Finite Group Databasebeta

← C3×#71040 #11781828

Subgroups — C3×#71040 #11781828

Order 1152.

380 conjugacy classes of subgroups.

The subgroup lattice has 353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#461C211yesmaximal, characteristic
2C3×#5080C211yesmaximal, characteristic, complemented
3C3×#5012C211yesmaximal, characteristic
4C3×#5008C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1691—31nomaximal
9#71040C311yesmaximal, characteristic, direct product factor
10C2×C32×SD16—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4×D4C2211yescharacteristic
13C2×C3×#208—21no—
14C3×#869C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×#103—21no—
17C3×#832—21no—
18C3×#830—21no—
19C3×#808—21no—
20C3×#808—21no—
21C3×#808—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#498—31no—
26C3×#476—31no—
27C3×#461—21no—
28C3×#461D311yescharacteristic
29C3×#461C2×C311yescharacteristic
30C3×#436—31no—
31#5080C2×C311yescharacteristic, complemented
32#5012C2×C311yescharacteristic
33#5008C2×C311yescharacteristic
34C3×#335—31no—
35C3×#333—31no—
36C3×#332—31no—
37#4547C2×C311yescharacteristic, complemented
38#4481C2×C311yescharacteristic, complemented
39#4479C2×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—
53C3×#208—42no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1691—31noSylow
59C2×C3×SD16—22no—
60C2×C3×SD16—21no—
61C2×C3×SD16—21no—
62C2×C3×M16—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
70C2×#208—21no—
71#869C22×C311yescharacteristic
72C3×#106—61no—
73C3×#106—61no—
74C3×#106—61no—
75C3×C4⋊C8—21no—
76C3×C4⋊C8—31no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4⋊C8C22×C311yescharacteristic
80C3×#103—22no—
81C3×#103—21no—
82C3×#103—21no—
83C3×#102—61no—
84C3×C22⋊C8—61no—
85C3×C4×C8—31no—
86#832—21no—
87#830—21no—
88#808—21no—
89#808—21no—
90#808—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×D4—21no—
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—81no—
108C32×C8—41no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8SD1612yescomplemented
113#498—31no—
114#476—31no—
115#461C3×D311yescharacteristic
116#436—31no—
117#335—31no—
118#333—31no—
119#332—31no—
120C2×C3×Q8—22no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—61no—
124C2×C3×D4—21no—
125C2×C3×D4#6711yescharacteristic
126C2×C3×D4C3×D411yescharacteristic
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—41no—
130C2×Dic6—21no—
131C3×SD16—44no—
132C3×SD16—42no—
133C3×SD16—42no—
134C3×M16—122no—
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—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—41no—
148C3×C4⋊C4—41no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4#6711yescharacteristic
152C3×C4⋊C4C3×D411yescharacteristic
153C3×C22⋊C4—21no—
154C3×C22⋊C4—21no—
155C3×C22⋊C4—41no—
156C3×C42—21no—
157C3×C42C22×D311yescharacteristic
158C3×C42C23×C311yescharacteristic
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161#208—42no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8C3×D411yescharacteristic
165C2×C3⋊C8C3×D411yescharacteristic
166C22×C32—41no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32#12111yescharacteristic
170C32×C4—21no—
171C32×C4—41no—
172C32×C4—81no—
173C32×C4C2×SD1611yescharacteristic
174C32×C4AGL(1,ℤ/8)11yescharacteristic
175C32×C4#13711yescharacteristic
176C32×C4#13711yescharacteristic
177C3×Dic3—81no—
178C2×SD16—21no—
179C2×M16—61no—
180C4⋊Q8—31no—
181C4⋊Q8C2×C3×D311yescharacteristic
182C4×D4C2×C3×D311yescharacteristic
183#106—61no—
184#106—61no—
185#106—61no—
186C4⋊C8—31no—
187C4⋊C8—31no—
188C4⋊C8C2×C3×D311yescharacteristic
189#103—21no—
190#102—61no—
191C22⋊C8—61no—
192C4×C8—31no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—41no—
196C3×Q8—42no—
197C3×Q8—42no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×Q8—41no—
201C3×Q8—41no—
202C3×Q8—241no—
203C3×D4—22no—
204C3×D4—21no—
205C3×D4—21no—
206C3×D4—21no—
207C3×D4—21no—
208C3×D4—41no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—42no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—81no—
223C2×C3×C4—81no—
224C2×C3×C4—121no—
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4#23711yescharacteristic
227C2×C3×C4C2×#6711yescharacteristic
228C2×C3×C4C2×C3×D411yescharacteristic
229C2×C3×C4C2×C3×D411yescharacteristic
230C2×C3×C4C3×#4111yescharacteristic
231C2×Dic3—41no—
232Dic6—81no—
233C3×C8—32no—
234C3×C8—42no—
235C3×C8—41no—
236C3×C8—41no—
237C3×C8—61no—
238C3×C8—121no—
239C3×C8—121no—
240C3⋊C8—21no—
241C3⋊C8—41no—
242C3⋊C8—41no—
243C3⋊C8C3×SD1612yescomplemented
244C2×C32—81no—
245C2×C32#46111yescharacteristic
246C2×C32#46811yescharacteristic
247C2×C32#47111yescharacteristic
248C2×Q8—21no—
249C2×Q8—61no—
250C2×D4C3×#6711yescharacteristic
251C22×C4—21no—
252SD16—42no—
253M16—122no—
254C2×C8—21no—
255C2×C8—31no—
256C2×C8—31no—
257C2×C8—61no—
258C2×C8—61no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C4⋊C4C3×#6711yescharacteristic
264C22⋊C4—21no—
265C42C22×C3×D311yescharacteristic
266C22×C3—21no—
267C22×C3—42no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—81no—
275C22×C3—81no—
276C22×C3#93911yescharacteristic
277C22×C3C3×#12111yescharacteristic
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—81no—
288C3×C4—82no—
289C3×C4—81no—
290C3×C4—81no—
291C3×C4—241no—
292C3×C4D3×SD1611yescharacteristic
293C3×C4#91511yescharacteristic
294C3×C4#93211yescharacteristic
295C3×C4#95111yescharacteristic
296C3×C4C2×C3×SD1611yescharacteristic
297C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
298C3×C4C3×#13711yescharacteristic
299C3×C4C3×#13711yescharacteristic
300Dic3—81no—
301C32#169111yescharacteristic, complemented, Sylow
302C23—21no—
303Q8—41no—
304Q8—41no—
305Q8—241no—
306D4—21no—
307D4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—121no—
313C2×C4C3×D3×D411yescharacteristic
314C2×C4C3×#23711yescharacteristic
315C2×C4C2×C3×#6711yescharacteristic
316C8—32no—
317C8—41no—
318C8—61no—
319C8—121no—
320C8—121no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—82no—
325C2×C3—81no—
326C2×C3—81no—
327C2×C3#504211yescharacteristic
328C2×C3#516211yescharacteristic
329C2×C3#520311yescharacteristic
330C2×C3C3×#46111yescharacteristic
331C2×C3C3×#46811yescharacteristic
332C2×C3C3×#47111yescharacteristic
333C22—41no—
334C22—41no—
335C22—41no—
336C22C3×#93911yescharacteristic
337C4—21no—
338C4—41no—
339C4—81no—
340C4—241no—
341C4C3×D3×SD1611yescharacteristic
342C4C3×#91511yescharacteristic
343C4C3×#93211yescharacteristic
344C4C3×#95111yescharacteristic
345C3—21no—
346C3#7104011yescharacteristic, direct product factor
347C3C3×#169111yescharacteristic, complemented
348C2—81no—
349C2C3×#504211yescharacteristic
350C2C3×#516211yescharacteristic
351C2C3×#520311yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#461C2
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC3×#461D3
hypocenterC3C3×#1691
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×#5080C2semidirect
5. C3×#4547C2semidirect
6. C3×#4481C2semidirect
7. C3×#4479C2semidirect
9. #71040C3direct (N × H)
31. #5080C2×C3semidirect
37. #4547C2×C3semidirect
38. #4481C2×C3semidirect
39. #4479C2×C3semidirect
112. C3×C3⋊C8SD16semidirect
243. C3⋊C8C3×SD16semidirect
301. C32#1691semidirect
346. C3#71040direct (N × H)
347. C3C3×#1691semidirect

Maximal subgroups

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

subgroupindex
C32×#4612
C3×#50802
C3×#50122
C3×#50082
C3×#45472
C3×#44812
C3×#44792
C3×#16913
#710403