Finite Group Databasebeta

← C3×#68266 #11779212

Subgroups — C3×#68266 #11779212

Order 1152.

535 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic, complemented
3C3×#4843C211yesmaximal, characteristic
4C3×#4694C211yesmaximal, characteristic, complemented
5C32×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1627—31nomaximal
9#68266C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×Q8—21no—
11C32×C4×Q8C2211yescharacteristic
12C2×C3×#215—21no—
13C2×C3×D24—21no—
14C3×#897—21no—
15C3×#897—22no—
16C3×#874C2211yescharacteristic
17C3×C4×D12—21no—
18C3×C4×D12C2211yescharacteristic
19C3×#869—21no—
20C3×#869C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C32×C4×C8C2211yescharacteristic
23C3×#821—22no—
24C3×#821—21no—
25C3×#809—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×D4×Q8—31no—
28Q8×D12C2×C311yescharacteristic, complemented
29C3×#486—31no—
30C3×#460—31no—
31C3×#459—31no—
32#5027C2×C311yescharacteristic, complemented
33#4843C2×C311yescharacteristic
34#4694C2×C311yescharacteristic, complemented
35C3×#332—31no—
36C3×Q8⋊C8—21no—
37C3×Q8⋊C8D311yescharacteristic, complemented
38C3×Q8⋊C8C2×C311yescharacteristic, complemented
39C3×D4⋊C8—31no—
40#4486C2×C311yescharacteristic, complemented
41#4459C2×C311yescharacteristic, complemented
42C2×C32×Q8D411yescharacteristic
43C3×D3×Q8—42no—
44C3×D3×Q8—42no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—22no—
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—22no—
52C2×C3×Dic6—21no—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C42—21no—
58C32×C42C2311yescharacteristic
59C3×#215—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—
67C3×D24—42no—
68#1627—31noSylow
69C22×C3×Q8—61no—
70C2×D3×Q8—21no—
71C2×C3×SD16—61no—
72C2×C3×D8—61no—
73C3×C4⋊Q8—31no—
74C3×C4⋊Q8—61no—
75C3×#127—31no—
76C3×C22⋊Q8—62no—
77C3×C22⋊Q8—61no—
78C3×C4×Q8—21no—
79C3×C4×Q8C2×D311yescharacteristic
80C3×C4×Q8C22×C311yescharacteristic
81C3×C4×D4—31no—
82C3×C4×D4—61no—
83C2×#215—21no—
84C2×D24—21no—
85#897—21no—
86#897—22no—
87#874C22×C311yescharacteristic
88C4×D12—21no—
89C4×D12C22×C311yescharacteristic
90#869—21no—
91#869C22×C311yescharacteristic
92C3×C4⋊C8—21no—
93C3×C4⋊C8—31no—
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C22×C311yescharacteristic
96C3×#102—61no—
97C3×#102—62no—
98C3×#102—61no—
99C3×C4×C8—21no—
100C3×C4×C8C2×D311yescharacteristic
101C3×C4×C8C22×C311yescharacteristic
102#821—22no—
103#821—21no—
104#809—21no—
105C4⋊(C3⋊C8)C22×C311yescharacteristic
106C22×C3×D3—21no—
107C22×C3×D3—41no—
108C32×Q8—21no—
109C32×Q8D812yescomplemented
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C3×Dic3—21no—
116C2×C3×Dic3—22no—
117C3×D12—21no—
118C3×D12—42no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12SD1612yescomplemented
124C3×C4×D3—44no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—44no—
128C3×Dic6—41no—
129C3×Dic6—41no—
130C32×C8—41no—
131C32×C8—41no—
132C3×C3⋊C8—41no—
133D4×Q8—31no—
134#486—31no—
135#460—31no—
136#459—31no—
137#332—31no—
138Q8⋊C8C3×D311yescharacteristic, complemented
139D4⋊C8—31no—
140C2×C3×Q8—21no—
141C2×C3×Q8—62no—
142C2×C3×Q8—61no—
143C2×C3×Q8—122no—
144C2×C3×Q8—122no—
145C2×C3×Q8D1211yescharacteristic
146C2×C3×Q8C3×D411yescharacteristic
147C2×C3×D4—31no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C22×C3×C4—62no—
152C22×C3×C4—61no—
153D3×Q8—42no—
154D3×Q8—42no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12C3×D411yescharacteristic
159C2×C4×D3—22no—
160C2×C4×D3—21no—
161C2×Dic6—22no—
162C2×Dic6—21no—
163C3×SD16—122no—
164C3×D8—122no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—41no—
170C2×C3×C8—41no—
171C2×C3×C8—61no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—32no—
177C3×C4⋊C4—41no—
178C3×C4⋊C4—62no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4D1211yescharacteristic
181C3×C4⋊C4C3×D411yescharacteristic
182C3×C22⋊C4—62no—
183C3×C22⋊C4—61no—
184C3×C42—21no—
185C3×C42—21no—
186C3×C42—21no—
187C3×C42—41no—
188C3×C42C22×D311yescharacteristic
189C3×C42C23×C311yescharacteristic
190#215—42no—
191(C2×D3)⋊C4—22no—
192(C2×D3)⋊C4—21no—
193C4⋊Dic3—22no—
194C4⋊Dic3—21no—
195C4⋊Dic3C3×D411yescharacteristic
196C4⋊Dic3C3×D412yes—
197C2×C3⋊C8—21no—
198D24—42no—
199C22×C32#12011yescharacteristic
200C2×C3×D3—22no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C2×C3×D3—81no—
206C32×C4—22no—
207C32×C4—21no—
208C32×C4—41no—
209C32×C4C2×D811yescharacteristic
210C32×C4C2×SD1611yescharacteristic
211C32×C4AGL(1,ℤ/8)11yescharacteristic
212C32×C4#13711yescharacteristic
213C3×Dic3—41no—
214C3×Dic3—42no—
215C22×Q8—61no—
216C2×SD16—61no—
217C2×D8—61no—
218C4⋊Q8—31no—
219C4⋊Q8—61no—
220#127—31no—
221C22⋊Q8—62no—
222C22⋊Q8—61no—
223C4×Q8C2×C3×D311yescharacteristic
224C4×D4—31no—
225C4×D4—61no—
226C4⋊C8—31no—
227C4⋊C8C2×C3×D311yescharacteristic
228#102—61no—
229#102—62no—
230#102—61no—
231C4×C8C2×C3×D311yescharacteristic
232C23×C3—61no—
233C23×C3—121no—
234C22×D3—21no—
235C22×D3—41no—
236C3×Q8—21no—
237C3×Q8—21no—
238C3×Q8—22no—
239C3×Q8—41no—
240C3×Q8—124no—
241C3×Q8—121no—
242C3×Q8—121no—
243C3×Q8D2412yescomplemented
244C3×Q8C3×D812yescomplemented
245C3×D4—32no—
246C3×D4—61no—
247C3×D4—122no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—121no—
251C3×D4—121no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—62no—
262C2×C3×C4—61no—
263C2×C3×C4—124no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4C2×D1211yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4C2×C3×D411yescharacteristic
270C2×C3×C4C2×C3×D411yescharacteristic
271C2×C3×C4C2×C3×D411yescharacteristic
272C2×Dic3—21no—
273C2×Dic3—22no—
274D12—21no—
275D12—42no—
276D12—41no—
277D12—41no—
278D12—41no—
279D12—41no—
280D12C3×SD1612yescomplemented
281C4×D3—44no—
282C4×D3—41no—
283C4×D3—41no—
284Dic6—44no—
285Dic6—41no—
286Dic6—41no—
287C3×C8—41no—
288C3×C8—41no—
289C3×C8—42no—
290C3×C8—41no—
291C3×C8—41no—
292C3×C8—81no—
293C3×C8—121no—
294C3⋊C8—41no—
295C2×C32#44711yescharacteristic
296C2×C32#44811yescharacteristic
297C2×C32#45411yescharacteristic
298C3×D3—42no—
299C3×D3—161no—
300C2×Q8—62no—
301C2×Q8—61no—
302C2×Q8—122no—
303C2×Q8—122no—
304C2×Q8C3×D1211yescharacteristic
305C2×D4—31no—
306C2×D4—61no—
307C2×D4—61no—
308C2×D4—61no—
309C22×C4—62no—
310C22×C4—61no—
311SD16—122no—
312D8—122no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—61no—
316C4⋊C4—21no—
317C4⋊C4—31no—
318C4⋊C4—32no—
319C4⋊C4—62no—
320C4⋊C4—61no—
321C4⋊C4C3×D1211yescharacteristic
322C22⋊C4—62no—
323C22⋊C4—61no—
324C42—21no—
325C42C22×C3×D311yescharacteristic
326C22×C3—21no—
327C22×C3—62no—
328C22×C3—121no—
329C22×C3—121no—
330C22×C3—241no—
331C22×C3—241no—
332C22×C3—241no—
333C22×C3#88211yescharacteristic
334C22×C3C3×#12011yescharacteristic
335C2×D3—22no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—81no—
339C2×D3—81no—
340C2×D3—81no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—42no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—81no—
354C3×C4—122no—
355C3×C4—121no—
356C3×C4C2×D2411yescharacteristic
357C3×C4#90811yescharacteristic
358C3×C4D3×SD1611yescharacteristic
359C3×C4#91811yescharacteristic
360C3×C4C2×C3×D811yescharacteristic
361C3×C4C2×C3×SD1611yescharacteristic
362C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
363C3×C4C3×#13711yescharacteristic
364Dic3—41no—
365Dic3—42no—
366C32#162711yescharacteristic, complemented, Sylow
367C23—61no—
368C23—121no—
369Q8—21no—
370Q8—124no—
371Q8—121no—
372Q8—121no—
373Q8C3×D2412yescomplemented
374D4—32no—
375D4—61no—
376D4—122no—
377D4—121no—
378D4—121no—
379D4—121no—
380D4—121no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—62no—
384C2×C4—61no—
385C2×C4—124no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4C2×C3×D1211yescharacteristic
389C2×C4C3×D3×D411yescharacteristic
390C2×C4C3×D3×D411yescharacteristic
391C8—41no—
392C8—41no—
393C8—121no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—122no—
398C2×C3—481no—
399C2×C3#473211yescharacteristic
400C2×C3#480611yescharacteristic
401C2×C3#482711yescharacteristic
402C2×C3C3×#44711yescharacteristic
403C2×C3C3×#44811yescharacteristic
404C2×C3C3×#45411yescharacteristic
405D3—42no—
406D3—161no—
407C22—62no—
408C22—121no—
409C22—121no—
410C22—241no—
411C22—241no—
412C22—241no—
413C22C3×#88211yescharacteristic
414C4—22no—
415C4—21no—
416C4—41no—
417C4—122no—
418C4—121no—
419C4C2×C3×D2411yescharacteristic
420C4C3×#90811yescharacteristic
421C4C3×D3×SD1611yescharacteristic
422C4C3×#91811yescharacteristic
423C3—21no—
424C3#6826611yescharacteristic, direct product factor
425C3C3×#162711yescharacteristic, complemented
426C2—122no—
427C2—481no—
428C2C3×#473211yescharacteristic
429C2C3×#480611yescharacteristic
430C2C3×#482711yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32#120
prime radicalC3×#4843C2
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1627
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×Q8×D12C2semidirect
2. C3×#5027C2semidirect
4. C3×#4694C2semidirect
5. C32×Q8⋊C8C2semidirect
6. C3×#4486C2semidirect
7. C3×#4459C2semidirect
9. #68266C3direct (N × H)
28. Q8×D12C2×C3semidirect
32. #5027C2×C3semidirect
34. #4694C2×C3semidirect
37. C3×Q8⋊C8D3semidirect
38. C3×Q8⋊C8C2×C3semidirect
40. #4486C2×C3semidirect
41. #4459C2×C3semidirect
109. C32×Q8D8semidirect
123. C3×D12SD16semidirect
138. Q8⋊C8C3×D3semidirect
243. C3×Q8D24semidirect
244. C3×Q8C3×D8semidirect
280. D12C3×SD16semidirect
366. C32#1627semidirect
373. Q8C3×D24semidirect
424. C3#68266direct (N × H)
425. 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
C3×#50272
C3×#48432
C3×#46942
C32×Q8⋊C82
C3×#44862
C3×#44592
C3×#16273
#682663