Finite Group Databasebeta

← C3×#68160 #11777751

Subgroups — C3×#68160 #11777751

Order 1152.

401 conjugacy classes of subgroups.

The subgroup lattice has 373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#213C211yesmaximal, characteristic
2C3×#5012C211yesmaximal, characteristic, complemented
3C3×#4838C211yesmaximal, characteristic, complemented
4C32×D4⋊C8C211yesmaximal, characteristic, complemented
5C3×#4479C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7C3×C8×C3⋊C8C211yesmaximal, characteristic, complemented
8C3×#1589—31nomaximal
9#68160C311yesmaximal, characteristic, direct product factor
10C32×C4×D4C2211yescharacteristic
11C2×C3×#213C411yescharacteristic
12C2×C3×#208—21no—
13C2×C3×ΓL(1,𝔽25)—21no—
14C3×C4×D12C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4×C8C2211yescharacteristic
17C3×#832C411yescharacteristic
18C3×#830—21no—
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—31no—
27C3×#436—31no—
28C4×#213C2×C311yescharacteristic
29#5012C2×C311yescharacteristic, complemented
30#4838C2×C311yescharacteristic, complemented
31C3×#335—31no—
32C3×D4⋊C8—21no—
33C3×D4⋊C8—31no—
34C3×D4⋊C8D311yescharacteristic, complemented
35C3×D4⋊C8C2×C311yescharacteristic, complemented
36C3×C82—31no—
37#4479C2×C311yescharacteristic, complemented
38#4459C2×C311yescharacteristic, complemented
39C8×C3⋊C8C2×C311yescharacteristic, complemented
40C2×C32×D4C2×C411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×D12C2×C411yescharacteristic
43C2×C3×C4×D3—21no—
44C2×C32×C8—21no—
45C2×C32×C8—21no—
46C32×C4⋊C4C2×C411yescharacteristic
47C32×C22⋊C4—21no—
48C32×C42C2311yescharacteristic
49C3×#213—22no—
50C3×(C2×D3)⋊C4—21no—
51C3×C4⋊Dic3C2×C411yescharacteristic
52C3×#208—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8C2×C411yescharacteristic
55C2×C3×C3⋊C8C2×C411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58C3×ΓL(1,𝔽25)—42no—
59#1589—31noSylow
60C2×C3×D8—31no—
61C2×C3×M16—61no—
62C2×C3×M16—61no—
63C3×C4×D4—21no—
64C3×C4×D4—31no—
65C3×C4×D4C2×D311yescharacteristic
66C3×C4×D4C22×C311yescharacteristic
67C2×#213C3×C411yescharacteristic
68C2×#208—21no—
69C2×ΓL(1,𝔽25)—21no—
70C4×D12C22×C311yescharacteristic
71C3×#107—31no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C22×C311yescharacteristic
76C3×#102—31no—
77C3×#102—31no—
78C3×C22⋊C8—61no—
79C3×C22⋊C8—61no—
80C3×C4×C8—21no—
81C3×C4×C8—31no—
82C3×C4×C8—31no—
83C3×C4×C8C2×D311yescharacteristic
84C3×C4×C8C22×C311yescharacteristic
85#832C3×C411yescharacteristic
86#830—21no—
87(C2×D3)⋊C8—21no—
88#809C3×C411yescharacteristic
89#807C3×C411yescharacteristic
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4×C3⋊C8C22×C311yescharacteristic
92C4×C3⋊C8C22×C311yescharacteristic
93C23×C32—21no—
94C22×C3×D3—21no—
95C32×D4—21no—
96C32×D4—21no—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3×Dic3—21no—
104C3×D12—21no—
105C3×D12—21no—
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C32×C8—22no—
109C32×C8—41no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8M1612yescomplemented
114C3×C3⋊C8D812yescomplemented
115C4×D8—31no—
116#436—31no—
117#436—31no—
118#335—31no—
119D4⋊C8—31no—
120D4⋊C8C3×D311yescharacteristic, complemented
121C82—31no—
122C2×C3×D4—21no—
123C2×C3×D4—31no—
124C2×C3×D4C4×D311yescharacteristic
125C2×C3×D4C2×C3×C411yescharacteristic
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—41no—
129C22×C3×C4—61no—
130C2×D12C2×C3×C411yescharacteristic
131C2×C4×D3—21no—
132C3×D8—62no—
133C3×M16—122no—
134C3×M16—122no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—31no—
140C2×C3×C8—31no—
141C2×C3×C8—31no—
142C2×C3×C8—31no—
143C2×C3×C8—41no—
144C2×C3×C8—41no—
145C2×C3×C8—61no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4C4×D311yescharacteristic
149C3×C4⋊C4C2×C3×C411yescharacteristic
150C3×C22⋊C4—21no—
151C3×C22⋊C4—21no—
152C3×C22⋊C4—41no—
153C3×C22⋊C4—61no—
154C3×C42—21no—
155C3×C42C22×D311yescharacteristic
156C3×C42C23×C311yescharacteristic
157#213—22no—
158(C2×D3)⋊C4—21no—
159C4⋊Dic3C2×C3×C411yescharacteristic
160#208—42no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8C2×C3×C411yescharacteristic
163C2×C3⋊C8C2×C3×C411yescharacteristic
164C2×C3⋊C8C3×D411yescharacteristic
165C2×C3⋊C8C3×D411yescharacteristic
166ΓL(1,𝔽25)—42no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32C4×D411yescharacteristic
171C2×C3×D3—41no—
172C2×C3×D3—41no—
173C2×C3×D3—41no—
174C32×C4—21no—
175C32×C4—41no—
176C32×C4C2×M1611yescharacteristic
177C32×C4#13111yescharacteristic
178C32×C4C2×D811yescharacteristic
179C32×C4#13511yescharacteristic
180C3×Dic3—41no—
181C2×D8—31no—
182C2×M16—61no—
183C2×M16—61no—
184C4×D4—31no—
185C4×D4C2×C3×D311yescharacteristic
186#107—31no—
187C4⋊C8—31no—
188C4⋊C8C2×C3×D311yescharacteristic
189#102—31no—
190#102—31no—
191C22⋊C8—61no—
192C22⋊C8—61no—
193C4×C8—31no—
194C4×C8—31no—
195C4×C8C2×C3×D311yescharacteristic
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—41no—
199C23×C3—61no—
200C22×D3—21no—
201C3×D4—22no—
202C3×D4—21no—
203C3×D4—21no—
204C3×D4—21no—
205C3×D4—21no—
206C3×D4—41no—
207C3×D4—61no—
208C3×D4—61no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—61no—
220C2×C3×C4—81no—
221C2×C3×C4—81no—
222C2×C3×C4—121no—
223C2×C3×C4—121no—
224C2×C3×C4C2×C4×D311yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4#23711yescharacteristic
227C2×C3×C4C22×C3×C411yescharacteristic
228C2×C3×C4C2×C3×D411yescharacteristic
229C2×C3×C4C3×#4111yescharacteristic
230C2×Dic3—21no—
231D12—21no—
232D12—21no—
233C4×D3—41no—
234C4×D3—41no—
235C3×C8—22no—
236C3×C8—22no—
237C3×C8—32no—
238C3×C8—32no—
239C3×C8—42no—
240C3×C8—41no—
241C3×C8—41no—
242C3×C8—61no—
243C3×C8—61no—
244C3×C8—81no—
245C3×C8—121no—
246C3⋊C8—21no—
247C3⋊C8—21no—
248C3⋊C8—41no—
249C3⋊C8C3×M1612yescomplemented
250C3⋊C8C3×D812yescomplemented
251C2×C32—81no—
252C2×C32#43611yescharacteristic
253C2×C32C4×D811yescharacteristic
254C2×C32#44311yescharacteristic
255C3×D3—81no—
256C2×D4—31no—
257C2×D4C3×C4×D311yescharacteristic
258C22×C4—21no—
259C22×C4—61no—
260D8—62no—
261M16—122no—
262M16—122no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—31no—
266C2×C8—31no—
267C2×C8—31no—
268C2×C8—31no—
269C2×C8—61no—
270C4⋊C4—31no—
271C4⋊C4C3×C4×D311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—61no—
274C42C22×C3×D311yescharacteristic
275C22×C3—21no—
276C22×C3—42no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—81no—
284C22×C3—81no—
285C22×C3—121no—
286C22×C3—121no—
287C22×C3—121no—
288C22×C3#67⋊C411yescharacteristic
289C22×C3C3×C4×D411yescharacteristic
290C2×D3—41no—
291C2×D3—41no—
292C2×D3—41no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—41no—
302C3×C4—81no—
303C3×C4—121no—
304C3×C4#90111yescharacteristic
305C3×C4D3×M1611yescharacteristic
306C3×C4D3×D811yescharacteristic
307C3×C4#91611yescharacteristic
308C3×C4C2×C3×M1611yescharacteristic
309C3×C4C3×#13111yescharacteristic
310C3×C4C2×C3×D811yescharacteristic
311C3×C4C3×#13511yescharacteristic
312Dic3—41no—
313C32#158911yescharacteristic, complemented, Sylow
314C23—21no—
315C23—61no—
316D4—21no—
317D4—21no—
318D4—61no—
319D4—61no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—61no—
324C2×C4—121no—
325C2×C4—121no—
326C2×C4C2×C3×C4×D311yescharacteristic
327C2×C4C3×D3×D411yescharacteristic
328C2×C4C3×#23711yescharacteristic
329C8—22no—
330C8—32no—
331C8—32no—
332C8—41no—
333C8—61no—
334C8—61no—
335C8—121no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—82no—
340C2×C3—81no—
341C2×C3—81no—
342C2×C3—241no—
343C2×C3#472911yescharacteristic
344C2×C3#475611yescharacteristic
345C2×C3#482411yescharacteristic
346C2×C3C3×#43611yescharacteristic
347C2×C3C3×C4×D811yescharacteristic
348C2×C3C3×#44311yescharacteristic
349D3—81no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—121no—
354C22—121no—
355C22—121no—
356C22C3×#67⋊C411yescharacteristic
357C4—21no—
358C4—41no—
359C4—121no—
360C4C3×#90111yescharacteristic
361C4C3×D3×M1611yescharacteristic
362C4C3×D3×D811yescharacteristic
363C4C3×#91611yescharacteristic
364C3—21no—
365C3#6816011yescharacteristic, direct product factor
366C3C3×#158911yescharacteristic, complemented
367C2—81no—
368C2—241no—
369C2C3×#472911yescharacteristic
370C2C3×#475611yescharacteristic
371C2C3×#482411yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×D4⋊C8C2
socleC22×C32C4×D4
prime radicalC2×C3×#213C4
cosocleC3×C42C23×C3
hypercenterC3×D4⋊C8D3
hypocenterC3C3×#1589
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#5012C2semidirect
3. C3×#4838C2semidirect
4. C32×D4⋊C8C2semidirect
5. C3×#4479C2semidirect
6. C3×#4459C2semidirect
7. C3×C8×C3⋊C8C2semidirect
9. #68160C3direct (N × H)
29. #5012C2×C3semidirect
30. #4838C2×C3semidirect
34. C3×D4⋊C8D3semidirect
35. C3×D4⋊C8C2×C3semidirect
37. #4479C2×C3semidirect
38. #4459C2×C3semidirect
39. C8×C3⋊C8C2×C3semidirect
113. C3×C3⋊C8M16semidirect
114. C3×C3⋊C8D8semidirect
120. D4⋊C8C3×D3semidirect
249. C3⋊C8C3×M16semidirect
250. C3⋊C8C3×D8semidirect
313. C32#1589semidirect
365. C3#68160direct (N × H)
366. C3C3×#1589semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2132
C3×#50122
C3×#48382
C32×D4⋊C82
C3×#44792
C3×#44592
C3×C8×C3⋊C82
C3×#15893
#681603