Finite Group Databasebeta

← C3×#70499 #11774825

Subgroups — C3×#70499 #11774825

Order 1152.

495 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic
2C32×#423C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4C3×#4484C212yesmaximal, complemented
5C3×#4483C212yesmaximal, complemented
6C3×#1495—31nomaximal
7#70499C311yesmaximal, characteristic, direct product factor
8C2×C32×M16—21no—
9C2×C32×C42C2211yescharacteristic
10C3×#930C411yescharacteristic
11C3×#929—21no—
12C3×C4×#67—21no—
13C3×#924C411yescharacteristic
14C3×#876—21no—
15C3×#875C411yescharacteristic
16C3×C4×D12C2211yescharacteristic
17C3×#872—21no—
18C3×#870C411yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×C4⋊C8—21no—
21C32×C4⋊C8C2212yes—
22C3×#830—21no—
23C3×C4⋊(C3⋊C8)—21no—
24C3×C4×C3⋊C8C2212yes—
25C3×#529—31no—
26#5479C2×C311yescharacteristic
27C3×#431—31no—
28C3×#423—21no—
29C3×#423D311yescharacteristic, complemented
30C3×#423C2×C311yescharacteristic, complemented
31#4925C2×C311yescharacteristic, complemented
32C3×Q8⋊C8—32no—
33C3×D4⋊C8—32no—
34#4484C2×C312yescomplemented
35#4483C2×C312yescomplemented
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C2×C3×#67—21no—
40C2×C3×D12C2×C411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×Dic6C2×C411yescharacteristic
43C32×M16—42no—
44C2×C32×C8—22no—
45C32×C42C2×C411yescharacteristic
46C32×C42D411yescharacteristic
47C32×C42D411yescharacteristic
48C32×C42C2311yescharacteristic
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⋊Dic3C2×C411yescharacteristic
55C3×C4⋊Dic3C2×C411yescharacteristic
56C3×Dic3⋊C4—21no—
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—21no—
61C2×C3×C3⋊C8—22no—
62#1495—31noSylow
63C2×C3×M16—22no—
64C2×C3×M16—21no—
65C2×C3×M16—21no—
66C3×#126—61no—
67C3×#125—31no—
68C3×#124—31no—
69C3×#123—61no—
70C3×C22⋊Q8—31no—
71C3×#121—31no—
72C3×C4×Q8—31no—
73C3×C4×D4—31no—
74C3×C4×D4—61no—
75C3×#117—61no—
76C2×C3×C42—21no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C22×C311yescharacteristic
79#930C3×C411yescharacteristic
80#929—21no—
81C4×#67—21no—
82#924C3×C411yescharacteristic
83#876—21no—
84#875C3×C411yescharacteristic
85C4×D12C22×C311yescharacteristic
86#872—21no—
87#870C3×C411yescharacteristic
88C4×Dic6C22×C311yescharacteristic
89C3×C4⋊C8—22no—
90C3×C4⋊C8—21no—
91C3×C4⋊C8—21no—
92C3×C4⋊C8—22no—
93C3×C4⋊C8—61no—
94C3×C4⋊C8C2×D312yes—
95C3×C4⋊C8C22×C312yes—
96C3×C22⋊C8—61no—
97C3×C4×C8—32no—
98#830—21no—
99C4⋊(C3⋊C8)—21no—
100C4×C3⋊C8C22×C312yes—
101C23×C32C22⋊C411yescharacteristic
102C22×C3×D3—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—22no—
106C2×C32×C4—41no—
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C3×#67—42no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—22no—
118C3×C4×D3—41no—
119C3×C4×D3—41no—
120C3×Dic6—22no—
121C32×C8—42no—
122C3×C3⋊C8—42no—
123#529—31no—
124#431—31no—
125#423C3×D311yescharacteristic, complemented
126Q8⋊C8—32no—
127D4⋊C8—32no—
128C2×C3×Q8—31no—
129C2×C3×D4—31no—
130C2×C3×D4—61no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—61no—
135C22×C3×C4C4×D311yescharacteristic
136C22×C3×C4D1211yescharacteristic
137C22×C3×C4#6711yescharacteristic
138C22×C3×C4C2×C3×C411yescharacteristic
139C22×C3×C4C3×D411yescharacteristic
140C22×C3×C4C3×D411yescharacteristic
141C2×#67—21no—
142C2×D12C2×C3×C411yescharacteristic
143C2×C4×D3—21no—
144C2×Dic6C2×C3×C411yescharacteristic
145C3×M16—44no—
146C3×M16—42no—
147C3×M16—42no—
148C2×C3×C8—24no—
149C2×C3×C8—22no—
150C2×C3×C8—22no—
151C2×C3×C8—62no—
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×C22⋊C4—61no—
159C3×C22⋊C4—61no—
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—61no—
168C3×C42C4×D311yescharacteristic
169C3×C42D1211yescharacteristic
170C3×C42#6711yescharacteristic
171C3×C42C2×C3×C411yescharacteristic
172C3×C42C3×D411yescharacteristic
173C3×C42C3×D411yescharacteristic
174C3×C42C22×D311yescharacteristic
175C3×C42C23×C311yescharacteristic
176#217—21no—
177(C2×D3)⋊C4—21no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—21no—
181C4⋊Dic3C2×C3×C411yescharacteristic
182C4⋊Dic3C2×C3×C411yescharacteristic
183Dic3⋊C4—21no—
184Dic3⋊C4—21no—
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187C4×Dic3—21no—
188C2×C3⋊C8—22no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32C2×C22⋊C411yescharacteristic
193C2×C3×D3—41no—
194C2×C3×D3—41no—
195C2×C3×D3—41no—
196C32×C4—21no—
197C32×C4—21no—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4#13112yes—
201C32×C4AGL(1,ℤ/8)11yescharacteristic
202C32×C4#13711yescharacteristic
203C3×Dic3—41no—
204C3×Dic3—41no—
205C3×Dic3—41no—
206C2×M16—21no—
207#126—61no—
208#125—31no—
209#124—31no—
210#123—61no—
211C22⋊Q8—31no—
212#121—31no—
213C4×Q8—31no—
214C4×D4—31no—
215C4×D4—61no—
216#117—61no—
217C2×C42C2×C3×D311yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—61no—
220C4⋊C8C2×C3×D312yes—
221C22⋊C8—61no—
222C4×C8—32no—
223C23×C3—21no—
224C23×C3—61no—
225C23×C3(C2×D3)⋊C411yescharacteristic
226C23×C3C3×C22⋊C411yescharacteristic
227C22×D3—21no—
228C3×Q8—62no—
229C3×D4—62no—
230C3×D4—122no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—22no—
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—21no—
245C2×C3×C4—42no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—42no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4—121no—
253C2×C3×C4—121no—
254C2×C3×C4(C2×D3)⋊C411yescharacteristic
255C2×C3×C4(C2×D3)⋊C411yescharacteristic
256C2×C3×C4(C2×D3)⋊C411yescharacteristic
257C2×C3×C4C3×C22⋊C411yescharacteristic
258C2×C3×C4C3×C22⋊C411yescharacteristic
259C2×C3×C4C3×C22⋊C411yescharacteristic
260C2×C3×C4C2×C4×D311yescharacteristic
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263C2×C3×C4C22×C3×C411yescharacteristic
264C2×C3×C4C2×C3×D411yescharacteristic
265C2×C3×C4C2×C3×D411yescharacteristic
266#67—42no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270D12—22no—
271C4×D3—41no—
272C4×D3—41no—
273Dic6—22no—
274C3×C8—44no—
275C3×C8—42no—
276C3×C8—42no—
277C3×C8—122no—
278C3⋊C8—42no—
279C2×C32—41no—
280C2×C32#40811yescharacteristic
281C2×C32#41711yescharacteristic
282C2×C32#42111yescharacteristic
283C3×D3—81no—
284C2×Q8—31no—
285C2×D4—31no—
286C2×D4—61no—
287C22×C4—61no—
288C22×C4C3×C4×D311yescharacteristic
289C22×C4C3×D1211yescharacteristic
290C22×C4C3×#6711yescharacteristic
291M16—42no—
292C2×C8—22no—
293C2×C8—62no—
294C4⋊C4—31no—
295C4⋊C4—31no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—61no—
299C4⋊C4—61no—
300C22⋊C4—61no—
301C22⋊C4—61no—
302C22⋊C4—61no—
303C22⋊C4—61no—
304C22⋊C4—61no—
305C42—61no—
306C42C3×C4×D311yescharacteristic
307C42C3×D1211yescharacteristic
308C42C3×#6711yescharacteristic
309C42C22×C3×D311yescharacteristic
310C22×C3—22no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—121no—
321C22×C3—121no—
322C22×C3—121no—
323C22×C3C2×(C2×D3)⋊C411yescharacteristic
324C22×C3C2×C3×C22⋊C411yescharacteristic
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—22no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—121no—
344C3×C4—121no—
345C3×C4—121no—
346C3×C4#90712yes—
347C3×C4#93211yescharacteristic
348C3×C4#94211yescharacteristic
349C3×C4C3×#13112yes—
350C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
351C3×C4C3×#13711yescharacteristic
352Dic3—41no—
353Dic3—41no—
354Dic3—41no—
355C32#149511yescharacteristic, complemented, Sylow
356C23—61no—
357C23C3×(C2×D3)⋊C411yescharacteristic
358Q8—62no—
359D4—62no—
360D4—122no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—121no—
369C2×C4—121no—
370C2×C4C3×(C2×D3)⋊C411yescharacteristic
371C2×C4C3×(C2×D3)⋊C411yescharacteristic
372C2×C4C3×(C2×D3)⋊C411yescharacteristic
373C2×C4C2×C3×C4×D311yescharacteristic
374C2×C4C2×C3×D1211yescharacteristic
375C2×C4C2×C3×#6711yescharacteristic
376C8—42no—
377C8—122no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—42no—
382C2×C3—41no—
383C2×C3—41no—
384C2×C3—241no—
385C2×C3#496611yescharacteristic
386C2×C3#512911yescharacteristic
387C2×C3#513911yescharacteristic
388C2×C3C3×#40811yescharacteristic
389C2×C3C3×#41711yescharacteristic
390C2×C3C3×#42111yescharacteristic
391D3—81no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22C2×C3×(C2×D3)⋊C411yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—121no—
404C4—121no—
405C4—121no—
406C4C3×#90712yes—
407C4C3×#93211yescharacteristic
408C4C3×#94211yescharacteristic
409C3—21no—
410C3#7049911yescharacteristic, direct product factor
411C3C3×#149511yescharacteristic, complemented
412C2—41no—
413C2—241no—
414C2C3×#496611yescharacteristic
415C2C3×#512911yescharacteristic
416C2C3×#513911yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#423C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C4
cosocleC3×C42C23×C3
hypercenterC3×#423D3
hypocenterC3C3×#1495
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#423

Complements

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

NH ≅ G/Ntype
2. C32×#423C2semidirect
3. C3×#4925C2semidirect
4. C3×#4484C2semidirect
5. C3×#4483C2semidirect
7. #70499C3direct (N × H)
29. C3×#423D3semidirect
30. C3×#423C2×C3semidirect
31. #4925C2×C3semidirect
34. #4484C2×C3semidirect
35. #4483C2×C3semidirect
125. #423C3×D3semidirect
355. C32#1495semidirect
410. C3#70499direct (N × H)
411. C3C3×#1495semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C32×#4232
C3×#49252
C3×#44842
C3×#44832
C3×#14953
#704993