Finite Group Databasebeta

← C3×#71571 #11773757

Subgroups — C3×#71571 #11773757

Order 1152.

693 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic
2C3×#4925C212yesmaximal, complemented
3C3×#4528C212yesmaximal, complemented
4C3×#4525C212yesmaximal
5C3×#1458—31nomaximal
6#71571C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C411yescharacteristic
8C32×#117—22no—
9C32×#117—22no—
10C2×C32×C4⋊C4C411yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4C411yescharacteristic
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×C32×C42C411yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C3×#830C2214yes—
17C3×C4⋊(C3⋊C8)—22no—
18C3×C4×C3⋊C8—22no—
19C2×C3×#117—21no—
20C2×C3×#117D311yescharacteristic
21C2×C3×#117C2×C311yescharacteristic
22C3×#431—32no—
23#4925C2×C312yescomplemented
24C3×#324—32no—
25C3×#323—32no—
26#4528C2×C312yescomplemented
27#4525C2×C312yes—
28C24×C32C2×C411yescharacteristic
29C22×C32×C4—21no—
30C22×C32×C4—21no—
31C22×C32×C4—22no—
32C22×C32×C4C814yescomplemented
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C32×C4⋊C4—22no—
40C32×C4⋊C4—22no—
41C32×C22⋊C4—22no—
42C32×C22⋊C4—22no—
43C32×C42—21no—
44C32×C42—21no—
45C32×C42D412yes—
46C32×C42D412yes—
47C2×C3×C3⋊C8—24no—
48#1458—31noSylow
49C23×C3×C4—21no—
50C23×C3×C4Dic311yescharacteristic
51C23×C3×C4C3×C411yescharacteristic
52C3×#117—24no—
53C3×#117—24no—
54C3×#117—22no—
55C3×#117—22no—
56C3×#117—22no—
57C3×#117—22no—
58C2×C3×C4⋊C4—21no—
59C2×C3×C4⋊C4—21no—
60C2×C3×C4⋊C4Dic311yescharacteristic
61C2×C3×C4⋊C4C3×C411yescharacteristic
62C2×C3×C4⋊C4C2×D311yescharacteristic
63C2×C3×C4⋊C4C22×C311yescharacteristic
64C2×C3×C22⋊C4—21no—
65C2×C3×C22⋊C4—21no—
66C2×C3×C22⋊C4Dic311yescharacteristic
67C2×C3×C22⋊C4C3×C411yescharacteristic
68C2×C3×C22⋊C4C2×D311yescharacteristic
69C2×C3×C22⋊C4C22×C311yescharacteristic
70C2×C3×C42—21no—
71C2×C3×C42—21no—
72C2×C3×C42Dic311yescharacteristic
73C2×C3×C42C3×C411yescharacteristic
74C2×C3×C42C2×D311yescharacteristic
75C2×C3×C42C22×C311yescharacteristic
76C3×C4⋊C8—62no—
77C3×C22⋊C8—34no—
78C3×C4×C8—62no—
79#830C22×C314yes—
80C4⋊(C3⋊C8)—22no—
81C4×C3⋊C8—22no—
82C23×C32—21no—
83C23×C32—21no—
84C23×C32—41no—
85C23×C32—41no—
86C23×C32C2×C812yes—
87C23×C32C22×C411yescharacteristic
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—24no—
91C2×C32×C4—24no—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C22⋊C412yes—
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C2×C812yes—
102C2×C32×C4C2×C812yes—
103C2×C32×C4M1612yes—
104C2×C32×C4C2×D412yes—
105C3×C3⋊C8—44no—
106C2×#117C3×D311yescharacteristic
107#431—32no—
108#324—32no—
109#323—32no—
110C24×C3—21no—
111C24×C3C2×Dic311yescharacteristic
112C24×C3C2×C3×C411yescharacteristic
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—24no—
116C22×C3×C4—22no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—22no—
122C22×C3×C4—24no—
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4C3⋊C814yescomplemented
130C22×C3×C4C3×C814yescomplemented
131C22×C3×C4C2×Dic311yescharacteristic
132C22×C3×C4C2×Dic311yescharacteristic
133C22×C3×C4C2×Dic311yescharacteristic
134C22×C3×C4C2×Dic311yescharacteristic
135C22×C3×C4C2×Dic311yescharacteristic
136C22×C3×C4C2×C3×C411yescharacteristic
137C22×C3×C4C2×C3×C411yescharacteristic
138C22×C3×C4C2×C3×C411yescharacteristic
139C22×C3×C4C2×C3×C411yescharacteristic
140C22×C3×C4C2×C3×C411yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C23×C311yescharacteristic
143C2×C3×C8—64no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4—24no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—22no—
149C3×C4⋊C4—22no—
150C3×C22⋊C4—24no—
151C3×C22⋊C4—24no—
152C3×C22⋊C4—22no—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—22no—
155C3×C22⋊C4—22no—
156C3×C42—22no—
157C3×C42—22no—
158C3×C42—21no—
159C3×C42—21no—
160C3×C42—21no—
161C3×C42—21no—
162C3×C42—22no—
163C3×C42—22no—
164C3×C42#6712yes—
165C3×C42#6712yes—
166C3×C42C3×D412yes—
167C3×C42C3×D412yes—
168C2×C3⋊C8—24no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32—22no—
172C22×C32—42no—
173C22×C32—42no—
174C22×C32—41no—
175C22×C32—41no—
176C22×C32C2×C22⋊C411yescharacteristic
177C22×C32C22×C811yescharacteristic
178C22×C32C2×M1611yescharacteristic
179C32×C4—22no—
180C32×C4—22no—
181C32×C4—22no—
182C32×C4—41no—
183C32×C4—41no—
184C32×C4C22⋊C812yes—
185C32×C4C22⋊C812yes—
186C23×C4C3×Dic311yescharacteristic
187#117—22no—
188#117—22no—
189C2×C4⋊C4C3×Dic311yescharacteristic
190C2×C4⋊C4C2×C3×D311yescharacteristic
191C2×C22⋊C4C3×Dic311yescharacteristic
192C2×C22⋊C4C2×C3×D311yescharacteristic
193C2×C42C3×Dic311yescharacteristic
194C2×C42C2×C3×D311yescharacteristic
195C4⋊C8—62no—
196C22⋊C8—34no—
197C4×C8—62no—
198C23×C3—22no—
199C23×C3—22no—
200C23×C3—21no—
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—22no—
205C23×C3—21no—
206C23×C3—41no—
207C23×C3—41no—
208C23×C3—41no—
209C23×C3—41no—
210C23×C3—42no—
211C23×C3—42no—
212C23×C3C2×C3⋊C812yes—
213C23×C3C2×C3×C812yes—
214C23×C3C22×Dic311yescharacteristic
215C23×C3C22×C3×C411yescharacteristic
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—28no—
219C2×C3×C4—28no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—24no—
227C2×C3×C4—24no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—42no—
246C2×C3×C4—42no—
247C2×C3×C4—42no—
248C2×C3×C4—42no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4C2×C3⋊C812yes—
254C2×C3×C4C2×C3⋊C812yes—
255C2×C3×C4#20812yes—
256C2×C3×C4#21712yes—
257C2×C3×C4#21711yescharacteristic
258C2×C3×C4#21711yescharacteristic
259C2×C3×C4C3×C22⋊C412yes—
260C2×C3×C4C3×C22⋊C411yescharacteristic
261C2×C3×C4C3×C22⋊C411yescharacteristic
262C2×C3×C4C2×C3×C812yes—
263C2×C3×C4C2×C3×C812yes—
264C2×C3×C4C3×M1612yes—
265C2×C3×C4C2×#6712yes—
266C2×C3×C4C2×C3×D412yes—
267C3×C8—124no—
268C3⋊C8—44no—
269C2×C32—21no—
270C2×C32—21no—
271C2×C32—42no—
272C2×C32C2×C22⋊C811yescharacteristic
273C2×C32#41011yescharacteristic
274C2×C32#41311yescharacteristic
275C24C2×C3×Dic311yescharacteristic
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4C3×C3⋊C814yescomplemented
280C22×C4C2×C3×Dic311yescharacteristic
281C22×C4C2×C3×Dic311yescharacteristic
282C22×C4C2×C3×Dic311yescharacteristic
283C22×C4C2×C3×Dic311yescharacteristic
284C22×C4C2×C3×Dic311yescharacteristic
285C22×C4C22×C3×D311yescharacteristic
286C2×C8—64no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C42—21no—
292C42—21no—
293C42C3×#6712yes—
294C42C3×#6712yes—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—24no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—42no—
308C22×C3—42no—
309C22×C3—44no—
310C22×C3—44no—
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—42no—
314C22×C3—42no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3C22×C3⋊C811yescharacteristic
320C22×C3C2×#20811yescharacteristic
321C22×C3C2×#21711yescharacteristic
322C22×C3C2×C3×C22⋊C411yescharacteristic
323C22×C3C22×C3×C811yescharacteristic
324C22×C3C2×C3×M1611yescharacteristic
325C3×C4—24no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—22no—
331C3×C4—22no—
332C3×C4—22no—
333C3×C4—22no—
334C3×C4—42no—
335C3×C4—42no—
336C3×C4—42no—
337C3×C4—42no—
338C3×C4—41no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—41no—
342C3×C4#83012yes—
343C3×C4#83012yes—
344C3×C4C3×C22⋊C812yes—
345C3×C4C3×C22⋊C812yes—
346C32#145811yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—41no—
350C23—41no—
351C23C2×C3×C3⋊C812yes—
352C23C22×C3×Dic311yescharacteristic
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4C2×C3×C3⋊C812yes—
364C2×C4C2×C3×C3⋊C812yes—
365C2×C4C3×#20812yes—
366C2×C4C3×#21712yes—
367C2×C4C3×#21711yescharacteristic
368C2×C4C3×#21711yescharacteristic
369C2×C4C2×C3×#6712yes—
370C8—124no—
371C2×C3—22no—
372C2×C3—22no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—44no—
381C2×C3—42no—
382C2×C3—42no—
383C2×C3C2×#83011yescharacteristic
384C2×C3#523711yescharacteristic
385C2×C3#524011yescharacteristic
386C2×C3C2×C3×C22⋊C811yescharacteristic
387C2×C3C3×#41011yescharacteristic
388C2×C3C3×#41311yescharacteristic
389C22—21no—
390C22—21no—
391C22—22no—
392C22—42no—
393C22—42no—
394C22—41no—
395C22—41no—
396C22C22×C3×C3⋊C811yescharacteristic
397C22C2×C3×#20811yescharacteristic
398C22C2×C3×#21711yescharacteristic
399C4—22no—
400C4—22no—
401C4—22no—
402C4—41no—
403C4—41no—
404C4C3×#83012yes—
405C4C3×#83012yes—
406C3—21no—
407C3#7157111yescharacteristic, direct product factor
408C3C3×#145811yescharacteristic, complemented
409C2—21no—
410C2—21no—
411C2—42no—
412C2C2×C3×#83011yescharacteristic
413C2C3×#523711yescharacteristic
414C2C3×#524011yescharacteristic
subgroupG/H
centerC2×C3×C4#217
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#117C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#117D3
hypocenterC3C3×#1458
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. C3×#4528C2semidirect
6. #71571C3direct (N × H)
23. #4925C2×C3semidirect
26. #4528C2×C3semidirect
32. C22×C32×C4C8semidirect
129. C22×C3×C4C3⋊C8semidirect
130. C22×C3×C4C3×C8semidirect
279. C22×C4C3×C3⋊C8semidirect
346. C32#1458semidirect
407. C3#71571direct (N × H)
408. C3C3×#1458semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C3×#49252
C3×#45282
C3×#45252
C3×#14583
#715713