Finite Group Databasebeta

← C3×#71598 #11774548

Subgroups — C3×#71598 #11774548

Order 1152.

837 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
1C2×C32×C4×D4C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic, complemented
3C3×#4924C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C214yesmaximal, complemented
5C3×#1486—31nomaximal
6#71598C311yesmaximal, 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)—21no—
19C3×C4⋊(C3⋊C8)—21no—
20C3×C4⋊(C3⋊C8)C2212yescomplemented
21C3×C4×C3⋊C8C2212yescomplemented
22C2×C3×C4×D4—21no—
23C2×C3×C4×D4D311yescharacteristic
24C2×C3×C4×D4C2×C311yescharacteristic
25C3×#431—31no—
26C3×#423—31no—
27#4925C2×C311yescharacteristic, complemented
28#4924C2×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—42no—
39C22×C32×C4—42no—
40C22×C32×C4C2×C411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C412yes—
45C32×C22⋊C4—22no—
46C32×C22⋊C4—22no—
47C32×C42C2×C411yescharacteristic
48C32×C42D411yescharacteristic
49C32×C42D411yescharacteristic
50C32×C42C2311yescharacteristic
51C3×#208—42no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8—22no—
54#1486—31noSylow
55C22×C3×D4—21no—
56C22×C3×D4Dic311yescharacteristic
57C22×C3×D4C3×C411yescharacteristic
58C23×C3×C4—22no—
59C23×C3×C4—21no—
60C23×C3×C4—21no—
61C2×C3×M16—61no—
62C3×C4×D4—22no—
63C3×C4×D4—22no—
64C3×C4×D4—21no—
65C3×C4×D4—21no—
66C3×C4×D4—21no—
67C3×C4×D4—21no—
68C3×C4×D4—22no—
69C3×C4×D4—22no—
70C3×C4×D4Dic312yes—
71C3×C4×D4C3×C412yes—
72C3×C4×D4C2×D312yes—
73C3×C4×D4C22×C312yes—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4Dic311yescharacteristic
76C2×C3×C4⋊C4C3×C411yescharacteristic
77C2×C3×C22⋊C4—22no—
78C2×C3×C22⋊C4—21no—
79C2×C3×C22⋊C4—21no—
80C2×C3×C42—21no—
81C2×C3×C42C2×D311yescharacteristic
82C2×C3×C42C22×C311yescharacteristic
83C2×#208—21no—
84C3×C4⋊C8—32no—
85C3×C4⋊C8—61no—
86C3×C4⋊C8—61no—
87C3×C22⋊C8—61no—
88C3×C4×C8—32no—
89#830—21no—
90C4⋊(C3⋊C8)—21no—
91C4⋊(C3⋊C8)—21no—
92C4⋊(C3⋊C8)C22×C312yescomplemented
93C4×C3⋊C8C22×C312yescomplemented
94C23×C32—24no—
95C23×C32—22no—
96C23×C32—42no—
97C23×C32—42no—
98C23×C32C22⋊C411yescharacteristic
99C32×D4—24no—
100C32×D4—22no—
101C32×D4M1614yescomplemented
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—41no—
105C2×C32×C4—42no—
106C2×C32×C4—44no—
107C2×C32×C4—42no—
108C2×C32×C4—42no—
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22⋊C411yescharacteristic
112C2×C32×C4D812yes—
113C2×C32×C4SD1612yes—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C3×C3⋊C8—42no—
118C3×C3⋊C8—42no—
119C2×C4×D4C3×D311yescharacteristic
120#431—31no—
121#423—31no—
122D4⋊C8—34no—
123C24×C3—22no—
124C24×C3—21no—
125C24×C3—21no—
126C2×C3×D4—22no—
127C2×C3×D4—28no—
128C2×C3×D4—24no—
129C2×C3×D4—24no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—22no—
133C2×C3×D4C2×Dic312yes—
134C2×C3×D4C2×C3×C412yes—
135C22×C3×C4—22no—
136C22×C3×C4—24no—
137C22×C3×C4—24no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—44no—
148C22×C3×C4—44no—
149C22×C3×C4—42no—
150C22×C3×C4—42no—
151C22×C3×C4—42no—
152C22×C3×C4—42no—
153C22×C3×C4C2×Dic311yescharacteristic
154C22×C3×C4#6711yescharacteristic
155C22×C3×C4#6711yescharacteristic
156C22×C3×C4C2×C3×C411yescharacteristic
157C22×C3×C4C3×D411yescharacteristic
158C22×C3×C4C3×D411yescharacteristic
159C3×M16—122no—
160C2×C3×C8—62no—
161C2×C3×C8—62no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4C2×Dic312yes—
167C3×C4⋊C4C2×C3×C412yes—
168C3×C22⋊C4—24no—
169C3×C22⋊C4—24no—
170C3×C22⋊C4—22no—
171C3×C22⋊C4—22no—
172C3×C22⋊C4—22no—
173C3×C22⋊C4—22no—
174C3×C42—21no—
175C3×C42—21no—
176C3×C42—21no—
177C3×C42—21no—
178C3×C42C2×Dic311yescharacteristic
179C3×C42#6711yescharacteristic
180C3×C42#6711yescharacteristic
181C3×C42C2×C3×C411yescharacteristic
182C3×C42C3×D411yescharacteristic
183C3×C42C3×D411yescharacteristic
184C3×C42C22×D311yescharacteristic
185C3×C42C23×C311yescharacteristic
186#208—42no—
187C2×C3⋊C8—22no—
188C2×C3⋊C8—22no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—24no—
192C22×C32—48no—
193C22×C32—42no—
194C22×C32—42no—
195C22×C32#10212yes—
196C22×C32C2×C22⋊C411yescharacteristic
197C32×C4—21no—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4—42no—
201C32×C4#10212yes—
202C32×C4C2×M1612yes—
203C32×C4C2×D811yescharacteristic
204C32×C4C2×SD1611yescharacteristic
205C22×D4C3×Dic311yescharacteristic
206C23×C4—21no—
207C2×M16—61no—
208C4×D4—21no—
209C4×D4—21no—
210C4×D4C3×Dic312yes—
211C4×D4C2×C3×D312yes—
212C2×C4⋊C4C3×Dic311yescharacteristic
213C2×C22⋊C4—21no—
214C2×C42C2×C3×D311yescharacteristic
215C4⋊C8—32no—
216C4⋊C8—61no—
217C4⋊C8—61no—
218C22⋊C8—61no—
219C4×C8—32no—
220C23×C3—24no—
221C23×C3—28no—
222C23×C3—24no—
223C23×C3—24no—
224C23×C3—22no—
225C23×C3—22no—
226C23×C3—21no—
227C23×C3—44no—
228C23×C3—44no—
229C23×C3—42no—
230C23×C3—42no—
231C23×C3—42no—
232C23×C3—42no—
233C23×C3#21711yescharacteristic
234C23×C3C3×C22⋊C411yescharacteristic
235C3×D4—28no—
236C3×D4—24no—
237C3×D4—24no—
238C3×D4—24no—
239C3×D4—22no—
240C3×D4—22no—
241C3×D4—24no—
242C3×D4#20814yescomplemented
243C3×D4C3×M1614yescomplemented
244C2×C3×C4—24no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—24no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
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—41no—
259C2×C3×C4—41no—
260C2×C3×C4—44no—
261C2×C3×C4—44no—
262C2×C3×C4—48no—
263C2×C3×C4—42no—
264C2×C3×C4—44no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—44no—
268C2×C3×C4—44no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
273C2×C3×C4#21312yes—
274C2×C3×C4#21412yes—
275C2×C3×C4#21711yescharacteristic
276C2×C3×C4#21711yescharacteristic
277C2×C3×C4#21711yescharacteristic
278C2×C3×C4C3×C22⋊C411yescharacteristic
279C2×C3×C4C3×C22⋊C411yescharacteristic
280C2×C3×C4C3×C22⋊C411yescharacteristic
281C2×C3×C4C3×D812yes—
282C2×C3×C4C3×SD1612yes—
283C2×C3×C4C22×Dic311yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C22×C3×C411yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288C2×C3×C4C2×C3×D411yescharacteristic
289C3×C8—122no—
290C3×C8—122no—
291C3⋊C8—42no—
292C3⋊C8—42no—
293C2×C32—22no—
294C2×C32—44no—
295C2×C32#40711yescharacteristic
296C2×C32C2×#10211yescharacteristic
297C2×C32#42111yescharacteristic
298C24—21no—
299C2×D4—24no—
300C2×D4—21no—
301C2×D4C2×C3×Dic312yes—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4C2×C3×Dic311yescharacteristic
308C22×C4C3×#6711yescharacteristic
309C22×C4C3×#6711yescharacteristic
310M16—122no—
311C2×C8—62no—
312C2×C8—62no—
313C4⋊C4—21no—
314C4⋊C4C2×C3×Dic312yes—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C42C2×C3×Dic311yescharacteristic
318C42C3×#6711yescharacteristic
319C42C3×#6711yescharacteristic
320C42C22×C3×D311yescharacteristic
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—28no—
328C22×C3—24no—
329C22×C3—24no—
330C22×C3—21no—
331C22×C3—22no—
332C22×C3—44no—
333C22×C3—416no—
334C22×C3—48no—
335C22×C3—48no—
336C22×C3—44no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3—42no—
340C22×C3—42no—
341C22×C3#83212yes—
342C22×C3C3×#10212yes—
343C22×C3C2×#21711yescharacteristic
344C22×C3C2×C3×C22⋊C411yescharacteristic
345C3×C4—22no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—22no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—22no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—44no—
359C3×C4—42no—
360C3×C4—42no—
361C3×C4#83212yes—
362C3×C4C3×#10212yes—
363C3×C4C2×#20812yes—
364C3×C4C2×#21311yescharacteristic
365C3×C4C2×#21411yescharacteristic
366C3×C4C2×C3×M1612yes—
367C3×C4C2×C3×D811yescharacteristic
368C3×C4C2×C3×SD1611yescharacteristic
369C32#148611yescharacteristic, complemented, Sylow
370C23—24no—
371C23—22no—
372C23—42no—
373C23—42no—
374C23C3×#21711yescharacteristic
375D4—24no—
376D4—22no—
377D4C3×#20814yescomplemented
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4C3×#21312yes—
386C2×C4C3×#21412yes—
387C2×C4C3×#21711yescharacteristic
388C2×C4C3×#21711yescharacteristic
389C2×C4C3×#21711yescharacteristic
390C2×C4C22×C3×Dic311yescharacteristic
391C2×C4C2×C3×#6711yescharacteristic
392C2×C4C2×C3×#6711yescharacteristic
393C8—122no—
394C8—122no—
395C2×C3—24no—
396C2×C3—22no—
397C2×C3—22no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—48no—
402C2×C3—44no—
403C2×C3—44no—
404C2×C3#520711yescharacteristic
405C2×C3C2×#83211yescharacteristic
406C2×C3#523611yescharacteristic
407C2×C3C3×#40711yescharacteristic
408C2×C3C2×C3×#10211yescharacteristic
409C2×C3C3×#42111yescharacteristic
410C22—21no—
411C22—21no—
412C22—24no—
413C22—48no—
414C22—42no—
415C22—42no—
416C22C3×#83212yes—
417C22C2×C3×#21711yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4C3×#83212yes—
423C4C2×C3×#20812yes—
424C4C2×C3×#21311yescharacteristic
425C4C2×C3×#21411yescharacteristic
426C3—21no—
427C3#7159811yescharacteristic, direct product factor
428C3C3×#148611yescharacteristic, complemented
429C2—22no—
430C2—44no—
431C2C3×#520711yescharacteristic
432C2C2×C3×#83211yescharacteristic
433C2C3×#523611yescharacteristic
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×#1486
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×#4925C2semidirect
3. C3×#4924C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
6. #71598C3direct (N × H)
20. C3×C4⋊(C3⋊C8)C22semidirect
21. C3×C4×C3⋊C8C22semidirect
27. #4925C2×C3semidirect
28. #4924C2×C3semidirect
30. D4⋊(C3⋊C8)C2×C3semidirect
92. C4⋊(C3⋊C8)C22×C3semidirect
93. C4×C3⋊C8C22×C3semidirect
101. C32×D4M16semidirect
242. C3×D4#208semidirect
243. C3×D4C3×M16semidirect
369. C32#1486semidirect
377. D4C3×#208semidirect
427. C3#71598direct (N × H)
428. C3C3×#1486semidirect

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×#49252
C3×#49242
C3×D4⋊(C3⋊C8)2
C3×#14863
#715983