Finite Group Databasebeta

← C3×#71006 #11781233

Subgroups — C3×#71006 #11781233

Order 1152.

422 conjugacy classes of subgroups.

The subgroup lattice has 383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#459C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1677—31nomaximal
9#71006C311yesmaximal, characteristic, direct product factor
10C2×C32×D8—21no—
11C32×#127C2211yescharacteristic
12C32×C4×D4C2211yescharacteristic
13C22×C3×C3⋊C8—21no—
14C3×#869C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×#102—21no—
17C3×#832—21no—
18C3×#832—21no—
19C3×#832—21no—
20C3×#830—21no—
21C3×#808—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#486—31no—
26C3×#476—31no—
27C3×#459—21no—
28C3×#459D311yescharacteristic
29C3×#459C2×C311yescharacteristic
30C3×C8×D4—31no—
31#5070C2×C311yescharacteristic, complemented
32D4×C3⋊C8C2×C311yescharacteristic, complemented
33#5008C2×C311yescharacteristic, complemented
34C3×#334—31no—
35C3×#333—31no—
36C3×#331—31no—
37#4544C2×C311yescharacteristic, complemented
38#4481C2×C311yescharacteristic, complemented
39#4480C2×C311yescharacteristic, complemented
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C2×C3×Dic6—21no—
46C32×D8—42no—
47C2×C32×C8—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—42no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1677—31noSylow
59C2×C3×D8—22no—
60C2×C3×D8—21no—
61C2×C3×D8—21no—
62C22×C3×C8—61no—
63C3×C4⋊Q8—31no—
64C3×#127—21no—
65C3×#127C2×D311yescharacteristic
66C3×#127C22×C311yescharacteristic
67C3×C4×D4—21no—
68C3×C4×D4C2×D311yescharacteristic
69C3×C4×D4C22×C311yescharacteristic
70C22×C3⋊C8—21no—
71#869C22×C311yescharacteristic
72C3×#106—61no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×#102—22no—
79C3×#102—21no—
80C3×#102—21no—
81C3×#102—61no—
82C3×#102—61no—
83C3×#102—61no—
84C3×C22⋊C8—61no—
85C3×C4×C8—31no—
86#832—21no—
87#832—21no—
88#832—21no—
89#830—21no—
90#808—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4×C3⋊C8C22×C311yescharacteristic
94C23×C32—21no—
95C23×C32—41no—
96C32×D4—21no—
97C32×D4—41no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—41no—
101C32×D4—81no—
102C32×D4SD1612yes—
103C2×C32×C4—21no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C3×Dic3—41no—
110C3×Dic6—81no—
111C32×C8—41no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—21no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#486—31no—
117#476—31no—
118#459C3×D311yescharacteristic
119C8×D4—31no—
120#334—31no—
121#333—31no—
122#331—31no—
123C2×C3×Q8—61no—
124C2×C3×D4—22no—
125C2×C3×D4—21no—
126C2×C3×D4—21no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—41no—
133C2×C3×D4—41no—
134C2×C3×D4#6711yescharacteristic
135C2×C3×D4C3×D411yescharacteristic
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—41no—
139C2×Dic6—21no—
140C3×D8—44no—
141C3×D8—42no—
142C3×D8—42no—
143C2×C3×C8—22no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—31no—
147C2×C3×C8—31no—
148C2×C3×C8—61no—
149C2×C3×C8—61no—
150C2×C3×C8—122no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4#6711yescharacteristic
155C3×C4⋊C4C3×D411yescharacteristic
156C3×C22⋊C4—21no—
157C3×C22⋊C4—21no—
158C3×C22⋊C4—41no—
159C3×C42—21no—
160C3×C42C22×D311yescharacteristic
161C3×C42C23×C311yescharacteristic
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—21no—
166C2×C3⋊C8—42no—
167C2×C3⋊C8C3×D411yescharacteristic
168C2×C3⋊C8C3×D411yescharacteristic
169C22×C32—22no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32—81no—
173C22×C32—81no—
174C22×C32—81no—
175C22×C32#12111yescharacteristic
176C32×C4—21no—
177C32×C4—41no—
178C32×C4C2×SD1611yescharacteristic
179C32×C4#13511yescharacteristic
180C32×C4#13511yescharacteristic
181C32×C4AGL(1,ℤ/8)11yescharacteristic
182C3×Dic3—81no—
183C2×D8—21no—
184C22×C8—61no—
185C4⋊Q8—31no—
186#127C2×C3×D311yescharacteristic
187C4×D4C2×C3×D311yescharacteristic
188#106—61no—
189C4⋊C8—31no—
190C4⋊C8—31no—
191C4⋊C8C2×C3×D311yescharacteristic
192#102—21no—
193#102—61no—
194#102—61no—
195#102—61no—
196C22⋊C8—61no—
197C4×C8—31no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—41no—
201C23×C3—42no—
202C23×C3—41no—
203C23×C3—41no—
204C3×Q8—241no—
205C3×D4—21no—
206C3×D4—21no—
207C3×D4—22no—
208C3×D4—41no—
209C3×D4—42no—
210C3×D4—42no—
211C3×D4—41no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—41no—
216C3×D4—41no—
217C3×D4—41no—
218C3×D4—41no—
219C3×D4—81no—
220C3×D4—81no—
221C3×D4—81no—
222C3×D4—81no—
223C3×D4—82no—
224C3×D4#21412yes—
225C3×D4C3×SD1612yes—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—81no—
237C2×C3×C4—81no—
238C2×C3×C4—121no—
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4#23711yescharacteristic
241C2×C3×C4C2×#6711yescharacteristic
242C2×C3×C4C2×C3×D411yescharacteristic
243C2×C3×C4C2×C3×D411yescharacteristic
244C2×C3×C4C3×#4111yescharacteristic
245C2×Dic3—41no—
246Dic6—81no—
247C3×C8—42no—
248C3×C8—41no—
249C3×C8—41no—
250C3×C8—61no—
251C3×C8—61no—
252C3×C8—121no—
253C3×C8—121no—
254C3⋊C8—21no—
255C3⋊C8—21no—
256C3⋊C8—41no—
257C3⋊C8—41no—
258C2×C32—42no—
259C2×C32—161no—
260C2×C32#46311yescharacteristic
261C2×C32#46511yescharacteristic
262C2×C32#47211yescharacteristic
263C2×Q8—61no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4C3×#6711yescharacteristic
268C22×C4—21no—
269D8—42no—
270C2×C8—21no—
271C2×C8—31no—
272C2×C8—31no—
273C2×C8—61no—
274C2×C8—61no—
275C2×C8—122no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4C3×#6711yescharacteristic
279C22⋊C4—21no—
280C42C22×C3×D311yescharacteristic
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—21no—
284C22×C3—42no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—81no—
290C22×C3—81no—
291C22×C3—82no—
292C22×C3—82no—
293C22×C3—82no—
294C22×C3—81no—
295C22×C3—81no—
296C22×C3—81no—
297C22×C3—81no—
298C22×C3—81no—
299C22×C3—81no—
300C22×C3#93911yescharacteristic
301C22×C3C3×#12111yescharacteristic
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—81no—
312C3×C4—241no—
313C3×C4#91111yescharacteristic
314C3×C4#91211yescharacteristic
315C3×C4C2×#21411yescharacteristic
316C3×C4#95011yescharacteristic
317C3×C4C2×C3×SD1611yescharacteristic
318C3×C4C3×#13511yescharacteristic
319C3×C4C3×#13511yescharacteristic
320C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
321Dic3—81no—
322C32#167711yescharacteristic, complemented, Sylow
323C23—21no—
324C23—41no—
325Q8—241no—
326D4—21no—
327D4—41no—
328D4—41no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4C3×#21412yes—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—121no—
337C2×C4C3×D3×D411yescharacteristic
338C2×C4C3×#23711yescharacteristic
339C2×C4C2×C3×#6711yescharacteristic
340C8—41no—
341C8—61no—
342C8—61no—
343C8—121no—
344C8—121no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—42no—
349C2×C3—42no—
350C2×C3—82no—
351C2×C3—162no—
352C2×C3—161no—
353C2×C3—161no—
354C2×C3#504111yescharacteristic
355C2×C3#515311yescharacteristic
356C2×C3#519911yescharacteristic
357C2×C3C3×#46311yescharacteristic
358C2×C3C3×#46511yescharacteristic
359C2×C3C3×#47211yescharacteristic
360C22—22no—
361C22—41no—
362C22—41no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22C3×#93911yescharacteristic
367C4—21no—
368C4—41no—
369C4—241no—
370C4C3×#91111yescharacteristic
371C4C3×#91211yescharacteristic
372C4C2×C3×#21411yescharacteristic
373C4C3×#95011yescharacteristic
374C3—21no—
375C3#7100611yescharacteristic, direct product factor
376C3C3×#167711yescharacteristic, complemented
377C2—42no—
378C2—161no—
379C2C3×#504111yescharacteristic
380C2C3×#515311yescharacteristic
381C2C3×#519911yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
Fitting, prime radicalC32×#459C2
socleC22×C32#121
hypercenterC3×#459D3
hypocenterC3C3×#1677
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
2. C3×#5070C2semidirect
3. C3×D4×C3⋊C8C2semidirect
4. C3×#5008C2semidirect
5. C3×#4544C2semidirect
6. C3×#4481C2semidirect
7. C3×#4480C2semidirect
9. #71006C3direct (N × H)
31. #5070C2×C3semidirect
32. D4×C3⋊C8C2×C3semidirect
33. #5008C2×C3semidirect
37. #4544C2×C3semidirect
38. #4481C2×C3semidirect
39. #4480C2×C3semidirect
322. C32#1677semidirect
375. C3#71006direct (N × H)
376. C3C3×#1677semidirect

Maximal subgroups

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

subgroupindex
C32×#4592
C3×#50702
C3×D4×C3⋊C82
C3×#50082
C3×#45442
C3×#44812
C3×#44802
C3×#16773
#710063