Finite Group Databasebeta

← #11785832

Subgroups — #11785832

Order 1152.

582 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 79 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×#63957C211yesmaximal, characteristic
2C2×C22⋊#622C211yesmaximal, characteristic
3#10591720C211yesmaximal, characteristic
4#10590075C212yesmaximal, complemented
5#10590075C212yesmaximal, complemented
6C23×C3⋊Dic3C2211yescharacteristic
7C22×#622C2212yes—
8C2×C3×#217—21no—
9C2×C3×#217—21no—
10C2×#3724C2212yes—
11C2×#3724C2211yescharacteristic
12C2×#3724C2211yescharacteristic
13#63957—22no—
14#63957C414yescomplemented
15C2×Dic32—21no—
16C22⋊#622—22no—
17#63579—21no—
18C2×#877—61no—
19#4942—61no—
20C24×C32D411yescharacteristic
21C22×C3⋊Dic3—24no—
22C22×C3⋊Dic3C2×C412yes—
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3D412yes—
25C22×C3⋊Dic3C2311yescharacteristic
26C22×C3×Dic3—21no—
27C22×C3×Dic3—21no—
28C22×C3×Dic3—22no—
29C2×#622—22no—
30C2×#622—24no—
31C3×#217—24no—
32C3×#217—42no—
33#3724—21no—
34#3724—21no—
35#3724—24no—
36#3724C2×C412yes—
37#3724C2×C412yes—
38Dic32—24no—
39#1825—91nomaximal, Sylow
40C23×Dic3—61no—
41C23×Dic3—61no—
42C2×C3×C22⋊C4—61no—
43C2×C3×C22⋊C4—61no—
44C2×#217—21no—
45C2×#217—21no—
46C2×Dic3⋊C4—61no—
47C2×Dic3⋊C4—61no—
48C2×Dic3⋊C4—62no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51#877—64no—
52#877—64no—
53C3⋊#95—62no—
54C23×C32—22no—
55C23×C32—21no—
56C23×C32—21no—
57C23×C32—22no—
58C23×C32C22⋊C412yes—
59C23×C32C2×D411yescharacteristic
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—24no—
62C2×C3⋊Dic3—24no—
63C2×C3⋊Dic3C22⋊C412yes—
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C2×C3⋊Dic3#4114yes—
67C2×C3×Dic3—22no—
68C2×C3×Dic3—22no—
69C2×C3×Dic3—42no—
70C2×C3×Dic3—41no—
71C2×C3×Dic3—41no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—42no—
74C2×C3×Dic3—42no—
75#622—42no—
76C2×#117—91no—
77C2×C22⋊C8—91no—
78#380—91no—
79#340—92no—
80#340—92no—
81C24×C3—21no—
82C24×C3—21no—
83C22×C3×C4—61no—
84C22×C3×C4—61no—
85C22×C3×C4—62no—
86C22×Dic3—21no—
87C22×Dic3—21no—
88C22×Dic3—22no—
89C22×Dic3—62no—
90C22×Dic3—62no—
91C22×Dic3—61no—
92C22×Dic3—61no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95C22×Dic3—62no—
96C22×Dic3—62no—
97C22×Dic3—68no—
98C22×Dic3—124no—
99C3×C22⋊C4—64no—
100C3×C22⋊C4—122no—
101#217—24no—
102#217—42no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
105Dic3⋊C4—62no—
106Dic3⋊C4—62no—
107Dic3⋊C4—124no—
108C4×Dic3—64no—
109C4×Dic3—64no—
110C22×C32—22no—
111C22×C32—22no—
112C22×C32—22no—
113C22×C32—42no—
114C22×C32—42no—
115C22×C32C2×C22⋊C411yescharacteristic
116C22×C32#12312yes—
117C22×C32#13512yes—
118C22×C32AGL(1,ℤ/8)11yescharacteristic
119C22×C32#13711yescharacteristic
120C3⋊Dic3—22no—
121C3⋊Dic3#11712yes—
122C3⋊Dic3#12312yes—
123C3×Dic3—42no—
124C3×Dic3—42no—
125C3×Dic3—82no—
126C23×C4—91no—
127C22×C8—92no—
128#117—94no—
129#117—182no—
130C2×C4⋊C4—91no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4—92no—
133C2×C22⋊C4—61no—
134C2×C22⋊C4—61no—
135C2×C42—181no—
136C22⋊C8—182no—
137#95—181no—
138C23×C3—22no—
139C23×C3—24no—
140C23×C3—22no—
141C23×C3—21no—
142C23×C3—21no—
143C23×C3—22no—
144C23×C3—22no—
145C23×C3—42no—
146C23×C3—41no—
147C23×C3—42no—
148C23×C3—42no—
149C23×C3—41no—
150C2×C3×C4—62no—
151C2×C3×C4—62no—
152C2×C3×C4—121no—
153C2×C3×C4—122no—
154C2×C3×C4—121no—
155C2×C3×C4—122no—
156C2×C3×C4—122no—
157C2×C3×C4—122no—
158C2×Dic3—22no—
159C2×Dic3—22no—
160C2×Dic3—41no—
161C2×Dic3—42no—
162C2×Dic3—41no—
163C2×Dic3—42no—
164C2×Dic3—42no—
165C2×Dic3—42no—
166C2×Dic3—62no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—64no—
172C2×Dic3—64no—
173C2×Dic3—62no—
174C2×Dic3—68no—
175C2×Dic3—68no—
176C2×Dic3—64no—
177C2×Dic3—124no—
178C2×Dic3—124no—
179C2×Dic3—122no—
180C2×C32—42no—
181C2×C32#38111yescharacteristic
182C2×C32#41611yescharacteristic
183C2×C32#41711yescharacteristic
184C2×C32#48212yes—
185C2×C32#48512yes—
186C24GO+(4,𝔽2)11yescharacteristic
187C22×C4—61no—
188C22×C4—61no—
189C22×C4—62no—
190C22×C4—91no—
191C22×C4—91no—
192C22×C4—92no—
193C22×C4—92no—
194C22×C4—184no—
195C2×C8—182no—
196C2×C8—184no—
197C4⋊C4—92no—
198C4⋊C4—92no—
199C4⋊C4—181no—
200C4⋊C4—181no—
201C4⋊C4—184no—
202C22⋊C4—64no—
203C22⋊C4—122no—
204C42—184no—
205C22×C3—24no—
206C22×C3—24no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—22no—
210C22×C3—22no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—22no—
214C22×C3—22no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—42no—
218C22×C3—42no—
219C22×C3—42no—
220C22×C3—42no—
221C22×C3—44no—
222C22×C3—44no—
223C22×C3—44no—
224C22×C3—44no—
225C3×C4—122no—
226C3×C4—122no—
227C3×C4—242no—
228Dic3—42no—
229Dic3—42no—
230Dic3—62no—
231Dic3—62no—
232Dic3—62no—
233Dic3—62no—
234Dic3—64no—
235Dic3—82no—
236Dic3—122no—
237C32#182511yescharacteristic, complemented, Sylow
238C23—22no—
239C23—21no—
240C23—22no—
241C23—21no—
242C23D32⋊C412yes—
243C23C2×GO+(4,𝔽2)11yescharacteristic
244C2×C4—62no—
245C2×C4—62no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C4—94no—
249C2×C4—92no—
250C2×C4—121no—
251C2×C4—122no—
252C2×C4—121no—
253C2×C4—122no—
254C2×C4—122no—
255C2×C4—122no—
256C2×C4—184no—
257C2×C4—184no—
258C2×C4—182no—
259C8—362no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—22no—
263C2×C3—22no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—22no—
269C2×C3—22no—
270C2×C3—44no—
271C2×C3—44no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22C2×D32⋊C411yescharacteristic
278C22#6423312yes—
279C22#6423611yescharacteristic
280C22#6423712yes—
281C22#6423911yescharacteristic
282C4—92no—
283C4—92no—
284C4—122no—
285C4—122no—
286C4—182no—
287C4—242no—
288C3—21no—
289C3—21no—
290C2—42no—
291C2#1059348811yescharacteristic
292C2#1059349412yes—
293C2#1059349611yescharacteristic
294C2#1059349811yescharacteristic
295C2#1059350112yes—
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
Fitting, prime radicalC24×C32D4
socleC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1825
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
4. #10590075C2semidirect
5. #10590075C2semidirect
14. #63957C4semidirect
237. C32#1825semidirect

Maximal subgroups

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

subgroupindex
C2×#639572
C2×C22⋊#6222
#105917202
#105900752
#18259