Finite Group Databasebeta

← C3×#70861 #11777949

Subgroups — C3×#70861 #11777949

Order 1152.

413 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#436C211yesmaximal, characteristic, complemented
2C3×C4×#213C211yesmaximal, characteristic
3C3×#4688C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7C3×#4454C211yesmaximal, characteristic, complemented
8C3×#1594—31nomaximal
9#70861C311yesmaximal, characteristic, direct product factor
10C2×C32×M16—21no—
11C32×C4×D4C2211yescharacteristic
12C2×C3×#213C411yescharacteristic
13C2×C3×ΓL(1,𝔽25)—21no—
14C3×C4×D12C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C22⋊C8—21no—
17C32×C4×C8C2211yescharacteristic
18C3×#832C411yescharacteristic
19C3×(C2×D3)⋊C8—21no—
20C3×#809C411yescharacteristic
21C3×#807C411yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×C4×D8—31no—
26C3×#436—21no—
27C3×#436—31no—
28C3×#436D311yescharacteristic, complemented
29C3×#436C2×C311yescharacteristic, complemented
30C4×#213C2×C311yescharacteristic
31#4688C2×C311yescharacteristic, complemented
32C3×#334—31no—
33C3×D4⋊C8—31no—
34C3×D4⋊C8—31no—
35C3×#322—31no—
36D4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
37#4483C2×C311yescharacteristic, complemented
38#4480C2×C311yescharacteristic, complemented
39#4454C2×C311yescharacteristic, complemented
40C2×C32×D4C2×C411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×D12C2×C411yescharacteristic
43C2×C3×C4×D3—21no—
44C32×M16—42no—
45C2×C32×C8—21no—
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51C3×#213—22no—
52C3×(C2×D3)⋊C4—21no—
53C3×C4⋊Dic3C2×C411yescharacteristic
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8C2×C411yescharacteristic
57C2×C3×C3⋊C8C2×C411yescharacteristic
58C3×ΓL(1,𝔽25)—42no—
59#1594—31noSylow
60C2×C3×D8—31no—
61C2×C3×M16—22no—
62C2×C3×M16—21no—
63C2×C3×M16—21no—
64C2×C3×M16—61no—
65C3×C4×D4—21no—
66C3×C4×D4—31no—
67C3×C4×D4C2×D311yescharacteristic
68C3×C4×D4C22×C311yescharacteristic
69C2×#213C3×C411yescharacteristic
70C2×ΓL(1,𝔽25)—21no—
71C4×D12C22×C311yescharacteristic
72C3×#107—31no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×#102—31no—
78C3×#102—31no—
79C3×C22⋊C8—22no—
80C3×C22⋊C8—21no—
81C3×C22⋊C8—21no—
82C3×C22⋊C8—61no—
83C3×C4×C8—21no—
84C3×C4×C8—31no—
85C3×C4×C8—31no—
86C3×C4×C8C2×D311yescharacteristic
87C3×C4×C8C22×C311yescharacteristic
88#832C3×C411yescharacteristic
89(C2×D3)⋊C8—21no—
90#809C3×C411yescharacteristic
91#807C3×C411yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4×C3⋊C8C22×C311yescharacteristic
94C4×C3⋊C8C22×C311yescharacteristic
95C23×C32—21no—
96C22×C3×D3—21no—
97C32×D4—21no—
98C32×D4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3×Dic3—21no—
106C3×D12—21no—
107C3×D12—21no—
108C3×C4×D3—41no—
109C3×C4×D3—41no—
110C32×C8—21no—
111C32×C8—21no—
112C32×C8—41no—
113C3×C3⋊C8—21no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116C3×C3⋊C8M1612yescomplemented
117C4×D8—31no—
118#436—31no—
119#436C3×D311yescharacteristic, complemented
120#334—31no—
121D4⋊C8—31no—
122D4⋊C8—31no—
123#322—31no—
124C2×C3×D4—21no—
125C2×C3×D4—31no—
126C2×C3×D4C4×D311yescharacteristic
127C2×C3×D4C2×C3×C411yescharacteristic
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—61no—
132C2×D12C2×C3×C411yescharacteristic
133C2×C4×D3—21no—
134C3×D8—62no—
135C3×M16—44no—
136C3×M16—42no—
137C3×M16—42no—
138C3×M16—122no—
139C2×C3×C8—22no—
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—31no—
145C2×C3×C8—31no—
146C2×C3×C8—61no—
147C2×C3×C8—61no—
148C2×C3×C8#6711yescharacteristic
149C2×C3×C8#6711yescharacteristic
150C2×C3×C8C3×D411yescharacteristic
151C2×C3×C8C3×D411yescharacteristic
152C3×C4⋊C4—21no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4C4×D311yescharacteristic
155C3×C4⋊C4C2×C3×C411yescharacteristic
156C3×C22⋊C4—22no—
157C3×C22⋊C4—21no—
158C3×C22⋊C4—21no—
159C3×C22⋊C4—61no—
160C3×C42—21no—
161C3×C42C22×D311yescharacteristic
162C3×C42C23×C311yescharacteristic
163#213—22no—
164(C2×D3)⋊C4—21no—
165C4⋊Dic3C2×C3×C411yescharacteristic
166C2×C3⋊C8—21no—
167C2×C3⋊C8—21no—
168C2×C3⋊C8C2×C3×C411yescharacteristic
169C2×C3⋊C8C2×C3×C411yescharacteristic
170ΓL(1,𝔽25)—42no—
171C22×C32—41no—
172C22×C32—41no—
173C22×C32—41no—
174C22×C32C4×D411yescharacteristic
175C2×C3×D3—41no—
176C2×C3×D3—41no—
177C2×C3×D3—41no—
178C32×C4—21no—
179C32×C4—41no—
180C32×C4C2×M1611yescharacteristic
181C32×C4#13111yescharacteristic
182C32×C4AGL(1,ℤ/8)11yescharacteristic
183C32×C4AGL(1,ℤ/8)11yescharacteristic
184C3×Dic3—41no—
185C2×D8—31no—
186C2×M16—21no—
187C2×M16—61no—
188C4×D4—31no—
189C4×D4C2×C3×D311yescharacteristic
190#107—31no—
191C4⋊C8—31no—
192C4⋊C8C2×C3×D311yescharacteristic
193#102—31no—
194#102—31no—
195C22⋊C8—21no—
196C22⋊C8—61no—
197C4×C8—31no—
198C4×C8—31no—
199C4×C8C2×C3×D311yescharacteristic
200C23×C3—22no—
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—61no—
204C22×D3—21no—
205C3×D4—21no—
206C3×D4—21no—
207C3×D4—21no—
208C3×D4—21no—
209C3×D4—41no—
210C3×D4—41no—
211C3×D4—61no—
212C3×D4—61no—
213C2×C3×C4—22no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—42no—
220C2×C3×C4—42no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—61no—
226C2×C3×C4—121no—
227C2×C3×C4—121no—
228C2×C3×C4C2×C4×D311yescharacteristic
229C2×C3×C4#23511yescharacteristic
230C2×C3×C4C2×#6711yescharacteristic
231C2×C3×C4C22×C3×C411yescharacteristic
232C2×C3×C4C2×C3×D411yescharacteristic
233C2×C3×C4C3×#4111yescharacteristic
234C2×Dic3—21no—
235D12—21no—
236D12—21no—
237C4×D3—41no—
238C4×D3—41no—
239C3×C8—22no—
240C3×C8—21no—
241C3×C8—21no—
242C3×C8—21no—
243C3×C8—21no—
244C3×C8—32no—
245C3×C8—41no—
246C3×C8—42no—
247C3×C8—41no—
248C3×C8—41no—
249C3×C8—61no—
250C3×C8—121no—
251C3×C8—121no—
252C3⋊C8—21no—
253C3⋊C8—41no—
254C3⋊C8—41no—
255C3⋊C8C3×M1612yescomplemented
256C2×C32—81no—
257C2×C32#43611yescharacteristic
258C2×C32#44211yescharacteristic
259C2×C32#44411yescharacteristic
260C3×D3—81no—
261C2×D4—31no—
262C2×D4C3×C4×D311yescharacteristic
263C22×C4—21no—
264C22×C4—61no—
265D8—62no—
266M16—42no—
267M16—122no—
268C2×C8—21no—
269C2×C8—31no—
270C2×C8—31no—
271C2×C8—61no—
272C2×C8—61no—
273C2×C8C3×#6711yescharacteristic
274C2×C8C3×#6711yescharacteristic
275C4⋊C4—31no—
276C4⋊C4C3×C4×D311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—61no—
279C42C22×C3×D311yescharacteristic
280C22×C3—21no—
281C22×C3—42no—
282C22×C3—42no—
283C22×C3—42no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—41no—
290C22×C3—121no—
291C22×C3—121no—
292C22×C3—121no—
293C22×C3C4×#6711yescharacteristic
294C22×C3C3×C4×D411yescharacteristic
295C2×D3—41no—
296C2×D3—41no—
297C2×D3—41no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4—42no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—121no—
309C3×C4D3×M1611yescharacteristic
310C3×C4#90711yescharacteristic
311C3×C4#93211yescharacteristic
312C3×C4#94911yescharacteristic
313C3×C4C2×C3×M1611yescharacteristic
314C3×C4C3×#13111yescharacteristic
315C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
316C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
317Dic3—41no—
318C32#159411yescharacteristic, complemented, Sylow
319C23—21no—
320C23—61no—
321D4—21no—
322D4—21no—
323D4—61no—
324D4—61no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—61no—
329C2×C4—121no—
330C2×C4—121no—
331C2×C4C2×C3×C4×D311yescharacteristic
332C2×C4C3×#23511yescharacteristic
333C2×C4C2×C3×#6711yescharacteristic
334C8—21no—
335C8—21no—
336C8—32no—
337C8—41no—
338C8—61no—
339C8—121no—
340C8—121no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—82no—
345C2×C3—81no—
346C2×C3—81no—
347C2×C3—241no—
348C2×C3#501411yescharacteristic
349C2×C3#512811yescharacteristic
350C2×C3#514511yescharacteristic
351C2×C3C3×#43611yescharacteristic
352C2×C3C3×#44211yescharacteristic
353C2×C3C3×#44411yescharacteristic
354D3—81no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—121no—
359C22—121no—
360C22—121no—
361C22C3×C4×#6711yescharacteristic
362C4—21no—
363C4—41no—
364C4—121no—
365C4C3×D3×M1611yescharacteristic
366C4C3×#90711yescharacteristic
367C4C3×#93211yescharacteristic
368C4C3×#94911yescharacteristic
369C3—21no—
370C3#7086111yescharacteristic, direct product factor
371C3C3×#159411yescharacteristic, complemented
372C2—81no—
373C2—241no—
374C2C3×#501411yescharacteristic
375C2C3×#512811yescharacteristic
376C2C3×#514511yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#436C2
socleC22×C32C4×D4
prime radicalC2×C3×#213C4
cosocleC3×C42C23×C3
hypercenterC3×#436D3
hypocenterC3C3×#1594
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×C8 ◁ C3×#436

Complements

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

NH ≅ G/Ntype
1. C32×#436C2semidirect
3. C3×#4688C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
5. C3×#4483C2semidirect
6. C3×#4480C2semidirect
7. C3×#4454C2semidirect
9. #70861C3direct (N × H)
28. C3×#436D3semidirect
29. C3×#436C2×C3semidirect
31. #4688C2×C3semidirect
36. D4⋊(C3⋊C8)C2×C3semidirect
37. #4483C2×C3semidirect
38. #4480C2×C3semidirect
39. #4454C2×C3semidirect
116. C3×C3⋊C8M16semidirect
119. #436C3×D3semidirect
255. C3⋊C8C3×M16semidirect
318. C32#1594semidirect
370. C3#70861direct (N × H)
371. C3C3×#1594semidirect

Maximal subgroups

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

subgroupindex
C32×#4362
C3×C4×#2132
C3×#46882
C3×D4⋊(C3⋊C8)2
C3×#44832
C3×#44802
C3×#44542
C3×#15943
#708613