Finite Group Databasebeta

← #11795440

Subgroups — #11795440

Order 1152.

709 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 709 conjugacy classes of subgroups — too many to draw. Only its 154 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×#832C212yesmaximal
3#10591359C211yesmaximal, characteristic, complemented
4C2×#63575C212yesmaximal, complemented
5#10589156C211yesmaximal, characteristic, complemented
6#70183—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C2×#3757—22no—
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C22×C3×C3⋊C8C2212yes—
13C2×#3724—22no—
14C3×#832—24no—
15#63575—24no—
16C2×C3×#102—32no—
17#5221—32no—
18#5221—61no—
19C2×#832D312yes—
20C2×#818—32no—
21#4975—32no—
22C2×#807—32no—
23#4550—32no—
24C24×C32—21no—
25C2×C32×D4—22no—
26C2×C32×D4—22no—
27C2×C32×D4—21no—
28C2×C32×D4Q812yes—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D412yes—
32C22×C3×Dic3—22no—
33#3757—44no—
34C4⋊(C3⋊Dic3)—22no—
35C4×C3⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8—22no—
39C2×C3×C3⋊C8—22no—
40C2×C3×C3⋊C8D414yes—
41#3724—44no—
42#2093—91noSylow
43C22×C3×D4—21no—
44C22×C3×D4C2×D312yes—
45C22×C3×C8—32no—
46C2×C3×C4⋊C4—32no—
47C2×#217—64no—
48C2×#217—64no—
49C2×C4⋊Dic3—32no—
50C2×C4⋊Dic3—61no—
51C2×C4⋊Dic3C2×D312yes—
52C2×Dic3⋊C4—64no—
53C2×C4×Dic3—32no—
54C2×C4×Dic3—61no—
55C22×C3⋊C8C2×D312yes—
56C3×#102—64no—
57#832—24no—
58#818—64no—
59#807—64no—
60C23×C32—22no—
61C23×C32—41no—
62C23×C32—41no—
63C23×C32—42no—
64C23×C32—42no—
65C23×C32C2×D411yescharacteristic
66C32×D4—24no—
67C32×D4—42no—
68C2×C32×C4C2×D412yes—
69C2×C32×C4C2×Q811yescharacteristic
70C2×C32×C4#4112yes—
71C2×C32×C4#4111yescharacteristic
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3—42no—
76C2×C3⋊Dic3D814yes—
77C2×C3×Dic3—42no—
78C2×C3×Dic3—44no—
79C3×C3⋊C8—24no—
80C2×#107—92no—
81C2×#102—32no—
82#390—91no—
83#384—91no—
84#336—91no—
85C24×C3—22no—
86C24×C3—22no—
87C2×C3×D4—22no—
88C2×C3×D4—22no—
89C2×C3×D4—22no—
90C2×C3×D4—22no—
91C2×C3×D4—22no—
92C2×C3×D4—22no—
93C2×C3×D4—22no—
94C2×C3×D4—42no—
95C2×C3×D4—42no—
96C2×C3×D4Dic614yes—
97C22×C3×C4—21no—
98C22×C3×C4—62no—
99C22×C3×C4C22×D312yes—
100C22×Dic3—22no—
101C22×Dic3—34no—
102C22×Dic3—62no—
103C22×Dic3—62no—
104C22×Dic3—62no—
105C2×C3×C8—34no—
106C2×C3×C8—62no—
107C2×C3×C8—62no—
108C3×C4⋊C4—62no—
109C3×C4⋊C4—62no—
110#217—128no—
111#217—128no—
112C4⋊Dic3—22no—
113C4⋊Dic3—22no—
114C4⋊Dic3—62no—
115C4⋊Dic3—62no—
116C4⋊Dic3—122no—
117Dic3⋊C4—128no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120C4×Dic3—122no—
121C2×C3⋊C8—22no—
122C2×C3⋊C8—22no—
123C2×C3⋊C8#6714yes—
124C22×C32—42no—
125C22×C32—44no—
126C22×C32—82no—
127C22×C32—81no—
128C22×C32—81no—
129C22×C32C22⋊Q811yescharacteristic
130C22×C32#12311yescharacteristic
131C22×C32#12711yescharacteristic
132C22×C32C2×D812yes—
133C22×C32#13712yes—
134C32×C4C22⋊Q812yes—
135C32×C4#12312yes—
136C3⋊Dic3—24no—
137C3⋊Dic3—81no—
138C3×Dic3—82no—
139C22×D4D3211yescharacteristic
140C22×C8—32no—
141C2×C4⋊C4—32no—
142C2×C4⋊C4—91no—
143C2×C4⋊C4—182no—
144C2×C22⋊C4—182no—
145C2×C42—91no—
146#107—184no—
147#102—64no—
148C23×C3—24no—
149C23×C3—24no—
150C23×C3—21no—
151C23×C3—44no—
152C23×C3—42no—
153C23×C3—42no—
154C23×C3—44no—
155C23×C3—42no—
156C23×C3—44no—
157C23×C3—44no—
158C23×C3—42no—
159C23×C3D3×D412yes—
160C3×D4—24no—
161C3×D4—24no—
162C3×D4—44no—
163C3×D4—44no—
164C3×D4—42no—
165C3×D4—42no—
166C2×C3×C4—22no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—22no—
170C2×C3×C4—124no—
171C2×C3×C4—122no—
172C2×C3×C4C2×Dic612yes—
173C2×C3×C4#23512yes—
174C2×C3×C4D3×D412yes—
175C2×C3×C4#23712yes—
176C2×C3×C4#23712yes—
177C2×C3×C4C2×#6712yes—
178C2×Dic3—38no—
179C2×Dic3—44no—
180C2×Dic3—42no—
181C2×Dic3—64no—
182C2×Dic3—64no—
183C2×Dic3—64no—
184C2×Dic3—122no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C2×Dic3—124no—
188C2×Dic3—124no—
189C2×Dic3—122no—
190C3×C8—64no—
191C3⋊C8—24no—
192C2×C32—82no—
193C2×C32#39911yescharacteristic
194C2×C32#47412yes—
195C2×C32#48012yes—
196C2×C32#49311yescharacteristic
197C2×C32#49711yescharacteristic
198C24—21no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—22no—
202C2×D4#62712yes—
203C22×C4—62no—
204C22×C4—92no—
205C22×C4—181no—
206C22×C4C2×D3211yescharacteristic
207C2×C8—34no—
208C2×C8—62no—
209C2×C8—62no—
210C4⋊C4—62no—
211C4⋊C4—62no—
212C4⋊C4—182no—
213C4⋊C4—364no—
214C22⋊C4—364no—
215C42—182no—
216C22×C3—22no—
217C22×C3—22no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—44no—
222C22×C3—48no—
223C22×C3—44no—
224C22×C3—48no—
225C22×C3—82no—
226C22×C3—84no—
227C22×C3—82no—
228C22×C3—82no—
229C22×C3—82no—
230C22×C3—84no—
231C22×C3#87812yes—
232C22×C3#88312yes—
233C22×C3D3×D814yes—
234C22×C3#91514yes—
235C22×C3#94012yes—
236C3×C4—22no—
237C3×C4—22no—
238C3×C4—242no—
239C3×C4#87812yes—
240C3×C4#88312yes—
241C3×C4#92412yes—
242C3×C4#93512yes—
243Dic3—68no—
244Dic3—82no—
245Dic3—124no—
246Dic3—242no—
247Dic3—242no—
248C32#209311yescharacteristic, complemented, Sylow
249C23—22no—
250C23—42no—
251C23—42no—
252C23—41no—
253C23—41no—
254C23#381111yescharacteristic
255D4—24no—
256D4—42no—
257C2×C4—94no—
258C2×C4—124no—
259C2×C4—122no—
260C2×C4—182no—
261C2×C4—182no—
262C2×C4—362no—
263C2×C4—361no—
264C2×C4#380412yes—
265C2×C4#380511yescharacteristic
266C2×C4C2×#62711yescharacteristic
267C2×C4D3×#6712yes—
268C8—64no—
269C2×C3—21no—
270C2×C3—22no—
271C2×C3—22no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—84no—
275C2×C3—84no—
276C2×C3#475914yes—
277C2×C3#477414yes—
278C2×C3#494912yes—
279C2×C3#515112yes—
280C2×C3#516712yes—
281C22—44no—
282C22—42no—
283C22—81no—
284C22—82no—
285C22—81no—
286C22#6392612yes—
287C22#6393112yes—
288C22#6397511yescharacteristic
289C22#6397911yescharacteristic
290C22#6398211yescharacteristic
291C4—184no—
292C4—242no—
293C4—721no—
294C4#6396412yes—
295C4#6396912yes—
296C3—21no—
297C3#7018312yescomplemented
298C2—82no—
299C2#1059141712yes—
300C2#1059148411yescharacteristic
301C2#1059149311yescharacteristic
302C2#1059149412yes—
303C2#1059171511yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32#2093
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10591359C2semidirect
4. C2×#63575C2semidirect
5. #10589156C2semidirect
248. C32#2093semidirect
297. C3#70183semidirect

Maximal subgroups

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

subgroupindex
#105929202
C2×C3×#8322
#105913592
C2×#635752
#105891562
#701833