Finite Group Databasebeta

← #11800025

Subgroups — #11800025

Order 1152.

299 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 299 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592592C211yesmaximal, characteristic
2#10590858C211yesmaximal, characteristic
3C3×#4496C211yesmaximal, characteristic, complemented
4C3×#4494C211yesmaximal, characteristic, complemented
5#10589136C211yesmaximal, characteristic, complemented
6#10589130C211yesmaximal, characteristic, complemented
7#10589110C211yesmaximal, characteristic
8#69314—31nomaximal
9#69267—31nomaximal
10M16×C3⋊D3—21no—
11C2×#3743C2211yescharacteristic
12C2×C3×Dic12C2211yescharacteristic
13#63871—21no—
14C32×#108C2211yescharacteristic
15#63649—21no—
16#63646C2211yescharacteristic
17C3×#817C2211yescharacteristic
18C3×#812C2211yescharacteristic
19C3×#812C2211yescharacteristic
20#63565—21no—
21#5189—31no—
22#4893—31no—
23#4893—31no—
24#4893—61no—
25#4867—31no—
26C3×#365—31no—
27C3×#362—31no—
28#4565—31no—
29#4517—31no—
30#4514—31no—
31#4514—31no—
32#4513—31no—
33#4496D311yescharacteristic, complemented
34#4494D311yescharacteristic, complemented
35#4487—31no—
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C3×Dic6—21no—
38C32×M16—21no—
39C2×C32×C8C2311yescharacteristic
40#3748—21no—
41C2×C3⋊(C3⋊C8)D411yescharacteristic
42#3743—21no—
43#3743—21no—
44#3743—41no—
45C8×C3⋊D3—41no—
46C3×C4⋊Dic3—21no—
47C3×Dic12—21no—
48C3×Dic12—21no—
49Dic3⋊Dic3—41no—
50#3722—41no—
51C3×C3⋊C16—21no—
52C3×C3⋊C16—21no—
53#2239—91noSylow
54C2×C3×Q16—31no—
55#946—61no—
56D3×M16—61no—
57D3×M16—61no—
58D3×M16—62no—
59C2×Dic12C2×D311yescharacteristic
60C2×ΓL(1,𝔽25)—31no—
61C2×ΓL(1,𝔽25)—31no—
62C2×ΓL(1,𝔽25)—61no—
63#897—61no—
64C3×M32—31no—
65C3×M32—31no—
66C3×#108—21no—
67C3×#108C2×D311yescharacteristic
68C3×#108C2×D311yescharacteristic
69C3×#106—31no—
70#835—61no—
71#822—61no—
72#822—61no—
73#822—62no—
74#819—31no—
75#819—31no—
76#819—61no—
77#817C2×D311yescharacteristic
78#812C2×D311yescharacteristic
79#812C2×D311yescharacteristic
80#810—61no—
81C22×C3⋊D3SD1611yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3SD1611yescharacteristic
84C4×C3⋊D3—21no—
85C4×C3⋊D3—21no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3—41no—
88C3×Dic6—41no—
89C3×Dic6—41no—
90C32×C8—41no—
91C32×C8#4111yescharacteristic
92C32×C8#4111yescharacteristic
93C3⋊(C3⋊C8)—21no—
94C3⋊(C3⋊C8)—41no—
95#470—91no—
96#430—91no—
97#365—31no—
98#365—91no—
99#362—31no—
100#362—91no—
101#349—91no—
102C2×C3×Q8—61no—
103C2×C4×D3—31no—
104C2×C4×D3—31no—
105C2×C4×D3—61no—
106C2×Dic6—21no—
107C3×Q16—61no—
108C3×Q16—61no—
109C3×M16—22no—
110C3×M16—21no—
111C3×M16—21no—
112C2×C3×C8—21no—
113C2×C3×C8C22×D311yescharacteristic
114C2×C3×C8C22×D311yescharacteristic
115C3×C4⋊C4—61no—
116(C2×D3)⋊C4—121no—
117(C2×D3)⋊C4—121no—
118C4⋊Dic3—21no—
119C4⋊Dic3—121no—
120Dic3⋊C4—121no—
121#208—62no—
122#208—61no—
123#208—61no—
124C2×C3⋊C8—31no—
125C2×C3⋊C8—31no—
126C2×C3⋊C8—61no—
127Dic12—21no—
128Dic12—21no—
129ΓL(1,𝔽25)—62no—
130ΓL(1,𝔽25)—62no—
131ΓL(1,𝔽25)—61no—
132ΓL(1,𝔽25)—61no—
133ΓL(1,𝔽25)—61no—
134ΓL(1,𝔽25)—61no—
135ΓL(1,𝔽25)—122no—
136ΓL(1,𝔽25)—121no—
137ΓL(1,𝔽25)—121no—
138D3×C8—122no—
139D3×C8—121no—
140D3×C8—121no—
141C3×C16—61no—
142C3×C16—61no—
143C3⋊C16—21no—
144C3⋊C16—21no—
145C22×C32C2×SD1611yescharacteristic
146C2×C3⋊D3—21no—
147C2×C3⋊D3—41no—
148C32×C4#12311yescharacteristic
149C32×C4AGL(1,ℤ/8)11yescharacteristic
150C3⋊Dic3—21no—
151C3×Dic3—81no—
152C3×Dic3—81no—
153C2×Q16—31no—
154C2×M16—91no—
155C2×M16—181no—
156C22⋊Q8—181no—
157M32—31no—
158M32—31no—
159#108—91no—
160#108—181no—
161#108D3211yescharacteristic
162#106—31no—
163#103—181no—
164C22×D3—31no—
165C22×D3—31no—
166C22×D3—61no—
167C3×Q8—121no—
168C3×Q8—121no—
169C2×C3×C4—21no—
170C2×C3×C4—121no—
171C2×C3×C4—121no—
172C2×C3×C4D3×D411yescharacteristic
173C2×C3×C4D3×D411yescharacteristic
174C2×Dic3—31no—
175C2×Dic3—31no—
176C2×Dic3—41no—
177C2×Dic3—41no—
178C2×Dic3—61no—
179C4×D3—62no—
180C4×D3—62no—
181C4×D3—61no—
182C4×D3—61no—
183C4×D3—61no—
184C4×D3—61no—
185Dic6—41no—
186Dic6—41no—
187C3×C8—21no—
188C3×C8—21no—
189C3×C8—42no—
190C3×C8—41no—
191C3×C8—41no—
192C3×C8#23511yescharacteristic
193C3×C8#23511yescharacteristic
194C3×C8#23711yescharacteristic
195C3×C8#23911yescharacteristic
196C3⋊C8—62no—
197C3⋊C8—61no—
198C3⋊C8—61no—
199C3⋊C8—122no—
200C3⋊C8—121no—
201C3⋊C8—121no—
202C2×C32—21no—
203C2×C32#48111yescharacteristic
204C3⋊D3—41no—
205C2×Q8—61no—
206C22×C4—91no—
207Q16—61no—
208Q16—61no—
209M16—21no—
210M16—181no—
211M16—181no—
212M16—181no—
213M16—361no—
214C2×C8—91no—
215C2×C8—361no—
216C2×C8C2×D3211yescharacteristic
217C4⋊C4—61no—
218C4⋊C4—361no—
219C22⋊C4—361no—
220C16—61no—
221C16—61no—
222C22×C3—21no—
223C22×C3D3×SD1611yescharacteristic
224C22×C3D3×SD1611yescharacteristic
225C2×D3—62no—
226C2×D3—61no—
227C2×D3—61no—
228C2×D3—121no—
229C2×D3—121no—
230C2×D3—241no—
231C3×C4—21no—
232C3×C4—21no—
233C3×C4—241no—
234C3×C4—241no—
235C3×C4#88311yescharacteristic
236C3×C4#89411yescharacteristic
237C3×C4#91111yescharacteristic
238C3×C4#91411yescharacteristic
239Dic3—62no—
240Dic3—61no—
241Dic3—61no—
242Dic3—81no—
243Dic3—81no—
244C32#223911yescharacteristic, complemented, Sylow
245C23—91no—
246Q8—121no—
247Q8—121no—
248C2×C4—91no—
249C2×C4—121no—
250C2×C4—121no—
251C2×C4—181no—
252C2×C4—181no—
253C2×C4#381111yescharacteristic
254C8—41no—
255C8—181no—
256C8—361no—
257C8#379611yescharacteristic
258C8#379811yescharacteristic
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—41no—
263C2×C3#477711yescharacteristic
264C2×C3#486311yescharacteristic
265D3—122no—
266D3—121no—
267D3—121no—
268C22—181no—
269C22—361no—
270C22#6394011yescharacteristic
271C4—181no—
272C4—241no—
273C4—241no—
274C4#6385311yescharacteristic
275C4#6393711yescharacteristic
276C3—21no—
277C3#6926711yescharacteristic, complemented
278C3#6931411yescharacteristic, complemented
279C2—21no—
280C2—361no—
281C2#1059051111yescharacteristic
subgroupG/H
centerC2#10590511
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32#481
prime radicalC22×C3⋊D3SD16
hypercenter#108D32
hypocenterC32#2239
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
3. C3×#4496C2semidirect
4. C3×#4494C2semidirect
5. #10589136C2semidirect
6. #10589130C2semidirect
33. #4496D3semidirect
34. #4494D3semidirect
244. C32#2239semidirect
277. C3#69267semidirect
278. C3#69314semidirect

Maximal subgroups

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

subgroupindex
#105925922
#105908582
C3×#44962
C3×#44942
#105891362
#105891302
#105891102
#693143
#692673