Finite Group Databasebeta

← #11782678

Subgroups — #11782678

Order 1152.

473 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 473 conjugacy classes of subgroups — too many to draw. Only its 100 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×#4694C211yesmaximal, characteristic, complemented
2C3×#4693C211yesmaximal, characteristic, complemented
3#10590375C211yesmaximal, characteristic, complemented
4#10590352C211yesmaximal, characteristic
5#10590309C211yesmaximal, characteristic, complemented
6#10590277C211yesmaximal, characteristic, complemented
7#10589320C211yesmaximal, characteristic, complemented
8#71259—31nomaximal
9#71185—31nomaximal
10C2×C3×#204—22no—
11C3×#874C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C2×#3715—22no—
16C2×#3713—22no—
17C32×C4×C8C2211yescharacteristic
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C4×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×#821—22no—
21#63574—22no—
22#63562—22no—
23C3×#492—31no—
24C3×#486—31no—
25#5088—31no—
26#5085—31no—
27#5080—31no—
28#5080—31no—
29#5076—31no—
30#5073—31no—
31#5073—31no—
32#5070—31no—
33#4694D311yescharacteristic, complemented
34#4693D311yescharacteristic, complemented
35#4454—31no—
36#4454—31no—
37#4454—61no—
38C2×C3×D12—21no—
39C2×C3×D12—21no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8D412yes—
47C32×C42C2311yescharacteristic
48C2×C3⋊(C3⋊C8)D412yes—
49C2×C3⋊(C3⋊C8)D412yes—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×#204—44no—
55#3715—44no—
56#3713—44no—
57#1715—91noSylow
58C2×C3×SD16—62no—
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8—31no—
61C3×#127—31no—
62C3×#127—31no—
63C2×#215—62no—
64C2×#214—62no—
65C2×#213—62no—
66C2×#213—62no—
67C2×#204—22no—
68#874C2×D311yescharacteristic
69#874C2×D311yescharacteristic
70#869C2×D311yescharacteristic
71#869C2×D311yescharacteristic
72C3×#102—62no—
73C3×C4×C8—21no—
74C3×C4×C8C2×D311yescharacteristic
75C3×C4×C8C2×D311yescharacteristic
76#832—62no—
77#821—22no—
78#809—62no—
79#808—62no—
80#808—62no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—31no—
83C4×C3⋊C8—31no—
84C4×C3⋊C8—31no—
85C4×C3⋊C8—61no—
86C4×C3⋊C8—61no—
87C22×C3×D3—41no—
88C22×C3×D3—41no—
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C3×Dic3—41no—
93C2×C3×Dic3—41no—
94C3×D12—42no—
95C3×D12—42no—
96C3×D12—42no—
97C3×D12—42no—
98C3×D12—42no—
99C3×D12—42no—
100C3×Dic6—42no—
101C3×Dic6—42no—
102C32×C8—22no—
103C3⋊(C3⋊C8)—22no—
104C3⋊(C3⋊C8)SD1614yescomplemented
105#498—91no—
106#493—91no—
107#492—31no—
108#492—91no—
109#486—31no—
110#486—91no—
111#322—91no—
112C2×C3×Q8—61no—
113C2×C3×Q8—61no—
114C2×C3×D4—61no—
115C2×C3×D4—61no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C2×C3×D4—61no—
119C2×C3×D4—61no—
120C2×D12—21no—
121C2×D12—21no—
122C2×D12—21no—
123C2×D12—21no—
124C2×D12—21no—
125C2×D12—21no—
126C2×Dic6—21no—
127C2×Dic6—21no—
128C3×SD16—124no—
129C2×C3×C8—22no—
130C2×C3×C8#6712yes—
131C2×C3×C8#6712yes—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C42—21no—
137C3×C42C22×D311yescharacteristic
138C3×C42C22×D311yescharacteristic
139#215—124no—
140#214—124no—
141#213—124no—
142#213—124no—
143C4⋊Dic3—21no—
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C2×C3⋊C8—32no—
148C2×C3⋊C8—32no—
149C2×C3⋊C8—32no—
150C2×C3⋊C8—32no—
151C2×C3⋊C8—62no—
152C2×C3⋊C8—62no—
153#204—44no—
154C22×C32#12711yescharacteristic
155C2×C3×D3—81no—
156C2×C3×D3—81no—
157C2×C3×D3—81no—
158C2×C3×D3—81no—
159C2×C3×D3—81no—
160C2×C3×D3—81no—
161C32×C4C2×SD1612yes—
162C32×C4AGL(1,ℤ/8)12yes—
163C32×C4AGL(1,ℤ/8)12yes—
164C3×Dic3—81no—
165C3×Dic3—81no—
166C2×SD16—62no—
167C2×SD16—182no—
168C2×D8—182no—
169C4⋊Q8—31no—
170C4⋊Q8—31no—
171#127—31no—
172#127—31no—
173#106—182no—
174#102—62no—
175#102—182no—
176C4×C8—91no—
177C4×C8—91no—
178C4×C8D3211yescharacteristic
179C23×C3—121no—
180C23×C3—121no—
181C22×D3—41no—
182C22×D3—41no—
183C3×Q8—122no—
184C3×Q8—122no—
185C3×D4—122no—
186C3×D4—122no—
187C3×D4—122no—
188C3×D4—122no—
189C3×D4—122no—
190C3×D4—122no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—121no—
195C2×C3×C4—121no—
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4D3×D411yescharacteristic
198C2×C3×C4D3×D411yescharacteristic
199C2×C3×C4D3×D411yescharacteristic
200C2×C3×C4C2×#6711yescharacteristic
201C2×C3×C4C2×#6711yescharacteristic
202C2×Dic3—41no—
203C2×Dic3—41no—
204D12—42no—
205D12—42no—
206D12—42no—
207D12—42no—
208D12—42no—
209D12—42no—
210Dic6—42no—
211Dic6—42no—
212C3×C8—22no—
213C3×C8—22no—
214C3×C8—42no—
215C3⋊C8—34no—
216C3⋊C8—34no—
217C3⋊C8—64no—
218C3⋊C8—62no—
219C3⋊C8—62no—
220C3⋊C8—122no—
221C2×C32#49211yescharacteristic
222C2×C32#49611yescharacteristic
223C2×C32#49611yescharacteristic
224C3×D3—161no—
225C3×D3—161no—
226C2×Q8—61no—
227C2×Q8—61no—
228C2×D4—61no—
229C2×D4—61no—
230C2×D4—61no—
231C2×D4—61no—
232C2×D4—61no—
233C2×D4—61no—
234SD16—124no—
235SD16—364no—
236D8—364no—
237C2×C8—92no—
238C2×C8—92no—
239C2×C8#62512yes—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C42C2×D3211yescharacteristic
245C22×C3—21no—
246C22×C3—241no—
247C22×C3—241no—
248C22×C3—241no—
249C22×C3—241no—
250C22×C3—241no—
251C22×C3—241no—
252C22×C3#94011yescharacteristic
253C22×C3#94011yescharacteristic
254C2×D3—81no—
255C2×D3—81no—
256C2×D3—81no—
257C2×D3—81no—
258C2×D3—81no—
259C2×D3—81no—
260C3×C4—22no—
261C3×C4—22no—
262C3×C4—22no—
263C3×C4—241no—
264C3×C4—241no—
265C3×C4#91112yes—
266C3×C4D3×SD1612yes—
267C3×C4D3×SD1612yes—
268C3×C4#91412yes—
269C3×C4#93212yes—
270C3×C4#94912yes—
271Dic3—81no—
272Dic3—81no—
273C32#171511yescharacteristic, complemented, Sylow
274C23—121no—
275C23—121no—
276Q8—122no—
277Q8—122no—
278D4—122no—
279D4—122no—
280D4—122no—
281D4—122no—
282D4—122no—
283D4—122no—
284C2×C4—121no—
285C2×C4—121no—
286C2×C4#380211yescharacteristic
287C2×C4#380211yescharacteristic
288C2×C4C2×#62511yescharacteristic
289C8—22no—
290C8—94no—
291C8—182no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—481no—
296C2×C3—481no—
297C2×C3#505811yescharacteristic
298C2×C3#507411yescharacteristic
299C2×C3#515411yescharacteristic
300C2×C3#517511yescharacteristic
301C2×C3#517511yescharacteristic
302C2×C3#517611yescharacteristic
303D3—161no—
304D3—161no—
305C22—241no—
306C22—241no—
307C22—241no—
308C22—241no—
309C22—241no—
310C22—241no—
311C22#6391411yescharacteristic
312C4—241no—
313C4—241no—
314C4#6379612yes—
315C4#6379812yes—
316C4#6382312yes—
317C3—21no—
318C3#7118511yescharacteristic, complemented
319C3#7125911yescharacteristic, complemented
320C2—481no—
321C2—481no—
322C2#1059035411yescharacteristic
323C2#1059088411yescharacteristic
324C2#1059088711yescharacteristic
subgroupG/H
centerC22#63914
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
prime radical#10590352C2
hypercenterC4×C8D32
hypocenterC32#1715
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×#4694C2semidirect
2. C3×#4693C2semidirect
3. #10590375C2semidirect
5. #10590309C2semidirect
6. #10590277C2semidirect
7. #10589320C2semidirect
33. #4694D3semidirect
34. #4693D3semidirect
104. C3⋊(C3⋊C8)SD16semidirect
273. C32#1715semidirect
318. C3#71185semidirect
319. C3#71259semidirect

Maximal subgroups

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

subgroupindex
C3×#46942
C3×#46932
#105903752
#105903522
#105903092
#105902772
#105893202
#712593
#711853