Finite Group Databasebeta

← C3×#83586 #11895400

Subgroups — C3×#83586 #11895400

Order 1152.

940 conjugacy classes of subgroups.

The subgroup lattice has 349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#550C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C3×#5075C213yesmaximal, complemented
4C3×#5070C213yesmaximal, complemented
5C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
6C3×C4×#214C213yesmaximal, complemented
7C3×#5008C213yesmaximal, complemented
8C3×#3362—31nomaximal
9#83586C311yesmaximal, characteristic, direct product factor
10C2×C32×#41—21no—
11C32×#127C2213yes—
12C32×#121—23no—
13C32×C4×Q8C2211yescharacteristic
14C32×C4×D4C2213yes—
15C3×Q8×Dic3—21no—
16C2×C3×#214C2213yes—
17C3×#888—23no—
18C3×#869C2213yes—
19C3×C4×Dic6C2213yes—
20C3×#832C2216yes—
21C3×#832C2213yes—
22C3×#810C2211yescharacteristic
23C3×#808C2213yes—
24C3×C4⋊(C3⋊C8)C2213yes—
25C3×C4×C3⋊C8C2213yes—
26C3×Q82—31no—
27C3×#550—21no—
28C3×#550D311yescharacteristic
29C3×#550C2×C311yescharacteristic
30Q8×Dic6C2×C311yescharacteristic, complemented
31C3×#486—33no—
32C3×#476—33no—
33C3×#460—33no—
34C3×C8×Q8—31no—
35C3×C4×SD16—33no—
36#5075C2×C313yescomplemented
37#5070C2×C313yescomplemented
38Q8×C3⋊C8C2×C311yescharacteristic, complemented
39C4×#214C2×C313yescomplemented
40#5008C2×C313yescomplemented
41C32×#41—44no—
42C2×C32×Q8D411yescharacteristic
43C2×C32×D4—23no—
44C2×C32×D4—23no—
45C2×C32×D4C2313yes—
46C22×C32×C4—23no—
47C2×C3×Dic6—23no—
48C2×C3×Dic6C2311yescharacteristic
49C32×C4⋊C4D413yes—
50C32×C4⋊C4C2311yescharacteristic
51C32×C22⋊C4—23no—
52C32×C42C2313yes—
53C3×#214—26no—
54C3×C4⋊Dic3—23no—
55C3×C4⋊Dic3C2313yes—
56C3×Dic3⋊C4—23no—
57C3×C4×Dic3—23no—
58C2×C3×C3⋊C8C2313yes—
59C2×C3×C3⋊C8C2311yescharacteristic
60#3362—31noSylow
61C2×C3×#41—22no—
62C2×C3×#41—21no—
63C2×C3×#41—21no—
64C2×C3×SD16—33no—
65C3×C4⋊Q8—33no—
66C3×C4⋊Q8—63no—
67C3×#127—23no—
68C3×#127C2×D313yes—
69C3×#127C22×C313yes—
70C3×#121—26no—
71C3×#121—23no—
72C3×#121—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#888—23no—
84#869C22×C313yes—
85C4×Dic6C22×C313yes—
86C3×#106—33no—
87C3×C4⋊C8—33no—
88C3×#103—31no—
89C3×#102—33no—
90C3×#102—36no—
91C3×C4×C8—33no—
92#832C22×C316yes—
93#832C22×C313yes—
94#810C22×C311yescharacteristic
95#808C22×C313yes—
96C4⋊(C3⋊C8)C22×C313yes—
97C4×C3⋊C8C22×C313yes—
98C23×C32—23no—
99C32×Q8SD1614yescomplemented
100C32×D4—23no—
101C32×D4—23no—
102C32×D4—46no—
103C32×D4—83no—
104C2×C32×C4—21no—
105C2×C32×C4—46no—
106C2×C32×C4C2×D413yes—
107C2×C32×C4C2×D413yes—
108C2×C32×C4C2411yescharacteristic
109C2×C3×Dic3—21no—
110C2×C3×Dic3—23no—
111C3×Dic6—21no—
112C3×Dic6—83no—
113C3×Dic6#4112yescomplemented
114C3×C3⋊C8—23no—
115C3×C3⋊C8—21no—
116Q82—31no—
117#550C3×D311yescharacteristic
118#486—33no—
119#476—33no—
120#460—33no—
121C8×Q8—31no—
122C4×SD16—33no—
123C3×#41—48no—
124C3×#41—44no—
125C3×#41—44no—
126C2×C3×Q8—21no—
127C2×C3×Q8—31no—
128C2×C3×Q8—63no—
129C2×C3×Q8#6711yescharacteristic
130C2×C3×Q8C3×D411yescharacteristic
131C2×C3×D4—26no—
132C2×C3×D4—26no—
133C2×C3×D4—23no—
134C2×C3×D4—23no—
135C2×C3×D4—23no—
136C2×C3×D4—23no—
137C2×C3×D4—23no—
138C2×C3×D4C22×D313yes—
139C2×C3×D4C23×C313yes—
140C22×C3×C4—26no—
141C22×C3×C4—23no—
142C22×C3×C4—23no—
143C2×Dic6—23no—
144C2×Dic6C23×C311yescharacteristic
145C3×SD16—66no—
146C2×C3×C8—31no—
147C2×C3×C8—33no—
148C3×C4⋊C4—23no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—33no—
151C3×C4⋊C4—63no—
152C3×C4⋊C4—63no—
153C3×C4⋊C4#6713yes—
154C3×C4⋊C4C3×D413yes—
155C3×C4⋊C4C22×D311yescharacteristic
156C3×C4⋊C4C23×C311yescharacteristic
157C3×C22⋊C4—26no—
158C3×C22⋊C4—23no—
159C3×C22⋊C4—23no—
160C3×C42—23no—
161C3×C42—63no—
162C3×C42C22×D313yes—
163C3×C42C23×C313yes—
164#214—26no—
165C4⋊Dic3—23no—
166C4⋊Dic3C23×C313yes—
167Dic3⋊C4—23no—
168C4×Dic3—23no—
169C2×C3⋊C8C23×C311yescharacteristic
170C2×C3⋊C8C23×C313yes—
171C22×C32—43no—
172C22×C32—43no—
173C22×C32—43no—
174C22×C32C22×D411yescharacteristic
175C32×C4—23no—
176C32×C4—41no—
177C32×C4C2×SD1616yes—
178C32×C4C2×#4111yescharacteristic
179C32×C42−1+411yescharacteristic
180C3×Dic3—22no—
181C3×Dic3—43no—
182C2×#41—21no—
183C2×SD16—33no—
184C4⋊Q8—33no—
185C4⋊Q8—63no—
186#127C2×C3×D313yes—
187#121—23no—
188C4×Q8—33no—
189C4×Q8—61no—
190C4×Q8C2×C3×D311yescharacteristic
191C4×D4C2×C3×D313yes—
192#106—33no—
193C4⋊C8—33no—
194#103—31no—
195#102—33no—
196#102—36no—
197C4×C8—33no—
198C23×C3—26no—
199C23×C3—23no—
200C23×C3—23no—
201C3×Q8—24no—
202C3×Q8—32no—
203C3×Q8—61no—
204C3×Q8—243no—
205C3×Q8#21414yescomplemented
206C3×Q8C3×SD1614yescomplemented
207C3×D4—23no—
208C3×D4—23no—
209C3×D4—23no—
210C3×D4—23no—
211C3×D4—43no—
212C3×D4—43no—
213C3×D4—412no—
214C3×D4—46no—
215C3×D4—46no—
216C3×D4—83no—
217C3×D4—83no—
218C3×D4—86no—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—23no—
224C2×C3×C4—23no—
225C2×C3×C4—412no—
226C2×C3×C4—46no—
227C2×C3×C4—46no—
228C2×C3×C4—61no—
229C2×C3×C4—63no—
230C2×C3×C4C2×#6713yes—
231C2×C3×C4C2×#6713yes—
232C2×C3×C4C2×C3×D413yes—
233C2×C3×C4C2×C3×D413yes—
234C2×C3×C4C23×D311yescharacteristic
235C2×C3×C4C24×C311yescharacteristic
236C2×Dic3—21no—
237C2×Dic3—23no—
238Dic6—21no—
239Dic6—83no—
240Dic6C3×#4112yescomplemented
241C3×C8—63no—
242C3×C8—61no—
243C3⋊C8—23no—
244C3⋊C8—21no—
245C2×C32—83no—
246C2×C32#54811yescharacteristic
247C2×C32C22×SD1611yescharacteristic
248C2×C32#57611yescharacteristic
249#41—44no—
250C2×Q8—31no—
251C2×Q8—63no—
252C2×Q8C3×#6711yescharacteristic
253C2×D4—23no—
254C2×D4—23no—
255C2×D4C22×C3×D313yes—
256C22×C4—23no—
257SD16—66no—
258C2×C8—31no—
259C2×C8—33no—
260C4⋊C4—33no—
261C4⋊C4—63no—
262C4⋊C4—63no—
263C4⋊C4C3×#6713yes—
264C4⋊C4C22×C3×D311yescharacteristic
265C22⋊C4—23no—
266C42—63no—
267C42C22×C3×D313yes—
268C22×C3—21no—
269C22×C3—46no—
270C22×C3—46no—
271C22×C3—46no—
272C22×C3—43no—
273C22×C3—43no—
274C22×C3—43no—
275C22×C3—43no—
276C22×C3—43no—
277C22×C3—43no—
278C22×C3C22×#6711yescharacteristic
279C22×C3C22×C3×D411yescharacteristic
280C3×C4—23no—
281C3×C4—23no—
282C3×C4—26no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—43no—
286C3×C4—42no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—62no—
290C3×C4—123no—
291C3×C4C2×#21416yes—
292C3×C4C2×C3×SD1616yes—
293C3×C4D3×#4111yescharacteristic
294C3×C4#101011yescharacteristic
295C3×C4C2×C3×#4111yescharacteristic
296C3×C4C3×2−1+411yescharacteristic
297Dic3—22no—
298Dic3—43no—
299C32#336211yescharacteristic, complemented, Sylow
300C23—23no—
301Q8—32no—
302Q8—61no—
303Q8—243no—
304Q8C3×#21414yescomplemented
305D4—23no—
306D4—23no—
307D4—46no—
308D4—83no—
309C2×C4—21no—
310C2×C4—46no—
311C2×C4—61no—
312C2×C4—63no—
313C2×C4C2×C3×#6713yes—
314C2×C4C2×C3×#6713yes—
315C2×C4C23×C3×D311yescharacteristic
316C8—63no—
317C8—61no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—86no—
322C2×C3—83no—
323C2×C3—83no—
324C2×C3C22×#21411yescharacteristic
325C2×C3#583111yescharacteristic
326C2×C3#583511yescharacteristic
327C2×C3C3×#54811yescharacteristic
328C2×C3C22×C3×SD1611yescharacteristic
329C2×C3C3×#57611yescharacteristic
330C22—43no—
331C22—43no—
332C22—43no—
333C22C22×C3×#6711yescharacteristic
334C4—23no—
335C4—41no—
336C4—62no—
337C4—123no—
338C4C2×C3×#21416yes—
339C4C3×D3×#4111yescharacteristic
340C4C3×#101011yescharacteristic
341C3—21no—
342C3#8358611yescharacteristic, direct product factor
343C3C3×#336211yescharacteristic, complemented
344C2—83no—
345C2C22×C3×#21411yescharacteristic
346C2C3×#583111yescharacteristic
347C2C3×#583511yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC32×#550C2
socleC22×C32C22×D4
hypercenterC3×#550D3
hypocenterC3C3×#3362
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#550

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. C3×#5075C2semidirect
4. C3×#5070C2semidirect
5. C3×Q8×C3⋊C8C2semidirect
6. C3×C4×#214C2semidirect
7. C3×#5008C2semidirect
9. #83586C3direct (N × H)
30. Q8×Dic6C2×C3semidirect
36. #5075C2×C3semidirect
37. #5070C2×C3semidirect
38. Q8×C3⋊C8C2×C3semidirect
39. C4×#214C2×C3semidirect
40. #5008C2×C3semidirect
99. C32×Q8SD16semidirect
113. C3×Dic6#41semidirect
205. C3×Q8#214semidirect
206. C3×Q8C3×SD16semidirect
240. Dic6C3×#41semidirect
299. C32#3362semidirect
304. Q8C3×#214semidirect
342. C3#83586direct (N × H)
343. C3C3×#3362semidirect

Maximal subgroups

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

subgroupindex
C32×#5502
C3×Q8×Dic62
C3×#50752
C3×#50702
C3×Q8×C3⋊C82
C3×C4×#2142
C3×#50082
C3×#33623
#835863