Finite Group Databasebeta

← #11791006

Subgroups — #11791006

Order 1152.

705 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 705 conjugacy classes of subgroups — too many to draw. Only its 168 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
1C22×#3718C211yesmaximal, characteristic
2C2×C8×C3⋊Dic3C211yesmaximal, characteristic
3C2×C3×#816C212yesmaximal
4#10591221C212yesmaximal
5C2×#63576C211yesmaximal, characteristic
6#70258—32nomaximal
7C22×C3×Dic6C2212yes—
8C22×C32×C8C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×#3718—22no—
13C2×#3718—22no—
14C2×#3718C414yescomplemented
15C8×C3⋊Dic3—22no—
16C3×#816—24no—
17#63579—24no—
18#63576—22no—
19C22×#216—32no—
20C2×C3×#103—32no—
21#5229—32no—
22C2×#816D312yes—
23C2×C8×Dic3—32no—
24C2×C8×Dic3—61no—
25#4973—32no—
26C2×#807—32no—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3D412yes—
29C22×C3×Dic3—22no—
30C22×C3×Dic3—22no—
31C2×C3×Dic6—22no—
32C2×C3×Dic6—22no—
33C2×C3×Dic6—22no—
34C2×C3×Dic6—22no—
35C2×C3×Dic6—22no—
36C2×C3×Dic6C2×C414yes—
37C2×C32×C8—21no—
38C2×C32×C8—21no—
39C2×C32×C8D412yes—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3—21no—
42C2×C3⋊(C3⋊C8)C2×C412yes—
43C2×C3⋊(C3⋊C8)D412yes—
44C2×C3⋊(C3⋊C8)D412yes—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3—22no—
47#3718—28no—
48#1969—91noSylow
49C22×C3×Q8—32no—
50C22×Dic6C2×D312yes—
51C22×C3×C8—21no—
52C22×C3×C8C2×D312yes—
53C2×C3×C4⋊C4—32no—
54C2×#216—38no—
55C2×#216—64no—
56C2×#216—64no—
57C2×C4⋊Dic3C2×D312yes—
58C2×C4×Dic3—32no—
59C2×C4×Dic3—61no—
60C22×C3⋊C8—32no—
61C22×C3⋊C8—61no—
62C3×#103—64no—
63C3⋊#95—64no—
64C3⋊#95—64no—
65#816—24no—
66C8×Dic3—64no—
67C8×Dic3—64no—
68#807—64no—
69C23×C32C2×D411yescharacteristic
70C2×C32×C4C22×C411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4#4111yescharacteristic
75C2×C32×C4#4111yescharacteristic
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3Q1614yescomplemented
79C2×C3×Dic3—24no—
80C2×C3×Dic3—42no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C2×C3×Dic3—44no—
84C3×Dic6—24no—
85C3×Dic6—24no—
86C3×Dic6—42no—
87C3×Dic6—42no—
88C32×C8—22no—
89C3⋊(C3⋊C8)C22⋊C414yes—
90C22×Q16—91no—
91C2×#107—91no—
92C2×#103—32no—
93C2×C4×C8—91no—
94#391—92no—
95C2×C3×Q8—34no—
96C2×C3×Q8—62no—
97C2×C3×Q8—62no—
98C2×C3×Q8—62no—
99C2×C3×Q8—62no—
100C2×C3×Q8—62no—
101C22×C3×C4—21no—
102C22×C3×C4—62no—
103C22×C3×C4—62no—
104C22×C3×C4C22×D312yes—
105C22×Dic3—22no—
106C22×Dic3—22no—
107C22×Dic3—34no—
108C22×Dic3—62no—
109C2×Dic6—22no—
110C2×Dic6—22no—
111C2×Dic6—22no—
112C2×Dic6—22no—
113C2×Dic6—22no—
114C2×Dic6C4×D314yes—
115C2×C3×C8—22no—
116C2×C3×C8—22no—
117C2×C3×C8—22no—
118C2×C3×C8—22no—
119C2×C3×C8—22no—
120C2×C3×C8#6714yes—
121C3×C4⋊C4—62no—
122C3×C4⋊C4—62no—
123#216—616no—
124C4⋊Dic3—22no—
125C4⋊Dic3—22no—
126C4×Dic3—62no—
127C4×Dic3—62no—
128C4×Dic3—62no—
129C4×Dic3—62no—
130C2×C3⋊C8—34no—
131C2×C3⋊C8—34no—
132C2×C3⋊C8—34no—
133C2×C3⋊C8—62no—
134C2×C3⋊C8—62no—
135C2×C3⋊C8—62no—
136C22×C32C4×D411yescharacteristic
137C22×C32#12111yescharacteristic
138C22×C32#12711yescharacteristic
139C22×C32C2×Q1612yes—
140C22×C32#13512yes—
141C32×C4C2×C22⋊C411yescharacteristic
142C32×C4C4×D411yescharacteristic
143C32×C4#12111yescharacteristic
144C32×C4#12411yescharacteristic
145C3⋊Dic3—24no—
146C3×Dic3—44no—
147C3×Dic3—82no—
148C22×Q8—32no—
149C2×Q16—94no—
150C2×Q16—182no—
151C2×Q16—182no—
152C22×C8—91no—
153C22×C8D3211yescharacteristic
154C2×C4⋊C4—32no—
155C2×C42—91no—
156#107—182no—
157#103—64no—
158C4×C8—182no—
159#95—184no—
160C23×C3—21no—
161C23×C3D3×D412yes—
162C3×Q8—64no—
163C3×Q8—64no—
164C3×Q8—122no—
165C3×Q8—122no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—64no—
173C2×C3×C4—122no—
174C2×C3×C4—122no—
175C2×C3×C4—124no—
176C2×C3×C4—122no—
177C2×C3×C4C2×C4×D312yes—
178C2×C3×C4#23512yes—
179C2×C3×C4D3×D412yes—
180C2×C3×C4D3×D412yes—
181C2×C3×C4#23712yes—
182C2×C3×C4C2×#6712yes—
183C2×Dic3—24no—
184C2×Dic3—38no—
185C2×Dic3—42no—
186C2×Dic3—42no—
187C2×Dic3—44no—
188C2×Dic3—42no—
189C2×Dic3—64no—
190C2×Dic3—64no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194Dic6—24no—
195Dic6—24no—
196Dic6—42no—
197Dic6—42no—
198C3×C8—24no—
199C3×C8—24no—
200C3⋊C8—38no—
201C3⋊C8—64no—
202C2×C32#39011yescharacteristic
203C2×C32C4×Q1612yes—
204C2×C32#46712yes—
205C2×C32#49411yescharacteristic
206C2×C32#49511yescharacteristic
207C2×Q8—34no—
208C2×Q8—62no—
209C2×Q8—62no—
210C2×Q8—62no—
211C2×Q8—62no—
212C2×Q8—62no—
213C22×C4—62no—
214C22×C4—62no—
215C22×C4—92no—
216C22×C4C2×D3211yescharacteristic
217Q16—188no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—92no—
221C2×C8—92no—
222C2×C8—92no—
223C2×C8#62512yes—
224C4⋊C4—62no—
225C4⋊C4—62no—
226C42—181no—
227C42—181no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3#67⋊C412yes—
234C22×C3#88412yes—
235C22×C3#91614yes—
236C22×C3D3×Q1614yes—
237C22×C3#94012yes—
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—124no—
243C3×C4—242no—
244C3×C4D3×C22⋊C412yes—
245C3×C4#88512yes—
246C3×C4C4×#6712yes—
247C3×C4#93912yes—
248Dic3—44no—
249Dic3—68no—
250Dic3—68no—
251Dic3—82no—
252C32#196911yescharacteristic, complemented, Sylow
253C23#380211yescharacteristic
254Q8—64no—
255Q8—64no—
256Q8—122no—
257Q8—122no—
258C2×C4—64no—
259C2×C4—94no—
260C2×C4—122no—
261C2×C4—122no—
262C2×C4—124no—
263C2×C4—122no—
264C2×C4—182no—
265C2×C4—182no—
266C2×C4#379811yescharacteristic
267C2×C4C4×D3211yescharacteristic
268C2×C4#380211yescharacteristic
269C2×C4#380511yescharacteristic
270C2×C4C2×#62511yescharacteristic
271C2×C4#381111yescharacteristic
272C8—22no—
273C8—94no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3#479014yes—
280C2×C3#481314yes—
281C2×C3#495712yes—
282C2×C3#516812yes—
283C2×C3#518312yes—
284C22#6380212yes—
285C22#6380912yes—
286C22#6390211yescharacteristic
287C22#6391211yescharacteristic
288C22#6391411yescharacteristic
289C4—124no—
290C4—184no—
291C4—242no—
292C4C4×#62511yescharacteristic
293C4#6391511yescharacteristic
294C4#6392111yescharacteristic
295C4#6398011yescharacteristic
296C3—21no—
297C3#7025812yescomplemented
298C2#1059079012yes—
299C2#1059085512yes—
300C2#1059086711yescharacteristic
301C2#1059090511yescharacteristic
302C2#1059138511yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1969
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
14. C2×#3718C4semidirect
78. C2×C3⋊Dic3Q16semidirect
252. C32#1969semidirect
297. C3#70258semidirect

Maximal subgroups

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

subgroupindex
C22×#37182
C2×C8×C3⋊Dic32
C2×C3×#8162
#105912212
C2×#635762
#702583