Finite Group Databasebeta

← C3×#68590 #11781476

Subgroups — C3×#68590 #11781476

Order 1152.

359 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4849C211yesmaximal, characteristic, complemented
2C3×#4848C211yesmaximal, characteristic
3C3×#4694C211yesmaximal, characteristic
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5C32×#335C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1682—31nomaximal
9#68590C311yesmaximal, characteristic, direct product factor
10C2×C3×Dic12—21no—
11C2×C3×#204—21no—
12C3×#874C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×C4×C8C2211yescharacteristic
18C3×#821—21no—
19C3×#821—21no—
20C3×#821—21no—
21C3×#816—21no—
22C3×Dic3⋊C8—21no—
23C3×C8×Dic3—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#486—31no—
26C3×#462—31no—
27C3×#460—31no—
28C3×C8×Q8—31no—
29#4849C2×C311yescharacteristic, complemented
30#4848C2×C311yescharacteristic
31#4694C2×C311yescharacteristic
32C8×Dic6C2×C311yescharacteristic, complemented
33C3×#335—21no—
34C3×#335D311yescharacteristic, complemented
35C3×#335C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×#331—31no—
38#4485C2×C311yescharacteristic
39#4482C2×C311yescharacteristic, complemented
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C2×C32×C8D411yescharacteristic
48C2×C32×C8D411yescharacteristic
49C32×C42C2311yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C3×Dic12—42no—
57C3×#204—42no—
58#1682—31noSylow
59C2×C3×Q16—61no—
60C2×C3×SD16—61no—
61C3×C4⋊Q8—31no—
62C3×#127—31no—
63C3×C4×Q8—31no—
64C2×Dic12—21no—
65C2×#204—21no—
66#874C22×C311yescharacteristic
67#869C22×C311yescharacteristic
68C4×Dic6C22×C311yescharacteristic
69C3×C4⋊C8—21no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—61no—
73C3×C4⋊C8C2×D311yescharacteristic
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C22×C311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×#103—61no—
78C3×#102—61no—
79C3×#102—61no—
80C3×#102—61no—
81C3×C4×C8—21no—
82C3×C4×C8—61no—
83C3×C4×C8C2×D311yescharacteristic
84C3×C4×C8C22×C311yescharacteristic
85#821—21no—
86#821—21no—
87#821—21no—
88#816—21no—
89Dic3⋊C8—21no—
90C8×Dic3—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C22×C3×D3—41no—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3×Dic3—21no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—41no—
99C3×D12—41no—
100C3×D12—41no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—81no—
104C3×Dic6—21no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3×Dic6D812yes—
108C32×C8—21no—
109C32×C8—21no—
110C32×C8—41no—
111C32×C8—41no—
112C3×C3⋊C8—41no—
113#486—31no—
114#462—31no—
115#460—31no—
116C8×Q8—31no—
117#335C3×D311yescharacteristic, complemented
118#332—31no—
119#331—31no—
120C2×C3×Q8—31no—
121C2×C3×Q8—61no—
122C2×C3×D4—61no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C2×D12—21no—
126C2×D12—21no—
127C2×D12—21no—
128C2×Dic6—21no—
129C2×Dic6C3×D411yescharacteristic
130C3×Q16—122no—
131C3×SD16—122no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—41no—
139C2×C3×C8—41no—
140C2×C3×C8—61no—
141C2×C3×C8D1211yescharacteristic
142C2×C3×C8D1211yescharacteristic
143C2×C3×C8C3×D411yescharacteristic
144C2×C3×C8C3×D411yescharacteristic
145C3×C4⋊C4—31no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C42—21no—
150C3×C42—61no—
151C3×C42C22×D311yescharacteristic
152C3×C42C23×C311yescharacteristic
153C4⋊Dic3—21no—
154C4⋊Dic3—21no—
155C4⋊Dic3C3×D411yescharacteristic
156Dic3⋊C4—21no—
157C4×Dic3—21no—
158C2×C3⋊C8—21no—
159Dic12—42no—
160#204—42no—
161C22×C32#12111yescharacteristic
162C2×C3×D3—81no—
163C2×C3×D3—81no—
164C2×C3×D3—81no—
165C32×C4—21no—
166C32×C4C2×D811yescharacteristic
167C32×C4#13511yescharacteristic
168C32×C4#13511yescharacteristic
169C32×C4#13711yescharacteristic
170C3×Dic3—22no—
171C3×Dic3—41no—
172C3×Dic3—81no—
173C2×Q16—61no—
174C2×SD16—61no—
175C4⋊Q8—31no—
176#127—31no—
177C4×Q8—31no—
178C4⋊C8—31no—
179C4⋊C8—61no—
180C4⋊C8C2×C3×D311yescharacteristic
181C4⋊C8C2×C3×D311yescharacteristic
182#103—61no—
183#102—61no—
184#102—61no—
185#102—61no—
186C4×C8—61no—
187C4×C8C2×C3×D311yescharacteristic
188C23×C3—121no—
189C22×D3—41no—
190C3×Q8—32no—
191C3×Q8—61no—
192C3×Q8—121no—
193C3×Q8—121no—
194C3×D4—121no—
195C3×D4—121no—
196C3×D4—121no—
197C3×D4—121no—
198C3×D4—241no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—61no—
203C2×C3×C4—61no—
204C2×C3×C4—121no—
205C2×C3×C4C2×D1211yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4#23911yescharacteristic
208C2×C3×C4C2×C3×D411yescharacteristic
209C2×C3×C4C2×C3×D411yescharacteristic
210C2×C3×C4C3×#4111yescharacteristic
211C2×Dic3—21no—
212C2×Dic3—21no—
213C2×Dic3—41no—
214D12—41no—
215D12—41no—
216D12—41no—
217D12—41no—
218D12—81no—
219Dic6—21no—
220Dic6—41no—
221Dic6—41no—
222Dic6C3×D812yes—
223C3×C8—22no—
224C3×C8—21no—
225C3×C8—21no—
226C3×C8—21no—
227C3×C8—21no—
228C3×C8—41no—
229C3×C8—41no—
230C3×C8—41no—
231C3×C8—41no—
232C3×C8—41no—
233C3×C8—81no—
234C3×C8—81no—
235C3×C8—121no—
236C3⋊C8—41no—
237C2×C32#46411yescharacteristic
238C2×C32#46611yescharacteristic
239C2×C32#47111yescharacteristic
240C3×D3—161no—
241C2×Q8—31no—
242C2×Q8—61no—
243C2×D4—61no—
244C2×D4—61no—
245C2×D4—61no—
246Q16—122no—
247SD16—122no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—61no—
251C2×C8C3×D1211yescharacteristic
252C2×C8C3×D1211yescharacteristic
253C4⋊C4—31no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C42—61no—
258C42C22×C3×D311yescharacteristic
259C22×C3—21no—
260C22×C3—241no—
261C22×C3—241no—
262C22×C3—241no—
263C22×C3#89511yescharacteristic
264C22×C3C3×#12111yescharacteristic
265C2×D3—81no—
266C2×D3—81no—
267C2×D3—81no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—41no—
275C3×C4—62no—
276C3×C4—121no—
277C3×C4—241no—
278C3×C4#90411yescharacteristic
279C3×C4#90911yescharacteristic
280C3×C4D3×D811yescharacteristic
281C3×C4#91911yescharacteristic
282C3×C4C2×C3×D811yescharacteristic
283C3×C4C3×#13511yescharacteristic
284C3×C4C3×#13511yescharacteristic
285C3×C4C3×#13711yescharacteristic
286Dic3—22no—
287Dic3—41no—
288Dic3—81no—
289C32#168211yescharacteristic, complemented, Sylow
290C23—121no—
291Q8—32no—
292Q8—61no—
293Q8—121no—
294Q8—121no—
295D4—121no—
296D4—121no—
297D4—121no—
298D4—121no—
299D4—241no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—121no—
303C2×C4C2×C3×D1211yescharacteristic
304C2×C4C3×D3×D411yescharacteristic
305C2×C4C3×#23911yescharacteristic
306C8—21no—
307C8—21no—
308C8—41no—
309C8—41no—
310C8—121no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—481no—
315C2×C3#484511yescharacteristic
316C2×C3#488311yescharacteristic
317C2×C3#489811yescharacteristic
318C2×C3C3×#46411yescharacteristic
319C2×C3C3×#46611yescharacteristic
320C2×C3C3×#47111yescharacteristic
321D3—161no—
322C22—241no—
323C22—241no—
324C22—241no—
325C22C3×#89511yescharacteristic
326C4—21no—
327C4—62no—
328C4—121no—
329C4—241no—
330C4C3×#90411yescharacteristic
331C4C3×#90911yescharacteristic
332C4C3×D3×D811yescharacteristic
333C4C3×#91911yescharacteristic
334C3—21no—
335C3#6859011yescharacteristic, direct product factor
336C3C3×#168211yescharacteristic, complemented
337C2—481no—
338C2C3×#484511yescharacteristic
339C2C3×#488311yescharacteristic
340C2C3×#489811yescharacteristic
subgroupG/H
centerC22×C3#895
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#335C2
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC3×#335D3
hypocenterC3C3×#1682
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#335

Complements

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

NH ≅ G/Ntype
1. C3×#4849C2semidirect
4. C3×C8×Dic6C2semidirect
5. C32×#335C2semidirect
7. C3×#4482C2semidirect
9. #68590C3direct (N × H)
29. #4849C2×C3semidirect
32. C8×Dic6C2×C3semidirect
34. C3×#335D3semidirect
35. C3×#335C2×C3semidirect
39. #4482C2×C3semidirect
117. #335C3×D3semidirect
289. C32#1682semidirect
335. C3#68590direct (N × H)
336. C3C3×#1682semidirect

Maximal subgroups

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

subgroupindex
C3×#48492
C3×#48482
C3×#46942
C3×C8×Dic62
C32×#3352
C3×#44852
C3×#44822
C3×#16823
#685903