Finite Group Databasebeta

← C3×#87483 #11923694

Subgroups — C3×#87483 #11923694

Order 1152.

1564 conjugacy classes of subgroups; only the 204 normal subgroups are shown.

normal subgroups only

This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 204 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
1C2×C3×Q8×A4C211yesmaximal, characteristic, complemented
2C3×#5919C214yesmaximal, complemented
3C3×Q8×S4C214yesmaximal, complemented
4C3×#5912C216yesmaximal, complemented
5#87483C311yesmaximal, characteristic, direct product factor
6C3×#3486—31nomaximal
7C3×#1007—41nomaximal
8C3×Q8×A4C2214yes—
9C2×C3×C4×A4C2213yes—
10C3×GL(2,ℤ/4)C2214yes—
11C3×C4⋊S4C2216yes—
12C3×C4×S4C22112yes—
13C3×A4⋊Q8C2216yes—
14C2×C3×2−1+4—31no—
15C23×C3×Q8D311yescharacteristic, complemented
16C2×Q8×A4—21no—
17C2×Q8×A4C2×C311yescharacteristic, complemented
18#5919C2×C314yescomplemented
19Q8×S4C2×C314yescomplemented
20#5912C2×C316yescomplemented
21C3×D4×Q8—34no—
22C3×D4×Q8—34no—
23C3×#548—34no—
24C3×#548—34no—
25C3×#536—36no—
26C3×#525—36no—
27C3×#519—31no—
28C22×C3×A4C2311yescharacteristic
29C2×C3×S4C2314yes—
30C2×C32×Q8—41no—
31C3×#239—44no—
32C3×D3×Q8—44no—
33C3×#235—46no—
34C3×C4×A4C2316yes—
35C3×SL(2,ℤ/4)C2314yes—
36#3486—31noSylow
37C3×2−1+4—64no—
38C3×2−1+4—63no—
39C3×2−1+4—61no—
40C2×C3×#41—36no—
41C2×C3×#41—34no—
42C22×C3×Q8—31no—
43C22×C3×Q8—33no—
44C22×C3×Q8—34no—
45C22×C3×Q8—34no—
46C22×C3×Q8C2×D314yes—
47C23×C3×C4C2×D313yes—
48#1007—41no—
49Q8×A4—24no—
50Q8×A4C22×C314yes—
51C2×C4×A4—23no—
52C2×C4×A4C22×C313yes—
53GL(2,ℤ/4)C22×C314yes—
54C4⋊S4C22×C316yes—
55C4×S4C22×C3112yes—
56A4⋊Q8C22×C316yes—
57C3×C4⋊Q8—312no—
58C3×#124—312no—
59C3×#123—312no—
60C3×C22⋊Q8—36no—
61C3×C22⋊Q8—312no—
62C3×C22⋊Q8—312no—
63C3×C22⋊Q8—36no—
64C3×#121—36no—
65C3×#121—36no—
66C3×#120—34no—
67C3×C4×Q8—34no—
68C3×C4×Q8—34no—
69C3×C4×D4—312no—
70C3×C4×D4—312no—
71C3×#117—36no—
72C2×C3×A4—21no—
73C2×C3×A4C2411yescharacteristic
74C3×S4—24no—
75C32×Q8—44no—
76C2×C32×C4—43no—
77C3×#67—44no—
78C3×D12—46no—
79C3×C4×D3—412no—
80C3×Dic6—46no—
81C2×2−1+4—31no—
82C23×Q8C3×D311yescharacteristic, complemented
83D4×Q8—34no—
84D4×Q8—34no—
85#548—34no—
86#548—34no—
87#536—36no—
88#525—36no—
89#519—31no—
90C24×C3C22×D311yescharacteristic
91C22×A4—21no—
92C22×A4C23×C311yescharacteristic
93C2×S4C23×C314yes—
94C3×#41—66no—
95C3×#41—66no—
96C3×#41—66no—
97C3×#41—612no—
98C3×#41—64no—
99C3×#41—66no—
100C2×C3×Q8—34no—
101C2×C3×Q8—34no—
102C2×C3×Q8—312no—
103C2×C3×Q8—36no—
104C2×C3×Q8—33no—
105C2×C3×Q8—41no—
106C2×C3×Q8—61no—
107C2×C3×Q8—66no—
108C2×C3×Q8—612no—
109C2×C3×Q8—64no—
110C2×C3×Q8—81no—
111C2×C3×Q8S411yescharacteristic, complemented
112C2×C3×D4—34no—
113C2×C3×D4—34no—
114C2×C3×D4—36no—
115C2×C3×D4—34no—
116C22×C3×C4—33no—
117C22×C3×C4—36no—
118C22×C3×C4—33no—
119C22×C3×C4—312no—
120C22×C3×C4C22×D316yes—
121#239—44no—
122D3×Q8—44no—
123#235—46no—
124C4×A4—26no—
125C4×A4C23×C316yes—
126SL(2,ℤ/4)C23×C314yes—
127C3×C4⋊C4—36no—
128C3×C4⋊C4—36no—
129C3×C4⋊C4—312no—
130C3×C4⋊C4—312no—
131C3×C22⋊C4—34no—
132C3×C22⋊C4—34no—
133C3×C22⋊C4—312no—
134C3×C22⋊C4—312no—
135C3×C22⋊C4—34no—
136C3×C42—312no—
137C22×C32—41no—
138C2×C3×D3—44no—
139C3×A42−1+411yescharacteristic, complemented
140C32×C4—46no—
141C3×Dic3—44no—
1422−1+4—64no—
1432−1+4—63no—
1442−1+4—61no—
145C2×#41—36no—
146C2×#41—34no—
147C22×Q8—31no—
148C22×Q8—33no—
149C22×Q8—34no—
150C22×Q8—34no—
151C22×Q8C2×C3×D314yes—
152C23×C4C2×C3×D313yes—
153C4⋊Q8—312no—
154#124—312no—
155#123—312no—
156C22⋊Q8—36no—
157C22⋊Q8—312no—
158C22⋊Q8—312no—
159C22⋊Q8—36no—
160#121—36no—
161#121—36no—
162#120—34no—
163C4×Q8—34no—
164C4×Q8—34no—
165C4×D4—312no—
166C4×D4—312no—
167#117—36no—
168C23×C3—21no—
169C23×C3—31no—
170C23×C3—31no—
171C23×C3—34no—
172C23×C3—61no—
173C23×C3C23×D311yescharacteristic
174C2×A4—22no—
175C2×A4—21no—
176C2×A4—21no—
177C2×A4C24×C311yescharacteristic
178S4—24no—
179C3×Q8—312no—
180C3×Q8—44no—
181C3×Q8—64no—
182C3×Q8—66no—
183C3×Q8—66no—
184C3×Q8—84no—
185C3×Q8C2×S414yes—
186C3×D4—66no—
187C3×D4—64no—
188C3×D4—68no—
189C3×D4—64no—
190C3×D4—64no—
191C3×D4—64no—
192C3×D4—66no—
193C2×C3×C4—33no—
194C2×C3×C4—36no—
195C2×C3×C4—36no—
196C2×C3×C4—36no—
197C2×C3×C4—34no—
198C2×C3×C4—34no—
199C2×C3×C4—34no—
200C2×C3×C4—43no—
201C2×C3×C4—63no—
202C2×C3×C4—612no—
203C2×C3×C4—612no—
204C2×C3×C4—83no—
205C2×C3×C4C2×S413yes—
206#67—44no—
207D12—46no—
208C4×D3—412no—
209Dic6—46no—
210C2×C32—41no—
211C2×C32—81no—
212C3×D3—84no—
213C24C22×C3×D311yescharacteristic
214#41—66no—
215#41—66no—
216#41—66no—
217#41—612no—
218#41—64no—
219#41—66no—
220C2×Q8—34no—
221C2×Q8—34no—
222C2×Q8—312no—
223C2×Q8—36no—
224C2×Q8—33no—
225C2×Q8—61no—
226C2×Q8—66no—
227C2×Q8—612no—
228C2×Q8—64no—
229C2×Q8C3×S411yescharacteristic, complemented
230C2×D4—34no—
231C2×D4—34no—
232C2×D4—36no—
233C2×D4—34no—
234C22×C4—33no—
235C22×C4—36no—
236C22×C4—33no—
237C22×C4—312no—
238C22×C4C22×C3×D316yes—
239C4⋊C4—36no—
240C4⋊C4—36no—
241C4⋊C4—312no—
242C4⋊C4—312no—
243C22⋊C4—34no—
244C22⋊C4—34no—
245C22⋊C4—312no—
246C22⋊C4—312no—
247C22⋊C4—34no—
248C42—312no—
249C22×C3—31no—
250C22×C3—31no—
251C22×C3—32no—
252C22×C3—31no—
253C22×C3—41no—
254C22×C3—61no—
255C22×C3—61no—
256C22×C3—61no—
257C22×C3—64no—
258C22×C3—64no—
259C22×C3—64no—
260C22×C3—81no—
261C22×C3#100711yescharacteristic, complemented
262C22×C3C22×S411yescharacteristic
263C2×D3—44no—
264A4—21no—
265A4C3×2−1+411yescharacteristic, complemented
266C3×C4—36no—
267C3×C4—46no—
268C3×C4—64no—
269C3×C4—64no—
270C3×C4—64no—
271C3×C4—86no—
272C3×C4C22×S416yes—
273Dic3—44no—
274C32—41noSylow
275C23—21no—
276C23—31no—
277C23—31no—
278C23—34no—
279C23—61no—
280C23C23×C3×D311yescharacteristic
281Q8—312no—
282Q8—64no—
283Q8—66no—
284Q8—66no—
285Q8C2×C3×S414yes—
286D4—66no—
287D4—64no—
288D4—64no—
289D4—68no—
290D4—64no—
291D4—64no—
292D4—66no—
293C2×C4—33no—
294C2×C4—36no—
295C2×C4—36no—
296C2×C4—36no—
297C2×C4—34no—
298C2×C4—34no—
299C2×C4—34no—
300C2×C4—63no—
301C2×C4—612no—
302C2×C4—612no—
303C2×C4C2×C3×S413yes—
304C2×C3—21no—
305C2×C3—31no—
306C2×C3—31no—
307C2×C3—41no—
308C2×C3—61no—
309C2×C3—81no—
310C2×C3—82no—
311C2×C3—81no—
312C2×C3—124no—
313C2×C3C23×S411yescharacteristic
314D3—84no—
315C22—31no—
316C22—31no—
317C22—32no—
318C22—31no—
319C22—61no—
320C22—61no—
321C22—61no—
322C22—64no—
323C22—64no—
324C22—64no—
325C22C3×#100711yescharacteristic, complemented
326C22C22×C3×S411yescharacteristic
327C4—36no—
328C4—64no—
329C4—64no—
330C4—64no—
331C4C22×C3×S416yes—
332C3—41no—
333C3—81no—
334C3#8748311yescharacteristic, direct product factor
335C2—21no—
336C2—31no—
337C2—31no—
338C2—61no—
339C2—124no—
340C2C23×C3×S411yescharacteristic
subgroupG/H
centerC2×C3C23×S4
commutator, cosocleC2×A4C24×C3
FrattiniC2C23×C3×S4
FittingC23×C3×Q8D3
socleC23×C3C23×D3
hypercenterC2×C3×Q8S4
hypocenterA4C3×2−1+4
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3 ◁ C2×C3×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×A4C2semidirect
2. C3×#5919C2semidirect
3. C3×Q8×S4C2semidirect
4. C3×#5912C2semidirect
5. #87483C3direct (N × H)
15. C23×C3×Q8D3semidirect
17. C2×Q8×A4C2×C3semidirect
18. #5919C2×C3semidirect
19. Q8×S4C2×C3semidirect
20. #5912C2×C3semidirect
82. C23×Q8C3×D3semidirect
111. C2×C3×Q8S4semidirect
139. C3×A42−1+4semidirect
229. C2×Q8C3×S4semidirect
261. C22×C3#1007semidirect
265. A4C3×2−1+4semidirect
325. C22C3×#1007semidirect
334. C3#87483direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
C3×#59192
C3×Q8×S42
C3×#59122
#874833
C3×#34863
C3×#10074