Finite Group Databasebeta

← #11797932

Subgroups — #11797932

Order 1152.

325 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 325 conjugacy classes of subgroups — too many to draw. Only its 80 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#10592878C211yesmaximal, characteristic
2C3×#5184C211yesmaximal, characteristic, complemented
3#10590918C211yesmaximal, characteristic
4C3×#4565C211yesmaximal, characteristic, complemented
5#10589138C211yesmaximal, characteristic, complemented
6#10589125C211yesmaximal, characteristic
7#10589105C211yesmaximal, characteristic, complemented
8#70917—31nomaximal
9#69264—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11#64113C2211yescharacteristic
12C3×Q8×Dic3—21no—
13#63817—21no—
14#63656C412yescomplemented
15#63655C412yescomplemented
16#63639C2211yescharacteristic
17C3×#835—21no—
18C3×#819C2211yescharacteristic
19C3×#817C2211yescharacteristic
20C3×#815C2211yescharacteristic
21C3×#812C2211yescharacteristic
22#63570—21no—
23C3×#441—31no—
24#5184D311yescharacteristic, complemented
25#5179—31no—
26#5179—31no—
27#5179—61no—
28#4894—31no—
29#4717—31no—
30C3×#362—31no—
31#4565D311yescharacteristic, complemented
32#4518—31no—
33#4512—31no—
34#4494—31no—
35#4488—31no—
36#4487—31no—
37#4466—31no—
38C2×C32×Q8—21no—
39#3828—21no—
40C32×Q16—21no—
41C32×Q16C2×C412yes—
42C2×C32×C8C2311yescharacteristic
43#3746C2×C411yescharacteristic
44#3745C2×C411yescharacteristic
45#3744—21no—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3—41no—
48C3×C4×Dic3—41no—
49C3×C4×Dic3D411yescharacteristic
50C3×#208—21no—
51C2×C3×C3⋊C8D411yescharacteristic
52#3712—41no—
53#3710—41no—
54C3⋊(C3⋊C16)C2×C412yes—
55C3×C3⋊C16—21no—
56#2180—91noSylow
57C2×C3×Q16—21no—
58C2×C3×Q16C2×D311yescharacteristic
59C2×C3×Q16C2×D311yescharacteristic
60C3×C4×Q8—61no—
61Q8×Dic3—21no—
62#907—61no—
63#904—31no—
64#904—31no—
65#904—61no—
66#901—61no—
67C3×M32—31no—
68C3×#108—31no—
69C3×#106—31no—
70C3×#103—61no—
71C3×#97—31no—
72#835—21no—
73#829—32no—
74#829—32no—
75#829—62no—
76#828—32no—
77#828—32no—
78#828—62no—
79#825—61no—
80#819C2×D311yescharacteristic
81#817C2×D311yescharacteristic
82#815C2×D311yescharacteristic
83#812—31no—
84#812—31no—
85#812—61no—
86#812C2×D311yescharacteristic
87#805—61no—
88C32×Q8—22no—
89C32×Q8—41no—
90C2×C32×C4—41no—
91C2×C32×C4C2×D411yescharacteristic
92#638—41no—
93C4⋊(C3⋊D3)—21no—
94C4×C3⋊D3—41no—
95#634—21no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—41no—
98C32×C8C22×C411yescharacteristic
99C32×C8#4111yescharacteristic
100C3×C3⋊C8—21no—
101C3×C3⋊C8—41no—
102#510—91no—
103#444—91no—
104#441—31no—
105#365—91no—
106#362—31no—
107#360—91no—
108#347—91no—
109C2×C3×Q8—21no—
110C2×C3×Q8—21no—
111C2×C3×Q8—41no—
112#235—61no—
113#235—61no—
114#235—121no—
115C3×Q16—21no—
116C3×Q16—21no—
117C3×Q16—22no—
118C3×Q16—41no—
119C3×Q16C4×D312yes—
120C3×Q16C4×D312yes—
121C3×M16—61no—
122C2×C3×C8—21no—
123C2×C3×C8—31no—
124C2×C3×C8C22×D311yescharacteristic
125C2×C3×C8C22×D311yescharacteristic
126C3×C4⋊C4—61no—
127C3×C4⋊C4—121no—
128C3×C42—31no—
129C3×C42—121no—
130C4⋊Dic3—21no—
131C4⋊Dic3—41no—
132C4×Dic3—41no—
133C4×Dic3#6711yescharacteristic
134#208—21no—
135C2×C3⋊C8#6711yescharacteristic
136Dic12—31no—
137Dic12—31no—
138Dic12—61no—
139D24—31no—
140D24—31no—
141D24—61no—
142#204—61no—
143#204—61no—
144#204—121no—
145ΓL(1,𝔽25)—121no—
146ΓL(1,𝔽25)—121no—
147D3×C8—121no—
148D3×C8—121no—
149C3×C16—61no—
150C3⋊C16—21no—
151C3⋊C16—32no—
152C3⋊C16—32no—
153C3⋊C16—62no—
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—41no—
161C3×Dic3—81no—
162#135—91no—
163C2×Q16D3211yescharacteristic
164#131—181no—
165C4×Q8—61no—
166Q32—92no—
167SD32—92no—
168M32—31no—
169M32—91no—
170#108—31no—
171#106—31no—
172#104—181no—
173#103—61no—
174#97—31no—
175C3×Q8—22no—
176C3×Q8—22no—
177C3×Q8—42no—
178C3×Q8—41no—
179C3×Q8—41no—
180C3×Q8—81no—
181C2×C3×C4—21no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—61no—
185C2×C3×C4—81no—
186C2×C3×C4—121no—
187C2×C3×C4D3×D411yescharacteristic
188C2×C3×C4C2×#6711yescharacteristic
189#67—121no—
190#67—121no—
191#67—241no—
192C2×Dic3—21no—
193C2×Dic3—41no—
194D12—61no—
195D12—61no—
196D12—121no—
197C4×D3—121no—
198C4×D3—121no—
199C4×D3—241no—
200Dic6—61no—
201Dic6—61no—
202Dic6—121no—
203C3×C8—21no—
204C3×C8—21no—
205C3×C8—61no—
206C3×C8—121no—
207C3×C8C2×C4×D311yescharacteristic
208C3×C8C2×C4×D311yescharacteristic
209C3×C8#23511yescharacteristic
210C3×C8#23711yescharacteristic
211C3⋊C8—21no—
212C3⋊C8—41no—
213C2×C32—21no—
214C2×C32#44211yescharacteristic
215C3⋊D3—81no—
216#41—181no—
217C2×Q8—21no—
218Q16—21no—
219Q16—91no—
220Q16#62412yes—
221SD16—181no—
222D8—91no—
223M16—61no—
224M16—361no—
225C2×C8—31no—
226C2×C8—361no—
227C2×C8C2×D3211yescharacteristic
228C4⋊C4—61no—
229C4⋊C4—121no—
230C42—31no—
231C42—121no—
232C16—61no—
233C16—92no—
234C22×C3—21no—
235C22×C3#91411yescharacteristic
236C22×C3#93211yescharacteristic
237C2×D3—121no—
238C2×D3—121no—
239C2×D3—241no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—42no—
243C3×C4—42no—
244C3×C4—82no—
245C3×C4—121no—
246C3×C4—241no—
247C3×C4#67⋊C411yescharacteristic
248C3×C4#91111yescharacteristic
249C3×C4C4×#6711yescharacteristic
250C3×C4#94911yescharacteristic
251Dic3—41no—
252Dic3—81no—
253Dic3—121no—
254Dic3—121no—
255Dic3—241no—
256C32#218011yescharacteristic, complemented, Sylow
257Q8—22no—
258Q8—41no—
259Q8—181no—
260D4—181no—
261D4—361no—
262C2×C4—41no—
263C2×C4—61no—
264C2×C4—121no—
265C2×C4—361no—
266C2×C4D3×#6711yescharacteristic
267C8—61no—
268C8—121no—
269C8#380411yescharacteristic
270C8C2×#62411yescharacteristic
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—41no—
275C2×C3#478511yescharacteristic
276C2×C3#501411yescharacteristic
277D3—241no—
278D3—241no—
279D3—481no—
280C22—361no—
281C22#6393411yescharacteristic
282C4—42no—
283C4—121no—
284C4—241no—
285C4—361no—
286C4#6392511yescharacteristic
287C4#6395211yescharacteristic
288C3—21no—
289C3#6926411yescharacteristic, complemented
290C3#7091711yescharacteristic, complemented
291C2—21no—
292C2—721no—
293C2#1059140411yescharacteristic
subgroupG/H
centerC2#10591404
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC2×C32#442
prime radical#64113C22
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
2. C3×#5184C2semidirect
4. C3×#4565C2semidirect
5. #10589138C2semidirect
7. #10589105C2semidirect
14. #63656C4semidirect
15. #63655C4semidirect
24. #5184D3semidirect
31. #4565D3semidirect
256. C32#2180semidirect
289. C3#69264semidirect
290. C3#70917semidirect

Maximal subgroups

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

subgroupindex
#105928782
C3×#51842
#105909182
C3×#45652
#105891382
#105891252
#105891052
#709173
#692643