Finite Group Databasebeta

← C3×#67625 #11770970

Subgroups — C3×#67625 #11770970

Order 1152.

573 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#380C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C3×#1289—31nomaximal
5#67625C311yesmaximal, characteristic, direct product factor
6C23×C32×C4C2211yescharacteristic
7C2×C32×C4⋊C4—21no—
8C2×C32×C22⋊C4—21no—
9C2×C3×#217—21no—
10C2×C3×C4⋊Dic3—21no—
11C22×C3×C3⋊C8C412yescomplemented
12C32×#95C412yescomplemented
13C3×C3⋊#95C412yescomplemented
14C3×#830—21no—
15C3×#830—21no—
16C2×C3×C22⋊C8—31no—
17C3×#380—21no—
18C3×#380—31no—
19C3×#380D311yescharacteristic
20C3×#380C2×C311yescharacteristic
21#5212C2×C311yescharacteristic
22C2×#830C2×C311yescharacteristic
23C24×C32D411yescharacteristic
24C22×C32×C4—22no—
25C22×C32×C4—42no—
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4Q811yescharacteristic
32C22×C3×Dic3—22no—
33C32×C4⋊C4—42no—
34C32×C22⋊C4—41no—
35C32×C22⋊C4—41no—
36C3×#217—41no—
37C3×#217—41no—
38C3×C4⋊Dic3—42no—
39C2×C3×C3⋊C8—22no—
40C2×C3×C3⋊C8—42no—
41#1289—31noSylow
42C23×C3×C4—21no—
43C23×C3×C4C2×D311yescharacteristic
44C23×C3×C4C22×C311yescharacteristic
45C22×C3×C8—32no—
46C2×C3×C4⋊C4—22no—
47C2×C3×C4⋊C4—21no—
48C2×C3×C4⋊C4—21no—
49C2×C3×C4⋊C4—61no—
50C2×C3×C22⋊C4—22no—
51C2×C3×C22⋊C4—21no—
52C2×C3×C22⋊C4—21no—
53C2×C3×C22⋊C4—61no—
54C2×#217—21no—
55C2×C4⋊Dic3—21no—
56C22×C3⋊C8C3×C412yescomplemented
57C3×C22⋊C8—61no—
58C3×C22⋊C8—61no—
59C3×#95—22no—
60C3×#95—32no—
61C3×#95Dic312yescomplemented
62C3×#95C3×C412yescomplemented
63C3⋊#95C3×C412yescomplemented
64#830—21no—
65#830—21no—
66C23×C32—41no—
67C23×C32—41no—
68C23×C32C22⋊C411yescharacteristic
69C23×C32C22⋊C411yescharacteristic
70C23×C32C4⋊C411yescharacteristic
71C23×C32D811yescharacteristic
72C23×C32SD1611yescharacteristic
73C23×C32SD1611yescharacteristic
74C23×C32Q1611yescharacteristic
75C2×C32×C4—22no—
76C2×C32×C4—22no—
77C2×C32×C4—22no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4—42no—
82C2×C32×C4—42no—
83C2×C32×C4—42no—
84C2×C32×C4C4211yescharacteristic
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C4⋊C411yescharacteristic
87C2×C32×C4C4⋊C411yescharacteristic
88C2×C3×Dic3—42no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91C3×C3⋊C8—42no—
92C2×C22⋊C8—31no—
93#380—31no—
94#380C3×D311yescharacteristic
95C24×C3—21no—
96C24×C3#6711yescharacteristic
97C24×C3C3×D411yescharacteristic
98C22×C3×C4—24no—
99C22×C3×C4—22no—
100C22×C3×C4—22no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4—21no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4—42no—
108C22×C3×C4—42no—
109C22×C3×C4—44no—
110C22×C3×C4—62no—
111C22×C3×C4Dic611yescharacteristic
112C22×C3×C4C4×D311yescharacteristic
113C22×C3×C4C4×D311yescharacteristic
114C22×C3×C4D1211yescharacteristic
115C22×C3×C4C2×Dic311yescharacteristic
116C22×C3×C4#6711yescharacteristic
117C22×C3×C4C2×C3×C411yescharacteristic
118C22×C3×C4C2×C3×C411yescharacteristic
119C22×C3×C4C2×C3×C411yescharacteristic
120C22×C3×C4C3×D411yescharacteristic
121C22×C3×C4C3×D411yescharacteristic
122C22×C3×C4C3×Q811yescharacteristic
123C22×Dic3—22no—
124C2×C3×C8—62no—
125C2×C3×C8—122no—
126C3×C4⋊C4—44no—
127C3×C4⋊C4—42no—
128C3×C4⋊C4—42no—
129C3×C4⋊C4—122no—
130C3×C22⋊C4—42no—
131C3×C22⋊C4—42no—
132C3×C22⋊C4—41no—
133C3×C22⋊C4—41no—
134C3×C22⋊C4—41no—
135C3×C22⋊C4—41no—
136C3×C22⋊C4—121no—
137C3×C22⋊C4—121no—
138#217—41no—
139#217—41no—
140C4⋊Dic3—42no—
141C2×C3⋊C8—22no—
142C2×C3⋊C8—42no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32—21no—
149C22×C32—41no—
150C22×C32—41no—
151C22×C32—41no—
152C22×C32—41no—
153C22×C32#9511yescharacteristic
154C22×C32#10211yescharacteristic
155C22×C32#10211yescharacteristic
156C22×C32#10311yescharacteristic
157C22×C32#10311yescharacteristic
158C22×C32#10611yescharacteristic
159C22×C32#10711yescharacteristic
160C32×C4—21no—
161C32×C4—21no—
162C32×C4—21no—
163C32×C4—82no—
164C32×C4#9912yes—
165C3×Dic3—82no—
166C23×C4C2×C3×D311yescharacteristic
167C22×C8—32no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—61no—
170C2×C22⋊C4—21no—
171C2×C22⋊C4—61no—
172C22⋊C8—61no—
173C22⋊C8—61no—
174#95—32no—
175#95C3×Dic312yescomplemented
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—41no—
184C23×C3—41no—
185C23×C3—41no—
186C23×C3—41no—
187C23×C3—42no—
188C23×C3—42no—
189C23×C3Dic3⋊C411yescharacteristic
190C23×C3(C2×D3)⋊C411yescharacteristic
191C23×C3#21311yescharacteristic
192C23×C3#21411yescharacteristic
193C23×C3#21511yescharacteristic
194C23×C3#21611yescharacteristic
195C23×C3#21711yescharacteristic
196C23×C3C3×C22⋊C411yescharacteristic
197C23×C3C3×C22⋊C411yescharacteristic
198C23×C3C3×C4⋊C411yescharacteristic
199C23×C3C3×D811yescharacteristic
200C23×C3C3×SD1611yescharacteristic
201C23×C3C3×SD1611yescharacteristic
202C23×C3C3×Q1611yescharacteristic
203C2×C3×C4—24no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—42no—
215C2×C3×C4—42no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—42no—
223C2×C3×C4—42no—
224C2×C3×C4—42no—
225C2×C3×C4—44no—
226C2×C3×C4—44no—
227C2×C3×C4—42no—
228C2×C3×C4—42no—
229C2×C3×C4—44no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—122no—
235C2×C3×C4—122no—
236C2×C3×C4—122no—
237C2×C3×C4C4×Dic311yescharacteristic
238C2×C3×C4Dic3⋊C411yescharacteristic
239C2×C3×C4C4⋊Dic311yescharacteristic
240C2×C3×C4(C2×D3)⋊C411yescharacteristic
241C2×C3×C4C3×C4211yescharacteristic
242C2×C3×C4C3×C22⋊C411yescharacteristic
243C2×C3×C4C3×C4⋊C411yescharacteristic
244C2×C3×C4C3×C4⋊C411yescharacteristic
245C2×Dic3—42no—
246C2×Dic3—42no—
247C2×Dic3—42no—
248C3×C8—122no—
249C3⋊C8—42no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32—21no—
253C2×C32—21no—
254C2×C32—21no—
255C2×C32—21no—
256C2×C32H(3,ℤ/4)11yescharacteristic
257C2×C32#34011yescharacteristic
258C2×C32#34211yescharacteristic
259C24C3×#6711yescharacteristic
260C22×C4—22no—
261C22×C4—42no—
262C22×C4—62no—
263C22×C4C3×Dic611yescharacteristic
264C22×C4C3×C4×D311yescharacteristic
265C22×C4C3×C4×D311yescharacteristic
266C22×C4C3×D1211yescharacteristic
267C22×C4C2×C3×Dic311yescharacteristic
268C22×C4C3×#6711yescharacteristic
269C2×C8—62no—
270C2×C8—122no—
271C4⋊C4—42no—
272C4⋊C4—122no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—121no—
276C22⋊C4—121no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—42no—
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—42no—
314C22×C3#80711yescharacteristic
315C22×C3#80811yescharacteristic
316C22×C3#80911yescharacteristic
317C22×C3#81011yescharacteristic
318C22×C3C3⋊#9511yescharacteristic
319C22×C3#83211yescharacteristic
320C22×C3#83511yescharacteristic
321C22×C3C3×#9511yescharacteristic
322C22×C3C3×#10211yescharacteristic
323C22×C3C3×#10211yescharacteristic
324C22×C3C3×#10311yescharacteristic
325C22×C3C3×#10311yescharacteristic
326C22×C3C3×#10611yescharacteristic
327C22×C3C3×#10711yescharacteristic
328C3×C4—22no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—22no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—84no—
339C3×C4—82no—
340C3×C4—82no—
341C3×C4—242no—
342C3×C4#80612yes—
343C3×C4C3×#9912yes—
344Dic3—82no—
345C32#128911yescharacteristic, complemented, Sylow
346C23—41no—
347C23—41no—
348C23C3×Dic3⋊C411yescharacteristic
349C23C3×(C2×D3)⋊C411yescharacteristic
350C23C3×#21311yescharacteristic
351C23C3×#21411yescharacteristic
352C23C3×#21511yescharacteristic
353C23C3×#21611yescharacteristic
354C23C3×#21711yescharacteristic
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—122no—
365C2×C4—122no—
366C2×C4—122no—
367C2×C4C3×C4×Dic311yescharacteristic
368C2×C4C3×Dic3⋊C411yescharacteristic
369C2×C4C3×C4⋊Dic311yescharacteristic
370C2×C4C3×(C2×D3)⋊C411yescharacteristic
371C8—122no—
372C2×C3—22no—
373C2×C3—22no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—41no—
390C2×C3—41no—
391C2×C3—41no—
392C2×C3—41no—
393C2×C3#452711yescharacteristic
394C2×C3#452911yescharacteristic
395C2×C3#453111yescharacteristic
396C2×C3C3×H(3,ℤ/4)11yescharacteristic
397C2×C3C3×#34011yescharacteristic
398C2×C3C3×#34211yescharacteristic
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22C3×#80711yescharacteristic
410C22C3×#80811yescharacteristic
411C22C3×#80911yescharacteristic
412C22C3×#81011yescharacteristic
413C22C3×C3⋊#9511yescharacteristic
414C22C3×#83211yescharacteristic
415C22C3×#83511yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—82no—
420C4—242no—
421C4C3×#80612yes—
422C3—21no—
423C3#6762511yescharacteristic, direct product factor
424C3C3×#128911yescharacteristic, complemented
425C2—21no—
426C2—21no—
427C2—21no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2C3×#452711yescharacteristic
432C2C3×#452911yescharacteristic
433C2C3×#453111yescharacteristic
subgroupG/H
centerC22×C3C3⋊#95
commutatorC2×C3×C4C3×C42
FrattiniC23×C4C2×C3×D3
FittingC32×#380C2
socleC22×C32#95
prime radicalC24×C32D4
cosocleC23×C3×C4C22×C3
hypercenterC3×#380D3
hypocenterC3C3×#1289
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
5. #67625C3direct (N × H)
11. C22×C3×C3⋊C8C4semidirect
12. C32×#95C4semidirect
13. C3×C3⋊#95C4semidirect
56. C22×C3⋊C8C3×C4semidirect
61. C3×#95Dic3semidirect
62. C3×#95C3×C4semidirect
63. C3⋊#95C3×C4semidirect
175. #95C3×Dic3semidirect
345. C32#1289semidirect
423. C3#67625direct (N × H)
424. C3C3×#1289semidirect

Maximal subgroups

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

subgroupindex
C32×#3802
C3×#52122
C2×C3×#8302
C3×#12893
#676253