Finite Group Databasebeta

← C3×#71134 #11781245

Subgroups — C3×#71134 #11781245

Order 1152.

406 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#476C211yesmaximal, characteristic, complemented
2C3×#5088C211yesmaximal, characteristic, complemented
3C3×#5015C211yesmaximal, characteristic
4C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
5C3×#4546C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1677—31nomaximal
9#71134C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×D4C2211yescharacteristic
12C2×C3×#213—21no—
13C22×C3×C3⋊C8—21no—
14C3×#874C2211yescharacteristic
15C32×#106—21no—
16C32×C4⋊C8C2211yescharacteristic
17C32×#102—21no—
18C3×#830—21no—
19C3×#809—21no—
20C3×#809—21no—
21C3×#809—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#486—31no—
26C3×#476—21no—
27C3×#476D311yescharacteristic, complemented
28C3×#476C2×C311yescharacteristic, complemented
29C3×#459—31no—
30C3×C8×D4—31no—
31#5088C2×C311yescharacteristic, complemented
32#5015C2×C311yescharacteristic
33D4×C3⋊C8C2×C311yescharacteristic, complemented
34C3×#334—31no—
35C3×#333—31no—
36C3×#331—31no—
37#4546C2×C311yescharacteristic, complemented
38#4485C2×C311yescharacteristic, complemented
39#4480C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×D4D411yescharacteristic
42C22×C32×C4—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C32×C8—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C22⋊C4—21no—
51C32×C42C2311yescharacteristic
52C3×#213—42no—
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—61no—
60C22×C3×C8—61no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4⋊Q8C22×C311yescharacteristic
64C3×#127—31no—
65C3×C4×D4—21no—
66C3×C4×D4C2×D311yescharacteristic
67C3×C4×D4C22×C311yescharacteristic
68C2×#213—21no—
69C22×C3⋊C8—21no—
70#874C22×C311yescharacteristic
71C3×#106—22no—
72C3×#106—21no—
73C3×#106—21no—
74C3×C4⋊C8—21no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×C4⋊C8C2×D311yescharacteristic
78C3×C4⋊C8C22×C311yescharacteristic
79C3×#102—22no—
80C3×#102—21no—
81C3×#102—21no—
82C3×#102—61no—
83C3×#102—61no—
84C3×#102—61no—
85C3×C22⋊C8—61no—
86C3×C4×C8—31no—
87#830—21no—
88#809—21no—
89#809—21no—
90#809—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4×C3⋊C8C22×C311yescharacteristic
94C23×C32—21no—
95C22×C3×D3—41no—
96C32×Q8—81no—
97C32×D4—21no—
98C32×D4SD1612yes—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—81no—
111C32×C8—41no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—21no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#486—31no—
117#476C3×D311yescharacteristic, complemented
118#459—31no—
119C8×D4—31no—
120#334—31no—
121#333—31no—
122#331—31no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×Q8—41no—
126C2×C3×D4—21no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4#6711yescharacteristic
131C2×C3×D4C3×D411yescharacteristic
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—41no—
135C2×D12—21no—
136C2×D12—21no—
137C2×D12—21no—
138C3×D8—122no—
139C2×C3×C8—22no—
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—31no—
143C2×C3×C8—31no—
144C2×C3×C8—61no—
145C2×C3×C8—61no—
146C2×C3×C8—122no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—41no—
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
162#213—42no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—42no—
166C2×C3⋊C8C3×D411yescharacteristic
167C2×C3⋊C8C3×D411yescharacteristic
168C22×C32—22no—
169C22×C32—41no—
170C22×C32—41no—
171C22×C32#12111yescharacteristic
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C2×C3×D3—81no—
175C32×C4—21no—
176C32×C4—41no—
177C32×C4—81no—
178C32×C4C2×SD1611yescharacteristic
179C32×C4#13511yescharacteristic
180C32×C4#13511yescharacteristic
181C32×C4AGL(1,ℤ/8)11yescharacteristic
182C2×D8—61no—
183C22×C8—61no—
184C4⋊Q8C2×C3×D311yescharacteristic
185#127—31no—
186C4×D4C2×C3×D311yescharacteristic
187#106—21no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8C2×C3×D311yescharacteristic
191#102—21no—
192#102—61no—
193#102—61no—
194#102—61no—
195C22⋊C8—61no—
196C4×C8—31no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3—41no—
200C23×C3—121no—
201C22×D3—41no—
202C3×Q8—81no—
203C3×Q8—81no—
204C3×Q8—82no—
205C3×D4—21no—
206C3×D4—21no—
207C3×D4—22no—
208C3×D4—41no—
209C3×D4—121no—
210C3×D4—121no—
211C3×D4—121no—
212C3×D4—121no—
213C3×D4—241no—
214C3×D4#21512yes—
215C3×D4C3×SD1612yes—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—42no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—81no—
230C2×C3×C4—81no—
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4#23711yescharacteristic
233C2×C3×C4C2×#6711yescharacteristic
234C2×C3×C4C2×C3×D411yescharacteristic
235C2×C3×C4C2×C3×D411yescharacteristic
236C2×C3×C4C3×#4111yescharacteristic
237D12—41no—
238D12—41no—
239D12—41no—
240D12—41no—
241D12—81no—
242C3×C8—42no—
243C3×C8—41no—
244C3×C8—41no—
245C3×C8—61no—
246C3×C8—61no—
247C3×C8—121no—
248C3×C8—121no—
249C3⋊C8—21no—
250C3⋊C8—21no—
251C3⋊C8—41no—
252C3⋊C8—41no—
253C2×C32—42no—
254C2×C32#46311yescharacteristic
255C2×C32#46511yescharacteristic
256C2×C32#47211yescharacteristic
257C3×D3—161no—
258C2×Q8—21no—
259C2×D4—61no—
260C2×D4—61no—
261C2×D4—61no—
262C2×D4C3×#6711yescharacteristic
263C22×C4—21no—
264D8—122no—
265C2×C8—21no—
266C2×C8—31no—
267C2×C8—31no—
268C2×C8—61no—
269C2×C8—61no—
270C2×C8—122no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4C3×#6711yescharacteristic
274C22⋊C4—21no—
275C42C22×C3×D311yescharacteristic
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—21no—
279C22×C3—42no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—81no—
285C22×C3—81no—
286C22×C3—241no—
287C22×C3—241no—
288C22×C3—241no—
289C22×C3#93911yescharacteristic
290C22×C3C3×#12111yescharacteristic
291C2×D3—81no—
292C2×D3—81no—
293C2×D3—81no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—41no—
301C3×C4—41no—
302C3×C4—41no—
303C3×C4—81no—
304C3×C4—82no—
305C3×C4—81no—
306C3×C4—81no—
307C3×C4#91411yescharacteristic
308C3×C4#91611yescharacteristic
309C3×C4C2×#21511yescharacteristic
310C3×C4#95011yescharacteristic
311C3×C4C2×C3×SD1611yescharacteristic
312C3×C4C3×#13511yescharacteristic
313C3×C4C3×#13511yescharacteristic
314C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
315C32#167711yescharacteristic, complemented, Sylow
316C23—21no—
317C23—121no—
318Q8—81no—
319D4—21no—
320D4—121no—
321D4—121no—
322D4—121no—
323D4—121no—
324D4—241no—
325D4C3×#21512yes—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4C3×D3×D411yescharacteristic
331C2×C4C3×#23711yescharacteristic
332C2×C4C2×C3×#6711yescharacteristic
333C8—41no—
334C8—61no—
335C8—61no—
336C8—121no—
337C8—121no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—42no—
342C2×C3—42no—
343C2×C3—82no—
344C2×C3—481no—
345C2×C3#504811yescharacteristic
346C2×C3#516511yescharacteristic
347C2×C3#519911yescharacteristic
348C2×C3C3×#46311yescharacteristic
349C2×C3C3×#46511yescharacteristic
350C2×C3C3×#47211yescharacteristic
351D3—161no—
352C22—22no—
353C22—41no—
354C22—41no—
355C22—241no—
356C22—241no—
357C22—241no—
358C22C3×#93911yescharacteristic
359C4—21no—
360C4—41no—
361C4—81no—
362C4C3×#91411yescharacteristic
363C4C3×#91611yescharacteristic
364C4C2×C3×#21511yescharacteristic
365C4C3×#95011yescharacteristic
366C3—21no—
367C3#7113411yescharacteristic, direct product factor
368C3C3×#167711yescharacteristic, complemented
369C2—42no—
370C2—481no—
371C2C3×#504811yescharacteristic
372C2C3×#516511yescharacteristic
373C2C3×#519911yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#476C2
socleC22×C32#121
prime radicalC3×#5015C2
hypercenterC3×#476D3
hypocenterC3C3×#1677
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
1. C32×#476C2semidirect
2. C3×#5088C2semidirect
4. C3×D4×C3⋊C8C2semidirect
5. C3×#4546C2semidirect
6. C3×#4485C2semidirect
7. C3×#4480C2semidirect
9. #71134C3direct (N × H)
27. C3×#476D3semidirect
28. C3×#476C2×C3semidirect
31. #5088C2×C3semidirect
33. D4×C3⋊C8C2×C3semidirect
37. #4546C2×C3semidirect
38. #4485C2×C3semidirect
39. #4480C2×C3semidirect
117. #476C3×D3semidirect
315. C32#1677semidirect
367. C3#71134direct (N × H)
368. C3C3×#1677semidirect

Maximal subgroups

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

subgroupindex
C32×#4762
C3×#50882
C3×#50152
C3×D4×C3⋊C82
C3×#45462
C3×#44852
C3×#44802
C3×#16773
#711343