Finite Group Databasebeta

← C3×#71345 #11781825

Subgroups — C3×#71345 #11781825

Order 1152.

369 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#498C211yesmaximal, characteristic, complemented
2C3×#5084C211yesmaximal, characteristic
3C3×#5083C211yesmaximal, characteristic
4C3×#4688C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4546C211yesmaximal, characteristic, complemented
7C3×#4458C211yesmaximal, characteristic, complemented
8C3×#1691—31nomaximal
9#71345C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4⋊Q8C2211yescharacteristic
12C2×C3×#215—21no—
13C2×C3×ΓL(1,𝔽25)—21no—
14C3×C4×D12C2211yescharacteristic
15C32×#106—21no—
16C32×#106—21no—
17C32×C4×C8C2211yescharacteristic
18C3×#835—21no—
19C3×(C2×D3)⋊C8—21no—
20C3×#809—21no—
21C3×#808—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#498—21no—
26C3×#498D311yescharacteristic, complemented
27C3×#498C2×C311yescharacteristic, complemented
28C3×#476—31no—
29C3×#461—31no—
30C3×#436—31no—
31#5084C2×C311yescharacteristic
32#5083C2×C311yescharacteristic
33#4688C2×C311yescharacteristic
34C3×#335—31no—
35C3×#333—31no—
36C3×#332—31no—
37#4547C2×C311yescharacteristic, complemented
38#4546C2×C311yescharacteristic, complemented
39#4458C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×Q8—21no—
42C2×C3×D12D411yescharacteristic
43C2×C3×C4×D3—21no—
44C2×C32×C8D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C42C2311yescharacteristic
51C3×#215—42no—
52C3×(C2×D3)⋊C4—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C3×ΓL(1,𝔽25)—42no—
58#1691—31noSylow
59C2×C3×SD16—61no—
60C2×C3×M16—61no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8—21no—
63C3×C4⋊Q8C2×D311yescharacteristic
64C3×C4⋊Q8C2×D311yescharacteristic
65C3×C4⋊Q8C22×C311yescharacteristic
66C3×C4⋊Q8C22×C311yescharacteristic
67C3×C4×D4—31no—
68C2×#215—21no—
69C2×ΓL(1,𝔽25)—21no—
70C4×D12C22×C311yescharacteristic
71C3×#106—22no—
72C3×#106—22no—
73C3×#106—21no—
74C3×#106—21no—
75C3×#106—21no—
76C3×#106—21no—
77C3×#106—61no—
78C3×C4⋊C8—31no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8—31no—
81C3×#103—61no—
82C3×#102—61no—
83C3×C22⋊C8—61no—
84C3×C4×C8—21no—
85C3×C4×C8C2×D311yescharacteristic
86C3×C4×C8C22×C311yescharacteristic
87#835—21no—
88(C2×D3)⋊C8—21no—
89#809—21no—
90#808—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C22×C3×D3—21no—
95C32×Q8—41no—
96C32×Q8—41no—
97C32×Q8—81no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
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—21no—
109C32×C8SD1612yescomplemented
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#498C3×D311yescharacteristic, complemented
114#476—31no—
115#461—31no—
116#436—31no—
117#335—31no—
118#333—31no—
119#332—31no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×Q8—41no—
125C2×C3×Q8—41no—
126C2×C3×D4—31no—
127C22×C3×C4—61no—
128C2×D12C3×D411yescharacteristic
129C2×C4×D3—21no—
130C3×SD16—122no—
131C3×M16—122no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C2×C3×C8#6711yescharacteristic
138C2×C3×C8#6711yescharacteristic
139C2×C3×C8C3×D411yescharacteristic
140C2×C3×C8C3×D411yescharacteristic
141C3×C4⋊C4—22no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—41no—
153C3×C4⋊C4—41no—
154C3×C22⋊C4—61no—
155C3×C42—21no—
156C3×C42C22×D311yescharacteristic
157C3×C42C23×C311yescharacteristic
158#215—42no—
159(C2×D3)⋊C4—21no—
160C4⋊Dic3C3×D411yescharacteristic
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—21no—
164ΓL(1,𝔽25)—42no—
165C22×C32#12111yescharacteristic
166C2×C3×D3—41no—
167C2×C3×D3—41no—
168C2×C3×D3—41no—
169C32×C4—21no—
170C32×C4—81no—
171C32×C4—81no—
172C32×C4C2×SD1611yescharacteristic
173C32×C4AGL(1,ℤ/8)11yescharacteristic
174C32×C4#13711yescharacteristic
175C32×C4#13711yescharacteristic
176C3×Dic3—41no—
177C2×SD16—61no—
178C2×M16—61no—
179C4⋊Q8C2×C3×D311yescharacteristic
180C4⋊Q8C2×C3×D311yescharacteristic
181C4×D4—31no—
182#106—21no—
183#106—21no—
184#106—61no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8—31no—
188#103—61no—
189#102—61no—
190C22⋊C8—61no—
191C4×C8C2×C3×D311yescharacteristic
192C23×C3—61no—
193C22×D3—21no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—41no—
197C3×Q8—41no—
198C3×Q8—81no—
199C3×Q8—81no—
200C3×Q8—81no—
201C3×Q8—81no—
202C3×Q8—82no—
203C3×D4—61no—
204C3×D4—61no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—42no—
209C2×C3×C4—42no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—61no—
215C2×C3×C4—121no—
216C2×C3×C4—121no—
217C2×C3×C4D3×D411yescharacteristic
218C2×C3×C4#23711yescharacteristic
219C2×C3×C4C2×#6711yescharacteristic
220C2×C3×C4C2×C3×D411yescharacteristic
221C2×C3×C4C2×C3×D411yescharacteristic
222C2×C3×C4C3×#4111yescharacteristic
223C2×Dic3—21no—
224D12—21no—
225D12—21no—
226C4×D3—41no—
227C4×D3—41no—
228C3×C8—22no—
229C3×C8—21no—
230C3×C8—21no—
231C3×C8—22no—
232C3×C8—121no—
233C3×C8—121no—
234C3×C8—121no—
235C3×C8#21512yescomplemented
236C3×C8C3×SD1612yescomplemented
237C3⋊C8—41no—
238C3⋊C8—41no—
239C3⋊C8—41no—
240C2×C32#46111yescharacteristic
241C2×C32#46811yescharacteristic
242C2×C32#47111yescharacteristic
243C3×D3—81no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×D4—31no—
247C22×C4—61no—
248SD16—122no—
249M16—122no—
250C2×C8—61no—
251C2×C8—61no—
252C2×C8—61no—
253C2×C8C3×#6711yescharacteristic
254C2×C8C3×#6711yescharacteristic
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—31no—
260C22⋊C4—61no—
261C42C22×C3×D311yescharacteristic
262C22×C3—21no—
263C22×C3—121no—
264C22×C3—121no—
265C22×C3—121no—
266C22×C3#93811yescharacteristic
267C22×C3C3×#12111yescharacteristic
268C2×D3—41no—
269C2×D3—41no—
270C2×D3—41no—
271C3×C4—22no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—82no—
279C3×C4—82no—
280C3×C4—81no—
281C3×C4—81no—
282C3×C4—81no—
283C3×C4—81no—
284C3×C4—121no—
285C3×C4#91411yescharacteristic
286C3×C4#91511yescharacteristic
287C3×C4C2×#21511yescharacteristic
288C3×C4#94211yescharacteristic
289C3×C4C2×C3×SD1611yescharacteristic
290C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
291C3×C4C3×#13711yescharacteristic
292C3×C4C3×#13711yescharacteristic
293Dic3—41no—
294C32#169111yescharacteristic, complemented, Sylow
295C23—61no—
296Q8—41no—
297Q8—41no—
298Q8—81no—
299D4—61no—
300D4—61no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—61no—
304C2×C4—121no—
305C2×C4—121no—
306C2×C4C3×D3×D411yescharacteristic
307C2×C4C3×#23711yescharacteristic
308C2×C4C2×C3×#6711yescharacteristic
309C8—21no—
310C8—121no—
311C8—121no—
312C8—121no—
313C8C3×#21512yescomplemented
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—241no—
318C2×C3#508311yescharacteristic
319C2×C3#517411yescharacteristic
320C2×C3#517711yescharacteristic
321C2×C3C3×#46111yescharacteristic
322C2×C3C3×#46811yescharacteristic
323C2×C3C3×#47111yescharacteristic
324D3—81no—
325C22—121no—
326C22—121no—
327C22—121no—
328C22C3×#93811yescharacteristic
329C4—21no—
330C4—81no—
331C4—81no—
332C4—121no—
333C4C3×#91411yescharacteristic
334C4C3×#91511yescharacteristic
335C4C2×C3×#21511yescharacteristic
336C4C3×#94211yescharacteristic
337C3—21no—
338C3#7134511yescharacteristic, direct product factor
339C3C3×#169111yescharacteristic, complemented
340C2—241no—
341C2C3×#508311yescharacteristic
342C2C3×#517411yescharacteristic
343C2C3×#517711yescharacteristic
subgroupG/H
centerC22×C3#938
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#498C2
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC3×#498D3
hypocenterC3C3×#1691
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#498

Complements

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

NH ≅ G/Ntype
1. C32×#498C2semidirect
5. C3×#4547C2semidirect
6. C3×#4546C2semidirect
7. C3×#4458C2semidirect
9. #71345C3direct (N × H)
26. C3×#498D3semidirect
27. C3×#498C2×C3semidirect
37. #4547C2×C3semidirect
38. #4546C2×C3semidirect
39. #4458C2×C3semidirect
109. C32×C8SD16semidirect
113. #498C3×D3semidirect
235. C3×C8#215semidirect
236. C3×C8C3×SD16semidirect
294. C32#1691semidirect
313. C8C3×#215semidirect
338. C3#71345direct (N × H)
339. C3C3×#1691semidirect

Maximal subgroups

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

subgroupindex
C32×#4982
C3×#50842
C3×#50832
C3×#46882
C3×#45472
C3×#45462
C3×#44582
C3×#16913
#713453