Finite Group Databasebeta

← C3×#85482 #11922766

Subgroups — C3×#85482 #11922766

Order 1152.

876 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 876 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×A4C211yesmaximal, characteristic
2C3×#5432C212yesmaximal
3C3×C4⋊SL(2,ℤ/4)C212yesmaximal, complemented
4C3×C4×SL(2,ℤ/4)C212yesmaximal, complemented
5#85482C311yesmaximal, characteristic, direct product factor
6C3×#2280—31nomaximal
7C23×C3×A4C2211yescharacteristic
8C2×C3×C4×A4C414yescomplemented
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3×SL(2,ℤ/4)C2214yes—
12C3×#926—41nomaximal
13C24×C3×C4D311yescharacteristic
14C22×C4×A4—21no—
15C22×C4×A4C2×C311yescharacteristic
16C2×C3×#117—31no—
17C2×C3×#117—31no—
18#5432C2×C312yes—
19C4⋊SL(2,ℤ/4)C2×C312yescomplemented
20C4×SL(2,ℤ/4)C2×C312yescomplemented
21C3×#381—32no—
22C3×#380—32no—
23C3×#380—32no—
24C3×#379—32no—
25C3×C4×C22⋊C4—32no—
26C3×C4×C22⋊C4—32no—
27C22×C3×A4—22no—
28C22×C3×A4C2×C412yes—
29C22×C3×A4C2311yescharacteristic
30C22×C32×C4—41no—
31C3×C4×A4C2×C412yes—
32C3×C4×A4C2×C412yes—
33C3×SL(2,ℤ/4)—24no—
34C3×#217—42no—
35C3×C4⋊Dic3—42no—
36C3×C4×Dic3—42no—
37#2280—31noSylow
38C25×C3C2×D311yescharacteristic
39C23×A4—21no—
40C23×A4C22×C311yescharacteristic
41C23×C3×C4—31no—
42C23×C3×C4—34no—
43C23×C3×C4—31no—
44C23×C3×C4—31no—
45C23×C3×C4—31no—
46C23×C3×C4Dic314yescomplemented
47C23×C3×C4C2×D311yescharacteristic
48C23×C3×C4C2×D311yescharacteristic
49C2×C4×A4—24no—
50C2×C4×A4—21no—
51C2×C4×A4—21no—
52C2×C4×A4C3×C414yescomplemented
53C2×C4×A4C22×C311yescharacteristic
54C2×C4×A4C22×C311yescharacteristic
55C2×SL(2,ℤ/4)C22×C314yes—
56C3×#117—64no—
57C3×#117—61no—
58C3×#117—61no—
59C3×#117—61no—
60C3×#117—61no—
61C2×C3×C4⋊C4—32no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C22⋊C4—34no—
64C2×C3×C22⋊C4—32no—
65C2×C3×C22⋊C4—32no—
66C2×C3×C22⋊C4—34no—
67C2×C3×C42—32no—
68C2×C3×C42—32no—
69#926—41no—
70C3×#95—34no—
71C3×#95—34no—
72C23×C32—41no—
73C2×C3×A4—22no—
74C2×C3×A4C22×C411yescharacteristic
75C2×C3×A4#4112yes—
76C2×C32×C4—44no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C3×Dic3—44no—
80C24×C4C3×D311yescharacteristic
81C2×#117—31no—
82C2×#117—31no—
83#381—32no—
84#380—32no—
85#380—32no—
86#379—32no—
87C4×C22⋊C4—32no—
88C4×C22⋊C4—32no—
89C24×C3—22no—
90C24×C3—31no—
91C24×C3—31no—
92C24×C3—32no—
93C24×C3—62no—
94C24×C3C2×Dic312yes—
95C24×C3C22×D311yescharacteristic
96C22×A4—24no—
97C22×A4—22no—
98C22×A4—22no—
99C22×A4—21no—
100C22×A4C2×C3×C412yes—
101C22×A4C23×C311yescharacteristic
102C22×C3×C4—31no—
103C22×C3×C4—34no—
104C22×C3×C4—34no—
105C22×C3×C4—31no—
106C22×C3×C4—31no—
107C22×C3×C4—31no—
108C22×C3×C4—31no—
109C22×C3×C4—31no—
110C22×C3×C4—31no—
111C22×C3×C4—34no—
112C22×C3×C4—34no—
113C22×C3×C4—34no—
114C22×C3×C4—32no—
115C22×C3×C4—32no—
116C22×C3×C4—34no—
117C22×C3×C4—34no—
118C22×C3×C4—41no—
119C22×C3×C4—62no—
120C22×C3×C4—62no—
121C22×C3×C4—62no—
122C22×C3×C4—61no—
123C22×C3×C4—81no—
124C22×C3×C4C2×Dic312yes—
125C22×C3×C4C2×Dic312yes—
126C22×C3×C4S411yescharacteristic
127C4×A4—22no—
128C4×A4—22no—
129C4×A4C2×C3×C412yes—
130C4×A4C2×C3×C412yes—
131SL(2,ℤ/4)—24no—
132C3×C4⋊C4—62no—
133C3×C4⋊C4—64no—
134C3×C4⋊C4—62no—
135C3×C22⋊C4—64no—
136C3×C22⋊C4—68no—
137C3×C22⋊C4—64no—
138C3×C22⋊C4—62no—
139C3×C22⋊C4—64no—
140C3×C22⋊C4—62no—
141C3×C42—62no—
142C3×C42—64no—
143C3×C42—62no—
144#217—42no—
145C4⋊Dic3—42no—
146C4×Dic3—42no—
147C22×C32—42no—
148C22×C32—41no—
149C22×C32—82no—
150C3×A4#11711yescharacteristic, complemented
151C32×C4—42no—
152C32×C4—42no—
153C3×Dic3—84no—
154C25C2×C3×D311yescharacteristic
155C23×C4—31no—
156C23×C4—31no—
157C23×C4—31no—
158C23×C4—31no—
159C23×C4—34no—
160C23×C4C3×Dic314yescomplemented
161C23×C4C2×C3×D311yescharacteristic
162C23×C4C2×C3×D311yescharacteristic
163#117—64no—
164#117—61no—
165#117—61no—
166#117—61no—
167#117—61no—
168C2×C4⋊C4—32no—
169C2×C4⋊C4—32no—
170C2×C22⋊C4—32no—
171C2×C22⋊C4—32no—
172C2×C22⋊C4—34no—
173C2×C22⋊C4—34no—
174C2×C42—32no—
175C2×C42—32no—
176#95—34no—
177#95—34no—
178C23×C3—22no—
179C23×C3—31no—
180C23×C3—32no—
181C23×C3—32no—
182C23×C3—31no—
183C23×C3—34no—
184C23×C3—32no—
185C23×C3—32no—
186C23×C3—31no—
187C23×C3—41no—
188C23×C3—62no—
189C23×C3—62no—
190C23×C3—62no—
191C23×C3—61no—
192C23×C3—64no—
193C23×C3—62no—
194C23×C3—64no—
195C23×C3—81no—
196C23×C3#23512yes—
197C23×C3C22×Dic311yescharacteristic
198C23×C3C2×S411yescharacteristic
199C2×A4—24no—
200C2×A4—22no—
201C2×A4—22no—
202C2×A4—21no—
203C2×A4C22×C3×C411yescharacteristic
204C2×A4C3×#4112yes—
205C2×C3×C4—34no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—32no—
209C2×C3×C4—32no—
210C2×C3×C4—32no—
211C2×C3×C4—32no—
212C2×C3×C4—34no—
213C2×C3×C4—34no—
214C2×C3×C4—32no—
215C2×C3×C4—32no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—44no—
219C2×C3×C4—61no—
220C2×C3×C4—61no—
221C2×C3×C4—64no—
222C2×C3×C4—64no—
223C2×C3×C4—64no—
224C2×C3×C4—64no—
225C2×C3×C4—64no—
226C2×C3×C4—64no—
227C2×C3×C4—64no—
228C2×C3×C4—81no—
229C2×C3×C4—81no—
230C2×C3×C4—84no—
231C2×C3×C4SL(2,ℤ/4)14yescomplemented
232C2×C3×C4C2×S411yescharacteristic
233C2×C3×C4C2×S411yescharacteristic
234C2×Dic3—44no—
235C2×C32—42no—
236C2×C32—41no—
237C2×C32—82no—
238C24—22no—
239C24—31no—
240C24—31no—
241C24—32no—
242C24—62no—
243C24C2×C3×Dic312yes—
244C24C22×C3×D311yescharacteristic
245C22×C4—31no—
246C22×C4—31no—
247C22×C4—31no—
248C22×C4—31no—
249C22×C4—31no—
250C22×C4—34no—
251C22×C4—34no—
252C22×C4—31no—
253C22×C4—31no—
254C22×C4—34no—
255C22×C4—34no—
256C22×C4—34no—
257C22×C4—32no—
258C22×C4—32no—
259C22×C4—34no—
260C22×C4—34no—
261C22×C4—62no—
262C22×C4—62no—
263C22×C4—62no—
264C22×C4—61no—
265C22×C4C2×C3×Dic312yes—
266C22×C4C2×C3×Dic312yes—
267C22×C4C3×S411yescharacteristic
268C4⋊C4—62no—
269C4⋊C4—64no—
270C4⋊C4—62no—
271C22⋊C4—64no—
272C22⋊C4—62no—
273C22⋊C4—64no—
274C22⋊C4—68no—
275C22⋊C4—62no—
276C22⋊C4—64no—
277C42—62no—
278C42—64no—
279C42—62no—
280C22×C3—22no—
281C22×C3—32no—
282C22×C3—31no—
283C22×C3—32no—
284C22×C3—32no—
285C22×C3—31no—
286C22×C3—31no—
287C22×C3—34no—
288C22×C3—32no—
289C22×C3—42no—
290C22×C3—41no—
291C22×C3—62no—
292C22×C3—64no—
293C22×C3—62no—
294C22×C3—61no—
295C22×C3—62no—
296C22×C3—64no—
297C22×C3—62no—
298C22×C3—82no—
299C22×C3—84no—
300C22×C3—82no—
301C22×C3—81no—
302C22×C3#92611yescharacteristic, complemented
303C22×C3C2×SL(2,ℤ/4)12yes—
304C22×C3C22×S411yescharacteristic
305A4—21no—
306A4C3×#11711yescharacteristic, complemented
307C3×C4—32no—
308C3×C4—32no—
309C3×C4—42no—
310C3×C4—42no—
311C3×C4—82no—
312C3×C4—82no—
313C3×C4—124no—
314C3×C4—124no—
315C3×C4C2×SL(2,ℤ/4)12yes—
316C3×C4C2×SL(2,ℤ/4)12yes—
317Dic3—84no—
318C32—41noSylow
319C23—22no—
320C23—31no—
321C23—32no—
322C23—32no—
323C23—31no—
324C23—34no—
325C23—32no—
326C23—32no—
327C23—31no—
328C23—62no—
329C23—62no—
330C23—62no—
331C23—61no—
332C23—64no—
333C23—62no—
334C23—64no—
335C23C3×#23512yes—
336C23C22×C3×Dic311yescharacteristic
337C23C2×C3×S411yescharacteristic
338C2×C4—34no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—32no—
342C2×C4—32no—
343C2×C4—32no—
344C2×C4—32no—
345C2×C4—34no—
346C2×C4—34no—
347C2×C4—32no—
348C2×C4—32no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—64no—
352C2×C4—64no—
353C2×C4—64no—
354C2×C4—64no—
355C2×C4—64no—
356C2×C4—64no—
357C2×C4—64no—
358C2×C4C3×SL(2,ℤ/4)14yescomplemented
359C2×C4C2×C3×S411yescharacteristic
360C2×C4C2×C3×S411yescharacteristic
361C2×C3—22no—
362C2×C3—32no—
363C2×C3—31no—
364C2×C3—31no—
365C2×C3—42no—
366C2×C3—41no—
367C2×C3—62no—
368C2×C3—82no—
369C2×C3—84no—
370C2×C3—82no—
371C2×C3—81no—
372C2×C3#591212yes—
373C2×C3C22×SL(2,ℤ/4)11yescharacteristic
374C22—22no—
375C22—32no—
376C22—31no—
377C22—32no—
378C22—32no—
379C22—31no—
380C22—31no—
381C22—34no—
382C22—32no—
383C22—62no—
384C22—64no—
385C22—62no—
386C22—61no—
387C22—62no—
388C22—64no—
389C22—62no—
390C22C3×#92611yescharacteristic, complemented
391C22C2×C3×SL(2,ℤ/4)12yes—
392C22C22×C3×S411yescharacteristic
393C4—32no—
394C4—32no—
395C4—124no—
396C4—124no—
397C4C2×C3×SL(2,ℤ/4)12yes—
398C4C2×C3×SL(2,ℤ/4)12yes—
399C3—41no—
400C3—81no—
401C3#8548211yescharacteristic, direct product factor
402C2—22no—
403C2—32no—
404C2—31no—
405C2—31no—
406C2—62no—
407C2C3×#591212yes—
408C2C22×C3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC2×C3×C4C2×S4
commutatorC2×A4C22×C3×C4
FrattiniC22C22×C3×S4
FittingC24×C3×C4D3
socleC24×C3C22×D3
prime radicalC23×C3×A4C22
cosocleC22×A4C23×C3
hypercenterC22×C3×C4S4
hypocenterA4C3×#117
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
3. C3×C4⋊SL(2,ℤ/4)C2semidirect
4. C3×C4×SL(2,ℤ/4)C2semidirect
5. #85482C3direct (N × H)
8. C2×C3×C4×A4C4semidirect
19. C4⋊SL(2,ℤ/4)C2×C3semidirect
20. C4×SL(2,ℤ/4)C2×C3semidirect
46. C23×C3×C4Dic3semidirect
52. C2×C4×A4C3×C4semidirect
150. C3×A4#117semidirect
160. C23×C4C3×Dic3semidirect
231. C2×C3×C4SL(2,ℤ/4)semidirect
302. C22×C3#926semidirect
306. A4C3×#117semidirect
358. C2×C4C3×SL(2,ℤ/4)semidirect
390. C22C3×#926semidirect
401. C3#85482direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C3×#54322
C3×C4⋊SL(2,ℤ/4)2
C3×C4×SL(2,ℤ/4)2
#854823
C3×#22803
C3×#9264