Finite Group Databasebeta

← C3×#68242 #11774828

Subgroups — C3×#68242 #11774828

Order 1152.

467 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5580C211yesmaximal, characteristic
2C3×#4837C211yesmaximal, characteristic, complemented
3C3×#4685C211yesmaximal, characteristic, complemented
4C32×Q8⋊C8C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1495—31nomaximal
9#68242C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C3×#947C411yescharacteristic
12C3×#946C411yescharacteristic
13C2×C3×ΓL(1,𝔽25)—21no—
14C3×#898—21no—
15C3×#895C411yescharacteristic
16C3×#894—21no—
17C3×#890C411yescharacteristic
18C3×C4×D12—21no—
19C3×C4×D12C2211yescharacteristic
20C3×#872—21no—
21C3×C42×D3C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23C32×C4×C8C2211yescharacteristic
24C3×(C2×D3)⋊C8—21no—
25C3×Dic3⋊C8—21no—
26C3×Dic3⋊C8—21no—
27C3×C4⋊(C3⋊C8)C2211yescharacteristic
28C3×C4×C3⋊C8C2211yescharacteristic
29C3×#529—31no—
30#5580C2×C311yescharacteristic
31C3×#431—31no—
32C3×#423—31no—
33#4837C2×C311yescharacteristic, complemented
34#4685C2×C311yescharacteristic, complemented
35C3×Q8⋊C8—21no—
36C3×Q8⋊C8—31no—
37C3×Q8⋊C8D311yescharacteristic, complemented
38C3×Q8⋊C8C2×C311yescharacteristic, complemented
39C3×D4⋊C8—31no—
40C3×D4⋊C8—31no—
41#4535C2×C311yescharacteristic, complemented
42#4483C2×C311yescharacteristic, complemented
43#4459C2×C311yescharacteristic, complemented
44C2×C32×Q8C2×C411yescharacteristic
45C2×C3×D12—21no—
46C2×C3×D12C2×C411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3C2×C411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×C3×C4×D3D411yescharacteristic
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C42—21no—
56C32×C42C2311yescharacteristic
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3C2×C411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C3×ΓL(1,𝔽25)—42no—
72#1495—31noSylow
73C2×C3×M16—61no—
74C3×#126—61no—
75C3×#125—31no—
76C3×#124—31no—
77C3×#123—61no—
78C3×C22⋊Q8—31no—
79C3×#121—31no—
80C3×C4×Q8—21no—
81C3×C4×Q8C2×D311yescharacteristic
82C3×C4×Q8C22×C311yescharacteristic
83C3×C4×D4—31no—
84C3×C4×D4—61no—
85C3×#117—61no—
86C2×C3×C42—31no—
87#947C3×C411yescharacteristic
88#946C3×C411yescharacteristic
89C2×ΓL(1,𝔽25)—21no—
90#898—21no—
91#895C3×C411yescharacteristic
92#894—21no—
93#890C3×C411yescharacteristic
94C4×D12—21no—
95C4×D12C22×C311yescharacteristic
96#872—21no—
97C42×D3C22×C311yescharacteristic
98C3×C4⋊C8—21no—
99C3×C4⋊C8—31no—
100C3×C4⋊C8—61no—
101C3×C4⋊C8—61no—
102C3×C4⋊C8C2×D311yescharacteristic
103C3×C4⋊C8C22×C311yescharacteristic
104C3×C22⋊C8—61no—
105C3×C4×C8—21no—
106C3×C4×C8—31no—
107C3×C4×C8C2×D311yescharacteristic
108C3×C4×C8C22×C311yescharacteristic
109(C2×D3)⋊C8—21no—
110Dic3⋊C8—21no—
111Dic3⋊C8—21no—
112C4⋊(C3⋊C8)C22×C311yescharacteristic
113C4×C3⋊C8C22×C311yescharacteristic
114C22×C3×D3—21no—
115C22×C3×D3C22⋊C411yescharacteristic
116C32×Q8—21no—
117C32×Q8—21no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3×Dic3—21no—
124C2×C3×Dic3C22⋊C411yescharacteristic
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C3×D12—21no—
128C3×D12—21no—
129C3×D12—42no—
130C3×C4×D3—21no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136C3×C4×D3—41no—
137C32×C8—41no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141#529—31no—
142#431—31no—
143#423—31no—
144Q8⋊C8—31no—
145Q8⋊C8C3×D311yescharacteristic, complemented
146D4⋊C8—31no—
147D4⋊C8—31no—
148C2×C3×Q8—21no—
149C2×C3×Q8C4×D311yescharacteristic
150C2×C3×Q8C2×C3×C411yescharacteristic
151C2×C3×D4—31no—
152C2×C3×D4—61no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—61no—
157C2×D12—21no—
158C2×D12C2×C3×C411yescharacteristic
159C2×C4×D3—21no—
160C2×C4×D3C2×C3×C411yescharacteristic
161C2×C4×D3C3×D411yescharacteristic
162C2×C4×D3C3×D411yescharacteristic
163C3×M16—122no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—41no—
169C2×C3×C8—41no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—41no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4C4×D311yescharacteristic
181C3×C4⋊C4C2×C3×C411yescharacteristic
182C3×C22⋊C4—61no—
183C3×C22⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—31no—
191C3×C42—31no—
192C3×C42—31no—
193C3×C42—41no—
194C3×C42C22×D311yescharacteristic
195C3×C42C23×C311yescharacteristic
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3C2×C3×C411yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205C4×Dic3C2×C3×C411yescharacteristic
206C4×Dic3C3×D411yescharacteristic
207C4×Dic3C3×D411yescharacteristic
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210ΓL(1,𝔽25)—42no—
211C22×C32C2×C22⋊C411yescharacteristic
212C2×C3×D3—21no—
213C2×C3×D3—21no—
214C2×C3×D3—21no—
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—41no—
221C32×C4#13111yescharacteristic
222C32×C4#13111yescharacteristic
223C32×C4AGL(1,ℤ/8)11yescharacteristic
224C32×C4#13711yescharacteristic
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3—41no—
229C2×M16—61no—
230#126—61no—
231#125—31no—
232#124—31no—
233#123—61no—
234C22⋊Q8—31no—
235#121—31no—
236C4×Q8C2×C3×D311yescharacteristic
237C4×D4—31no—
238C4×D4—61no—
239#117—61no—
240C2×C42—31no—
241C4⋊C8—31no—
242C4⋊C8—61no—
243C4⋊C8—61no—
244C4⋊C8C2×C3×D311yescharacteristic
245C22⋊C8—61no—
246C4×C8—31no—
247C4×C8C2×C3×D311yescharacteristic
248C23×C3—31no—
249C23×C3—61no—
250C22×D3—21no—
251C22×D3C3×C22⋊C411yescharacteristic
252C3×Q8—22no—
253C3×Q8—21no—
254C3×Q8—21no—
255C3×Q8—21no—
256C3×Q8—21no—
257C3×Q8—41no—
258C3×D4—61no—
259C3×D4—61no—
260C3×D4—122no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—31no—
269C2×C3×C4—31no—
270C2×C3×C4—31no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C22×C3×C411yescharacteristic
285C2×C3×C4C2×C3×D411yescharacteristic
286C2×C3×C4C2×C3×D411yescharacteristic
287C2×Dic3—21no—
288C2×Dic3C3×C22⋊C411yescharacteristic
289C2×Dic3C3×C22⋊C411yescharacteristic
290C2×Dic3C3×C22⋊C411yescharacteristic
291D12—21no—
292D12—21no—
293D12—42no—
294C4×D3—21no—
295C4×D3—21no—
296C4×D3—21no—
297C4×D3—21no—
298C4×D3—41no—
299C4×D3—41no—
300C4×D3—41no—
301C3×C8—41no—
302C3×C8—41no—
303C3×C8—42no—
304C3×C8—41no—
305C3×C8—41no—
306C3×C8—81no—
307C3×C8—121no—
308C3×C8—121no—
309C3⋊C8—41no—
310C3⋊C8—41no—
311C2×C32#40811yescharacteristic
312C2×C32#41711yescharacteristic
313C2×C32#42111yescharacteristic
314C3×D3—41no—
315C3×D3—81no—
316C2×Q8C3×C4×D311yescharacteristic
317C2×D4—31no—
318C2×D4—61no—
319C22×C4—31no—
320C22×C4—31no—
321C22×C4—31no—
322C22×C4—61no—
323M16—122no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—61no—
327C2×C8—61no—
328C4⋊C4—21no—
329C4⋊C4—31no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4C3×C4×D311yescharacteristic
334C22⋊C4—61no—
335C22⋊C4—61no—
336C22⋊C4—61no—
337C22⋊C4—61no—
338C22⋊C4—61no—
339C42—21no—
340C42—31no—
341C42—31no—
342C42—31no—
343C42C22×C3×D311yescharacteristic
344C22×C3—21no—
345C22×C3—61no—
346C22×C3—61no—
347C22×C3—61no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—121no—
351C22×C3D3×C22⋊C411yescharacteristic
352C22×C3C2×C3×C22⋊C411yescharacteristic
353C2×D3—21no—
354C2×D3—21no—
355C2×D3—21no—
356C2×D3—41no—
357C2×D3—41no—
358C2×D3—41no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—41no—
366C3×C4—42no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—41no—
371C3×C4—61no—
372C3×C4—61no—
373C3×C4—61no—
374C3×C4—81no—
375C3×C4—121no—
376C3×C4#90111yescharacteristic
377C3×C4#90711yescharacteristic
378C3×C4#91411yescharacteristic
379C3×C4#91811yescharacteristic
380C3×C4C3×#13111yescharacteristic
381C3×C4C3×#13111yescharacteristic
382C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
383C3×C4C3×#13711yescharacteristic
384Dic3—21no—
385Dic3—21no—
386Dic3—21no—
387Dic3—41no—
388C32#149511yescharacteristic, complemented, Sylow
389C23—31no—
390C23—61no—
391Q8—21no—
392Q8—21no—
393D4—61no—
394D4—61no—
395D4—122no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—31no—
399C2×C4—31no—
400C2×C4—31no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4C2×C3×C4×D311yescharacteristic
410C2×C4C3×D3×D411yescharacteristic
411C2×C4C3×D3×D411yescharacteristic
412C8—41no—
413C8—41no—
414C8—121no—
415C8—121no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—121no—
420C2×C3—241no—
421C2×C3#472711yescharacteristic
422C2×C3#480311yescharacteristic
423C2×C3#482111yescharacteristic
424C2×C3C3×#40811yescharacteristic
425C2×C3C3×#41711yescharacteristic
426C2×C3C3×#42111yescharacteristic
427D3—41no—
428D3—81no—
429C22—61no—
430C22—61no—
431C22—61no—
432C22—121no—
433C22—121no—
434C22—121no—
435C22C3×D3×C22⋊C411yescharacteristic
436C4—21no—
437C4—41no—
438C4—41no—
439C4—61no—
440C4—61no—
441C4—61no—
442C4—121no—
443C4C3×#90111yescharacteristic
444C4C3×#90711yescharacteristic
445C4C3×#91411yescharacteristic
446C4C3×#91811yescharacteristic
447C3—21no—
448C3#6824211yescharacteristic, direct product factor
449C3C3×#149511yescharacteristic, complemented
450C2—121no—
451C2—241no—
452C2C3×#472711yescharacteristic
453C2C3×#480311yescharacteristic
454C2C3×#482111yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#895C4
cosocleC3×C42C23×C3
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1495
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4837C2semidirect
3. C3×#4685C2semidirect
4. C32×Q8⋊C8C2semidirect
5. C3×#4535C2semidirect
6. C3×#4483C2semidirect
7. C3×#4459C2semidirect
9. #68242C3direct (N × H)
33. #4837C2×C3semidirect
34. #4685C2×C3semidirect
37. C3×Q8⋊C8D3semidirect
38. C3×Q8⋊C8C2×C3semidirect
41. #4535C2×C3semidirect
42. #4483C2×C3semidirect
43. #4459C2×C3semidirect
145. Q8⋊C8C3×D3semidirect
388. C32#1495semidirect
448. C3#68242direct (N × H)
449. C3C3×#1495semidirect

Maximal subgroups

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

subgroupindex
C3×#55802
C3×#48372
C3×#46852
C32×Q8⋊C82
C3×#45352
C3×#44832
C3×#44592
C3×#14953
#682423