Finite Group Databasebeta

← #11782891

Subgroups — #11782891

Order 1152.

405 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 405 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#4699C211yesmaximal, characteristic, complemented
2C3×#4694C211yesmaximal, characteristic
3#10590309C211yesmaximal, characteristic, complemented
4#10590290C211yesmaximal, characteristic, complemented
5#10590277C211yesmaximal, characteristic
6#10590277C211yesmaximal, characteristic
7#10589320C211yesmaximal, characteristic, complemented
8#71300—31nomaximal
9#71193—31nomaximal
10C2×C3×Dic12—22no—
11C3×#874C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4×C8C2211yescharacteristic
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#821—22no—
19#63574—22no—
20#63565—22no—
21#63562—22no—
22#63562—22no—
23C3×#494—31no—
24C3×#486—31no—
25#5093—31no—
26#5088—31no—
27#5088—31no—
28#5080—31no—
29#5080—31no—
30#5079—31no—
31#5070—31no—
32#5070—31no—
33#4699D311yescharacteristic, complemented
34#4694D311yescharacteristic
35#4454—31no—
36#4454—31no—
37#4454—61no—
38C2×C3×D12—21no—
39C2×C3×D12—21no—
40C2×C3×D12—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8D412yes—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)D412yes—
47C2×C3⋊(C3⋊C8)D412yes—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×Dic12—44no—
55#1720—91noSylow
56C2×C3×Q16—62no—
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C3×#127—31no—
61C2×Dic12—22no—
62#874C2×D311yescharacteristic
63#869C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65#869C2×D311yescharacteristic
66C3×#102—62no—
67C3×C4×C8—21no—
68C3×C4×C8C2×D311yescharacteristic
69C3×C4×C8C2×D311yescharacteristic
70#835—62no—
71#832—62no—
72#832—62no—
73#821—22no—
74#810—62no—
75#809—62no—
76#809—62no—
77#808—62no—
78#808—62no—
79C4×C3⋊C8—31no—
80C4×C3⋊C8—31no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—31no—
83C4×C3⋊C8—61no—
84C4×C3⋊C8—61no—
85C22×C3×D3—41no—
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C3×Dic3—41no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—41no—
92C3×D12—42no—
93C3×D12—42no—
94C3×D12—42no—
95C3×Dic6—42no—
96C3×Dic6—42no—
97C3×Dic6—42no—
98C32×C8—22no—
99C3⋊(C3⋊C8)—22no—
100C3⋊(C3⋊C8)—22no—
101#498—91no—
102#494—31no—
103#487—91no—
104#486—31no—
105#486—91no—
106#486—91no—
107#322—91no—
108C2×C3×Q8—61no—
109C2×C3×Q8—61no—
110C2×C3×Q8—61no—
111C2×C3×D4—61no—
112C2×C3×D4—61no—
113C2×C3×D4—61no—
114C2×D12—21no—
115C2×D12—21no—
116C2×D12—21no—
117C2×Dic6—21no—
118C2×Dic6—21no—
119C2×Dic6—21no—
120C3×Q16—124no—
121C2×C3×C8—22no—
122C2×C3×C8#6712yes—
123C2×C3×C8#6712yes—
124C3×C4⋊C4—61no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—61no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C42—21no—
131C3×C42C22×D311yescharacteristic
132C3×C42C22×D311yescharacteristic
133C4⋊Dic3—21no—
134C4⋊Dic3—21no—
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C2×C3⋊C8—32no—
140C2×C3⋊C8—32no—
141C2×C3⋊C8—32no—
142C2×C3⋊C8—32no—
143C2×C3⋊C8—62no—
144C2×C3⋊C8—62no—
145Dic12—44no—
146C22×C32#12711yescharacteristic
147C2×C3×D3—81no—
148C2×C3×D3—81no—
149C2×C3×D3—81no—
150C32×C4#13512yes—
151C32×C4AGL(1,ℤ/8)12yes—
152C32×C4#13712yes—
153C3×Dic3—81no—
154C3×Dic3—81no—
155C3×Dic3—81no—
156C2×Q16—62no—
157C4⋊Q8—31no—
158C4⋊Q8—31no—
159C4⋊Q8—31no—
160#127—31no—
161#106—182no—
162#103—182no—
163#102—62no—
164#102—182no—
165#102—182no—
166C4×C8—91no—
167C4×C8—91no—
168C4×C8D3211yescharacteristic
169C23×C3—121no—
170C22×D3—41no—
171C3×Q8—122no—
172C3×Q8—122no—
173C3×Q8—122no—
174C3×D4—122no—
175C3×D4—122no—
176C3×D4—122no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—121no—
181C2×C3×C4—121no—
182C2×C3×C4—121no—
183C2×C3×C4D3×D411yescharacteristic
184C2×C3×C4D3×D411yescharacteristic
185C2×C3×C4D3×D411yescharacteristic
186C2×C3×C4D3×D411yescharacteristic
187C2×C3×C4C2×#6711yescharacteristic
188C2×C3×C4C2×#6711yescharacteristic
189C2×Dic3—41no—
190C2×Dic3—41no—
191C2×Dic3—41no—
192D12—42no—
193D12—42no—
194D12—42no—
195Dic6—42no—
196Dic6—42no—
197Dic6—42no—
198C3×C8—22no—
199C3×C8—22no—
200C3×C8—42no—
201C3⋊C8—64no—
202C3⋊C8—62no—
203C3⋊C8—62no—
204C3⋊C8—62no—
205C3⋊C8—62no—
206C3⋊C8—122no—
207C2×C32#49511yescharacteristic
208C2×C32#49611yescharacteristic
209C2×C32#49711yescharacteristic
210C3×D3—161no—
211C2×Q8—61no—
212C2×Q8—61no—
213C2×Q8—61no—
214C2×D4—61no—
215C2×D4—61no—
216C2×D4—61no—
217Q16—124no—
218C2×C8—92no—
219C2×C8—92no—
220C2×C8#62512yes—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—61no—
224C4⋊C4—61no—
225C4⋊C4—61no—
226C4⋊C4—61no—
227C42C2×D3211yescharacteristic
228C22×C3—21no—
229C22×C3—241no—
230C22×C3—241no—
231C22×C3—241no—
232C22×C3#94011yescharacteristic
233C22×C3#94011yescharacteristic
234C2×D3—81no—
235C2×D3—81no—
236C2×D3—81no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—241no—
241C3×C4—241no—
242C3×C4—241no—
243C3×C4#91212yes—
244C3×C4#91512yes—
245C3×C4#91812yes—
246C3×C4#91912yes—
247C3×C4#93212yes—
248C3×C4#94912yes—
249Dic3—81no—
250Dic3—81no—
251Dic3—81no—
252C32#172011yescharacteristic, complemented, Sylow
253C23—121no—
254Q8—122no—
255Q8—122no—
256Q8—122no—
257D4—122no—
258D4—122no—
259D4—122no—
260C2×C4—121no—
261C2×C4—121no—
262C2×C4—121no—
263C2×C4#380211yescharacteristic
264C2×C4#380211yescharacteristic
265C2×C4C2×#62511yescharacteristic
266C8—22no—
267C8—182no—
268C8—182no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—481no—
273C2×C3#505811yescharacteristic
274C2×C3#507411yescharacteristic
275C2×C3#515511yescharacteristic
276C2×C3#516711yescharacteristic
277C2×C3#519011yescharacteristic
278C2×C3#519111yescharacteristic
279D3—161no—
280C22—241no—
281C22—241no—
282C22—241no—
283C22#6391411yescharacteristic
284C4—241no—
285C4—241no—
286C4—241no—
287C4#6381012yes—
288C4#6381112yes—
289C4#6382312yes—
290C3—21no—
291C3#7119311yescharacteristic, complemented
292C3#7130011yescharacteristic, complemented
293C2—481no—
294C2#1059035411yescharacteristic
295C2#1059086911yescharacteristic
296C2#1059087011yescharacteristic
subgroupG/H
centerC22#63914
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
prime radicalC3×#874C22
hypercenterC4×C8D32
hypocenterC32#1720
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. C3×#4699C2semidirect
3. #10590309C2semidirect
4. #10590290C2semidirect
7. #10589320C2semidirect
33. #4699D3semidirect
252. C32#1720semidirect
291. C3#71193semidirect
292. C3#71300semidirect

Maximal subgroups

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

subgroupindex
C3×#46992
C3×#46942
#105903092
#105902902
#105902772
#105893202
#713003
#711933