Finite Group Databasebeta

← C3×#71323 #11798960

Subgroups — C3×#71323 #11798960

Order 1152.

405 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#495C211yesmaximal, characteristic, complemented
2C2×C3×#828C211yesmaximal, characteristic, complemented
3C2×C3×#826C211yesmaximal, characteristic
4C3×C4×D24C211yesmaximal, characteristic, complemented
5C3×#4564C211yesmaximal, characteristic, complemented
6C3×#4562C211yesmaximal, characteristic, complemented
7C3×C4⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
8C3×#2210—31nomaximal
9#71323C311yesmaximal, characteristic, direct product factor
10C2×C32×Q16C2211yescharacteristic
11C2×C32×SD16—21no—
12C2×C32×D8C2211yescharacteristic
13C32×#124—21no—
14C2×C3×D24C2211yescharacteristic
15C3×C4×D12—21no—
16C32×C4×C8C2211yescharacteristic
17C3×#828—22no—
18C3×#826—22no—
19C3×#821—21no—
20C3×#818C2211yescharacteristic
21C2×C3×C3⋊C16C2211yescharacteristic
22C2×C3×C3⋊C16C2211yescharacteristic
23C2×C3×SD32—31no—
24C2×C3×D16—31no—
25C3×#495—21no—
26C3×#495D311yescharacteristic, complemented
27C3×#495C2×C311yescharacteristic, complemented
28C3×C4×D8—31no—
29C2×#828C2×C311yescharacteristic, complemented
30C2×#826C2×C311yescharacteristic
31C4×D24C2×C311yescharacteristic, complemented
32C3×C4⋊C16—31no—
33C3×#358—31no—
34C3×#357—31no—
35#4564C2×C311yescharacteristic, complemented
36#4562C2×C311yescharacteristic, complemented
37C4⋊(C3⋊C16)C2×C311yescharacteristic, complemented
38C2×C32×Q8—21no—
39C2×C32×D4—21no—
40C2×C3×D12—21no—
41C2×C3×C4×D3—41no—
42C32×Q16—21no—
43C32×Q16—21no—
44C32×SD16—42no—
45C32×D8—21no—
46C32×D8—21no—
47C2×C32×C8D411yescharacteristic
48C2×C32×C8C2311yescharacteristic
49C32×C22⋊C4—41no—
50C32×C22⋊C4—41no—
51C32×C42D411yescharacteristic
52C3×(C2×D3)⋊C4—41no—
53C3×C4⋊Dic3—21no—
54C3×D24—21no—
55C3×D24D412yes—
56C3×C3⋊C16—21no—
57C3×C3⋊C16—21no—
58#2210—31noSylow
59C2×C3×Q16—21no—
60C2×C3×Q16C2×D311yescharacteristic
61C2×C3×Q16C22×C311yescharacteristic
62C2×C3×SD16—22no—
63C2×C3×SD16—21no—
64C2×C3×SD16—21no—
65C2×C3×D8—21no—
66C2×C3×D8—31no—
67C2×C3×D8C2×D311yescharacteristic
68C2×C3×D8C22×C311yescharacteristic
69C3×#124—22no—
70C3×#124—21no—
71C3×#124—21no—
72C3×C4×D4—61no—
73C2×D24C22×C311yescharacteristic
74C4×D12—21no—
75C3×SD32—62no—
76C3×D16—62no—
77C2×C3×C16—31no—
78C2×C3×C16—31no—
79C3×#107—31no—
80C3×#102—61no—
81C3×C4×C8—21no—
82C3×C4×C8C2×D311yescharacteristic
83C3×C4×C8C22×C311yescharacteristic
84#828—22no—
85#826—22no—
86#821—21no—
87#818C22×C311yescharacteristic
88C2×C3⋊C16C22×C311yescharacteristic
89C2×C3⋊C16C22×C311yescharacteristic
90C23×C32—41no—
91C22×C3×D3—41no—
92C32×Q8—41no—
93C32×Q8—41no—
94C32×D4—41no—
95C32×D4—41no—
96C2×C32×C4—41no—
97C2×C32×C4D811yescharacteristic
98C2×C32×C4D811yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C3×Dic3—41no—
101C3×D12—22no—
102C3×D12—41no—
103C3×C4×D3—82no—
104C32×C8—21no—
105C32×C8C2×D411yescharacteristic
106C32×C8#4111yescharacteristic
107C2×SD32—31no—
108C2×D16—31no—
109#495C3×D311yescharacteristic, complemented
110C4×D8—31no—
111C4⋊C16—31no—
112#358—31no—
113#357—31no—
114C2×C3×Q8—22no—
115C2×C3×Q8—21no—
116C2×C3×Q8—21no—
117C2×C3×D4—22no—
118C2×C3×D4—21no—
119C2×C3×D4—21no—
120C2×C3×D4—61no—
121C22×C3×C4—121no—
122C2×D12—21no—
123C2×C4×D3—41no—
124C3×Q16—21no—
125C3×Q16—21no—
126C3×Q16—21no—
127C3×Q16—21no—
128C3×Q16—41no—
129C3×Q16—41no—
130C3×SD16—44no—
131C3×SD16—42no—
132C3×SD16—42no—
133C3×D8—21no—
134C3×D8—21no—
135C3×D8—21no—
136C3×D8—21no—
137C3×D8—32no—
138C3×D8—41no—
139C3×D8—41no—
140C3×D8—61no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8#6711yescharacteristic
144C2×C3×C8C3×D411yescharacteristic
145C2×C3×C8C22×D311yescharacteristic
146C2×C3×C8C23×C311yescharacteristic
147C3×C4⋊C4—61no—
148C3×C22⋊C4—42no—
149C3×C22⋊C4—42no—
150C3×C22⋊C4—41no—
151C3×C22⋊C4—41no—
152C3×C22⋊C4—41no—
153C3×C22⋊C4—41no—
154C3×C22⋊C4—121no—
155C3×C42—21no—
156C3×C42#6711yescharacteristic
157C3×C42C3×D411yescharacteristic
158(C2×D3)⋊C4—41no—
159C4⋊Dic3—21no—
160D24—21no—
161D24C3×D412yes—
162C3×C16—61no—
163C3×C16—61no—
164C3⋊C16—21no—
165C3⋊C16—21no—
166C22×C32—81no—
167C22×C32—81no—
168C22×C32—81no—
169C22×C32C2×D811yescharacteristic
170C2×C3×D3—42no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C32×C4—21no—
174C32×C4—21no—
175C32×C4—81no—
176C32×C4#12111yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C3×Dic3—81no—
179C2×Q16C2×C3×D311yescharacteristic
180C2×SD16—21no—
181C2×D8—31no—
182C2×D8C2×C3×D311yescharacteristic
183#124—21no—
184C4×D4—61no—
185SD32—62no—
186D16—62no—
187C2×C16—31no—
188C2×C16—31no—
189#107—31no—
190#102—61no—
191C4×C8C2×C3×D311yescharacteristic
192C23×C3—42no—
193C23×C3—41no—
194C23×C3—41no—
195C23×C3—121no—
196C22×D3—41no—
197C3×Q8—42no—
198C3×Q8—42no—
199C3×Q8—41no—
200C3×Q8—41no—
201C3×Q8—41no—
202C3×Q8—41no—
203C3×D4—42no—
204C3×D4—42no—
205C3×D4—41no—
206C3×D4—41no—
207C3×D4—41no—
208C3×D4—41no—
209C3×D4—62no—
210C3×D4—121no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—42no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—121no—
218C2×C3×C4—242no—
219C2×C3×C4#21311yescharacteristic
220C2×C3×C4#21311yescharacteristic
221C2×C3×C4C3×D811yescharacteristic
222C2×C3×C4C3×D811yescharacteristic
223C2×C3×C4C2×#6711yescharacteristic
224C2×C3×C4C2×C3×D411yescharacteristic
225C2×Dic3—41no—
226D12—22no—
227D12—41no—
228C4×D3—82no—
229C3×C8—22no—
230C3×C8—21no—
231C3×C8—21no—
232C3×C8—21no—
233C3×C8—21no—
234C3×C8D3×D411yescharacteristic
235C3×C8#23711yescharacteristic
236C3×C8C2×C3×D411yescharacteristic
237C3×C8C3×#4111yescharacteristic
238C2×C32—161no—
239C2×C32#45911yescharacteristic
240C2×C32#50811yescharacteristic
241C2×C32#50911yescharacteristic
242C3×D3—82no—
243C2×Q8—21no—
244C2×D4—21no—
245C2×D4—61no—
246C22×C4—121no—
247Q16—21no—
248Q16—21no—
249SD16—42no—
250D8—21no—
251D8—21no—
252D8—32no—
253D8—61no—
254C2×C8C3×#6711yescharacteristic
255C2×C8C22×C3×D311yescharacteristic
256C4⋊C4—61no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—121no—
260C42C3×#6711yescharacteristic
261C16—61no—
262C16—61no—
263C22×C3—21no—
264C22×C3—82no—
265C22×C3—82no—
266C22×C3—82no—
267C22×C3—81no—
268C22×C3—81no—
269C22×C3—81no—
270C22×C3—81no—
271C22×C3—81no—
272C22×C3—81no—
273C22×C3—122no—
274C22×C3—241no—
275C22×C3—241no—
276C22×C3C2×#21311yescharacteristic
277C22×C3C2×C3×D811yescharacteristic
278C2×D3—42no—
279C2×D3—81no—
280C2×D3—81no—
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—82no—
290C3×C4—81no—
291C3×C4—81no—
292C3×C4—241no—
293C3×C4#93211yescharacteristic
294C3×C4#93811yescharacteristic
295C3×C4C3×#12111yescharacteristic
296C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
297Dic3—81no—
298C32#221011yescharacteristic, complemented, Sylow
299C23—41no—
300C23—121no—
301Q8—41no—
302Q8—41no—
303D4—41no—
304D4—41no—
305D4—62no—
306D4—121no—
307C2×C4—41no—
308C2×C4—121no—
309C2×C4—242no—
310C2×C4C3×#21311yescharacteristic
311C2×C4C3×#21311yescharacteristic
312C2×C4C2×C3×#6711yescharacteristic
313C8—21no—
314C8C3×D3×D411yescharacteristic
315C8C3×#23711yescharacteristic
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—162no—
320C2×C3—161no—
321C2×C3—161no—
322C2×C3—242no—
323C2×C3#507211yescharacteristic
324C2×C3#519311yescharacteristic
325C2×C3#519411yescharacteristic
326C2×C3C3×#45911yescharacteristic
327C2×C3C3×#50811yescharacteristic
328C2×C3C3×#50911yescharacteristic
329D3—82no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—122no—
334C22—241no—
335C22—241no—
336C22C2×C3×#21311yescharacteristic
337C4—21no—
338C4—21no—
339C4—81no—
340C4—241no—
341C4C3×#93211yescharacteristic
342C4C3×#93811yescharacteristic
343C3—21no—
344C3#7132311yescharacteristic, direct product factor
345C3C3×#221011yescharacteristic, complemented
346C2—161no—
347C2—242no—
348C2C3×#507211yescharacteristic
349C2C3×#519311yescharacteristic
350C2C3×#519411yescharacteristic
subgroupG/H
centerC22×C3C2×#213
commutator, cosocleC2×C3×C8C23×C3
FrattiniC2×C8C22×C3×D3
FittingC32×#495C2
socleC22×C32C2×D8
prime radicalC2×C3×#826C2
hypercenterC3×#495D3
hypocenterC3C3×#2210
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×C8 ◁ C3×#495

Complements

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

NH ≅ G/Ntype
1. C32×#495C2semidirect
2. C2×C3×#828C2semidirect
4. C3×C4×D24C2semidirect
5. C3×#4564C2semidirect
6. C3×#4562C2semidirect
7. C3×C4⋊(C3⋊C16)C2semidirect
9. #71323C3direct (N × H)
26. C3×#495D3semidirect
27. C3×#495C2×C3semidirect
29. C2×#828C2×C3semidirect
31. C4×D24C2×C3semidirect
35. #4564C2×C3semidirect
36. #4562C2×C3semidirect
37. C4⋊(C3⋊C16)C2×C3semidirect
109. #495C3×D3semidirect
298. C32#2210semidirect
344. C3#71323direct (N × H)
345. C3C3×#2210semidirect

Maximal subgroups

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

subgroupindex
C32×#4952
C2×C3×#8282
C2×C3×#8262
C3×C4×D242
C3×#45642
C3×#45622
C3×C4⋊(C3⋊C16)2
C3×#22103
#713233