Finite Group Databasebeta

← #11776958

Subgroups — #11776958

Order 1152.

359 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic
2#10590336C211yesmaximal, characteristic
3#10590263C211yesmaximal, characteristic
4#10589324C211yesmaximal, characteristic, complemented
5C3×#4457C211yesmaximal, characteristic, complemented
6#10589099C211yesmaximal, characteristic, complemented
7#10589097C211yesmaximal, characteristic, complemented
8#69851—31nomaximal
9#68531—31nomaximal
10C2×C3×ΓL(1,𝔽25)C411yescharacteristic
11C2×C3×ΓL(1,𝔽25)C411yescharacteristic
12C3×C42×D3C2211yescharacteristic
13C2×#3711—21no—
14C32×C4×C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#815C411yescharacteristic
18C3×#815C411yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22Dic3⋊(C3⋊C8)—21no—
23(C2×D3)⋊(C3⋊C8)—21no—
24#63554—21no—
25C3×C4×M16—31no—
26#4926—31no—
27#4924—31no—
28#4837—31no—
29#4835—31no—
30C4×ΓL(1,𝔽25)D311yescharacteristic
31C3×#334—31no—
32#4480—31no—
33#4479—31no—
34#4458—31no—
35#4458—31no—
36#4458—31no—
37#4458—61no—
38#4457—31no—
39#4457D311yescharacteristic, complemented
40C2×C3×C4×D3C2×C411yescharacteristic
41C2×C3×C4×D3D411yescharacteristic
42C2×C3×C4×D3Q811yescharacteristic
43C2×C32×C8C2×C411yescharacteristic
44C2×C32×C8C2×C411yescharacteristic
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4×Dic3C2×C411yescharacteristic
49C3×C4×Dic3D411yescharacteristic
50C3×C4×Dic3Q811yescharacteristic
51C2×C3×C3⋊C8—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8C2×C411yescharacteristic
54C2×C3×C3⋊C8C2×C411yescharacteristic
55C3×ΓL(1,𝔽25)—22no—
56C3×ΓL(1,𝔽25)—22no—
57#3711—42no—
58#1569—91noSylow
59C2×C3×M16—31no—
60C2×C3×M16—31no—
61C2×C3×C42—31no—
62C2×#208—61no—
63C2×ΓL(1,𝔽25)—61no—
64C2×ΓL(1,𝔽25)Dic311yescharacteristic
65C2×ΓL(1,𝔽25)Dic311yescharacteristic
66C42×D3C2×D311yescharacteristic
67C3×C4⋊C8—31no—
68C3×C4⋊C8—31no—
69C3×#97—31no—
70C3×#97—31no—
71C3×C4×C8—21no—
72C3×C4×C8—31no—
73C3×C4×C8C2×D311yescharacteristic
74C3×C4×C8C2×D311yescharacteristic
75#830—61no—
76(C2×D3)⋊C8—61no—
77#815—61no—
78#815Dic311yescharacteristic
79#815Dic311yescharacteristic
80Dic3⋊C8—61no—
81C4⋊(C3⋊C8)—31no—
82C4⋊(C3⋊C8)—31no—
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90#803—61no—
91C4×C3⋊C8C2×D311yescharacteristic
92C22×C3×D3C4⋊C411yescharacteristic
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×Q811yescharacteristic
96C2×C3×Dic3C4⋊C411yescharacteristic
97C2×C3×Dic3C4⋊C411yescharacteristic
98C2×C3×Dic3C4⋊C411yescharacteristic
99C3×C4×D3—21no—
100C3×C4×D3—21no—
101C3×C4×D3—21no—
102C3×C4×D3—21no—
103C3×C4×D3—41no—
104C32×C8—21no—
105C32×C8M1612yescomplemented
106C3⋊(C3⋊C8)—41no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8M1612yescomplemented
112#432—91no—
113#423—91no—
114C4×M16—31no—
115#335—91no—
116#335—91no—
117#334—31no—
118#334—91no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C2×C4×D3Dic611yescharacteristic
123C2×C4×D3D1211yescharacteristic
124C2×C4×D3C2×Dic311yescharacteristic
125C3×M16—62no—
126C3×M16—62no—
127C2×C3×C8—21no—
128C2×C3×C8—21no—
129C2×C3×C8—31no—
130C2×C3×C8—31no—
131C2×C3×C8—61no—
132C2×C3×C8—61no—
133C2×C3×C8C4×D311yescharacteristic
134C2×C3×C8C4×D311yescharacteristic
135C2×C3×C8C2×Dic311yescharacteristic
136C2×C3×C8C2×Dic311yescharacteristic
137C3×C42—21no—
138C3×C42—31no—
139C3×C42—31no—
140C3×C42—31no—
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143C4×Dic3Dic611yescharacteristic
144C4×Dic3D1211yescharacteristic
145C4×Dic3C2×Dic311yescharacteristic
146#208—122no—
147C2×C3⋊C8—21no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—121no—
154C2×C3⋊C8—121no—
155C2×C3⋊C8C2×Dic311yescharacteristic
156C2×C3⋊C8C2×Dic311yescharacteristic
157ΓL(1,𝔽25)—22no—
158ΓL(1,𝔽25)—22no—
159ΓL(1,𝔽25)—122no—
160C22×C32C2×C4⋊C411yescharacteristic
161C2×C3×D3—21no—
162C2×C3×D3—21no—
163C2×C3×D3—21no—
164C32×C4—21no—
165C32×C4C2×M1611yescharacteristic
166C32×C4C2×M1611yescharacteristic
167C32×C4AGL(1,ℤ/8)11yescharacteristic
168C32×C4#13711yescharacteristic
169C3×Dic3—21no—
170C3×Dic3—21no—
171C3×Dic3—21no—
172C2×M16—31no—
173C2×M16—31no—
174C2×M16—181no—
175C2×C42—31no—
176C4⋊C8—31no—
177C4⋊C8—31no—
178C4⋊C8—91no—
179C4⋊C8—91no—
180C4⋊C8—181no—
181C22⋊C8—181no—
182#97—31no—
183#97—31no—
184#97—181no—
185C4×C8—31no—
186C4×C8D3211yescharacteristic
187C23×C3—31no—
188C22×D3C4⋊Dic311yescharacteristic
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—31no—
195C2×C3×C4—61no—
196C2×C3×C4—61no—
197C2×C3×C4—61no—
198C2×C3×C4—61no—
199C2×C3×C4—121no—
200C2×C3×C4C2×Dic611yescharacteristic
201C2×C3×C4C2×C4×D311yescharacteristic
202C2×C3×C4C2×D1211yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4D3×Q811yescharacteristic
205C2×C3×C4C22×Dic311yescharacteristic
206C2×Dic3C4⋊Dic311yescharacteristic
207C2×Dic3C4⋊Dic311yescharacteristic
208C2×Dic3C4⋊Dic311yescharacteristic
209C4×D3—21no—
210C4×D3—21no—
211C4×D3—21no—
212C4×D3—21no—
213C4×D3—41no—
214C3×C8—21no—
215C3×C8—21no—
216C3×C8—22no—
217C3×C8—32no—
218C3×C8—41no—
219C3×C8—61no—
220C3×C8—121no—
221C3×C8—121no—
222C3×C8ΓL(1,𝔽25)12yescomplemented
223C3×C8#20812yescomplemented
224C3⋊C8—21no—
225C3⋊C8—41no—
226C3⋊C8—41no—
227C3⋊C8—121no—
228C3⋊C8—121no—
229C3⋊C8—121no—
230C3⋊C8—121no—
231C3⋊C8—241no—
232C3⋊C8—241no—
233C3⋊C8#20812yescomplemented
234C2×C32#42311yescharacteristic
235C2×C32#42811yescharacteristic
236C2×C32#43011yescharacteristic
237C3×D3—41no—
238C22×C4—31no—
239C22×C4—31no—
240C22×C4—31no—
241M16—62no—
242M16—62no—
243M16—362no—
244C2×C8—31no—
245C2×C8—31no—
246C2×C8—61no—
247C2×C8—61no—
248C2×C8—181no—
249C2×C8—181no—
250C2×C8D3×Dic311yescharacteristic
251C2×C8D3×Dic311yescharacteristic
252C42—31no—
253C42—31no—
254C42—31no—
255C42C2×D3211yescharacteristic
256C22×C3—21no—
257C22×C3—61no—
258C22×C3—61no—
259C22×C3—61no—
260C22×C3D3×C4⋊C411yescharacteristic
261C22×C3C2×C4⋊Dic311yescharacteristic
262C2×D3—21no—
263C2×D3—21no—
264C2×D3—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—41no—
272C3×C4—61no—
273C3×C4—61no—
274C3×C4—61no—
275C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
276C3×C4D3×M1611yescharacteristic
277C3×C4#90811yescharacteristic
278C3×C4#90911yescharacteristic
279C3×C4#91411yescharacteristic
280C3×C4#91511yescharacteristic
281C3×C4C2×#20811yescharacteristic
282C3×C4C2×#20811yescharacteristic
283Dic3—21no—
284Dic3—21no—
285Dic3—21no—
286C32#156911yescharacteristic, complemented, Sylow
287C23—31no—
288C2×C4—31no—
289C2×C4—31no—
290C2×C4—31no—
291C2×C4—61no—
292C2×C4—61no—
293C2×C4—61no—
294C2×C4—61no—
295C2×C4—121no—
296C2×C4D3×Dic611yescharacteristic
297C2×C4D3×D1211yescharacteristic
298C2×C4C2×D3×Dic311yescharacteristic
299C8—21no—
300C8—32no—
301C8—61no—
302C8—121no—
303C8—121no—
304C8—361no—
305C8—361no—
306C8#371112yescomplemented
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—121no—
311C2×C3#483711yescharacteristic
312C2×C3#486111yescharacteristic
313C2×C3#489311yescharacteristic
314C2×C3#492411yescharacteristic
315C2×C3#512111yescharacteristic
316C2×C3#512511yescharacteristic
317D3—41no—
318C22—61no—
319C22—61no—
320C22—61no—
321C22D3×C4⋊Dic311yescharacteristic
322C4—21no—
323C4—61no—
324C4—61no—
325C4—61no—
326C4#6379411yescharacteristic
327C4#6380011yescharacteristic
328C4D3×#20811yescharacteristic
329C4C2×#371111yescharacteristic
330C3—21no—
331C3#6853111yescharacteristic, complemented
332C3#6985111yescharacteristic, complemented
333C2—121no—
334C2#1059033611yescharacteristic
335C2#1059068111yescharacteristic
336C2#1059091211yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C4⋊C4
prime radicalC22×C3×D3C4⋊C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1569
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
4. #10589324C2semidirect
5. C3×#4457C2semidirect
6. #10589099C2semidirect
7. #10589097C2semidirect
39. #4457D3semidirect
105. C32×C8M16semidirect
111. C3×C3⋊C8M16semidirect
222. C3×C8ΓL(1,𝔽25)semidirect
223. C3×C8#208semidirect
233. C3⋊C8#208semidirect
286. C32#1569semidirect
306. C8#3711semidirect
331. C3#68531semidirect
332. C3#69851semidirect

Maximal subgroups

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

subgroupindex
C3×C4×ΓL(1,𝔽25)2
#105903362
#105902632
#105893242
C3×#44572
#105890992
#105890972
#698513
#685313