Finite Group Databasebeta

← C3×#71599 #11774678

Subgroups — C3×#71599 #11774678

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C3×#4926C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C214yesmaximal, complemented
5C3×#1490—31nomaximal
6#71599C311yesmaximal, characteristic, direct product factor
7C22×C32×D4C411yescharacteristic
8C23×C32×C4—21no—
9C32×C4×D4—21no—
10C32×C4×D4—21no—
11C32×C4×D4C412yes—
12C32×C4×D4C2212yes—
13C2×C32×C4⋊C4C411yescharacteristic
14C2×C32×C22⋊C4—21no—
15C2×C32×C42C2211yescharacteristic
16C2×C3×#208—21no—
17C3×#830—21no—
18C3×C4⋊(C3⋊C8)C2212yescomplemented
19C3×#803—21no—
20C3×#803—21no—
21C3×C4×C3⋊C8C2212yescomplemented
22C2×C3×C4×D4—21no—
23C2×C3×C4×D4D311yescharacteristic
24C2×C3×C4×D4C2×C311yescharacteristic
25C3×#432—31no—
26C3×C4×M16—31no—
27#4926C2×C311yescharacteristic, complemented
28C4×#208C2×C311yescharacteristic, complemented
29C3×D4⋊C8—34no—
30D4⋊(C3⋊C8)C2×C314yescomplemented
31C24×C32—21no—
32C2×C32×D4—24no—
33C2×C32×D4—21no—
34C2×C32×D4C2×C412yes—
35C22×C32×C4—21no—
36C22×C32×C4—22no—
37C22×C32×C4—22no—
38C22×C32×C4—44no—
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C32×C4⋊C4—21no—
43C32×C4⋊C4C2×C412yes—
44C32×C22⋊C4—22no—
45C32×C22⋊C4—22no—
46C32×C42C2×C411yescharacteristic
47C32×C42D411yescharacteristic
48C32×C42D411yescharacteristic
49C32×C42C2311yescharacteristic
50C3×#208—24no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53#1490—31noSylow
54C22×C3×D4—21no—
55C22×C3×D4Dic311yescharacteristic
56C22×C3×D4C3×C411yescharacteristic
57C23×C3×C4—22no—
58C23×C3×C4—21no—
59C23×C3×C4—21no—
60C2×C3×M16—61no—
61C3×C4×D4—22no—
62C3×C4×D4—22no—
63C3×C4×D4—21no—
64C3×C4×D4—21no—
65C3×C4×D4—21no—
66C3×C4×D4—21no—
67C3×C4×D4—22no—
68C3×C4×D4—22no—
69C3×C4×D4Dic312yes—
70C3×C4×D4C3×C412yes—
71C3×C4×D4C2×D312yes—
72C3×C4×D4C22×C312yes—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4Dic311yescharacteristic
75C2×C3×C4⋊C4C3×C411yescharacteristic
76C2×C3×C22⋊C4—22no—
77C2×C3×C22⋊C4—21no—
78C2×C3×C22⋊C4—21no—
79C2×C3×C42—21no—
80C2×C3×C42C2×D311yescharacteristic
81C2×C3×C42C22×C311yescharacteristic
82C2×#208—21no—
83C3×C4⋊C8—32no—
84C3×C22⋊C8—61no—
85C3×#97—61no—
86C3×#97—61no—
87C3×C4×C8—32no—
88#830—21no—
89C4⋊(C3⋊C8)C22×C312yescomplemented
90#803—21no—
91#803—21no—
92C4×C3⋊C8C22×C312yescomplemented
93C23×C32—24no—
94C23×C32—22no—
95C23×C32—42no—
96C23×C32—42no—
97C23×C32C22⋊C411yescharacteristic
98C32×D4—24no—
99C32×D4—22no—
100C32×D4M1614yescomplemented
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—44no—
106C2×C32×C4—42no—
107C2×C32×C4—44no—
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C3×C3⋊C8—24no—
115C3×C3⋊C8—42no—
116C2×C4×D4C3×D311yescharacteristic
117#432—31no—
118C4×M16—31no—
119D4⋊C8—34no—
120C24×C3—22no—
121C24×C3—21no—
122C24×C3—21no—
123C2×C3×D4—22no—
124C2×C3×D4—28no—
125C2×C3×D4—24no—
126C2×C3×D4—24no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—22no—
130C2×C3×D4C2×Dic312yes—
131C2×C3×D4C2×C3×C412yes—
132C22×C3×C4—22no—
133C22×C3×C4—24no—
134C22×C3×C4—24no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—48no—
145C22×C3×C4—44no—
146C22×C3×C4—44no—
147C22×C3×C4C2×Dic311yescharacteristic
148C22×C3×C4#6711yescharacteristic
149C22×C3×C4#6711yescharacteristic
150C22×C3×C4C2×C3×C411yescharacteristic
151C22×C3×C4C3×D411yescharacteristic
152C22×C3×C4C3×D411yescharacteristic
153C3×M16—64no—
154C2×C3×C8—62no—
155C2×C3×C8—62no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4C2×Dic312yes—
161C3×C4⋊C4C2×C3×C412yes—
162C3×C22⋊C4—24no—
163C3×C22⋊C4—24no—
164C3×C22⋊C4—22no—
165C3×C22⋊C4—22no—
166C3×C22⋊C4—22no—
167C3×C22⋊C4—22no—
168C3×C42—21no—
169C3×C42—21no—
170C3×C42—21no—
171C3×C42—21no—
172C3×C42C2×Dic311yescharacteristic
173C3×C42#6711yescharacteristic
174C3×C42#6711yescharacteristic
175C3×C42C2×C3×C411yescharacteristic
176C3×C42C3×D411yescharacteristic
177C3×C42C3×D411yescharacteristic
178C3×C42C22×D311yescharacteristic
179C3×C42C23×C311yescharacteristic
180#208—24no—
181C2×C3⋊C8—22no—
182C2×C3⋊C8—22no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—24no—
186C22×C32—48no—
187C22×C32—42no—
188C22×C32—42no—
189C22×C32#10412yes—
190C22×C32C2×C22⋊C411yescharacteristic
191C32×C4—21no—
192C32×C4—21no—
193C32×C4—21no—
194C32×C4—21no—
195C32×C4—42no—
196C32×C4C2×M1612yes—
197C32×C4AGL(1,ℤ/8)12yes—
198C22×D4C3×Dic311yescharacteristic
199C23×C4—21no—
200C2×M16—61no—
201C4×D4—21no—
202C4×D4—21no—
203C4×D4C3×Dic312yes—
204C4×D4C2×C3×D312yes—
205C2×C4⋊C4C3×Dic311yescharacteristic
206C2×C22⋊C4—21no—
207C2×C42C2×C3×D311yescharacteristic
208C4⋊C8—32no—
209C22⋊C8—61no—
210#97—61no—
211#97—61no—
212C4×C8—32no—
213C23×C3—24no—
214C23×C3—28no—
215C23×C3—24no—
216C23×C3—24no—
217C23×C3—22no—
218C23×C3—22no—
219C23×C3—21no—
220C23×C3—44no—
221C23×C3—42no—
222C23×C3—42no—
223C23×C3—44no—
224C23×C3—42no—
225C23×C3—42no—
226C23×C3#21711yescharacteristic
227C23×C3C3×C22⋊C411yescharacteristic
228C3×D4—28no—
229C3×D4—24no—
230C3×D4—24no—
231C3×D4—24no—
232C3×D4—22no—
233C3×D4—22no—
234C3×D4—24no—
235C3×D4#20814yescomplemented
236C3×D4C3×M1614yescomplemented
237C2×C3×C4—24no—
238C2×C3×C4—24no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—24no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—42no—
255C2×C3×C4—48no—
256C2×C3×C4—44no—
257C2×C3×C4—44no—
258C2×C3×C4—48no—
259C2×C3×C4—44no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—44no—
263C2×C3×C4—44no—
264C2×C3×C4#21711yescharacteristic
265C2×C3×C4#21711yescharacteristic
266C2×C3×C4#21711yescharacteristic
267C2×C3×C4C3×C22⋊C411yescharacteristic
268C2×C3×C4C3×C22⋊C411yescharacteristic
269C2×C3×C4C3×C22⋊C411yescharacteristic
270C2×C3×C4C22×Dic311yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×C3×C4C22×C3×C411yescharacteristic
274C2×C3×C4C2×C3×D411yescharacteristic
275C2×C3×C4C2×C3×D411yescharacteristic
276C3×C8—64no—
277C3×C8—122no—
278C3⋊C8—24no—
279C3⋊C8—42no—
280C2×C32—22no—
281C2×C32—44no—
282C2×C32#40711yescharacteristic
283C2×C32#41811yescharacteristic
284C2×C32C2×#10411yescharacteristic
285C24—21no—
286C2×D4—24no—
287C2×D4—21no—
288C2×D4C2×C3×Dic312yes—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—44no—
293C22×C4C2×C3×Dic311yescharacteristic
294C22×C4C3×#6711yescharacteristic
295C22×C4C3×#6711yescharacteristic
296M16—64no—
297C2×C8—62no—
298C2×C8—62no—
299C4⋊C4—21no—
300C4⋊C4C2×C3×Dic312yes—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C42C2×C3×Dic311yescharacteristic
304C42C3×#6711yescharacteristic
305C42C3×#6711yescharacteristic
306C42C22×C3×D311yescharacteristic
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—28no—
314C22×C3—24no—
315C22×C3—24no—
316C22×C3—21no—
317C22×C3—22no—
318C22×C3—44no—
319C22×C3—416no—
320C22×C3—48no—
321C22×C3—48no—
322C22×C3—44no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3#83712yes—
328C22×C3C3×#10412yes—
329C22×C3C2×#21711yescharacteristic
330C22×C3C2×C3×C22⋊C411yescharacteristic
331C3×C4—22no—
332C3×C4—22no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—41no—
344C3×C4—41no—
345C3×C4—44no—
346C3×C4—42no—
347C3×C4—42no—
348C3×C4C2×#20812yes—
349C3×C4#93212yes—
350C3×C4C2×C3×M1612yes—
351C3×C4C3×AGL(1,ℤ/8)12yes—
352C32#149011yescharacteristic, complemented, Sylow
353C23—24no—
354C23—22no—
355C23—42no—
356C23—42no—
357C23C3×#21711yescharacteristic
358D4—24no—
359D4—22no—
360D4C3×#20814yescomplemented
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—44no—
366C2×C4—42no—
367C2×C4—44no—
368C2×C4C3×#21711yescharacteristic
369C2×C4C3×#21711yescharacteristic
370C2×C4C3×#21711yescharacteristic
371C2×C4C22×C3×Dic311yescharacteristic
372C2×C4C2×C3×#6711yescharacteristic
373C2×C4C2×C3×#6711yescharacteristic
374C8—64no—
375C8—122no—
376C2×C3—24no—
377C2×C3—22no—
378C2×C3—22no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—48no—
383C2×C3—44no—
384C2×C3—44no—
385C2×C3#520711yescharacteristic
386C2×C3#521511yescharacteristic
387C2×C3C2×#83711yescharacteristic
388C2×C3C3×#40711yescharacteristic
389C2×C3C3×#41811yescharacteristic
390C2×C3C2×C3×#10411yescharacteristic
391C22—21no—
392C22—21no—
393C22—24no—
394C22—48no—
395C22—42no—
396C22—42no—
397C22C3×#83712yes—
398C22C2×C3×#21711yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4C2×C3×#20812yes—
405C4C3×#93212yes—
406C3—21no—
407C3#7159911yescharacteristic, direct product factor
408C3C3×#149011yescharacteristic, complemented
409C2—22no—
410C2—44no—
411C2C3×#520711yescharacteristic
412C2C3×#521511yescharacteristic
413C2C2×C3×#83711yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC2×C32×C4×D4C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C32×D4C4
cosocleC3×C42C23×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#1490
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#4926C2semidirect
3. C3×C4×#208C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
6. #71599C3direct (N × H)
18. C3×C4⋊(C3⋊C8)C22semidirect
21. C3×C4×C3⋊C8C22semidirect
27. #4926C2×C3semidirect
28. C4×#208C2×C3semidirect
30. D4⋊(C3⋊C8)C2×C3semidirect
89. C4⋊(C3⋊C8)C22×C3semidirect
92. C4×C3⋊C8C22×C3semidirect
100. C32×D4M16semidirect
235. C3×D4#208semidirect
236. C3×D4C3×M16semidirect
352. C32#1490semidirect
360. D4C3×#208semidirect
407. C3#71599direct (N × H)
408. C3C3×#1490semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C3×#49262
C3×C4×#2082
C3×D4⋊(C3⋊C8)2
C3×#14903
#715993