Finite Group Databasebeta

← C3×#68472 #11781666

Subgroups — C3×#68472 #11781666

Order 1152.

368 conjugacy classes of subgroups.

The subgroup lattice has 349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5094C211yesmaximal, characteristic, complemented
2C3×#5085C211yesmaximal, characteristic
3C3×#4848C211yesmaximal, characteristic
4C3×#4831C211yesmaximal, characteristic, complemented
5C32×#332C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1686—31nomaximal
9#68472C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×#215—21no—
12C2×C3×#215—21no—
13C2×C3×#204—21no—
14C3×#874C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C3×#821—21no—
19C3×#815—21no—
20C3×Dic3⋊C8—21no—
21C3×#810—21no—
22C3×#808—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#492—31no—
26C3×#475—31no—
27C3×#460—31no—
28C3×#446—31no—
29#5094C2×C311yescharacteristic, complemented
30#5085C2×C311yescharacteristic
31#4848C2×C311yescharacteristic
32#4831C2×C311yescharacteristic, complemented
33C3×#335—31no—
34C3×#332—21no—
35C3×#332D311yescharacteristic, complemented
36C3×#332C2×C311yescharacteristic, complemented
37C3×#331—31no—
38#4485C2×C311yescharacteristic
39#4479C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C42C2311yescharacteristic
50C3×#215—42no—
51C3×#215—42no—
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58C3×#204—42no—
59#1686—31noSylow
60C2×C3×SD16—61no—
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C3×C4⋊Q8—21no—
64C3×C4⋊Q8C2×D311yescharacteristic
65C3×C4⋊Q8C22×C311yescharacteristic
66C3×#127—31no—
67C3×C4×Q8—31no—
68C2×#215—21no—
69C2×#215—21no—
70C2×#204—21no—
71#874C22×C311yescharacteristic
72C4×Dic6C22×C311yescharacteristic
73C3×#106—61no—
74C3×C4⋊C8—21no—
75C3×C4⋊C8—21no—
76C3×C4⋊C8—31no—
77C3×C4⋊C8—61no—
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4⋊C8C2×D311yescharacteristic
80C3×C4⋊C8C22×C311yescharacteristic
81C3×C4⋊C8C22×C311yescharacteristic
82C3×#103—61no—
83C3×#102—61no—
84C3×#97—61no—
85C3×C4×C8—31no—
86#821—21no—
87#815—21no—
88Dic3⋊C8—21no—
89#810—21no—
90#808—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4×C3⋊C8C22×C311yescharacteristic
93C22×C3×D3—41no—
94C32×Q8—41no—
95C32×Q8—41no—
96C2×C32×C4—41no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3×Dic3—21no—
101C2×C3×Dic3—21no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—81no—
107C3×Dic6—21no—
108C3×Dic6—21no—
109C32×C8—41no—
110C32×C8—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8SD1612yescomplemented
114#492—31no—
115#475—31no—
116#460—31no—
117#446—31no—
118#335—31no—
119#332C3×D311yescharacteristic, complemented
120#331—31no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—31no—
124C2×C3×Q8—41no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×D12—21no—
129C2×D12—21no—
130C2×D12—21no—
131C2×Dic6C3×D411yescharacteristic
132C3×SD16—122no—
133C3×SD16—122no—
134C3×SD16—122no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—31no—
140C2×C3×C8—31no—
141C2×C3×C8—41no—
142C2×C3×C8—41no—
143C2×C3×C8—61no—
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#215—42no—
157#215—42no—
158C4⋊Dic3C3×D411yescharacteristic
159Dic3⋊C4—21no—
160C4×Dic3—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8C3×D411yescharacteristic
163C2×C3⋊C8C3×D411yescharacteristic
164#204—42no—
165C22×C32#12111yescharacteristic
166C2×C3×D3—81no—
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C32×C4—21no—
170C32×C4—81no—
171C32×C4C2×SD1611yescharacteristic
172C32×C4AGL(1,ℤ/8)11yescharacteristic
173C32×C4AGL(1,ℤ/8)11yescharacteristic
174C32×C4#13711yescharacteristic
175C3×Dic3—41no—
176C3×Dic3—41no—
177C2×SD16—61no—
178C2×SD16—61no—
179C2×SD16—61no—
180C4⋊Q8C2×C3×D311yescharacteristic
181#127—31no—
182C4×Q8—31no—
183#106—61no—
184C4⋊C8—31no—
185C4⋊C8—61no—
186C4⋊C8C2×C3×D311yescharacteristic
187C4⋊C8C2×C3×D311yescharacteristic
188#103—61no—
189#102—61no—
190#97—61no—
191C4×C8—31no—
192C23×C3—121no—
193C22×D3—41no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—41no—
197C3×Q8—41no—
198C3×Q8—61no—
199C3×Q8—61no—
200C3×Q8—81no—
201C3×Q8—81no—
202C3×D4—121no—
203C3×D4—121no—
204C3×D4—121no—
205C3×D4—121no—
206C3×D4—241no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—42no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—61no—
214C2×C3×C4—61no—
215C2×C3×C4#23511yescharacteristic
216C2×C3×C4D3×D411yescharacteristic
217C2×C3×C4D3×D411yescharacteristic
218C2×C3×C4C2×C3×D411yescharacteristic
219C2×C3×C4C2×C3×D411yescharacteristic
220C2×C3×C4C3×#4111yescharacteristic
221C2×Dic3—21no—
222C2×Dic3—21no—
223D12—41no—
224D12—41no—
225D12—41no—
226D12—41no—
227D12—81no—
228Dic6—21no—
229Dic6—21no—
230C3×C8—32no—
231C3×C8—41no—
232C3×C8—41no—
233C3×C8—41no—
234C3×C8—41no—
235C3×C8—61no—
236C3×C8—81no—
237C3×C8—81no—
238C3×C8—121no—
239C3⋊C8—21no—
240C3⋊C8—41no—
241C3⋊C8C3×SD1612yescomplemented
242C2×C32#46011yescharacteristic
243C2×C32#46811yescharacteristic
244C2×C32#47111yescharacteristic
245C3×D3—161no—
246C2×Q8—21no—
247C2×Q8—31no—
248C2×D4—61no—
249C2×D4—61no—
250C2×D4—61no—
251SD16—122no—
252SD16—122no—
253SD16—122no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—31no—
257C2×C8—31no—
258C2×C8—61no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—31no—
262C4⋊C4—61no—
263C42—61no—
264C42C22×C3×D311yescharacteristic
265C22×C3—21no—
266C22×C3—241no—
267C22×C3—241no—
268C22×C3—241no—
269C22×C3#88411yescharacteristic
270C22×C3C3×#12111yescharacteristic
271C2×D3—81no—
272C2×D3—81no—
273C2×D3—81no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—41no—
281C3×C4—82no—
282C3×C4—81no—
283C3×C4—81no—
284C3×C4—121no—
285C3×C4—121no—
286C3×C4#91111yescharacteristic
287C3×C4D3×SD1611yescharacteristic
288C3×C4#91411yescharacteristic
289C3×C4#91811yescharacteristic
290C3×C4C2×C3×SD1611yescharacteristic
291C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
292C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
293C3×C4C3×#13711yescharacteristic
294Dic3—41no—
295Dic3—41no—
296C32#168611yescharacteristic, complemented, Sylow
297C23—121no—
298Q8—41no—
299Q8—41no—
300Q8—61no—
301Q8—61no—
302D4—121no—
303D4—121no—
304D4—121no—
305D4—121no—
306D4—241no—
307C2×C4—41no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4C3×#23511yescharacteristic
311C2×C4C3×D3×D411yescharacteristic
312C2×C4C3×D3×D411yescharacteristic
313C8—32no—
314C8—41no—
315C8—41no—
316C8—61no—
317C8—121no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—481no—
322C2×C3#475411yescharacteristic
323C2×C3#476211yescharacteristic
324C2×C3#481211yescharacteristic
325C2×C3C3×#46011yescharacteristic
326C2×C3C3×#46811yescharacteristic
327C2×C3C3×#47111yescharacteristic
328D3—161no—
329C22—241no—
330C22—241no—
331C22—241no—
332C22C3×#88411yescharacteristic
333C4—21no—
334C4—81no—
335C4—121no—
336C4—121no—
337C4C3×#91111yescharacteristic
338C4C3×D3×SD1611yescharacteristic
339C4C3×#91411yescharacteristic
340C4C3×#91811yescharacteristic
341C3—21no—
342C3#6847211yescharacteristic, direct product factor
343C3C3×#168611yescharacteristic, complemented
344C2—481no—
345C2C3×#475411yescharacteristic
346C2C3×#476211yescharacteristic
347C2C3×#481211yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC3×#332D3
hypocenterC3C3×#1686
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
1. C3×#5094C2semidirect
4. C3×#4831C2semidirect
5. C32×#332C2semidirect
7. C3×#4479C2semidirect
9. #68472C3direct (N × H)
29. #5094C2×C3semidirect
32. #4831C2×C3semidirect
35. C3×#332D3semidirect
36. C3×#332C2×C3semidirect
39. #4479C2×C3semidirect
113. C3×C3⋊C8SD16semidirect
119. #332C3×D3semidirect
241. C3⋊C8C3×SD16semidirect
296. C32#1686semidirect
342. C3#68472direct (N × H)
343. C3C3×#1686semidirect

Maximal subgroups

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

subgroupindex
C3×#50942
C3×#50852
C3×#48482
C3×#48312
C32×#3322
C3×#44852
C3×#44792
C3×#16863
#684723