Finite Group Databasebeta

← C3×#68470 #11781482

Subgroups — C3×#68470 #11781482

Order 1152.

364 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5090C211yesmaximal, characteristic, complemented
2C3×#5088C211yesmaximal, characteristic
3C3×#4848C211yesmaximal, characteristic
4C3×#4830C211yesmaximal, characteristic, complemented
5C32×#332C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1682—31nomaximal
9#68470C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×#216—21no—
12C2×C3×#204—21no—
13C3×#874C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C3×#835—21no—
18C3×#821—21no—
19C3×Dic3⋊C8—21no—
20C3×C8×Dic3—21no—
21C3×#809—21no—
22C3×#809—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#486—31no—
26C3×#462—31no—
27C3×#460—31no—
28C3×C8×Q8—31no—
29#5090C2×C311yescharacteristic, complemented
30#5088C2×C311yescharacteristic
31#4848C2×C311yescharacteristic
32#4830C2×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×#216—42no—
51C3×C4⋊Dic3D411yescharacteristic
52C3×Dic3⋊C4—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57C3×#204—42no—
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—31no—
65C3×C4×Q8—31no—
66C2×#216—21no—
67C2×#204—21no—
68#874C22×C311yescharacteristic
69C4×Dic6C22×C311yescharacteristic
70C3×C4⋊C8—21no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—61no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×#103—61no—
79C3×#102—61no—
80C3×#102—61no—
81C3×#102—61no—
82C3×C4×C8—31no—
83C3×C4×C8—61no—
84#835—21no—
85#821—21no—
86Dic3⋊C8—21no—
87C8×Dic3—21no—
88#809—21no—
89#809—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4×C3⋊C8C22×C311yescharacteristic
92C22×C3×D3—41no—
93C32×Q8—41no—
94C32×Q8—41no—
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3×Dic3—21no—
100C2×C3×Dic3—21no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—81no—
106C3×Dic6—21no—
107C3×Dic6D812yes—
108C32×C8—41no—
109C32×C8—41no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113#486—31no—
114#462—31no—
115#460—31no—
116C8×Q8—31no—
117#335—31no—
118#332C3×D311yescharacteristic, complemented
119#331—31no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—31no—
123C2×C3×Q8—41no—
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×D12—21no—
128C2×D12—21no—
129C2×D12—21no—
130C2×Dic6C3×D411yescharacteristic
131C3×Q16—122no—
132C3×SD16—122no—
133C2×C3×C8—21no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—31no—
138C2×C3×C8—31no—
139C2×C3×C8—41no—
140C2×C3×C8—41no—
141C2×C3×C8—61no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—41no—
149C3×C4⋊C4—61no—
150C3×C42—21no—
151C3×C42—61no—
152C3×C42C22×D311yescharacteristic
153C3×C42C23×C311yescharacteristic
154#216—42no—
155C4⋊Dic3C3×D411yescharacteristic
156Dic3⋊C4—21no—
157C4×Dic3—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8C3×D411yescharacteristic
160C2×C3⋊C8C3×D411yescharacteristic
161#204—42no—
162C22×C32#12111yescharacteristic
163C2×C3×D3—81no—
164C2×C3×D3—81no—
165C2×C3×D3—81no—
166C32×C4—21no—
167C32×C4—81no—
168C32×C4C2×D811yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4#13711yescharacteristic
172C3×Dic3—22no—
173C3×Dic3—41no—
174C2×Q16—61no—
175C2×SD16—61no—
176C4⋊Q8C2×C3×D311yescharacteristic
177#127—31no—
178C4×Q8—31no—
179C4⋊C8—31no—
180C4⋊C8—61no—
181C4⋊C8C2×C3×D311yescharacteristic
182C4⋊C8C2×C3×D311yescharacteristic
183#103—61no—
184#102—61no—
185#102—61no—
186#102—61no—
187C4×C8—31no—
188C4×C8—61no—
189C23×C3—121no—
190C22×D3—41no—
191C3×Q8—32no—
192C3×Q8—41no—
193C3×Q8—41no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—61no—
197C3×Q8—81no—
198C3×Q8—81no—
199C3×D4—121no—
200C3×D4—121no—
201C3×D4—121no—
202C3×D4—121no—
203C3×D4—241no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—42no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—61no—
211C2×C3×C4—61no—
212C2×C3×C4#23511yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4C2×C3×D411yescharacteristic
216C2×C3×C4C2×C3×D411yescharacteristic
217C2×C3×C4C3×#4111yescharacteristic
218C2×Dic3—21no—
219C2×Dic3—21no—
220D12—41no—
221D12—41no—
222D12—41no—
223D12—41no—
224D12—81no—
225Dic6—21no—
226Dic6C3×D812yes—
227C3×C8—41no—
228C3×C8—41no—
229C3×C8—41no—
230C3×C8—41no—
231C3×C8—61no—
232C3×C8—61no—
233C3×C8—81no—
234C3×C8—81no—
235C3×C8—121no—
236C3⋊C8—21no—
237C3⋊C8—21no—
238C3⋊C8—41no—
239C2×C32#46411yescharacteristic
240C2×C32#46611yescharacteristic
241C2×C32#47111yescharacteristic
242C3×D3—161no—
243C2×Q8—21no—
244C2×Q8—31no—
245C2×D4—61no—
246C2×D4—61no—
247C2×D4—61no—
248Q16—122no—
249SD16—122no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—31no—
253C2×C8—31no—
254C2×C8—61no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—31no—
258C4⋊C4—61no—
259C42—61no—
260C42C22×C3×D311yescharacteristic
261C22×C3—21no—
262C22×C3—241no—
263C22×C3—241no—
264C22×C3—241no—
265C22×C3#88411yescharacteristic
266C22×C3C3×#12111yescharacteristic
267C2×D3—81no—
268C2×D3—81no—
269C2×D3—81no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—41no—
277C3×C4—62no—
278C3×C4—82no—
279C3×C4—81no—
280C3×C4—81no—
281C3×C4—121no—
282C3×C4D3×D811yescharacteristic
283C3×C4#91611yescharacteristic
284C3×C4#91611yescharacteristic
285C3×C4#91811yescharacteristic
286C3×C4C2×C3×D811yescharacteristic
287C3×C4C3×#13511yescharacteristic
288C3×C4C3×#13511yescharacteristic
289C3×C4C3×#13711yescharacteristic
290Dic3—22no—
291Dic3—41no—
292C32#168211yescharacteristic, complemented, Sylow
293C23—121no—
294Q8—32no—
295Q8—41no—
296Q8—41no—
297Q8—61no—
298D4—121no—
299D4—121no—
300D4—121no—
301D4—121no—
302D4—241no—
303C2×C4—41no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4C3×#23511yescharacteristic
307C2×C4C3×D3×D411yescharacteristic
308C2×C4C3×D3×D411yescharacteristic
309C8—41no—
310C8—41no—
311C8—61no—
312C8—61no—
313C8—121no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—481no—
318C2×C3#475411yescharacteristic
319C2×C3#477511yescharacteristic
320C2×C3#479811yescharacteristic
321C2×C3C3×#46411yescharacteristic
322C2×C3C3×#46611yescharacteristic
323C2×C3C3×#47111yescharacteristic
324D3—161no—
325C22—241no—
326C22—241no—
327C22—241no—
328C22C3×#88411yescharacteristic
329C4—21no—
330C4—62no—
331C4—81no—
332C4—121no—
333C4C3×D3×D811yescharacteristic
334C4C3×#91611yescharacteristic
335C4C3×#91611yescharacteristic
336C4C3×#91811yescharacteristic
337C3—21no—
338C3#6847011yescharacteristic, direct product factor
339C3C3×#168211yescharacteristic, complemented
340C2—481no—
341C2C3×#475411yescharacteristic
342C2C3×#477511yescharacteristic
343C2C3×#479811yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC3×#332D3
hypocenterC3C3×#1682
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×#5090C2semidirect
4. C3×#4830C2semidirect
5. C32×#332C2semidirect
7. C3×#4479C2semidirect
9. #68470C3direct (N × H)
29. #5090C2×C3semidirect
32. #4830C2×C3semidirect
35. C3×#332D3semidirect
36. C3×#332C2×C3semidirect
39. #4479C2×C3semidirect
118. #332C3×D3semidirect
292. C32#1682semidirect
338. C3#68470direct (N × H)
339. C3C3×#1682semidirect

Maximal subgroups

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

subgroupindex
C3×#50902
C3×#50882
C3×#48482
C3×#48302
C32×#3322
C3×#44852
C3×#44792
C3×#16823
#684703