Finite Group Databasebeta

← C3×#70950 #11777793

Subgroups — C3×#70950 #11777793

Order 1152.

379 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#446C211yesmaximal, characteristic, complemented
2C3×C4×#215C211yesmaximal, characteristic
3C3×#4688C211yesmaximal, characteristic
4C3×#4535C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic
6C3×#4480C211yesmaximal, characteristic, complemented
7C3×C8×C3⋊C8C211yesmaximal, characteristic, complemented
8C3×#1590—31nomaximal
9#70950C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C2×C3×#215C411yescharacteristic
12C2×C3×ΓL(1,𝔽25)—21no—
13C3×C4×D12C2211yescharacteristic
14C32×C4⋊C8—21no—
15C32×C4⋊C8C2211yescharacteristic
16C32×#97—21no—
17C32×C4×C8C2211yescharacteristic
18C3×#835C411yescharacteristic
19C3×(C2×D3)⋊C8—21no—
20C3×#809C411yescharacteristic
21C3×#808C411yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#446—21no—
26C3×#446D311yescharacteristic, complemented
27C3×#446C2×C311yescharacteristic, complemented
28C3×C4×SD16—31no—
29C3×#436—31no—
30C4×#215C2×C311yescharacteristic
31#4688C2×C311yescharacteristic
32C3×#334—31no—
33C3×Q8⋊C8—31no—
34C3×D4⋊C8—31no—
35C3×C82—31no—
36#4535C2×C311yescharacteristic, complemented
37#4483C2×C311yescharacteristic
38#4480C2×C311yescharacteristic, complemented
39C8×C3⋊C8C2×C311yescharacteristic, complemented
40C2×C32×Q8C2×C411yescharacteristic
41C2×C3×D12C2×C411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C32×C8—21no—
44C2×C32×C8D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C32×C4⋊C4—21no—
47C32×C4⋊C4C2×C411yescharacteristic
48C32×C42—21no—
49C32×C42C2311yescharacteristic
50C3×#215—22no—
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3C2×C411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8C2×C411yescharacteristic
56C2×C3×C3⋊C8C2×C411yescharacteristic
57C3×ΓL(1,𝔽25)—42no—
58#1590—31noSylow
59C2×C3×SD16—31no—
60C2×C3×M16—61no—
61C3×C4×Q8—21no—
62C3×C4×Q8C2×D311yescharacteristic
63C3×C4×Q8C22×C311yescharacteristic
64C3×C4×D4—31no—
65C2×#215C3×C411yescharacteristic
66C2×ΓL(1,𝔽25)—21no—
67C4×D12C22×C311yescharacteristic
68C3×#106—31no—
69C3×C4⋊C8—22no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C22×C311yescharacteristic
76C3×#103—31no—
77C3×#102—31no—
78C3×C22⋊C8—61no—
79C3×#97—22no—
80C3×#97—21no—
81C3×#97—21no—
82C3×C4×C8—21no—
83C3×C4×C8—31no—
84C3×C4×C8—31no—
85C3×C4×C8C2×D311yescharacteristic
86C3×C4×C8C22×C311yescharacteristic
87#835C3×C411yescharacteristic
88(C2×D3)⋊C8—21no—
89#809C3×C411yescharacteristic
90#808C3×C411yescharacteristic
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4×C3⋊C8C22×C311yescharacteristic
93C4×C3⋊C8C22×C311yescharacteristic
94C22×C3×D3—21no—
95C32×Q8—21no—
96C32×Q8—21no—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—21no—
103C3×D12—21no—
104C3×D12—21no—
105C3×C4×D3—41no—
106C3×C4×D3—41no—
107C32×C8—21no—
108C32×C8—41no—
109C32×C8SD1612yescomplemented
110C3×C3⋊C8—22no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8M1612yescomplemented
114#446C3×D311yescharacteristic, complemented
115C4×SD16—31no—
116#436—31no—
117#334—31no—
118Q8⋊C8—31no—
119D4⋊C8—31no—
120C82—31no—
121C2×C3×Q8—21no—
122C2×C3×Q8C4×D311yescharacteristic
123C2×C3×Q8C2×C3×C411yescharacteristic
124C2×C3×D4—31no—
125C22×C3×C4—61no—
126C2×D12C2×C3×C411yescharacteristic
127C2×C4×D3—21no—
128C3×SD16—62no—
129C3×M16—122no—
130C2×C3×C8—22no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—21no—
135C2×C3×C8—31no—
136C2×C3×C8—31no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C2×C3×C8#6711yescharacteristic
140C2×C3×C8#6711yescharacteristic
141C2×C3×C8C3×D411yescharacteristic
142C2×C3×C8C3×D411yescharacteristic
143C3×C4⋊C4—22no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4C4×D311yescharacteristic
149C3×C4⋊C4C2×C3×C411yescharacteristic
150C3×C22⋊C4—61no—
151C3×C42—22no—
152C3×C42—21no—
153C3×C42—21no—
154C3×C42—21no—
155C3×C42C22×D311yescharacteristic
156C3×C42C23×C311yescharacteristic
157#215—22no—
158(C2×D3)⋊C4—21no—
159C4⋊Dic3C2×C3×C411yescharacteristic
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8C2×C3×C411yescharacteristic
163C2×C3⋊C8C2×C3×C411yescharacteristic
164ΓL(1,𝔽25)—42no—
165C22×C32C4×D411yescharacteristic
166C2×C3×D3—41no—
167C2×C3×D3—41no—
168C2×C3×D3—41no—
169C32×C4—21no—
170C32×C4—41no—
171C32×C4—41no—
172C32×C4C2×M1611yescharacteristic
173C32×C4#13111yescharacteristic
174C32×C4C2×SD1611yescharacteristic
175C32×C4#13511yescharacteristic
176C3×Dic3—41no—
177C2×SD16—31no—
178C2×M16—61no—
179C4×Q8C2×C3×D311yescharacteristic
180C4×D4—31no—
181#106—31no—
182C4⋊C8—21no—
183C4⋊C8—31no—
184C4⋊C8C2×C3×D311yescharacteristic
185#103—31no—
186#102—31no—
187C22⋊C8—61no—
188#97—21no—
189C4×C8—31no—
190C4×C8—31no—
191C4×C8C2×C3×D311yescharacteristic
192C23×C3—61no—
193C22×D3—21no—
194C3×Q8—21no—
195C3×Q8—21no—
196C3×Q8—21no—
197C3×Q8—21no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×D4—61no—
201C3×D4—61no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—61no—
212C2×C3×C4—121no—
213C2×C3×C4—121no—
214C2×C3×C4C2×C4×D311yescharacteristic
215C2×C3×C4#23511yescharacteristic
216C2×C3×C4C2×#6711yescharacteristic
217C2×C3×C4C22×C3×C411yescharacteristic
218C2×C3×C4C2×C3×D411yescharacteristic
219C2×C3×C4C3×#4111yescharacteristic
220C2×Dic3—21no—
221D12—21no—
222D12—21no—
223C4×D3—41no—
224C4×D3—41no—
225C3×C8—21no—
226C3×C8—21no—
227C3×C8—22no—
228C3×C8—32no—
229C3×C8—41no—
230C3×C8—42no—
231C3×C8—41no—
232C3×C8—41no—
233C3×C8—62no—
234C3×C8—61no—
235C3×C8—121no—
236C3×C8#21512yescomplemented
237C3×C8C3×SD1612yescomplemented
238C3⋊C8—22no—
239C3⋊C8—21no—
240C3⋊C8—41no—
241C3⋊C8C3×M1612yescomplemented
242C2×C32#43611yescharacteristic
243C2×C32C4×SD1611yescharacteristic
244C2×C32#44311yescharacteristic
245C3×D3—81no—
246C2×Q8C3×C4×D311yescharacteristic
247C2×D4—31no—
248C22×C4—61no—
249SD16—62no—
250M16—122no—
251C2×C8—21no—
252C2×C8—31no—
253C2×C8—31no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8C3×#6711yescharacteristic
257C2×C8C3×#6711yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—31no—
260C4⋊C4C3×C4×D311yescharacteristic
261C22⋊C4—61no—
262C42—21no—
263C42C22×C3×D311yescharacteristic
264C22×C3—21no—
265C22×C3—121no—
266C22×C3—121no—
267C22×C3—121no—
268C22×C3C4×#6711yescharacteristic
269C22×C3C3×C4×D411yescharacteristic
270C2×D3—41no—
271C2×D3—41no—
272C2×D3—41no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—41no—
280C3×C4—42no—
281C3×C4—42no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—121no—
287C3×C4D3×M1611yescharacteristic
288C3×C4#90711yescharacteristic
289C3×C4C2×#21511yescharacteristic
290C3×C4#95011yescharacteristic
291C3×C4C2×C3×M1611yescharacteristic
292C3×C4C3×#13111yescharacteristic
293C3×C4C2×C3×SD1611yescharacteristic
294C3×C4C3×#13511yescharacteristic
295Dic3—41no—
296C32#159011yescharacteristic, complemented, Sylow
297C23—61no—
298Q8—21no—
299Q8—21no—
300D4—61no—
301D4—61no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—61no—
305C2×C4—121no—
306C2×C4—121no—
307C2×C4C2×C3×C4×D311yescharacteristic
308C2×C4C3×#23511yescharacteristic
309C2×C4C2×C3×#6711yescharacteristic
310C8—21no—
311C8—32no—
312C8—41no—
313C8—62no—
314C8—61no—
315C8—121no—
316C8C3×#21512yescomplemented
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—241no—
321C2×C3C4×#21511yescharacteristic
322C2×C3#512811yescharacteristic
323C2×C3#514411yescharacteristic
324C2×C3C3×#43611yescharacteristic
325C2×C3C3×C4×SD1611yescharacteristic
326C2×C3C3×#44311yescharacteristic
327D3—81no—
328C22—121no—
329C22—121no—
330C22—121no—
331C22C3×C4×#6711yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—121no—
336C4C3×D3×M1611yescharacteristic
337C4C3×#90711yescharacteristic
338C4C2×C3×#21511yescharacteristic
339C4C3×#95011yescharacteristic
340C3—21no—
341C3#7095011yescharacteristic, direct product factor
342C3C3×#159011yescharacteristic, complemented
343C2—241no—
344C2C3×C4×#21511yescharacteristic
345C2C3×#512811yescharacteristic
346C2C3×#514411yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#446C2
socleC22×C32C4×D4
prime radicalC2×C3×D12C2×C4
cosocleC3×C42C23×C3
hypercenterC3×#446D3
hypocenterC3C3×#1590
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×C8 ◁ C3×#446

Complements

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

NH ≅ G/Ntype
1. C32×#446C2semidirect
4. C3×#4535C2semidirect
6. C3×#4480C2semidirect
7. C3×C8×C3⋊C8C2semidirect
9. #70950C3direct (N × H)
26. C3×#446D3semidirect
27. C3×#446C2×C3semidirect
36. #4535C2×C3semidirect
38. #4480C2×C3semidirect
39. C8×C3⋊C8C2×C3semidirect
109. C32×C8SD16semidirect
113. C3×C3⋊C8M16semidirect
114. #446C3×D3semidirect
236. C3×C8#215semidirect
237. C3×C8C3×SD16semidirect
241. C3⋊C8C3×M16semidirect
296. C32#1590semidirect
316. C8C3×#215semidirect
341. C3#70950direct (N × H)
342. C3C3×#1590semidirect

Maximal subgroups

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

subgroupindex
C32×#4462
C3×C4×#2152
C3×#46882
C3×#45352
C3×#44832
C3×#44802
C3×C8×C3⋊C82
C3×#15903
#709503