Finite Group Databasebeta

← #11783792

Subgroups — #11783792

Order 1152.

933 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 933 conjugacy classes of subgroups — too many to draw. Only its 190 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×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#833C212yesmaximal
3#10591060C212yesmaximal, complemented
4#10589168C212yesmaximal, complemented
5Dic3×#100—32nomaximal
6C22×C32×D4C2211yescharacteristic
7C23×C3⋊Dic3C412yes—
8C2×#3757C412yes—
9D4×C3⋊Dic3—22no—
10D4×C3⋊Dic3—22no—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×#208C2214yes—
14C3×#833C418yescomplemented
15#63555—22no—
16#63553—22no—
17C2×D4×Dic3—32no—
18C2×D4×Dic3—61no—
19C2×C3×#100—32no—
20C2×#833D312yes—
21Dic3×M16—34no—
22#4554—34no—
23C24×C32C2×C412yes—
24C2×C32×D4—22no—
25C2×C32×D4—22no—
26C2×C32×D4C2×C414yes—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3—22no—
29C22×C3⋊Dic3—22no—
30C22×C3⋊Dic3—44no—
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C412yes—
33C22×C3⋊Dic3C2×C411yescharacteristic
34#3757—24no—
35C4⋊(C3⋊Dic3)—22no—
36C4×C3⋊Dic3D412yes—
37C4×C3⋊Dic3D412yes—
38C3×#208—24no—
39C3×#208C2×C418yescomplemented
40C2×C3×C3⋊C8—24no—
41C4×#100—91noSylow
42C22×C3×D4—21no—
43C22×C3×D4C2×D312yes—
44C23×Dic3—34no—
45C23×Dic3—62no—
46C2×C3×M16—34no—
47C2×#217—34no—
48C2×#217—62no—
49D4×Dic3—64no—
50D4×Dic3—64no—
51D4×Dic3—64no—
52D4×Dic3—64no—
53C2×C4⋊Dic3—32no—
54C2×C4⋊Dic3—61no—
55C2×C4×Dic3—32no—
56C2×C4×Dic3—61no—
57C2×#208C2×D314yes—
58C3×#100—38no—
59#833Dic318yescomplemented
60#815—64no—
61C8×Dic3—64no—
62C23×C32—22no—
63C23×C32—22no—
64C23×C32—42no—
65C23×C32—42no—
66C23×C32C4214yes—
67C23×C32C22×C411yescharacteristic
68C32×D4—28no—
69C2×C32×C4C22×C412yes—
70C2×C32×C4C2×D412yes—
71C2×C32×C4#4112yes—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3—44no—
76C2×C3⋊Dic3—44no—
77C2×C3⋊Dic3—42no—
78C2×C3⋊Dic3C22⋊C412yes—
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C3×C3⋊C8—28no—
82C2×C4×D4—91no—
83C2×#100—32no—
84C4×M16—92no—
85#343—92no—
86C24×C3—22no—
87C24×C3C4×D314yes—
88C2×C3×D4—24no—
89C2×C3×D4—24no—
90C2×C3×D4—24no—
91C2×C3×D4—24no—
92C2×C3×D4—24no—
93C2×C3×D4C4×D314yes—
94C2×C3×D4C2×Dic314yes—
95C22×C3×C4—21no—
96C22×C3×C4C22×D312yes—
97C22×Dic3—32no—
98C22×Dic3—32no—
99C22×Dic3—34no—
100C22×Dic3—61no—
101C22×Dic3—61no—
102C22×Dic3—62no—
103C22×Dic3—64no—
104C22×Dic3—64no—
105C22×Dic3—64no—
106C22×Dic3—64no—
107C22×Dic3—128no—
108C22×Dic3—128no—
109C3×M16—38no—
110C3×M16—64no—
111C2×C3×C8—64no—
112#217—68no—
113#217—68no—
114C4⋊Dic3—64no—
115C4⋊Dic3—64no—
116C4×Dic3—34no—
117C4×Dic3—34no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120#208—24no—
121#208C2×Dic318yescomplemented
122C2×C3⋊C8—24no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32—24no—
126C22×C32—44no—
127C22×C32—44no—
128C22×C32—42no—
129C22×C32—42no—
130C22×C32C2×C4211yescharacteristic
131C22×C32C2×C22⋊C411yescharacteristic
132C22×C32#11711yescharacteristic
133C32×C4C4×D414yes—
134C3⋊Dic3—21no—
135C3⋊Dic3—22no—
136C3⋊Dic3—42no—
137C3⋊Dic3#10012yescomplemented
138C22×D4D3211yescharacteristic
139C23×C4—92no—
140C2×M16—34no—
141C4×D4—182no—
142C4×D4—182no—
143C2×C4⋊C4—91no—
144C2×C22⋊C4—92no—
145C2×C42—91no—
146#100—38no—
147#97—182no—
148C4×C8—182no—
149C23×C3—24no—
150C23×C3—24no—
151C23×C3—24no—
152C23×C3—24no—
153C23×C3—24no—
154C23×C3—21no—
155C23×C3—44no—
156C23×C3—44no—
157C23×C3—44no—
158C23×C3—44no—
159C23×C3C4×Dic318yes—
160C23×C3C2×C4×D312yes—
161C3×D4—216no—
162C3×D4—28no—
163C3×D4—28no—
164C2×C3×C4—22no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4C2×C4×D312yes—
168C2×C3×C4D3×D414yes—
169C2×C3×C4#23714yes—
170C2×C3×C4C22×Dic312yes—
171C2×Dic3—32no—
172C2×Dic3—34no—
173C2×Dic3—32no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—62no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C2×Dic3—64no—
180C2×Dic3—64no—
181C2×Dic3—128no—
182C2×Dic3—122no—
183C2×Dic3—128no—
184C2×Dic3—128no—
185C2×Dic3—128no—
186C2×Dic3—122no—
187C2×Dic3—124no—
188C2×Dic3—124no—
189C3×C8—68no—
190C3⋊C8—28no—
191C2×C32—21no—
192C2×C32—21no—
193C2×C32—44no—
194C2×C32C4×C22⋊C411yescharacteristic
195C2×C32C2×#10011yescharacteristic
196C2×C32#41311yescharacteristic
197C24#62412yes—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4D3×Dic314yes—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—92no—
204C22×C4—182no—
205C22×C4—182no—
206C22×C4—364no—
207C22×C4C2×D3211yescharacteristic
208M16—38no—
209M16—64no—
210C2×C8—64no—
211C4⋊C4—182no—
212C22⋊C4—184no—
213C42—92no—
214C42—92no—
215C22×C3—22no—
216C22×C3—22no—
217C22×C3—22no—
218C22×C3—22no—
219C22×C3—28no—
220C22×C3—28no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—48no—
225C22×C3—44no—
226C22×C3—48no—
227C22×C3—48no—
228C22×C3—48no—
229C22×C3—44no—
230C22×C3—44no—
231C22×C3—44no—
232C22×C3#87712yes—
233C22×C3D3×C22⋊C412yes—
234C22×C3C2×C4×Dic312yes—
235C3×C4—24no—
236C3×C4#67⋊C414yes—
237C3×C4D4×Dic314yes—
238Dic3—34no—
239Dic3—62no—
240Dic3—62no—
241Dic3—62no—
242Dic3—64no—
243Dic3—122no—
244Dic3—124no—
245Dic3—124no—
246C32C4×#10011yescharacteristic, complemented, Sylow
247C23—22no—
248C23—22no—
249C23—42no—
250C23—42no—
251C23Dic3214yes—
252C23C2×#62411yescharacteristic
253D4—28no—
254C2×C4—91no—
255C2×C4—92no—
256C2×C4—91no—
257C2×C4—182no—
258C2×C4—182no—
259C2×C4—364no—
260C2×C4—361no—
261C2×C4—364no—
262C2×C4—362no—
263C2×C4C2×D3×Dic312yes—
264C2×C4#380512yes—
265C2×C4#381112yes—
266C8—68no—
267C2×C3—22no—
268C2×C3—22no—
269C2×C3—22no—
270C2×C3—22no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—48no—
275C2×C3—48no—
276C2×C3D3×#10012yes—
277C2×C3#474512yes—
278C2×C3Dic3×C22⋊C412yes—
279C22—21no—
280C22—21no—
281C22—24no—
282C22—44no—
283C22—44no—
284C22—42no—
285C22—42no—
286C22C2×Dic3211yescharacteristic
287C22#6395711yescharacteristic
288C22#6397411yescharacteristic
289C4—92no—
290C4—181no—
291C4—182no—
292C4—362no—
293C4#67⋊Dic314yes—
294C3—21no—
295C3Dic3×#10012yescomplemented
296C2—21no—
297C2—21no—
298C2—44no—
299C2#1059150311yescharacteristic
300C2#1059150411yescharacteristic
301C2#1059170511yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32C4×#100
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10591060C2semidirect
4. #10589168C2semidirect
14. C3×#833C4semidirect
39. C3×#208C2×C4semidirect
59. #833Dic3semidirect
121. #208C2×Dic3semidirect
137. C3⋊Dic3#100semidirect
246. C32C4×#100semidirect
295. C3Dic3×#100semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#8332
#105910602
#105891682
Dic3×#1003