Finite Group Databasebeta

← C3×#69854 #11774648

Subgroups — C3×#69854 #11774648

Order 1152.

603 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×C4×#235C211yesmaximal, characteristic
2C32×C4×M16C211yesmaximal, characteristic, complemented
3C3×#4924C211yesmaximal, characteristic, complemented
4C3×#4459C212yesmaximal, complemented
5C3×#4456C212yesmaximal, complemented
6C3×#1489—31nomaximal
7#69854C311yesmaximal, characteristic, direct product factor
8C2×C3×#235C411yescharacteristic
9C2×C32×M16—21no—
10C2×C32×C42C2211yescharacteristic
11C3×C4×#67—21no—
12C3×C4×#67—21no—
13C3×#926C411yescharacteristic
14C2×C3×#208—21no—
15C3×C4×D12C411yescharacteristic
16C3×C4×D12C2211yescharacteristic
17C3×#872—21no—
18C3×C42×D3—21no—
19C3×C4×Dic6C411yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C32×#97—21no—
22C32×C4×C8C2212yes—
23C3×C4⋊(C3⋊C8)—21no—
24C3×C4⋊(C3⋊C8)C2212yes—
25C3×C4×#41—31no—
26C4×#235C2×C311yescharacteristic
27C3×#423—31no—
28C3×C4×M16—21no—
29C3×C4×M16D311yescharacteristic, complemented
30C3×C4×M16C2×C311yescharacteristic, complemented
31#4924C2×C311yescharacteristic, complemented
32C3×Q8⋊C8—32no—
33C3×D4⋊C8—32no—
34#4459C2×C312yescomplemented
35#4456C2×C312yescomplemented
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C2×C3×#67—21no—
40C3×#235—22no—
41C3×#235—22no—
42C2×C3×D12C2×C411yescharacteristic
43C2×C3×C4×D3—21no—
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—21no—
46C2×C3×Dic6C2×C411yescharacteristic
47C32×M16—24no—
48C2×C32×C8—22no—
49C32×C42C2×C411yescharacteristic
50C32×C42D411yescharacteristic
51C32×C42D411yescharacteristic
52C32×C42C2311yescharacteristic
53C3×#217—21no—
54C3×(C2×D3)⋊C4—21no—
55C3×(C2×D3)⋊C4—21no—
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×C4⋊Dic3C2×C411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C3×C4×Dic3—21no—
63C3×#208—42no—
64C2×C3×C3⋊C8—22no—
65#1489—31noSylow
66C2×C3×#41—31no—
67C2×#235C3×C411yescharacteristic
68C2×C3×M16—22no—
69C2×C3×M16—21no—
70C2×C3×M16—21no—
71C2×C3×M16—61no—
72C3×C4×Q8—31no—
73C3×C4×Q8—31no—
74C3×C4×D4—31no—
75C3×C4×D4—31no—
76C3×C4×D4—61no—
77C3×C4×D4—61no—
78C3×#117—31no—
79C3×#117—61no—
80C2×C3×C42—21no—
81C2×C3×C42—61no—
82C2×C3×C42C2×D311yescharacteristic
83C2×C3×C42C22×C311yescharacteristic
84C4×#67—21no—
85C4×#67—21no—
86#926C3×C411yescharacteristic
87C2×#208—21no—
88C4×D12C3×C411yescharacteristic
89C4×D12C22×C311yescharacteristic
90#872—21no—
91C42×D3—21no—
92C4×Dic6C3×C411yescharacteristic
93C4×Dic6C22×C311yescharacteristic
94C3×C4⋊C8—32no—
95C3×C4⋊C8—61no—
96C3×#97—22no—
97C3×#97—21no—
98C3×#97—21no—
99C3×C4×C8—22no—
100C3×C4×C8C2×D312yes—
101C3×C4×C8C22×C312yes—
102C4⋊(C3⋊C8)—21no—
103C4⋊(C3⋊C8)C22×C312yes—
104C23×C32C22⋊C411yescharacteristic
105C22×C3×D3—21no—
106C2×C32×C4—22no—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C22⋊C411yescharacteristic
112C2×C32×C4C22⋊C411yescharacteristic
113C2×C32×C4C22⋊C411yescharacteristic
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C3×#67—24no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C3×D12—21no—
122C3×D12M1612yescomplemented
123C3×C4×D3—24no—
124C3×C4×D3—42no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—21no—
128C3×Dic6M1612yescomplemented
129C32×C8—24no—
130C3×C3⋊C8—42no—
131C4×#41—31no—
132#423—31no—
133C4×M16C3×D311yescharacteristic, complemented
134Q8⋊C8—32no—
135D4⋊C8—32no—
136C3×#41—62no—
137C3×#41—62no—
138C2×C3×Q8—31no—
139C2×C3×D4—31no—
140C2×C3×D4—61no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—61no—
145C22×C3×C4—61no—
146C22×C3×C4—61no—
147C22×C3×C4C4×D311yescharacteristic
148C22×C3×C4D1211yescharacteristic
149C22×C3×C4#6711yescharacteristic
150C22×C3×C4C2×C3×C411yescharacteristic
151C22×C3×C4C3×D411yescharacteristic
152C22×C3×C4C3×D411yescharacteristic
153C2×#67—21no—
154#235—22no—
155#235—22no—
156C2×D12C2×C3×C411yescharacteristic
157C2×C4×D3—21no—
158C2×C4×D3—21no—
159C2×C4×D3—21no—
160C2×Dic6C2×C3×C411yescharacteristic
161C3×M16—28no—
162C3×M16—24no—
163C3×M16—24no—
164C3×M16—122no—
165C2×C3×C8—24no—
166C2×C3×C8—22no—
167C2×C3×C8—22no—
168C2×C3×C8—62no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C22⋊C4—61no—
174C3×C22⋊C4—61no—
175C3×C22⋊C4—61no—
176C3×C42—21no—
177C3×C42—21no—
178C3×C42—21no—
179C3×C42—21no—
180C3×C42—61no—
181C3×C42—61no—
182C3×C42—61no—
183C3×C42C4×D311yescharacteristic
184C3×C42D1211yescharacteristic
185C3×C42#6711yescharacteristic
186C3×C42C2×C3×C411yescharacteristic
187C3×C42C3×D411yescharacteristic
188C3×C42C3×D411yescharacteristic
189C3×C42C22×D311yescharacteristic
190C3×C42C23×C311yescharacteristic
191#217—21no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194C4⋊Dic3C2×C3×C411yescharacteristic
195C4⋊Dic3C2×C3×C411yescharacteristic
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198C4×Dic3—21no—
199C4×Dic3—21no—
200C4×Dic3—21no—
201#208—42no—
202C2×C3⋊C8—22no—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32—21no—
206C22×C32C2×C22⋊C411yescharacteristic
207C2×C3×D3—22no—
208C2×C3×D3—41no—
209C2×C3×D3—41no—
210C32×C4—21no—
211C32×C4—21no—
212C32×C4—21no—
213C32×C4#10412yes—
214C32×C4C2×M1611yescharacteristic
215C32×C4C2×M1611yescharacteristic
216C32×C4AGL(1,ℤ/8)11yescharacteristic
217C32×C4#13711yescharacteristic
218C3×Dic3—22no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C2×#41—31no—
222C2×M16—21no—
223C2×M16—61no—
224C4×Q8—31no—
225C4×Q8—31no—
226C4×D4—31no—
227C4×D4—31no—
228C4×D4—61no—
229C4×D4—61no—
230#117—31no—
231#117—61no—
232C2×C42—61no—
233C2×C42C2×C3×D311yescharacteristic
234C4⋊C8—32no—
235C4⋊C8—61no—
236#97—21no—
237C4×C8C2×C3×D312yes—
238C23×C3—21no—
239C23×C3—61no—
240C23×C3(C2×D3)⋊C411yescharacteristic
241C23×C3C3×C22⋊C411yescharacteristic
242C22×D3—21no—
243C3×Q8—32no—
244C3×Q8—61no—
245C3×D4—32no—
246C3×D4—64no—
247C3×D4—61no—
248C2×C3×C4—24no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—21no—
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—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—64no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—122no—
274C2×C3×C4—121no—
275C2×C3×C4—121no—
276C2×C3×C4(C2×D3)⋊C411yescharacteristic
277C2×C3×C4(C2×D3)⋊C411yescharacteristic
278C2×C3×C4(C2×D3)⋊C411yescharacteristic
279C2×C3×C4C3×C22⋊C411yescharacteristic
280C2×C3×C4C3×C22⋊C411yescharacteristic
281C2×C3×C4C3×C22⋊C411yescharacteristic
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4C2×D1211yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×C3×C4C22×C3×C411yescharacteristic
286C2×C3×C4C2×C3×D411yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288#67—24no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292D12—21no—
293D12C3×M1612yescomplemented
294C4×D3—24no—
295C4×D3—42no—
296C4×D3—41no—
297C4×D3—41no—
298Dic6—21no—
299Dic6C3×M1612yescomplemented
300C3×C8—28no—
301C3×C8—24no—
302C3×C8—24no—
303C3×C8—122no—
304C3⋊C8—42no—
305C2×C32—41no—
306C2×C32#40711yescharacteristic
307C2×C32#41711yescharacteristic
308C2×C32C2×#10411yescharacteristic
309C3×D3—42no—
310#41—62no—
311#41—62no—
312C2×Q8—31no—
313C2×D4—31no—
314C2×D4—61no—
315C22×C4—61no—
316C22×C4—61no—
317C22×C4—61no—
318C22×C4C3×C4×D311yescharacteristic
319C22×C4C3×D1211yescharacteristic
320C22×C4C3×#6711yescharacteristic
321M16—24no—
322M16—122no—
323C2×C8—22no—
324C2×C8—62no—
325C4⋊C4—31no—
326C4⋊C4—31no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C22⋊C4—61no—
330C22⋊C4—61no—
331C22⋊C4—61no—
332C42—61no—
333C42—61no—
334C42—61no—
335C42C3×C4×D311yescharacteristic
336C42C3×D1211yescharacteristic
337C42C3×#6711yescharacteristic
338C42C22×C3×D311yescharacteristic
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—62no—
350C22×C3—121no—
351C22×C3—121no—
352C22×C3C2×(C2×D3)⋊C411yescharacteristic
353C22×C3C2×C3×C22⋊C411yescharacteristic
354C2×D3—22no—
355C2×D3—41no—
356C2×D3—41no—
357C3×C4—22no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—22no—
369C3×C4—41no—
370C3×C4—41no—
371C3×C4—62no—
372C3×C4—121no—
373C3×C4—121no—
374C3×C4#80512yes—
375C3×C4C3×#10412yes—
376C3×C4D3×M1611yescharacteristic
377C3×C4D3×M1611yescharacteristic
378C3×C4#90811yescharacteristic
379C3×C4#90911yescharacteristic
380C3×C4C2×C3×M1611yescharacteristic
381C3×C4C2×C3×M1611yescharacteristic
382C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
383C3×C4C3×#13711yescharacteristic
384Dic3—22no—
385Dic3—41no—
386Dic3—41no—
387C32#148911yescharacteristic, complemented, Sylow
388C23—61no—
389C23C3×(C2×D3)⋊C411yescharacteristic
390Q8—32no—
391Q8—61no—
392D4—32no—
393D4—64no—
394D4—61no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—64no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—122no—
407C2×C4C3×(C2×D3)⋊C411yescharacteristic
408C2×C4C3×(C2×D3)⋊C411yescharacteristic
409C2×C4C3×(C2×D3)⋊C411yescharacteristic
410C2×C4C2×C3×C4×D311yescharacteristic
411C2×C4C2×C3×D1211yescharacteristic
412C2×C4C2×C3×#6711yescharacteristic
413C8—24no—
414C8—122no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—42no—
419C2×C3—41no—
420C2×C3—41no—
421C2×C3—122no—
422C2×C3C2×#80511yescharacteristic
423C2×C3#512611yescharacteristic
424C2×C3#513311yescharacteristic
425C2×C3C3×#40711yescharacteristic
426C2×C3C3×#41711yescharacteristic
427C2×C3C2×C3×#10411yescharacteristic
428D3—42no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—62no—
433C22—121no—
434C22—121no—
435C22C2×C3×(C2×D3)⋊C411yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—62no—
440C4—121no—
441C4—121no—
442C4C3×#80512yes—
443C4C3×D3×M1611yescharacteristic
444C4C3×D3×M1611yescharacteristic
445C4C3×#90811yescharacteristic
446C4C3×#90911yescharacteristic
447C3—21no—
448C3#6985411yescharacteristic, direct product factor
449C3C3×#148911yescharacteristic, complemented
450C2—41no—
451C2—122no—
452C2C2×C3×#80511yescharacteristic
453C2C3×#512611yescharacteristic
454C2C3×#513311yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×C4×M16C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C4
cosocleC3×C42C23×C3
hypercenterC3×C4×M16D3
hypocenterC3C3×#1489
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×M16

Complements

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

NH ≅ G/Ntype
2. C32×C4×M16C2semidirect
3. C3×#4924C2semidirect
4. C3×#4459C2semidirect
5. C3×#4456C2semidirect
7. #69854C3direct (N × H)
29. C3×C4×M16D3semidirect
30. C3×C4×M16C2×C3semidirect
31. #4924C2×C3semidirect
34. #4459C2×C3semidirect
35. #4456C2×C3semidirect
122. C3×D12M16semidirect
128. C3×Dic6M16semidirect
133. C4×M16C3×D3semidirect
293. D12C3×M16semidirect
299. Dic6C3×M16semidirect
387. C32#1489semidirect
448. C3#69854direct (N × H)
449. C3C3×#1489semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2352
C32×C4×M162
C3×#49242
C3×#44592
C3×#44562
C3×#14893
#698543