Finite Group Databasebeta

← C3×#71038 #11781339

Subgroups — C3×#71038 #11781339

Order 1152.

392 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#461C211yesmaximal, characteristic
2C3×#5093C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊C8C211yesmaximal, characteristic
4C3×#5007C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1679—31nomaximal
9#71038C311yesmaximal, characteristic, direct product factor
10C2×C32×SD16—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4×D4C2211yescharacteristic
13C22×C3×C3⋊C8—21no—
14C3×#869C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×#103—21no—
17C3×#832—21no—
18C3×#830—21no—
19C3×#810—21no—
20C3×#810—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#487—31no—
26C3×#474—31no—
27C3×#461—21no—
28C3×#461D311yescharacteristic
29C3×#461C2×C311yescharacteristic
30C3×C8×D4—31no—
31#5093C2×C311yescharacteristic, complemented
32D4×C3⋊C8C2×C311yescharacteristic
33#5007C2×C311yescharacteristic
34C3×#334—31no—
35C3×#332—31no—
36C3×#332—31no—
37#4547C2×C311yescharacteristic, complemented
38#4486C2×C311yescharacteristic, complemented
39#4480C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×D4D411yescharacteristic
42C22×C32×C4—21no—
43C2×C3×Dic6—21no—
44C32×SD16—42no—
45C2×C32×C8—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—42no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1679—31noSylow
59C2×C3×SD16—22no—
60C2×C3×SD16—21no—
61C2×C3×SD16—21no—
62C22×C3×C8—61no—
63C3×C4⋊Q8—21no—
64C3×C4⋊Q8—31no—
65C3×C4⋊Q8C2×D311yescharacteristic
66C3×C4⋊Q8C22×C311yescharacteristic
67C3×C4×D4—21no—
68C3×C4×D4C2×D311yescharacteristic
69C3×C4×D4C22×C311yescharacteristic
70C22×C3⋊C8—21no—
71#869C22×C311yescharacteristic
72C3×#107—61no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×#103—22no—
79C3×#103—21no—
80C3×#103—21no—
81C3×#103—61no—
82C3×#103—61no—
83C3×#102—61no—
84C3×C22⋊C8—61no—
85C3×C4×C8—31no—
86#832—21no—
87#830—21no—
88#810—21no—
89#810—21no—
90#807—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4×C3⋊C8C22×C311yescharacteristic
94C23×C32—21no—
95C32×Q8—41no—
96C32×Q8—41no—
97C32×D4—21no—
98C32×D4SD1612yes—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C3×Dic3—41no—
107C3×Dic6—41no—
108C3×Dic6—41no—
109C32×C8—41no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114#487—31no—
115#474—31no—
116#461C3×D311yescharacteristic
117C8×D4—31no—
118#334—31no—
119#332—31no—
120#332—31no—
121C2×C3×Q8—22no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×Q8—61no—
125C2×C3×D4—21no—
126C2×C3×D4#6711yescharacteristic
127C2×C3×D4C3×D411yescharacteristic
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—41no—
131C2×Dic6—21no—
132C3×SD16—44no—
133C3×SD16—42no—
134C3×SD16—42no—
135C2×C3×C8—22no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—31no—
139C2×C3×C8—31no—
140C2×C3×C8—61no—
141C2×C3×C8—61no—
142C2×C3×C8—122no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—41no—
149C3×C4⋊C4—41no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4#6711yescharacteristic
153C3×C4⋊C4C3×D411yescharacteristic
154C3×C22⋊C4—21no—
155C3×C22⋊C4—21no—
156C3×C22⋊C4—41no—
157C3×C42—21no—
158C3×C42C22×D311yescharacteristic
159C3×C42C23×C311yescharacteristic
160C4⋊Dic3—21no—
161C4⋊Dic3—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—42no—
165C2×C3⋊C8C3×D411yescharacteristic
166C2×C3⋊C8C3×D411yescharacteristic
167C22×C32—22no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32#12111yescharacteristic
171C32×C4—21no—
172C32×C4—41no—
173C32×C4—81no—
174C32×C4C2×SD1611yescharacteristic
175C32×C4#13511yescharacteristic
176C32×C4#13511yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C3×Dic3—81no—
179C2×SD16—21no—
180C22×C8—61no—
181C4⋊Q8—31no—
182C4⋊Q8C2×C3×D311yescharacteristic
183C4×D4C2×C3×D311yescharacteristic
184#107—61no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8C2×C3×D311yescharacteristic
188#103—21no—
189#103—61no—
190#103—61no—
191#102—61no—
192C22⋊C8—61no—
193C4×C8—31no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—41no—
197C3×Q8—42no—
198C3×Q8—42no—
199C3×Q8—41no—
200C3×Q8—41no—
201C3×Q8—41no—
202C3×Q8—41no—
203C3×Q8—121no—
204C3×Q8—121no—
205C3×D4—21no—
206C3×D4—21no—
207C3×D4—22no—
208C3×D4—41no—
209C3×D4#21412yes—
210C3×D4C3×SD1612yes—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—42no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—81no—
225C2×C3×C4—81no—
226C2×C3×C4—121no—
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4#23711yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×C3×C4C2×C3×D411yescharacteristic
231C2×C3×C4C2×C3×D411yescharacteristic
232C2×C3×C4C3×#4111yescharacteristic
233C2×Dic3—41no—
234Dic6—41no—
235Dic6—41no—
236C3×C8—42no—
237C3×C8—41no—
238C3×C8—41no—
239C3×C8—61no—
240C3×C8—61no—
241C3×C8—121no—
242C3×C8—121no—
243C3⋊C8—21no—
244C3⋊C8—21no—
245C3⋊C8—41no—
246C3⋊C8—41no—
247C2×C32—42no—
248C2×C32#46311yescharacteristic
249C2×C32#46511yescharacteristic
250C2×C32#47311yescharacteristic
251C2×Q8—21no—
252C2×Q8—61no—
253C2×D4C3×#6711yescharacteristic
254C22×C4—21no—
255SD16—42no—
256C2×C8—21no—
257C2×C8—31no—
258C2×C8—31no—
259C2×C8—61no—
260C2×C8—61no—
261C2×C8—122no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—61no—
265C4⋊C4—61no—
266C4⋊C4C3×#6711yescharacteristic
267C22⋊C4—21no—
268C42C22×C3×D311yescharacteristic
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—21no—
272C22×C3—42no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—81no—
278C22×C3—81no—
279C22×C3#93911yescharacteristic
280C22×C3C3×#12111yescharacteristic
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—81no—
291C3×C4—82no—
292C3×C4—81no—
293C3×C4—81no—
294C3×C4—241no—
295C3×C4#91411yescharacteristic
296C3×C4#91611yescharacteristic
297C3×C4C2×#21411yescharacteristic
298C3×C4#95011yescharacteristic
299C3×C4C2×C3×SD1611yescharacteristic
300C3×C4C3×#13511yescharacteristic
301C3×C4C3×#13511yescharacteristic
302C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
303Dic3—81no—
304C32#167911yescharacteristic, complemented, Sylow
305C23—21no—
306Q8—41no—
307Q8—41no—
308Q8—121no—
309Q8—121no—
310D4—21no—
311D4C3×#21412yes—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—121no—
317C2×C4C3×D3×D411yescharacteristic
318C2×C4C3×#23711yescharacteristic
319C2×C4C2×C3×#6711yescharacteristic
320C8—41no—
321C8—61no—
322C8—61no—
323C8—121no—
324C8—121no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—42no—
329C2×C3—42no—
330C2×C3—82no—
331C2×C3#504111yescharacteristic
332C2×C3#516511yescharacteristic
333C2×C3#520411yescharacteristic
334C2×C3C3×#46311yescharacteristic
335C2×C3C3×#46511yescharacteristic
336C2×C3C3×#47311yescharacteristic
337C22—22no—
338C22—41no—
339C22—41no—
340C22C3×#93911yescharacteristic
341C4—21no—
342C4—41no—
343C4—81no—
344C4—241no—
345C4C3×#91411yescharacteristic
346C4C3×#91611yescharacteristic
347C4C2×C3×#21411yescharacteristic
348C4C3×#95011yescharacteristic
349C3—21no—
350C3#7103811yescharacteristic, direct product factor
351C3C3×#167911yescharacteristic, complemented
352C2—42no—
353C2C3×#504111yescharacteristic
354C2C3×#516511yescharacteristic
355C2C3×#520411yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#461C2
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC3×#461D3
hypocenterC3C3×#1679
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
2. C3×#5093C2semidirect
5. C3×#4547C2semidirect
6. C3×#4486C2semidirect
7. C3×#4480C2semidirect
9. #71038C3direct (N × H)
31. #5093C2×C3semidirect
37. #4547C2×C3semidirect
38. #4486C2×C3semidirect
39. #4480C2×C3semidirect
304. C32#1679semidirect
350. C3#71038direct (N × H)
351. C3C3×#1679semidirect

Maximal subgroups

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

subgroupindex
C32×#4612
C3×#50932
C3×D4×C3⋊C82
C3×#50072
C3×#45472
C3×#44862
C3×#44802
C3×#16793
#710383