Finite Group Databasebeta

← C3×#83568 #11895155

Subgroups — C3×#83568 #11895155

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D4×Q8C211yesmaximal, characteristic
2C3×#5570C211yesmaximal, characteristic, complemented
3C3×#5094C213yesmaximal, complemented
4C3×#5093C213yesmaximal, complemented
5C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
6C3×#5019C213yesmaximal
7C3×C4×#214C213yesmaximal
8C3×#3359—31nomaximal
9#83568C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8—21no—
11C32×C4⋊Q8C2213yes—
12C32×C22⋊Q8—23no—
13C32×C4×Q8C2211yescharacteristic
14C32×C4×D4C2213yes—
15C3×Q8×Dic3—21no—
16C2×C3×#214C2213yes—
17C3×#890—23no—
18C3×#869C2213yes—
19C3×C4×Dic6C2213yes—
20C3×#832C2211yescharacteristic
21C3×#810C2213yes—
22C3×#810C2216yes—
23C3×#808C2213yes—
24C3×C4⋊(C3⋊C8)C2213yes—
25C3×C4×C3⋊C8C2213yes—
26C3×#557—31no—
27C3×D4×Q8—21no—
28C3×D4×Q8D311yescharacteristic
29C3×D4×Q8C2×C311yescharacteristic
30#5570C2×C311yescharacteristic, complemented
31C3×#487—33no—
32C3×#475—33no—
33C3×#461—33no—
34C3×C8×Q8—31no—
35C3×C4×SD16—33no—
36#5094C2×C313yescomplemented
37#5093C2×C313yescomplemented
38Q8×C3⋊C8C2×C311yescharacteristic, complemented
39#5019C2×C313yes—
40C4×#214C2×C313yes—
41C2×C32×Q8—23no—
42C2×C32×Q8—44no—
43C2×C32×Q8D411yescharacteristic
44C2×C32×D4C2311yescharacteristic
45C22×C32×C4—23no—
46C2×C3×Dic6C2313yes—
47C32×C4⋊C4—23no—
48C32×C4⋊C4D413yes—
49C32×C4⋊C4C2313yes—
50C32×C22⋊C4—23no—
51C32×C42C2313yes—
52C3×#214—26no—
53C3×C4⋊Dic3—23no—
54C3×C4⋊Dic3—23no—
55C3×C4⋊Dic3C2311yescharacteristic
56C3×Dic3⋊C4—23no—
57C3×C4×Dic3—23no—
58C2×C3×C3⋊C8C2313yes—
59C2×C3×C3⋊C8C2311yescharacteristic
60#3359—31noSylow
61C22×C3×Q8—22no—
62C22×C3×Q8—21no—
63C22×C3×Q8—21no—
64C2×C3×SD16—33no—
65C3×C4⋊Q8—23no—
66C3×C4⋊Q8—33no—
67C3×C4⋊Q8C2×D313yes—
68C3×C4⋊Q8C22×C313yes—
69C3×#125—63no—
70C3×C22⋊Q8—26no—
71C3×C22⋊Q8—23no—
72C3×C22⋊Q8—23no—
73C3×C4×Q8—21no—
74C3×C4×Q8—33no—
75C3×C4×Q8—61no—
76C3×C4×Q8C2×D311yescharacteristic
77C3×C4×Q8C22×C311yescharacteristic
78C3×C4×D4—23no—
79C3×C4×D4C2×D313yes—
80C3×C4×D4C22×C313yes—
81Q8×Dic3—21no—
82C2×#214C22×C313yes—
83#890—23no—
84#869C22×C313yes—
85C4×Dic6C22×C313yes—
86C3×#106—33no—
87C3×C4⋊C8—33no—
88C3×#103—33no—
89C3×#103—36no—
90C3×#102—31no—
91C3×C4×C8—33no—
92#832C22×C311yescharacteristic
93#810C22×C313yes—
94#810C22×C316yes—
95#808C22×C313yes—
96C4⋊(C3⋊C8)C22×C313yes—
97C4×C3⋊C8C22×C313yes—
98C23×C32—21no—
99C32×Q8—46no—
100C32×Q8SD1614yescomplemented
101C32×D4—21no—
102C32×D4#4112yes—
103C2×C32×C4—23no—
104C2×C32×C4—46no—
105C2×C32×C4C2×D413yes—
106C2×C32×C4C2×D413yes—
107C2×C32×C4C2411yescharacteristic
108C2×C3×Dic3—21no—
109C2×C3×Dic3—23no—
110C3×Dic6—23no—
111C3×Dic6—23no—
112C3×C3⋊C8—23no—
113C3×C3⋊C8—21no—
114#557—31no—
115D4×Q8C3×D311yescharacteristic
116#487—33no—
117#475—33no—
118#461—33no—
119C8×Q8—31no—
120C4×SD16—33no—
121C2×C3×Q8—26no—
122C2×C3×Q8—23no—
123C2×C3×Q8—23no—
124C2×C3×Q8—21no—
125C2×C3×Q8—33no—
126C2×C3×Q8—48no—
127C2×C3×Q8—44no—
128C2×C3×Q8—44no—
129C2×C3×Q8#6711yescharacteristic
130C2×C3×Q8C3×D411yescharacteristic
131C2×C3×D4—21no—
132C2×C3×D4C22×D311yescharacteristic
133C2×C3×D4C23×C311yescharacteristic
134C22×C3×C4—26no—
135C22×C3×C4—23no—
136C22×C3×C4—23no—
137C2×Dic6C23×C313yes—
138C3×SD16—66no—
139C2×C3×C8—31no—
140C2×C3×C8—33no—
141C3×C4⋊C4—26no—
142C3×C4⋊C4—23no—
143C3×C4⋊C4—23no—
144C3×C4⋊C4—23no—
145C3×C4⋊C4—23no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—63no—
148C3×C4⋊C4—63no—
149C3×C4⋊C4—63no—
150C3×C4⋊C4#6713yes—
151C3×C4⋊C4C3×D413yes—
152C3×C4⋊C4C22×D313yes—
153C3×C4⋊C4C23×C313yes—
154C3×C22⋊C4—26no—
155C3×C22⋊C4—23no—
156C3×C22⋊C4—23no—
157C3×C42—23no—
158C3×C42—63no—
159C3×C42C22×D313yes—
160C3×C42C23×C313yes—
161#214—26no—
162C4⋊Dic3—23no—
163C4⋊Dic3—23no—
164C4⋊Dic3C23×C311yescharacteristic
165Dic3⋊C4—23no—
166C4×Dic3—23no—
167C2×C3⋊C8C23×C311yescharacteristic
168C2×C3⋊C8C23×C313yes—
169C22×C32—22no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32C22×D411yescharacteristic
173C32×C4—23no—
174C32×C4—43no—
175C32×C4C2×SD1616yes—
176C32×C4C2×#4111yescharacteristic
177C32×C42−1+411yescharacteristic
178C3×Dic3—43no—
179C3×Dic3—41no—
180C22×Q8—21no—
181C2×SD16—33no—
182C4⋊Q8—33no—
183C4⋊Q8C2×C3×D313yes—
184#125—63no—
185C22⋊Q8—23no—
186C4×Q8—33no—
187C4×Q8—61no—
188C4×Q8C2×C3×D311yescharacteristic
189C4×D4C2×C3×D313yes—
190#106—33no—
191C4⋊C8—33no—
192#103—33no—
193#103—36no—
194#102—31no—
195C4×C8—33no—
196C23×C3—22no—
197C23×C3—21no—
198C23×C3—21no—
199C3×Q8—24no—
200C3×Q8—412no—
201C3×Q8—46no—
202C3×Q8—46no—
203C3×Q8—63no—
204C3×Q8—63no—
205C3×Q8#21414yescomplemented
206C3×Q8C3×SD1614yescomplemented
207C3×D4—22no—
208C3×D4—21no—
209C3×D4—21no—
210C3×D4—22no—
211C3×D4#23912yes—
212C3×D4C3×#4112yes—
213C2×C3×C4—26no—
214C2×C3×C4—23no—
215C2×C3×C4—23no—
216C2×C3×C4—21no—
217C2×C3×C4—23no—
218C2×C3×C4—23no—
219C2×C3×C4—412no—
220C2×C3×C4—46no—
221C2×C3×C4—46no—
222C2×C3×C4—61no—
223C2×C3×C4—63no—
224C2×C3×C4C2×#6713yes—
225C2×C3×C4C2×#6713yes—
226C2×C3×C4C2×C3×D413yes—
227C2×C3×C4C2×C3×D413yes—
228C2×C3×C4C23×D311yescharacteristic
229C2×C3×C4C24×C311yescharacteristic
230C2×Dic3—21no—
231C2×Dic3—23no—
232Dic6—23no—
233Dic6—23no—
234C3×C8—63no—
235C3×C8—61no—
236C3⋊C8—23no—
237C3⋊C8—21no—
238C2×C32—42no—
239C2×C32#54811yescharacteristic
240C2×C32C22×SD1611yescharacteristic
241C2×C32#57811yescharacteristic
242C2×Q8—23no—
243C2×Q8—33no—
244C2×Q8—44no—
245C2×Q8C3×#6711yescharacteristic
246C2×D4C22×C3×D311yescharacteristic
247C22×C4—23no—
248SD16—66no—
249C2×C8—31no—
250C2×C8—33no—
251C4⋊C4—23no—
252C4⋊C4—31no—
253C4⋊C4—63no—
254C4⋊C4—63no—
255C4⋊C4—63no—
256C4⋊C4C3×#6713yes—
257C4⋊C4C22×C3×D313yes—
258C22⋊C4—23no—
259C42—63no—
260C42C22×C3×D313yes—
261C22×C3—24no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—21no—
265C22×C3—42no—
266C22×C3—42no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3C22×#6711yescharacteristic
272C22×C3C22×C3×D411yescharacteristic
273C3×C4—23no—
274C3×C4—23no—
275C3×C4—26no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—43no—
279C3×C4—46no—
280C3×C4—43no—
281C3×C4—43no—
282C3×C4—123no—
283C3×C4—121no—
284C3×C4C2×#21416yes—
285C3×C4C2×C3×SD1616yes—
286C3×C4C2×#23911yescharacteristic
287C3×C4#100711yescharacteristic
288C3×C4C2×C3×#4111yescharacteristic
289C3×C4C3×2−1+411yescharacteristic
290Dic3—41no—
291Dic3—43no—
292C32#335911yescharacteristic, complemented, Sylow
293C23—21no—
294Q8—46no—
295Q8—63no—
296Q8—63no—
297Q8C3×#21414yescomplemented
298D4—21no—
299D4C3×#23912yes—
300C2×C4—23no—
301C2×C4—46no—
302C2×C4—61no—
303C2×C4—63no—
304C2×C4C2×C3×#6713yes—
305C2×C4C2×C3×#6713yes—
306C2×C4C23×C3×D311yescharacteristic
307C8—63no—
308C8—61no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—44no—
313C2×C3—42no—
314C2×C3—42no—
315C2×C3C22×#21411yescharacteristic
316C2×C3#581711yescharacteristic
317C2×C3#583811yescharacteristic
318C2×C3C3×#54811yescharacteristic
319C2×C3C22×C3×SD1611yescharacteristic
320C2×C3C3×#57811yescharacteristic
321C22—22no—
322C22—41no—
323C22—41no—
324C22C22×C3×#6711yescharacteristic
325C4—23no—
326C4—43no—
327C4—123no—
328C4—121no—
329C4C2×C3×#21416yes—
330C4C2×C3×#23911yescharacteristic
331C4C3×#100711yescharacteristic
332C3—21no—
333C3#8356811yescharacteristic, direct product factor
334C3C3×#335911yescharacteristic, complemented
335C2—42no—
336C2C22×C3×#21411yescharacteristic
337C2C3×#581711yescharacteristic
338C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×D4×Q8C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×D4×Q8D3
hypocenterC3C3×#3359
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×D4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5570C2semidirect
3. C3×#5094C2semidirect
4. C3×#5093C2semidirect
5. C3×Q8×C3⋊C8C2semidirect
9. #83568C3direct (N × H)
30. #5570C2×C3semidirect
36. #5094C2×C3semidirect
37. #5093C2×C3semidirect
38. Q8×C3⋊C8C2×C3semidirect
100. C32×Q8SD16semidirect
205. C3×Q8#214semidirect
206. C3×Q8C3×SD16semidirect
292. C32#3359semidirect
297. Q8C3×#214semidirect
333. C3#83568direct (N × H)
334. C3C3×#3359semidirect

Maximal subgroups

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

subgroupindex
C32×D4×Q82
C3×#55702
C3×#50942
C3×#50932
C3×Q8×C3⋊C82
C3×#50192
C3×C4×#2142
C3×#33593
#835683