Finite Group Databasebeta

← #11772605

Subgroups — #11772605

Order 1152.

593 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 593 conjugacy classes of subgroups — too many to draw. Only its 104 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
1#10592920C211yesmaximal, characteristic
2C2×C3×#834C212yesmaximal
3#67695—32nomaximal
4C22×C32×D4C2211yescharacteristic
5C2×#3757—22no—
6C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
7C2×C4×C3⋊Dic3C411yescharacteristic, complemented
8C2×C3×#217—22no—
9C3×#834—22no—
10C3×#834C414yescomplemented
11C2×C3×#99—32no—
12#5221—32no—
13#5221—61no—
14C2×#834D312yes—
15C24×C32D412yes—
16C2×C32×D4—41no—
17C2×C32×D4—41no—
18C2×C32×D4C2×C412yes—
19C2×C32×D4D411yescharacteristic
20C2×C32×D4Q811yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C3⋊Dic3—21no—
23C22×C3⋊Dic3—21no—
24C22×C3×Dic3—42no—
25#3757—44no—
26C4⋊(C3⋊Dic3)—41no—
27C4×C3⋊Dic3—41no—
28C3×#217—24no—
29C3×#217—42no—
30#1393—91noSylow
31C22×C3×D4—21no—
32C22×C3×D4C2×D312yes—
33C2×C3×C22⋊C4—62no—
34C2×#217—22no—
35C2×#217—64no—
36C2×#217—62no—
37C2×#217—62no—
38C2×C4⋊Dic3—32no—
39C2×C4⋊Dic3—61no—
40C2×C4×Dic3—32no—
41C2×C4×Dic3—61no—
42C3×#99—34no—
43C3×#99—62no—
44#834—22no—
45#834Dic314yescomplemented
46C23×C32—22no—
47C23×C32—22no—
48C23×C32—42no—
49C23×C32—42no—
50C23×C32C22⋊C411yescharacteristic
51C23×C32C22⋊C412yes—
52C23×C32C4⋊C412yes—
53C32×D4—42no—
54C32×D4—41no—
55C32×D4—41no—
56C2×C32×C4—21no—
57C2×C32×C4—21no—
58C2×C32×C4C4211yescharacteristic
59C2×C32×C4C4⋊C411yescharacteristic
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—41no—
62C2×C3⋊Dic3—41no—
63C2×C3⋊Dic3—42no—
64C2×C3⋊Dic3—41no—
65C2×C3×Dic3—44no—
66C2×C3×Dic3—82no—
67C2×C3×Dic3—82no—
68C2×#99—32no—
69#390—91no—
70C24×C3—22no—
71C24×C3D1212yes—
72C24×C3#6712yes—
73C2×C3×D4—22no—
74C2×C3×D4—21no—
75C2×C3×D4—21no—
76C2×C3×D4—42no—
77C2×C3×D4—42no—
78C2×C3×D4—42no—
79C2×C3×D4—42no—
80C2×C3×D4Dic612yes—
81C2×C3×D4C4×D312yes—
82C2×C3×D4C2×Dic312yes—
83C2×C3×D4#6712yes—
84C22×C3×C4—21no—
85C22×C3×C4—122no—
86C22×C3×C4C4×D312yes—
87C22×Dic3—42no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C22×Dic3—62no—
91C22×Dic3—62no—
92C3×C22⋊C4—64no—
93C3×C22⋊C4—122no—
94#217—24no—
95#217—42no—
96#217—124no—
97#217—124no—
98#217—128no—
99C4⋊Dic3—122no—
100C4⋊Dic3—122no—
101C4×Dic3—122no—
102C4×Dic3—122no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32—22no—
106C22×C32—22no—
107C22×C32—42no—
108C22×C32—42no—
109C22×C32—42no—
110C22×C32—42no—
111C22×C32—82no—
112C22×C32#9511yescharacteristic
113C22×C32#9911yescharacteristic
114C22×C32#9911yescharacteristic
115C32×C4—21no—
116C32×C4—21no—
117C3⋊Dic3—42no—
118C3⋊Dic3—81no—
119C3×Dic3—84no—
120C22×D4D3211yescharacteristic
121C2×C4⋊C4—91no—
122C2×C22⋊C4—62no—
123C2×C22⋊C4—182no—
124C2×C42—91no—
125#99—34no—
126#99—62no—
127C23×C3—22no—
128C23×C3—22no—
129C23×C3—22no—
130C23×C3—22no—
131C23×C3—22no—
132C23×C3—21no—
133C23×C3—22no—
134C23×C3—42no—
135C23×C3—42no—
136C23×C3—42no—
137C23×C3—42no—
138C23×C3—42no—
139C23×C3—42no—
140C23×C3—44no—
141C23×C3—44no—
142C23×C3Dic3⋊C412yes—
143C23×C3C4⋊Dic312yes—
144C23×C3(C2×D3)⋊C412yes—
145C23×C3(C2×D3)⋊C412yes—
146C23×C3#21712yes—
147C3×D4—42no—
148C3×D4—42no—
149C3×D4—42no—
150C3×D4—42no—
151C3×D4—44no—
152C3×D4—42no—
153C3×D4—42no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—124no—
161C2×C3×C4—242no—
162C2×C3×C4—242no—
163C2×C3×C4C4×Dic312yes—
164C2×C3×C4Dic3⋊C412yes—
165C2×Dic3—44no—
166C2×Dic3—64no—
167C2×Dic3—64no—
168C2×Dic3—82no—
169C2×Dic3—82no—
170C2×Dic3—122no—
171C2×Dic3—122no—
172C2×Dic3—122no—
173C2×Dic3—122no—
174C2×Dic3—122no—
175C2×Dic3—124no—
176C2×Dic3—122no—
177C2×Dic3—122no—
178C2×Dic3—122no—
179C2×C32—21no—
180C2×C32—21no—
181C2×C32—42no—
182C2×C32—42no—
183C2×C32#34211yescharacteristic
184C2×C32#35311yescharacteristic
185C2×C32#35411yescharacteristic
186C24#62612yes—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4D3×Dic312yes—
190C2×D4#62511yescharacteristic
191C2×D4#62711yescharacteristic
192C22×C4—122no—
193C22×C4—181no—
194C22×C4—181no—
195C22×C4#62411yescharacteristic
196C4⋊C4—361no—
197C22⋊C4—64no—
198C22⋊C4—122no—
199C22⋊C4—364no—
200C42—361no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—22no—
208C22×C3—22no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—42no—
213C22×C3—42no—
214C22×C3—42no—
215C22×C3—42no—
216C22×C3—42no—
217C22×C3—42no—
218C22×C3—44no—
219C22×C3—44no—
220C22×C3—42no—
221C22×C3—42no—
222C22×C3—42no—
223C22×C3—42no—
224C22×C3—82no—
225C22×C3—82no—
226C22×C3—82no—
227C22×C3—82no—
228C22×C3—84no—
229C22×C3#80612yes—
230C22×C3#80612yes—
231C22×C3C3⋊#9512yes—
232C3×C4—22no—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—244no—
237Dic3—84no—
238Dic3—124no—
239Dic3—124no—
240Dic3—242no—
241Dic3—242no—
242C32#139311yescharacteristic, complemented, Sylow
243C23—22no—
244C23—22no—
245C23—42no—
246C23—42no—
247C23(C2×D3)⋊Dic312yes—
248C23#372211yescharacteristic
249C23Dic3⋊Dic312yes—
250D4—42no—
251D4—41no—
252D4—41no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—124no—
256C2×C4—182no—
257C2×C4—242no—
258C2×C4—242no—
259C2×C4—361no—
260C2×C4—361no—
261C2×C4—362no—
262C2×C4—361no—
263C2×C4Dic3211yescharacteristic
264C2×C4#372411yescharacteristic
265C2×C3—22no—
266C2×C3—22no—
267C2×C3—22no—
268C2×C3—22no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—42no—
273C2×C3—42no—
274C2×C3—42no—
275C2×C3—42no—
276C2×C3—82no—
277C2×C3—82no—
278C2×C3#447312yes—
279C2×C3#447412yes—
280C2×C3#452712yes—
281C22—21no—
282C22—21no—
283C22—22no—
284C22—22no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—82no—
290C22#6357911yescharacteristic
291C22#6358111yescharacteristic
292C22#6358111yescharacteristic
293C4—21no—
294C4—21no—
295C4—244no—
296C4—362no—
297C4—721no—
298C3—21no—
299C3#6769512yescomplemented
300C2—21no—
301C2—21no—
302C2—42no—
303C2—42no—
304C2#1058917911yescharacteristic
305C2#1058918111yescharacteristic
306C2#1058918711yescharacteristic
subgroupG/H
centerC22#63581
commutatorC2×C32×C4C42
Frattini, hypercenterC22×D4D32
Fitting, prime radical, cosocleC22×C32×D4C22
socleC22×C32#99
hypocenterC32#1393
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
6. C2×C4⋊(C3⋊Dic3)C4semidirect
7. C2×C4×C3⋊Dic3C4semidirect
10. C3×#834C4semidirect
45. #834Dic3semidirect
242. C32#1393semidirect
299. C3#67695semidirect

Maximal subgroups

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

subgroupindex
#105929202
C2×C3×#8342
#676953