Finite Group Databasebeta

← C3×#71209 #11781464

Subgroups — C3×#71209 #11781464

Order 1152.

391 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#486C211yesmaximal, characteristic
2C3×#5090C211yesmaximal, characteristic, complemented
3C3×#5075C211yesmaximal, characteristic
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4544C211yesmaximal, characteristic
7C3×#4458C211yesmaximal, characteristic, complemented
8C3×#1682—31nomaximal
9#71209C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×#127C2211yescharacteristic
12C2×C3×#216—21no—
13C2×C3×#214—21no—
14C3×C4×Dic6C2211yescharacteristic
15C32×#102—21no—
16C32×#102—21no—
17C32×C4×C8C2211yescharacteristic
18C3×#835—21no—
19C3×#832—21no—
20C3×Dic3⋊C8—21no—
21C3×C8×Dic3—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×#462—31no—
29C3×#460—31no—
30C3×C8×Q8—31no—
31#5090C2×C311yescharacteristic, complemented
32#5075C2×C311yescharacteristic
33C8×Dic6C2×C311yescharacteristic, complemented
34C3×#335—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4547C2×C311yescharacteristic, complemented
38#4544C2×C311yescharacteristic
39#4458C2×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×#216—42no—
51C3×#214—42no—
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58#1682—31noSylow
59C2×C3×Q16—61no—
60C2×C3×SD16—61no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4⋊Q8C22×C311yescharacteristic
64C3×#127—21no—
65C3×#127C2×D311yescharacteristic
66C3×#127C22×C311yescharacteristic
67C3×C4×Q8—31no—
68C2×#216—21no—
69C2×#214—21no—
70C4×Dic6C22×C311yescharacteristic
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—61no—
75C3×#103—61no—
76C3×#102—22no—
77C3×#102—22no—
78C3×#102—21no—
79C3×#102—21no—
80C3×#102—21no—
81C3×#102—21no—
82C3×#102—61no—
83C3×C4×C8—21no—
84C3×C4×C8—61no—
85C3×C4×C8C2×D311yescharacteristic
86C3×C4×C8C22×C311yescharacteristic
87#835—21no—
88#832—21no—
89Dic3⋊C8—21no—
90C8×Dic3—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C23×C32—41no—
95C32×Q8—41no—
96C32×Q8—41no—
97C32×D4—41no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—41no—
101C32×D4—81no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C3×Dic3—21no—
107C2×C3×Dic3—21no—
108C3×Dic6—21no—
109C3×Dic6D812yes—
110C32×C8—21no—
111C32×C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#486C3×D311yescharacteristic
116#462—31no—
117#460—31no—
118C8×Q8—31no—
119#335—31no—
120#332—31no—
121#331—31no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×Q8—31no—
125C2×C3×Q8—41no—
126C2×C3×D4—22no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—41no—
134C2×C3×D4—41no—
135C2×Dic6C3×D411yescharacteristic
136C3×Q16—122no—
137C3×SD16—122no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—61no—
141C2×C3×C8—61no—
142C2×C3×C8—61no—
143C2×C3×C8#6711yescharacteristic
144C2×C3×C8#6711yescharacteristic
145C2×C3×C8C3×D411yescharacteristic
146C2×C3×C8C3×D411yescharacteristic
147C3×C4⋊C4—22no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4—61no—
155C3×C42—21no—
156C3×C42—61no—
157C3×C42C22×D311yescharacteristic
158C3×C42C23×C311yescharacteristic
159#216—42no—
160#214—42no—
161C4⋊Dic3C3×D411yescharacteristic
162Dic3⋊C4—21no—
163C4×Dic3—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—21no—
166C2×C3⋊C8—21no—
167C22×C32—81no—
168C22×C32—81no—
169C22×C32—81no—
170C22×C32#12111yescharacteristic
171C32×C4—21no—
172C32×C4—81no—
173C32×C4C2×D811yescharacteristic
174C32×C4#13511yescharacteristic
175C32×C4#13511yescharacteristic
176C32×C4#13711yescharacteristic
177C3×Dic3—22no—
178C3×Dic3—41no—
179C2×Q16—61no—
180C2×SD16—61no—
181C4⋊Q8C2×C3×D311yescharacteristic
182#127C2×C3×D311yescharacteristic
183C4×Q8—31no—
184C4⋊C8—31no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8—61no—
188#103—61no—
189#102—21no—
190#102—21no—
191#102—61no—
192C4×C8—61no—
193C4×C8C2×C3×D311yescharacteristic
194C23×C3—42no—
195C23×C3—41no—
196C23×C3—41no—
197C3×Q8—32no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×Q8—41no—
201C3×Q8—41no—
202C3×Q8—61no—
203C3×Q8—81no—
204C3×Q8—81no—
205C3×D4—42no—
206C3×D4—42no—
207C3×D4—41no—
208C3×D4—41no—
209C3×D4—41no—
210C3×D4—41no—
211C3×D4—41no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—81no—
216C3×D4—81no—
217C3×D4—81no—
218C3×D4—81no—
219C3×D4—82no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—42no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—61no—
227C2×C3×C4—61no—
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4#23711yescharacteristic
230C2×C3×C4C2×#6711yescharacteristic
231C2×C3×C4C2×C3×D411yescharacteristic
232C2×C3×C4C2×C3×D411yescharacteristic
233C2×C3×C4C3×#4111yescharacteristic
234C2×Dic3—21no—
235C2×Dic3—21no—
236Dic6—21no—
237Dic6C3×D812yes—
238C3×C8—21no—
239C3×C8—21no—
240C3×C8—21no—
241C3×C8—21no—
242C3×C8—41no—
243C3×C8—41no—
244C3×C8—121no—
245C3×C8—121no—
246C3×C8—121no—
247C3⋊C8—41no—
248C3⋊C8—41no—
249C3⋊C8—41no—
250C2×C32—161no—
251C2×C32#46411yescharacteristic
252C2×C32#46611yescharacteristic
253C2×C32#47111yescharacteristic
254C2×Q8—21no—
255C2×Q8—31no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259Q16—122no—
260SD16—122no—
261C2×C8—61no—
262C2×C8—61no—
263C2×C8—61no—
264C2×C8C3×#6711yescharacteristic
265C2×C8C3×#6711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—31no—
269C4⋊C4—61no—
270C42—61no—
271C42C22×C3×D311yescharacteristic
272C22×C3—21no—
273C22×C3—82no—
274C22×C3—82no—
275C22×C3—82no—
276C22×C3—81no—
277C22×C3—81no—
278C22×C3—81no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3—81no—
282C22×C3#93811yescharacteristic
283C22×C3C3×#12111yescharacteristic
284C3×C4—22no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—62no—
292C3×C4—82no—
293C3×C4—81no—
294C3×C4—81no—
295C3×C4—121no—
296C3×C4D3×D811yescharacteristic
297C3×C4#91211yescharacteristic
298C3×C4#95011yescharacteristic
299C3×C4#95111yescharacteristic
300C3×C4C2×C3×D811yescharacteristic
301C3×C4C3×#13511yescharacteristic
302C3×C4C3×#13511yescharacteristic
303C3×C4C3×#13711yescharacteristic
304Dic3—22no—
305Dic3—41no—
306C32#168211yescharacteristic, complemented, Sylow
307C23—41no—
308Q8—32no—
309Q8—41no—
310Q8—41no—
311Q8—61no—
312D4—41no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—81no—
317C2×C4—41no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4C3×D3×D411yescharacteristic
321C2×C4C3×#23711yescharacteristic
322C2×C4C2×C3×#6711yescharacteristic
323C8—21no—
324C8—21no—
325C8—121no—
326C8—121no—
327C8—121no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—162no—
332C2×C3—161no—
333C2×C3—161no—
334C2×C3#505411yescharacteristic
335C2×C3#515711yescharacteristic
336C2×C3#517711yescharacteristic
337C2×C3C3×#46411yescharacteristic
338C2×C3C3×#46611yescharacteristic
339C2×C3C3×#47111yescharacteristic
340C22—81no—
341C22—81no—
342C22—81no—
343C22C3×#93811yescharacteristic
344C4—21no—
345C4—62no—
346C4—81no—
347C4—121no—
348C4C3×D3×D811yescharacteristic
349C4C3×#91211yescharacteristic
350C4C3×#95011yescharacteristic
351C4C3×#95111yescharacteristic
352C3—21no—
353C3#7120911yescharacteristic, direct product factor
354C3C3×#168211yescharacteristic, complemented
355C2—161no—
356C2C3×#505411yescharacteristic
357C2C3×#515711yescharacteristic
358C2C3×#517711yescharacteristic
subgroupG/H
centerC22×C3#938
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#486C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenterC3×#486D3
hypocenterC3C3×#1682
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×#5090C2semidirect
4. C3×C8×Dic6C2semidirect
5. C3×#4547C2semidirect
7. C3×#4458C2semidirect
9. #71209C3direct (N × H)
31. #5090C2×C3semidirect
33. C8×Dic6C2×C3semidirect
37. #4547C2×C3semidirect
39. #4458C2×C3semidirect
306. C32#1682semidirect
353. C3#71209direct (N × H)
354. C3C3×#1682semidirect

Maximal subgroups

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

subgroupindex
C32×#4862
C3×#50902
C3×#50752
C3×C8×Dic62
C3×#45472
C3×#45442
C3×#44582
C3×#16823
#712093