Finite Group Databasebeta

← #11790620

Subgroups — #11790620

Order 1152.

745 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 745 conjugacy classes of subgroups — too many to draw. Only its 180 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
1C2×#63873C211yesmaximal, characteristic
2C2×C8×C3⋊Dic3C211yesmaximal, characteristic
3C2×C3×#816C212yesmaximal
4#10591359C211yesmaximal, characteristic
5C2×#63565C212yesmaximal
6#70225—32nomaximal
7C22×C3×Dic6C2212yes—
8C22×C32×C8C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×#3724—22no—
13C2×#3724—22no—
14#63873—22no—
15#63873C414yescomplemented
16C8×C3⋊Dic3—22no—
17C3×#816—24no—
18#63565—24no—
19C2×#944—32no—
20C2×C3×#103—32no—
21C2×#835—32no—
22C2×#816D312yes—
23C2×C8×Dic3—32no—
24C2×C8×Dic3—61no—
25#4975—32no—
26C2×#810—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⋊Dic3C2×C412yes—
41C4×C3⋊Dic3D412yes—
42C2×C3⋊(C3⋊C8)—21no—
43C2×C3⋊(C3⋊C8)—21no—
44C2×C3⋊(C3⋊C8)D412yes—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3—22no—
47#3724—28no—
48#3724—44no—
49#1956—91noSylow
50C22×C3×Q8—32no—
51C22×Dic6C2×D312yes—
52C22×C3×C8—21no—
53C22×C3×C8C2×D312yes—
54C2×C3×C4⋊C4—32no—
55#944—38no—
56#944—64no—
57C2×C4⋊Dic3C2×D312yes—
58C2×Dic3⋊C4—64no—
59C2×Dic3⋊C4—64no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62C22×C3⋊C8—32no—
63C22×C3⋊C8—61no—
64C3×#103—64no—
65#835—64no—
66#816—24no—
67C8×Dic3—64no—
68C8×Dic3—64no—
69#810—64no—
70C23×C32C2×D411yescharacteristic
71C2×C32×C4C22×C411yescharacteristic
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4#4111yescharacteristic
76C2×C32×C4#4111yescharacteristic
77C2×C3⋊Dic3C22⋊C414yes—
78C2×C3⋊Dic3SD1614yes—
79C2×C3⋊Dic3Q1614yes—
80C2×C3×Dic3—24no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—44no—
85C3×Dic6—24no—
86C3×Dic6—24no—
87C3×Dic6—42no—
88C3×Dic6—42no—
89C32×C8—22no—
90C3⋊(C3⋊C8)—22no—
91C2×C4⋊Q8—91no—
92C2×#103—32no—
93C2×#103—92no—
94C2×C4×C8—91no—
95#384—91no—
96C2×C3×Q8—34no—
97C2×C3×Q8—62no—
98C2×C3×Q8—62no—
99C2×C3×Q8—62no—
100C2×C3×Q8—62no—
101C2×C3×Q8—62no—
102C22×C3×C4—21no—
103C22×C3×C4—62no—
104C22×C3×C4—62no—
105C22×C3×C4C22×D312yes—
106C22×Dic3—22no—
107C22×Dic3—22no—
108C22×Dic3—34no—
109C22×Dic3—62no—
110C2×Dic6—22no—
111C2×Dic6—22no—
112C2×Dic6—22no—
113C2×Dic6—22no—
114C2×Dic6—22no—
115C2×Dic6C4×D314yes—
116C2×C3×C8—22no—
117C2×C3×C8—22no—
118C2×C3×C8—22no—
119C2×C3×C8—22no—
120C2×C3×C8—22no—
121C2×C3×C8#6714yes—
122C3×C4⋊C4—62no—
123C3×C4⋊C4—62no—
124C4⋊Dic3—22no—
125C4⋊Dic3—22no—
126Dic3⋊C4—616no—
127Dic3⋊C4—128no—
128C4×Dic3—34no—
129C4×Dic3—34no—
130C4×Dic3—62no—
131C4×Dic3—62no—
132C2×C3⋊C8—34no—
133C2×C3⋊C8—62no—
134C2×C3⋊C8—62no—
135C2×C3⋊C8—62no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—62no—
138C22×C32C2×C22⋊C411yescharacteristic
139C22×C32#12411yescharacteristic
140C22×C32#12711yescharacteristic
141C22×C32C2×SD1612yes—
142C22×C32C2×Q1612yes—
143C32×C4C4×D411yescharacteristic
144C32×C4C4×D411yescharacteristic
145C32×C4#12111yescharacteristic
146C32×C4#12111yescharacteristic
147C3⋊Dic3#10318yescomplemented
148C3×Dic3—44no—
149C3×Dic3—82no—
150C22×Q8—32no—
151C22×C8—91no—
152C22×C8D3211yescharacteristic
153C4⋊Q8—94no—
154C4⋊Q8—182no—
155C2×C4⋊C4—32no—
156C2×C4⋊C4—182no—
157C2×C4⋊C4—182no—
158C2×C42—91no—
159#103—64no—
160#103—184no—
161C4×C8—182no—
162C23×C3—21no—
163C23×C3D3×D412yes—
164C3×Q8—64no—
165C3×Q8—64no—
166C3×Q8—122no—
167C3×Q8—122no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—64no—
175C2×C3×C4—122no—
176C2×C3×C4—122no—
177C2×C3×C4—124no—
178C2×C3×C4—122no—
179C2×C3×C4C2×C4×D312yes—
180C2×C3×C4#23512yes—
181C2×C3×C4D3×D412yes—
182C2×C3×C4D3×D412yes—
183C2×C3×C4#23712yes—
184C2×C3×C4C2×#6712yes—
185C2×Dic3—24no—
186C2×Dic3—38no—
187C2×Dic3—38no—
188C2×Dic3—38no—
189C2×Dic3—42no—
190C2×Dic3—42no—
191C2×Dic3—44no—
192C2×Dic3—42no—
193C2×Dic3—64no—
194C2×Dic3—64no—
195C2×Dic3—64no—
196Dic6—24no—
197Dic6—24no—
198Dic6—42no—
199Dic6—42no—
200C3×C8—24no—
201C3×C8—24no—
202C3⋊C8—64no—
203C3⋊C8—64no—
204C2×C32#39011yescharacteristic
205C2×C32C2×#10312yes—
206C2×C32#48712yes—
207C2×C32#49211yescharacteristic
208C2×C32#49411yescharacteristic
209C2×Q8—34no—
210C2×Q8—62no—
211C2×Q8—62no—
212C2×Q8—62no—
213C2×Q8—62no—
214C2×Q8—62no—
215C22×C4—62no—
216C22×C4—62no—
217C22×C4—92no—
218C22×C4C2×D3211yescharacteristic
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—92no—
222C2×C8—181no—
223C2×C8—181no—
224C2×C8#62512yes—
225C4⋊C4—62no—
226C4⋊C4—62no—
227C4⋊C4—188no—
228C4⋊C4—364no—
229C42—92no—
230C42—92no—
231C22×C3—22no—
232C22×C3—22no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3D3×C22⋊C412yes—
237C22×C3#88512yes—
238C22×C3D3×SD1614yes—
239C22×C3D3×Q1614yes—
240C22×C3#94012yes—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—124no—
246C3×C4—242no—
247C3×C4#67⋊C412yes—
248C3×C4#88412yes—
249C3×C4C4×#6712yes—
250C3×C4#93912yes—
251Dic3—316no—
252Dic3—44no—
253Dic3—68no—
254Dic3—82no—
255C32#195611yescharacteristic, complemented, Sylow
256C23#380211yescharacteristic
257Q8—64no—
258Q8—64no—
259Q8—122no—
260Q8—122no—
261C2×C4—64no—
262C2×C4—94no—
263C2×C4—94no—
264C2×C4—94no—
265C2×C4—122no—
266C2×C4—122no—
267C2×C4—124no—
268C2×C4—122no—
269C2×C4#379811yescharacteristic
270C2×C4C4×D3211yescharacteristic
271C2×C4#380211yescharacteristic
272C2×C4#380511yescharacteristic
273C2×C4C2×#62511yescharacteristic
274C2×C4#381111yescharacteristic
275C8—22no—
276C8—182no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—22no—
280C2×C3—21no—
281C2×C3—22no—
282C2×C3#479214yes—
283C2×C3D3×#10314yes—
284C2×C3#495712yes—
285C2×C3#517512yes—
286C2×C3#518312yes—
287C22#6379612yes—
288C22#6380212yes—
289C22#6391411yescharacteristic
290C22#6391511yescharacteristic
291C22#6392111yescharacteristic
292C4—98no—
293C4—124no—
294C4—242no—
295C4C4×#62511yescharacteristic
296C4#6390211yescharacteristic
297C4#6391211yescharacteristic
298C4#6398011yescharacteristic
299C3—21no—
300C3#7022512yescomplemented
301C2#1059067212yes—
302C2#1059088411yescharacteristic
303C2#1059090112yes—
304C2#1059090511yescharacteristic
305C2#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#1956
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
15. #63873C4semidirect
147. C3⋊Dic3#103semidirect
255. C32#1956semidirect
300. C3#70225semidirect

Maximal subgroups

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

subgroupindex
C2×#638732
C2×C8×C3⋊Dic32
C2×C3×#8162
#105913592
C2×#635652
#702253