Finite Group Databasebeta

← #11797933

Subgroups — #11797933

Order 1152.

338 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592883C211yesmaximal, characteristic, complemented
2C3×#5179C211yesmaximal, characteristic
3#10590920C211yesmaximal, characteristic
4C3×#4565C211yesmaximal, characteristic, complemented
5#10589137C211yesmaximal, characteristic, complemented
6#10589124C211yesmaximal, characteristic
7#10589106C211yesmaximal, characteristic, complemented
8#71521—31nomaximal
9#69264—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11Q8×C3⋊Dic3—21no—
12C3×#904C2211yescharacteristic
13#63815—21no—
14#63662—21no—
15#63644C2211yescharacteristic
16#63642C2211yescharacteristic
17C3×#829C412yescomplemented
18C3×#828C412yescomplemented
19C3×#819C2211yescharacteristic
20C3×#812C2211yescharacteristic
21C3×#812C2211yescharacteristic
22#63568—21no—
23C3×#510—31no—
24#5197—31no—
25#5184—31no—
26#5184—31no—
27#5184—61no—
28#5179D311yescharacteristic
29#4894—31no—
30C3×#362—31no—
31#4566—31no—
32#4565D311yescharacteristic, complemented
33#4518—31no—
34#4513—31no—
35#4512—31no—
36#4512—31no—
37#4494—31no—
38C2×C32×Q8—21no—
39C3×#235—21no—
40C32×Q16—21no—
41C32×Q16C2×C412yes—
42C2×C32×C8C2311yescharacteristic
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—41no—
45C4×C3⋊Dic3—41no—
46C4×C3⋊Dic3D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C3×#208—21no—
49C3×Dic12C2×C411yescharacteristic
50C3×D24C2×C411yescharacteristic
51C3×#204—21no—
52#3711—41no—
53D3×C3⋊C8—41no—
54C3×C3⋊C16—21no—
55C3×C3⋊C16C2×C412yes—
56#2180—91noSylow
57C3×#135—31no—
58C2×C3×Q16—21no—
59C2×C3×Q16C2×D311yescharacteristic
60C2×C3×Q16C2×D311yescharacteristic
61#948—61no—
62Q8×Dic3—61no—
63Q8×Dic3—61no—
64Q8×Dic3—62no—
65#907—61no—
66#904C2×D311yescharacteristic
67C3×Q32—32no—
68C3×SD32—32no—
69C3×M32—31no—
70C3×M32—31no—
71C3×#108—31no—
72#837—61no—
73#835—61no—
74#835—61no—
75#835—62no—
76#829Dic312yescomplemented
77#828Dic312yescomplemented
78#825—61no—
79#819C2×D311yescharacteristic
80#817—31no—
81#817—31no—
82#817—61no—
83#815—31no—
84#815—31no—
85#815—61no—
86#812C2×D311yescharacteristic
87#812C2×D311yescharacteristic
88C32×Q8—22no—
89C32×Q8—41no—
90C2×C32×C4—41no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—41no—
94C3×#67—41no—
95C3×D12—21no—
96C3×C4×D3—41no—
97C3×Dic6—21no—
98C32×C8C22×C411yescharacteristic
99C32×C8#4111yescharacteristic
100C3⋊(C3⋊C8)—21no—
101C3×C3⋊C8—41no—
102#510—31no—
103#444—91no—
104#441—91no—
105#365—91no—
106#362—31no—
107#360—91no—
108#347—91no—
109C3×#41—61no—
110C2×C3×Q8—22no—
111C2×C3×Q8—21no—
112C2×C3×Q8—21no—
113#235—21no—
114C3×Q16—22no—
115C3×Q16—21no—
116C3×Q16—21no—
117C3×Q16—22no—
118C3×Q16—31no—
119C3×Q16C4×D312yes—
120C3×Q16C2×Dic312yes—
121C3×SD16—61no—
122C3×D8—31no—
123C3×M16—61no—
124C2×C3×C8—21no—
125C2×C3×C8C22×D311yescharacteristic
126C2×C3×C8C22×D311yescharacteristic
127C4⋊Dic3—62no—
128C4⋊Dic3—61no—
129C4⋊Dic3—61no—
130C4⋊Dic3—122no—
131C4⋊Dic3—121no—
132C4⋊Dic3—121no—
133C4×Dic3—31no—
134C4×Dic3—31no—
135C4×Dic3—61no—
136C4×Dic3—122no—
137C4×Dic3—121no—
138C4×Dic3—121no—
139#208—21no—
140#208—121no—
141C2×C3⋊C8—31no—
142C2×C3⋊C8—31no—
143C2×C3⋊C8—61no—
144C2×C3⋊C8—121no—
145Dic12C2×Dic311yescharacteristic
146D24C2×Dic311yescharacteristic
147#204—21no—
148ΓL(1,𝔽25)—121no—
149D3×C8—121no—
150C3×C16—32no—
151C3×C16—61no—
152C3⋊C16—21no—
153C3⋊C16C2×Dic312yes—
154C22×C32AGL(1,ℤ/8)11yescharacteristic
155C2×C3×D3—41no—
156C32×C4—42no—
157C32×C4C4×D411yescharacteristic
158C32×C4AGL(1,ℤ/8)11yescharacteristic
159C3⋊Dic3—41no—
160C3⋊Dic3—81no—
161C3×Dic3—41no—
162#135—31no—
163C2×Q16D3211yescharacteristic
164#131—181no—
165C4×Q8—181no—
166Q32—32no—
167SD32—32no—
168M32—31no—
169M32—31no—
170#108—31no—
171#106—91no—
172#104—181no—
173#103—181no—
174#97—91no—
175C3×Q8—24no—
176C3×Q8—22no—
177C3×Q8—22no—
178C3×Q8—42no—
179C3×Q8—41no—
180C3×Q8—41no—
181C3×Q8—61no—
182C3×D4—61no—
183C3×D4—121no—
184C2×C3×C4—21no—
185C2×C3×C4—42no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—121no—
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191#67—41no—
192C2×Dic3—62no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—122no—
196C2×Dic3—121no—
197C2×Dic3—121no—
198D12—21no—
199C4×D3—41no—
200Dic6—21no—
201C3×C8—21no—
202C3×C8—21no—
203C3×C8—121no—
204C3×C8C2×C4×D311yescharacteristic
205C3×C8#23711yescharacteristic
206C3×C8#23711yescharacteristic
207C3×C8C22×Dic311yescharacteristic
208C3⋊C8—41no—
209C3⋊C8—61no—
210C3⋊C8—61no—
211C3⋊C8—121no—
212C2×C32—21no—
213C2×C32#44211yescharacteristic
214C3×D3—81no—
215#41—61no—
216C2×Q8—21no—
217Q16—21no—
218Q16—31no—
219Q16D3×Dic312yes—
220SD16—61no—
221D8—31no—
222M16—61no—
223M16—361no—
224C2×C8—91no—
225C2×C8—361no—
226C2×C8C2×D3211yescharacteristic
227C4⋊C4—181no—
228C4⋊C4—361no—
229C42—91no—
230C42—361no—
231C16—32no—
232C16—61no—
233C22×C3—21no—
234C22×C3—121no—
235C22×C3#91111yescharacteristic
236C22×C3#91411yescharacteristic
237C2×D3—41no—
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—44no—
241C3×C4—42no—
242C3×C4—42no—
243C3×C4—121no—
244C3×C4#67⋊C411yescharacteristic
245C3×C4#91111yescharacteristic
246C3×C4#91111yescharacteristic
247C3×C4D4×Dic311yescharacteristic
248Dic3—41no—
249Dic3—122no—
250Dic3—121no—
251Dic3—121no—
252Dic3—242no—
253Dic3—241no—
254Dic3—241no—
255C32#218011yescharacteristic, complemented, Sylow
256Q8—22no—
257Q8—41no—
258Q8—61no—
259D4—61no—
260D4—121no—
261C2×C4—41no—
262C2×C4—121no—
263C2×C4—181no—
264C2×C4—361no—
265C2×C4#381111yescharacteristic
266C8—121no—
267C8—181no—
268C8C2×D3×Dic311yescharacteristic
269C8#380511yescharacteristic
270C2×C3—22no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—241no—
275C2×C3#478511yescharacteristic
276C2×C3#515211yescharacteristic
277D3—81no—
278C22—121no—
279C22#6393711yescharacteristic
280C4—42no—
281C4—121no—
282C4—361no—
283C4—721no—
284C4#6392711yescharacteristic
285C4#67⋊Dic311yescharacteristic
286C3—21no—
287C3#6926411yescharacteristic, complemented
288C3#7152111yescharacteristic, complemented
289C2—21no—
290C2—241no—
291C2#1059143611yescharacteristic
subgroupG/H
centerC2#10591436
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC2×C32#442
prime radicalC3×#904C22
cosocleC2×C32×C8C23
hypercenterC2×Q16D32
hypocenterC32#2180
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #10592883C2semidirect
4. C3×#4565C2semidirect
5. #10589137C2semidirect
7. #10589106C2semidirect
17. C3×#829C4semidirect
18. C3×#828C4semidirect
32. #4565D3semidirect
76. #829Dic3semidirect
77. #828Dic3semidirect
255. C32#2180semidirect
287. C3#69264semidirect
288. C3#71521semidirect

Maximal subgroups

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

subgroupindex
#105928832
C3×#51792
#105909202
C3×#45652
#105891372
#105891242
#105891062
#715213
#692643