Finite Group Databasebeta

← C3×#71208 #11781277

Subgroups — C3×#71208 #11781277

Order 1152.

379 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#486C211yesmaximal, characteristic
2C3×#5091C211yesmaximal, characteristic, complemented
3C3×#5075C211yesmaximal, characteristic
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5C3×#4546C211yesmaximal, characteristic, complemented
6C3×#4544C211yesmaximal, characteristic
7C3×#4457C211yesmaximal, characteristic, complemented
8C3×#1678—31nomaximal
9#71208C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×#127C2211yescharacteristic
12C2×C3×#214—21no—
13C3×C4×Dic6C2211yescharacteristic
14C32×#102—21no—
15C32×#102—21no—
16C32×C4×C8C2211yescharacteristic
17C3×#832—21no—
18C3×Dic3⋊C8—21no—
19C3×C8×Dic3—21no—
20C3×#810—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#486—21no—
26C3×#486D311yescharacteristic
27C3×#486C2×C311yescharacteristic
28C3×#477—31no—
29C3×#460—31no—
30C3×C8×Q8—31no—
31#5091C2×C311yescharacteristic, complemented
32#5075C2×C311yescharacteristic
33C8×Dic6C2×C311yescharacteristic, complemented
34C3×#334—31no—
35C3×#333—31no—
36C3×#331—31no—
37#4546C2×C311yescharacteristic, complemented
38#4544C2×C311yescharacteristic
39#4457C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C2×C32×C8D411yescharacteristic
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C42C2311yescharacteristic
50C3×#214—42no—
51C3×C4⋊Dic3D411yescharacteristic
52C3×Dic3⋊C4—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#1678—31noSylow
58C2×C3×SD16—61no—
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C22×C311yescharacteristic
62C3×#127—21no—
63C3×#127C2×D311yescharacteristic
64C3×#127C22×C311yescharacteristic
65C3×C4×Q8—31no—
66C2×#214—21no—
67C4×Dic6C22×C311yescharacteristic
68C3×#107—61no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—61no—
73C3×#103—61no—
74C3×#102—22no—
75C3×#102—22no—
76C3×#102—21no—
77C3×#102—21no—
78C3×#102—21no—
79C3×#102—21no—
80C3×#102—61no—
81C3×C4×C8—21no—
82C3×C4×C8—61no—
83C3×C4×C8C2×D311yescharacteristic
84C3×C4×C8C22×C311yescharacteristic
85#832—21no—
86Dic3⋊C8—21no—
87C8×Dic3—21no—
88#810—21no—
89#807—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C23×C32—41no—
94C32×Q8—81no—
95C32×D4—41no—
96C32×D4—41no—
97C32×D4—41no—
98C32×D4—41no—
99C32×D4—81no—
100C2×C32×C4—41no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3×Dic3—21no—
105C2×C3×Dic3—21no—
106C3×Dic6—21no—
107C3×Dic6SD1612yes—
108C32×C8—21no—
109C32×C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#486C3×D311yescharacteristic
114#477—31no—
115#460—31no—
116C8×Q8—31no—
117#334—31no—
118#333—31no—
119#331—31no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—31no—
123C2×C3×Q8—41no—
124C2×C3×D4—22no—
125C2×C3×D4—21no—
126C2×C3×D4—21no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—41no—
132C2×C3×D4—41no—
133C2×Dic6C3×D411yescharacteristic
134C3×SD16—122no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C2×C3×C8—61no—
140C2×C3×C8#6711yescharacteristic
141C2×C3×C8#6711yescharacteristic
142C2×C3×C8C3×D411yescharacteristic
143C2×C3×C8C3×D411yescharacteristic
144C3×C4⋊C4—22no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—41no—
151C3×C4⋊C4—61no—
152C3×C42—21no—
153C3×C42—61no—
154C3×C42C22×D311yescharacteristic
155C3×C42C23×C311yescharacteristic
156#214—42no—
157C4⋊Dic3C3×D411yescharacteristic
158Dic3⋊C4—21no—
159C4×Dic3—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C22×C32—81no—
164C22×C32—81no—
165C22×C32—81no—
166C22×C32#12111yescharacteristic
167C32×C4—21no—
168C32×C4—81no—
169C32×C4C2×SD1611yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4#13511yescharacteristic
172C32×C4#13711yescharacteristic
173C3×Dic3—22no—
174C3×Dic3—41no—
175C2×SD16—61no—
176C4⋊Q8C2×C3×D311yescharacteristic
177#127C2×C3×D311yescharacteristic
178C4×Q8—31no—
179#107—61no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—31no—
183C4⋊C8—61no—
184#103—61no—
185#102—21no—
186#102—21no—
187#102—61no—
188C4×C8—61no—
189C4×C8C2×C3×D311yescharacteristic
190C23×C3—42no—
191C23×C3—41no—
192C23×C3—41no—
193C3×Q8—32no—
194C3×Q8—61no—
195C3×Q8—81no—
196C3×Q8—81no—
197C3×Q8—82no—
198C3×D4—42no—
199C3×D4—42no—
200C3×D4—41no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—41no—
204C3×D4—41no—
205C3×D4—41no—
206C3×D4—41no—
207C3×D4—41no—
208C3×D4—81no—
209C3×D4—81no—
210C3×D4—81no—
211C3×D4—81no—
212C3×D4—82no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—42no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—61no—
220C2×C3×C4—61no—
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4#23711yescharacteristic
223C2×C3×C4C2×#6711yescharacteristic
224C2×C3×C4C2×C3×D411yescharacteristic
225C2×C3×C4C2×C3×D411yescharacteristic
226C2×C3×C4C3×#4111yescharacteristic
227C2×Dic3—21no—
228C2×Dic3—21no—
229Dic6—21no—
230Dic6C3×SD1612yes—
231C3×C8—21no—
232C3×C8—21no—
233C3×C8—21no—
234C3×C8—21no—
235C3×C8—41no—
236C3×C8—41no—
237C3×C8—121no—
238C3×C8—121no—
239C3×C8—121no—
240C3⋊C8—41no—
241C3⋊C8—41no—
242C3⋊C8—41no—
243C2×C32—161no—
244C2×C32#46411yescharacteristic
245C2×C32#46511yescharacteristic
246C2×C32#47211yescharacteristic
247C2×Q8—21no—
248C2×Q8—31no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—21no—
252SD16—122no—
253C2×C8—61no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8C3×#6711yescharacteristic
257C2×C8C3×#6711yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—31no—
261C4⋊C4—61no—
262C42—61no—
263C42C22×C3×D311yescharacteristic
264C22×C3—21no—
265C22×C3—82no—
266C22×C3—82no—
267C22×C3—82no—
268C22×C3—81no—
269C22×C3—81no—
270C22×C3—81no—
271C22×C3—81no—
272C22×C3—81no—
273C22×C3—81no—
274C22×C3#93811yescharacteristic
275C22×C3C3×#12111yescharacteristic
276C3×C4—22no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—62no—
284C3×C4—82no—
285C3×C4—81no—
286C3×C4—81no—
287C3×C4—121no—
288C3×C4D3×SD1611yescharacteristic
289C3×C4#91611yescharacteristic
290C3×C4#95011yescharacteristic
291C3×C4#95111yescharacteristic
292C3×C4C2×C3×SD1611yescharacteristic
293C3×C4C3×#13511yescharacteristic
294C3×C4C3×#13511yescharacteristic
295C3×C4C3×#13711yescharacteristic
296Dic3—22no—
297Dic3—41no—
298C32#167811yescharacteristic, complemented, Sylow
299C23—41no—
300Q8—32no—
301Q8—61no—
302Q8—81no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—41no—
307D4—81no—
308C2×C4—41no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4C3×D3×D411yescharacteristic
312C2×C4C3×#23711yescharacteristic
313C2×C4C2×C3×#6711yescharacteristic
314C8—21no—
315C8—21no—
316C8—121no—
317C8—121no—
318C8—121no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—162no—
323C2×C3—161no—
324C2×C3—161no—
325C2×C3#505411yescharacteristic
326C2×C3#516011yescharacteristic
327C2×C3#517111yescharacteristic
328C2×C3C3×#46411yescharacteristic
329C2×C3C3×#46511yescharacteristic
330C2×C3C3×#47211yescharacteristic
331C22—81no—
332C22—81no—
333C22—81no—
334C22C3×#93811yescharacteristic
335C4—21no—
336C4—62no—
337C4—81no—
338C4—121no—
339C4C3×D3×SD1611yescharacteristic
340C4C3×#91611yescharacteristic
341C4C3×#95011yescharacteristic
342C4C3×#95111yescharacteristic
343C3—21no—
344C3#7120811yescharacteristic, direct product factor
345C3C3×#167811yescharacteristic, complemented
346C2—161no—
347C2C3×#505411yescharacteristic
348C2C3×#516011yescharacteristic
349C2C3×#517111yescharacteristic
subgroupG/H
centerC22×C3#938
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#486C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenterC3×#486D3
hypocenterC3C3×#1678
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#486

Complements

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

NH ≅ G/Ntype
2. C3×#5091C2semidirect
4. C3×C8×Dic6C2semidirect
5. C3×#4546C2semidirect
7. C3×#4457C2semidirect
9. #71208C3direct (N × H)
31. #5091C2×C3semidirect
33. C8×Dic6C2×C3semidirect
37. #4546C2×C3semidirect
39. #4457C2×C3semidirect
298. C32#1678semidirect
344. C3#71208direct (N × H)
345. C3C3×#1678semidirect

Maximal subgroups

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

subgroupindex
C32×#4862
C3×#50912
C3×#50752
C3×C8×Dic62
C3×#45462
C3×#45442
C3×#44572
C3×#16783
#712083