Finite Group Databasebeta

← C3×#68412 #11781654

Subgroups — C3×#68412 #11781654

Order 1152.

378 conjugacy classes of subgroups.

The subgroup lattice has 355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5076C211yesmaximal, characteristic
2C3×#5075C211yesmaximal, characteristic
3C3×#4851C211yesmaximal, characteristic, complemented
4C3×#4831C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1686—31nomaximal
9#68412C311yesmaximal, characteristic, direct product factor
10C32×#127C2211yescharacteristic
11C2×C3×#214—21no—
12C2×C3×#214—21no—
13C2×C3×#214—21no—
14C3×#869C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C3×#832—21no—
19C3×#817—21no—
20C3×#816—21no—
21C3×#815—21no—
22C3×Dic3⋊C8—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#492—31no—
26C3×#475—31no—
27C3×#460—31no—
28C3×#446—31no—
29#5076C2×C311yescharacteristic
30#5075C2×C311yescharacteristic
31#4851C2×C311yescharacteristic, complemented
32#4831C2×C311yescharacteristic, complemented
33C3×#335—31no—
34C3×#332—31no—
35C3×#331—21no—
36C3×#331D311yescharacteristic
37C3×#331C2×C311yescharacteristic
38#4482C2×C311yescharacteristic, complemented
39#4479C2×C311yescharacteristic, complemented
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C3×#214—42no—
49C3×#214—42no—
50C3×#214—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C3×Dic3⋊C4—21no—
55C3×C4×Dic3—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59#1686—31noSylow
60C2×C3×SD16—61no—
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C3×C4⋊Q8—31no—
64C3×#127—21no—
65C3×#127C2×D311yescharacteristic
66C3×#127C22×C311yescharacteristic
67C3×C4×Q8—31no—
68C2×#214—21no—
69C2×#214—21no—
70C2×#214—21no—
71#869C22×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#832—21no—
87#817—21no—
88#816—21no—
89#815—21no—
90Dic3⋊C8—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4×C3⋊C8C22×C311yescharacteristic
93C23×C32—41no—
94C32×D4—41no—
95C32×D4—41no—
96C32×D4—41no—
97C32×D4—41no—
98C32×D4—81no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—21no—
103C2×C3×Dic3—21no—
104C2×C3×Dic3—41no—
105C3×Dic6—21no—
106C3×Dic6—21no—
107C3×Dic6—41no—
108C3×Dic6—41no—
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#332—31no—
120#331C3×D311yescharacteristic
121C2×C3×Q8—31no—
122C2×C3×Q8—61no—
123C2×C3×D4—22no—
124C2×C3×D4—21no—
125C2×C3×D4—21no—
126C2×C3×D4—21no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—41no—
131C2×C3×D4—41no—
132C2×Dic6—21no—
133C2×Dic6C3×D411yescharacteristic
134C3×SD16—122no—
135C3×SD16—122no—
136C3×SD16—122no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141C2×C3×C8—31no—
142C2×C3×C8—31no—
143C2×C3×C8—41no—
144C2×C3×C8—41no—
145C2×C3×C8—61no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C42—21no—
151C3×C42—61no—
152C3×C42C22×D311yescharacteristic
153C3×C42C23×C311yescharacteristic
154#214—42no—
155#214—42no—
156#214—42no—
157C4⋊Dic3—21no—
158C4⋊Dic3—21no—
159C4⋊Dic3C3×D411yescharacteristic
160Dic3⋊C4—21no—
161C4×Dic3—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8C3×D411yescharacteristic
164C2×C3⋊C8C3×D411yescharacteristic
165C22×C32—81no—
166C22×C32—81no—
167C22×C32—81no—
168C22×C32#12111yescharacteristic
169C32×C4—21no—
170C32×C4C2×SD1611yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C32×C4AGL(1,ℤ/8)11yescharacteristic
173C32×C4#13711yescharacteristic
174C3×Dic3—41no—
175C3×Dic3—41no—
176C3×Dic3—81no—
177C2×SD16—61no—
178C2×SD16—61no—
179C2×SD16—61no—
180C4⋊Q8—31no—
181#127C2×C3×D311yescharacteristic
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—42no—
193C23×C3—41no—
194C23×C3—41no—
195C3×Q8—61no—
196C3×Q8—61no—
197C3×Q8—121no—
198C3×Q8—121no—
199C3×D4—41no—
200C3×D4—41no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—41no—
204C3×D4—41no—
205C3×D4—41no—
206C3×D4—41no—
207C3×D4—81no—
208C3×D4—81no—
209C3×D4—81no—
210C3×D4—81no—
211C3×D4—81no—
212C3×D4—81no—
213C3×D4—82no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—61no—
218C2×C3×C4—61no—
219C2×C3×C4—121no—
220C2×C3×C4#23511yescharacteristic
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4D3×D411yescharacteristic
223C2×C3×C4C2×C3×D411yescharacteristic
224C2×C3×C4C2×C3×D411yescharacteristic
225C2×C3×C4C3×#4111yescharacteristic
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—41no—
229Dic6—21no—
230Dic6—21no—
231Dic6—41no—
232Dic6—41no—
233C3×C8—32no—
234C3×C8—41no—
235C3×C8—41no—
236C3×C8—41no—
237C3×C8—41no—
238C3×C8—61no—
239C3×C8—81no—
240C3×C8—81no—
241C3×C8—121no—
242C3⋊C8—21no—
243C3⋊C8—41no—
244C3⋊C8C3×SD1612yescomplemented
245C2×C32—161no—
246C2×C32#46011yescharacteristic
247C2×C32#46811yescharacteristic
248C2×C32#47111yescharacteristic
249C2×Q8—31no—
250C2×Q8—61no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254SD16—122no—
255SD16—122no—
256SD16—122no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—31no—
260C2×C8—31no—
261C2×C8—61no—
262C4⋊C4—31no—
263C4⋊C4—61no—
264C4⋊C4—61no—
265C4⋊C4—61no—
266C42—61no—
267C42C22×C3×D311yescharacteristic
268C22×C3—21no—
269C22×C3—82no—
270C22×C3—82no—
271C22×C3—82no—
272C22×C3—81no—
273C22×C3—81no—
274C22×C3—81no—
275C22×C3—81no—
276C22×C3—81no—
277C22×C3—81no—
278C22×C3#88411yescharacteristic
279C22×C3C3×#12111yescharacteristic
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—121no—
288C3×C4—121no—
289C3×C4—241no—
290C3×C4#91111yescharacteristic
291C3×C4#91111yescharacteristic
292C3×C4D3×SD1611yescharacteristic
293C3×C4#91511yescharacteristic
294C3×C4C2×C3×SD1611yescharacteristic
295C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
296C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
297C3×C4C3×#13711yescharacteristic
298Dic3—41no—
299Dic3—41no—
300Dic3—81no—
301C32#168611yescharacteristic, complemented, Sylow
302C23—41no—
303Q8—61no—
304Q8—61no—
305Q8—121no—
306Q8—121no—
307D4—41no—
308D4—41no—
309D4—41no—
310D4—41no—
311D4—81no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—121no—
315C2×C4C3×#23511yescharacteristic
316C2×C4C3×D3×D411yescharacteristic
317C2×C4C3×D3×D411yescharacteristic
318C8—32no—
319C8—41no—
320C8—41no—
321C8—61no—
322C8—121no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—162no—
327C2×C3—161no—
328C2×C3—161no—
329C2×C3#474811yescharacteristic
330C2×C3#476211yescharacteristic
331C2×C3#478011yescharacteristic
332C2×C3C3×#46011yescharacteristic
333C2×C3C3×#46811yescharacteristic
334C2×C3C3×#47111yescharacteristic
335C22—81no—
336C22—81no—
337C22—81no—
338C22C3×#88411yescharacteristic
339C4—21no—
340C4—121no—
341C4—121no—
342C4—241no—
343C4C3×#91111yescharacteristic
344C4C3×#91111yescharacteristic
345C4C3×D3×SD1611yescharacteristic
346C4C3×#91511yescharacteristic
347C3—21no—
348C3#6841211yescharacteristic, direct product factor
349C3C3×#168611yescharacteristic, complemented
350C2—161no—
351C2C3×#474811yescharacteristic
352C2C3×#476211yescharacteristic
353C2C3×#478011yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenterC3×#331D3
hypocenterC3C3×#1686
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
3. C3×#4851C2semidirect
4. C3×#4831C2semidirect
6. C3×#4482C2semidirect
7. C3×#4479C2semidirect
9. #68412C3direct (N × H)
31. #4851C2×C3semidirect
32. #4831C2×C3semidirect
38. #4482C2×C3semidirect
39. #4479C2×C3semidirect
113. C3×C3⋊C8SD16semidirect
244. C3⋊C8C3×SD16semidirect
301. C32#1686semidirect
348. C3#68412direct (N × H)
349. C3C3×#1686semidirect

Maximal subgroups

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

subgroupindex
C3×#50762
C3×#50752
C3×#48512
C3×#48312
C32×#3312
C3×#44822
C3×#44792
C3×#16863
#684123