Finite Group Databasebeta

← #11797922

Subgroups — #11797922

Order 1152.

305 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 305 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4853C211yesmaximal, characteristic, complemented
2#10590916C211yesmaximal, characteristic
3#10590636C211yesmaximal, characteristic
4#10589353C211yesmaximal, characteristic, complemented
5C3×#4488C211yesmaximal, characteristic
6#10589130C211yesmaximal, characteristic, complemented
7#10589105C211yesmaximal, characteristic, complemented
8#70917—31nomaximal
9#69248—31nomaximal
10C2×C3×Dic12C2211yescharacteristic
11C3×#904C2211yescharacteristic
12C3×#887—21no—
13#63814—21no—
14C32×#106C2211yescharacteristic
15#63646C2211yescharacteristic
16#63639C2211yescharacteristic
17C3×#815C2211yescharacteristic
18C3×#812C2211yescharacteristic
19C3×#810—21no—
20#63569—21no—
21#63550C412yescomplemented
22#63547C412yescomplemented
23C3×#441—31no—
24#5197—31no—
25#5195—31no—
26#5179—31no—
27#4853D311yescharacteristic, complemented
28#4717—31no—
29C3×#360—31no—
30#4565—31no—
31#4517—31no—
32#4512—31no—
33#4488D311yescharacteristic
34#4487—31no—
35#4487—31no—
36#4487—61no—
37#4466—31no—
38C3×#235—21no—
39C2×C3×Dic6—21no—
40C2×C32×C8C2311yescharacteristic
41C32×C4⋊C4—21no—
42#3748—21no—
43C3×Dic3⋊C4—41no—
44C3×C4×Dic3—41no—
45C3×C4×Dic3D411yescharacteristic
46C2×C3×C3⋊C8D411yescharacteristic
47C3×Dic12—21no—
48C3×Dic12C2×C411yescharacteristic
49C3×Dic12C2×C412yes—
50C3×D24C2×C411yescharacteristic
51C3×#204—21no—
52#3711—41no—
53D3×C3⋊C8—41no—
54C3⋊(C3⋊C16)C2×C412yes—
55C3×C3⋊C16—21no—
56#2180—91noSylow
57C3×#135—31no—
58C2×C3×Q16—31no—
59C3×C4×Q8—61no—
60#948—61no—
61C2×Dic12C2×D311yescharacteristic
62#904C2×D311yescharacteristic
63#901—61no—
64#887—21no—
65C3×M32—31no—
66C3×#106—21no—
67C3×#106C2×D311yescharacteristic
68C3×#106C2×D311yescharacteristic
69C3×#103—61no—
70C3×#97—31no—
71#837—61no—
72#829—32no—
73#829—32no—
74#828—32no—
75#827—32no—
76#819—31no—
77#819—31no—
78#819—61no—
79#815C2×D311yescharacteristic
80#812—31no—
81#812—31no—
82#812—61no—
83#812C2×D311yescharacteristic
84#810—21no—
85#805—61no—
86C2×C32×C4—41no—
87C2×C32×C4C2×D411yescharacteristic
88C3×#67—41no—
89C2×C3×Dic3—21no—
90C2×C3×Dic3—41no—
91C3×D12—21no—
92C3×C4×D3—41no—
93C3×Dic6—21no—
94C3×Dic6—22no—
95C3×Dic6—41no—
96C32×C8C22×C411yescharacteristic
97C32×C8#4111yescharacteristic
98C3⋊(C3⋊C8)—41no—
99C3×C3⋊C8—21no—
100#510—91no—
101#444—91no—
102#441—31no—
103#365—91no—
104#362—91no—
105#360—31no—
106#347—91no—
107C3×#41—61no—
108C2×C3×Q8—61no—
109#235—21no—
110C2×Dic6—21no—
111C3×Q16—32no—
112C3×Q16—31no—
113C3×Q16—61no—
114C3×SD16—61no—
115C3×D8—31no—
116C2×C3×C8—21no—
117C2×C3×C8—31no—
118C2×C3×C8C22×D311yescharacteristic
119C2×C3×C8C22×D311yescharacteristic
120C3×C4⋊C4—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4—41no—
123C3×C4⋊C4—121no—
124C3×C42—31no—
125C3×C42—121no—
126Dic3⋊C4—41no—
127C4×Dic3—41no—
128C4×Dic3#6711yescharacteristic
129#208—61no—
130#208—61no—
131#208—121no—
132#208—121no—
133C2×C3⋊C8—121no—
134C2×C3⋊C8#6711yescharacteristic
135Dic12—21no—
136Dic12C4×D312yes—
137Dic12C4×D311yescharacteristic
138D24C4×D311yescharacteristic
139#204—21no—
140ΓL(1,𝔽25)—121no—
141D3×C8—121no—
142C3×C16—61no—
143C3⋊C16—21no—
144C3⋊C16—32no—
145C3⋊C16—32no—
146C3⋊C16—62no—
147C22×C32AGL(1,ℤ/8)11yescharacteristic
148C2×C3×D3—41no—
149C32×C4—81no—
150C32×C4C4×D411yescharacteristic
151C32×C4AGL(1,ℤ/8)11yescharacteristic
152C3×Dic3—41no—
153C3×Dic3—42no—
154C3×Dic3—41no—
155#135—31no—
156C2×Q16—31no—
157#131—181no—
158C4×Q8—61no—
159Q32—92no—
160SD32—92no—
161M32—31no—
162M32—91no—
163#108—91no—
164#106D3211yescharacteristic
165#104—181no—
166#103—61no—
167#97—31no—
168C3×Q8—62no—
169C3×Q8—61no—
170C3×Q8—121no—
171C3×D4—61no—
172C3×D4—121no—
173C2×C3×C4—21no—
174C2×C3×C4—41no—
175C2×C3×C4—41no—
176C2×C3×C4—61no—
177C2×C3×C4—81no—
178C2×C3×C4—121no—
179C2×C3×C4—121no—
180C2×C3×C4D3×D411yescharacteristic
181C2×C3×C4C2×#6711yescharacteristic
182#67—41no—
183C2×Dic3—21no—
184C2×Dic3—41no—
185D12—21no—
186C4×D3—41no—
187Dic6—21no—
188Dic6—22no—
189Dic6—41no—
190C3×C8—21no—
191C3×C8—21no—
192C3×C8—61no—
193C3×C8C2×C4×D311yescharacteristic
194C3×C8C2×C4×D311yescharacteristic
195C3×C8#23511yescharacteristic
196C3×C8#23711yescharacteristic
197C3⋊C8—21no—
198C3⋊C8—121no—
199C3⋊C8—121no—
200C3⋊C8—241no—
201C2×C32—21no—
202C2×C32#44211yescharacteristic
203C3×D3—81no—
204#41—61no—
205C2×Q8—61no—
206Q16—32no—
207Q16—31no—
208Q16—61no—
209SD16—61no—
210D8—31no—
211M16—181no—
212M16—361no—
213C2×C8—31no—
214C2×C8—361no—
215C2×C8C2×D3211yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—121no—
218C42—31no—
219C42—121no—
220C16—61no—
221C16—92no—
222C22×C3—21no—
223C22×C3—121no—
224C22×C3#91111yescharacteristic
225C22×C3#93211yescharacteristic
226C2×D3—41no—
227C3×C4—21no—
228C3×C4—21no—
229C3×C4—81no—
230C3×C4—81no—
231C3×C4—121no—
232C3×C4—121no—
233C3×C4—122no—
234C3×C4—161no—
235C3×C4#67⋊C411yescharacteristic
236C3×C4#91411yescharacteristic
237C3×C4C4×#6711yescharacteristic
238C3×C4#94911yescharacteristic
239Dic3—41no—
240Dic3—42no—
241Dic3—41no—
242C32#218011yescharacteristic, complemented, Sylow
243Q8—61no—
244Q8—62no—
245Q8—121no—
246D4—61no—
247D4—121no—
248C2×C4—41no—
249C2×C4—61no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4D3×#6711yescharacteristic
253C8—61no—
254C8—361no—
255C8#379511yescharacteristic
256C8C4×D3211yescharacteristic
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—41no—
261C2×C3—241no—
262C2×C3#478511yescharacteristic
263C2×C3#501411yescharacteristic
264D3—81no—
265C22—121no—
266C22#6393211yescharacteristic
267C4—81no—
268C4—121no—
269C4—121no—
270C4—122no—
271C4#6387911yescharacteristic
272C4#6393911yescharacteristic
273C3—21no—
274C3#6924811yescharacteristic, complemented
275C3#7091711yescharacteristic, complemented
276C2—21no—
277C2—241no—
278C2#1059045511yescharacteristic
subgroupG/H
centerC2#10590455
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#106C22
socleC2×C32#442
prime radicalC3×#904C22
cosocleC2×C32×C8C23
hypercenter#106D32
hypocenterC32#2180
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C3×#4853C2semidirect
4. #10589353C2semidirect
6. #10589130C2semidirect
7. #10589105C2semidirect
21. #63550C4semidirect
22. #63547C4semidirect
27. #4853D3semidirect
242. C32#2180semidirect
274. C3#69248semidirect
275. C3#70917semidirect

Maximal subgroups

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

subgroupindex
C3×#48532
#105909162
#105906362
#105893532
C3×#44882
#105891302
#105891052
#709173
#692483