteristic
418C2×C3C3×#44811yescharacteristic
419C2×C3C3×#45411yescharacteristic
420D3—42no—
421C22—62no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—121no—
426C22—121no—
427C22C3×#93711yescharacteristic
428C4—21no—
429C4—22no—
430C4—41no—
431C4—122no—
432C4—121no—
433C4C3×D3×SD1611yescharacteristic
434C4C3×#91511yescharacteristic
435C4C2×C3×#21311yescharacteristic
436C4C3×#94911yescharacteristic
437C3—21no—
438C3#7103511yescharacteristic, direct product factor
439C3C3×#162711yescharacteristic, complemented
440C2—122no—
441C2—161no—
442C2C3×#503611yescharacteristic
443C2C3×#517011yescharacteristic
444C2C3×#520111yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#460C2
socleC22×C32#120
prime radicalC3×#5072C2
hypercenterC3×#460D3
hypocenterC3C3×#1627
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
1. C3×Q8×D12C2semidirect
2. C32×#460C2semidirect
4. C3×#5070C2semidirect
5. C3×#4535C2semidirect
6. C3×#4483C2semidirect
7. C3×#4482C2semidirect
9. #71035C3direct (N × H)
28. Q8×D12C2×C3semidirect
31. C3×#460D3semidirect
32. C3×#460C2×C3semidirect
35. #5070C2×C3semidirect
39. #4535C2×C3semidirect
40. #4483C2×C3semidirect
41. #4482C2×C3semidirect
111. C32×Q8D8semidirect
125. C3×D12SD16semidirect
137. #460C3×D3semidirect
249. C3×Q8#213semidirect
250. C3×Q8C3×D8semidirect
291. D12C3×SD16semidirect
379. C32#1627semidirect
386. Q8C3×#213semidirect
438. C3#71035direct (N × H)
439. C3C3×#1627semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
C32×#4602
C3×#50722
C3×#50702
C3×#45352
C3×#44832
C3×#44822
C3×#16273
#710353