Finite Group Databasebeta

← #11791676

Subgroups — #11791676

Order 1152.

900 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic
2C2×C8×C3⋊Dic3C211yesmaximal, characteristic
3#10592674C211yesmaximal, characteristic
4C32×#340C211yesmaximal, characteristic
5#10589417C211yesmaximal, characteristic
6#10589395C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic
8#68803—34nomaximal
9C22×#634—21no—
10C22×C32×C8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3750—21no—
16C2×#3750—21no—
17C2×#3750—21no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20#64097—22no—
21#64097C414yescomplemented
22C8×C3⋊Dic3—22no—
23C2×#888—34no—
24C2×C8×Dic3—34no—
25#4975—34no—
26C3×#340D314yes—
27#4551—34no—
28#4529—34no—
29#4529—34no—
30C22×C32×C4—21no—
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C2×#634—24no—
38C2×#634—42no—
39C2×#634—42no—
40C2×C32×C8—21no—
41C2×C32×C8—21no—
42C2×C32×C8Q812yescomplemented
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4C2×C412yes—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)C2×C412yes—
51#3750—24no—
52#3750—42no—
53#3750—42no—
54C4×C3⋊Dic3C2×C412yes—
55C4×C3⋊Dic3D412yes—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)Q812yescomplemented
59#1990—91noSylow
60C22×Dic6—64no—
61C22×C3×C8C2×D314yes—
62C2×C3×C4⋊C4C2×D314yes—
63C2×C3×C4⋊C4C2×D314yes—
64C2×C4⋊Dic3—34no—
65C2×C4⋊Dic3—34no—
66C2×Dic3⋊C4—64no—
67C2×Dic3⋊C4—64no—
68C2×Dic3⋊C4—64no—
69C2×C4×Dic3—34no—
70C22×C3⋊C8—34no—
71#888—316no—
72#888—68no—
73C8×Dic3—68no—
74C23×C32C2×D411yescharacteristic
75C2×C32×C4—22no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×Q811yescharacteristic
84C2×C32×C4C2×Q811yescharacteristic
85C2×C32×C4#4111yescharacteristic
86C2×C32×C4#4111yescharacteristic
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3—41no—
93C2×C3⋊Dic3C22⋊C412yes—
94C2×C3⋊Dic3C22⋊C412yes—
95C2×C3⋊Dic3D812yes—
96C2×C3⋊Dic3SD1612yes—
97C2×C3⋊Dic3SD1612yes—
98C2×C3⋊Dic3Q1612yes—
99#634—48no—
100C32×C8—22no—
101C3⋊(C3⋊C8)—22no—
102C2×C4⋊Q8—91no—
103C2×C4×C8—91no—
104#384—91no—
105#340—91no—
106#340—91no—
107#340—91no—
108#340C3⋊D311yescharacteristic
109C22×C3×C4—24no—
110C22×C3×C4—24no—
111C22×C3×C4C22×D314yes—
112C22×Dic3—34no—
113C22×Dic3—34no—
114C22×Dic3—64no—
115C22×Dic3—64no—
116C2×Dic6—616no—
117C2×Dic6—128no—
118C2×Dic6—128no—
119C2×C3×C8—24no—
120C2×C3×C8—24no—
121C2×C3×C8Dic618yescomplemented
122C3×C4⋊C4—24no—
123C3×C4⋊C4—24no—
124C3×C4⋊C4—24no—
125C3×C4⋊C4C4×D318yes—
126C4⋊Dic3—38no—
127C4⋊Dic3—64no—
128C4⋊Dic3—64no—
129C4⋊Dic3—64no—
130Dic3⋊C4—616no—
131Dic3⋊C4—128no—
132Dic3⋊C4—128no—
133C4×Dic3—38no—
134C4×Dic3—38no—
135C2×C3⋊C8—38no—
136C2×C3⋊C8—64no—
137C2×C3⋊C8—64no—
138C22×C32C2×C22⋊C411yescharacteristic
139C22×C32#12411yescharacteristic
140C22×C32C4⋊Q811yescharacteristic
141C22×C32C2×D811yescharacteristic
142C22×C32C2×SD1611yescharacteristic
143C22×C32C2×SD1611yescharacteristic
144C22×C32C2×Q1611yescharacteristic
145C32×C4—42no—
146C32×C4—81no—
147C32×C4C4×Q811yescharacteristic
148C32×C4C4×Q811yescharacteristic
149C32×C4C22⋊Q811yescharacteristic
150C32×C4C22⋊Q811yescharacteristic
151C3⋊Dic3—42no—
152C3⋊Dic3—81no—
153C3⋊Dic3#10214yes—
154C3⋊Dic3#10314yes—
155C22×Q8—181no—
156C22×C8—91no—
157C22×C8C2×C3⋊D311yescharacteristic
158C4⋊Q8—94no—
159C4⋊Q8—182no—
160C2×C4⋊C4—91no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—181no—
163C2×C4⋊C4—181no—
164C2×C4⋊C4—181no—
165C2×C4⋊C4C2×C3⋊D311yescharacteristic
166C2×C4⋊C4C2×C3⋊D311yescharacteristic
167C2×C42—91no—
168C4×C8—182no—
169C23×C3D3×D414yes—
170C2×C3×C4—28no—
171C2×C3×C4—44no—
172C2×C3×C4—44no—
173C2×C3×C4—44no—
174C2×C3×C4—44no—
175C2×C3×C4—44no—
176C2×C3×C4C2×Dic614yes—
177C2×C3×C4C2×C4×D314yes—
178C2×C3×C4#23514yes—
179C2×C3×C4D3×D414yes—
180C2×C3×C4#23714yes—
181C2×C3×C4D3×Q814yes—
182C2×Dic3—38no—
183C2×Dic3—38no—
184C2×Dic3—38no—
185C2×Dic3—38no—
186C2×Dic3—38no—
187C2×Dic3—38no—
188C2×Dic3—68no—
189C2×Dic3—124no—
190C2×Dic3—124no—
191C2×Dic3—124no—
192C2×Dic3—124no—
193C2×Dic3—124no—
194Dic6—1232no—
195C3×C8—28no—
196C3⋊C8—68no—
197C2×C32#39111yescharacteristic
198C2×C32C2×#10211yescharacteristic
199C2×C32C2×#10311yescharacteristic
200C2×C32#48611yescharacteristic
201C2×C32#48711yescharacteristic
202C2×C32#49811yescharacteristic
203C2×C32#50011yescharacteristic
204C2×Q8—184no—
205C2×Q8—362no—
206C2×Q8—362no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—181no—
212C22×C4—181no—
213C22×C4C22×C3⋊D311yescharacteristic
214C2×C8—21no—
215C2×C8—21no—
216C2×C8—92no—
217C2×C8—181no—
218C2×C8—181no—
219C2×C8#63412yescomplemented
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—92no—
224C4⋊C4—184no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C4⋊C4—181no—
228C4⋊C4—362no—
229C4⋊C4—362no—
230C4⋊C4C4×C3⋊D312yes—
231C42—92no—
232C42—92no—
233C22×C3D3×C22⋊C414yes—
234C22×C3#88514yes—
235C22×C3#88814yes—
236C22×C3D3×D814yes—
237C22×C3D3×SD1614yes—
238C22×C3D3×SD1614yes—
239C22×C3D3×Q1614yes—
240C3×C4—48no—
241C3×C4—84no—
242C3×C4C4×Dic614yes—
243C3×C4#87814yes—
244C3×C4#88714yes—
245C3×C4#89614yes—
246Dic3—316no—
247Dic3—316no—
248Dic3—128no—
249Dic3—244no—
250C32#199011yescharacteristic, complemented, Sylow
251C23D4×C3⋊D311yescharacteristic
252Q8—368no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—92no—
260C2×C4—92no—
261C2×C4—92no—
262C2×C4—92no—
263C2×C4—92no—
264C2×C4—92no—
265C2×C4—182no—
266C2×C4—361no—
267C2×C4—361no—
268C2×C4—361no—
269C2×C4—361no—
270C2×C4—361no—
271C2×C4C2×#63411yescharacteristic
272C2×C4C2×C4×C3⋊D311yescharacteristic
273C2×C4#382811yescharacteristic
274C2×C4D4×C3⋊D311yescharacteristic
275C2×C4#383011yescharacteristic
276C2×C4Q8×C3⋊D311yescharacteristic
277C8—22no—
278C8—182no—
279C2×C3#464614yes—
280C2×C3#476014yes—
281C2×C3D3×#10214yes—
282C2×C3#479214yes—
283C2×C3D3×#10314yes—
284C2×C3#485514yes—
285C2×C3#487414yes—
286C22C22⋊C4×C3⋊D311yescharacteristic
287C22#6409411yescharacteristic
288C22#6409711yescharacteristic
289C22D8×C3⋊D311yescharacteristic
290C22SD16×C3⋊D311yescharacteristic
291C22SD16×C3⋊D311yescharacteristic
292C22Q16×C3⋊D311yescharacteristic
293C4—42no—
294C4—81no—
295C4—94no—
296C4—94no—
297C4—362no—
298C4—721no—
299C4C4×#63411yescharacteristic
300C4#6408711yescharacteristic
301C4#6409611yescharacteristic
302C4#6410511yescharacteristic
303C3#6880314yescomplemented
304C2#1059234511yescharacteristic
305C2#1059245911yescharacteristic
306C2C3⋊D3×#10211yescharacteristic
307C2#1059249111yescharacteristic
308C2C3⋊D3×#10311yescharacteristic
309C2#1059255411yescharacteristic
310C2#1059257311yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1990
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
21. #64097C4semidirect
42. C2×C32×C8Q8semidirect
58. C2×C3⋊(C3⋊C8)Q8semidirect
121. C2×C3×C8Dic6semidirect
219. C2×C8#634semidirect
250. C32#1990semidirect
303. C3#68803semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
C2×C8×C3⋊Dic32
#105926742
C32×#3402
#105894172
#105893952
#688033